Abstract: Travelling wave ultrasonic motors have recently been attracting considerable attention: they are beginning to replace -at least in certain areas- small electromagnetic motors. This development has been made possible by recent advances in power electronics, material sciences and digital control, permitting the utilization of the piezoelectric effect for low power motors. In these motors, the mechanical energy is generated with frequencies of the order of 40 kHz via piezoelectric elements producing elastic waves in a stator, which usually has the form of approximately a circular plate, a ring or a thin walled cylindrical tube. The rotor is then driven by the stator via contact forces. With an extremely simple mechanism, frequency reductions of 1:40,000 and more are obtained between the stator vibration and the rotor motion. As a consequence, one can work in the 40 kHz range on the electrical side, while a low frequency of rotation is obtained on the mechanical side, as is desirable for many applications. Travelling wave ultrasonic motors combine features such as high holding and driving torque, low speed, etc. which make them extremely attractive and promising for many applications. In many cases they can be used directly without an intermediate speed reducer.
The lecture addresses the problem of mathematical modeling of ultrasonic travelling wave motors and recent advances in this field. In developing mathematical models for piezoceramic motors and carrying out laboratory experiments, some unexpected nonlinearities were found. The main nonlinearity is due to the contact between rotor and stator, leading to jump phenomena in the torque-frequency characteristic, as well as to self-excited vibrations. An unexpected nonlinearity was experimentally found in the material laws for the piezoceramic material under weak electric fields but moderately large strains. This nonlinear piezoceramic behavior also may be of importance for piezoceramic actuators used in other fields.

Biography: Dr. Peter Hagedorn received a doctor's degree in Mechanical Engineering 1966 from the University of Sao Paulo, Brazil, and in 1972 got the `Habilitation' (D.Sc. degree) from the University of Karlsruhe, Germany. He is Professor of Mechanics at Darmstadt University of Technology, Germany, where he has been on the faculty for 25 years. He has repeatedly served as Department Chair, Director of the Mechanics Institute and more recently also as Vice-President to the University. From 1969 to 1971, he served as a visiting professor to COPPE (Rio de Janeiro) and from 1973 to 1974 as a visiting research fellow to the Department of Aeronautics and Astronautics of Stanford University. He has also served as Russel Severance Springer visiting professor to the University of California at Berkeley, a visiting Erskine Fellow to the University of Canterbury (New Zealand) and has also been a visiting professor to Paris and Irbid (Jordan). He is the first recipient of the Brazilian Alexander von Humboldt Research Award. His main professional interests are vibrations and stability of discrete and continuous systems (such as beams, plates and cables), and vibration control. While his early work was more analytical (e.g. the converse of the Lagrange-Dirichlet theorem, differential games, etc.), during the last 20 years, he has worked more and more also with problems related to industrial applications, also being involved in experimental work, the emphasis however usually being on producing practical mathematical models. Recently, he has done research on piezoelectric ultrasonic travelling wave motors, wind excited vibrations of overhead transmission lines, and the vibrations of travelling webs and belts. He is the author of about 150 technical papers and several books on linear and nonlinear vibrations as well as of a three volume German textbook on elementary statics, strength of materials and dynamics. Together with several colleagues, he is organizing a workshop in the year 2000 dealing with the question of how today engineering students should be taught mechanics.

Time:Dec. 3, 1999 @2:30 P.M.
Place:Room 1202, Martin Hall
Hosts: Professors B. Balachandran and H. Bruck, Department of Mechanical Engineering