Arch. Comput. Meth. Engng. Vol. 9, 3, 257-282 (2002) Archives of Computational Methods in Engineering State of the art reviews Structural Optimization in Magnetic Fields Using the Homogenization Design Method – Part II: Re- duction of Vibration Caused by Magnetic Forces J. Yoo ∗ School of Mechanical Engineering Yonsei University, Seoul, Korea 120-749 Summary The homogenization design method has been expanded to obtain the optimal topology of a structure in magnetic fields to maximize the magnetic energy. In this study, the homogenization design method (HDM) is applied to a structure in magnetic fields to reduce the vibration level of a structure excited by the magnetic forces, especially by the magnetic harmonic forces. This is accomplished by obtaining the optimal material distribution of the structure to minimize the frequency response. The Maxwell stress method is used to compute the magnetic force and the HDM is applied for the optimization. It is verified that the HDM is useful to minimize the frequency response by some actual applications. The effects of mesh density of the design domain and the rotor-stator position are also examined. 1 INTRODUCTION For the design of a structure in magnetic fields, we have to consider the mechanical effect as well as the magnetic characteristics caused by the structure. Even though the requirement for the magnetic characteristics is satisfied, there can be a serious problem in mechanical point of view, such as stiffness or vibration. Vibration in an electrical machine has an adverse effect on the performance of the ma- chine, especially in case that it is required for the machine to be accurate and quiet. There are numerous sources of vibration in electrical machines such as rotor imbalance, bearing defects, and magnetic forces generated in the electromagnetic circuits of the machine. The contribution of each source to vibration is dependent on the design of each machine. Espe- cially, it results in severe vibration when the natural frequency of the structure coincides with the frequency of deformation. Although vibration in electrical machines has been studied for decades, new problems appear continuously mostly caused by the rapid devel- opment and increasing complexity of new types of electrical machinery. Therefore, for the structural design considering vibration, we have to consider many design factors related not only with vibration but also with other electrical and mechanical performances. That is why the design of electrical machines can be explained as a process for finding an optimal solution considering related constraints. There are many possible sources of vibration in a structure excited by magnetic harmonic excitation as following: - Radial attraction between the stator and the rotor: could produce the stator phase current pulses and the associated flux - Torque ripple: could excite stator vibrations - Current in the stator windings: could interact with the local magnetic field to produce a force on the windings * Assistant Professor c 2002 by CIMNE, Barcelona (Spain). ISSN: 1134–3060 Received: March 2002