This paper proposes a new analytical model for helical gears that characterizes the contact plane dynamics and captures the velocity reversal at the pitch line due to sliding friction. First, the tooth stiffness density function along the contact lines is calculated by using a finite element code. Analytical formulations are then derived for the multidimensional mesh forces and moments. Contact zones for multiple tooth pairs in contact are identified, and the associated integration algorithms are derived. A new 12-degree-of-freedom, linear time-varying model with sliding friction is then developed. It includes rotational and translational motions along the line-of-action, off-line-of-action, and axial directions. The methodology is also illustrated by predicting time and frequency domain results for several values of the coefficient of friction.
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