Towards the Virtual Product UsingIntegrated Calculation Methods

Dr.-Ing. Christoph L�ffel and Dipl.-Ing. Hermann Golbach

INA reprint from ÒVDI Berichte 1487ÓConference ÒReduction in development process times through theintegration of design and calculationÓ, Stuttgart, 8-9 June 1999VDI-Verlag GmbH, D�sseldorf

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Towards the Virtual Product UsingIntegrated Calculation MethodsDr.-Ing. Christoph L�ffel and Dipl.-Ing. Hermann Golbach

Computer-assisted productdevelopment processes which areintended to satisfy the demand forimproved efficiency require newintegrated software products.Significant problems may arise,however, where the CAE toolsrequired for product developmentare not sufficiently compatible orare poorly integrated with eachother. Using the concept of virtualproduct development, new initiativesare being taken with the aim ofeliminating the recogniseddeficiencies of current CAE appli-cations. Taking as an example theinvolvement in the developmentprocess of an “Engineering

Calculation” department of asupplier to the automotive andmechanical engineering sectors,the methods and procedures beingharnessed in order to achieveprocess optimization and improveddigital communication with thecustomer are presented.The first example concerns thedevelopment of a system componentat component level and showsseamless integration into the CAprocess chain at INA, using mainlycommercial programs and moduleswhich have been developed in-housein INA’s strategic 3-D CAD system.The development of a castingdesign, beginning with the initial

decision as to form and proceedingto its verification. The secondexample concerns calculationmethods specific to the company.The BEARINX® calculation system,an interface between BEARINX® anda 3-D CAD system and thedevelopment of an FE user elementfor rolling bearings are presented.These methods are presentedusing the example of rolling bear-ing design in an industrial gearbox,starting with the customer’s 3-D CAD model.

Fig. 1 INA product range for passenger cars

Alternatoroverrunning pulley

FEADauto-tensioner

Switchingtappet

Encapsulated thrust bearing

Clutchreleasesystem

Synchronizerring

Needle rollerbearing

Sensor ringfor ABSGear selector

moduleDetentpin

Strut bearingGear shift guide plate

Water pumpbearing

Variable camtiming system

Hydraulic pivot elementfinger follower lever

Shimlessmechanical tappet

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1 INA Wälzlager Schaeffler oHG

INA is a leading worldwide manufacturerof needle roller bearings. It also offers awide range of special rolling bearings andengine components (Figure 1). In the fieldof linear technology, for example,customers are offered a full range oflinear bearings and guidance systems forthe production machinery sector. INA isalso a leading manufacturer of mechan-ical and hydraulic engine components(e.g. valve lash adjustment elements). In all product areas, the clear trend istowards system suppliers providingcomplete solutions to customers.The firm has more than 24 000 employeesworldwide. Some 6 500 people areemployed at the company’s headquartersin Herzogenaurach, near Nuremberg.Additional information is available on theInternet at http://www.ina.com. As a supplier to the automobile industry,INA must meet the constantly increasingdemands of motorists. As a result of thefirm’s strongly customer-orienteddevelopment process and the drive todevelop technologically advancedproducts with shorter and shortertimescales and to be able to offer thecustomer cost-effective products, the useof the latest CAE technology, once amanagement dream, has long sincebecome an essential prerequisite forbeing able to offer customers a compre-hensive package of products and service.This is already clearly seen in the fact

that customers provide their productrequirements, such as design envelopeand adjacent construction, in electronicform and expect in return to receive INA’sdeveloped system component as anelectronic model. This therefore meetsthe first prerequisite for the virtualproduct. Development at INA is characterised byapplication-oriented product developmentas previously mentioned. Applicationengineering as a central function is of keyimportance here (Figure 2). All the otherareas of the company support this centralfunction through co-operation in projectand development teams. The applicationengineer looks after the customer,providing advice as appropriate, preparesinstallation proposals, leads new designand development work and supervisesthe development of new products untilthey are ready for volume production.

