Motion of a friction belt drive at mixed kinematic description

Abstract

The planar problem of a two-pulley belt drive is revisited with account for large transverse deflections due to gravity and frictional contact between the pulleys and the belt, which is modelled as an extensible string. An existing mixed Eulerian-Lagrangian finite element model is extended to simulate the quasistatic, non-stationary motion of the system, where the method of augmented Lagrangian multipliers is adopted for contact treatment, which relies on the penalty regularisation to iteratively update the contact tractions. To validate the numerical results, a semi-analytic solution of the steady state is developed based on belt creep theory. In a comparative study numerical and semi-analytic steady state solutions are verified. The transient evolution of the contact state during quasistatic, non-stationary motion is studied with the finite element scheme.