The Analysis of Secondary Motion and Lubrication ...

Research ArticleThe Analysis of Secondary Motion and Lubrication Performanceof Piston considering the Piston Skirt Profile

Yanjun Lu12 Sha Li12 PengWang12 Cheng Liu12

Yongfang Zhang 3 and Norbert Muumlller4

1School of Mechanical and Precision Instrument Engineering Xirsquoan University of Technology Xirsquoan 710048 China2State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and TechnologyWuhan 430074 China3School of Printing Packaging Engineering and Digital Media Technology Xirsquoan University of Technology Xirsquoan 710048 China4College of Engineering Michigan State University East Lansing MI 48824 USA

Correspondence should be addressed to Yongfang Zhang zhangyfxauteducn

Received 17 July 2017 Revised 26 January 2018 Accepted 8 February 2018 Published 27 March 2018

Academic Editor Giorgio Dalpiaz

Copyright copy 2018 Yanjun Lu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The work performance of piston-cylinder liner system is affected by the lubrication condition and the secondary motion of thepiston Therefore more and more attention has been paid to the secondary motion and lubrication of the piston In this paperthe Jakobson-Floberg-Olsson (JFO) boundary condition is employed to describe the rupture and reformation of oil film Theaverage Reynolds equation of skirt lubrication is solved by the finite difference method (FDM) The secondary motion of piston-connecting rod system is modeled the trajectory of the piston is calculated by the Runge-Kutta method By considering the inertiaof the connecting rod the influence of the longitudinal and horizontal profiles of piston skirt the offset of the piston pin and thethermal deformation on the secondary motion and lubrication performance is investigated The parabolic longitudinal profile thesmaller top radial reduction and ellipticities of the middle-convex piston and the bigger bottom radial reduction and ellipticitiescan effectively reduce the secondary displacement and velocity the skirt thrust friction and the friction power loss The resultsshow that the connecting rod inertia piston skirt profile and thermal deformation have important influence on secondary motionand lubrication performance of the piston

1 Introduction

The piston-cylinder liner system is a key subsystem of theinternal combustion engines (ICEs) the performance of thepiston-cylinder liner system influences the efficiency and per-formance of ICEs The work performance of piston-cylinderliner system is affected by the lubrication condition and thesecondary motion of the piston Therefore more and moreattention has been paid to the piston skirt lubrication and thesecondary motion of the piston by many scholars recently[1ndash6] Meng et al [7] introduced the oil film inertia forceeffects to the Reynolds lubrication equation the effects of oilfilm inertia on film pressure hydrodynamic friction forceand transverse displacement were investigated A nonlinearmodel of the piston considering the reciprocating lateraland rotational degree of freedom was established by Tan and

Ripin [8] In their work the piston secondary motion andthe induced vibration behavior were studied the proposedmodel was validated by the experimental data Tan and Ripin[9] identified the intermittent transient contact of the pistonskirt with the cylinder liner bymeasuring the tilting angle andsecondary displacement The impacting force was computedfrom the equation of motion and the frictional force ratio ofthe total friction force and torque was obtained Murakamiet al [10] proposed a piston secondary motion analysismethod coupling the structure analysis and the multibodydynamics analysis The presented method was verified bycomparing the numerical results with the measurementdata of the piston skirt stress secondary motion and thevibrational acceleration produced on the cylinder Besidesthe above works more researches on the piston secondarymotion have been carried out by taking some factors into

HindawiShock and VibrationVolume 2018 Article ID 3240469 27 pageshttpsdoiorg10115520183240469

2 Shock and Vibration

consideration such as surface roughness and lubrication con-dition Meng et al [11] investigated the influence of cylindervibration on the lateralmotion and tribological performancesof the piston The fluctuations of the cylinder vibration canbe reduced by increasing mass stiffness and damping ofthe cylinder Narayan [12] implemented a modeling of thepiston secondary motion The dynamic characteristics ofthe part of piston skirt and cylinder liner were analyzedand the proposed model was validated by comparing thesimulated results with the experimental data Obert et al[13] developed a reciprocating model test to investigate theinfluence of the temperature and oil supply on the tribologicalbehavior of the piston ring-cylinder liner contacts The realengine situation at fired top dead center was simulated bycarefully adjusting the friction scuffing wear oil supplyand temperature Mazouzi et al [14] presented a numericalsecondary motion model to investigate the influence of thepiston design parameters on the dynamic characteristics ofa piston-cylinder contact In their work it was verified thatthe modification of clearance of the piston skirt-liner systemand the axial location of piston pin can reduce the frictionand piston slap Fang et al [15] modeled the piston skirt-linerlubrication and crank-rod-pistonmultibody systemby takingthe microgrooves on the piston skirt surface Based on thepresentedmodel the tribodynamic performance of the pistonwith skirt surface grooves was obtained and analyzed

Regarding the influencing factors the piston skirt profilehas extreme significance for the secondary motion of thepiston Hence the study of the effects of the piston skirtprofile on the secondary motion and piston dynamics isessential Littlefair et al [16] analyzed the piston dynamicsthermoelastic distortion and transient elastohydrodynamicsof the lightweight piston with preferentially compliant shortpartial skirt The greater entrainment wedge at bottomskirt and better conforming contact geometry at top skirtwere achieved and therefore the load-carrying capacitywas improved and the friction was reduced McFadden andTurnbull [17] presented a model of the interface betweena barrelled piston skirt and cylinder In their work thesecondary motion and the pressure distribution of the oilfilm for changing the skirt profile were investigated Theresearch revealed that the wear of the cylinder arising fromthe rotation of the piston can be decreased by appropriatepositioning of piston skirt Gunelsu and Akalin [18] devel-oped a dynamics model to investigate the secondary motionof piston for the different radius of curvature around thebulge of the barrel the ellipse and the aspect ratio Thesecondary motion and frictional performance of the pistonwith the barrel and elliptical form of the skirt were analyzedThe results showed that the frictional performance can beimproved via optimizing the piston skirt profiles He et al [19]established a numerical model of coupling lubrication anddynamicmotionThe effects of the piston skirt parameters ondynamic performance were investigated including the offsetof piston pin length of piston skirt curvature parameterand ellipticity Furthermore an asymmetrical skirt profilewasproposed to reduce the thrust force on the liner In order toinvestigate the influence of the design parameters of the pis-ton skirt on the slap noise and the lubrication performance

the lubrication model of piston skirt-liner system and thedynamics model of multibody system were coupled byZhao et al [20]

Apart from the piston skirt profiles the influence ofthe connecting rod inertia on lubrication performance ofthe piston skirt-liner system cannot be neglected Thereforemore detailed dynamic analyses of the secondary motion byconsidering the inertia of the connecting rod were conducted[21ndash25] Zhang et al [21] developed a mathematical modelof piston-connecting-rod-crankshaft system Based on thecoupling model of the secondary motion and the fluiddynamic lubrication the influence of the variation in thesystem inertia on the piston secondarymotion and the pistonside force was investigated The center-of-mass position wasconfirmed to be significant for the design of the connectingrod Meng et al [22 23] conducted a numerical analysis ofthe piston dynamics the oil film and the friction loss of thepiston skirt-liner system by taking the connecting rod inertiainto consideration The numerical results revealed that theinfluence of the connecting rod inertia on the side forcethe oil film thickness the frictional force and the pistondynamics cannot be ignored in particular at high speedFurthermore Meng et al [24] presented a transient tribody-namic model by coupling the tribological performance andthe dynamic characteristics of the piston skirt-liner systemBy considering the angular acceleration of the crankshaft andthe transient variable engine speeds the secondary motionof the piston and engine performance were investigated Zhuet al [25] calculated the stress distribution of the connectingrod with consideration of the film lubrication or not Theminimum oil film thickness and maximum oil film pressurewere calculated by the Reynolds equationThe results showedthat the stress concentration can be reduced using smootherrounded fillet and longer fillet radius

The thermal deformation is also an important influencingfactor of the piston secondary motion and frictional charac-teristicsTherefore the thermal deformationwas increasinglyintroduced to relevant studies of the lubrication performanceof the piston skirt Pelosi and Ivantysynova [26] built a fullycoupled simulationmodel for the pistoncylinder interface ofaxial piston machines and validated the model by comparingthe prediction values with measurements of the fluid filmboundary temperature distributionThe influence of the heattransfer and solids-induced thermal elastic deformation onthe piston skirt-cylinder lubricating interface behavior wasanalyzed Ning et al [27] built a comprehensive lubricationmodel of the piston skirt-liner system By considering thethermal and the elastic deformations of the piston skirtand the cylinder liner the piston secondary motion wasinvestigated

The above-mentioned researches were carried out basedon the Reynolds boundary It is reasonable on the ruptureboundary of oil film but not on the reformation boundaryJacoboson et al [28 29] presented the boundary conditions ofconservation of mass on rupture and reformation boundariesof oil film that is JFO boundary condition Since then JFOboundary condition was considered as important factor inthe investigation of the tribological properties Zhao et al[30] investigated the cavitation effects on the dynamic axial

Shock and Vibration 3

x

y

g

FIC

F + FIP

FICFIC Fg

d－

CM

MIC

dP

Mf

B

M

FBx

FBy

y－

Ff

L

yP

dc

C

A

D

Figure 1 Geometrical model of piston-connecting rod mechanism

stiffness and damping coefficients of spiral-groove rotaryseals for the Reynolds and JFO boundary conditions Bycontrasting the theoretical value with the experimental datathe verification result was obtained that computation valuesof JFO boundary condition were in better agreement withthe experimental values than the values using the Reynoldsmodel Kango et al [31] conducted a mathematical modelto investigate the influence of the surface microtexture onthe performance parameters of the bearing by JFO boundarycondition The realistic results can be obtained based on JFOboundary condition in comparison to theReynolds boundarycondition Liu et al [32] investigated the influence of thecylinder liner dimples on the lubrication performance ofthe compression ring-cylinder liner system based on JFOboundary condition For different dimple area density radiusand depth the minimum oil film thickness and frictionforce were compared and analyzed under the engine-likeconditionsThe results showed that the spherical dimples canimprove the tribological performance

In this paper the average Reynolds equation of the pistonskirt lubrication is solved by FDM and the secondarymotiontrajectory of the piston is calculated by the Runge-Kutta

methodThe difference of the secondarymotion of the pistonunder JFO and the Reynolds boundary conditions is signif-icant In order to approach the actual working conditionJFO boundary condition is employed and the variable 120601 andcavitation index 119865 are introduced to describe the full andrupture areas of oil film By considering the connecting rodinertia the effects of the longitudinal profiles of the pistonskirt the horizontal profiles the offset of the piston pinand the thermal deformation on the secondary motion andlubrication performance are investigated

2 Secondary Motion Model

The piston makes reciprocating movement along cylinderliner the crankshaft makes nonuniform rotation caused bypiston Figure 1 shows the geometrical model of piston-connecting rod mechanism

In Figure 1 119865119892 is the thrust of the gas on the top surfaceof the piston 119865119868119862 and 119865119868119875 are the inertia forces of the pistonand piston pin caused by reciprocating motion of pistonrespectively 119865119868119862 119865119868119875 and119872119868119875 are the inertia forces of pistonpiston pin and the inertia moment of piston caused by the


secondary motion of piston respectively 119865119905 and 119872119905 are thetotal lateral thrust force and lateral thrust moment of pistonskirt respectively 119865119891 and 119872119891 are the friction and frictiontorque of piston skirt respectively 119865119861119883 and 119865119861119884 are the forcesof connecting rod acting on piston in the 119909 and 119910 directionsrespectively 119892 is the gravitational acceleration 120581 is the anglebetween gravity direction and 119910-axis 119889CM and 119910CM are thedistances from center ofmass of piston to center line of pistonand to top skirt respectively 119889119875 and119910119875 are the distances fromcenter of piston pin hole to center line of piston and to topskirt respectively 119871 is the length of the piston skirt and 120572 isthe angle between the connecting rod and the center line ofpiston

According to Figure 1 the force equation and momentequation of piston are established

119865119905 + 119865119868119862 + 119865119868119875 + 119865119861119883 + 119898119901119892 sin 120581 + 119898pin119892 sin 120581 = 0 (1)

where 119898119901 and 119898pin are the mass of piston and piston pinrespectively

119865119892 + 119865119891 + 119865119868119862 + 119865119868119875 + 119865119861119884 + 119898119901119892 cos 120581+ 119898pin119892 cos 120581 = 0

119872119905 + 119872119891 + 119872119868119862 minus 119865119892119889119901 minus 119898119901119892 cos 120581 (119889CM + 119889119901)+ 119898119901119892 sin 120581 (119910119875 minus 119910CM) + 119865119868119862 (119910119875 minus 119910CM)minus 119865119868119862 (119889CM + 119889119901) = 0

(2)

The angle 120572 between the center line of piston and theconnecting rod is

120572= tanminus1 ((119889119888 + 119890119888 sin 120579) times [1198972cr minus (119889119888 + 119890119888 sin 120579)2]minus05) (3)

where 119890119888 is the length of the crankshaft 119889119888 is the eccentricityof the centers of crankshaft and piston pin and 120579 is the crankangle

The inertia forces of piston and piston pin caused byreciprocating motion of piston are

119865119868119862 = minus119898119901 119910119861119865119868119875 = minus119898pin 119910119861

