A novel semi-analytical coefficient of restitution model based on new characteristics length and time for the nonlinear colliding viscoelastic particles

The coefficient of restitution (CoR) is a critical parameter for predicting the impact behavior of colliding particles. This investigation aims to develop a novel CoR model for viscoelastic particles by incorporating improved characteristic length and time parameters. Initially, a new characteristic length is defined by considering energy dissipation during the compression phase of the impact process, providing a foundation for deriving the characteristic time in cases of damped impact behavior. Subsequently, a new equation of motion of colliding particles is formulated based on two new characteristic length and time. The approximate analytical solution of the new equation of motion is solved using Taylor expansion when considering energy dissipation during the compression phase. Likewise, the proposed motion equation is solved simultaneously based on the inverse collision method. The impact velocity of colliding particles can be obtained by combining two different solutions from the new equation of motion. Therefore, a new CoR model can be derived based on the definition of the Newtonian’s CoR. Moreover, the dimensionless maximum contact time during the compression phase is obtained based on the energy conservation of the whole compression phase. However, the new CoR model encounters a limitation when the impact velocity is zero as the denominator, which depends on impact velocity and the dimensionless maximum contact time leads to an undefined value. An infinitesimal quantity ε is introduced to the dimensionless maximum contact time to remove this issue, ensuring the CoR model remains finite when the impact velocity approaches or equals zero. Finally, the advantages of the new CoR model are demonstrated in comparison to existing CoR models. A series of experimental data involving metallic and non-metallic contact materials validates the accuracy and reliability of the proposed model.