Physics-based modeling of a chain continuously variable transmission

This paper focuses on a physics-based model of a chain CVT. The study starts from kinematics of an infinitely small chain segment, and then investigates the fundamental dynamics of the chain segment. A speed-dependent continuous friction model is employed that accounts for both micro-slip and macro-slip conditions. Pulley axial dynamics is studied and is coupled with chain segment radial movement. The classical pulley deformation (Sattler's model) is included in the model. Simulation results show that pulley deformation plays an important role in defining the chain CVT dynamics. Unlike a rigid pulley, sliding angle with a deformable pulley is not a constant. Internal forces like chain tension and normal contact force are not monotonic function of angular position within the wrap. The simulation results compare well, qualitatively and quantitatively, with data published in literature and clamp force ratio (KpKs) values from dynamometer testing.