Analytical synthesis of air-gap field in permanent magnet machines with rotor eccentricity by superposition method

Summary form only given. Permanent magnet (PM) machines have been widely employed in electric vehicles, wind power generators, domestic appliances, and industrial servos etc. When the rotor is eccentric, either static or dynamic due to manufacturing or operating tolerances, the full machine model is necessary for finite element analysis (FEA), because the model cannot be simplified by utilizing the periodicity any more. This is problematic and time-consuming for FEA especially when the slot number and pole number are high, such as in direct-drive low-speed PM machines. This paper proposes a new analytical model which combines the superposition method and the subdomain method [1] for predicting air-gap field in PM machines with rotor eccentricity. A 12-slot/10-pole surface-mounted PM machine is taken as example to illustrate the developed method. The original machine with rotor eccentricity, Fig.1(a), is divided into a number of air-gap sections along the circumference. For each air-gap section, an equivalent air-gap length is determined, corresponding to the center point of the slot opening in this example. Then, the subdomain method is employed for each of concentric models with different equivalent air-gap lengths to analytically synthesize the air-gap field in the original eccentric machine. By way of example, Figs.1(b), (c) and (d) show 3 concentric models according to the three selected air-gap lengths shown in Fig.1(a) respectively. It is worth noting that the whole synthesis process can be carried out analytically and integrated into the CAD software. The open-circuit air-gap flux densities and back-EMFs obtained by the proposed superposition method is shown in Fig.2 and validated by the direct FEA for a specific rotor eccentricity. The results clearly show that 3 phase back-EMFs are unbalanced due to rotor eccentricity. Therefore, it has demonstrated that the proposed method can accurately predict the air-gap field in PM machines with rotor eccentricity and can be used to predict the electromagnetic performance. The details of analytical method and application to a very high slot and pole number PM machine will be given in the full paper .