(4)

where 119910119861 is the acceleration of the reciprocating motion ofpiston

As shown in Figure 2 the piston swings around the centerof pin hole between themajor thrust side (the side acted uponby the expansion thrust120593 = 0) and theminor thrust side (theside acted upon by the compression thrust 120593 = 120587) In orderto describe the motion of the piston the displacement 119890119905 oftop skirt and displacement 119890119887 of bottom skirt are introducedto express the displacement velocity and tilting angle ofpiston secondarymotion In Figure 2 120593 is the circumferentialcoordinate of piston 120593119897 is the loading angle of piston skirt 120574is the tilting angle of piston around center of pin and 119877 is theradius of piston

Maj

or th

rust

side

Min

or th

rust

side

L

R

Center line of cylinder Center of piston

Cylinder

PinPiston skirt

Loading surfaceLoading surface

= 0

ll

12

=

et

eb

Figure 2 Schematic diagram of the piston-cylinder system

The inertia forces of piston and piston pin and theinertia moment of piston caused by secondary motion arerespectively

119865119868119862 = minus119898119901 [ 119890119905 + 119910CM119871 ( 119890119887 minus 119890119905)] (5)

where 119890119887 119890119905 are the acceleration values of the top skirt andbottom skirt

119872119868119862 = minus119868119901 ( 119890119905 minus 119890119887)119871 (6)

where 119868119901 is the inertiamoment of piston around center of pin

119865119868119875 = minus119898pin [ 119890119905 + 119910119875119871 ( 119890119887 minus 119890119905)] (7)

By considering the inertia of connecting rod the equilib-rium equation of connecting rod is obtained

119865119860119883 minus 119865119861119883 + 119898cr119892 sin 120581 minus 119898crcr = 0119865119860119884 minus 119865119861119884 + 119898cr119892 cos 120581 minus 119898cr 119910cr = 0 (8)

where 119865119860119883 and 119865119860119884 are the component forces caused by thecrank acting on the connecting rod in the x and 119910 directionsrespectively 119898cr is the mass of the connecting rod and cr


and 119910cr are the components of acceleration of center of massof the connecting rod in the 119909 and 119910 directions respectively

The moment equilibrium equation of the connecting rodis

minus 119865119861119883 (1 minus 119895) 119897cr cos120572 minus 119865119860119883119895119897cr cos120572+ 119865119861119884 (1 minus 119895) 119897cr sin120572 + 119865119860119884119895119897cr sin120572 minus 119868cr = 0 (9)

where 119868cr is the moment of the connecting rod and 119895 is theratio of distances from center of mass and big side to lengthof connecting rod as follows

119895 = 119897119860119862119897119860119861 (10)

According to the equilibrium equation of force andmoment of the piston and connecting rod the equations arewritten as follows

[11986011 1198601211986021 11986022][ 119890119905119890119887] = [ 119865119904 + 119865119904119904 + 119865119905119872119904 + 119872119891 + 119872119905] (11)

where 119872119905 is the lateral thrust moment of piston skirt 1198601111986012 11986021 and 11986022 are relevant coefficients 119865119905 is the lateralthrust force of piston skirt 119865119904 and 119872119904 are the physicalquantities of the parameters of the piston structure and 119865119904119904is the physical quantity of the parameters of the connectingrod the expressions are as follows

11986011 = 119898pin (1 minus 119910119875119871 ) + 119898119901 (1 minus 119910CM119871 ) + 1198952119898cr (1minus 119910119875119871 )

11986012 = 119898pin119910119875119871 + 119898119901119910CM119871 + 1198952119898cr

11991011987511987111986021 = 119898119901 (1 minus 119910CM119871 ) (119910119875 minus 119910CM) + 11986811990111987111986022 = 119898119901 (119910119875 minus 119910CM) 119910CM119871 minus 119868119901119871119865119904 = (minus119865119892 minus 119865119891 minus 119865119868119862 minus 119865119868119875 minus 119898119901119892 cos 120581

minus 119898pin119892 cos 120581) tan120572 + 119898119901119892 sin 120581 + 119898pin119892 sin 120581119872119904 = minus119865119892119889119901 minus 119898119901119892 cos 120581 (119889CM + 119889119901) + 119898119901119892

sdot sin 120581 (119910119875 minus 119910CM) minus 119865119868119862 (119889CM + 119889119875)119865119904119904 = (119895119898cr 119910cr minus 119895119898cr119892 cos 120581) tan120572 + 119895119898cr119892 sin 120581

+ 119895 (1 minus 119895)119898cr1198901198881205962 sin 120579 minus 119868cr119897cr cos120572

(12)

Δ

d1

d2

Figure 3 Horizontal profile of piston skirt

L

Top skirt

Bottom skirt

Middle-bulged point

t

Ly

L0

b

Figure 4 Longitudinal profile of piston skirt

3 Profile Design of Piston Skirt

31 Horizontal Profile Design The top surface of piston isacted upon by a larger gas pressure when the ICE operatesthe piston expands outward along the pin direction becauseof the span between the right and left pin bosses Thereforethe horizontal profile of piston skirt is designed as ellipse InFigure 3 1198891 1198892 are the diameters of the major andminor axisof ellipse 120593 is the circumferential angle and Δ is the radialreduction of ellipse

Because of the special structure and working condition ofpiston the external expansion deformation of bottom skirt ismore than top skirtTherefore the top ellipse profile of pistonis designed to be slightly smaller than the bottom one

32 Longitudinal Profile Design In order to improve thelubrication condition of piston skirt the longitudinal profileof piston skirt is generally designed as dolioform to reducethe friction force of the motion and strengthen the guidanceeffect Meanwhile it is beneficial to form the hydrodynamicoil film The longitudinal profile is shown in Figure 4 120575is the radial reduction of longitudinal profile of the piston


skirt 120575119905 is the radial reduction of top skirt 120575119887 is the radialreduction of bottom skirt and 1198710 is the distance from themiddle-convex point to top skirt The dolioform profiles ofskirt are normally designed as parabola ellipse and circlecurve

4 Mixed-Lubrication Model of Piston Skirt

41 Hydrodynamic Lubrication Model By considering theeffect of lubricated surface roughness on flow of oil filmthe oil film pressure between piston skirt and cylinder lineris solved using two-dimensional average Reynolds equa-tion based on the theory proposed by Patir and Cheng[33 34]

120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880(120597ℎ119879120597119909 + 120590120597120601119904120597119909 ) + 12120583120597ℎ119879120597119905

(13)

where ℎ119879 is the average value of actual oil film thickness 119901is the average hydrodynamic pressure ℎ is the theoretical oilfilm thickness 120583 is the dynamic viscosity of lubricant 120590 isthe roughness of friction surface 120601119909 and 120601119910 are the pressureflow factors respectively 120601119904 is the shear flow factor and 119880is the relative velocity between the piston skirt and cylinderliner

The pressure flow factors 120601119909 120601119910 [33] and shear flow factor120601119904 [34] can be calculated as follows

120601119909 = 120601119910 = 1 minus 09119890minus0561198671015840120601119904=

18991198671015840098 sdot exp (minus0921198671015840 + 00511986710158402) 11986710158401015840 le 51126 sdot exp (minus0251198671015840) 1198671015840 gt 5

(14)

where 1198671015840 = ℎ120590 is the ratio of oil film thickness 120590 is thecombined surface roughness and Ω119901 is the surface wavinessof the piston

Define touch factor 120601119888 = 120597ℎ119879120597ℎ [35] while 0 le 1198671015840 lt 3120601119888 can be calculated from

120601119888 = exp (minus06912 + 07821198671015840 minus 030411986710158402+ 0040111986710158403) (15)

while1198671015840 ge 3 120601119888 = 1The Reynolds equation can be written as

120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880120601119888 120597ℎ120597119909 + 6120583119880120590120597120601119904120597119909 + 12120583120601119888 120597ℎ120597119905

(16)

ℎ can be calculated from

ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) (17)

By considering the elastic deformation of the piston theoil film thickness can be rewritten as

ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) + 119889 (119909 119910) (18)

where 119889(119909 119910) is the elastic deformation of the piston causedby the oil film pressure 119889(119909 119910) is obtained by the followingformula [36]

119889 (119909 119910) = 11205871198641015840 int119871

0int1198870

119901 (119909 119910) 119889119909 119889119910radic(119909 minus 1199091)2 minus (119910 minus 1199101)2

(19)

where 1198641015840 is the comprehensive elastic modulus of contactsurface which is related to elastic moduli 1198641 1198642 and Poissonratios of piston and cylinder liner ]1 ]2

1198641015840 = 2[(1 minus ]21)1198641 + (1 minus ]22)1198642 ] (20)

By considering the symmetry of the structure of pistonsskirt the oil film force is calculated in a half of area (120593 = 0 sim120587) On major thrust side (120593 = 0) and minor thrust side (120593 =120587) the boundary conditions can be expressed as

12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=0 =

12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=120587 = 0 (21)

On the top skirt (119910 = 0) and the bottom skirt (119910 = 119871) theboundary conditions can be written as

119901 (120593 0) = 119901 (120593 119871) = 0 (22)

Because the squeeze effect of the oil film decreasesgradually with the increase of the loading angle it has smallerinfluence on the lubrication performance and the secondarymotion Taking certain value of loading angle the oil filmpressure approximates to zero outside of the loading anglearea the corresponding boundary condition is

119901 = 0 (1205931 le 120593 le 1205932) (23)

According to JFO boundary condition the rupture boundarycondition of oil film is

120597119901120597119899 = 0 (24)


Table 1 The numbers of the node in 120593 and 119910 directions

119872 (120593) 119873 (119910) Oil film pressure at point 1 Oil film pressure at point 2 Oil film pressure at point 336 20 554091MPa 155160MPa 103411MPa50 30 559202MPa 156861MPa 103376MPa80 60 561570MPa 157100MPa 103729MPa

y

2

1

3

N

21 3 M

Start edge Termination edge

middot middot middot

M minus 1 M+ 1

Δ

= 0 =

N minus 1

N + 1

i minus 1 j

i j + 1

i j i + 1 j

i j minus 1

Δy

Figure 5 Grid of oil film region of the piston skirt

the reformation boundary condition of oil film is

ℎ212120583 120597119901120597119899 = 1198801198992 (1 minus 1205881205880) (25)

where 119899 is the flowing direction of the oil filmIn order to couple the full oil film zone and the cavitation

zone and determine the rupture and reformation boundaryof the oil film the dimensionless independent variable 120601 andcavitation index 119865 are introduced

119865120601 = 119901 (120601 ge 0) on full oil film region

1205881205880 minus 1 = (1 minus 119865) 120601 on rupture region of oil film (26)

where 120588 is the fluid density in the full film region and 1205880 is themix-density of the gas-fluid in the cavitation region

The cavitation index 119865 is

119865 = 1 120601 ge 00 120601 lt 0 (27)

The Reynolds equation is converted into dimensionlessequation and solved by the finite difference method

As shown in Figure 5 the area of the oil film is divided into119872 times 119873 elements In the 120593 direction the number of the nodeis 119872 and the grid step is Δ120593 in the 119910 direction the numberof the node is119873 and the grid step is Δ119910

The grid independence is verified for three sets of differ-ent numbers of the node in the 120593 and 119910 directions Table 1

shows the comparison of the oil film pressures for differentnumbers of the grid (the pressures are at three points Point 1for120593 = 0∘119910 = 00414 Point 2 for120593 = 288∘119910 = 00207 Point3 for 120593 = 165∘ 119910 = 00621 crankshaft angle is 90∘) It can beseen that the changes of the oil film pressures are small withthe increase of the grid number the deviations among the oilfilm pressures are about 1 that can be neglected The gridis independent of the calculations but the calculation costwill increase when the grid with a bigger number is chosenTherefore the node numbers119872 = 36 and119873 = 20 are chosenas calculation grid number

The tangential pressure of oil filmon the skirt is calculatedby (28)

120591ℎ = minus120583119880ℎ (Φ119891 + Φ119891119904) + Φ119891119901 ℎ2 120597119901120597119910 (28)

where Φ119891 Φ119891119904 and Φ119891119901 are shear stress factors related tolubrication surface roughness [37]

42 Solid-to-Solid Contact Model Because the instantaneousgas pressure of piston is variable the lubricant film thicknessbetween the piston skirt and cylinder liner may get thinnerduring strenuous movement Therefore the solid-solid con-tact may be caused by the collision of the surface asperity byconsidering the surface roughness In this situation the totallateral thrust force consists of the lateral thrust force of oilfilm and lateral thrust force of solid-solid contact and the totalfriction force consists of the oil film shear stress and asperityshear stress

The ratio of oil film thickness 1198671015840 is normally used toevaluate the lubrication condition when 1198671015840 ge 4 thepiston skirt-cylinder liner system is under hydrodynamiclubrication condition when 1198671015840 lt 4 the piston skirt-cylinder liner system is under mixed-lubrication conditionand asperity contact [38] is inescapable

Based on the rough surface contact theory presented byGreenwood and Tripp [39] the solid-solid contact pressure119901119888 of the piston skirt and cylinder liner is calculated by

119901119888 = 16radic215 120587 (120578120573120590)2 1198641015840radic12059012057311986552 (1198671015840) (29)

where 120578 is the asperity density of the rough surface 120573 is theradius of the asperity curvature and 120578120573120590 = 003sim005 120590120573 =10minus4sim10minus2

120572119888 = 1205872 (120578120573120590)2 1198652 (1198671015840) (30)

where 120572119888 is the asperity contact area


The shear force 120591119888 of solid-solid contact of piston skirt andcylinder liner is

120591119888 = 120583119891 sdot 119901119888 (31)

where 120583119891 is the frictional coefficient of solid-solid contact

43 Calculation of Force andMoment The lateral thrust force119865ℎ caused by hydrodynamic lubrication is

119865ℎ = 119877int1198710int21205870

119901 cos120593119889120593119889119910 (32)

