This paper describes a shape optimization formulation to design the frame system of an induction motor to reduce noise and vibration. The natural frequency most sensitive to acoustic noise of the motor is found to correspond to an oval mode and chosen as the objective function to be maximized. Another objective function, surface vibration level(S.V.L) in terms of an integrated value of the square of vibration velocity of the outer surface of the frame and the cooling fins is also considered to be minimized. The electromagnetic forces by the theory of magnetic field was considered as input loads.
A variational approach which uses the material derivative concept of the continuum mechanics and domain methods is taken for derivation of shape design sensitivity. It is numerically implemented by postprocessing analysis data of ABAQUS finite element code to get the design sensitivity information of natural frequency of the structure and S.V.L in steady state. The results have been in good agreement, in most cases, as compared with those by finite differencing.
Two sets of design variables describing the shape are studied. The first is a set of 9 outer radii of frame for circumferential stiffening. As the second group of design variables, the heights of cooling fins and stiffeners are considered.
A 5-hp, 4-pole and 3-phase induction motor was studied. As results of this study, the oval mode frequency of the motor was increased by 100Hz and the S.V.L corresponding to the exciting frequency of 1320Hz could be decreased by 30\% using either of the two design variable sets. It is shown that the natural frequency near the exciting frequency has been lowered in this case. Information on the spectrums of both natural and exciting frequencies is important for a practical design decision.