Elastic Modelling of Bodies and Contacts in Continuous Variable Transmissions

This report presents an elastic multibody model for a Continuous Variable Transmission (CVT), used in a numerical simulations. The system is subdivided into the pulleys, the belt and the contacts. Since the deformation of the pulleys is of major importance for the mechanical behaviour, three different approaches are presented and discussed, whereat the best results are achieved by the use of Castigliano’s Strain Energy Theorem. The deflection of the belt is specified by separate longitudinal and transversal Ritz approaches, with the use of hierarchical shape functions. The belt dynamics is calculated in Euler coordinates and is transformed to Lagrange description. The system contains a large number of contacts, whose unilateral constraints as well as the deformation of the colliding bodies are modelled. 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. Although this report deals with a metal pushing V-belt, the models can be modified for other CVTs. The simulation model was implemented in the object-orientated programming language C++, because common MBD-programms do not support the used approaches. Without them, it is not possible to achieve reasonable simulation times. The simulation allows to calculate the kinematics of the belt and the local distribution of all contact forces. It permits to evaluate the necessary pulley thrust, the maximum transmittable torque and the efficiency for defined loading cases. After introducing the models, results of numerical simulations are illustrated.