2 Towards Virtual ProductDevelopment

Ever since the introduction of computer-assisted calculation methods, effortshave been directed towards achieving themaximum efficiency in generating thegeometry of the structure to be analysed,and in further processing with CADsystems. The current status ofcommunication between the geometry-based system (the CAD system) and thecalculation-supporting systems (pre- andpostprocessors) is characterised byefficient methods of data exchange which

extend as far as complete merging of thesystems [1]. Present and future efforts toincrease the efficiency of the use of CAEare directed at the process- or product-oriented integration of all CA toolsinvolved in the process [2]. In calculation,these include the implementation ofdevelopment-associated calculationmethods directly within the CAD system(process optimization), and the moreintensive use of calculation over theInternet/Intranet. The goal of VirtualProduct Development is a result of logicalextension of the above methods and thefurther development of generic, moreflexible data structures (Figure 3) whichmeet the above requirements.The goal of Virtual Product Developmentis being pursued in a variety of ways byINA, of which two different examples willbe discussed below. These are integratedmethods for achieving efficient dataexchange between the INA customer and the INA-specific calculation toolsand, on the other hand, for acceleratinginternal product development by theintegration of calculations into the CAEtools used by INA.

Fig. 3 Towards Virtual Product DevelopmentFig. 2 Application-oriented product development at INA

Automotive/mechanicalengineering industry

Partial CAD implemention

Company wide useof CAD implementation

EDM/PDM implementation

Integration of development-associated analyses into CAD systems

Internet applications(e.g. Java etc.)

Virtual Product Development

CAD/CAE implementation

Supplier industry

Partial CAD implemention

Company wide useof CAD implementation

EDM/PDM implementation

Integration of development-associated analyses into CAD systems

Internet applications(e.g. Java etc.)

Virtual Product Development

CAD/CAE implementation

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Due to the INA product range and itsapplication-oriented development, thecentral CAE department plays a veryimportant role in design. The form anddimensions are determined decisively bythe loads which must be transmitted. For this reason, every newly developedproduct is processed by the CAEdepartment or is designed using acalculation program developed by thisdepartment. While commercially availablecalculation methods such as structuralanalysis are used in the design of INAproducts, there is greater emphasis onthe use of methods developed in-house,which are based to a substantial degreeon the extensive experience gathered byINA. These INA-specific calculationprograms are made available to INAdevelopment engineers throughout theINA Group in the form of a user-friendly,standardized interface and are known asBEARINX®. The BEARINX® calculationsystem includes modules for the designof rolling bearings and power transmissionsystems.

3 Integration of calculation inthe INA development process

The first example shows calculationmethods which can be used to acceleratethe development of an idler lever for ahydraulic belt tensioner. The idler lever isintended to combine the tension pulley,hydraulic tensioner and the function ofthe pivot support in a single subassembly(Figure 4). The belt tensioner unit ensuresa constant belt tension in the ancillarydrive of an engine.

In the early draft design phase, thedesigner must aim to achieve a generalform for the component which links thefunctionally important areas together andwhich meets the identified restrictions,e.g. arising from production and fitting.An essential factor here is the stresscapability of the component. Thedefinition of a general form can beassisted significantly by topologicaloptimization, since this provides a simplemeans of computing “stiffness-optimizedstructures”. On the basis of a discretelydefined design envelope (includingfrozen, functionally important areas) and the boundary conditions imposed,the designer obtains information aboutthe position and dimensions of openingsand ribs [3].

When defining the belt tensioner unit, the applications department is generallyprovided with a CAD model showing theexternal surfaces of the engine block onwhich the ancillary drive is to bepositioned (Figure 5). This preventsproblems due to erroneous informationfrom the customer about the adjacentconstruction. Based on the customer’srequirements, the designer determinesthe appropriate spatial position for thecomplete belt tensioner unit using theCAD system and thus also obtains themaximum design envelope for the idlerlever. Once the functionally importantareas of the lever have been defined inthe CAD system, the calculation modelfor topological optimization can begenerated automatically by means of an

