Creating an application for machines with step skewing

Introduction

In a Flux Skew project, the type of skewing (i.e., continuous or step) of a machine is a property of the application.

How to create an application with step skewing

• Topology description: two approaches are available, namely the Simple (homogenous layers) method and the Advanced (layer by layer) method.
• The Simple (homogenous layers) description method is straightforward and requires only three parameters (accordingly with part (a) of Figure 1):
  • the Length unit allowing to choose the unit (or to create a new one) for the Layer thickness;
  • the Layer thickness;
  • the Rotation angle between adjacent layers, in degrees;
  • the Number of layers, or the axial discretization of the skewed machine after its 3D reconstruction (in post-processing).
    Note: This parameter also corresponds to the total number of linked 2D finite element problems solved by Flux Skew along the axial length of the machine during resolution, as discussed in the topic: What is Flux Skew?

• The Advanced (layer by layer) method is also available and allows the description of more complex topologies (V, W or zig-zag skewing, for instance). In this approach, the user must fill a table in which each line represents a skewed layer. Two parameters are required for each layer (accordingly with part (b) of Figure 1):
  • the Length unit allowing to choose the unit (or to create a new one) for the Layer thickness;
  • the Layer thickness;
  • the Layer rotation angle with respect to the previous one, in degrees.

Figure 1. Planar representation of the magnetic core (either the rotor or stator) of an electrical machine with step skewed magnets. The parameters required by Flux Skew to describe the topology of a machine with step skewing are highlighted: the Simple description is shown in (a), and the Advanced description in (b).

The remaining tabs of the application creation window are similar to their Flux 2D and Flux 3D counterparts and depend on the specific application chosen by the user.

Once the description of the application is completed, the user is ready to proceed with the 2D description of a rotating electric machine with step skewing in Flux Skew's environment.

Example of application

This example considers the modeling of a step-skewed permanent magnet synchronous machine (PMSM), both in Flux Skew and in Flux 3D.

To compare these modules and the results yielded by them, a three-phase, eight-pole PMSM is considered. Its three-phase winding is distributed between several stator slots, with one phase per slot. Moreover, its rotor (which contains the magnets) is step-skewed: its permanent magnets are distributed into three skewed layers along the axial direction. Each layer has an axial length equal to 125 mm, and the rotation angle between them is 10°.

Figure 2 displays a first modeling approach for this device based on a transient magnetic simulation performed in Flux Skew. It is worth remembering that, in Flux Skew, the whole project description is performed in 2D, as discussed in the section What is Flux Skew?.

Figure 2. The 2D pre-processing of the PMSM in the Flux Skew module (a) and the 3D post-processing representation of its step-skewed rotor, also in the Flux Skew (b). The permanent magnets are displayed in blue.

A simulation representing the same PMSM with step-skewed rotor has been performed in Flux 3D as well.

A first comparison between the results obtained with Flux 3D and Flux Skew is highlighted in Figure 3, which compares the machine torque and the flux linked to a phase winding yielded by both approaches. The values in the plots were evaluated with the help of sensors and I/O parameters. It may be remarked that the results computed with Flux Skew are higher and overestimate their Flux 3D counterparts.

Figure 3. The machine torque and the flux linked to a phase winding as functions of the rotor angular position, evaluated both with Flux 3D and Flux Skew.

This behavior is not really surprising, since the Flux 3D project takes into account the flux leakage at the extremities of the machine. This effect is not taken into account in Flux Skew, since it solves a series of linked 2D finite element problems instead, as discussed in the section What is Flux Skew?.

Another comparison between the results computed by Flux 3D and Flux Skew for the machine considered in this example is provided in Figure 4. In this figure, the graph displays the magnetic flux density along a path going from the front of the machine (z = 0 mm) to its end (z = 375 mm) and passing through the center of a stator tooth (the red line shown in part (a) of Figure 4).

Figure 4. Comparison between magnetic flux density results yielded by Flux 3D and Flux Skew. The graph in (b) displays the magnetic flux density values evaluated along the red line shown in (a).

Figure 4 shows that Flux Skew evaluates a constant magnetic flux density in each layer of the step-skewed machine along that specific path in the stator. This result follows once again from the aforementioned multi-2D approach implemented in Flux Skew, that describes the step-skewed machine problem in terms of a series of linked 2D finite element simulations. On the other hand, Flux 3D evaluates a more realistic magnetic flux density that varies continuously along the machine's axial length. Both solutions are in good agreement, especially at axial positions corresponding to the center of a layer of the Flux Skew project.

It follows from this example that Flux Skew provides results that are in overall good agreement with Flux 3D. This is achieved with a simplified project description and shortened computation times. Even so, the user should always keep in mind the underlying approximations in a Flux Skew simulation, notably while post-processing the results or when comparing them with Flux 3D or with the real device.