Numerical Algorithms for Simulation of One-Dimensional Mechanical Systems With Clearance-Type Nonlinearities

Abstract

In many mechanical systems there are nonlinearities of clearance type. This type of nonlinearity often causes problems with convergence and accuracy in simulations, due to the discontinuities at impact. For systems with gap-activated springs connected to ground, it has been proposed in previous work to reformulate the problem as a linear complementary problem (LCP), which can be solved in a very efficient way. In this paper, a generalization of the LCP approach is proposed for systems with gap-activated springs connecting different bodies. The generalizations enable the LCP approach to be used for an arbitrary number of gap-activated springs connecting either different bodies or connecting bodies to ground. The springs can be activated in either compression or expansion or both and a gear ratio can be included between the bodies. The efficiency of the algorithm is demonstrated with an application example of a dual mass flywheel (DMF).