Modelling of steady motion of solid specimens conveyed by travelling wave ultrasonic feeding

On the basis of the research on the morphology of the contact surfaces, a contact model is proposed, which regards the rough contact surfaces as the collections of elastic micro peaks. These micro peaks generate elastic contact force due to elastic deformation and the contact force has relationship to the morphology of the contact surfaces, the motion of the vibrator as well as the materials of the specimen and the vibrator. And using Newton’s second law to the specimen’s motion, the normal dynamical equation for the specimen with the actuation of the ultrasonic vibrator is established. Solving the dynamical equation, the normal kinetic function of specimen and the normal elastic contact force are obtained. Furthermore, the normalized contact time could be analyzed theoretically, which is defined as the ratio of contact time to period. The calculated results indicate that the normalized contact time decreases with the vibrator’s normal amplitude increasing, and increases with the standard deviation of the height of micro peaks on the contact surfaces. Finally, the average tangential velocity of the specimen, conveyed by a travelling wave ultrasonic feeding device, is discussed on the basis of the research on the normalized contact time. The formula of the specimen’s average tangential velocity is derived and it is the function of the normalized contact time, the tangential amplitude, the angular frequency and the phase difference of the tangential and the normal vibrations. Using this formula, the tangential velocity of the specimen is theoretically analyzed; in addition, the theoretical conclusions are compared with the experimental data.