Research Papers

On Planar Impacts of Cylinders and Balls

[+] Author and Article Information
Khalid Alluhydan

Department of Mechanical Engineering,
Southern Methodist University,
Dallas, TX 75205
e-mail: kalluhydan@smu.edu

Pouria Razzaghi

Department of Mechanical Engineering,
Southern Methodist University,
Dallas, TX 75205
e-mail: prazzaghi@smu.edu

Yildirim Hurmuzlu

Fellow ASME
Department of Mechanical Engineering,
Southern Methodist University,
Dallas, TX 75205
e-mail: hurmuzlu@lyle.smu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received January 24, 2019; final manuscript received March 9, 2019; published online April 19, 2019. Assoc. Editor: Ahmet S. Yigit.

J. Appl. Mech 86(7), 071009 (Apr 19, 2019) (8 pages) Paper No: JAM-19-1040; doi: 10.1115/1.4043143 History: Received January 24, 2019; Accepted March 09, 2019

In this paper, we studied planar collisions of balls and cylinders with an emphasis on the coefficient of restitution (COR). We conducted a set of experiments using three types of materials: steel, wood, and rubber. Then, we estimated the kinematic COR for all collision pairs. We discovered unusual variations among the ball–ball (B–B) and ball–cylinder (B–C) CORs. We proposed a discretization method to investigate the cause of the variations in the COR. Three types of local contact models were used for the simulation: rigid body, bimodal linear, and bimodal Hertz models.

