Utilisation of Finite Element Analysis Force Calculations Method

180 160 140 120 100

60 40 20 0

Figure 5.22: Comparison of force calculation method

There are two methods available for calculating forces in an axisymmetirc simulation, the Maxwell stress tensor used in section 4.3.1 of the VHM Chapter and Lorenz's force, given in the first part of Equation (3.17) in Chapter 3. Figure 5.22 shows a comparison of the two methods for calculating the axial force. The Lorenz's force, whereby the product of current density and flux density is integrated over the coil area, gives the smoother result and is hence the preferred method.

In this section the single coil FEA simulation of Section 5.2 is used and all the forces are therefore per coil.

- B x J

55 60 65 70 75 80 85 90 95 100

position (mm)

55 60 65 70 75 80 85 90 95 100

position (mm)

N. J. Baker Chapter 5: The Air-Cored Tubular Machine 5.4.1.2 Normal / Radial Force radial force

id 0

o o radial force

id 0

-100

-150

----- 10 Amps

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30 40 50 60 70 80 90 100 110 120

position (mm)

-100

-150

-200

30 40 50 60 70 80 90 100 110 120

position (mm)

Figure 5.23: Calculated radial force

Figure 5.23 shows the variation of radial force over two pole pitches for a variety of coil currents. The maximum, which occurs as the coil passes above the centre point of the magnet, increases linearly with current with 10 Amps reacting 190 N. Inspection of the maxima demonstrate that its value is dependent on the current direction. This may be explained by inspection of flux plots.

Figure 5.24 shows the detailed flux plot of a coil above the centre line of a magnet section. In Figure 5.24A there is no current and the natural behaviour of the flux due to the presence of a magnet is observed. In Figure 5.24B a 20 Amp current is present in the coil, flowing in the direction that enforces the mmf of the magnet. In Figure 5.24C the current is in the opposite direction such that its mmf opposes that of the magnet. As the distance from the magnet surface increases, the major contributor of mmf switches from the magnet to the coil and the flux pattern alters accordingly. The radial force is a product of the current density and the axial flux density, the effect of current opposing the mmf of the magnets is to align the flux lines in the axial direction and so produce a greater force.

Figure 5.24: Flux plots for (A) 0, (B) +20 and (C)-20 Amp current aligned with centre of

5.4.1.3 Axial Force

Figure 5.25: calculated axial force

The axial force of Figure 5.25 is a similar pattern to that of the radial, but half a pole out of phase, such that the maximum occurs as the coil passes over the centre of the steel. Again, the magnitude of the force is dependent on the direction of the current, with the maxima at 10 Amps being 216 N or 173 N.

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