Fig. 4 Drive arrangement, functional areas and actual belt tensioner unit

Idler lever

Belt tensioner unit

Drive arrangement Functionally important areas

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interface developed by INA. A geometry-based hexahedral mesh generator hasbeen developed for this purpose. In theCAD system, the designer selects thedesign envelope and the areas whichhave been frozen for the optimization,and enters the fineness of the FE mesh.The size of the elements is based onvalues obtained from experience inprevious optimizations. In a further step,the calculation model is provided to theCAE department, where boundaryconditions (loads and bearings) for thecalculation are defined using apreprocessor. In a forthcoming develop-ment, it will also be possible to definethese in the CAD system.The result of the topological optimizationis provided to the designer in the form ofa VRML animation (Figure 6). He can thussee at his workplace the precise positionof the ribs and openings. Moreover, the topologically optimized model canalso be incorporated into the CADsystem so that the geometrical positionof ribs etc. can be precisely determined.On the basis of this “idea”, the designermust then derive a suitable modelmeeting the many other restrictionsimposed by the development process.This process necessarily entails the lossof some of the optimizer’s “designproposals”. A further topologicaloptimization may show further potentialweight saving. Supporting areas of the

design are thus made visible, as theoptimizer removes no material from them.

A subsequent FE analysis shows thedeveloper where areas of high stressconcentration occur in the design.Because of the design “smoothingprocess” on the basis of the topologicaloptimization, it is often not possible toavoid the occurrence of areas with highstress concentrations. The FE calculationis carried out in the CAE department onthe basis of the designer's CAD model. Inthis particular case, the definitively opti-mized 3-D CAD model was up to 30%superior to comparable components in itsstructural and mechanical behaviour inrelation to stresses and stiffness.

The procedure described has decisiveadvantages in the development processfor the belt tensioner unit. Through theexclusive use of electronic data, beginningwith the customer's adjacent construction,and the development and application ofintegrated calculation methods running inparallel with the development process, it is possible to not only shorten thedevelopment time but also to improveprocess reliability. Furthermore, theintensive use of these methods results infaster communications between theapplication engineering function and thecentral CAE department (Figure 7). Thisprocedure can also be applied to otherproduct areas and represents INA’s initialapproach to Virtual Product Development.

Fig. 7 Communication during design between Application and Calculation departments

Fig. 6 Evaluation of results, preparation of CAD model and FE resultFig. 5 From the adjacent construction to the calculation model

Definition of spatial position andmaximum design envelope

Adjacent construction of customer (e.g. surface copy)

Definition of functionally importantareas and boundary conditions

Definition of the CAD model – designenvelope and frozen areas

Automatic preparation of thecalculation model

Display of the result of topological optimization,

e.g. by VRML Editor

CAD model of the idler lever on the basis of the topological

optimization

FE result

3-D CAD model of thefinished product

3-D CAD model of the design envelope

Calculation model for topological optimization

DocumentationVRML file

Feedback into the 3-D CAD system

Design department

Technical Calculation

Housing:– undeformed– deformed

External force

Bearing reactions

Ball bearingShaft Roller bearing Contact pressure

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4 Design of rolling bearings forgearboxes

Rolling bearings are advanced machinecomponents with high load carryingcapacity and accuracy [6]. If they are tobe used correctly, the load distribution inthe complete elastic system must beanalysed precisely. Manufacturers ofrolling bearings have developed suitableprograms for this purpose in order toadvise customers regarding selection andcorrect installation. As a first step, INAoffers a CD or the option of carrying outinitial calculations via the Internet [4], [5].At a later stage, the customer canconsult INA directly. Depending on thenature of the problem, design and ratinglife calculation can be carried out not onlywith the BEARINX® program system butalso with the FE method, where speciallydeveloped FE elements represent therolling bearing (Figure 8).

