Advanced Techniques for Predicting Mechanical Product Design via COMSOL Multiphysics

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1 Advanced Techniqes for Predicting Mechanical Prodct Design via COMSOL Mltiphsics Shobing Zhang 1 1 CAEaid, Inc. *Corresponding athor: 184 Jeffs Ln, Astin, TX 78717, shobing.hang@caeaid.com Abstract: Mechanical prodct design is crcial in man engineering field and lots of indstries. To redce the cost and shorten the design life ccle, CAE simlation has been widel applied for predicting virtal prodct design. Becase of complicated geometr, material/geometrical nonlinearit and complex conditions, it is painfl to efficientl and accratel simlate and predict challenging mechanical prodct designs, especiall for those having joint connections or contact interactions. Both joint connections and contact interactions reslt in severe nonlinearit and stress concentration in local areas, so it is prohibitive to predict prodct designs with these two featres via CAE simlation. COMSOL is known for its powerfl Model Bilder and complete simlation capabilities. In this paper, COMSOL Mltiphsics is applied to predict tpical mechanical prodct designs, where rigid connectors represent joint connections and penalt method exectes contact interactions. Kewords: Prodct Design, Joint, Rigid connector, Contact, Penalt Method 1. Introdction Mechanical prodct design appears in man engineering field and lots of indstries, sch as atomotive components, mechanism design, compter hardware, semicondctor devices, and offshore strctres. CAE simlation has been widel applied for predicting and simlating virtal prodct designs to help redce the cost and shorten the design life ccle. However, it is still painfl to efficientl and accratel simlate and predict challenging mechanical prodct designs becase of complicated geometr, material/geometrical nonlinearit and complex conditions, especiall for those having joint connections [1] or contact interactions [2, 3]. Both joint connections and contact interactions reslt in severe nonlinearit and stress concentration in local areas, so it is prohibitive to predict prodct designs with these two featres via CAE simlation. In this paper, the featre of rigid connector in COMSOL Mltiphsics is presented to represent joint connections and simplif corresponding simlation. Contact exected b penalt method is also discssed and investigated. Two tpical mechanical design models are simlated and discssed for the prpose of verification. 2. Joint Represented b Rigid Connector Joints have tmost importance commonl in virtal mechanical prodcts. However, prodct designers sall pa more attention to prediction and evalation of whole mechanical design rather than the small geometrical featres sch as joints. Moreover, in the prediction and simlation process, joints generate tons of elements which significantl increase the comptation time and memor allocation. COMSOL provides a powerfl featre rigid connector, which is a special kinematic constraint that works like attaching all connected bondaries b a common rigid bod. One rigid connector can be attached to one or several bondaries. To represent the real mechanism of a joint connection in virtal design, it is necessar to well set p the rigid connector, inclding coordinate sstem, center of rotation, prescribed displacement at center of rotation (,, ), and prescribed rotation (Ωx, Ω, Ω). 3. Contact Exected b Penalt Method In COMSOL Mltiphsics, there are two contact algorithms available: the agmented Lagrangian method and the penalt method. The penalt method has an advantage of no increase in degrees of freedom of global sstem [4, ]. Moreover, it can be easil implemented into existing software. It is also known that the performance of the penalt method depends on the penalt parameter, as shown in Table of Appendix. A large penalt parameter reslts in slow convergence, while a small penalt parameter ma redce the accrac. In

2 COMSOL Mltiphsics, the penalt method sall shows better convergence, and the defalt contact pressre penalt factor sall works qite well. Figre 1.a shows that the distance (DS) of a slave node on the destination bondar is calclated between the slave node and its mapping on the sorce bondar. DS is sed to check contact stats. In COMSOL Mltiphsics, there are two contact srface offsets: one is the contact srface offset from geometric destination srface (D o,d ), and the other is the contact srface offset from geometric sorce srface (D o,s ), Note that these two offsets are also sed in contact checking and contact pressre calclation, as show in Figre 1.b, based on contact pressre penalt factor (CPS). Note that if DS is larger than the sm of D o,d and D o,s, the contact pressre is ero. Figre 1. Contact exected b penalt method: definition of contact distance and contact srface offsets, Calclation of contact pressre. If there is bad convergence, the contact pressre penalt factor can be redced, while if there is a big penetration, the contact pressre penalt factor can be enlarged. There is another trick that a small vale of contact srface offset can be sed to redce the penetration withot the increase of the contact pressre penalt factor. 4. Nmerical Examples This section presents two nmerical examples to demonstrate the ke discssed methods and technologies. 4.1 Piston The CAD model of the piston is imported into COMSOL. Steel AISI 434 is applied to the model from Bilt in material librar of COMSOL. The basic material properties are shown in Table 2 of Appendix. The bondar conditions inclde a rotation of 6.28 rot and a pressre of 1 Pa, as shown in Figre 3. Figre 4 shows rigid connectors (RC1~RC) are defined to represent joint connections in the piston model, where global coordinate sstem is applied. The prescribed displacements (,, ) at center of rotation and prescribed/constrained rotation (Ωx, Ω, Ω) for each rigid connector are set p: RC1: RC2: RC3: RC4: RC: x 6.28rad, 2 3 2,, ,, 4 4,

