The controversial coefficient of restitution for impact problems

YAO Wenli1

Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (19) : 43-48.

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (19) : 43-48.

The controversial coefficient of restitution for impact problems

  •  YAO Wenli1
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Abstract

The coefficient of restitution for impact problems is an important and controversial parameter. The controversial problems are as follows: (1) which definition is more suitable among these in common use. (2) Whether the coefficients are only related to material of colliding bodies or not. (3) Whether the coefficients of restitution can be expressed as the function of other variables. (4) Whether another coefficient with stable and constant properties during collision can be found or not. (5) How to use different types of coefficients of restitution. Center on these problems, the review on impact problems is made. The existing problems are analyzed when solving the collision problems by using the coefficient of restitution and the future research direction is discussed.

Key words

coefficient of restitution / oblique collision / multibody / friction / instantaneous impulse method

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YAO Wenli1 . The controversial coefficient of restitution for impact problems[J]. Journal of Vibration and Shock, 2015, 34(19): 43-48

References

[1] Brogliato B. Nonsmooth Mechanics[M]. Springer, 1999.
[2] 董富祥,洪嘉振. 多体系统动力学碰撞问题研究综述[J].力学进展, 2009, 39(3):352-359.
Dong F X, Hong J Z. Review of Impact Problem for Dynamics of Multibody System[J]. Advances in Mechanics, 2009, 39(3): 352-359.
[3] 姚文莉,王育平,边力, . 多刚体系统接触碰撞动力学研究进展[J].力学与实践, 2007, 29(6):9-12.
Yao W L, Wang Y P, Bian L, Zhao Z. Survey for Dynamics on impact and contact of multi-rigid-body systems[J]. Mechanics in engeneering. 2007, 29(6):9-12.
[4] Khulief Y A. Modeling of Impact in Multibody Systems: An overview[J]. Journal of Computational and Nonlinear Dynamics, 2013, 8:1-15.
[5] Boulanger G. Note sur le Choc avec Frottement des Crops non Parfaitment Elastique[J]. Revue Sci. 1939, 77:325-327.
[6] Stronge W J. Rigid body Collisions with Friction[J]. Proceedings of Royal Society of London. 1990, A431:169-181.
[7] Stronge W J. Friction in collisions: Resolution of a paradox[J]. Journal of Applied Physics. 1991, 69(2):610-612.
[8] Stronge W J. Impact Mechanics[M]. Cambridge University Press, 2000.
[9] Ivanov A P. Energetics of a collision with friction[J]. J.Appl. Math. Mech. 1992, 564:527-534.
[10] Wagg D J. A note on coefficient of restitution models including the effects of impact induced vibration[J]. Journal of Sound and Vibration. 2007, 300:1071–1078.
[11] Stronge W J. Smooth dynamics of oblique impact with friction[J]. international journal of impact engineering, 2013, 51: 6-49.
[12] Djerassi S. Collision with friction; Part A: Newton’s hypothesis[J]. Multibody Syst Dyn. 2009, 21:37-54.
[13] Djerassi S. Collision with friction; Part B: Poisson’s and stronge’s hypothesis[J]. Multibody Syst Dyn. 2009, 21:55-70.
[14] Djerassi S. Stronge’s hypothesis-based solution to the planar collision-with friction problem[J]. Multibody Syst Dyn. 2010, 24:493-515.
[15] Stronge W J. Comment:Collision with friction; Part B: Poisson’s and stronge’s hypothesis[J]. Multibody Syst Dyn. 2010, 24:123-127.
[16] 吕茂烈. 碰撞恢复系数及其测定[J]. 固体力学学报. 1984, 3: 318-329.
Lü M L. Coefficients of restitution of their measurement [J]. ACTA Mechanica Solida sinica. 1984, 3:318-329.
[17] 张九铸. 一般运动刚体的恢复系数公式的适用条件[J]. 力学与实践. 2010, 32(3):116-117.
Zhang J Z. The suitable situation of formula of coefficient of restitution for general rigid body of motion[J]. Mechanics in Engineering. 2010, 32(3):116-117. 
[18] Pfeiffer F. Multibody Systems with Unilateral Constraints[J]. J. AppL Maths Mechs. 2001, 65( 4): 665-670
[19] Pfeiffer F, Foerg M, Ulbrich H. Numerical aspects of non-smooth multibody dynamics[J]. Comput. Methods Appl. Mech. Engrg., 2006, 195:6891–6908
[20] Kilmister C W, Reeve J E. Rational Mechanics[M]. Elsevier. NewYork.189, 1966.
[21] Andrés K, Jens L. Rigid and elastic approaches for the modelling of collisions with friction in multibody system[J]. ZAMM. Z.angew.Math.Mech. 1996, 76:243-244
