Post on 25-Jun-2020
Modeling a drum motor for illustrating wearout phenomena
Olaf Enge-Rosenblatt1, Christian Bayer1, Joachim Schnüttgen2 1Fraunhofer Institute for Integrated Circuits, Division Design Automation,
Zeunerstraße 38, 01069 Dresden, Germany {Christian.Bayer; Olaf.Enge}@eas.iis.fraunhofer.de 2Interroll Holding GmbH, Interroll Research Center,
Lothforster Straße 32-40, 41849 Wassenberg, Germany J.Schnuettgen@interroll.com
Abstract
In this contribution, a model of a drum motor is pre-sented. This model was designed for description of dynamic behaviour of the drum motor as well as for the possible implementation of several wearing phe-nomena. Using this model, a better understanding of wear and tear phenomena has been achieved by car-rying out a considerable number of simulation runs using different operational and wearing conditions. Using this information, important knowledge about detection of wearout signs was able to be gained.
Often, mathematical models with different levels of detail are used. In these cases, it may be a difficult task to obtain reliable parameters. In this paper, we present three different approaches for establishing a model structure and for the determination of needed parameters. This way, we were able to define every part of the model with an appropriate level of detail and equip them with adequate parameter values.
Keywords: drum motor; mathematical model; wearout phenomena modeling; parameter determi-nation; condition monitoring
1 Introduction
Applications of mathematical models of technical systems are widespread in today’s product develop-ment cycle. Mathematical models help to increase the understanding of physical properties of a product. The usage of mathematical models in the design phase allows investigations of functional properties under changing operational conditions. Both proper-ties and operational conditions are described in the models by certain parameters. In the early phase of product development, only a certain range of values for these parameters is needed. Later on, these pa-
rameters have to be determined with higher accuracy to benefit from the model-based investigations.
Correct and robust operation under changing cir-cumstances is the most important requirement con-cerning machines and facilities in today’s industry. Additionally, all equipment must guarantee a very high level of availability. These two demands are competing against each other because every tech-nical system is characterized by a certain appearance of wear and tear. This applies to mechanical and electrical systems but also for any other physical domain. This appearance of wear and tear increas-ingly causes a less correct operation of any technical system with progressing time of operation. There-fore, compliance checks concerning the allowed tol-erances have to be performed either in certain time intervals or depending on the current condition of wearing. However, those checks take time and, therefore, decrease the machine’s availability.
Using a mathematical model of a machine or a facility that is able to reconstruct phenomena of wearing is one promising way of getting out of the dilemma. Still, the model must be able to describe functional and dynamic properties, too. That is the reason why such mathematical models cannot be implemented in an easy and straight forward manner. The model structure developed first has to be laid out with necessary parameters. Some of them can be cal-culated while other ones may only be measured. Cal-culation may be performed analytically or, e.g., by using a Finite Element model. Parameter measure-ments mostly need considerable effort for establish-ing an appropriate test set-up. All three methods were applied for the development of the model pre-sented here. Using a well-parameterized model, we can carry out investigations about impacts of effects of wear and tear on functional properties of a ma-chine or a facility.
