Modeling and optimization of ultrasonic linear motors

Ultrasonic motors have received much attention these last years, in particular with regard to their modeling and their design principle. Their operating principle is based on piezoelectric ceramics that convert electrical energy into mechanical energy in the form of vibrations of an elastic body whose surface points perform an elliptic motion with a frequency in the ultrasonic range (≥ 20 kHz). The moving part, which is pressed against the vibrating body by a prestressing force, can move thanks to the friction forces presented at the interface between the stator (resonator) and the rotor (slider). Their specific properties make ultrasonic motors a very attractive solution for a direct transmission for different applications like precise positioning devices. Indeed, they present the possibility to obtain unlimited motions, high resolution and excellent dynamics of positioning. Then, it is obvious that ultrasonic motors could be used in new application fields, in particular to replace conventional electromagnetic motors. However, they have to overcome two principal difficulties: their efficiency is rather poor and they are often too expensive. Moreover, their use in the car industry or for the positioning of axes in machine tools for example requires driving forces and velocities higher than those which they currently present. Analytical modeling of such motors is not obvious and assumptions that are made are often too restrictive. This is why the use of a numerical modeling (3-D) is necessary to model the behavior of this type of motors. Thus, finite element simulations are used but they often require high computing times. To avoid it, the number of simulations can be decreased by choosing the input parameters (dimensions, materials, boundary conditions,...) more judiciously according to their influence on the output parameters. Thus, one can obtain the sensitivity of an input parameter on the value of the output parameter. With this intention, the application of design of experiments has been adopted in this thesis work. This methodology, applied to finite element simulations, is an innovative technique in the field of theoretical modeling of such motors. This methodology is particularly interesting in sight of predicting the results but also to find out an optimal set of input parameters for the motor. According to the results obtained and presented in this thesis work, the use of design of experiments in the field of ultrasonic motors modeling proves to be very promising and demonstrates to be a powerful tool. The application of the proposed methodology for the optimization of an ultrasonic linear motor used for the auto-focus function of the lens of an optical system also made it possible to show the validity and the potential of this optimization method.

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