Research of Contact Response of an Elastic Sphere Impacting a Rigid Plate Based on the Mass-Spring-Damped Oscillator Model and Dimensionless Parameter \omega_\Omega

The contact theory, such as the Hertz theory and Hunt-Crossley model can just solve the contact response when the sphere goes to the maximum compression but can’t solve the contact process. In traditional research the impact process is considered as a single degree of freedom dynamical spring-damping system, however, the calculated contact force is much greater than the actual one. Based on the shortage of the conducted studies, a new dimensionless parameter ωΩ is proposed in this paper, the mass-spring-damped oscillator model (MSDOM) and the new contact theory with the consideration of the sphere mass and ωΩ are established. The correctness of the theoretical model is verified by 3D simulation, and the optimal contact force model is obtained. Furthermore, influence rules of material properties and contact parameters on contact response were studied. The results show that the contact deformation, velocity, piecewise nonlinear contact force and acceleration based on MSDOM and ωΩ are effective to calculate the contact response. The contact stiffness, damping, material properties of sphere and elastic modulus of the plate have different influence on the contact response while the Poisson’s ratio ν2 has little effect on it.