DOI Proceedings of the 9th International Modelica Conference 889 10.3384/ecp12076889 September 3-5, 2012, Munich, Germany
Figure 1 S
Figure 2 S
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2 Desig
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Modeling a drum motor for illustrating wearout phenomena
890 Proceedings of the 9th International Modelica Conference DOI September 3-5, 2012, Munich Germany 10.3384/ecp12076889
Figure 3 M
3 Mode
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e roller bearicomponent
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f the Bearinard Library [9of inner and finition of thnted by frictis (balls in mthe inner and. [12]). The
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of this forced by all balring. ws a simple s the applicatelt force BF
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ings is implewith only on
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a l -s e h . s e e r t n s y -e -
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Olaf Enge-Rosenblatt, Christian Bayer and Joachim Schnüttgen
DOI Proceedings of the 9th International Modelica Conference 891 10.3384/ecp12076889 September 3-5, 2012, Munich, Germany
Figure 4 S
The pres
Hertzian cocally modedisplacemenvery small and outer rdisplacemeneach ball wfound that idisplacemen
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escribe the anhe inner and tes an initial
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We defined tall angular pduces high flspots on theon torque du
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wearout phebetween rollihe most imps (e.g. dull s
gs) can be mon momenta
(3)
pendent. They with angu-balls presents slight fluc-e the bearing
mulate abra-eased rolling
rtional to the
ds further on
be a function
lative to the
these factorspositions be-lexibility fore rings. Theue to rolling
(4)
er and outer
ary to calcu-y to the ring connectingof the ballsring and the
are a suitablens become
(5a)
(5b)
ion of a ballrespectively,the ball. Us-
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modeled by aary angles of
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Modeling a drum motor for illustrating wearout phenomena
892 Proceedings of the 9th International Modelica Conference DOI September 3-5, 2012, Munich Germany 10.3384/ecp12076889
3.2 O-rin
The drum mnot leak outO-rings areshell prevenintroduce hiof very highdrum motor
To modewere carriedSection 4. Tonly to accoto obtain utorque. Wemainly on tthe used lublubricant amfixed combsimpler struhaviour of the frictionproportionaHence, it ca
OO k
where isThe parame
performing proximationtorque with of measuredmodel BearO-rings bec
For bothfriction doeforces and aabsorbed bynomena at they are notwe found thoperation – increasing ences have ments, too.
3.3 One-
The drum stage planetthe standardbination of any featureapproach th
ng friction
motor is partt during ope
e used for senting the oiligh friction vh influence r. el such frictd out by IntThe goal of ount for the useful absol
e found thatthe material bricant (usedmount). But ination of m
ucture in comroller bearin
n may be a al share andan be written
0,O ,
s the rotationeters Ok an
appropriaten was implem rotational spd values. To ringFriction wcause it offerh approximates not vary wany load in ay the main bO-rings are t dependent ohat O-ring fri
because of wwearout, e.gto be determ
-stage gear
motor inclutary gear, wd library mo
f two of it. Hes to emulatehe usually ex
tly filled witeration. At leealing both el from leakivalues and, thon dynamic
tion, extensivterroll as wilf these investnon-linear blute values t the frictionof the O-rin
d or used notthe friction
material and lmparison witngs. A first a
combinatiod a nearly
n like
nal speed ofnd 0,O have
e experimentmented by fpeed by usinthis end, the
was finally us such possibtions, we asswith any outaxial directio
bearings. Henexpected to
on the drum iction vary bwearing in eg. by abrasimined by ex
udes a singlewhich can beodel IdealPlaHowever, it e wearout e
xisting backla
th oil which east two so-cends of the ng out. But herefore, thebehaviour o
ve measuremll be describtigations waehaviour butfor the fri
n values dengs as well at, lubricant g
n behaviour lubricant shoth the frictioapproximatio
on of a veloconstant s
f the drum se to be foun
ts. A secondfull correlationg a look-up e standard libused to modebilities. umed that Oter load. Theon are complnce, wearouto be uniformshell’s angle
both with houeffects – andion. These ixtensive mea
e-stage or mimplemente
anetary or a does not incffects. As aash and rotat
must called drum they
ey are of the
ments bed in as not t also iction epend as on
grade, for a
ows a n be-on of ocity-share.
(6)
shell. nd by
d ap-on of table brary el the
O-ring e belt letely t phe-
m, i.e. e. But urs of
d with influ-asure-
multi-ed by com-clude
a first tional
stiffnand dampbehaabra
Gmizetoothbetwripplto hmay wouthrounite geargularectiyieldHerture 5wheeleadsbothtion alonfuncFE s
Figu
F
two for s
indep
linea
ness can be the gear’s per system. T
aviour of thesion.
