Multi-field coupled dynamics for a movable tooth drive system integrated with shape memory alloys

The harmonic movable tooth drive system integrated with shape memory alloys has a small size and a large output torque. Its dynamics performance is the key factor for evaluating the drive system. Here, for the drive system, based on its structure and working principle, the coupled dynamics equations are deduced. Using the equations, changes of the natural frequencies of the drive system during the operation are investigated. Effects of the system parameters and SMA wires phase change process on the natural frequencies are analyzed. The nonlinear resonant frequencies of the drive system and its amplitude-frequency relationship are studied. Results show that natural frequencies of the drive system change periodically which is caused by SMA phase transformation during operation. The eccentricity, movable tooth radius, the wave generator radius and SMA wire length have also important effects on the natural frequencies of the drive system. The nonlinear resonant frequencies are smaller than linear resonant frequencies. In the design of the drive system, the coupled nonlinear effects of the temperature, phase change, stress and strain of the SMA wires, and the system parameters of the movable tooth drive system should be considered. In this paper, the coupled nonlinear dynamics model of the harmonic movable tooth drive system integrated with shape memory alloys is proposed in which the coupled effects of the temperature, phase change, stress and strain of the SMA, and the system parameters of the movable tooth drive system are considered.