Keywords: reliability based design optimization, random variable, risk of failure, contact, optimal safety factors.

Under normal operational conditions, ultrasonic motors are subjected to: (i) an axial static pre-stressing load producing axial and radial deformations in the stator and rotor, (ii) a dynamic excitation of the stator, involving out of the plane bending deformations, which produce a rigid displacement of the rotor's body and (iii) efforts of contact and friction (static and dynamic) in the contact zone between the stator and the rotor.

The aim of this study is to propose a numerical model using the finite element method for the mechanical behaviour of an ultrasonic motor SHINSEI USR 60 under dynamic loading taking into account the contact without friction by using the reliability analysis. Generally, the life of these motors is limited by important abrasion of the different components. So, the notion of random variables and the risk of failure must be integrated in the mechanical analysis to ensure the good working of the system.

Contact problems are treated using an augmented Lagrangian approach to identify the candidate contact surface and contact stresses [1]. The stochastic role of each parameter of design is highlighted. For this reliability analysis, we propose a direct coupling mechanical-reliability between the augmented Lagrangian method to solve the contact and the probabilistic method FORM [2].

In this paper, we present a new method based on optimal safety factors (OSF) in the context of the reliability-based design optimization (RBDO) analysis [3] of the ultrasonic motors with a travelling wave taking into account the contact between the different components (stator and rotor). We present the different methods for the RBDO analysis and we highlight the advantage of our approach based on OSF. Some numerical results are given to validate the proposed method.

1

O.A. Baba, B. Radi, J.-C. Gelin, "An Augmented Lagrangian Treatment of the metal forming process", Mathematical and Computer Modelling, 32(10), 171-179, 2000. doi:10.1016/S0895-7177(00)00198-9

2

T. Moro, A. El Hami, A. El Moudni, "Reliability analysis of a mechanical contact between deformable solids", Probabilistic Engineering Mechanics, 17(3), 227-232, 2002. doi:10.1016/S0266-8920(02)00007-3

3

A. Mohsine, G. Kharmanda, A. El Hami, "Improved hybrid method as a robust tool for reliability-based design optimization", Structural and Multidisciplinary Optimization, 32(3), 203-213, 2006. doi:10.1007/s00158-006-0013-2

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