A Comprehensive and Efficient Model of Belt-Drive Systems

Belt-drive systems are a commonly used for power transmission in automotive applications, notably in engine and vehicle auxiliary subsystem drives. In order to characterize the physics of a belt drive system and its response to speed and load excitations, a comprehensive model of belt elasticity and of belt-pulley contact and friction is required. In practical applications such models are utilized in parametric design and optimization studies, and computational efficiency is therefore also a key requirement. In this paper a belt drive dynamics model is presented, in which the belt is modeled by means of geometrically exact cables that can undergo large rigid body motions but whose strains remain small. The Finite Element approach is used in order to efficiently discretize these elastic components. In addition, a state-of-the-art dynamic friction model (LuGre) is used in order to model the friction loads between the belt and pulleys. The contact and friction loads are treated as distributed forces acting on the belt and pulleys. This results in a more efficient system since it requires fewer belt or beam elements; at the same time eliminates the polygonal effect common to lumped characterizations of belt-pulley contact and friction interactions. The model has been implemented within a general-purpose tool in which a complete belt drive system can be modeled, including excitations from the driven/driving torsional systems, belt tensioners and structural stiffness at pulley hubs. Several numerical examples are analyzed to validate the proposed model. First, two validation examples are presented. Next, an automotive belt drive system is described and its predictions are discussed.