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Measurement of Contact Force–Deformation Curves of Colliding Two Identical Spheres

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Abstract

Background

The contact force–deformation relation between two spheres is one fundamental property which determines the mechanical response of the colliding bodies. In general, collisions of solid spheres occur in a very short time, so a highly accurate and a non-contact measurement method is required.

Objective

In this study, a concept for the experimental determination of contact force–deformation curves of two colliding spheres is presented. Thereby two identical steel spheres collide by using a pendular setup and the sphere's velocities are measured by Laser Doppler Vibrometers (LDVs).

Methods

The displacements are obtained by integrating the velocity with time and the accelerations are obtained by differentiating the velocity with time. From these values, the deformation and the contact forces can be calculated. Then, the elastic results are compared with the Hertzian theory of impact and experiments are conducted with elasto-plastic spheres.

Results

Although the deformations are in good agreement with these analytical values, the influence of numerical differentiation is observed in the contact force. However, it is shown that the elastic contact force–deformation curve of two colliding spheres can be obtained with reasonable accuracy by using LDVs. For elasto-plastic spheres the coefficient of restitution became smaller than for the purely elastic case, and the force–deformation curve with hysteresis are measured.

Conclusions

The results of this study are considered to be reasonable as far as comparisons with those for elastic collisions. Therefore, more detailed verification by numerical analysis, such as finite element analysis, is desirable.

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Funding

No funding was received to assist with the preparation of this manuscript.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shizuoka Institute of Science and Technology, 2200-2 Toyosawa, Fukuroi, Shizuoka, 437-8555, Japan

    H. Minamoto

  2. Institute of Mechanics and Ocean Engineering, Hamburg University of Technology, Eißendorfer Straße 42, 21073, Hamburg, Germany

    R. Seifried

  3. Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany

    P. Eberhard

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  1. H. Minamoto
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  2. R. Seifried
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  3. P. Eberhard
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Correspondence to H. Minamoto.

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Minamoto, H., Seifried, R. & Eberhard, P. Measurement of Contact Force–Deformation Curves of Colliding Two Identical Spheres. Exp Mech 63, 1033–1042 (2023). https://doi.org/10.1007/s11340-023-00965-8

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  • DOI: https://doi.org/10.1007/s11340-023-00965-8

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