Finite element modelling of a rotating piezoelectric ultrasonic motor A. Frangi a, * , A. Corigliano a , M. Binci a , P. Faure b a Dipartimento di Ingegneria Strutturale, Politecnico di Milano, P.za. L. da Vinci 32, 20133 Milano, Italy b ABB AT Italy Simulation Group, viale dell’Industria 18, 20010 Vittuone (MI), Italy Received 31 August 2004; received in revised form 31 March 2005; accepted 20 April 2005 Available online 25 May 2005 Abstract The evaluation of the performance of ultrasonic motors as a function of input parameters such as the driving frequency, voltage input and pre-load on the rotor is of key importance to their development and is here addressed by means of a finite element three- dimensional model. First the stator is simulated as a fully deformable elastic body and the travelling wave dynamics is accurately reproduced; secondly the interaction through contact between the stator and the rotor is accounted for by assuming that the rotor behaves as a rigid surface. Numerical results for the whole motor are finally compared to available experimental data. Ó 2005 Elsevier B.V. All rights reserved. PACS: 77.65.j; 85.50.n Keywords: Ultrasonic motors; Piezoelectricity; FEM modelling; Thermal analogy 1. Introduction Piezoelectric materials belong to the larger domain of smart materials, i.e. materials based on the systematic re- sponse to particular inputs [1–6]. A specific field in which piezoelectric materials show an increasing importance is that of piezoelectric motors. The travelling wave ultrasonic motors (TWUSM) repre- sent a new generation of motors, suited for many appli- cations [7,8] and their technology has experienced growing interest in the last decade due to the particular advantages that new piezoelectric materials offer. Ultra- sonic motors have been commercially employed for automated focusing systems of cameras, for special instruments and X–Y positioning systems, while practi- cal researches aiming at producing systems for transport and office automation are now being undertaken. Any- way, a large-scale employment has been somehow hin- dered so far by some problems related to their long- term reliability and high cost (see e.g. the review in [9]). Even if they do not represent, at present, a global alternative solution to electromagnetic motors, their fea- tures are preferable for specific tasks. Piezoelectric mo- tors have several unique properties such as: high output torque (at least one order of magnitude larger than conventional electromagnetic motors of the same size and weight [10]), large breaking torque due to the friction force without energy consumption (self-break- ing motors), low leakage of magnetic flux. The high out- put torque makes it possible to eliminate reduction gears from the transmission system, which means a reduction in noise level and the possibility to construct a position- ing system with high rigidity. Moreover, some ultrasonic motors have unique shapes, such as thin disks or rings, that are difficult to produce with electromagnetic motors. The travelling wave ultrasonic motors are based essentially on the sequence of two energy conversions: (i) electromagnetic energy conversion employing a film of piezoceramics to induce the propagation of a 0041-624X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2005.04.005 * Corresponding author. Tel.: +39 223994213; fax: +39 223994220. E-mail address: attilio.frangi@polimi.it (A. Frangi). www.elsevier.com/locate/ultras Ultrasonics 43 (2005) 747–755