# Electromagnetic and electrostatic devices (Electrical Machine) Part 3

By

## Electromagnetic shielding

Electromagnetic compatibility (EMC) is becoming more and more important in the design of electromagnetic devices. The product must satisfy international and national regulations and standards. The developer of a product has to be aware of two items: the generation of electromagnetic waves by his product, and the influence from outside Fields to his product. This topic will discuss the second issue, the problem of electromagnetic shielding. Magnetic fields can be shielded by applying two phenomena:

• high permeable material and/or

• induced currents.

Both problems will be discussed here. Studying shielding problems with the FEM analysis raises the difficulty of a sufficiently fine discretisation of the considered domain. The skin depth (penetration depth) of magnetic fields into high permeable or conducting material plays an important role in the pre-processing of the FEM model. The choice for 2D or 3D modelling will not be discussed, as this decision is based mainly on the model geometry.

Depending on the type of shielding (permeable material/eddy currents), the penetration depth of the field into the structural elements must be estimated beforehand. The estimation of the penetration depth can be performed by:

with the permeabilityconductivityand the angular frequencyIf the penetration depth can be discretised sufficiently finely to allow a potential variation that approximates the exponential change of the field, the full structure can be modelled. Practically, this is the case if at least 3 first-order elements can be defined in the skin depth. The best choice is a FEM analysis using mesh refinement. However, sometimes it is impossible to discretise the model finely enough to cover large extensions of the modelling domain. For instance, in the case of a transformer shielding, the model dimensions are in the range of metres, whereas the dimensions of shielding walls are in millimetres. In this case, special formulations may be applied, like thin-iron-plate elements or impedance-boundary conditions.

### Thin iron plate elements

If the thickness of an iron wall is too fine to be discretised with finite elements, thin iron plate elements provide a way to model such structures. In 2D these are line elements and in 3D they are surface elements (triangular-shaped using tetrahedrons as the 3D finite elements). With such elements a material characteristic and a thickness is associated. Within the thin-plate element there is no component of magnetic flux density perpendicular to the plate. In reality this will be the case if a low permeable material such as air surrounds a high permeable material such as iron. For the time-varying field analysis, the material is assumed to be non-conducting.

The magnetic shielding of a monitor serves as an example. The analysis is performed to compare measurements taken in a test rig. This test installation employs a set of Helmholtz coils to generate a homogeneous field of defined direction in which the monitor is placed (Fig. 10.17).

Fig. 10.17. Monitor located inside a set of 6 coils generating a homogeneous field of defined direction.

The shape and position of the set of coils requires a 3D analysis. The extent of the volume span by the set of coils is 1 metre. The surrounding air is modelled up to 6 metres. The iron-plates are modelling the surface of the monitor housing. They are assumed to have a thickness of 3 mm and are surrounded by air. A magnetostatic 3D analysis is performed. The Helmholtz coils are excited with currents producing a homogeneous field directed in parallel to the view-axis into the screen of the monitor. This is the worst case, as the screen area cannot be shielded.

Local field quantities outside the thin plates can be derived in the usual way using the form functions of the element types used. Field quantities inside the thin plate elements require a special post-processing and the results may be viewed using a surface mapping technique.

No field component perpendicular to the plate is considered inside the element. This could introduce large errors if the thickness of the material is in the range of the other dimensions of the plate, or if the surrounding material’s permeability is of similar value.

Fig. 10.18. Magnitude of the flux density inside the monitor nearby to the shielding.

### Impedance boundary condition

Whereas the thin-plate elements can be used only for non-conducting, highly permeable material, impedance boundary conditions may be used to model conductors with a small skin depth. They can be applied only for time-harmonic or transient problems.

The idea is to provide a boundary condition specifying the ratio of the electric to the magnetic field, at a surface, to be equal to a complex number. It is assumed that the actual distribution of the field inside the material, which is replaced by this boundary, is not of interest. Such boundary conditions may be used when the skin depth is relatively small compared to the size of the conductor.

The value of the impedance to replace the conductor can be estimated by:

withthe conductivity of the conductor andthe skin depth estimated with (10.33). This can be performed automatically by the FEM program, if implemented, or can be provided by the user.

