Sensitivity analysis and parameter optimization for vibration reduction of undamped multi-ribbed belt drive systems

Tensioner is a critical mechanism to ensure a constant tension level within a serpentine belt drive that is widely used in modern passenger vehicles. For a belt drive with n pulleys, generic and explicit formulae about sensitivities of both frequency and steady harmonic responses are established in terms of system matrices with respect to any design parameter of the system. Deductions from the formulae results in frequency and steady response sensitivities relative to key tensioner parameters and the belt speed. Based on sensitivity analysis, optimizations are conducted on tensioner so as to suppress dynamic responses of the system by frequency detuning. A new approach for searching optimal parameters is put forward by incorporating sensitivity information into a classical coordinate alternating procedure. Examples are given to validate the analytical formulae of the frequency sensitivity and to demonstrate the effect of optimization.