4.1 Fundamentals of rollingbearing calculation

Rolling bearings transmit an external loadfrom one raceway, distributed overseveral rolling elements, to anotherraceway. As the rolling bearing rotates,very high local dynamic stresses occur atthe contact point between the rollingelement and the raceway. If the rollingbearings are to withstand the high loads,it is imperative that they are not only ofexcellent quality but also that their designtakes account of all relevant factors.Analysis of load distribution in the bearingis a key requirement here and is the firststep in determining the life of the bearing.The best rolling bearing will fail if itssystem behaviour is not matched to themachine in which it is fitted. The analysisof load distribution must therefore takeaccount of the interactions between thebearings and their adjacent construction,allowing their behaviour to be predicted.In a system comprising a bearing, shaftand housing, for example, bending of the

shaft and deformation of the housingaffect the reaction of the bearing andthus the distribution of forces in thebearing while, conversely, the stiffness ofthe bearing affects the bending curve ofthe shaft (Figure 9).From a mechanical point of view, thesystem components of the bearing, shaftand housing represent elastic elementswhich form a statically indeterminateelastic system. The bearing itself, whichusually has several load-transmittingrolling elements, is also a highly indeter-minate part of the system which is alsocharacterised by the strongly non-linearelastic behaviour of its rolling elements.In the past, the calculation methods forthese demanding non-linear, staticallyindeterminate systems were developedand refined step by step. As a rule, thesemethods are based on analytical principles.Reference should be made at this pointto [8] and [9], which give an excellentoverview of the current status of rollingbearing engineering.

Fig. 8 INA calculation methods for the design of rolling bearings

FEM

3-D CAD ¨

Fig. 9 Deformed bearing/shaft/housing system

Stiffness matrix• Housing• Machine bed• Linear guidance tables

Bearing load distributionContact pressure

Deformation

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4.2 Conventional rolling bearinganalysis with BEARINX®

At INA, the analytical principles havebeen converted into a powerfulcalculation program for rolling bearingdesign called “BEARINX®”. This programcan be used to analyse the smallestelement of a rolling bearing, the rollingelement, the complete rolling bearingitself or even complete gearboxes. In thecase of gearboxes, BEARINX® determinesthe equilibrium of the statically indeter-minate elastic systems in a closedmathematical procedure (down to theequilibrium of the individual rollingelement) and thus takes precise accountof interactions between the individual

components. The use of a powerfuliterative solver means that the set ofequations describing a system can besolved on a normal PC within a fewminutes, even in the case of complexsystems.In accordance with current standards,the core of this calculation program isembedded in a user-friendly Windowsinterface enabling comfortable operationfrom modelling to result analysis. Inparticular, the 3-D representation ofsystem geometry, which permits a visualcheck on input data, is a valuable aid tothe user during preprocessing. Figure 10shows as an example a 3-D model of atwo-speed industrial gearbox. All further

statements (including those relating tofinite-element analysis) refer to thisapplication example. Once calculationhas been performed, all relevant resultssuch as shaft bending curves, distributionof forces in the bearings and pressurecurves for each individual rolling bearingare directly accessible (see Figure 11 fora typical results display). A further high-light of BEARINX® is the so-called para-metric analysis, which can be used tooptimize each parameter in the system toachieve the longest possible system life.Due to its outstanding features, whichcannot be described in detail here,BEARINX® is now INA's standard tool forrolling bearing design.

Fig. 10 3-D model of a two-speed industrial gearbox in BEARINX®

Fig. 11 Results views in BEARINX®

Fig. 12 Communication between customer and INA Application Engineering

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4.3 Data exchange with thecustomer

In order to permit the most efficientpossible data exchange between thecustomer and INA, a standard interfacewas created between a 3-D CAD systemand the BEARINX® gearbox module (seeFigure 12). This interface conforms to thephilosophy of Virtual Product Developmentin that the customer can, at a very earlystage, directly generate the informationrequired for calculation from his CADsystem. Not only geometrical informationabout the gearbox stage but all thetechnological data required for calculationare determined. One clear advantage isthat the geometry does not have to beentered a second time for calculation,thus eliminating input errors. A furthereffect is the considerable reduction in theresponse time within the INA application

engineering department, since direct useis made of data provided by thecustomer.In the development of the interface,particular emphasis was given to ease ofuse. The determination of the geometryof the gearbox stage (shafts, gears etc.)is thus independent of the modellinghistory of the CAD model. The rollingbearings and gears can also theoreticallybe saved simply as discs in the CADmodel. In the derivation, only the datapresent in the CAD model are interpreted.This is an important point for client useand acceptance.It is intended to provide INA customerswith this interface as an application. Thecustomer creates an encoded BEARINX®

file which he can send to INA by E-mail or FTP. In consultation with the customer,the INA application engineer then

optimizes the design in relation to rollingbearing engineering. Once a definitivespecification has been achieved,documentation of the results is suppliedto the customer. A special feature allowsdata from the BEARINX® calculation to beautomatically fed back into the CADsystem. For example, the spatial positionof the rolling bearings in the gearbox isthus defined, since this contributes toincreasing the operating life.

