| Traditional analysis of permanent magnet synchronous machines has focused upon establishing a relationship between the q- and d-axis stator current (or voltage) and the tangential component of electromagnetic force (torque), which is created to yield rotor rotation. Although useful, traditional analysis fails to consider the vector component-nature of force generation, i.e. that both radial and tangential components of force are created. The research described herein documents the effort to characterize the behavior of both radial and tangential components of force. Specifically, using a combination of analytical and numerical techniques, the influence of q- and d-axis stator current on both the radial and tangential component of airgap flux density is first evaluated. A Maxwell Stress Tensor approach is then used to evaluate the radial and tangential component of force. The analysis shows that the d-axis current has a significant influence on the radial force component and the q-axis current contributes to both radial and tangential force components nearly equally. Interestingly, it is also shown that under standard operating conditions, the radial force far exceeds that of the tangential component of force. Therefore, one can conclude that the magnetic fields established create a significant component of force in a direction that does not produce rotor rotation.; The research is then extended to develop schemes to reduce both torque and radial force ripple using a microscopic-based analysis. A field reconstruction approach is introduced to obtain the phase current excitation for a number of possible operating scenarios, including zero ripple in both tangential/radial force and/or minimal copper loss for a fixed value of torque. The waveforms obtained are validated using finite element analysis of a 3-phase machine. |
