Z.P. Xia

An Accurate Subdomain Model for Magnetic Field Computation in Slotted Surface-Mounted Permanent-Magnet Machines

The paper presents an accurate analytical subdomain model for computation of the open-circuit magnetic field in surface-mounted permanent-magnet machines with any pole and slot combinations, including fractional slot machines, accounting for stator slotting effect. It is derived by solving the field governing equations in each simple and regular subdomain, i.e., magnet, air-gap and stator slots, and applying the boundary conditions to the interfaces between these subdomains. The model accurately accounts for the influence of interaction between slots, radial/parallel magnetization, internal/external rotor topologies, relative recoil permeability of magnets, and odd/even periodic boundary conditions. The back-electromotive force, electromagnetic torque, cogging torque, and unbalanced magnetic force are obtained based on the field model. The relationship between this accurate subdomain model and the conventional subdomain model, which is based on the simplified one slot per pole machine model, is also discussed. The investigation shows that the proposed accurate subdomain model has better accuracy than the subdomain model based on one slot/pole machine model. The finite element and experimental results validate the analytical prediction.

Analytical magnetic field analysis of Halbach magnetized permanent-magnet machines

We develop analytical models for predicting the magnetic field distribution in Halbach magnetized machines. They are formulated in polar coordinates and account for the relative recoil permeability of the magnets. They are applicable to both internal and external rotor permanent-magnet machines with either an iron-cored or air-cored stator and/or rotor. We compare predicted results with those obtained by finite-element analyses and measurements. We show that the air-gap flux density varies significantly with the pole number and that an optimal combination of the magnet thickness and the pole number exists for maximum air-gap flux density, while the back iron can enhance the air-gap field and electromagnetic torque when the radial thickness of the magnet is small.

Analytical Modeling and Finite-Element Computation of Radial Vibration Force in Fractional-Slot Permanent-Magnet Brushless Machines

An analytical model has been developed for analyzing the radial vibration force in fractional-slot permanent-magnet machines. It is compared extensively by finite-element analyses and used to investigate the influence of the following: 1) stator slotting; 2) tangential field component; 3) radius in the air gap for computation; 4) load condition, etc. The major findings include the following: 1) even on an open circuit, the low harmonic component (e.g., the second for a 10-pole/12-slot machine) of the radial force exists due to the slotting effect, although the amplitude is relatively low, while the slotless analytical model cannot predict this phenomenon; 2) on a load, the slotless analytical model is accurate enough for the radial force analysis since the low-order harmonic component of the radial force is mainly due to the interaction between the magnet field and the armature-reaction field and is largely determined by the combination of the pole and slot numbers; 3) it is much more reliable to calculate the radial force in the middle of the air gap rather than close to the stator bore; and 4) the simple formula accounting only for the radial field component in the middle of the air gap is accurate enough for the radial force calculation.

Influence of slot and pole number combination on radial force and vibration modes in fractional slot PM brushless machines having single- and double-layer windings

This paper systematically investigates the radial force and vibration modes in fractional slot surface-mounted permanent magnet (PM) brushless machines having different slot and pole numbers, viz. 2 p = Ns ± 2 , 2 p = Ns ±1, q=0.5, respectively, with either single- or double-layer winding. The dominant vibration mode can be determined from the lowest order of radial force harmonic. It shows that for integer slot PM machines, q=1, the dominant radial force is mainly caused by the fundamental magnet field itself, and the dominant vibration mode order is equal to pole number which is usually high. However, in all fractional slot PM machines, the dominant radial force is mainly produced by the interaction between the harmonic in magnet field and the harmonic in armature reaction field, while the noise and vibration can be significantly higher since the dominant vibration mode order can be as low as 1 or 2, which strongly depends on the slot and pole number combinations, as well as the winding topologies, as confirmed by both developed analytical model and finite element (FE) analyses.

