Albers, A.

Deigendesch, T.

Enkler, H.-G.

Hauser, S.

Leslaby, P.

Oerding, J.

English

Albers, Albert

Deigendesch, Tobias

Enkler, Hans-Georg

Hauser, Stefan

Leslabay, Pablo

Oerding, Jochen

Hochschulschriftenserver der Hochschule Furtwangen

An integrated approach for validating micro mechanical systems based on simulation and test

Albert Albers

Tobias Deigendesch

Hans-Georg Enkler

Stefan Hauser

Pablo Leslabay

Jochen Oerding

Crossref

KITopen

TECHNICAL PAPERAn integrated approach for validating micro mechanical systemsbased on simulation and testAlbert Albers Æ Tobias Deigendesch ÆHans-Georg Enkler Æ Stefan Hauser ÆPablo Leslabay Æ Jochen OerdingReceived: 26 October 2007 / Accepted: 19 March 2008 / Published online: 14 May 2008 Springer-Verlag 2008Abstract Miniaturization of macroscopic mechanicalsystems enables the opening of new areas of application formicro technological systems. Because of technologicalrestrictions, especially when applying miniaturized con-ventional manufacturing techniques, shape and materialdeviations cannot be scaled down in the same dimensionlike micro parts. Thus, the long-term objective is to ensurethe functioning by appropriate design measures. In doingso, determination of the transfer behavior by modeling andsimulation is required. This work presents two ways forensuring the required properties of micro gears anddescribes how the results do correlate. The experimentalway uses the radial composite inspection as it is used in themacroscopic world. The simulative way deploys a rollingsimulation by utilization of finite element analysis. Thevirtual prototypes are originated on measured real testgears. When comparing experiment and simulation of therolling behavior, in some short and long wave areasdeviations can be recognized. These can be ascribed to thereduction from three to two dimensions when modeling.Other deviations might be based on inaccuracies whenmounting into the test rig. In other areas quite good cor-relations of test and simulation could be ascertained.1 Introduction and motivationIncreasing miniaturization of mechanical systems impli-cates new challenges for the development, production andquality assurance. Due to technological restrictions, espe-cially when apply miniaturized manufacturing techniquesfrom the macro world shape and material deviations cannotbe scaled down in the same way.Respecting the influence of such deviations during thevery early stages the product development process is ofmaximum importance (Marz 2005). For supporting thedesign process, new methods are required that enable thedesigner to model the later system behavior reliably.The present work demonstrates two ways for ensuringthe desired properties of micro gears and describes how theresults correlate (cp. Fig. 1). As an experimental methodthe radial composite inspection is depicted, which is anaccepted test for macro gears. The simulative method is arolling simulation applying the finite element analysis. Thevirtual test gears are modelled on the basis of measured realgears and not on the nominal shape. The long termobjective for an early assurance of system properties is todestermine the transfer behaviour and to derive adequatedesign measures. In doing so function fulfilment and thus arobust design can be provided.The fundament for the determination of the validity ofthe model is a comparison with test of real micro gears.A. Albers (&)  T. Deigendesch  H.-G. Enkler  S. Hauser P. Leslabay  J. OerdingIPEK–Institute of Product Development, Universität Karlsruhe(TH), Kaiserstraße 10, 76131 Karlsruhe, Germanye-mail: albers@ipek.uni-karlsruhe.deT. Deigendesche-mail: deigendesch@ipek.uni-karlsruhe.deH.-G. Enklere-mail: enkler@ipek.uni-karlsruhe.deS. Hausere-mail: hauser@ipek.uni-karlsruhe.deP. Leslabaye-mail: leslabay@ipek.uni-karlsruhe.deJ. Oerdinge-mail: oerding@ipek.uni-karlsruhe.de123Microsyst Technol (2008) 14:1781–1787DOI 10.1007/s00542-008-0615-2First published in:EVA-STAR (Elektronisches Volltextarchiv – Scientific Articles Repository) http://digbib.ubka.uni-karlsruhe.de/volltexte/1000011696 Only in case of validity, the virtual model can be extrap-olated to such designs that are impossible to test. Becauseof reaching the cutting edge of connection, joining and testtechnology for micro parts, measurement range and mea-surement deviation might be in the same dimension. Thus,a valid forecast of properties is a necessity for furtherproduct miniaturization.For revision of this approach first tests were made withoff-the-shelf plastic gears (module 1 mm). The actualspecimens a high stressable ceramic micro gears (cp.Fig. 2) made of zirconium oxide with a module of 169 lmand a tooth width of 156 lm. which were developed,produced and measured within the Collaborative ResearchCenter (CRC) 499 of the German Research Foundation.Fig. 1 schematically depicts the approach.2 Measurement and modelingFor simulation of the test an appropriate model has to be setup. First of all, the geometry of the particular componenthas to be created virtually.In order