Variability of modal behavior in terms of critical speeds of a gear pair due to manufacturing errors and shaft misalignments

This paper deals with the variability of the dynamic behavior induced by transmission error of a mass production gear pair. The origins of this variability are due to the manufacturing errors. The tolerances that are associated with shaft misalignment errors, gear tooth profile and lead errors, are considered as geometric independent random parameters. A procedure based on Taguchi's method is used to treat the tolerances statistically. The efficiency of this methodology is demonstrated by considering a simple dynamic model of a single spur gear pair. The predicted variations in dynamic behavior due to tolerances are verified by comparison with results obtained using Monte Carlo simulations. The analyzed parameters are firstly the static transmission error and the time-average mesh stiffness. As a consequence of the variability of the mesh stiffness, statistical variations of natural frequencies are observed for critical modes (high-energy modes). The related critical speed ranges are given too. At last, the variations of the high-energy mode shapes are also observed.