Skewed Synchronous Machine Design

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Vincent Marché

Vincent Marché graduated first in electronics, and then went on to refine his skills at business school. After more than 10 years in the industry, working on product marketing and sales of sensors, switches and electronic devices, he fell into a melting pot called electrical engineering simulation. Supporting FluxTM electromagnetic simulation software since 2009, he is passionate about the large fields of applications addressed by simulation tools and the application expertise of the users. He is constantly looking for solutions that address the innovation needs of electrical engineers. Since the recent acquisition of Cedrat by Altair, he manages the promotion of electromagnetic applications, electrical engineering and e-Mobility.

Latest posts by Vincent Marché (see all)

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• Computing Capacitances Matrix with Flux PEEC – Power Module Example - January 16, 2018

Rotating electrical machine designers are looking for to design high-reliability, minimum power losses, maximum power, maximum torque and low mechanical resonance vibration and noise motor. To meet the needs of electrical machine designers, Flux team 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.

Fig.1 3D modeling and schematic of classical / skew synchronous machine geometry in Flux

Cogging torque analysis with Flux

Several 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.

Fig.2 Cogging torque.

Fig. 3  Cogging torque vs rotor position.

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. 4  Cogging torque vs rotor position

Table I: Peak value of the cogging torque:

Without Skew      With Skew

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

Skew angle effect

As 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.5  Isolvalues of flux density at no-load

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

Back electro-motive force analysis (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.

Fig.7  Isovalues of flux density at no-load computed in Flux 3D

Fig.8   BAck EMF vs time analysis in Flux

Table II: Amplitude of back EMF fundamental:

Skew      3D with Skew

Back EMF fundamental           11.82             11.43

Torque and current

In 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
electrical circuit implemented in Flux environment (see Fig.9).

Fig.9   Electrical circuit in Flux

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

Fig. 10 & 11   Current & torque comparison

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

Conclusion

Results 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.

Learn more about Flux finite element electromagnetic analysis