An elastic simulation model of a metal pushing V-belt CVT

Abstract

This contribution presents the modelling of a metal pushing V-belt CVT to be used in numerical simulations. The system is subdivided into the pulleys, the belt and different types of contacts. The modelling is described in detail. Since the deformation of the CVT is of major importance for the mechanical behaviour, the elasticity of the colliding bodies has to be taken into account. The deflection of the pulleys is split up into three parts. First the shaft is bent by radial forces. Here a spatial model of an elastic beam is used. Second the pulley sheaves tilt due to elasticity and clearance of the shaft-to-collar connection. This is modelled by a force element. And third, as a consequence of the asymmetrical loading, the elastic sheaves deform. This is calculated by different approaches, in which the best results are achieved by the use of CASTIGLIANO's Strain Energy Theorem. The motion of the belt is specified in EULER-coordinates for the axial plane by separate longitudinal and transversal approaches. Therefore continuous RITZapproximations are used in combination with hierarchical shape functions. For the kinematics of the moving elements a transformation to LAGRANGE-description is used. The system contains a large number of contacts. The contact between the pulley sheaves and the belt elements is modelled spatial. The contact between two adjacent elements is modelled one dimensional. Both types of contacts consider unilateral constraints. In the contact between two ring layers the radial expansion has to be modelled accurately. The simulation model is implemented in the object-orientated programming language C++. This allows to calculate the kinematics of the belt and the local distribution of all contact forces. It permits to compute the necessary pulley thrust, the maximum transmittable torque and the efficiency for given loading cases. Some results of the numerical simulation are presented at the end of this contribution. Although this work deals with a metal pushing V-belt, the models can be modified for other CVTs.