Dynamic Modeling of Timing Belt Frictional Contact using an Explicit Finite Element Formulation

In this study, an efficient dynamic finite element model is developed for timing (also known as synchronous) belt drive systems capable of determining the transient and steady-state response of systems consisting of any number of driver and driven sprockets. For validation purposes, a two-sprocket drive is studied in detail and a comparison is made between tooth loads predicted by the finite element model and experimental data available from the literature. The drive belt is modeled using truss or beam finite elements, while the sprockets are modeled using rigid constraints. Two types of belt contact nodes are identified: tooth nodes and groove nodes. Tooth nodes experience frictionless penalty contact forces associated with radial sprocket penetration, as well as penalty contact forces associated with trapezoidal sprocket tooth interaction. Groove nodes interact frictionally with the sprocket pitch circles in regions away from the trapezoidal teeth. The resulting contact algorithms are a natural extension of previously published and validated algorithms developed for non-toothed belt-pulley contact (Leamy and Wasfy, 2002) and therefore inherit much of the previous models' accuracy and efficiency. A complete simulation tool is achieved by incorporating the model into an in-house explicit finite element code, which can maintain time-accuracy for large rotations and for long simulation times. Simulation results of the validation drive's tooth loads are shown to compare favorably with available experimental data.