to establish a basis for this modeling, thegeometries of the gearwheels have been comprised bymeans of a tactile coordinate measuring machine (cp.Fig. 3) and special measuring software (Zeiss 2007;Mitutoyo 2007). Though, application of commercial sys-tems offers the advantage of being proven, tested andcertified.In principal, it is possible to generate a three dimen-sional model of the individual components. However, asimulation on the basis of three dimensional modelsincreases computational effort considerably. In addition,components have to be measured in multiple layers. Forthis reason, a two dimensional approach was chosen forthis work, i.e. all components have been reduced to twodimensions. Validity of this simplification has to bechecked in the following.To set up a model, measuring points of the profile in themidplane of the gearwheel were regarded.Since not all measuring points lie exactly within oneplane, they are projected onto one common plane initially.Afterwards the projected points are connected by means ofa spline (Schoenberg 1969) that replicates the outline of thecomponent. Simulation is based on the finite elementmethod (FEM), i.e. the geometric model has to be dis-cretized. Hence, the real component is being simulated by aFig. 1 ApproachFig. 2 CRC-gearwheels in micro test rigFig. 3 Gearwheel measuring via tactile coordinate measuringmachine1782 Microsyst Technol (2008) 14:1781–1787123finite number of data points as usual in measuring. Mea-suring points can be used directly to generate a finiteelement (FE) mesh. Thereto, measuring points should beequidistant, especially at the tooth flanks so that an ade-quate mesh for the subsequent analysis can be generated.For this work, the former approach was used, i.e. the meshis based on a spline.For generating virtual geometries an automated processhas been set up generating a geometry that is prepared forthe FE Preprocessor and based on the measuring points.The number of measuring points that are taken for geom-etry creation can be influenced by means of a reductionfactor if desired. The number of points that are taken intoaccount is geared to the element size of the subsequentlygenerated FE mesh.To analyze deviations of the real is-profile from thedesired profile and to investigate the influence of thesedeviations on the system via the subsequently obtainedsimulation results and tests, a curvature analysis of theindividual flanks can be used, for instance. Figure 4 showsthe curvature, i.e. the turnaround per unit length, exempl-arily for a measured and the desired tooth geometry (up tothe base circle). In general, further options such as tippingangle of the individual teeth are cogitable.3 Radial composite inspectionThe radial composite inspection is a test used in macroworld for quality assurance of gearwheels (VDI 2001) inwhich a pair of gearwheels is being revolved free fromclearance. This is achieved by a radial pre-load of thegearwheels in such a way as to constitute an engagementboth on the left and the right flank (Fig. 5). Driving one ofthe gearwheels, the second one that is locomotive linearlydodges due to geometry deviations. Quality of gearwheelscan then be evaluated and compared on the basis of thehighest radial deviation difference.In general, master gearwheels [NaFuO 1972a, b] thathave to be at least two quality levels better than the testedgearwheels (NAN 1987) are used for such an evaluation. Inthis way, measured deviations can be related to the testgearwheel. But regarding molded micro mechanical sys-tems such master gearwheels with higher quality levelwould have to be manufactured with an unjustifiableadditional effort. In addition, currently there is a lack ofaccordant norms inclusive a definition of an applicabledefinition of the quality term.For this work no master gearwheels but two test gear-wheels have been coupled. The measured deviations inaxis-center distances therefore cannot be related to onesingle gearwheel but the system of both. However, bysystematic measurements of multiple gear tooth pairings ofone and the same gearwheel pair, distinctive deviations inthe characteristics can be investigated and related to singlegearwheels (Albers et al. 2007a).Tests have been conducted by using the micro test rigthat has been developed within the Institute of ProductDevelopment Karlsruhe.4 SimulationThe validation of the simulation results against the microtest rig has been performed through the radial compositeFig. 