Study of mounted surface permanent magnet syn-chronous machine using Flux® Skew. A. Soualmi ; P. Lombard - CEDRAT.

Requirements: rotating electrical machine designers want high-reliability, minimum power losses, maximum power, maximum torque and low mechanical resonance vibration

and noise. To meet the needs of electrical machine designers, CEDRAT started developing tools that take Skew into account in 2003. Several improvements have been made to this tool. Skew is usually accounted for by sub-dividing the active length of the machine into several 2D slices. In the latest Skew version of Flux the post processing is directly a full 3D post-processing. Among the advantages of Skew: minimizing harmonic content in the back EMF, reducing the cogging torque, reducing the torque ripple (the torque ripples in electrical machines are due to several factors: space harmonics, time harmonics and cogging torque) and the average torque.In order to compare the impact of the Skew of permanent magnet on the rotor, PM motors were designed in 3D as shown in Fig.1.

The period of cogging torque can be determined by:

Where LCM is the least common multiplier, Ns the number of slots and Np the number of poles.

As we can see in Fig.4 a significant reduction in the cogging torque is achieved.

Fig.3. Cogging torque VS rotor position.

Fig.3. Cogging torque VS rotor position.

Fig.2. Cogging torque.

Fig.1. 3D modeling and schematic of Skew diagram.

1a) 3D with Skew

1b) 3D without Skew

Table I: Peak value of the cogging torque

Fig.5. Isovalues of flux density at no-load.

Cogging torqueSeveral cogging torque minimization techniques exist for permanent magnet machines. One of the foremost ones is Skew. Cogging torque results from the interaction of the rotor permanent magnets with the stator teeth (see Fig. 2). This torque produces vibration and noise which are considered undesirable in most permanent magnet machines. The strength of the torque ripple depends on the sum of both cogging torque and synchronous torque. Hence there is interest in reducing the cogging torque.

Without Skew With Skew

Cogging torque (N.m) 3e-3 1e-3

Skew angle effectAs can be seen from Fig.6 a significant reduction in the cogging torque can be achieved as the Skew angle is increased. A 34% reduction in the peak cogging torque being achieved when the Skew angle= 15C° (the number of slices in this case is 5).

Fig.11. Torque comparison: cyan: Skew, magenta: 3D with Skew.

Fig.10. Current comparison: cyan: Skew, magenta: 3D with Skew.

7b) 3D with Skew

7a) Skew

7c) 3D without Skew

Table II: amplitude of Back EMF fundamental.

Fig.6. Cogging torque VS rotor position for different values of Skew angle.

Fig.7. Isovalues of flux density at no-load.

Fig.8. Back EMF Vs time.

Table III: Comparison skew and 3D at no-load.

Skew 3D with Skew

Back EMF Fundamen-tal(V)

11.82 11.43

Back EMF The value of the no-load voltage E0 depends on the flux produced by the magnet in the air gap and the speed of the rotor.The Figure 8 and table II summarize the computation of the back EMF for all examples shown in the paper. They both show that the peak value of back EMF is the same for the two cases of simulation. A small difference between Skew, 3D with Skew is probably found due to end effect.

Torque and currentIn this part, we are interested in calculating the torque and the current for a power supply with a converter (see Fig.9). Both simulations: Skew and 3D with Skew are supplied by the same circuit (see Fig.9).

Fig. 10 and 11 show the comparison at load of the current and torque respectively between the Skew and 3D with Skew. A good agreement between the curve is observed for both current and torque.

ConclusionResults from table III clearly indicate that the Skew allows reducing the computational solving time compared with 3D Skew and 3D modeling keeping the same result as the 3D. By selecting an optimum Skew angle, the cogging torque can be greatly reduced. Furthermore, parametric computation can be run in the Skew to optimize the machine.

Fig.9. Electrical circuit.

3D with Skew Skew

At no-load

Number of nodes 127728 57272

Number of slices 1 5

Calculation time (minute) 156 20

Acceleration 1 8

At no-load

Number of nodes 127728 57272

Number of slices 1 5

Calculation time (minute) 449 10

Acceleration 1 15

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