Gears have spe abrasion [2h flank, whi
ween teeth anle. During opigh loads or
break off ld be very ugh multi-boElement (FE. In the idear position siion. Actuallyds a slight detzian contact5 for one whel is transmis to a little d
h wheels and of the w
g the evolvection of simulation.
ure 5 Gearwthat thmagnishape
Figure 6 showgear wheels
small loads, i
pendent of t
arly on
inserted beinput wheelThe backlashe drum moto
pecial kinds 2], [13]. Mosch ensures t
nd that the trperation the r improper munder certaichallenging
ody simulatiE) model staal case, both imultaneously, the driveneformation omodel. This
heel. The torqtted by this mdeviation
d depends alswheels, as thent. The tran
and whi
wheel with strhe deformatioification of 10of the wheel)
ws the resuls of equal sii.e. for small
the angular p
. However
etween the dl by a rotath influences or and is a
of tooth flast gears use that there is ransmitted toflank might
maintenancein circumstato model t
ion, we devearting from wheels chan
ly but with n wheel movof teeth accos effect is shque applied tmeans. The in angularso on the ab
the contact pnsmitted torqich is determ
retching of teon is displaye00 in relation)
lting torque ize. We can l , the tra
position a
r, for heavy
driving shaftional springthe dynamicmeasure for
nks to mini-the evolventno grinding
orque has nodegrade due. Even teethances. As itthese effectseloped a Fi-a two-wheelnge their an-opposite di-
ves first andording to thehown in Fig-to the drivendeformationr position ofbsolute posi-point movesque thus is amined by the
eeth (Note ed using a n to the
function fordeduce that
ansmission is
and depends
y loads the
t g c r
-t g o e h t s -l --d e -n n f -s a e
r t s
s
e
Olaf Enge-Rosenblatt, Christian Bayer and Joachim Schnüttgen
DOI Proceedings of the 9th International Modelica Conference 893 10.3384/ecp12076889 September 3-5, 2012, Munich, Germany
transmissiondepends on
odic in .
Figure 6 D
t
The resu
develop a Mnation. Theand their abof missing t
3.4 Envi
The drum mSuch envirocial Belts lstatic and dThe key comadded interfit can act alibrary comlate the moinvestigate tear.
Our Modmotor. Thisas a Matlabing torque from our mosimulation wfeature in Scombined mmechanical parts and cogations are n
n function b . Note tha
Dependency otheir differen
ults of the FModelica moe investigatibrasion is thuteeth can be
ronment of
motor is inteonments can library, whicdynamic anamponents arfaces to our
as a pulley amponents. Thotor within a the effects o
delica models component b Simulink m
and uses anodel to contrwas carried Simulink (semodel is to
properties ontroller of not content o
becomes nonat the torque
of torque on bnce
FE simulationdel of any gon of differ
us possible anevaluated.
the model
ended for bebe modeled
ch includes alysis of bere belt spansdrum motor
and is fully chis way we a
realistic envof different s
l does not inwas provide
model [5]. It pngular positrol the electrout using th
ee [8]). Theinvestigate
and setups the motor. Bof this paper
n-linear ande function is
both angles a
n can be usear wheel corent tooth fnd even the e
elt drive systd by the comelements folt drive syst and pulleysr model suchcompatible tare able to svironment ansigns of wear
nclude the eleed by a third provides the tion and velic motor. Thhe Dymola be purpose of
the influencto the elect
But these inv.
d also peri-
and
ed to ombi-flanks effect
tems. mmer-or the tems. s. We h that to the simu-nd to
ar and
ectric party driv-
locity he co-block f this ce of tronic vesti-
4
Deteis a read mencoefurem
Fneedperfonatioringsgearated ley i(firstand (seco
Tcal qtempcarritypicwas
Figu
F
uredtachefrictishapspee0.3 Nfrictimodbetteformfricti
Foute
Determin
ermination overy imporfrom geom
ts of inertiafficients needments carriedFor an apprded to measuormed. Theson of frictions without an. To this endto a certain
is retarded ot test set-updue to frictiond test set-u
Temperature quantities inperature can ied out withcal use casefound to be
ure 7 Frictio
Figure 7 showd across rotaed to the teion because
pe which ised because Nm (see alsoion torque
del by a coner integration
med using a lion torque va
Figure 8 depir O-rings are
nation of
f parametersrtant task. S
metrical value. But other
d to be determd out using reropriate assiure, a numbee tests were n losses becany influence d, a single rerotational sp
only by frict) or by friction between up). and lubricati
nfluencing thbe ignored
in a range oe. Lubricatioof no noticea
on torque wit
ws the curve ational speedst set-up. It of bearings o
nearly indtorque valu
o [12]). In ais, therefor
nstant value n of the mealook-up tablealues dependicts the meae attached to
paramete
s used withiome paramees like massparameters
rmined by speal devices. ignment of er of roll-oufocused on
ause of beare from electreturn pulley peed. After ttion torques tion torques drum shell
tion are addithe friction tif all measu
of temperatuon, if effecteable influenc
thout any O-
of friction td if no O-ris a result
only. The cudependent oues range fa first approxre, implemeof Coulomb
asured curvee containing
ding on rotatiasurement rethe drum sh
ers
n the modeleters can beses and mo-like friction
pecific meas-
f parametersut tests werethe determi-
rings and O-ric motor orwas acceler-that, the pul-
in bearingsin bearings
and O-rings
tional physi-torques. Buturements areure like in aed correctly,ce.
