Design of elements machine, bearing, shaft, spur gear and others, superficie profile, lubrication,...

7/25/2019 Design of elements machine, bearing, shaft, spur gear and others, superficie profile, lubrication, friction

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Fundamentals of Machine Elements, 3rd

ed.Schmid, Hamrock and Jacobson

201 !"! #ress

Chapter 8: Lubrication, Friction and Wear

...among all those who have writtenon the subject of moving forces,probably not a single one has givensufficient attention to the effect offriction in machines...

Guillaume Amontons

Greases are a necessary lubricant for many applications,including rolling element bearings, for the reduction offriction and wear.Source:Courtesy of SKF USA, Inc.


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ed.Schmid, Hamrock and Jacobson

201 !"! #ress

Surface Profiles

Figure 8.1: Surface profile showingsurface height variation relative to

mean reference line.

Two common surface measures:


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ed.Schmid, Hamrock and Jacobson 201 !"! #ress

Typical Surface Roughness

Figure 8.2: Typical arithmeticaverage surface roughness(Ra) for various

manufacturing processes andmachine components.Source:Adapted from Kalpakjianand Schmid [2010] andHamrock, et al. [2004].


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Conformal and Nonconformal

Figure 8.3: Conformal surfaces.Figure 8.4: Nonconformal surfaces.


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NonconformalGeometry

Figure 8.5: Geometry of contactingelastic solids.

Effective radius:

where

Radius ratio:


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Sign Convention

Figure 8.6: Sign designations for radii of curvature. (a) Rolling elements; (b) ballbearing races; (c) rolling bearing races.


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Hertz Pressure Distribution

Figure 8.7: Pressure distribution inellipsoidal contact.

Pressure distribution:

wherepmaxis the central pressure:

Note: no general solution, onlyparticular solutions for point andline contacts.


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Simplified Contact Equations

Define the ellipticity parameter as:

The contact diameters are:

The maximum deflection is:

where


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Simplified Contact

Figure 8.8: Variation of ellipticityparameter and elliptic integrals offirst and second kinds as function ofradius ratio.

Table 8.1: Simplified ellipticalcontact equations.Source:FromHamrock and Brewe [1983].


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Rectangular (Line) Contacts

The Hertz solution for Rectangular contacts is as follows. The contactsemiwidth is:

The dimensionless load is

The maximum deflection is

The maximum contact pressure, or Hertz pressure, is:


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Metallic Bearing Materials

Table 8.2: Physical and mechanical properties of selected white metal bearing alloys.Source:From Hamrock et al. [2004].

Table 8.3: Mechanical properties of selected bronze and copper alloy bearingmaterials.Source:Abstracted from Hamrock, et al.~[2004].

Material Designation

Tensile Maximum Allowablestrength, temperature, stress,

MPa C MPa

Copperlead SAE480 25 55.2 177 13.8High-leadtinbronze AMS4840 48 172.5 204 20.7Semiplasticbronze SAE67 55 207 232 20.7Leadedredbronze SAE40 60 242 232 24.2

Bronze SAE660 60 242 232 27.6Phosphorbronze SAE64 63 242 232 27.6Gunmetal SAE62 65 310 260 27.6NavyG SAE620 68 276 260 27.6Leadedgunmetal SAE63 70 276 260 27.6Aluminumbronze ASTMB148-52-9c 195 621 260 31.1

Brinellhardness


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Non-metallic Bearing Materials

Table 8.4: Limits of application of nonmetallic bearing materials.

Material

Allowable Maximum Maximum pustress, temperature, speed, limit,MPa C m/s N/m-s

Carbongraphite 4.1 399 12.7 525 103

Phenolics 41.4 93 12.7 525 103

Nylon 6.9 93 5.1 105 103PTFE(Teflo

n) 3.4 260 .51 35103

ReinforcedPTFE 17.2 260 5.1 350 103

PTFEfabric 414.0 260 .25 875 103

Polycarbonate(Lexan) 6.9 104 5.1 105 103

Acetalresin(Delrin) 6.9 82 5.1 105 103

Rubber 0.34 66 7.6 525 103

Wood 13.8 66 10.2 525

103


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Bearing Materials and Forms

Figure 8.9: Phenolic laminate bearings.