4 Comparison of the curvature of a real tooth flank and thedesired flank profile (up to base circle) Fig. 5 Radial composite inspectionMicrosyst Technol (2008) 14:1781–1787 1783123inspection, as mentioned in the previous section. The runshave been simulated with slow rotational speed, so to keepthe inertial forces as low as possible. From a numericalpoint of view, it is then possible to consider the test as asequence of static load cases (Albers et al. 2007b). Thepressing force acting on the flanks has been kept as low aspossible, in order to avoid deformation on the profile of theteeth.For this simulation, both a multi body simulation (MBS)with rigid bodies or an FE-Simulation are well suited. Onthe current work, and due to the ‘‘static’’ nature of theproblem, the way over an FE-Simulation with the FEASolver Abaqus has been chosen. The inertial effects arethen taken out of consideration. It is also possible to dividethe task on many parallel jobs within Abaqus, what reducesthe wall-time needed for processing.Because the model’s complexity required in simulatinga radial composite inspection is not previously known, andin hand of the geometrical data available, it has beendecided to start with a simple model and run the simula-tions on a 2D basis. This makes also easier to model thejoints of the system. On the computer modeling, the outputgear remains fixed on a point and is free to rotate, con-nected to ground through a revolute joint. The input gearrotates with constant velocity, and is free to move on oneradial direction. The pre-load or pressing force acts at theaxis of this gear. Output measures of interest are therotation angle on both gears and the linear displacement ofthe input gear.A very fine FE-mesh on the contour of the gears allows adetailed representation of the measured, irregular profile ofthe teeth. Load paths and stress distribution are not ofinterest in this work, so the mesh on the inner parts of thegears is kept relatively coarse, in order to reduce the totalamount of elements in the model. It could be also of benefitto consider both gears as rigid bodies, but the contactsolver of choose is not capable to solve this particularproblem with two rigid surfaces. Thus, only one gear andthe spoke of the second one are considered rigid, while theteeth of the second gear are modeled with standard linear-elastic material properties.In order to assure the comparability of simulation andtest results, the gears were coupled with the same orien-tation and tooth pairs, and then rotated one completerevolution. The center distance variations were measured,where zero means nominal center distance, and positivevariation means longer distances.Different tooth combinations on the gears were simu-lated and tested. Additionally, a series of simulations wereconducted on selected tooth pairs, to gain an insight on thequality of the simulation process developed. Each of thisseries consisted on rotating the gears on both directions forone revolution, and extra runs with higher pressing forces.The analysis of the simulation results for these parametersshowed an exact concordance between the runs in thedifferent directions, and pretty good agreement for the runswith altered pre-loads, as shown in Fig. 6. As expected, thecenter distance is slightly smaller for the cases with higherpressing forces.As shown in Table 1, the number of increments neededby the solver to perform a 360 rotation kept very stable forall the simulation cases. This can be used as an indicationfor the quality of the simulation process adopted as well asa sign that no extra difficult positions were encounteredduring the rotations.The also very stable amount of required iterations showsthat the convergence ratio of the model is not remarkablyaffected by the different teeth combinations.The processes to measuring, modeling and simulatingexplained on the lines above were conducted both on thealready described module 1 plastic gears, and on theceramic gears of the CRC.The smaller size of the CRC gears adds no additionaleffort to the simulation process, which behaves very stablein this case too. But the relative to their size bigger toler-ances of the micro gears introduced new geometrical issuesto the model. Cases have been found, where the contactbetween gears occurs on the outer sides of the teeth and noton the inner ones as expected, as shown in Fig. 7.Fig. 6 Simulation series for the Module 1 mm gearsTable 1 Statistics for all the simulation seriesIncrements IterationsMean SD Mean SDModule 1.0 mm 3220.0 27.726 10012.3 120.821Module 0.169 mm 3164.5 5.292 9549.4 36.8001784 Microsyst Technol (2008) 14:1781–1787123It is also possible, as depicted in Fig. 8, that the contactpoint lies wide under the base circle, in the middle of thefillet.5 Validation of simulation and testBased on the simulation results and the testing data, acomparison of the results for the center distance variationhas been performed. For the plastic gears, this comparisonshows good correlation between the simulated curves andthe measured ones on the long wave domain. But for themuch more interesting short wave domain, were the effectsof the profile deviations are controlling, satisfyingcorrelation could not be found. The compensation of theprofile deviations along the faces of the teeth is believed tobe one cause for this behavior. Due to the planar nature ofthe model, the contour variation along the width of the gearis not taken in account.For the ceramic micro gears, significant deviations onboth long wave and short wave domains have been foundbetween the curves. See Fig. 9. For some sections of thecurves, a good correlation even on the short wave domaincould be found, as shown in Fig. 10. The causes for thesignificant long wave deviations are believed to lie ondifficulties appeared on the gear mounting on the test rig.These induce then axes eccentricities and concentricityerrors, which were not simulated.Fig. 7 Undesirable engagementon the outer flanks due to profiledeviationFig. 