Local field quantities inside the model can be derived in the usual way by using the form functions of the element types used. Field quantities inside the replaced conductor require special post-processing and the results may be viewed using a surface mapping technique. It is possible to compute the ohmic losses in the replaced conductor as well.

## Permanent magnet mini-motors

The design of mini motors requires the use of advanced three-dimensional field analysis methods to obtain the field distribution and subsequently the elements of the equivalent circuit and the torque.

Very small motors based on the electromagnetic principle are excited by high-energy rare earth permanent material such as NdFeB. The overall dimensions of such motor devices are found in a range of some millimetres.

### 4-pole motor with block shaped magnets

The studied motor is from the axial flux type, equipped with an etched planar double layer winding in a double stator system (Fig. 10.19). In order to avoid cogging torques an air gap winding is used.

Fig. 10.19. Electromagnetic mini motor with 3D finite element model and armature winding layout.

In this type of application, the supply source is an essential part of the system. Due to the non-linearities of the ferromagnetic parts of the machine, the link with the time pattern of the supply voltage cannot be simulated using superposition. The motor is operated as a brushless DC motor. Constant DC currents are switched to the armature winding in the stator according to the signals of a position-sensing system equipped with hall sensors. The rotor is constructed with NdFeB permanent magnet blocks of the dimension 2x2x2 mm. The use of high-energy permanent magnet material can lead to significantly improved efficiency and performance of small electrical machines. The high remanence and coercivity at room temperature makes this material particularly attractive for this type of machine. However, the sensitivity of the coercivity of NdFeB to high temperatures calls for increased attention to the thermal aspects of a design. Integrated designs using NdFeB magnets are cost-effective for fractional and sub-fractional horse power motors.

In the design stage, the target is to obtain reliable results predicting the operational behaviour of this device. Macroscopic parameters, reactances and reluctances, describe the technical physical properties of the machine. Due to the presence of ferromagnetic materials, the calculations have to account for the non-linearities.

To extract the parameters for a simplified equivalent circuit, the inductance is found from the stored field energy after replacing the permanent magnets by air:

The torque is found from the virtual work:

The evaluation of the torque as a function of the rotor position is performed by a sequential analysis. Once the device-dependent parameters are determined, the equivalent circuit is modelled and in combination with the characteristic values of the supplying energy source (Fig. 10.20), the overall system is modelled, simulated and analysed.

The computed flux density distribution (Fig. 10.21) shows that the ferromagnetic material of this design is not saturated. A motor construction with less material could be designed in a following design approach.

Fig. 10.20. Switching scheme for the stator winding currents of phase 1 and 2.

Fig. 10.21. Magnetic flux density at no-load operation.

### Mini disc-type motor

The motor in this example is an axial field disc-type motor excited by permanent magnets. The outer diameter is about 45 mm, axial length about 15 mm (Fig. 10.22). The stator back-iron consists of two discs of ferromagnetic material. The armature winding is placed on the two stator sides.

The required torque recommends a multi-layer winding in order to realise a sufficiently high current layer. Therefore, each winding consists of four layers. On each stator side, eight windings are installed and connected to form two phases. The rotor consists of a thin disc constructed with a sintered NdFeB material magnetised in the axial direction in a multipole arrangement (Fig. 10.23).

Fig. 10.22. Main dimensions of the mini disc-type motor.

Fig. 10.23. Three-dimensional finite element model of the disc-type motor.

The supplying current source operates in the same way as introduced for the permanent motor (Fig. 10.19). To compute the induced voltage,the flux generated by the magnets and coupled with one winding, which is not carrying current, is computed by a sequential approach as a function of the rotor position (Fig. 10.24). The torque can be computed for each instant in time by integrating it along the current-carrying conductors of the winding (Fig. 10.25) and superimposing the torque generated by the single winding phases.

Fig. 10.24. Computed voltage induced in one phase at a rotor speed of 1000 rpm.

Fig. 10.25. Torque characteristics for the disc-type motor (winding coils operated with 0.5 A).