Elastic creep in serpentine belt drives and adopting a suitable strain measure

Abstract

The paper deals with the transient dynamics of serpentine belt drives. A model for the rotational motion that has been proposed in the literature is extended to elastic belt creep. However, unlike previous articles, this paper adopts a logarithmic strain measure to describe elastic creep. A condition for the existence of steady state motions with constant belt tensions, as a solution of the mass conservation law, is derived. This condition is violated for the linear strain measure together with Hooke's law, whereas it holds for the logarithmic strain measure. As a consequence, only the logarithmic strain measure, together with Hooke's law, leads to system equations that cover steady operating states. In the case of linear strain, belt tensions and tensioner position do not converge towards constant values when choosing a set of external torques that balance each other out. This is illustrated by two numerical examples. Furthermore, the considerations are reinforced and anchored in the automotive field by analysing the transient belt drive behaviour during a ‘revving-up’ manoeuvre of a common rail diesel engine. The considerations are generally applicable, not only to the classical elastic creep theory but also to any other, more sophisticated theory.