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Fig. 13 User element for balls and roller

Fig. 14 Exploded view of the FE structure of the industrial gearbox

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4.4 Rolling bearing analysis in anelastic environment with FEM

If the geometrical structure of the bearingsupport in the housing is complex,BEARINX® must either assume that thebearing rings are rigidly supported orread in a reduced stiffness matrix for thebearing location from a finite-elementcalculation carried out previously.Alternatively, however, an analysis of thebearing load distribution directly inte-grated in the FE environment is possiblewhich is an additional set of results givingthe customer the stresses on theadjacent construction of the bearing.

In the FE analysis of rolling bearingarrangements, modelling of the rollingcontact is a central problem. Due to thefine mesh required, modelling withconventional continuum elements quicklyreaches the performance limits of currentcomputing facilities. For this reason, INAhas developed a model for representingthis non-linear mechanical behaviour ofrolling elements in static FE calculationsand has converted this model into a user-defined element for the ABAQUS/Standardsystem [7]. This so-called user elementrecords, as a type of structural element,the non-linear contact stiffness in theHertzian contact zone between the rolling

element and raceway on the basis ofanalytical geometry and elasticity theory.The behaviour of the ball is recorded by a4 node element and that of the roller,discretised into n laminae, is recorded bya 2n node element (Figure 13). In contrastto representation of rolling elements usingconventional continuum elements and thevery fine mesh this requires, the userelement can work with a minimumnumber of degrees of freedom. At thesame time, the precision achieved ishighly satisfactory, as can be shown by a comparison with the results of acontinuum model of a given type of rollingelement.

Outer ring

4 node elementfor ball

Inner ring

Outer ring

2n node elementfor roller

Inner ring

CoverDrive side

LSL bearing

Screwconnection(preloaded)

Lowerhousing half

Intermediateshaft

Dowel and screw connection(preloaded)

LSL bearing

CoverDrive side

Upperhousing half

3

2

1

4

F

a1 n

Fig. 15 Results of FE calculation

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The user need only enter a few geometricdata about the rolling elements in order todefine the characteristics of the userelement. This module therefore givesquicker FE modelling of rolling elementsand will be made available to technicalcalculation personnel integrated into apreprocessor.In the BEARINX® calculation of the two-stage industrial gearbox, one of the twobearings on the intermediate shaftdisplayed the most critical loading orshortest life. The finite-element analysis toinvestigate the influence of the elasticenvironment on the bearing loaddistribution was therefore confined to this shaft.The geometry of the housing of the two-stage industrial gearbox was importedinto the preprocessor from a 3-D CADsystem, using a direct interface, and wasautomatically meshed there using atetrahedral mesh generator (see theexploded view of the FE structure inFigure 14). The bearing rings, shaft andside cover plates were meshed semi-automatically using hexahedral elements,while the screw connections wererepresented by beam elements and therolling elements in the bearings by user-defined elements.Under load, the deformation of thehousing shown in Figure 15 occurs: the walls with the two fixing holes areindented and partly conform to thebending curve of the shaft. The holes,

