Application of numerical integration methods to continuously variable transmission dynamics models

Abstract

The expansion of digital engineering technologies in the framework of the fourth industrial revolution relies on core technologies for mathematical modeling and computer simulation of physical processes. Time required for a computer simulation and the quality of numerical solutions are key factors that ultimately have impact on product quality and the amount of waste at product design stage. This paper is aimed on the reduction computer simulation time for continuously variable transmission (CVT) models. The modeling of the device as a set of deformable rigid bodies with numerous contact interactions is an extraordinary problem addressed in [1]. Model dynamics is described in terms of ordinary differential equations (ODE) of motion. The system of ODEs has about 3600 variables (generalized coordinates and speeds). Despite relatively low dimension of the model, computer simulation using traditional numerical integration methods takes long time to run. The reason for this is the stiffness of the ODE system. In this paper, we present the results of an investigation aimed on finding a numerical integration method appropriate for problems of this kind.