Nonlinear effect of tooth-slot transition on axial vibration, contact state and speed fluctuation in traveling wave ultrasonic motor

Abstract

The tooth-slot transition creates an axial excitation on traveling wave ultrasonic motors. It induces a rotor’s axial rigid vibration, which in turn affects the contact state and arouses speed fluctuation. To gain an insight into this problem, this work examines the relationships between the tooth-slot transition, axial vibration, nonlinear contact, and speed fluctuation. An analytical model governing rotor’s vibration is developed, where the transition force, nonlinear contact stiffness, and pre-pressure are included. The contact stiffness is demonstrated to decrease with an increase in stator’s vibration amplitude and it is approximated by polynomial fitting such that the nonlinear problem can be analytically solved. The primary, 1/2 subharmonic, and 2/1 superharmonic resonances are analyzed to determine the amplitude–frequency response and steady-state response. Nonlinear phenomena regarding the three types of resonances are identified. The interaction between the transition force, axial vibration, contact stiffness and speed fluctuation is investigated through a new contact model. The results imply that the rotor vibration induces rotating acceleration and leads to speed fluctuation. In addition, the rotor speed fluctuates in a similar fashion with the axial vibration.

Analysis of Preload of Three-Stator Ultrasonic Motor

“…In case of large preload and the contact area outstripping the position of the constant velocity point, the area is an obstructive area, that is, it obstructs the rotation of the rotor. According to Equation (23), it can be seen that under a given friction material, when µ d remains unchanged, the size of the driving friction force is proportional to the pre-pressure. Different friction materials have different parameters such as stiffness, modulus, and friction factor, which will lead to differences in the contact interface during contact and at the same time affect the kinetic energy transmission of the contact interface.…”

“…At this time, the contact range is mainly in the driving area, which has a more obvious effect on the rotor, so the speed will be increased accordingly. Under the same stress, with the enlargement of elastic modulus, its elastic deformation will shrink [22][23][24][25][26]. The elastic modulus of the composite material is:…”