CEDRAT News - N 66 - June 2014

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Cogging torque computation and mesh for non-radial electrical motors in Flux. Sylvain Perez - CEDRAT.All electrical motor designers know that the computation of cogging torque is a tricky task, particularly in 3D. Indeed, the amplitude of this variable is almost the same as numerical noise. In most cases, conventional mesh methodology is not sufficient and specific methodology must be used. At CEDRAT, thanks to its experience, the application team has developed methodologies to successfully compute cogging torque in most cases. This article presents a specific mesh methodology to compute cogging torque for 3D non-radial electrical motors.

Specific mesh methodology for non-extruded 3D electrical motor To explain this mesh methodology, the 3D motor presented is an Axial Flux Motor (Fig. 1). This kind of motor is generally used in environments involving compact lengths, like elevator systems.

The specific mesh methodology is based on Flux 3D mesh tools and some physical considerations. We will look at the various steps to follow. The first one is the starting point, whether, a conventional mesh imposed by Mesh Point Discretisation. Then, we will see how to use the Flux tool for analysing mesh quality. Afterwards, on the basis of analysis and some physics angles, we will apply a new mesh imposed by Mesh Line Discretisation with relaxation. Finally, we will compare results for the different meshes in terms of Accuracy/Computation time.

Starting with a conventional mesh imposed by Mesh Point Discretization

The conventional mesh method is to use discretisation imposed by point, i.e.: imposing mesh specifications at each point of the geometry. With Flux, we currently use this mesh method coupled with aided mesh options. In this case, we obtained the mesh presented in Fig. 2. From this conventional mesh with first-order elements, computation results are given in Fig. 3.

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Fig. 3 presents three different calculations for cogging torque evaluation. All calculations are based on a virtual works method but the contours under consideration are different. The first calculation considers the contour of the sliding cylinder (blue curve), the second the contour of the rotor and magnets (magenta curve) and the third the contour of the stator (green curve). All results are bad, cogging torque is not centred 0 N.m. However, these results give us some information. We can see that cogging torque evaluations considering stator contour are the most accurate. This suggests that mesh is more appropriate surrounding the stator than the rotor. For further information, we need to use dedicated tools to perform mesh analysis.

Analysis of mesh defect with Flux tools

To identify where the mesh can be improved, Flux offers dedicated tools based on error criterion calculation. In this example, cogging torque is dependent on a derivate of co-energy that means selecting the magnetic co-energy gradient as an error criterion (Fig. 4).We display error criteria on each volume element of magnets (Fig. 5) and of the sliding cylinder (Fig. 6). The greater the number of red spheres, the bigger the criterion error. Another important point to consider is the density of spheres which may also offer a good indicator.

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DD torque [ROTOR] (N.m) 4 TORQUE_ROT-4 TORQUE_STAT

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We note that the criterion error display on the sliding cylinder indicates that bad mesh elements are only in the airgap below the magnets. That tells us that shadow should be higher and that face relaxation is too fast. The criterion error display on magnets is less clear to analyse, the red sphere indicates that volume relaxation is too high and should be reduced. We also note high sphere density (not necessarily red ones) along magnet edges which suggests the mesh on edges should be refined. This information allows us defining a new efficient mesh.

Define a new efficient mesh based on Mesh Line Discretization

In the previous paragraph we highlighted the need to reduce relaxation and increase shadow. Based on CEDRAT application team knowledge and confirmed by the previous mesh analysis, we can conclude that for volumes bordering the air gap (magnets and stator tooth), mesh on edges has to be refined. Thin mesh on edges seems to be explained by the fact that where the magnetic flux density changes quickly, mesh has to be refined in order to precisely compute magnetic field paths. Accordingly, the mesh method consists of finely mesh edges of volumes next to the air gap (Fig. 7). Results of this second mesh with first-order elements are given by Fig. 8.

Cogging torque is centred on 0 N.m whatever the contour considers. Even though there are some differences, the 3 cogging torque calculations are now compliant. We can consider that the second mesh is efficient.

Final comparison

It is important to get a good precision, bearing in mind that a good Precision/Computation time trade-off is the objective. At this time, we have not considered computation time, this paragraph compares results and time computation for each mesh described previously with first-order elements and with second-order elements (Tab.1, Fig. 9 and Fig. 10).

According to Tab.1, Fig. 9 and Fig. 10, the new mesh with first-order elements offers the best compromise between accuracy and computation time.

ConclusionCogging torque computation has always been a complex exercise, especially in 3D. Nowadays, Flux tools combined with CEDRATs experience in this domain make life easier. In this article we have reviewed a methodology to obtain efficient mesh for your device to rapidly produce a reliable estimate of cogging torque.

In a next issue we are proud to present you a new article "Cogging torque computation and mesh for radial electrical motors".

Method Mesh element order

Number of nodes

Number of volumic elements

Computation time

Classical mesh

1st 8685 38270 2

2nd 59556 38270 10

New mesh

1st 36444 174892 8

2nd 258699 174982 72

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DD torque [ROTOR] (N.m) 4 TORQUE_ROT-4 TORQUE_STAT

DD torque [ROTOR] (N.m) 4 TORQUE_ROT-4 TORQUE_STAT

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DD torque [ROTOR] (N.m) 4 TORQUE_ROT-4 TORQUE_STAT

DD torque [ROTOR] (N.m) 4 TORQUE_ROT-4 TORQUE_STAT