Effect of magnet/slot combination on triple-frequency magnetic force and vibration of permanent magnet motors

• Magnetic triple-frequency forces are examined by superposition approach.
• Lower harmonic forces are addressed by analytical and numerical methods.
• Relationship between magnet/slot combination and UMF and CT is clarified.
• Typical vibration modes are found very similar to those in the planetary gears.
• The superposition idea can find potential utilization in other symmetric systems.

The relationship between magnet/slot combination and magnetic forces including unbalanced magnetic force (UMF) and cogging torque (CT) of permanent magnet (PM) motors is investigated by using superposition principle and mechanical and magnetic symmetries. The results show that magnetic force can be produced by all magnets passing a single slot, by all slots passing a single magnet, or by eccentricity, which respectively correspond to three frequency components. The results further show that net force/torque can be classified into three typical cases: UMF is suppressed and CT is excited, UMF excited and CT suppressed, and UMF and CT both suppressed, and consequently possible vibrations include three unique groups: rotational modes, translational modes, and balanced modes. The conclusion that combinations with the greatest common divisor (GCD) greater than unity can avoid UMF is mathematically verified, and at the same time lower CT harmonics are preliminarily addressed by the typical excitations. The above findings can create simple guidelines for the suppression of certain UMF and/or CT by using suitable combinations, which in turn can present approach to yield a more desirable response in high performance applications. The superposition effect and predicted relationship are verified by the transient magnetic Finite Element method. Since this work is motivated by symmetries, comparisons are made in order to give further insight into the inner force and vibration behaviors of general rotary power-transmission systems.

Representative magnetic forces acting on rotor, where Fςξƛlς imply the lςthlςth tangential (ξ=tξ=t) and radial (ξ=rξ=r) force on the i  th magnet (ς=mς=m, ƛ=iƛ=i), or those on the j  th tooth (ς=sς=s, ƛ=jƛ=j), and (a), (c), (e), (f) forces add, torques cancel; (d), (g) forces cancel, torques add; (b) forces cancel, and torques cancel.Figure optionsDownload as PowerPoint slide