modelica2012 enge-rosenblatt modeling a drum …modeling a drum motor for illustrating wearout...

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 [email protected]

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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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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a roller bear-e distribution

into several

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a l -s e h . s e e r t n s y -e -

-n l

n s

Olaf Enge-Rosenblatt, Christian Bayer and Joachim Schnüttgen


Figure 4 S

The pres

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escribe the anhe inner and tes an initial

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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-

enomena de-ing elementsortant formssurface, sur-

modeled by aary angles of

e -t -g

-g

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s -r e g

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3.2 O-rin

The drum mnot leak outO-rings areshell prevenintroduce hiof very highdrum motor

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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



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



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



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.

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modelica2012 enge-rosenblatt modeling a drum …modeling a drum motor for illustrating wearout...

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