Research Papers: Applications

Critical Plate Thickness for Energy Dissipation During Sphere–Plate Elastoplastic Impact Involving Flexural Vibrations

[+] 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@andrew.cmu.edu

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received April 27, 2016; final manuscript received November 14, 2016; published online April 4, 2017. Assoc. Editor: Sinan Muftu.

J. Tribol 139(4), 041104 (Apr 04, 2017) (9 pages) Paper No: TRIB-16-1141; doi: 10.1115/1.4035338 History: Received April 27, 2016; Revised November 14, 2016

Solid processing storage and conveying units (e.g., hoppers, silos, tumblers, etc.) often involve the collision of granular media with relatively thin walls. Therefore, the impact of a sphere with a thin plate is a problem with both fundamental and practical importance. In the present work, the normal elastoplastic impact between a sphere and a thin plate is analyzed using an explicit finite element method (FEM). The impact involves plastic deformation and flexural vibrations, which when combined results in significant energy dissipation. One way to quantify the energy dissipation is to employ the coefficient of restitution (COR), which is also a key input parameter needed in various granular flow models. The results were validated against the available experimental data. It is observed that, in addition to material properties and impact parameters, the energy dissipation is strongly dependent on the ratio of plate thickness to sphere diameter. A comprehensive parametric study is conducted to evaluate the effect of material properties, geometry, and impact parameters on the energy dissipation. For the impact velocities commonly observed in granular systems (V = 5 m/s or less), it was determined that the energy lost to flexural vibrations can be neglected if the plate thickness is more than twice the sphere diameter, i.e., tcr > 2d. In this scenario, the mode of energy dissipated is primarily due to the plasticity effects.

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Grahic Jump Location
Fig. 2

Mesh convergence results, 0.635 cm brass sphere impacting S7 steel plate at 2.13 m/s

Grahic Jump Location
Fig. 1

Finite element model mesh layout

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Fig. 3

Experimental versus simulation results for impact with S7 steel plate 0.635 cm thick

Grahic Jump Location
Fig. 4

COR variation with sphere size (brass sphere impacting S7 steel plate 0.635 cm thick)

Grahic Jump Location
Fig. 5

COR variation with plate thickness (brass sphere 0.635 cm diameter impacting S7 steel plate)

Grahic Jump Location
Fig. 7

Simulation results for various cases shown in Table 3

Grahic Jump Location
Fig. 6

COR variation with plate thickness to sphere diameter ratio: comparison with experiments and various analytical models for brass sphere impacting S7 steel plate at 2.56 m/s



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