(a) Tubular bearing; (b) circumferentiallylaminated bearing; (c) axially laminated

bearing; (d) stave bearing; (e) moldedbearing.Source:From Hamrock, et al.[2004].

Figure 8.10: Different forms of bearingsurfaces. (a) Solid bearing; (b) lined

bearing; (c) filled bearing; (d) shrink-fitbearing.


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Viscosity

Figure 8.11: Slider bearing illustratingabsolute viscosity.

Viscosity:

Viscosity depends on: Pressure

Temperature Shear strain rate


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Viscosity Conversion Factors

Table 8.5: Absolute viscosity conversion factors.

To conert To!rom cP

Multipl" b"

cP 1kgf-s/m2 1N-s/m2 103

reyn,orlb-s/in.2 1

#g!-s/m$ N-s/m$ lb-s/in%$

9.807 103

6.90 106

1.02 10-4

1.02 10-1

7.03 102

9.8071

6.9 103

10-3

1.45 10-7

1.422 10-3

1.45 10-4


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FluidViscosities

Figure 8.12: Absoluteviscosities of a number offluids for a wide range oftemperatures.


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Viscosity of Fluids

Table 8.6: Absolute and kinematic viscosities of various fluids at atmospheric

pressure and different temperatures.Source:From Jones, et al. [1975].

&luidTemperature, C

'( )) *+) '( )) *+)

Advancedester 0.0253 0.00475 0.00206 2.5810 5 0.5110 5 0.2310 5

Formulatedadvancedester 0.0276 0.00496 0.00215 2.8210 5 0.5310 5 0.2410 5

Polyalkylaromatic 0.0255 0.00408 0.00180 3.010 5 0.5010 5 0.2310 5

Syntheticparaffini coil 0.375 0.0347 0.0101 44.

710

5

4.

0410

5

1.

310

5

Syntheticparaffini coil 0.375 0.0347 0.0101 44.710 5 4

.0410 5 1

.310 5

plusantiwearadditiveC-ether 0.0295 0.00467 0.00220 2.510 5 0.4110 5 0.2010 5

Superrefine dnapthenicmineraloil 0.0681 0.00686 0.002.74 7.810 5 0.8210 5 0.3310 5

Synthetichydrocarbon(tractionflui d) 0.0343 0.00353 0.00162 3.7210 5 0.4010 5 0.1910 5

Fluorinatedpolyether 0.181 0.0202 0.00668 9.6610 5 1.1510 5 0.410 5

inematic iscosit"atp.,

m$/s

Absoluteiscosit"atp. ,

, N-s/m$

Temperature, C


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Pressure-Viscosity Coefficients

Table 8.7: Pressure-viscosity coefficients of various fluids at different temperatures.Source:From Jones, et al. [1975].

&luid

Temperature, C'( )) *+)

Pressure-iscosit" coe!!ici ent ,, m$/N

Advancedester 1.2810 8 0.98710 8 0.85110 8

Formulatedadvancedester 1.3710 8 1.0010 8 0.87410 8

Polyalkylaromatic 1.

5810

8

1.

2510

8

1.

0110

8

Syntheticparaffini coil 1.9910 8 1

.5110 8 1

.2910 8

Syntheticparaffini coil 1.9610 8 1.5510 8 1.2510 8

plusantiwearadditiveC-ether 1.8010 8 0.98010 8 0.79510 8

Superrefine dnapthenicmineraloil 2.5110 8 1.5410 8 1.2710 8

Synthetichydrocarbon(tractionflui d) 3.1210 8 1.7110 8 0.93910 8

Fluorinatedpolyether 4.1710 8 3.2410 8 3.0210 8


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Single Grade Oils

Figure 8.13: Absolute viscosities of SAE lubricating oils at atmospheric pressure. (a)Single grade oils;


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Multigrade Oils

Figure 8.13: Absolute viscosities of SAE lubricating oils at atmospheric pressure. (b)multigrade oils.


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Viscosity of Single Grade Oils

Table 8.8: Curve fit data for SAE single grade oils for use in Eq. (8.26).Source:FromSeirig and Dandage [1982].