8 Undesirable contact onthe fillet zone due to profiledeviationMicrosyst Technol (2008) 14:1781–1787 1785123This effect couldn’t be detected earlier because of therelative big size of the plastic gears when compared to themagnitude of the mounting errors.As in the tests with the plastic gears, the non completecorrelation on the short wave domain could be related tothe incomplete representation of the gear’s geometry due tothe two dimensional approximation.6 ConclusionThe comparison of simulation and test of gear rollingindicates deviations within short and long wave domains.These can be ascribed to the reduction of the model fromthree to two dimensions. Deviations might also derive frominaccuracies when mounting micro gears. Further on, goodcorrelation of test and simulation was demonstrated insome areas.Because the two dimensional model appeared not beinggood enough to replicate the real gearing behavior, thefollowing steps are aimed at modeling virtual gear wheelsby superposition of several layers of contour measurementstaken at different heights of the flank profile. Anotheralternative is to virtually engage a set of three-dimen-sionally modeled gear wheels, which will result in a muchbigger computing effort.The determined deviations excessing those of the gear-ing concerning eccentricity and runout have to be inspectedby further examinations of the specimen connection, of theshaft mounting and of the shaft manufacturing. In thiscontext the integration of such deviations into a simulativevalidation method has to be considered.The integrative approach of validation of microme-chanical systems in a simulative and experimental way is afirst step towards the objective of a very early propertyassurance that enables a robust design. Based on thisapproach, also those influences that cannot be testedexperimentally should be estimated through simulation infuture. This could help to ensure the function fulfillment ofmicromechanical products.Acknowledgments The authors would like to thank the GermanResearch Foundation for supporting this work within the Collabora-tive Research Center ‘‘Development, Production and QualityAssurance of primary-shaped Micro Parts made of Metallic andCeramic Materials’’ as well as all colleagues for providing specimensand measurement data.ReferencesAlbers A, Burkardt N, Deigendesch T, Ellmer C, Hauser S (2007a)Validation of micromechanical systems, Int. Workshop on high-aspect-ratio micro-structure technology HARMST, Besancon,France, 7–9 June 2007Albers A, Enkler H-G, Leslabay P, (2007b) On the simulation ofmolded micro components and systems, Int. Workshop on high-aspect-ratio micro-structure technology HARMST, Besancon,France, 7–9 June 2007Marz J (2005) Mikrospezifischer produktentwicklungsprozess (lPEP)für werkzeuggebundene Mikrotechniken. Dissertation, IPEKForschungsberichte Bd. 17, 2005Mitutoyo Messgeräte GmbH (2007) Neuss, Germany. http://www.mitutoyo.de. Accessed 31 July 2007Normenausschuss Feinmechanik und Optik (NaFuO) (1972a) Im DINDeutsches Institut für Normung e.V. IN 58405: Stirnradgetriebeder Feinwerktechnik. Beuth Verlag, BerlinNormenausschuss Feinmechanik und Optik (NaFuO) (1972b) Im DINDeutsches Institut für Normung e.V. DIN 58420: Lehrzahnräderzum Prüfen von Stirnrädern der Feinwerktechnik. Beuth Verlag,BerlinNormenausschuss Antriebstechnik (NAN) (1987) Im DIN DeutschesInstitut für Normung e.V. DIN 3960: Begriffe und Besti-mmungsgrößen für Stirnräder (Zylinderräder) und StirnradpaareFig. 9 Comparison between simulation and test for two micro gearsbased on a radial composite inspectionFig. 10 Section with good correlation between simulated andmeasured results1786 Microsyst Technol (2008) 14:1781–1787123(Zylinderradpaare) mit Evolventenverzahnung. Beuth Verlag,BerlinSchoenberg IJ (1969) Approximations with special emphasis onspline functions, proceedings of a symposium conducted by themathematics research center, United States Army, Madison, 5–7May 1969VDI (2001) VDI/VDE-Gesellschaft Mess- und Automatisierungs-technik (GMA) VDI/VDE 2608: Einflanken- und Zweiflanken-Wälzprüfung an Zylinderrädern. Kegelrädern, Schnecken undSchneckenrädern/Tangential composite and radial compositeinspection of cylindrical gears, bevel gears, worms and wormwheels. Beuth Verlag, BerlinCarl Zeiss AG (2007) Oberkochen, Germany. http://www.zeiss.de.Accessed 31 July 2007Microsyst Technol (2008) 14:1781–1787 1787123

An integrated Approach for Validating Micro Mechanical Systems based on Simulation and Test

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An integrated Approach for Validating Micro Mechanical Systems based on Simulation and Test

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