二球の弾性衝突における接触力－変位関係の計測

抄録

Sphere collision is considered to be one of the basic collision configuration, and it influences the accuracy of the collision motion analysis in multibody dynamics. Therefore, it is important to measure their impact property accurately. In general, various methods were used to measure the motion of the spheres during collision. In this study, elastic collisions of two identical spheres were conducted by a pendular impact setup. The velocity changes of the spheres during collision were measured by using laser Doppler vibrometers. The sphere's displacements were determined by integrating the measured velocities, and the accelerations were obtained by differentiating the measured velocities. The contact force was obtained by multiplying the acceleration by sphere's mass. Then, the contact force-deformation relationship was obtained. The obtained results are compared with Hertzian contact theory for validation. The experimental contact force-deformation curves matched pretty well with Hertzian contact theory. Good agreements were also obtained for the maximum compression time, contact time, and maximum relative displacement. However, the experimental maximum contact force showed about 10% higher than Hertzian contact theory. It is thought to be introduced by the discrete error in the numerical differentiation of the velocity. Also in the measured contact force-deformation curves a small hysteresis is observed. Since only very little kinetic energy is dissipated in the experiments, this small hysteresis might be a measurement artifact, originating from small variations between the different measurement signals. It is necessary to examine whether this measurement technique is applicable to inelastic collisions in the near future.