ring
torque meas-rings are at-of retarding
urve shows an rotational
from 0.2 toximation thented in the
b friction. A can be per-
g momentaryional speed.esult if bothhell. This is a
l e -n -
s e --r --s s s
-t e a ,
--g a l o e e
A -y
h a
Modeling a drum motor for illustrating wearout phenomena
894 Proceedings of the 9th International Modelica Conference DOI September 3-5, 2012, Munich Germany 10.3384/ecp12076889
result of reO-rings. Thon rotationasplit into omately 0.95cient for frspeed. The Here againcurve can b
Figure 8 F
5 Simu
As an examing the rollement resultpresent simtained usingment of thestant transvThis force i1 kN in a ty
Figure 9 N
bs
etarding fricthe curve shoal speed. Fo
one part with5 Nm) and onfriction depeconstant valu
n, a better ie performed
Friction torqu
ulation res
mple, we preser bearings. ts up to now
mulation resug Dymola [
e drum motorversal force is induced b
ypical applica
Normal forceball located wspace of the r
tion becauseows a non-lior simplificath constant fne part with ending linearue is about 0integration ovia a look-u
ue with O-rin
sults
sent simulatioBecause of
w, we can unults. These 3]. The appr consists of(like force
by the belt aation.
e against timewithin the forroller bearing
e of bearingsinear dependtion, the curfriction (appa constant corly on rotat
0.1 Nm/1000of the meas
up table.
ngs
on results relack of meanfortunately results were
plication envf a load by a
FB in Figuand reaches u
e acting on once loaded hal
g
s and dency rve is proxi-oeffi-tional rpm. sured
gard-asure-
only e ob-viron-a con-ure 4). up to
ne lf-
Fthe bthe bples timeloadthe hThe othethermbetwHencthe nballconsnormthe beverand this frictiand t
Figu
Ttatinload torquear afect damfrictidynacompwiththe ra cevani
First we inveballs of a beabearing modoriginates fr
e for the moed half spachalf circle onormal forcr half spacemore, we as
ween ball andce, the samenormal forceinstead of ti
sidered ball mal force likball-specific y point in tithe bearingresult for evion can be cthe load forc
ure 10 Torquacrosswith lo(dashe
To investigatng load (not
force), the due and the roand velocity of a spot dage was introion coefficieamically usipared the to
hout spot damresults. Both ertain range shed. The to
estigated the aring. This g
del works anrom. Figure 9otion of onee of the bear
on the right ce is expectee (left hand ssume that thd inner or oue curve shapee across the ime. The frican then b
ke shown in friction val
me dependin’s transversaery ball of thalculated fro
ce.
