The h -,p -,and r -refinements of Finite Element Analysis of Flexible Slider Crank Mechanism

Abstract

Three common refinement methods of achieving more accurate finite element solutions are to increase the number of elements, to employ higher-degree interpolation functions, and to implement an adaptive mesh by moving the nodes but maintaining the same number of elements as well as the degree of interpolation functions. This paper presents a finite element analysis by applying these refinements to a flexible slider crank mechanism. The formulation is based on the Euler—Lagrange equation, for which the Lagrangian includes the components related to the kinetic energy, the strain energy, and the work done by axial loads in a link that undergoes elastic transverse deflection. A beam element is modeled based on a translating and rotating motion. An error analysis is demonstrated by defining several error indicators, which are based on energy of an entire mechanism, transverse displacement, and bending strain of midpoints on crank and coupler. This paper also demonstrates the effect of the stiffness of the crank.

Keywords

Slider crank mechanism finite element method kineto-elasto-dynamics h-p-r-refinement

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References

Bathe, K.J. , 1996, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ , USA.

Chen, J.S. and Huang, C.L. , 2001, “ Dynamic analysis of flexible slider-crank mechanisms with nonlinear finite element method ,” Journal of Sound and Vibration 246(3), 389—402 .

Chen, J.S. and Chian, C.H. , 2003, “ On the nonlinear response of a flexible connecting rod ,” Journal of Mechanical Design 125, 757—763 .

Cleghorn, W.L. , 1980, Analysis and design of high-speed flexible mechanism. PhD Thesis, University of Toronto .

Cleghorn, W.L. , Fenton, R.G. , and Tabarrok, B. , 1981, “ Finite element analysis of high-speed flexible mechanisms,” Mechanism and Machine Theory 16(4), 407—424 .

Cleghorn, W.L. , Fenton, R.G. , and Tabarrok, B. , 1984, “ Steady-state vibrational response of high-speed flexible mechanisms,” Mechanism and Machine Theory 19(4/5), 417—423 .

Erdman, A.G. and Sandor, G.N. , 1972, “ Kineto-elastic dynamics — a review of state of art and trends,” Mechanism and Machine Theory 7, 19—33 .

Fallahi, B. , 1997, “ An enhanced computational scheme for the analysis of elastic mechanisms ,” Computers and Structures 62(2), 369—372 .

Giovagnoni, M. , 1993, “ Linear decoupled models for a slewing beam undergoing large rotations ,” Journal of Sound and Vibration 164(3), 485—501 .

10.

Grosse, I.R. , Katragadda, P. , and Benoit, J. , 1992, “ An adaptive accuracy-based a posteriori estimator ,” Finite Elements in Analysis and Design , 12, 75—90 .

11.

Jonker, B. , 1989, “ A finite element dynamic analysis of spatial mechanisms with flexible links ,” Computer Methods in Applied Mechanics and Engineering 76, 17—40 .

12.

Kuo, Y.L. , 2005, Applications of the h-, p- and r-refinements of the finite element method on elasto-dynamic problems. PhD thesis, University of Toronto .

13.

Kuo, Y.L. , Cleghorn, W.L. , Behdinan, K. , and Fenton, R.G. , 2006, “ The h-p-r-refinement finite element analysis of a planar high-speed four-bar mechanism,” Mechanism and Machine Theory 41(5), 505—524 .

14.

Kuo, Y.L. , Cleghorn, W.L. , and Behdinan, K. , 2005, “ The r-refinement finite element analysis of flexible four-bar linkage ,` ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference , Long Beach, CA, USA.

15.

Lowen, G.G. and Jandrastts, W.G. ., 1972, “ Survey of investigation into the dynamic behavior of mechanism containing links with distributed mass and elasticity,” Mechanism and Machine Theory 7, 3—17 .

16.

Meirovitch, L. , 1967, Analytical Methods in Vibrations, Macmillan, New York , pp.436—463.

17.

Ozturan, C. , deCougny, H.L. , Shephard, M.S. , and Flaherty, J.E. , 1994, “ Parallel adaptive mesh refinement and redistribution on distributed memory computers ,” Computer Methods in Applied Mechanics and Engineering 119, 123—137 .

18.

Schwab, A.L. and Meijaard, J.P. , 2002, “ Small vibrations superimposed on prescribed rigid body motion,” Multibody System Dynamics, 8, 29—49 .

19.

Song, J.O. and Haug, E.J. , 1980, “ Dynamic analysis of planar flexible mechanisms ,” Computer Methods in Applied Mechanics and Engineering 24, 359—381 .

20.

Sriram, B.R. and Mruthyunjaya, T.S. , 1995, Synthesis of path generating flexible-link mechanisms ,” Computers and Structures 56(4), 657—666 .

21.

Sunada, W. and Dubowsky, S. , 1981, “ The application of finite element methods to the dynamic analysis of flexible spatial and co-planar linkage systems ,” Journal of Mechanical Design 103, 643—651 .

22.

Thompson, B.S. and Sung, C.H. , 1986, “ A survey of finite element techniques for mechanism design,” Mechanism and Machine Theory 21, 351—359 .

23.

Trevisani, A. , 2003, “ Feedback control of flexible four-bar linkages: a numerical and experimental investigation ,” Journal of Sound and Vibration 268, 947—970 .

24.

Wang, Y.M. , 1999, “ The stability analysis of a slider-crank mechanism due to the existence of two-component parametric resonance ,” International Journal of Solids and Structures 36, 4225—4250 .

25.

Wasfy, T.M. and Noor, A.K. , 2003, “ Computational strategies for flexible multibody systems ,” Applied Mechanics Reviews 56(6), 553—632 .

26.

Yang, K.H. and Park, Y.S. , 1996, “ Dynamic stability analysis of a closed-loop flexible link mechanism,” Mechanism and Machine Theory 31(5), 545—560 .

27.

Yang, Z. and Sadler, J.P. , 1990, “ Large-displacement finite element analysis of flexible linkages ”, Journal of Mechanical Design 112, 175—182 .

28.

Zhu, J.Z. and Zienkiewicz, O.C. , 1997, “ A posteriori error estimation and three-dimensional automatic mesh generation ,” Finite Elements in Analysis and Design 25, 167—184 .