A dynamic model of an automotive belt-drive system with a noncircular sprocket instead of a round sprocket is developed in this work to study the effect of reducing the angular variation of camshafts. There are two submodels in the belt-drive system, which are an engine model and a belt-drive model, and they are decoupled to simplify the analysis. When the belt-drive system operates at a steady-state, it is described by a nonlinear model with forced excitation, which can be approximated by a linear model with combined parametric and forced excitations. Steady-state responses of the engine and belt-drive models are calculated by a modified incremental harmonic balance method that incorporates fast Fourier transform and Broyden's method, which is efficient and accurate to obtain a periodic response of a multi-degree-of-freedom system. Steady-state responses of the angular variation of camshafts with different values of sprocket parameters are compared to investigate their optimal values to reduce the angular variation of camshafts. The optimal eccentricity and installation angle are larger and smaller than those from the kinematic model, respectively, which is consistent with published experimental results. This study first shows from a dynamic point of view why use of a noncircular sprocket can reduce the angular variation of camshafts in the operating speed of an engine. Simulation of a speed-up procedure for different sprocket parameters shows results that are consistent with steady-state responses. The belt-drive model developed in this work can be used to select sprocket parameters to minimize the angular variation of camshafts and numerically evaluate the dynamic performance of a belt-drive system with a given design of sprocket parameters.

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