The lateral thrust moment 119872ℎ caused by hydrodynamiclubrication is

119872ℎ = 119877int1198710int21205870

119901 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (33)

The friction force 119865119891ℎ caused by hydrodynamic lubrication is

119865119891ℎ = minus sign (119880) 119877int1198710int21205870

120591ℎ 119889120593119889119910 (34)

where sign(119880) is sign functionThe friction torque 119872119891ℎ caused by hydrodynamic lubri-

cation is

119872119891ℎ = sign (119880) 119877int1198710int21205870

120591ℎ119877 cos120593119889120593119889119910 (35)

The lateral thrust 119865119888 caused by solid-solid contact is

119865119888 = 119877int1198710int21205870

119901119888 cos120593119889120593119889119910 (36)

The lateral thrust moment 119872119888 caused by solid-solid contactis

119872119888 = 119877int1198710int21205870

119901119888 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (37)

The friction force 119865119891119888 caused by solid-solid contact is

119865119891119888 = minus sign (119880) 119877int1198710int21205870

120591119888 119889120593119889119910 (38)

The friction moment119872119891119888 caused by solid-solid contact is

119872119891119888 = sign (119880) 119877int1198710int21205870

120591119888119877 cos120593119889120593119889119910 (39)

The total lateral thrust force 119865119905 of piston skirt is

119865119905 = 119865ℎ + 119865119888 (40)

The total friction force 119865119891 of piston skirt is

119865119891 = 119865119891ℎ + 119865119891119888 (41)

Top edge

Inner edge

Bottom edge

Cylinder liner

Coolantℎs ℎr

Δ t

Δ b

Δ c

dr

2

1c

Figure 6 Structure of piston ring groove area

The total lateral thrust moment119872119905 of piston skirt is

119872119905 = 119872ℎ + 119872119888 (42)

The total friction torque119872119891 of piston skirt is

119872119891 = 119872119891ℎ + 119872119891119888 (43)

5 Thermal Analysis Model of Piston

The heat of the piston side is mainly transferred to the oilfilm and gas film in the cylinder clearance through the pistonjunk piston ring and piston skirt surface Then the heatis transferred to coolant outside of cylinder liner throughcylinder liner The coolant is considered as heat conductionterminal Figure 6 shows the structure of the piston ringgroove

The heat transfer of the piston and cylinder liner issimplified to steady state heat conduction in multilayerflat wall the heat transfer of cylinder liner and coolant issimplified to convective heat conduction state

Φ = 1199051199081 minus 119905119908412057511205821119860 + 12057521205822119860 + 12057531205823119860 + 12057541205824119860 (44)

where Φ is the heat flow of the heat conduction 1199051199081 and1199051199084 are the starting and terminal temperature respectively1205751 is the thickness of gas or lubricant 1205752 is the thicknessof piston ring 1205753 is the thickness of cylinder wall 1205821 is theheat conduction coefficient of gas 120582119892 or heat conductioncoefficient of lubricant 120582119900 120582119892 = 0023W(m2sdotK) 120582119900 =04W(m2sdotK) 1205822 is the heat conduction coefficient of pistonring 1205822 = 02W(m2sdotK) 1205823 is the heat conduction coeffi-cient of cylinder liner 1205824 is the convective heat conductioncoefficient of cylinder liner and coolant and 119860 is the heatconduction area the heat conduction coefficient 119886 of differentpositions of the piston side is deduced from deformationformula of (44)

119886 = 112057511205821 + 12057521205822 + 12057531205823 + 11205824 (45)


0 90 180 270 360 450 540 630 7200

2

4

6

8

10

12

14

16

18

Pisto

n co

mbu

stion

gas

pre

ssur

e (M

Pa)

Crankshaft angle (∘)

Figure 7 Gas pressure inside of cylinder

The piston side consists of the piston junk piston ringgroove piston ring land piston pin area and piston skirtBecause the structures are different in different areas thecalculation of heat conduction coefficients is different

The heat conduction of the coolant and cylinder lineris simplified to convection heat transfer from tube banksin crossflow According to strong turbulence formula andNusselt number definition the convective heat conductioncoefficients of cylinder liner and coolant are obtained

1205824 = 0023Re08119891 Pr119898119891 119896119871 (46)

where 1205824 are the convective heat conduction coefficients ofcylinder liner and coolant Re119891 is within 104sim12 times 105 Re119891 =11000 Prf is within 07sim160 Prf = 100 when the fluid isheated by pipe 119898 = 04 119896 is the heat conduction coefficientof static fluid 119896 = 00036W(msdotK) and 119871 is the geometriccharacteristic length 119871 = 0005m

When the inner of cylinder liner contacts with the oil-gas mixture the convective heat conduction coefficient iscalculated by the following equation

119886119888 = 1120575119888120582119888 (47)

where 119886119888 is the convective heat conduction coefficient of theinner of the cylinder liner 120575119888 is the thickness of the oil-gasmixture of the inner of the cylinder liner and 120582119888 is the heatconduction coefficient of oil-gas mixture

6 Model Solutions

Equation (11) is solved by the Runge-Kutta method Takingthe four-stroke ICE as an example the piston motion isperiodic motion The simulation of the secondary motionis conducted in an engine cycle (ie the crankshaft angle isfrom 0∘ to 720∘) the time step is Δ119905 = 2 times 10minus6 s the initialvalues 119890119905 119890119887 119890119905 119890119887 119890119905 and 119890119887 at the moment 119905119894 are provided

and the oil film pressure and solid-solid contact pressure ofthe hydrodynamic lubrication are calculated by coupling themotion parameters of the crankshaft connecting rod systemThe shear stress of oil film and solid-solid contact shear stressare solved by (28) and (31) and the force and moment arecalculated using integral formula The values 119890119905 119890119887 119890119905 119890119887119890119905 and 119890119887 at the moment 119905119894+1 are calculated by the Runge-Kutta method Repeat the above procedure until meetingconvergence criteria

119890119905 minus 119890119905 (119905 + 4120587120596 ) lt 10minus5119890119887 minus 119890119887 (119905 + 4120587120596 ) lt 10minus5119890119905 minus 119890119905 (119905 + 4120587120596 ) lt 10minus5119890119887 minus 119890119887 (119905 + 4120587120596 ) lt 10minus5

(48)

where 120596 is the rotational angular velocity of the crankshaftThe convergence can be obtained after calculating 2-3 cycles

7 Numerical Examples

The simulation of the piston secondary motion is carriedout in a certain-type four-stroke four-cylinder turbochargeddiesel engineTheparameters used in the simulation are listedin Tables 2 and 3 Table 2 shows the structure parameters ofengine Table 3 shows the material characteristic parametersof piston and cylinder liner The variation curve of the gaspressure for different crankshaft angles is shown in Figure 7when the rotation speed is 1680 rpm

Figure 8 shows the comparison of the secondary motionsof the piston with and without considering elastic defor-mation When the elastic deformation of the piston is con-sidered the maximum secondary displacement and velocityincrease respectively about 015 and 037 the maximum


Table 2 Structure parameters of engine

Symbol Definition Value119877 Piston radius 55mm119871 Piston skirt length 828mm119903 Crankshaft radius 72mm119897119860119861 Connecting rod length 223mm119897119860119862 Connecting rod center-of-mass location 72mm119910CM Piston center-of-mass location 108mm119910119875 Piston pin axial location 373mm119898119875 Piston mass 139 kg119868119901 Piston inertia moment 0003 kgsdotm2119898cr Connecting rod mass 17 kg119868119887 Connecting rod inertia moment 0017 kgsdotm2119898119888 Crankshaft mass 235 kg119868119888 Crankshaft moment of inertia 2 kgsdotm2Ω Crankshaft rotation speed 1680 rpm119888 Theoretical piston skirt clearance 50120583m120590119904 Piston surface roughness 020 120583mΩ119901 External waviness root-mean-square value of piston 20 120583m120590119887 Inner hole surface roughness 050120583m120590 Combined roughness 054120583m119864 Modulus of elasticity (Al) 79GPa120583 Viscosity (100∘ SAE 10W40) 00056 Pasdots120583119891 Solid-solid friction coefficient 01119889119888 Offset of crankshaft 0mm119889119901 Offset of pin 0mm119889CM Offset of center of mass 0mm120581 Cylinder axial tilting angle 0∘

Table 3 Characteristic parameters of piston material

Physical quantity Piston (eutectic Al Si alloy) Cylinder liner (boron cast iron)Thermal conductivity (120582Wsdotmminus1sdotKminus1) 145 42Density (120588kgmminus3) 2700 7370Specific heat capacity (119888119901Jsdotkgminus1sdotKminus1) 880 470Elasticity modulus (119864GPa) 71 159Poisson ratio (]) 034 03Coefficient of linear expansion (120572Kminus1) 2 times 10minus6 12 times 10minus6

of the minimum oil film thickness increases about 020and the friction force and friction power loss increaserespectively about 0015 and 0016 From Figure 8 itcan be seen that the effect of elastic deformations is smallwithin the selected data set and therefore the piston wasassumed to be rigid So the elastic deformation of the pistonis not considered as the influence factor in the currentwork

71 Effect of the Boundary Condition on Secondary MotionFigure 9 shows the comparison of secondary motions of thepiston under the Reynolds and JFO boundary conditionsBy considering the rupture and reformation boundaries ofoil film the secondary displacement velocity and the tiltingangle under JFO boundary condition decrease obviouslyCompared with the Reynolds boundary condition becauseof the change of the oil film pressure the maximum of the



Seco

ndar

y di

spla

cem

ent (

m)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0

minus1 times 10minus5




329 times 10minus5

328 times 10minus5

327 times 10minus5

326 times 10minus5

0 90 180 270 360 450 540 630 720

146 147 148

et (with d)eb (with d)

et (without d)eb (without d)

(a) Secondary displacement


0 90 180 270 360 450 540 630 720

Seco

ndar

y ve

loci

ty (m

s)

0020

0015

0010

0005

0000

minus0005

minus0010

000570

000565

000560

000555

000550

000545

92 94 96 98



(b) Secondary velocity

Min

imum

oil

film

thic

knes

s (m

)

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

00000714

00000712

00000710

00000708


0 90 180 270 360 450 540 630 720

132

134

136

138

140

Major oil film thickness (with d)Minor oil film thickness (with d)Major oil film thickness (without d)Minor oil film thickness (without d)(c) Minimum oil film thickness

Fric

tion

forc

e (N

)

250

200

150

100

50

0

minus50

minus100

minus150

268 269 270


0 90 180 270 360 450 540 630 720

1365

1360

1355

1350

With d

Without d

(d) Friction force

Fric

tion

pow

er lo

ss (W

)

2000

1500

1000

500

0

175017401730172017101700


0 90 180 270 360 450 540 630 720

268

269

270

271

272

273

274

275

With d

Without d(e) Friction power loss

Figure 8 Comparison of secondary motions of the piston with and without elastic deformation



0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5



Under JFOUnder Reynolds

pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f

(a) Displacement of the center of the piston pin

Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

Major oil film thickness (under JFO)Minor oil film thickness (under JFO)Major oil film thickness (under Reynolds)Minor oil film thickness (under Reynolds)


0 90 180 270 360 450 540 630 720

(c) Minimum oil film thickness

2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720

(d) Friction power loss

Figure 9 Comparison of secondary motions of the piston under the Reynolds and JFO boundary conditions

minimum oil film thickness on major thrust side increasesat 135∘ and 495∘ and decreases at 270∘ and 630∘ the cor-responding friction force and friction power loss increaseto the peak at 270∘ and 630∘ The maximum friction forceand friction power loss under JFO boundary conditionincrease respectively about 484 and 447 The resultsshow that the reformation of oil film has effect on pistonsecondary motion so it is necessary to investigate thelubrication performance of the piston using JFO boundarycondition

72 Effect of Connecting Rod Inertia on Secondary MotionFigure 10 shows the curve of secondary motion of thepiston by considering the inertia of the connecting rod The

connecting rod inertia leads to the obvious change of theoil film pressure during the compression stroke and exhauststroke and the change of the pressure has an importantinfluence on the secondary motion In a cycle the maximumsecondary displacement and velocity and the maximums ofthe minimum oil film thicknesses on major andminor thrustsides increase slightly the maximum thrust and frictionforces increase respectively about 155 and 79 the pistontilting angle has obvious increase at 360∘ and 720∘ and themaximum friction power loss increases 6 By consideringthe effect of the connecting rod inertia the secondarymotionis closer to the actual working condition so the inertia ofconnecting rod is taken into consideration in the followingnumerical examples

Shock and Vibration 13Se

cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720

et (with I＝Ｌ)eb (with I＝Ｌ)

et (without I＝Ｌ)eb (without I＝Ｌ)



0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720

With I＝ＬWithout I＝Ｌ

(c) Displacement of the center of the piston pin

4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720


(d) Piston tilting angle

2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720


(e) Lateral thrust force

200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)

Major oil film thickness (with I＝Ｌ)Minor oil film thickness (with I＝Ｌ)Major oil film thickness (without I＝Ｌ)Minor oil film thickness (without I＝Ｌ)


