### Vincent Marché

#### Latest posts by Vincent Marché (see all)

- Thermal Analysis of Electrical Equipment – Different Methods Review - February 1, 2018
- Coupling Flux FEA to AcuSolve CFD solution –Thermal Analysis of Electrical Equipment - February 6, 2018
- 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.

**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.

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.

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).

**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.

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. 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.

**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