24. O.Yu.Zharii, Dynamical contact problems arising in mathematical modeling of ultrasonic motors, preprint, 50 p. (1997)

A consistent mathematical model of a travelling wave ultrasonic motor with a piezoceramic stator is suggested. The model is based on the theory of piezoelectric plates planar vibrations and on physically well-grounded ideas of classic contact mechanics. Mathematically, complete description of motion and energy transformation due to contact frictional forces in an ultrasonic motor is reduced to the solution of a mixed boundary-value problem of elastodynamics. This problem is a nonclassical one: Besides the contact stress fields one should determine an unknown in advance velocity of the relative motion of bodies in contact. For this, one should employ the equation of the rotor motion. Under the steady-state motion, it can be done on the base of the energy considerations. The theory developed provides an opportunity to calculate within the framework of a single model all characteristics of the motor, important in applications, including the rotor velocity, speed-voltage dependencies, the efficiency of energy transformation etc.

Contents

1 Introduction

2 General solution of a dynamic problem for periodically deformed half-plane
2.1 Equation of motion and its general solution
2.2 Formulation of boundary conditions
2.3 Derivation of the system of integral equations
2.4 Energy relations
3 Adhesive contact between the surface wave and a rigid strip under normal and tangential loadings
3.1 Derivation and solution of the integral equation
3.2 Kinematic characteristics
3.3 Contact area and rotor velocity
3.4 Analysis of solution
3.5 Summary of results
4 Complete sliding in the contact area
4.1 Integral equation of the problem
4.2 Solution of the integral equation
4.3 Kinematic characteristics
4.4 Problem of frictionless contact
4.5 Analysis of solution of the frictional contact problem
5 General problem with partial adhesion and partial slip
5.1 Reduction of resulting system of equations to a single Fredholm equation
5.2 Characteristics of contact stresses distributions
5.3 Kinematic characteristics of solution
5.4 Analysis in the vicinity of the separation point
6 Summary and discussion
Appendix
References

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