Prediction of open-circuit airgap field distribution in brushless machines having an inset permanent magnet rotor topology

A 2-dimensional analytical model for predicting the open-circuit airgap field distribution in radial-field brushless machines having an inset permanent magnet rotor is developed. It accounts for flux focusing and inter-pole leakage effects and arbitrary pole-arc/pole-pitch ratios, and is also applicable to machines having a surface mounted magnet rotor. Predicted results are compared with finite element analyses, and are shown to be in good agreement. >

Influence of design parameters on output torque of flux-switching permanent magnet machines

The influence of design parameters of a flux-switching PM (FSPM) machine for maximum output torque has been investigated by finite element analyses and validated by measurements made on a prototype FSPM motor. These parameters include the split ratio of the inner diameter to outer diameter of the stator, the stator tooth width, the stator magnet thickness, the stator back-iron thickness, the stator lamination bridge, the rotor tooth width and height, and the rotor back-iron thickness. In addition, the influence of the shape of the magnets and the rotor teeth has been investigated. It shows that the FSPM machine having equal stator tooth width, stator magnet thickness and slot opening produces the maximum output torque. The torque can be increased if the stator back-iron thickness is reduced to ~70% of the stator tooth width to increase the slot area. The output torque can be increased by ~8% if the rotor tooth width is increased by 40%~60%. The optimal split ratio for maximum output torque is ~0.55-0.6 when the copper loss is fixed to 50 W and increases with an increase in the copper loss. The influence of other design parameters is found to be less significant for an appropriately designed motor.

An Analytical Model of Unbalanced Magnetic Force in Fractional-Slot Surface-Mounted Permanent Magnet Machines

We present an analytical model of unbalanced magnetic force (UMF) in fractional-slot surface-mounted permanent magnet (PM) machines having diametrically asymmetrical winding distribution but no static/dynamic rotor eccentricities. It is based on a 2-D analytical field model and accounts for the influence of both the radial and tangential force waves under any load condition. It is capable of providing insight into the generation, harmonic contents, and characteristics of the UMF and accurately predicting the magnitudes, rotation directions, phase angles of its harmonics and various components, such as the UMFs due to armature reaction only, mutual interaction between both PM and armature reaction fields, and radial and tangential force waves. The cancellation and additive effects between the UMF components resulting from the radial and tangential force waves are revealed for the first time by the analytical model. We show that such effects strongly depend on the UMF harmonic order, slot/pole number combinations, and the internal/external rotor machine topologies. We have validated the analytical model by finite-element analyses and partially by experimental results.

Analytical modelling and finite element computation of radial vibration force in fractional-slot permanent magnet brushless machines

Analytical models have been developed for analysing the radial vibration force in fractional-slot permanent magnet machines and validated extensively by finite element analyses. They are used to investigate the influence of (a) stator slotting, (b) tangential field component, (c) radius in the airgap for computation, and (d) load condition etc. on the radial vibration force calculation. The major findings can be summarised as follows. (1) Even on open-circuit, the low harmonic component (e.g. 2nd for 10-pole/12-slot machine, and 1st for 8-pole/9-slot machine) of radial force exists due to slotting effect although the amplitude is relatively low, while the slotless analytical model cannot predict this phenomenon; (2) However, on load, slotless analytical model is accurate enough in the radial force analysis, since in this case, the low order harmonic component of radial force is mainly due to the interaction between the magnet field and the armature reaction field, and is largely determined by the combination of pole and slot numbers; (3) It is much more reliable to calculate the radial force in the middle of airgap, rather than close to the stator bore, while the harmonic contents of radial force are almost independent of radius in the airgap; (4) The simple formula accounts only for the radial field component in the middle of airgap is accurate enough for radial force calculation.

Optimal Split Ratio in Fractional-Slot Interior Permanent-Magnet Machines With Non-Overlapping Windings

The split ratio has been optimized for the maximum torque density when the airgap flux density is fixed in existing papers. However, the airgap flux density can vary with the split ratio significantly in interior permanent magnet (IPM) machines due to flux focusing. Therefore, an optimal airgap flux density may exist, together with the optimal split ratio, for the maximum torque in IPM machines. This paper analytically optimizes the airgap flux density and split ratio individually, as well as the global optimum in terms of the torque density in the fractionalslot IPM machines with non-overlapping windings. In addition, the influence of pole-slot combination and tooth-tips on the optimal split ratio and airgap flux density is discussed. The analytical result is verified by the finite element analysis. It shows that the optimal split ratio reduces with the increase of the airgap flux density, and the preferred airgap flux density is around 0.5–0.7 times of maximum flux density in the stator teeth when the rare earth permanent magnets are employed.

Performance of Halbach magnetized brushless ac motors

In this paper, an anisotropic bonded NdFeB Halbach magnetised ring magnet, which is oriented in powder alignment system during injection moulding and subsequently impulse magnetised, is employed. The features of such a Halbach magnetised machine, in terms of the airgap field distribution, and the back-emf and cogging torque waveforms, etc. have been compared with those which result with a Halbach magnet having discrete magnet segments have previously been compared.