Multiscale Methods for Multibody Systems with Impacts

Abstract

In the design of mechanical and structural systems, computer simulations are frequently used to check the dynamic response of the system being developed. This form of computer-aided engineering reduces strongly the need to construct and test prototypes. During the last decades modeling and simulation of multibody systems have been throughly investigated in theory and successfully applied in engineering, e.g., in automotive, aerospace and military industry as well as in biomechanics and robotics. The development of the multibody system method is reviewed by Schiehlen [38] for rigid multibody dynamics and Shabana [44] for flexible multibody dynamics. Both authors pointed out that further study should be devoted to modeling and simulation of multibody systems with impact and contact. For multibody systems with impact, there are mainly two methods known to analyse collisions depending on the duration of contact. The elastic collision approach and the rigid body approach. Both methods will be discussed in this paper based on contributions by Hu and Schiehlen [20] and Schiehlen and Seifried [41]. The first method, see e.g. Bauchau [5], is based on finite contact duration and a finite contact force. In contrast to the rigid body approach, the velocities of the colliding bodies vary continuously. During the contact period, there are two force components active at the point of contact, i.e., the normal contact force FN and the tangential contact force F T . The normal contact force follows from a compliant contact model where the local deformations of the colliding bodies in the neighborhood of the contact surface are considered. Usually, the contact force is modeled as a function of the indentation depth. Typical compliant contact models are the Kelvin-Voigt viscoelastic model or the extended Hertzian contact model. In the Kelvin-Voigt viscoelastic model, the contact force is modeled by a linear spring-damper element and results in a linear function of the indentation depth while in the extended Hertzian model the contact force is a nonlinear function of the indentation depth. For modeling the tangential contact force Coulomb’s friction law is usually used. It postulates that the friction force for slipping is equal to the normal contact force times the coefficient of kinetic friction and acts in a direction opposing the relative motion. For