A pair of spur gears with involute teeth is considered. Nondimensional expressions are derived for the dynamic tooth loading. The resulting parametrically excited equations are analyzed by the procedures of asymptotic analysis. The results show that instability regions can occur leading to large vibrations and failure. These instability regimes are presented as a function of speed and other parameters. Minimum damping values to prevent the instabilities are derived as a function of the gear ratio and number of pinion teeth. In addition, given some inherent damping, response amplitudes of the transmission error are presented as a function of nondimensional parameters.

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