0 90 180 270 360 450 540 630 720

(g) Minimum oil film thickness

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720


(h) Friction power loss

Figure 10 Effect of connecting rod inertia on secondary motion

Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3

Figure 11 Profiles of different longitudinal profile skirts

73 Effect of Longitudinal Profile on Lubrication PerformanceFigure 11 shows the profiles of three different longitudinalprofile skirts Profile 1 is the profile of parabola (the deviationsof top and bottom skirts are resp 80 120583mand 130 120583m) profile2 is the profile of ellipse (the deviations of top and bottomskirts are resp 9495 120583m and 13555 120583m) and profile 3 isthe circular curve (the deviations of top and bottom skirtsare resp 8889120583m and 10177 120583m) Figure 12 shows theeffects of different profiles on lubrication performance of thepiston-cylinder liner system The secondary displacementsand velocities of top and bottom skirts and the maximumof the minimum oil film thickness of profile 1 decrease

obviously contrastingwith profiles 2 and 3 and themaximumtilting angle of profile 1 decreases Due to the decrease of theminimum oil film thickness the friction force and frictionpower loss increase slightly By considering the secondarymotion of three profiles comprehensively profile 1 is chosenas longitudinal profile

74 Effect of Radial Reduction on Lubrication PerformanceFigure 13 shows the skirt profiles of different radial reductionson the top and bottom skirts the deviations of top and bottomskirts of profile 1 are respectively 80 120583m and 130 120583m thedeviations of profile 4 are both 100120583m and the deviations of


4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)

et (profile 1)et (profile 2)

et (profile 3)


0 90 180 270 360 450 540 630 720

(a) Secondary displacement of top skirt

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

eb (profile 1)eb (profile 2)

eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720


(b) Secondary displacement of bottom skirt

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)

(c) Secondary velocity of top skirt

0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

(d) Secondary velocity of bottom skirt

4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

(e) Piston tilting angle

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)

Major oil film thickness (profile 1)Minor oil film thickness (profile 1)Major oil film thickness (profile 2)Minor oil film thickness (profile 2)Major oil film thickness (profile 3)Minor oil film thickness (profile 3)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


Figure 12 Effect of longitudinal profile on lubrication performance

Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5

Figure 13 Profiles of different radial reduction skirts

profile 5 are respectively 130 120583m and 80 120583m Figure 14 showsthe effects of different radial reductions of top and bottomskirts on lubrication performance of the piston-cylinder linersystemThe secondary displacement and velocity of top skirtof profile 1 decrease while the secondary displacement andvelocity of bottom skirt increase The change of secondarydisplacements and velocities is beneficial to decrease thefriction force and friction power loss The maximum pistontilting angle of profile 1 decreases significantly compared

to profiles 4 and 5 and the friction power loss decreasesrespectively about 37 and 5 In Figure 14 the radialreduction of profile 1 is a more reasonable design parameter

75 Effect ofMiddle-Convex Point on Lubrication PerformanceFigure 15 shows the skirt profiles of different middle-convexpoints the middle-convex point of profile 1 is in the middleof piston that is 1198710 = 40mm the middle-convex point ofprofile 6 shifts to top skirt that is 1198710 = 30mm and the


cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720

Major oil film thickness (profile 1)Minor oil film thickness (profile 1)Major oil film thickness (profile 4)Minor oil film thickness (profile 4)Major oil film thickness (profile 5)Minor oil film thickness (profile 5)(g) Minimum oil film thickness

2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


Figure 14 Effect of radial reduction on lubrication performance

Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7

Figure 15 Profiles of different middle-convex point skirts

middle-convex point of profile 7 shifts to bottom skirt thatis 1198710 = 50mm Figure 16 shows the effects of differentmiddle-convex points on lubrication performance of thepiston-cylinder liner system The secondary displacementand velocity of top skirt of the profile 1 increase contrastingwith profile 6 the secondary displacement and velocity ofbottom skirt of the profile 1 increase contrasting with profile7Themaximumpiston tilting angle of profile 1 increases con-trasting with profile 6 and the maximum friction force andfriction power loss increase slightly Compared with profile 1

the major minimum oil film thickness of profile 6 decreasesobviously for 100∘ sim250∘ and 460∘ sim610∘ and the minorminimum oil film thickness of profile 7 decreases obviouslyfor 225∘sim315∘ and 585∘sim675∘ By considering the secondarydisplacements velocities and minimum oil film thicknessesprofile 1 is more reasonable to obtain better lubricationperformance

76 Effect of Horizontal Profile on Lubrication PerformanceFigure 17 shows thehorizontal profiles of different ellipticities


cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


Figure 16 Effect of middle-convex point on lubrication performance

Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35

Circumferential angle (∘)

Figure 17 Horizontal profiles of different ellipticities

The ellipticities of top and bottom skirts of profile 1 arerespectively 90 120583m and 150 120583m The ellipticities of profile 8are both 120 120583mThe ellipticities of profile 9 are respectively150 120583m and 90120583m Figure 18 shows the effects of horizontalprofiles of different ellipticities on lubrication performanceof the piston-cylinder liner system Contrasting with profiles8 and 9 the secondary displacement and velocity of the topskirt of profile 1 are smaller and the secondary displacementand velocity of bottom skirt are bigger The friction force and

friction power loss of profile 1 decrease slightly and the pistontilting angle of profile 1 increases compared with profiles 8and 9 The results indicate that the lubrication performanceis better when the horizontal profile is designed as thesmaller ellipticity of top skirt and bigger ellipticity of bottomskirt

77 Effect of the Offset of the Piston Pin Hole on SkirtLubrication Performance Figure 19 shows the effect of the


cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


Figure 18 Effect of horizontal profile on lubrication performance

offset of the piston pin hole on lubrication performance ofthe piston-cylinder liner system By contrasting with thenonoffset of piston pin hole the secondary displacementsand velocities of top and bottom piston skirts increase whenthe piston pin hole shifts to the major thrust side Thetrend of curve is contrary when the piston pin hole shiftsto the minor thrust side The reason of the difference is thatthe position of the piston pin hole determines the swingdirection of the piston Contrasting with the nonoffset ofpiston pin hole the maximum displacement of the pistonpin center decreases about 8 while the pin hole shifts tothe major thrust side the maximum friction force decreasesabout 196 and the friction power loss decreases about216

78 Effect of Thermal Deformation on Lubrication Per-formance Figure 20 shows the temperature distributionnephogram of the piston and the maximum temperature is52011 K and the minimum temperature is 36443 K Figure 21shows the profiles of piston skirt and cylinder liner beforeand after thermal deformation when the piston and cylinderliner are in the expansion stroke Figure 22 shows thecomparison of the secondarymotions of piston piston tiltingangles minimum oil film thicknesses friction forces andfriction power losses before and after thermal deformationAs Figure 22 shows the maximum secondary displacementof the piston pin center decreases and the piston tilting angleincreases after thermal deformation The minimum oil filmthickness decreases greatly due to the distortion of the pistonskirt profile caused by the thermal deformation and the fric-tion force and friction power loss increase correspondinglyFrom Figure 22 the effect of the thermal deformation on

lubrication performance of the piston-cylinder liner systemis obvious

8 Conclusion

In this paper JFO boundary condition is employed todescribe the rupture and reformation of oil film of thepiston-connecting rod system By considering the inertiaof the connecting rod the influence of the longitudinal andhorizontal profiles of piston skirt the offset of the piston pinand the thermal deformation on the secondary motion andlubrication performance is investigated The results are asfollows(1) Contrasting with the Reynolds boundary conditionthe secondary motion of the piston under JFO boundarycondition has a significant difference The tribological per-formance of the piston-cylinder liner system under JFOboundary condition is closer to the realistic conditionBy considering the connecting rod inertia based on JFOboundary condition the piston dynamic behaviors andmixed-lubrication performance of piston-cylinder liner sys-tem are analyzed The results show that the effects of theconnecting rod inertia piston skirt profile and thermaldeformation on piston secondary motion and lubricationperformance of piston skirt are significant and the effectof elastic deformation is small within the selected dataset (2) When the piston skirt profile is designed as parabolathe smaller the radial reduction of top skirt and the biggerthe radial reduction of bottom skirt the smaller the ellipticityof top skirt and the bigger the ellipticity of bottom skirt thelubrication performance of piston skirt is superior


cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(e) Displacement of piston pin center

200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720

Major oil film thickness (dp = 0)

Minor oil film thickness (dp = 0)



Major oil film thickness (dp = minus0006)

Minor oil film thickness (dp = minus0006)


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


Figure 19 Effect of piston pin offset on skirt lubrication performance

B steady-state thermalType temperatureUnit KTime 1Custom2018215 018

52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070

Figure 20 Distribution nephogram of the piston temperature

(3) When the piston pin slightly shifts to the majorthrust side the secondary displacement and velocity of pistonincrease the friction force and friction power loss decreaseand the friction characteristics of piston skirt are better(4) By considering thermal deformation of the pistonskirt the minimum oil film thickness obviously decreases

furthermore the piston tilting angle friction force andfriction power loss significantly increaseThe influence of thethermal deformation of the piston skirt on the lubricationperformance is a nonnegligible factor so further researchon the thermal deformation needs to be conducted in thefollowing work


Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150

NondeformationThermal deformation

(a) Profiles of piston skirt

Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200

Cylinder length (mm)


(b) Profiles of cylinder liner

Figure 21 Profiles of piston skirt and cylinder liner before and after thermal deformation

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)

(a) Secondary displacement of piston pin center





4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720


(b) Piston tilting angle

300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720

Major oil film thickness (nondeformation)Minor oil film thickness (nondeformation)Major oil film thickness (thermal deformation)Minor oil film thickness (thermal deformation)(d) Minimum oil film thickness

Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720


(e) Friction power loss

Figure 22 Effect of thermal deformation on lubrication performance

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research was supported by National Natural ScienceFoundation of China (Grant no 51775428) Open Projectof State Key Laboratory of Digital Manufacturing Equip-ment and Technology (Grant no DMETKF2017014) NaturalScience Foundation of Shaanxi Province of China (Grantno 2014JM2-5082) and Scientific Research Program ofShaanxi Provincial Education Department of China (Grantno 15JS068)

References

[1] S H Mansouri and V W Wong ldquoEffects of piston designparameters on piston secondary motion and skirt-liner fric-tionrdquo Proceedings of the Institution ofMechanical Engineers PartJ Journal of Engineering Tribology vol 219 no 6 Article IDJ03604 pp 435ndash449 2005

[2] G A Livanos and N P Kyrtatos ldquoFriction model of a marinediesel engine piston assemblyrdquo Tribology International vol 40no 10ndash12 pp 1441ndash1453 2007

[3] C Kirner J Halbhuber B Uhlig A Oliva S Graf and GWachtmeister ldquoExperimental and simulative research advancesin the piston assembly of an internal combustion enginerdquoTribology International vol 99 pp 159ndash168 2016

[4] Y Wang Y Li J Yang C Sun K Liu and R Feng ldquoEffects ofanodic oxidation for combustion chamber on heat transfer ofthe piston in an aero-enginerdquo Experimental Heat Transfer vol30 no 1 pp 46ndash65 2017

[5] H Shahmohamadi M Mohammadpour R Rahmani H Rah-nejat C P Garner and S Howell-Smith ldquoOn the boundaryconditions inmulti-phase flow through the piston ring-cylinder

liner conjunctionrdquo Tribology International vol 90 pp 164ndash1742015

[6] J Zhang and Y Meng ldquoDirect observation of cavitation phe-nomenon and hydrodynamic lubrication analysis of texturedsurfacesrdquo Tribology Letters vol 46 no 2 pp 147ndash158 2012

[7] F M Meng Y Y Zhang Y Z Hu and H Wang ldquoThermo-elasto-hydrodynamic lubrication analysis of piston skirt consid-ering oil film inertia effectrdquo Tribology International vol 40 no7 pp 1089ndash1099 2007

[8] Y-C Tan and Z M Ripin ldquoAnalysis of piston secondarymotionrdquo Journal of Sound and Vibration vol 332 no 20 pp5162ndash5176 2013

[9] Y-C Tan and Z M Ripin ldquoTechnique to determine instan-taneous piston skirt friction during piston slaprdquo TribologyInternational vol 74 pp 145ndash153 2014

[10] H Murakami N Nakanishi N Ono and T Kawano ldquoNewthree-dimensional piston secondary motion analysis methodcoupling structure analysis and multi body dynamics analysisrdquoSAE International Journal of Engines vol 5 no 1 pp 42ndash502012

[11] F M Meng X F Wang T T Li and Y P Chen ldquoInfluenceof cylinder liner vibration on lateral motion and tribologicalbehaviors for piston in internal combustion enginerdquoProceedingsof the Institution of Mechanical Engineers Part J Journal ofEngineering Tribology vol 229 no 2 pp 151ndash167 2015

[12] S Narayan ldquoEffects of Various Parameters on Piston SecondaryMotionrdquo SAE Technical Papers vol 2015- no March 2015

[13] P Obert T Muller H-J Fuszliger and D Bartel ldquoThe influence ofoil supply and cylinder liner temperature on friction wear andscuffing behavior of piston ring cylinder liner contactsmdasha newmodel testrdquo Tribology International vol 94 pp 306ndash314 2016

[14] R Mazouzi A Kellaci and A Karas ldquoEffects of piston designparameters on skirt-liner dynamic behaviorrdquo Industrial Lubri-cation and Tribology vol 68 no 2 pp 250ndash258 2016

[15] C Fang X Meng and Y Xie ldquoA piston tribodynamic modelwith deterministic consideration of skirt surface groovesrdquoTribology International vol 110 pp 232ndash251 2017


[16] B Littlefair M De La Cruz S Theodossiades et al ldquoTransienttribo-dynamics of thermo-elastic compliant high-performancepiston skirtsrdquo Tribology Letters vol 53 no 1 pp 51ndash70 2014

