Adaptive Control of Nonlinear Spur Gear Dynamics with Parametric Disturbance Rejection

This paper presents a model reference adaptive control method to reduce the excessive amplitude of nonlinear vibration occurring between the meshing teeth of a gear pair. Using this model reference adaptive control, it has been shown that harmonic components of a truncated Fourier series approximating the periodic mesh stiffness can be learned and finite number of harmonics of the periodic mesh stiffness can be canceled by a modulated torque. With the use of Lyapunov stability analysis, it has been shown that error dynamics of the closed-loop gear pair system driven by a torque generator supervised by the model reference adaptive control law is asymptotically stable.