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Research Papers: Contact Mechanics

# Experimental Investigations on the Coefficient of Restitution for Sphere–Thin Plate Elastoplastic Impact

[+] Author and Article Information
Deepak Patil

Mechanical Engineering Department,
Carnegie Mellon University,
Pittsburgh, PA 15213

C. Fred Higgs, III

Mechanical Engineering Department,
Carnegie Mellon University,
Pittsburgh, PA 15213
e-mail: higgs@rice.edu

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 11, 2017; final manuscript received June 29, 2017; published online August 22, 2017. Assoc. Editor: Sinan Muftu.

J. Tribol 140(1), 011406 (Aug 22, 2017) (13 pages) Paper No: TRIB-17-1081; doi: 10.1115/1.4037212 History: Received March 11, 2017; Revised June 29, 2017

## Abstract

In multiparticle simulations of industrial granular systems such as hoppers, tumblers, and mixers, the particle energy dissipation is governed by an important input parameter called the coefficient of restitution (COR). Oftentimes, the wall thickness in these systems is on the order of a particles diameter or less. However, the COR value implemented in event-driven simulations is either constant or a monotonically decreasing function of the impact velocity. The present work experimentally investigates the effect of wall thickness on the COR through sphere–thin plate elastoplastic impacts and elucidates the underlying impact phenomena. Experiments were performed on 0.635 cm and 0.476 cm diameter (d) spheres of various materials impacting aluminum 6061 plates of different thicknesses (t) with the low impact velocities up to 3.1 m/s. Besides COR, indentation measurements and numerical simulations are performed to gain a detailed understanding of the contact process and energy dissipation mechanism. As the “t/d” ratio decreases, a considerable amount of energy is dissipated into flexural vibrations leading to a significantly lower COR value. Based on the results, it can be concluded that using a constant COR input value in particle simulations may not always be an appropriate choice, especially, in the case of thin plates. However, these new COR results validate that when the wall thickness is more than twice the sphere diameter (i.e., t/d > 2), a constant COR value obtained for an impact with semi-infinite plate can be reasonably used.

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## Figures

Fig. 1

Drop test apparatus (COR rig): (a) laboratory photograph and (b) schematic side view (A) hollow metal support, (B) plate, (C) sphere, (D) sphere holder, (E) Plexiglass casing, (F) suction device, (G) hose, and (H) air pump

Fig. 2

Plate installation on the hollow metal support: (a) supporting metal frame, (b) plate mounted on the frame, and (c) clamped plate

Fig. 3

COR as a function of distance from plate support for tungsten carbide sphere (d = 0.635 cm) impacting aluminum 6061 plates at Vi = 3.1 m/s

Fig. 4

Coefficient of restitution results for brass spheres: (a) d = 0.476 cm and (b) d = 0.635 cm

Fig. 5

COR as a function t/d ratio for various materials, results plotted for impact velocity Vi = 1.1 m/s

Fig. 6

COR as a function t/d ratio for various materials, results plotted for impact velocity Vi = 2.3 m/s

Fig. 7

COR as a function t/d ratio for various materials, results plotted for impact velocity Vi = 3.1 m/s

Fig. 8

Comparison between analytical solutions and the current work's experimental data of S2 steel sphere for impact velocity Vi = 2.3 m/s

Fig. 9

Plate indentation measurements: (a) contour plot, (b) cross section profile, and (c) crater image

Fig. 10

Indentation depth on various plates after impact with brass sphere (d = 0.635 cm)

Fig. 11

Indentation depth on various plates after impact with tungsten carbide sphere (d = 0.635 cm)

Fig. 12

Indentation depth on various plates after impact with S2 tool steel sphere (d = 0.635 cm)

Fig. 13

Finite element model mesh layout

Fig. 14

Comparison of experimental and simulation COR results for various materials

Fig. 15

Contact forces developed during the impact for various plates, brass sphere (d = 0.635 cm) impacting at Vi = 2.3 m/s

Fig. 16

Sphere–plate energy transfer during the impact process, brass sphere (d = 0.635 cm) impacting at Vi = 2.3 m/s on plate t = 0.476 cm

Fig. 17

Stress (von Mises equivalent) and plastic strain contours at the instance of maximum contact force for brass sphere (d = 0.635 cm) impacting at Vi = 2.3 m/s on thickest and thinnest plate: (a) stress contours, t = 0.160 cm, (b) stress contours, t = 1.270 cm, (c) plastic strain contours, t = 0.160 cm, and (d) plastic strain contours, t = 1.270 cm

Fig. 18

Relative energy loss between plastic deformation and flexural vibrations during the impact process, brass sphere (d = 0.635 cm) impacting at Vi = 2.3 m/s

Fig. 19

Experimental versus simulation results for indentation, brass sphere (d = 0.635 cm) impacting at Vi = 2.3 m/s

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