ue transmittes time withouocalized damed line)
e the resultinto be mista
drum motor wotational loaddependent d
damage at ooduced by a ent Rk . This ng the pres
orques actingmage, respectorques are after the tr
orque withou
normal forcgives an impnd where the9 shows the e ball withinring (which hand side i
ed to be zeroside in Fig
there are nouter ring of e results whangular pos
iction torquebe determine Section 3.1lue can be cng on the baal load forche bearing, t
om present b
ed to the load ut damage (so
mage on the ou
ng torque ripaken for thewas driven bd was emuladamper. To sone of the ri
localized inc increase wasent bearingg on the loactively. Figudepicted acr
ransient effeut bearing da
ce acting onpression howe torque rip-result acrossn the force-is located inin Figure 4).o within the
gure 4). Fur-slip effects
the bearing.en depictingsition of the
e for the oneed from the1. This way,calculated atall’s positionce. Applyingthe complete
bearing angle
displayed olid line) and uter ring
pple at a ro-e transversalby a constantated by a lin-show the ef-ings, such acrease of theas calculatedg angle. Wead with and
ure 10 showsross time forect has beenamage (solid
n w -s -n . e -s . g e e e , t n g e e
-l t --a e d e d s r n d
Olaf Enge-Rosenblatt, Christian Bayer and Joachim Schnüttgen
DOI Proceedings of the 9th International Modelica Conference 895 10.3384/ecp12076889 September 3-5, 2012, Munich, Germany
line) is nearly constant during the complete simula-tion interval. Contrastingly, the torque with bearing damage (dashed line) shows distinct ripples. The ripples’ magnitude order is about 0.5 % of the torque’s mean value. That seems to be not so high but it is enough to detect some differences within a frequency plot. This way, a damage of sufficient di-mension could be detected by a dedicated condition monitoring system.
6 Conclusions
We presented an approach to simulate wear and tear phenomena within complex systems. For the case of a drum motor we proposed three different methods of modeling and parametrising components thereof. The roller bearing was described analytically, whereas the gear was simulated using the Finite El-ement method. A third access to unknown parame-ters is measurement as shown with the O-rings. Us-ing these well-parameterised models, we were able to establish a behavioural description for some im-portant wearout effects with the drum motor. Hence, these models can be used to predict the behaviour of a worn system within its usual environment. This opens the possibility to investigate some conse-quences of wearout effects in several simulation runs in order to establish design rules for condition moni-toring algorithms and thus support the development of adapted condition monitoring systems. This in turn allows for improved maintenance strategies and reduced costs.
Ackknowledgement
This work was funded by the German Federal Minis-try of Economy within the project AutASS.
References
[1] Ashtekar, A.; Sadeghi, F.; Stacke, L.-E.: Surface defects effects on bearing dynamics. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, Vol. 224, No. 1, pp. 25-35, 2010
[2] Colbourne, J.R.: The geometric design of in-ternal gear pairs, AGMA Technical Paper, 87 FTM 2, 1987
[3] Dymola 7.3, Dassault Systèmes
[4] Fritzson, P.: Principles of Object-Oriented Modeling and Simulation with Modelica 2.1, IEEE Press, 2004
[5] Herold, T.; Franck, D.; Lange, E.; Hameyer, K.: Extension of a d-q model of a permanent magnet excited synchronous machine by in-cluding saturation, cross-coupling and slot-ting effects. IEEE International Electric Ma-chines Drives Conference (IEMDC), Niagara Falls, Ontario, Canada, 15-18 May, 2011, Proc. pp. 1363-1367
[6] Hertz, H.: Über die Berührung fester elasti-scher Körper. Journal für die reine und an-gewandte Mathematik, 92:156-171, 1881
[7] Hertz, H.: Über die Berührung fester elasti-scher Körper (On the contact of rigid elastic solids). In: Miscellaneous Papers. Jones and Schott, Editors, J. reine und angewandte Ma-thematik 92, Macmillan, London, pp. 156ff., 1896
[8] MATLAB® 2010a, The MathWorks, Inc.
[9] www.modelica.org/libraries/Modelica/
[10] Paland, E.G.: Technisches Taschenbuch. INA Schaeffer KG, 2002
[11] Stacke, L.-E.; Fritzson, D.: Dynamic behavi-our of rolling bearings: simulations and expe-riments. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of En-gineering Tribology, Vol. 215, No. 6, pp. 499-508, 2001
[12] Tan, X.; Modafe, A.; Ghodssi, R.: Measure-ment and modeling of dynamic rolling fric-tion in linear microball bearings. Journal of Dynamic Systems, Measurement and Con-trol, Transactions of the ASME, 128 (4) , pp. 891-898, 2006
[13] Zhuravlev, G.A.; Ageev, A.I.: Gear Teeth Bending Strength Analysis. Izvestia vyssih ucebnyh zavedenij. Masinostroenie (11), pp. 44-48, 1978
Modeling a drum motor for illustrating wearout phenomena
896 Proceedings of the 9th International Modelica Conference DOI September 3-5, 2012, Munich Germany 10.3384/ecp12076889