# A method for efficient computation of forces in permanent magnet synchronous machines

#### Abstract

Knowledge of forces within permanent magnet synchronous machines (PMSMs) is of interest in numerous applications. To compute the vector forces, many analysts utilize the finite element (FE) method to compute the vector fields within the machine. The Maxwell Stress Tensor approach is then used to calculate vector forces from the vector fields. Although the combined FE/MST approach has been used for decades, it does have some common misconceptions and shortcomings associated with it. One is the confusion surrounding the physical meaning of the computed vector force densities. A second is the computational requirement of the FE method, which limits the approach to a tool for analysis rather than for comprehensive machine design. This thesis addresses both the misconceptions and the shortcomings. To begin, the theory behind the Maxwell Stress Tensor (MST) method is reviewed in detail. A focus is on the derivation of the tensor and force equations in non-conducting magnetic material. ^ To address the computational requirements, a new so-called Enhanced Field Reconstruction Technique (EFRT) has been developed. Using the EFRT, the vector fields inside a machine are computed using a minimum number of FE evaluations. Using the result of these evaluations, a set of basis functions are established that enable the calculation of forces inside the machine under arbitrary excitation and rotor position. The EFRT greatly reduces the computational effort required to compute the vector forces inside machines, enabling comprehensive fields-based design of PMSM drive systems. The accuracy of the EFRT has been validated using hardware and FE-based results. ^

#### Degree

Ph.D.

#### Advisors

Steven Pekarek, Purdue University.

#### Subject Area

Engineering, Electronics and Electrical

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