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Method-Specific Significance of Field Components in Three Methods of Torque Estimation

Magnetic field distribution in the airgap of rotating machines, consisting of tangential and normal components, determines the instantaneous value of torque. Lorentz force (LF), Maxwell stress tensor (MST), and virtual work (VW) methods are commonly used to estimate its value. In their well-known forms, as used by design engineers of rotating machines, these three methods reflect distinct significance for field components. The LF method does not require the distribution of tangential field components to compute torque, whereas in MST and VW, it is required. In this article, torque expression-based equivalence of LF, MST, and VW methods is presented, starting from a simple two-coil conceptual system. Using this equivalence as a basis, certain indicative factors are derived, which provide insights on the typical significance of the tangential component in average and ripple torque. The analysis presented here helps designers obtain a better overview of the method-specific significance of field components and flux paths in instantaneous torque, from a numerical perspective.