[17] P D McFadden and S R Turnbull ldquoA study of the secondarypiston motion arising from changes in the piston skirt profileusing a simplified piston skirt modelrdquo Proceedings of the Insti-tution of Mechanical Engineers Part C Journal of MechanicalEngineering Science vol 227 no 1 pp 38ndash47 2013

[18] O Gunelsu andO Akalin ldquoThe effects of piston skirt profiles onsecondary motion and frictionrdquo Journal of Engineering for GasTurbines and Power vol 136 no 6 Article ID 062503 2014

[19] Z He W Xie G Zhang Z Hong and J Zhang ldquoPistondynamic characteristics analyses based on FEM method PartI Effected by piston skirt parametersrdquo Advances in EngineeringSoftware vol 75 pp 68ndash85 2014

[20] B Zhao X-D Dai Z-N Zhang and Y-B Xie ldquoA new numer-ical method for piston dynamics and lubrication analysisrdquoTribology International vol 94 pp 395ndash408 2016

[21] Z Zhang Y Xie X Zhang and X Meng ldquoAnalysis of pistonsecondary motion considering the variation in the systeminertiardquo Proceedings of the Institution of Mechanical EngineersPart D Journal of Automobile Engineering vol 223 no 4 pp549ndash563 2009

[22] X Meng and Y Xie ldquoA new numerical analysis for piston skirt-liner system lubrication considering the effects of connectingrod inertiardquo Tribology International vol 47 pp 235ndash243 2012

[23] X Meng L Ning Y Xie and V W Wong ldquoEffects ofthe connecting-rod-related design parameters on the pistondynamics and the skirt-liner lubricationrdquo Proceedings of theInstitution of Mechanical Engineers Part D Journal of Automo-bile Engineering vol 227 no 6 pp 885ndash898 2013

[24] XMeng C Fang andY Xie ldquoTransient tribodynamicmodel ofpiston skirt-liner systems with variable speed effectsrdquo TribologyInternational vol 94 pp 640ndash651 2016

[25] J-C Zhu H-H Zhu S-D Fan L-J Xue and Y-F Li ldquoA studyon the influence of oil film lubrication to the strength of engineconnecting rod componentsrdquo Engineering Failure Analysis vol63 pp 94ndash105 2016

[26] M Pelosi and M Ivantysynova ldquoHeat transfer and thermalelastic deformation analysis on the PistonCylinder interfaceof axial piston machinesrdquo Journal of Tribology vol 134 no 4Article ID 041101 2012

[27] L Ning X Meng and Y Xie ldquoIncorporation of deformation ina lubrication analysis for automotive piston skirt-liner systemrdquoProceedings of the Institution of Mechanical Engineers Part JJournal of Engineering Tribology vol 227 no 6 pp 654ndash6702013

[28] B Jacoboson and L Floberg ldquoThe finite journal bearing consid-ering vaporizationrdquo Chalmers Tekniska Hogskolas Handlingarvol 190 p 72 1957

[29] K O Olsson ldquoCavitation in dynamically loaded bearingrdquoTransactions of Chalmers University of Technology vol 308 p60 1965

[30] Y Zhao C Wei S Yuan and J Hu ldquoTheoretical and experi-mental study of cavitation effects on the dynamic characteristicof spiral-groove rotary seals (SGRSs)rdquo Tribology Letters vol 64no 3 article no 50 2016

[31] S Kango R K Sharma and R K Pandey ldquoThermal analysis ofmicrotextured journal bearing using non-Newtonian rheologyof lubricant and JFO boundary conditionsrdquo Tribology Interna-tional vol 69 pp 19ndash29 2014

[32] C Liu Y-J Lu Y-F Zhang S Li and N Muller ldquoNumericalstudy on the lubrication performance of compression ring-cylinder liner system with spherical dimplesrdquo PLoS ONE vol12 no 7 Article ID e0181574 2017

[33] N Patir and H S Cheng ldquoAn average flow model fordetermining effects of three-dimensional roughness on partialhydrodynamic lubricationrdquo Transactions of the ASME vol 100no 1 pp 12ndash17 1978

[34] N Patir and H S Cheng ldquoApplication of average flow modelto lubrication between rough sliding surfacesrdquo Journal ofTribology vol 101 no 2 pp 220ndash230 1979

[35] CWuandL Zheng ldquoAverageReynolds equation for partial filmlubrication with a contact factorrdquo Journal of Tribology vol 111no 1 pp 188ndash191 1989

[36] Q Yang and T G Keith ldquoTwo-dimensional piston ringlubricationmdashpart i rigid ring and liner solutionrdquo TribologyTransactions vol 39 no 4 pp 757ndash768 1996

[37] D Zhu H Cheng T Arai and K Hamai ldquoNumerical analysisfor piston skirts in mixed lubrication Part I Basic modelingrdquoJournal of Tribology vol 114 no 3 pp 553ndash562 1992

[38] B Yin X Li Y Fu and W Yun ldquoEffect of laser textureddimples on the lubrication performance of cylinder liner indiesel enginerdquo Lubrication Science vol 24 no 7 pp 293ndash3122012

[39] J A Greenwood and J H Tripp ldquoThe contact of two nominallyflat rough surfacesrdquo Proceedings of the Institution of MechanicalEngineers vol 185 no 1 pp 625ndash633 2016

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consideration such as surface roughness and lubrication con-dition Meng et al [11] investigated the influence of cylindervibration on the lateralmotion and tribological performancesof the piston The fluctuations of the cylinder vibration canbe reduced by increasing mass stiffness and damping ofthe cylinder Narayan [12] implemented a modeling of thepiston secondary motion The dynamic characteristics ofthe part of piston skirt and cylinder liner were analyzedand the proposed model was validated by comparing thesimulated results with the experimental data Obert et al[13] developed a reciprocating model test to investigate theinfluence of the temperature and oil supply on the tribologicalbehavior of the piston ring-cylinder liner contacts The realengine situation at fired top dead center was simulated bycarefully adjusting the friction scuffing wear oil supplyand temperature Mazouzi et al [14] presented a numericalsecondary motion model to investigate the influence of thepiston design parameters on the dynamic characteristics ofa piston-cylinder contact In their work it was verified thatthe modification of clearance of the piston skirt-liner systemand the axial location of piston pin can reduce the frictionand piston slap Fang et al [15] modeled the piston skirt-linerlubrication and crank-rod-pistonmultibody systemby takingthe microgrooves on the piston skirt surface Based on thepresentedmodel the tribodynamic performance of the pistonwith skirt surface grooves was obtained and analyzed

Regarding the influencing factors the piston skirt profilehas extreme significance for the secondary motion of thepiston Hence the study of the effects of the piston skirtprofile on the secondary motion and piston dynamics isessential Littlefair et al [16] analyzed the piston dynamicsthermoelastic distortion and transient elastohydrodynamicsof the lightweight piston with preferentially compliant shortpartial skirt The greater entrainment wedge at bottomskirt and better conforming contact geometry at top skirtwere achieved and therefore the load-carrying capacitywas improved and the friction was reduced McFadden andTurnbull [17] presented a model of the interface betweena barrelled piston skirt and cylinder In their work thesecondary motion and the pressure distribution of the oilfilm for changing the skirt profile were investigated Theresearch revealed that the wear of the cylinder arising fromthe rotation of the piston can be decreased by appropriatepositioning of piston skirt Gunelsu and Akalin [18] devel-oped a dynamics model to investigate the secondary motionof piston for the different radius of curvature around thebulge of the barrel the ellipse and the aspect ratio Thesecondary motion and frictional performance of the pistonwith the barrel and elliptical form of the skirt were analyzedThe results showed that the frictional performance can beimproved via optimizing the piston skirt profiles He et al [19]established a numerical model of coupling lubrication anddynamicmotionThe effects of the piston skirt parameters ondynamic performance were investigated including the offsetof piston pin length of piston skirt curvature parameterand ellipticity Furthermore an asymmetrical skirt profilewasproposed to reduce the thrust force on the liner In order toinvestigate the influence of the design parameters of the pis-ton skirt on the slap noise and the lubrication performance

the lubrication model of piston skirt-liner system and thedynamics model of multibody system were coupled byZhao et al [20]

Apart from the piston skirt profiles the influence ofthe connecting rod inertia on lubrication performance ofthe piston skirt-liner system cannot be neglected Thereforemore detailed dynamic analyses of the secondary motion byconsidering the inertia of the connecting rod were conducted[21ndash25] Zhang et al [21] developed a mathematical modelof piston-connecting-rod-crankshaft system Based on thecoupling model of the secondary motion and the fluiddynamic lubrication the influence of the variation in thesystem inertia on the piston secondarymotion and the pistonside force was investigated The center-of-mass position wasconfirmed to be significant for the design of the connectingrod Meng et al [22 23] conducted a numerical analysis ofthe piston dynamics the oil film and the friction loss of thepiston skirt-liner system by taking the connecting rod inertiainto consideration The numerical results revealed that theinfluence of the connecting rod inertia on the side forcethe oil film thickness the frictional force and the pistondynamics cannot be ignored in particular at high speedFurthermore Meng et al [24] presented a transient tribody-namic model by coupling the tribological performance andthe dynamic characteristics of the piston skirt-liner systemBy considering the angular acceleration of the crankshaft andthe transient variable engine speeds the secondary motionof the piston and engine performance were investigated Zhuet al [25] calculated the stress distribution of the connectingrod with consideration of the film lubrication or not Theminimum oil film thickness and maximum oil film pressurewere calculated by the Reynolds equationThe results showedthat the stress concentration can be reduced using smootherrounded fillet and longer fillet radius

The thermal deformation is also an important influencingfactor of the piston secondary motion and frictional charac-teristicsTherefore the thermal deformationwas increasinglyintroduced to relevant studies of the lubrication performanceof the piston skirt Pelosi and Ivantysynova [26] built a fullycoupled simulationmodel for the pistoncylinder interface ofaxial piston machines and validated the model by comparingthe prediction values with measurements of the fluid filmboundary temperature distributionThe influence of the heattransfer and solids-induced thermal elastic deformation onthe piston skirt-cylinder lubricating interface behavior wasanalyzed Ning et al [27] built a comprehensive lubricationmodel of the piston skirt-liner system By considering thethermal and the elastic deformations of the piston skirtand the cylinder liner the piston secondary motion wasinvestigated

The above-mentioned researches were carried out basedon the Reynolds boundary It is reasonable on the ruptureboundary of oil film but not on the reformation boundaryJacoboson et al [28 29] presented the boundary conditions ofconservation of mass on rupture and reformation boundariesof oil film that is JFO boundary condition Since then JFOboundary condition was considered as important factor inthe investigation of the tribological properties Zhao et al[30] investigated the cavitation effects on the dynamic axial


x

y

g

FIC

F + FIP

FICFIC Fg

d－

CM

MIC

dP

Mf

B

M

FBx

FBy

y－

Ff

L

yP

dc

C

A

D











119865119905 + 119865119868119862 + 119865119868119875 + 119865119861119883 + 119898119901119892 sin 120581 + 119898pin119892 sin 120581 = 0 (1)


119865119892 + 119865119891 + 119865119868119862 + 119865119868119875 + 119865119861119884 + 119898119901119892 cos 120581+ 119898pin119892 cos 120581 = 0


(2)





119865119868119862 = minus119898119901 119910119861119865119868119875 = minus119898pin 119910119861

(4)



Maj

or th

rust

side

Min

or th

rust

side

L

R


Cylinder

PinPiston skirt


= 0

ll

12

=

et

eb



119865119868119862 = minus119898119901 [ 119890119905 + 119910CM119871 ( 119890119887 minus 119890119905)] (5)


119872119868119862 = minus119868119901 ( 119890119905 minus 119890119887)119871 (6)


119865119868119875 = minus119898pin [ 119890119905 + 119910119875119871 ( 119890119887 minus 119890119905)] (7)









119895 = 119897119860119862119897119860119861 (10)


[11986011 1198601211986021 11986022][ 119890119905119890119887] = [ 119865119904 + 119865119904119904 + 119865119905119872119904 + 119872119891 + 119872119905] (11)



11986012 = 119898pin119910119875119871 + 119898119901119910CM119871 + 1198952119898cr





(12)

Δ

d1

d2


L

Top skirt

Bottom skirt

Middle-bulged point

t

Ly

L0

b










120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880(120597ℎ119879120597119909 + 120590120597120601119904120597119909 ) + 12120583120597ℎ119879120597119905

(13)



120601119909 = 120601119910 = 1 minus 09119890minus0561198671015840120601119904=


(14)



120601119888 = exp (minus06912 + 07821198671015840 minus 030411986710158402+ 0040111986710158403) (15)


120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880120601119888 120597ℎ120597119909 + 6120583119880120590120597120601119904120597119909 + 12120583120601119888 120597ℎ120597119905

(16)


ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) (17)


ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) + 119889 (119909 119910) (18)


119889 (119909 119910) = 11205871198641015840 int119871

0int1198870


(19)


1198641015840 = 2[(1 minus ]21)1198641 + (1 minus ]22)1198642 ] (20)


12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=0 =

12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=120587 = 0 (21)


119901 (120593 0) = 119901 (120593 119871) = 0 (22)


119901 = 0 (1205931 le 120593 le 1205932) (23)


120597119901120597119899 = 0 (24)




y

2

1

3

N

21 3 M



M minus 1 M+ 1

Δ

= 0 =

N minus 1

N + 1

i minus 1 j

i j + 1

i j i + 1 j

i j minus 1

Δy



ℎ212120583 120597119901120597119899 = 1198801198992 (1 minus 1205881205880) (25)







119865 = 1 120601 ge 00 120601 lt 0 (27)