Based on simulation results, we discovered that the bimodal Hertz model produced collision outcomes that had the greatest agreement with the experimental results. In addition, our simulations showed that softer materials need to be segmented more than harder ones. Softer materials are materials with smaller collision stiffness values than harder ones. Moreover, we obtained a relationship between the collision stiffness ratio and the number of segments of softer materials to produce physically accurate simulations of B–C CORs. We validated this relationship and the proposed method by conducting two additional sets of experiments.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Brach, R. M., 1991, Mechanical Impact Dynamics: Rigid Body Collisions, Wiley, New York.
Werner, G., 2001, Impact: The Theory and Physical Behaviour of Colliding Solids, Dover Publication, Mineola.
Hurmuzlu, Y., 1993, “Dynamics of Bipedal Gait: Part I Objective Functions and the Contact Event of a Planar Five-Link Biped,” ASME J. Appl. Mech., 60(2), pp. 331–336. [CrossRef]
Hurmuzlu, Y., 1993, “Dynamics of Bipedal Gait: Part Ii Stability Analysis of a Planar Five-Link Biped,” ASME J. Appl. Mech., 60(2), pp. 337–343. [CrossRef]
Lankarani, H. M., and Nikravesh, P. E., 1990, “A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems,” ASME J. Mech. Des., 112(3), p. 369. [CrossRef]
Keller, J., 1986, “Impact With Friction,” ASME J. Appl. Mech., 53(1), pp. 1–4. [CrossRef]
Poisson, S. D., 1837, Recherches sur la probabilite des jugements en matirre criminelle et en matiere civile precedees des regles generales du calcul des probabilites par SD Poisson, Bachelier, Paris.
Stronge, W. J., 1990, “Rigid Body Collisions with Friction,” Proc. R. Soc. London. Series A: Math. Phys. Sci., 431(1881), pp. 169–181. [CrossRef]
Flickinger, D. M., and Bowling, A., 2010, “Simultaneous Oblique Impacts and Contacts in Multibody Systems With Friction,” Multibody. Syst. Dyn., 23(3), pp. 249–261. [CrossRef]
Meirovitch, L., 2010, Methods of Analytical Dynamics, Dover Publications Inc., Mineola, NY.
Kane, T. R., and Levinson, D. A., 1985, Dynamics, Theory and Applications, McGraw Hill, New York.
Wehage, R. A., Haug, E. J., and Beck, R. R., 1981, Generalized Coordinate Partitioning in Dynamic Analysis of Mechanical Systems. Technical Report, Iowa University Iowa City College of Engineering.
Khulief, Y., and Shabana, A., 1986, “Dynamic Analysis of Constrained System of Rigid and Flexible Bodies With Intermittent Motion,” J. Mech. Transm. Autom. Design, 108(1), pp. 38–45. [CrossRef]
Razzaghi, P., and Assadian, N., 2015, “Study of the Triple-Mass Tethered Satellite System Under Aerodynamic Drag and j2 Perturbations,” Adv. Space. Res., 56(10), pp. 2141–2150. [CrossRef]
Ceanga, V., and Hurmuzlu, Y., 2001, “A New Look at an Old Problem: Newton’s Cradle,” ASME J. Appl. Mech., 68(4), p. 575. [CrossRef]
Hurmuzlu, Y., 1998, “An Energy-Based Coefficient of Restitution for Planar Impacts of Slender Bars With Massive External Surfaces,” ASME J. Appl. Mech., 65(4), pp. 952–962. [CrossRef]
Stoianovici, D., and Hurmuzlu, Y., 1996, “A Critical Study of the Applicability of Rigid-Body Collision Theory,” ASME J. Appl. Mech., 63(2), pp. 307–316. [CrossRef]
Wang, S., Wang, Y., Huang, Z., and Yu, T. X., 2015, “Dynamic Behavior of Elastic Bars and Beams Impinging on Ideal Springs,” ASME J. Appl. Mech., 83(3), pp. 31002. [CrossRef]
Auerbach, D., 1994, “Colliding Rods: Dynamics and Relevance to Colliding Balls,” Am. J. Phys., 62(6), pp. 522. [CrossRef]
Freschi, A. A., Hessel, R., Yoshida, M., and Chinaglia, D. L., 2014, “Compression Waves and Kinetic Energy Losses in Collisions Between Balls and Rods of Different Lengths,” Am. J. Phys., 82(4), pp. 280–286. [CrossRef]
Hu, B., Schiehlen, W., and Eberhard, P., 2003, “Comparison of Analytical and Experimental Results for Longitudinal Impacts on Elastic Rods,” J. Vib. Control, 9(1–2), pp. 157–174. [CrossRef]
Schiehlen, W., Seifried, R., and Eberhard, P., 2006, “Elastoplastic Phenomena in Multibody Impact Dynamics,” Comput. Methods. Appl. Mech. Eng., 195(50–51), pp. 6874–6890. [CrossRef]
Ismail, K. A., and Stronge, W. J., 2008, “Impact of Viscoplastic Bodies: Dissipation and Restitution,” ASME J. Appl. Mech., 75(6), p. 061011. [CrossRef]
Liu, C., Zhao, Z., and Brogliato, B., 2008, “Frictionless Multiple Impacts in Multibody Systems. I. Theoretical Framework.” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 464, The Royal Society, London, pp. 3193–3211.
Gharib, M., and Hurmuzlu, Y., 2012, “A New Contact Force Model for Low Coefficient of Restitution Impact,” ASME J. Appl. Mech., 79(6), p. 64506. [CrossRef]


Grahic Jump Location
Fig. 1

B–B collision experimental setup

Grahic Jump Location
Fig. 2

B–C collision experimental setup

Grahic Jump Location
Fig. 3

Experimental contact stiffness testing

Grahic Jump Location
Fig. 4

General discrete B–C model

Grahic Jump Location
Fig. 5

Force–displacement curves: (a) bilinear force model and (b) nonlinear force model

Grahic Jump Location
Fig. 6

Average percentage error for all categories

Grahic Jump Location
Fig. 7

Percentage error of all B–C collisions: (a) category 1: B–C1, (b) category 1: B–C2, (c) category 2: B–C1, (d) category 2: B–C2, (e) category 3: B–C1, and (f) category 3: B–C2

Grahic Jump Location
Fig. 8

Average percentage error for all categories

Grahic Jump Location
Fig. 9

Numerical force–displacement profile

Grahic Jump Location
Fig. 10

Number of segments corresponding to APEm: (a) category 1, (b) category 2, and (c) category 3

Grahic Jump Location
Fig. 11

Numerical force–displacement profile

Grahic Jump Location
Fig. 12

COR versus the number of segments of the softer material: (a) SsS1 and (b) SsW1



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In