[22] 姚文莉. 含摩擦的多刚体系统动力学问题的研究,北京大学博士学位论文, 2005.
Yao Wen-Li. Dynamical Problems of Multi-Rigid-Body Systems with Friction. [Peking University] Doctorate degree dissertaton, 2005.
[23] Kane T R. A Dynamics Puzzle. Stanford Mech Alumni Club Newsletter, 1984.
[24] Kane T R, Levinson D A. Dynamics: Theory and Applications. McGraw-Hill[M]. New York, 1985.
[25] Seabra M,Nikravesh P. Impact Dynamics of Multibody Systems with Frictional Contact Using Joint Coordinates and Canonical Equations of Motion[J]. Nonlinear Dynamics. 1996, 9: 53-71.
[26] Wang Y, Mason M T. Two–Dimensional Rigid-body Collisions with Friction[J]. ASME Journal of Applied Mechanics. 1992, 59:635-642.
[27] Thornton C. Coefficient of Restitution for Collinear Collision of Eelastic Spheres[J]. ASME J. of Applied Mechanics. 1997, 64: 383—386.
[28] Zhang X, Voc V Q. Modeling the Dependence of the Coefficient of Restitution on the Impact Velocity in Elasto-Plastic Collisions[J]. International Journal of Impact Engineering. 2002, 27: 317-341.
[29] Wu C Y, Li L Y, Thornton C. Rebound Behaviour of Spheres for Plastic Impacts[J]. International Journal of Impact Engineering. 2003, 28: 929-946.
[30] Lu C J, Kuo M C. Coefficients of Restitution Based on a Fractal Surface Model[J]. ASME J. Appl. Mech. 2003, 70:339–345.
[31] Hurmuzlu Y. An energy Based coefficient of restitution for planar impact of slender bars with massive external surfaces[J]. ASME Journal of Applied Mechanics. 1998, 65(4):952-962.
[32] Yao W L, Chen B, Liu C S. Energetic Coefficient of Restitution for Planar Impact in Multi-Rigid- Body Systems with Friction[J]. International Journal of Impact Engineering. 2005, 31:255-265.
[33] Goldsmith W. Impact: The Theory and Physical Behaviour of Colliding Solids[M]. Edward Arnold Ltd. London, 1960.
[34] Zener C, Feshbach. A method of calculating energy losses during impact[J]. J. Appl. Mech. H. 1939, 61:A67–A70.
[35] Lim C T, Stronge W J. Oblique elastic-plastic impact between rough clinders in plane strain[J]. international journal of engineering science. 1999, 37: 97-122.
[36] Schiehlen W, Seifried R. Three approaches for elastodynamic contact in multibody systems[J]. Multibody Syst. Dyn. 2004, 12: 1–16.
[37] Stronge W J. Generalized impulse and momentum applied to multibody impact with friction[J]. Mech Struct Mach. 2001, 29(2):239–60.
[38] Johnson K L. Ccontact Mechanics[M]. Cambridge University Press. Cambridge, 1985.
[39] Lankarani H M,Nikravesh P E. Continuous Contact Force Models for Impact Analysis in Multibody Systems[J]. Nonlinear Dyn., 1994, 5:193–207.
[40] Carbonelli A, Perret-Liaudet J, Rigaud E, and Feki M S. Investigation of Restitution Coefficient and Spring-Damper Models for the Bouncing Ball Problems. Proceedings of the ASME 2011 International Design Engineering Technical Conferences, IDETC/CIE. Washington D C, Paper No. DETC2011-47870, 2011.
[41] Liu C S, Zhao Z, Brogliato B. Frictionless Multiple Impacts in Multibody Systems[J]. Part I. Theoretical Framework. Proc. R. Soc. A: Mathematical, Physical & Eng. Sci. 2008, 464(2100): 3193–3211.
[42] Liu C S, Zhang, K , Yang L. Normal Force-Displacement Relationship of Spherical Joints With Clearances[J]. ASME J. Comput. Nonlinear Dyn. 2006, 1: 161–167.
[43] Liu C S. Zhao Z, Brogliato B. Frictionless Multiple Impacts in Multibody Systems[J]. Part II. Numerical Algorithm and Simulation Results. Proc. R.Soc. London. 2009, 465(2101):1–23
[44] 赵振,刘才山,陈滨. 步进冲量法[J].北京大学学报自然科学版. 2006, 42(1):41-46
ZHAO Z, LIU C S, CHEN B. Stepping-Forward Impulse Method. Acta Scientiarum Naturalium Universitatis Pekinensis. 2006, 42(1):41-46.
[45] Stammers C W, Ghazavi M. A Theoretical and Experimental Study of the Dynamics of a Four-Bar Chain With Bearing Clearance: Pin Motion, Contact Loss and Impact,” [J]. J. Sound Vib. 1991, 150(2): 301–315.
[46] Herbert R G., Mcwhannel D C. Shape and Frequency of Pulses From an Impact Pair [J]. ASME J Eng Ind. 1997, 99: 513–518.
[47] Schiehlen W, Seifried R, Eberhard P. Elastoplastic phenomena in multibody impact dynamics[J]. Comput. Methods Appl. Mech. Engrg. 2006, 195: 6874–6890.
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