Dynamic responses of an engine front-end accessory belt drive system with pulley eccentricities via two spatial discretization methods

Abstract

In this study, a generic mathematical model for calculating the natural frequencies and the dynamic responses of a typical front-end accessory drive system with any number of pulleys and arbitrary configurations of the tensioner and pulleys is established. The belt bending stiffness and the pulley eccentricities are considered in this model, and their influences on the natural frequency and the dynamic responses of the front-end accessory drive system are examined. A generic spatial discretization method and a Galerkin discretization method, which uses Lagrange multipliers to enhance the boundary conditions, are presented to discretize the continuous belt spans and to transform the governing partial differential equations into ordinary differential equations. The accuracies of the generic spatial discretization method and the Galerkin discretization method are validated by modal tests, and the advantages of the generic spatial discretization method with respect to the efficiency and the convenience of implementation are assessed by comparing the generic spatial discretization method with the Galerkin discretization method and the two-layer iteration approach. The dynamic responses of the typical front-end accessory drive system at different operational velocities are calculated from the governing ordinary differential equations derived from these two methods. It is shown that large vibration amplitudes occur in certain belt spans owing to the resonance conditions or the beat phenomena in certain operational conditions and that the belt bending stiffness has a negligible influence on the vibrations of the belt drive system because its value is small.