Electromagnetic CAD systems

The use of the finite element technique for numerically solving the electromagnetic field equations is nowadays accomplished by fast, powerful and general-purpose software packages. Most of those packages are developed to solve general electro-magnetic systems rather than problem oriented programs. These systems are known as electromagnetic CAD systems (CAD being computer-aided design, a terminology that stresses the importance of these systems in the design). Electromagnetic field simulators or simply finite element packages are other popular ways of referring to these systems.

Most of the CAD systems for the numerical analysis of electromagnetic problems are based on the finite element method. The method has proved to be flexible, reliable and effective.

The finite element packages are powerful tools in research, development and design. By using only a personal computer, it is possible to analyse a number of dif-ferent geometries and operating conditions, without the need of building a physical prototype. Also, the numerical simulation provides, in most cases, reliable and accu-rate information about the device’s behaviour irrespective of geometric complexity and material non-linearity. For example, in permanent magnet motors, the FEM can analyse accurately various shapes and materials. There is no need to calculate reluc-tances, leakage factors or operating point on the recoil line. The PM demagnetisation curve is input to the FEM package, which can calculate the variation of magnetic flux density throughout the motor. Moreover, the ability to calculate accurately the arma-ture reaction effect and torque variation with rotor position is an important advantage of the FEM over the analytical approach.

Finite element design methods – availability of suitable data 105 9.3.1 General FEM steps

Generally most FEM packages share common steps in constructing electromagnetic models. These steps are as follows:

1. Pre-processing. In the pre-processing stage, the device under consideration needs to be drawn first. It could be drawn by the FEM package itself or it could be imported from other drawing packages. Only active components of the device need be drawn. An active component means one that is part of the magnetic circuit. The actual units of length need to be set out. Material properties need to be assigned to each component.

Usually a library of various material properties is available to the designer to choose from. The excitation in terms of current in coils in the circuit, number of turns, or permanent magnet nature and direction must be defined at this stage.

After that, the defined geometry will be meshed. Usually there is an automatic mesh generator which generates a uniform mesh for the whole geometry. The user may intervene to refine the mesh in the area of interest to increase the accuracy of the solution. Boundary conditions need to be set at this stage in ways which assist solution and minimise the model size.

2. Solving. In this stage the FEM programme starts to automatically solve the for-mulated field equations implicit in the pre-processing stage. The user needs to choose the appropriate solver for a given design. The solver will be chosen accord-ing to the required analysis. There are three main solver types usually used in electromagnetic design.

(a) Magnetostatics: This is used in analysing the magnetic field in and around specified current distributions or permanent magnets in the pres-ence of magnetic materials, which may be linear or non-linear, isotropic or anisotropic. The solved field values are time independent or are a snap-shot in time-varying fields.

(b) Time harmonics: This is applicable for devices with sinusoidal excitation and eddy currents, taking skin effects into account. The source and field are assumed to be time harmonic at one specified frequency. Complex phasors are used to represent them.

(c) Transient solver: This is used to analyse devices with arbitrary shaped cur-rent and voltage responses, or to model the effect of transient excitation or motion. It finds the time-varying magnetic field in the presence of material which may be magnetically linear or non-linear.

3. Post-processing. The solver output may be processed to find the required param-eters. The user may manipulate the solution to calculate, for example, torque, inductance, etc. Most FEM packages offer graphical representation of the solu-tion, where flux plots or flux density values may be plotted and graduations of colour produced according to the flux levels in different parts of the device.

Based on the steps mentioned before, most of the general purpose FEM packages could be tailored for design and analysis of specific electromagnetic devices like motors and actuators.

AutoCAD

Figure 9.4 CAD translated to FEM damain

Below is given an example of modelling a permanent magnet machine which explores the modelling steps mentioned before (Figure 9.4).

1. Pre-processing

• The model geometry could be drawn using AutoCAD and then exported to an FEM package, or it could be drawn directly in the FEM package using its drawing facilities as shown below:

• The magnetic materials assigned to each component of the machine, for exam-ple the stator laminations, have different magnetic material to that of the rotor.

Finite element design methods – availability of suitable data 107

–1E+06 –800000 –600000 –400000 –200000 0 H (A/m) H (A/m)

Figure 9.5 Preparation for FEM modelling

Permanent magnet material and its magnetisation direction are set in. The stator winding details and its excitation is also set in (Figure 9.5).

• An automatic mesh generator could be initiated to uniformly mesh the whole model. Refined mesh may be applied in the area of interest. Here, for example, a refined mesh is used near the pole tips to accurately calculate leakage flux (Figure 9.6).

2. Solving

The FEM package will solve the model defined in the previous step automatically.

The user needs to assign the proper solver. In this example, the magnetostatic solver can be used, as flux distribution and magnetisation level is required (Figure 9.5).

Automatic mesh generation

Mesh before refinement Mesh after refinement

Figure 9.6 Mesh refinement

3. Post-processing

The solved model result can be accessed in this stage. The flux and flux density values may be plotted over the whole area of the model or in particular parts.

The saturation effects may be examined. The parameters of the machine, like inductance, flux linkage or the torque, could be calculated for different saturation levels.