120591ℎ = minus120583119880ℎ (Φ119891 + Φ119891119904) + Φ119891119901 ℎ2 120597119901120597119910 (28)





119901119888 = 16radic215 120587 (120578120573120590)2 1198641015840radic12059012057311986552 (1198671015840) (29)


120572119888 = 1205872 (120578120573120590)2 1198652 (1198671015840) (30)




120591119888 = 120583119891 sdot 119901119888 (31)



119865ℎ = 119877int1198710int21205870

119901 cos120593119889120593119889119910 (32)


119872ℎ = 119877int1198710int21205870

119901 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (33)



120591ℎ 119889120593119889119910 (34)


cation is

119872119891ℎ = sign (119880) 119877int1198710int21205870

120591ℎ119877 cos120593119889120593119889119910 (35)


119865119888 = 119877int1198710int21205870

119901119888 cos120593119889120593119889119910 (36)


119872119888 = 119877int1198710int21205870

119901119888 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (37)



120591119888 119889120593119889119910 (38)


119872119891119888 = sign (119880) 119877int1198710int21205870

120591119888119877 cos120593119889120593119889119910 (39)


119865119905 = 119865ℎ + 119865119888 (40)


119865119891 = 119865119891ℎ + 119865119891119888 (41)

Top edge

Inner edge

Bottom edge

Cylinder liner

Coolantℎs ℎr

Δ t

Δ b

Δ c

dr

2

1c



119872119905 = 119872ℎ + 119872119888 (42)


119872119891 = 119872119891ℎ + 119872119891119888 (43)




Φ = 1199051199081 minus 119905119908412057511205821119860 + 12057521205822119860 + 12057531205823119860 + 12057541205824119860 (44)


119886 = 112057511205821 + 12057521205822 + 12057531205823 + 11205824 (45)


0 90 180 270 360 450 540 630 7200

2

4

6

8

10

12

14

16

18

Pisto

n co

mbu

stion

gas

pre

ssur

e (M

Pa)





1205824 = 0023Re08119891 Pr119898119891 119896119871 (46)



119886119888 = 1120575119888120582119888 (47)


6 Model Solutions




(48)














Seco

ndar

y di

spla

cem

ent (

m)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0





329 times 10minus5

328 times 10minus5

327 times 10minus5

326 times 10minus5

0 90 180 270 360 450 540 630 720

146 147 148





0 90 180 270 360 450 540 630 720

Seco

ndar

y ve

loci

ty (m

s)

0020

0015

0010

0005

0000

minus0005

minus0010

000570

000565

000560

000555

000550

000545

92 94 96 98




Min

imum

oil

film

thic

knes

s (m

)

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

00000714

00000712

00000710

00000708


0 90 180 270 360 450 540 630 720

132

134

136

138

140


Fric

tion

forc

e (N

)

250

200

150

100

50

0

minus50

minus100

minus150

268 269 270


0 90 180 270 360 450 540 630 720

1365

1360

1355

1350

With d

Without d

(d) Friction force

Fric

tion

pow

er lo

ss (W

)

2000

1500

1000

500

0

175017401730172017101700


0 90 180 270 360 450 540 630 720

268

269

270

271

272

273

274

275

With d





0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5




pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f


Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5



0 90 180 270 360 450 540 630 720


2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720







cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



x

y

g

FIC

F + FIP

FICFIC Fg

d－

CM

MIC

dP

Mf

B

M

FBx

FBy

y－

Ff

L

yP

dc

C

A

D











119865119905 + 119865119868119862 + 119865119868119875 + 119865119861119883 + 119898119901119892 sin 120581 + 119898pin119892 sin 120581 = 0 (1)


119865119892 + 119865119891 + 119865119868119862 + 119865119868119875 + 119865119861119884 + 119898119901119892 cos 120581+ 119898pin119892 cos 120581 = 0


(2)





119865119868119862 = minus119898119901 119910119861119865119868119875 = minus119898pin 119910119861

(4)



Maj

or th

rust

side

Min

or th

rust

side

L

R


Cylinder

PinPiston skirt


= 0

ll

12

=

et

eb



119865119868119862 = minus119898119901 [ 119890119905 + 119910CM119871 ( 119890119887 minus 119890119905)] (5)


119872119868119862 = minus119868119901 ( 119890119905 minus 119890119887)119871 (6)


119865119868119875 = minus119898pin [ 119890119905 + 119910119875119871 ( 119890119887 minus 119890119905)] (7)









119895 = 119897119860119862119897119860119861 (10)


[11986011 1198601211986021 11986022][ 119890119905119890119887] = [ 119865119904 + 119865119904119904 + 119865119905119872119904 + 119872119891 + 119872119905] (11)



11986012 = 119898pin119910119875119871 + 119898119901119910CM119871 + 1198952119898cr





(12)

Δ

d1

d2


L

Top skirt

Bottom skirt

Middle-bulged point

t

Ly

L0

b










120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880(120597ℎ119879120597119909 + 120590120597120601119904120597119909 ) + 12120583120597ℎ119879120597119905

(13)



120601119909 = 120601119910 = 1 minus 09119890minus0561198671015840120601119904=


(14)



120601119888 = exp (minus06912 + 07821198671015840 minus 030411986710158402+ 0040111986710158403) (15)


120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880120601119888 120597ℎ120597119909 + 6120583119880120590120597120601119904120597119909 + 12120583120601119888 120597ℎ120597119905

(16)


ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) (17)


ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) + 119889 (119909 119910) (18)


119889 (119909 119910) = 11205871198641015840 int119871

0int1198870


(19)


1198641015840 = 2[(1 minus ]21)1198641 + (1 minus ]22)1198642 ] (20)


12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=0 =

12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=120587 = 0 (21)


119901 (120593 0) = 119901 (120593 119871) = 0 (22)


119901 = 0 (1205931 le 120593 le 1205932) (23)


120597119901120597119899 = 0 (24)




y

2

1

3

N

21 3 M



M minus 1 M+ 1

Δ

= 0 =

N minus 1

N + 1

i minus 1 j

i j + 1

i j i + 1 j

i j minus 1

Δy



ℎ212120583 120597119901120597119899 = 1198801198992 (1 minus 1205881205880) (25)







119865 = 1 120601 ge 00 120601 lt 0 (27)






120591ℎ = minus120583119880ℎ (Φ119891 + Φ119891119904) + Φ119891119901 ℎ2 120597119901120597119910 (28)





119901119888 = 16radic215 120587 (120578120573120590)2 1198641015840radic12059012057311986552 (1198671015840) (29)


120572119888 = 1205872 (120578120573120590)2 1198652 (1198671015840) (30)




120591119888 = 120583119891 sdot 119901119888 (31)



119865ℎ = 119877int1198710int21205870

119901 cos120593119889120593119889119910 (32)


119872ℎ = 119877int1198710int21205870

119901 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (33)



120591ℎ 119889120593119889119910 (34)


cation is

119872119891ℎ = sign (119880) 119877int1198710int21205870

120591ℎ119877 cos120593119889120593119889119910 (35)


119865119888 = 119877int1198710int21205870

119901119888 cos120593119889120593119889119910 (36)


119872119888 = 119877int1198710int21205870

119901119888 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (37)



120591119888 119889120593119889119910 (38)


119872119891119888 = sign (119880) 119877int1198710int21205870

120591119888119877 cos120593119889120593119889119910 (39)


119865119905 = 119865ℎ + 119865119888 (40)


119865119891 = 119865119891ℎ + 119865119891119888 (41)

Top edge

Inner edge

Bottom edge

Cylinder liner

Coolantℎs ℎr

Δ t

Δ b

Δ c

dr

2

1c



119872119905 = 119872ℎ + 119872119888 (42)


119872119891 = 119872119891ℎ + 119872119891119888 (43)




Φ = 1199051199081 minus 119905119908412057511205821119860 + 12057521205822119860 + 12057531205823119860 + 12057541205824119860 (44)


119886 = 112057511205821 + 12057521205822 + 12057531205823 + 11205824 (45)


0 90 180 270 360 450 540 630 7200

2

4

6

8

10

12

14

16

18

Pisto

n co

mbu

stion

gas

pre

ssur

e (M

Pa)





1205824 = 0023Re08119891 Pr119898119891 119896119871 (46)



119886119888 = 1120575119888120582119888 (47)


6 Model Solutions




(48)














Seco

ndar

y di

spla

cem

ent (

m)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0





329 times 10minus5

328 times 10minus5

327 times 10minus5

326 times 10minus5

0 90 180 270 360 450 540 630 720

146 147 148





0 90 180 270 360 450 540 630 720

Seco

ndar

y ve

loci

ty (m

s)

0020

0015

0010

0005

0000

minus0005

minus0010

000570

000565

000560

000555

000550

000545

92 94 96 98




Min

imum

oil

film

thic

knes

s (m

)

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

00000714

00000712

00000710

00000708


0 90 180 270 360 450 540 630 720

132

134

136

138

140


Fric

tion

forc

e (N

)

250

200

150

100

50

0

minus50

minus100

minus150

268 269 270


0 90 180 270 360 450 540 630 720

1365

1360

1355

1350

With d

Without d

(d) Friction force

Fric

tion

pow

er lo

ss (W

)

2000

1500

1000

500

0

175017401730172017101700


0 90 180 270 360 450 540 630 720

268

269

270

271

272

273

274

275

With d





0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5




pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f


Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5



0 90 180 270 360 450 540 630 720


2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720







cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





119865119905 + 119865119868119862 + 119865119868119875 + 119865119861119883 + 119898119901119892 sin 120581 + 119898pin119892 sin 120581 = 0 (1)


119865119892 + 119865119891 + 119865119868119862 + 119865119868119875 + 119865119861119884 + 119898119901119892 cos 120581+ 119898pin119892 cos 120581 = 0


(2)





119865119868119862 = minus119898119901 119910119861119865119868119875 = minus119898pin 119910119861

(4)



Maj

or th

rust

side

Min

or th

rust

side

L

R


Cylinder

PinPiston skirt


= 0

ll

12

=

et

eb



119865119868119862 = minus119898119901 [ 119890119905 + 119910CM119871 ( 119890119887 minus 119890119905)] (5)


119872119868119862 = minus119868119901 ( 119890119905 minus 119890119887)119871 (6)


119865119868119875 = minus119898pin [ 119890119905 + 119910119875119871 ( 119890119887 minus 119890119905)] (7)









119895 = 119897119860119862119897119860119861 (10)


[11986011 1198601211986021 11986022][ 119890119905119890119887] = [ 119865119904 + 119865119904119904 + 119865119905119872119904 + 119872119891 + 119872119905] (11)



11986012 = 119898pin119910119875119871 + 119898119901119910CM119871 + 1198952119898cr





(12)

Δ

d1

d2


L

Top skirt

Bottom skirt

Middle-bulged point

t

Ly

L0

b










120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880(120597ℎ119879120597119909 + 120590120597120601119904120597119909 ) + 12120583120597ℎ119879120597119905

(13)



120601119909 = 120601119910 = 1 minus 09119890minus0561198671015840120601119904=


(14)



120601119888 = exp (minus06912 + 07821198671015840 minus 030411986710158402+ 0040111986710158403) (15)


120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880120601119888 120597ℎ120597119909 + 6120583119880120590120597120601119904120597119909 + 12120583120601119888 120597ℎ120597119905

(16)


ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) (17)


ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) + 119889 (119909 119910) (18)


119889 (119909 119910) = 11205871198641015840 int119871

0int1198870


(19)


1198641015840 = 2[(1 minus ]21)1198641 + (1 minus ]22)1198642 ] (20)


12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=0 =

12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=120587 = 0 (21)


119901 (120593 0) = 119901 (120593 119871) = 0 (22)


119901 = 0 (1205931 le 120593 le 1205932) (23)


120597119901120597119899 = 0 (24)




y

2

1

3

N

21 3 M



M minus 1 M+ 1

Δ

= 0 =

N minus 1

N + 1

i minus 1 j

i j + 1

i j i + 1 j

i j minus 1

Δy



ℎ212120583 120597119901120597119899 = 1198801198992 (1 minus 1205881205880) (25)







119865 = 1 120601 ge 00 120601 lt 0 (27)






120591ℎ = minus120583119880ℎ (Φ119891 + Φ119891119904) + Φ119891119901 ℎ2 120597119901120597119910 (28)





119901119888 = 16radic215 120587 (120578120573120590)2 1198641015840radic12059012057311986552 (1198671015840) (29)


120572119888 = 1205872 (120578120573120590)2 1198652 (1198671015840) (30)




120591119888 = 120583119891 sdot 119901119888 (31)



119865ℎ = 119877int1198710int21205870

119901 cos120593119889120593119889119910 (32)


119872ℎ = 119877int1198710int21205870

119901 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (33)



120591ℎ 119889120593119889119910 (34)


cation is

119872119891ℎ = sign (119880) 119877int1198710int21205870

120591ℎ119877 cos120593119889120593119889119910 (35)


119865119888 = 119877int1198710int21205870

119901119888 cos120593119889120593119889119910 (36)


119872119888 = 119877int1198710int21205870

119901119888 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (37)



120591119888 119889120593119889119910 (38)


119872119891119888 = sign (119880) 119877int1198710int21205870

120591119888119877 cos120593119889120593119889119910 (39)


119865119905 = 119865ℎ + 119865119888 (40)


119865119891 = 119865119891ℎ + 119865119891119888 (41)

Top edge

Inner edge

Bottom edge

Cylinder liner

Coolantℎs ℎr

Δ t

Δ b

Δ c

dr

2

1c



119872119905 = 119872ℎ + 119872119888 (42)


119872119891 = 119872119891ℎ + 119872119891119888 (43)