3 Figre 3. The schematic of piston: YZ view; XY view. (c) Figre 4. Defined rigid connectors (YZ view). Considering the clindrical srface shape of joint holes, Mapped node and Distribtion node in COMSOL are first sed to generate rectanglar srface mesh, and then rectanglar srface mesh is converted into trianglar srface mesh b se of Convert node. Once the special options are applied, Free tetrahedral is selected with the meshing properties in Table 4 of the Appendix. The meshed piston is meshed with tetrahedral elements as shown b Figre 6. (d) Figre 7. Simlation reslts of piston at the rotation of: rad; 1.7 rad; (c) 3.14 rad; (d) 4.71 rad. Figre 7 shows the simlated reslts of the states at the rotation with a vale of, 1.7, 3.24, and 4.71 rad. B se of rigid connector, the joint connections can be appropriatel represented, and the mechanism of the piston model can be predicted and simlated. 4.2 Steel Beam nder Contact Figre. Meshed joint srface: Mapped mesh; Convert mesh. Figre 6. Meshed piston. Figre 8. The schematic of steel beam nder contact.

4 The CAD model of the steel beam is imported into COMSOL. Three clinders are bilt sing COMSOL Model Bilder. Strctral steel is applied to steel beam and three clinders from Bilt in librar of COMSOL. The basic material properties are shown in Table 4 of the Appendix. Two srfaces on both sides of the bottom are wholl fixed on X-, Y- and Z- translations. The three clinders move downward to be in contact with the steel beam. The contact pair defined appears in Figre 1, where the sorce bondar is selected from the steel beam and the destination bondaries are selected from the three clinders. Here, the contact pressre penalt factor and contact srface offsets are sing the defalt vales. Considering the reglarit and smmetr of contact srfaces, Mapped node is sed to generate rectanglar mesh, which is transformed to trianglar mesh b Convert node. After that, Free tetrahedral is selected to generate mesh for the whole model, shown in Figre 12. Figre 13 shows the simlated reslts of Von Mises stress. Except for the contact areas, the high stress distribtion in the steel beam is the interesting point to the mechanical designer. Using penalt method, COMSOL Mltiphsics can well predict virtal strctres with contact. Figre 11. Meshed contact srfaces. Figre 12. Meshed clinders and steel beam. Figre 13. Von Mises stress distribtion.. Conclsions Figre 9. Fixed srfaces for steel beam. Figre 1. Definition of contact pair between clinders and steel beam. This paper presents the se of COMSOL Mltiphsics that sccessfll predicts and simlates two tpical mechanical designs. B se of rigid connector nodes to represent joint connections, the severe nonlinearit, contact interaction and stress concentration in local joint connection areas of the piston model can be neglected, which greatl redces the total DOF and then enhances the performance of modeling, meshing and simlation. Contact definition can be easil set p via COMSOL Mltiphsics. B se of penalt method, steel beam nder contact is sccessfll simlated with good convergence.

5 6. References 1. L. Molnár, K. Váradi, etc., Stress Analsis of Bolted Joints Part II. Contact and Slip Analsis of a For Bolt Joint, Modern Mechanical Engineering, 4, 46- (214) 2. O. C. Zienkiewic and A. Francavilla, A Note on Nmerical Comptation of Elastic Contact Problems, International Jornal for Nmerical Methods in Engineering, 9, (197) 3. P. Wriggers, Comptational Contact Mechanics, West Sssex: John Wile & Sons (22) 4. S. Zhang, Advanced Techniqes and Painless Procedres for Nonlinear Contact Analsis and Forming Simlation via Implicit FEM, AIP Conference Proceedings, 132, (213). K. W. Man, "Contact mechanics sing bondar elements", ed. C. A. Brebbia and J. J. Conner, UK: Comptational Mechanics Pblications (1994) 7. Acknowledgements The athor wold like to thank David Kan at COMSOL, Inc. for valable technical spport and discssions. 8. Appendix Table 1: Inflence of contact pressre penalt factor on convergence and Accrac Yong s Modls 2 GPa Poisson s Ration.33 _ Table 3: Meshing properties for piston model Meshing Propert Vale Unit Predefined Element Sie Maximm Element Sie Minimm Element Sie Extra fine _.29 m 8.94E-4 Maximm 1.3 _ Element Growth Rate Crvatre Factor.3 _ Resoltions of Narrow Regions m.8 _ Table 4: Material properties of Strctral Steel Material Propert Vale Unit Densit 78 kg/m 3 Contact Pressre Penalt Factor Convergence Accrac Yong s Modls 2 GPa Poisson s Ration.33 _ Table 2: Material properties of Steel AISI 434 Material Propert Vale Unit Densit 78 kg/m 3