Natural Modes/Frequencies of “Track-Type” Ultrasonic Motors

Natural modes and natural frequencies of a “track-type” ultrasonic motor, one of the “travelling-wave-type” ultrasonic motors, is discussed. For generating the out-of-plain travelling wave which rotates in the track-shaped ring, we must design the vibrator so as to obtain two natural modes whose rank (number of nodal diameters and nodal circles) and natural frequencies are the same, and whose natural modes are shifted 90 degrees in phase and in time. In general, the natural frequencies of these two modes are different. We study the change in the natural modes/frequencies by changing the length of the straight part of the vibrator using finite-element analysis. Consequently, we find some specific cases where the two natural frequencies correspond. We also fabricate the vibrator in order to confirm the calculation.