Φ = 1199051199081 minus 119905119908412057511205821119860 + 12057521205822119860 + 12057531205823119860 + 12057541205824119860 (44)


119886 = 112057511205821 + 12057521205822 + 12057531205823 + 11205824 (45)


0 90 180 270 360 450 540 630 7200

2

4

6

8

10

12

14

16

18

Pisto

n co

mbu

stion

gas

pre

ssur

e (M

Pa)





1205824 = 0023Re08119891 Pr119898119891 119896119871 (46)



119886119888 = 1120575119888120582119888 (47)


6 Model Solutions




(48)














Seco

ndar

y di

spla

cem

ent (

m)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0





329 times 10minus5

328 times 10minus5

327 times 10minus5

326 times 10minus5

0 90 180 270 360 450 540 630 720

146 147 148





0 90 180 270 360 450 540 630 720

Seco

ndar

y ve

loci

ty (m

s)

0020

0015

0010

0005

0000

minus0005

minus0010

000570

000565

000560

000555

000550

000545

92 94 96 98




Min

imum

oil

film

thic

knes

s (m

)

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

00000714

00000712

00000710

00000708


0 90 180 270 360 450 540 630 720

132

134

136

138

140


Fric

tion

forc

e (N

)

250

200

150

100

50

0

minus50

minus100

minus150

268 269 270


0 90 180 270 360 450 540 630 720

1365

1360

1355

1350

With d

Without d

(d) Friction force

Fric

tion

pow

er lo

ss (W

)

2000

1500

1000

500

0

175017401730172017101700


0 90 180 270 360 450 540 630 720

268

269

270

271

272

273

274

275

With d





0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5




pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f


Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5



0 90 180 270 360 450 540 630 720


2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720







cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







119895 = 119897119860119862119897119860119861 (10)


[11986011 1198601211986021 11986022][ 119890119905119890119887] = [ 119865119904 + 119865119904119904 + 119865119905119872119904 + 119872119891 + 119872119905] (11)



11986012 = 119898pin119910119875119871 + 119898119901119910CM119871 + 1198952119898cr





(12)

Δ

d1

d2


L

Top skirt

Bottom skirt

Middle-bulged point

t

Ly

L0

b










120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880(120597ℎ119879120597119909 + 120590120597120601119904120597119909 ) + 12120583120597ℎ119879120597119905

(13)



120601119909 = 120601119910 = 1 minus 09119890minus0561198671015840120601119904=


(14)



120601119888 = exp (minus06912 + 07821198671015840 minus 030411986710158402+ 0040111986710158403) (15)


120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880120601119888 120597ℎ120597119909 + 6120583119880120590120597120601119904120597119909 + 12120583120601119888 120597ℎ120597119905

(16)


ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) (17)


ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) + 119889 (119909 119910) (18)


119889 (119909 119910) = 11205871198641015840 int119871

0int1198870


(19)


1198641015840 = 2[(1 minus ]21)1198641 + (1 minus ]22)1198642 ] (20)


12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=0 =

12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=120587 = 0 (21)


119901 (120593 0) = 119901 (120593 119871) = 0 (22)


119901 = 0 (1205931 le 120593 le 1205932) (23)


120597119901120597119899 = 0 (24)




y

2

1

3

N

21 3 M



M minus 1 M+ 1

Δ

= 0 =

N minus 1

N + 1

i minus 1 j

i j + 1

i j i + 1 j

i j minus 1

Δy



ℎ212120583 120597119901120597119899 = 1198801198992 (1 minus 1205881205880) (25)







119865 = 1 120601 ge 00 120601 lt 0 (27)






120591ℎ = minus120583119880ℎ (Φ119891 + Φ119891119904) + Φ119891119901 ℎ2 120597119901120597119910 (28)





119901119888 = 16radic215 120587 (120578120573120590)2 1198641015840radic12059012057311986552 (1198671015840) (29)


120572119888 = 1205872 (120578120573120590)2 1198652 (1198671015840) (30)




120591119888 = 120583119891 sdot 119901119888 (31)



119865ℎ = 119877int1198710int21205870

119901 cos120593119889120593119889119910 (32)


119872ℎ = 119877int1198710int21205870

119901 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (33)



120591ℎ 119889120593119889119910 (34)


cation is

119872119891ℎ = sign (119880) 119877int1198710int21205870

120591ℎ119877 cos120593119889120593119889119910 (35)


119865119888 = 119877int1198710int21205870

119901119888 cos120593119889120593119889119910 (36)


119872119888 = 119877int1198710int21205870

119901119888 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (37)



120591119888 119889120593119889119910 (38)


119872119891119888 = sign (119880) 119877int1198710int21205870

120591119888119877 cos120593119889120593119889119910 (39)


119865119905 = 119865ℎ + 119865119888 (40)


119865119891 = 119865119891ℎ + 119865119891119888 (41)

Top edge

Inner edge

Bottom edge

Cylinder liner

Coolantℎs ℎr

Δ t

Δ b

Δ c

dr

2

1c



119872119905 = 119872ℎ + 119872119888 (42)


119872119891 = 119872119891ℎ + 119872119891119888 (43)




Φ = 1199051199081 minus 119905119908412057511205821119860 + 12057521205822119860 + 12057531205823119860 + 12057541205824119860 (44)


119886 = 112057511205821 + 12057521205822 + 12057531205823 + 11205824 (45)


0 90 180 270 360 450 540 630 7200

2

4

6

8

10

12

14

16

18

Pisto

n co

mbu

stion

gas

pre

ssur

e (M

Pa)





1205824 = 0023Re08119891 Pr119898119891 119896119871 (46)



119886119888 = 1120575119888120582119888 (47)


6 Model Solutions




(48)














Seco

ndar

y di

spla

cem

ent (

m)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0





329 times 10minus5

328 times 10minus5

327 times 10minus5

326 times 10minus5

0 90 180 270 360 450 540 630 720

146 147 148





0 90 180 270 360 450 540 630 720

Seco

ndar

y ve

loci

ty (m

s)

0020

0015

0010

0005

0000

minus0005

minus0010

000570

000565

000560

000555

000550

000545

92 94 96 98




Min

imum

oil

film

thic

knes

s (m

)

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

00000714

00000712

00000710

00000708


0 90 180 270 360 450 540 630 720

132

134

136

138

140


Fric

tion

forc

e (N

)

250

200

150

100

50

0

minus50

minus100

minus150

268 269 270


0 90 180 270 360 450 540 630 720

1365

1360

1355

1350

With d

Without d

(d) Friction force

Fric

tion

pow

er lo

ss (W

)

2000

1500

1000

500

0

175017401730172017101700


0 90 180 270 360 450 540 630 720

268

269

270

271

272

273

274

275

With d





0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5




pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f


Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5



0 90 180 270 360 450 540 630 720


2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720







cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880(120597ℎ119879120597119909 + 120590120597120601119904120597119909 ) + 12120583120597ℎ119879120597119905

(13)



120601119909 = 120601119910 = 1 minus 09119890minus0561198671015840120601119904=


(14)



120601119888 = exp (minus06912 + 07821198671015840 minus 030411986710158402+ 0040111986710158403) (15)


120597120597119909 (120601119909ℎ3 120597119901120597119909) + 120597120597119910 (120601119910ℎ3 120597119901120597119910)= 6120583119880120601119888 120597ℎ120597119909 + 6120583119880120590120597120601119904120597119909 + 12120583120601119888 120597ℎ120597119905

(16)


ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) (17)


ℎ (120593 119910 119905) = 119888 + 119890119905 (119905) cos120593 + [119890119887 (119905) minus 119890119905 (119905)] 119910119871 cos120593+ 119891 (120593 119910) + 119889 (119909 119910) (18)


119889 (119909 119910) = 11205871198641015840 int119871

0int1198870


(19)


1198641015840 = 2[(1 minus ]21)1198641 + (1 minus ]22)1198642 ] (20)


12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=0 =

12059711990112059712059310038161003816100381610038161003816100381610038161003816120593=120587 = 0 (21)


119901 (120593 0) = 119901 (120593 119871) = 0 (22)


119901 = 0 (1205931 le 120593 le 1205932) (23)


120597119901120597119899 = 0 (24)




y

2

1

3

N

21 3 M



M minus 1 M+ 1

Δ

= 0 =

N minus 1

N + 1

i minus 1 j

i j + 1

i j i + 1 j

i j minus 1

Δy



ℎ212120583 120597119901120597119899 = 1198801198992 (1 minus 1205881205880) (25)







119865 = 1 120601 ge 00 120601 lt 0 (27)






120591ℎ = minus120583119880ℎ (Φ119891 + Φ119891119904) + Φ119891119901 ℎ2 120597119901120597119910 (28)





119901119888 = 16radic215 120587 (120578120573120590)2 1198641015840radic12059012057311986552 (1198671015840) (29)


120572119888 = 1205872 (120578120573120590)2 1198652 (1198671015840) (30)




120591119888 = 120583119891 sdot 119901119888 (31)



119865ℎ = 119877int1198710int21205870

119901 cos120593119889120593119889119910 (32)


119872ℎ = 119877int1198710int21205870

119901 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (33)



120591ℎ 119889120593119889119910 (34)


cation is

119872119891ℎ = sign (119880) 119877int1198710int21205870

120591ℎ119877 cos120593119889120593119889119910 (35)


119865119888 = 119877int1198710int21205870

119901119888 cos120593119889120593119889119910 (36)


119872119888 = 119877int1198710int21205870

119901119888 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (37)



120591119888 119889120593119889119910 (38)


119872119891119888 = sign (119880) 119877int1198710int21205870

120591119888119877 cos120593119889120593119889119910 (39)


119865119905 = 119865ℎ + 119865119888 (40)


119865119891 = 119865119891ℎ + 119865119891119888 (41)

Top edge

Inner edge

Bottom edge

Cylinder liner

Coolantℎs ℎr

Δ t

Δ b

Δ c

dr

2

1c



119872119905 = 119872ℎ + 119872119888 (42)


119872119891 = 119872119891ℎ + 119872119891119888 (43)




Φ = 1199051199081 minus 119905119908412057511205821119860 + 12057521205822119860 + 12057531205823119860 + 12057541205824119860 (44)


119886 = 112057511205821 + 12057521205822 + 12057531205823 + 11205824 (45)


0 90 180 270 360 450 540 630 7200

2

4

6

8

10

12

14

16

18

Pisto

n co

mbu

stion

gas

pre

ssur

e (M

Pa)





1205824 = 0023Re08119891 Pr119898119891 119896119871 (46)



119886119888 = 1120575119888120582119888 (47)


6 Model Solutions




(48)














Seco

ndar

y di

spla

cem

ent (

m)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0





329 times 10minus5

328 times 10minus5

327 times 10minus5

326 times 10minus5

0 90 180 270 360 450 540 630 720

146 147 148





0 90 180 270 360 450 540 630 720

Seco

ndar

y ve

loci

ty (m

s)

0020

0015

0010

0005

0000

minus0005

minus0010

000570

000565

000560

000555

000550

000545

92 94 96 98




Min

imum

oil

film

thic

knes

s (m

)

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

00000714

00000712

00000710

00000708


0 90 180 270 360 450 540 630 720

132

134

136

138

140


Fric

tion

forc

e (N

)

250

200

150

100

50

0

minus50

minus100

minus150

268 269 270


0 90 180 270 360 450 540 630 720

1365

1360

1355

1350

With d

Without d

(d) Friction force

Fric

tion

pow

er lo

ss (W

)

2000

1500

1000

500

0

175017401730172017101700


0 90 180 270 360 450 540 630 720

268

269

270

271

272

273

274

275

With d





0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5




pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f


Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5



0 90 180 270 360 450 540 630 720


2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720







cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





y

2

1

3

N

21 3 M



M minus 1 M+ 1

Δ

= 0 =

N minus 1

N + 1

i minus 1 j

i j + 1

i j i + 1 j

i j minus 1

Δy



ℎ212120583 120597119901120597119899 = 1198801198992 (1 minus 1205881205880) (25)







119865 = 1 120601 ge 00 120601 lt 0 (27)






120591ℎ = minus120583119880ℎ (Φ119891 + Φ119891119904) + Φ119891119901 ℎ2 120597119901120597119910 (28)





119901119888 = 16radic215 120587 (120578120573120590)2 1198641015840radic12059012057311986552 (1198671015840) (29)


120572119888 = 1205872 (120578120573120590)2 1198652 (1198671015840) (30)




120591119888 = 120583119891 sdot 119901119888 (31)



119865ℎ = 119877int1198710int21205870

119901 cos120593119889120593119889119910 (32)


119872ℎ = 119877int1198710int21205870

119901 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (33)



120591ℎ 119889120593119889119910 (34)


cation is

119872119891ℎ = sign (119880) 119877int1198710int21205870

120591ℎ119877 cos120593119889120593119889119910 (35)


119865119888 = 119877int1198710int21205870

119901119888 cos120593119889120593119889119910 (36)


119872119888 = 119877int1198710int21205870

119901119888 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (37)



120591119888 119889120593119889119910 (38)


119872119891119888 = sign (119880) 119877int1198710int21205870

120591119888119877 cos120593119889120593119889119910 (39)


119865119905 = 119865ℎ + 119865119888 (40)


119865119891 = 119865119891ℎ + 119865119891119888 (41)

Top edge

Inner edge

Bottom edge

Cylinder liner

Coolantℎs ℎr

Δ t

Δ b

Δ c

dr

2

1c



119872119905 = 119872ℎ + 119872119888 (42)


119872119891 = 119872119891ℎ + 119872119891119888 (43)




