Stability analysis of motor-driven actuators in dry clutches with nonlinear stiffness element

Force-aided motor-driven actuators can be not only force-saving but energy-saving, therefore, has great potential to be applied to dry clutches which are key enablers to various automatic transmissions. However, the diaphragm spring in the dry clutch has high nonlinear stiffness, especially, with a negative phase. The high nonlinearity may induce complex dynamics. Taking the electromagnetic effect into consideration, a two degree of freedom dynamic model is developed. The stability analysis is conducted for system before and after control. Bifurcations are observed in the eigenvalue evolutions with respect to the spring deformation, proportional feedback gain and derivative feedback gain, respectively. Further, the numerical computations are implemented to illustrate free vibrations by phase portraits, time domain response and frequency spectra. The results show that the negative stiffness introduces instability, the proportional gain tunes the time delay of the response, but the derivative gain plays a major role in stabilizing the system.