due to the thick walls of the design,remain to a very large extent in theiroriginal round condition. This is alsoreflected in the distribution of the rollingbearing forces which, in comparison withthe BEARINX® calculation based on rigidbearing rings, remains virtuallyunchanged. The tilting of the bearing, onthe other hand, is partially compensatedby the indentation: in comparison withthe rigid BEARINX® calculation, the mosthighly loaded rolling element displays lesstilting, while the maximum Hertzian stressis slightly (9%) lower. The bearing lifedetermined from the bearing loaddistribution in accordance with the theoryof Ioannides and Harris is 25% greaterthan that from the rigid calculation.The differences between the standardcalculation on the basis of rigid bearingrings and the extended calculation takingaccount of the environmental elasticityare relatively small in this specialapplication of an industrial gearbox with arelatively solid bearing location. This is notgenerally true, however, especially in thecase of automotive applications where,given the lightweight constructions used,local deformations of the bearing location(such as ovality and conicity) play adominant role and substantially moredrastic differences are observed. In suchcases, results of sufficient accuracy areonly possible by using calculation whichtakes account of the elastic environment.The FEM and the BEARINX® calculationprogram, taking account of FE

environmental stiffness are two suchtools which give results of comparableand sufficient accuracy. It is only in caseswhere, due to additional non-linearities,the environmental stiffness is dependenton load (for example where the loadtransmission changes in the tooth area ofa pilot bearing), that only the FEM iscurrently capable of recording theseeffects.With the BEARINX® calculation programdeveloped in-house, the INA consultantengineers have a tool with which they canrepresent on a computer the customer’sdesign based on information from thecustomer and carry out comprehensivecalculations. In addition to this, the in-house development of the user elementfor rollers or balls can be used todetermine extremely accurately thebearing load distribution integrated intothe FE environment for systems havingadditional, significant nonlinearity.Integration into the CA process of thetools presented allows a substantialacceleration of the calculation process.

Exaggerated deformation

Force distribution

FE-analysisBEARINX® rigid

Contact pressure

FE-analysisBEARINX® rigid

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5 OutlookWith the consultation and calculationservice described, the central CAEdepartment is making a valuable contri-bution to reliable design, not only ofrolling bearings but also of the entirecustomer design. This service is availableboth to INA development personnel andto customers. The methods and pro-cedures described represent anadvanced level in calculation practicewhich has been achieved on the basis of the latest CAE technology. While Virtual Product Development is stillsome way off and will undoubtedly stillpresent major challenges, the foundationshave been laid by INA. Modern programssuch as BEARINX® will continue to bedeveloped further, precisely with a viewto the further integration of design andcalculation.

References[1] Löffel, C.; Göss, G.:

Data exchange for concurrent FE analyses of a supplier to theautomotive industry. NAFEMS Seminar: Experiences withFE Analysis Based on CAD Geometry;Wiesbaden, June 1998

[2] Grossmann, T.: Künftige Ausrichtung des CAE-Einsatzes in der PKW-Entwicklung.VDI Berichte 1411; VDI-Verlag GmbH,Düsseldorf 1998, pp. 459-480

[3] Löffel, C.: Einsatz von MSC/CONSTRUCT imEntwicklungsprozess einerAutomobilzulieferfirma. Presented at the German-languageMSC users’ conference, MacNealSchwendler GmbH München,Kloster Andechs, June 1998

[4] Köhler, H. D.: Information systems on CD-ROM for theselection of linear guidance systems.antriebstechnik 36 (1997), No. 4, pp. 84-89

[5] Köhler, H. D.: Calculation of roller bearings – theeasy way. antriebstechnik 36 (1997), No. 8, pp. 33-35

[6] Sarfert, J.: Calculation Service for RollingBearings. antriebstechnik 38 (1999),No. 4, pp. 118-120

[7] Golbach, H.: Integrated Non-linear FE Module forRolling Bearing Analysis. NAFEMSWorld Congress ‘99, USA, April 1999

[8] Harris, T.A.: Rolling Bearing Analysis. John Wiley & Sons, Inc., New York, 1991

[9] Eschmann P., Hasbargen L., Weigand K.: Die Wälzlagerpraxis. Oldenbourg Verlag München, 1978

About the authors:Dr.-Ing. Christoph Löffel works in thecentral CAE department of INA WälzlagerSchaeffler oHG, Herzogenaurach,Germany, heading the area on CAEintegration. Dipl.-Ing. Hermann Golbach works in thecentral CAE department of INA WälzlagerSchaeffler oHG, Herzogenaurach,Germany, specializing in complex, non-linear FE calculation.

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