Φ = 1199051199081 minus 119905119908412057511205821119860 + 12057521205822119860 + 12057531205823119860 + 12057541205824119860 (44)


119886 = 112057511205821 + 12057521205822 + 12057531205823 + 11205824 (45)


0 90 180 270 360 450 540 630 7200

2

4

6

8

10

12

14

16

18

Pisto

n co

mbu

stion

gas

pre

ssur

e (M

Pa)





1205824 = 0023Re08119891 Pr119898119891 119896119871 (46)



119886119888 = 1120575119888120582119888 (47)


6 Model Solutions




(48)














Seco

ndar

y di

spla

cem

ent (

m)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0





329 times 10minus5

328 times 10minus5

327 times 10minus5

326 times 10minus5

0 90 180 270 360 450 540 630 720

146 147 148





0 90 180 270 360 450 540 630 720

Seco

ndar

y ve

loci

ty (m

s)

0020

0015

0010

0005

0000

minus0005

minus0010

000570

000565

000560

000555

000550

000545

92 94 96 98




Min

imum

oil

film

thic

knes

s (m

)

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

00000714

00000712

00000710

00000708


0 90 180 270 360 450 540 630 720

132

134

136

138

140


Fric

tion

forc

e (N

)

250

200

150

100

50

0

minus50

minus100

minus150

268 269 270


0 90 180 270 360 450 540 630 720

1365

1360

1355

1350

With d

Without d

(d) Friction force

Fric

tion

pow

er lo

ss (W

)

2000

1500

1000

500

0

175017401730172017101700


0 90 180 270 360 450 540 630 720

268

269

270

271

272

273

274

275

With d





0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5




pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f


Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5



0 90 180 270 360 450 540 630 720


2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720







cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




120591119888 = 120583119891 sdot 119901119888 (31)



119865ℎ = 119877int1198710int21205870

119901 cos120593119889120593119889119910 (32)


119872ℎ = 119877int1198710int21205870

119901 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (33)



120591ℎ 119889120593119889119910 (34)


cation is

119872119891ℎ = sign (119880) 119877int1198710int21205870

120591ℎ119877 cos120593119889120593119889119910 (35)


119865119888 = 119877int1198710int21205870

119901119888 cos120593119889120593119889119910 (36)


119872119888 = 119877int1198710int21205870

119901119888 cos120593 (119910119875 minus 119910) 119889120593 119889119910 (37)



120591119888 119889120593119889119910 (38)


119872119891119888 = sign (119880) 119877int1198710int21205870

120591119888119877 cos120593119889120593119889119910 (39)


119865119905 = 119865ℎ + 119865119888 (40)


119865119891 = 119865119891ℎ + 119865119891119888 (41)

Top edge

Inner edge

Bottom edge

Cylinder liner

Coolantℎs ℎr

Δ t

Δ b

Δ c

dr

2

1c



119872119905 = 119872ℎ + 119872119888 (42)


119872119891 = 119872119891ℎ + 119872119891119888 (43)




Φ = 1199051199081 minus 119905119908412057511205821119860 + 12057521205822119860 + 12057531205823119860 + 12057541205824119860 (44)


119886 = 112057511205821 + 12057521205822 + 12057531205823 + 11205824 (45)


0 90 180 270 360 450 540 630 7200

2

4

6

8

10

12

14

16

18

Pisto

n co

mbu

stion

gas

pre

ssur

e (M

Pa)





1205824 = 0023Re08119891 Pr119898119891 119896119871 (46)



119886119888 = 1120575119888120582119888 (47)


6 Model Solutions




(48)














Seco

ndar

y di

spla

cem

ent (

m)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0





329 times 10minus5

328 times 10minus5

327 times 10minus5

326 times 10minus5

0 90 180 270 360 450 540 630 720

146 147 148





0 90 180 270 360 450 540 630 720

Seco

ndar

y ve

loci

ty (m

s)

0020

0015

0010

0005

0000

minus0005

minus0010

000570

000565

000560

000555

000550

000545

92 94 96 98




Min

imum

oil

film

thic

knes

s (m

)

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

00000714

00000712

00000710

00000708


0 90 180 270 360 450 540 630 720

132

134

136

138

140


Fric

tion

forc

e (N

)

250

200

150

100

50

0

minus50

minus100

minus150

268 269 270


0 90 180 270 360 450 540 630 720

1365

1360

1355

1350

With d

Without d

(d) Friction force

Fric

tion

pow

er lo

ss (W

)

2000

1500

1000

500

0

175017401730172017101700


0 90 180 270 360 450 540 630 720

268

269

270

271

272

273

274

275

With d





0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5




pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f


Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5



0 90 180 270 360 450 540 630 720


2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720







cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 90 180 270 360 450 540 630 7200

2

4

6

8

10

12

14

16

18

Pisto

n co

mbu

stion

gas

pre

ssur

e (M

Pa)





1205824 = 0023Re08119891 Pr119898119891 119896119871 (46)



119886119888 = 1120575119888120582119888 (47)


6 Model Solutions




(48)














Seco

ndar

y di

spla

cem

ent (

m)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0





329 times 10minus5

328 times 10minus5

327 times 10minus5

326 times 10minus5

0 90 180 270 360 450 540 630 720

146 147 148





0 90 180 270 360 450 540 630 720

Seco

ndar

y ve

loci

ty (m

s)

0020

0015

0010

0005

0000

minus0005

minus0010

000570

000565

000560

000555

000550

000545

92 94 96 98




Min

imum

oil

film

thic

knes

s (m

)

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

00000714

00000712

00000710

00000708


0 90 180 270 360 450 540 630 720

132

134

136

138

140


Fric

tion

forc

e (N

)

250

200

150

100

50

0

minus50

minus100

minus150

268 269 270


0 90 180 270 360 450 540 630 720

1365

1360

1355

1350

With d

Without d

(d) Friction force

Fric

tion

pow

er lo

ss (W

)

2000

1500

1000

500

0

175017401730172017101700


0 90 180 270 360 450 540 630 720

268

269

270

271

272

273

274

275

With d





0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5




pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f


Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5



0 90 180 270 360 450 540 630 720


2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720







cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











Seco

ndar

y di

spla

cem

ent (

m)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0





329 times 10minus5

328 times 10minus5

327 times 10minus5

326 times 10minus5

0 90 180 270 360 450 540 630 720

146 147 148





0 90 180 270 360 450 540 630 720

Seco

ndar

y ve

loci

ty (m

s)

0020

0015

0010

0005

0000

minus0005

minus0010

000570

000565

000560

000555

000550

000545

92 94 96 98




Min

imum

oil

film

thic

knes

s (m

)

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

00000714

00000712

00000710

00000708


0 90 180 270 360 450 540 630 720

132

134

136

138

140


Fric

tion

forc

e (N

)

250

200

150

100

50

0

minus50

minus100

minus150

268 269 270


0 90 180 270 360 450 540 630 720

1365

1360

1355

1350

With d

Without d

(d) Friction force

Fric

tion

pow

er lo

ss (W

)

2000

1500

1000

500

0

175017401730172017101700


0 90 180 270 360 450 540 630 720

268

269

270

271

272

273

274

275

With d





0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5




pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f


Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5



0 90 180 270 360 450 540 630 720


2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720







cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0

0

90 180 270 360 450 540 630 720

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5




pisto

n pi

n ce

nter

(m)

Seco

ndar

y di

spla

cem

ent o

f


Fric

tion

forc

e (N

)

200

150

100

50

0

minus50

minus100

minus150



0 90 180 270 360 450 540 630 720

(b) Friction force

Min

imum

oil

film

thic

knes

s (m

)

1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5



0 90 180 270 360 450 540 630 720


2500

2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)



0 90 180 270 360 450 540 630 720







cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



cond

ary

disp

lace

men

t (m

)

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0






0 90 180 270 360 450 540 630 720





0 90 180 270 360 450 540 630 720

0020

0015

0010

0005

0000

minus0005

minus0010

Seco

ndar

y ve

loci

ty (m

s)




3 times 10minus5

2 times 10minus5

1 times 10minus5



0

Seco

ndar

y di

spla

cem

ent o

f pist

on p

in ce

nter

(m)


0 90 180 270 360 450 540 630 720



4 times 10minus4

2 times 10minus4



0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



2000

1500

1000

500

minus500

minus1000

minus1500

Thru

st fo

rce (

N)


0

0

90 180 270 360 450 540 630 720



200

150

100

50

0

minus50

minus100

minus150

minus200

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(f) Friction force

Figure 10 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720




Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 2

Profile 3






4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



4 times 10minus5

2 times 10minus5

0



Seco

ndar

y di

spla

cem

ent o

f top

skirt

(m)


et (profile 3)


0 90 180 270 360 450 540 630 720


6 times 10minus5

4 times 10minus5

2 times 10minus5

0


eb (profile 3)

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

0 90 180 270 360 450 540 630 720



Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720


et (profile 3)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


4 times 10minus4

6 times 10minus4

2 times 10minus4

0




Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3


150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3

250

200

(f) Friction force

Figure 12 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)



0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 2

Profile 3



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 4

Profile 5






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0





0 90 180 270 360 450 540 630 720


et (profile 5)


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)

4 times 10minus5

2 times 10minus5

0



0 90 180 270 360 450 540 630 720


eb (profile 5)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 4)

et (profile 5)


0012

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


4 times 10minus4

6 times 10minus4

8 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5


250

200

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5

(f) Friction force

Figure 14 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 4

Profile 5



Dev

iatio

n(

Ｇ)

40

20

0

minus20

minus40

minus60

minus80

minus100

minus120

minus140

0 10 20 30 40 50 60 70 80

Skirt length (mm)

Profile 1Profile 6

Profile 7






cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

6 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 7)


4 times 10minus5

6 times 10minus5

8 times 10minus5

2 times 10minus5

0


Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 7)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

) 0020

0015

0010

0005

0000

minus0005

minus0010


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 6)

et (profile 7)


0012

0015

0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

minus0015Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


4 times 10minus4

6 times 10minus4

2 times 10minus4

0





Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7

(f) Friction force

Figure 16 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 6

Profile 7



Dev

iatio

n(

Ｇ)

Profile 1Profile 8

Profile 9

minus10

minus12

minus14

minus16

minus18

minus20

0 5 10 15 20 25 30 35







cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

4 times 10minus5

2 times 10minus5

0




0 90 180 270 360 450 540 630 720


et (profile 9)


4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720


eb (profile 9)


Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)

0015

0010

0005

0000

minus0005


0 90 180 270 360 450 540 630 720

et (profile 1)

et (profile 8)

et (profile 9)


0009

0006

0003

0000

minus0003

minus0006

minus0009

minus0012

Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


4 times 10minus4

2 times 10minus4

0



Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9

(f) Friction force

Figure 18 Continued


9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

Profile 1Profile 8

Profile 9






8 Conclusion



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



cond

ary

disp

lace

men

t of t

op sk

irt (m

)

9 times 10minus5

6 times 10minus5

3 times 10minus5

0




0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)






12 times 10minus4

1 times 10minus4

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

0

Seco

ndar

y di

spla

cem

ent o

f bot

tom

skirt

(m)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003

Seco

ndar

y ve

loci

ty o

f top

skirt

(ms

)


0 90 180 270 360 450 540 630 720

et (dp = 0)

et (dp = 0006)

et (dp = minus0006)


005

004

003

002

001

000

minus001

minus002

minus003Seco

ndar

y ve

loci

ty o

f bot

tom

skirt

(ms

)


0 90 180 270 360 450 540 630 720

eb (dp = 0)

eb (dp = 0006)

eb (dp = minus0006)


4 times 10minus5

3 times 10minus5

2 times 10minus5

1 times 10minus5

0




Disp

lace

men

t of p

iston

pin

cent

er (m

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006


200

250

150

100

50

0

minus50

minus100

minus150

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006

(f) Friction force

Figure 19 Continued


1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1 times 10minus4

9 times 10minus5

8 times 10minus5

7 times 10minus5

6 times 10minus5

5 times 10minus5

4 times 10minus5

3 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720








2000

2500

1500

1000

500

0

Fric

tion

pow

er lo

ss (W

)


0 90 180 270 360 450 540 630 720

dp = 0

dp = 0006

dp = minus0006




52011 Max502814855246822450924336241632399023817236443 Min

X

Y

Z

(m)0000 0018 0035 0053 0070





Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Dev

iatio

n(

Ｇ)

0 10 20 30 40 50 60 70 80

Skirt length (mm)

150

100

50

0

minus50

minus100

minus150



Dev

iatio

n(

Ｇ)

200

150

100

50

0

minus500 50 100 150 200





3 times 10minus5

2 times 10minus5

1 times 10minus5

0




0 90 180 270 360 450 540 630 720


Sec

onda

ry d

ispla

cem

ent o

f pist

on p

in ce

nter

(m)






4 times 10minus4

2 times 10minus4

0

Tilti

ng an

gle (

rad)


0 90 180 270 360 450 540 630 720



300

200

100

0

minus100

minus200

minus300

minus400

Fric

tion

forc

e (N

)


0 90 180 270 360 450 540 630 720


(c) Friction force

8 times 10minus5

6 times 10minus5

4 times 10minus5

2 times 10minus5

Min

imum

oil

film

thic

knes

s (m

)


0 90 180 270 360 450 540 630 720


Figure 22 Continued


4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



4000

5000

3000

2000

1000

0Fr

ictio

n po

wer

loss

(W)


0 90 180 270 360 450 540 630 720






Acknowledgments


References












































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


The Analysis of Secondary Motion and Lubrication ...

Documents

Transcript of The Analysis of Secondary Motion and Lubrication ...