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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

Professor
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.

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Figures

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Fig. 1

B–B collision experimental setup

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Fig. 2

B–C collision experimental setup

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Fig. 3

Experimental contact stiffness testing

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Fig. 4

General discrete B–C model

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Fig. 5

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

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Fig. 6

Average percentage error for all categories

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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

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Fig. 8

Average percentage error for all categories

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Fig. 9

Numerical force–displacement profile

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Fig. 10

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

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Fig. 11

Numerical force–displacement profile

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Fig. 12

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

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