A shape optimization formulation is adopted to design the stator and frame system of an induction motor. Two objective functions are studied. The natural frequency sensitive to acoustic noise of the motor is chosen as the first objective function and is to be maximized. As for the second objective, surface vibration level in terms of integrated value of the square of vibration velocity of the outer surface of the frame is selected, based on a previous study that this has direct relation to the noises of the motor. A harmonic exciting force is considered.
The variational approach which uses the material derivative concept of the continuum mechanics is taken for derivation of shape design sensitivity. The formulas resulted are then implemented in conjunction with the commercial code, ABAQUS. Treating it as a black box, postprocessing is heavily used and the problem of interfacing analysis software to an optimization software is considered.
Several sets of design variables describing the shape are studied and general trends analyzed. Thickening the anti-node area is one of the trend most influencing the shape. Since a better design in terms of the objective functions selected is obtained when more weight is allowed, an appropriate choice of the upper limit is very important. To be more realistic, manufacturability must also be studied and experimental verification is necessary.