A0 1rade ConstantC* ConstantC$

re"n N-s/m$

10 1.5810 8 1.0910 4 1157.520 1.3610 8 9.3810 5 1271.6

30 1.4110

8

9.7310

5

1360.040 1.2110 8 8.3510 5 1474.450 1.7010 8 1.1710 4 1509.660 1.8710 8 1.2910 4 1564.0


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Regimes of Lubrication

Figure 8.14: Regimes of lubrication. (a) Fluid filmlubrication - surfaces completely separated by bulklubricant film. This regime is sometimes further

classified as thick or thin film lubrication; (b)partial lubrication - both bulk lubricant andboundary film play a role; (c) boundary lubrication- performance depends essentially on a boundaryfilm.

Film parameter:

Note: Boundary lubrication, < 1 Partial lubrication, 1 < 3

Hydrodynamic lubrication,3 Elastohydrodynamiclubrication},3 < 10


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Lubrication Effect

Figure 8.15: Bar diagram showingcoefficient of friction for variouslubrication conditions.Source:FromHamrock, et al. [2004].

Figure 8.16: Wear rate for variouslubrication regimes.Source:FromBeerbower [1972].


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Hydrodynamic Lubrication

Figure 8.17: Characteristics ofhydrodynamic lubrication.Source:From Hamrock, et al. [2004].

Figure 8.18: Mechanisms of pressure

development for hydrodynamic lubrication. (a)Slider bearing; (b) squeeze film bearing; (c)externally pressurized bearing.Source:FromHamrock, et al. [2004].


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Elastohydrodynamic Lubrication

Figure 8.19: Characteristics of hardelastohydrodynamic lubrication.

Figure 8.20: Characteristics ofsoftelastohydrodynamic lubrication.


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Fundamentals of Machine Elements, 3

rd


FrictionValues

Table 8.9: Typical coefficients offriction for combinations ofunlubricated metals in air.

Material Coe!!ici ent

o!!riction, 3/el!-matedmetalsinair

5.2dloG1-8.0revliS

1niT

2.1-8.0munimulA 4.1-7.0reppoC2muidnI5.0muisengaM5.1daeL5.0muimdaC4.0muimorhC

Puremetalsandallo"sslidingonsteel 4.%*'5carbon6inair

5.0revliS5.0munimulA4.0muimdaC8.0reppoC5.0muimorhC

2muidnI2.1daeL2.0dael%02-reppoC8.0)desabnit(latemetihW

Whitemetal(leadbased) 0.5-brass(copper-30%zinc) 0.5Leaded/ brass(copper-40%zinc) 0.2

4.0noritsacyarGMidsteel(0.13%carbon) 0.8


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rd


Sliding and Rolling Friction

Figure 8.21: Friction force in (a) sliding and (b) rolling.


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rd


Adhesive and Abrasive Friction

Figure 8.22: Conical asperity havingmean angleplowing through asofter material. Also simulatesabrasive wear.

Figure 8.23: Adhesive wear model.


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rd


Wear Coefficients

Table 8.10: Coefficients of rubbing friction and adhesive wear constant for ninerubbing materials.

Coe!!ici en t o! Adhesiewear

,noitcir!slairetamgnibbu7 coe!!ici ent , k15.2dlognodloG2.1reppocnoreppoC6.0leetsdlimnoleetsdliM3.0leetsdrahnossarB2.0leetsnodaeL

Polytetrafluroethylene(teflon )onsteel 0.2

Stainlesssteelonhardsteel 0.5Tungstencarbideontungstencarbide 0.35

5.0leetsnoenelyhteyloP 5 10-8

2 10-5

2 10-5

2 10-5

10-2

10-3

0.01-0.10.1-1

10-6

Archard Wear Law:


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rd


Fatigue Wear

Figure 8.24: Fatigue wearsimulation. (a) Machine elementsurface is subjected to cyclicloading; (b) defects and cracksdevelop near the surface; (c) thecracks grow and coalesce,

eventually extending to thesurface until (d) a wear particleis produced, leaving a fatiguespall in the material.


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Fundamentals of Machine Elements, 3rded.Schmid Hamrock and Jacobson 201 !"! #ress

Orthopedic Implants

Figure 8.25: Examples of common orthopedic implants. (a) Total hip replacement,using a metal-on-metal interfaceSource:Courtesy DePuy, Inc.; (b) total kneereplacement using a metal-on-polymer interface.Source:Courtesy Zimmer, Inc.

Design of elements machine, bearing, shaft, spur gear and others, superficie profile, lubrication,...

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