Comparison of Machine Topologies

6.7.1.1 Introduction

When selecting an electrical machine for this application, the key criteria will be either the performance per kg, m3 or pound sterling. Using the relationships derived in previous Chapters and, for the VHM only, the lubrication system, it is possible to compare the two available topologies of machine for a given application. Nominally, the case study machine is required to extract 100 kW when travelling at 1ms-1 with a current density of 1 x 106 A m.

The cost estimate is very crude and based on the price of materials as bought for the prototypes. There would clearly be economies of scale associated with larger material orders, but the relative price between the two machines would likely remain the same. For example, at the time of writing, as a raw material copper is worth $1.6 US per kg, around a third the value used here. Furthermore, no attempt has been made to gauge the relative manufacturing costs, nor has any account been made for external load on translator.

Table 6-2: Material prices used in cost analysis

Steel bar (£/kg)

0.7

Nd-Fe-B magnets (£/kg)

27

Stainless steel bar (£/kg)

4.4

Copper (£/kg)

2.6

Laminated Steel (£/kg)

2.6

Plastics (£/kg)

Using the six module 100 kW machine described earlier in Section 6.5.3.1, combined with the 0.0728 m square hydrostatic bearings recommended in section 6.5.3.9 and the support method of section 6.5.4, the parameters of an entire VHM can be calculated. The proceeding paragraphs give details of the selection and calculation of the machine dimensions.

The stator back iron is equated to the height of the rib ('d' in Figure 6.29) above the pole face and 5 cm between pole faces where no force is felt and its only purpose is to carry magetic flux. A 1 cm gap is assumed between the upward support and the laminations, dimension 'a' in Figure 6.29, which is substituted into Equation (6.27) to reveal that a bar of 0.05 m width and 0.14 m height will have a maximum deflection of 0.05 mm when subjected to a distributed load summing to the 36 kN of magnetic force felt by the stator. The deflection of a bar of these dimensions is hence such that the 1 mm airgap will close to 0.95 mm in the centre of the machine. The upward support will have a compression of an order of magnitude below this, as calculated by (6.29) and thus these values are appropriate to maintain the airgap.

The hydrostatic bearings are modelled as solid steel 2 cm high blocks, and the track is a 0.072 m wide 0.01 m thick steel bar clamped on each side of the translator.

For a 2 m peak to peak stroke, the translator requires a length of 5.7 m with the other dimensions given in Table 6-4 below. The parameters of the resulting machine are given in Table 6-4 and Table 6-5.

Table 6-3: Mass of 100 kW VHM

Magnets

Copper

Stator and translator laminations

Total VHM unsupported

Support/lubrication steel

Total

67 kg

780 kg

5.6 tonnes

6.4 tonnes

0.9 tonnes

7.3 tonnes

Table 6-4: Size of 100 kW VHM

Stator length

Stator width

Stator breadth

Stator volume

1.72 m

1.2 m

0.4 m

0.8 m3

Table 6-5: Cost of lGGkw VHM

Magnets

Copper

Steel

Laminated steel

Total

£1 800

£2 100

£630

£14 600

£19 100

6.7.1.3 Tubular machine

For the tubular machine, no relationships have been defined for the size of the support and lubrication systems. The mass is likely to be dominated by the translator and coils, however, which have been defined. A tubular translator has been designed consisting of 0.2 m diameter 50 mm thickness magnets mounted alternately with steel pieces of the same dimensions on a stainless steel shaft of 80 mm diameter. The stator consists of a 4 mm thick internal support for the coils mounted concentric to the translator with an airgap of a 1 mm. The magnetic gap of the machine is hence 5 mm. The external support of the coil is a tube of 20 mm wall thickness and the inter-coil spacers are nominally set to 10 % of the copper volume. All the plastic components are assumed to have a density of 3600 kg/m3. Table 6-6-Table 6-8 describe the resulting machine.

Table 6-6: Mass of 100 kW tubular machine

Magnets

Copper

Steel

Stainless Steel

Plastics

Total

1.7 tonnes

1.1 tonnes

1.6 tonnes

130 kg

240 kg

4.6 tonnes

Table 6-7: Size of 100 kW tubular machine

Stator height

Stator diameter

Stator volume

1.4 m

0.58 m

0.4 m3

Table 6-8: Cost of 100 kW tubular machine

Magnets

Copper

Steel

Stainless Steel

Plastics

Total

£45 900

£2 900

£1 600

£565

£170

£50 200

6.7.1.4 Comparison

Table 6-9: Comparison of VHM and tubular machines

Force

Power

kN/kg

kN/m3

N/£

kW/kg

kW/m3

£/W

VHM

13.7

125

5.2

13.7

125

190

Tubular

21.7

250

2

21.7

250

502

Table 6-9 allows a direct comparison of the two 100 kW machines in terms of performance. The VHM is less than half the price of the tubular machine, yet requires twice the volume to house the stator. The VHM machine is likely to be the heavier of the two machines. Figure 6.30 and Figure 6.31 show a comparison of the dimensions of the two machines.

Figure 6.30: Side view comparisons of both 100 kW machines
Figure 6.31: Rendered view of both 100 kW machines

Whilst the conclusions regarding total mass and cost should be taken only as guidelines, comparison of the mass of copper and magnet material used in each machines is more credible. The tubular machine requires about 25 times the mass of magnet material and 50 % more copper.

The total mass of the VHM is based on simplified theory of both lubrication and structural support to counteract the strong magnetic forces, whereas the tubular machine accounts for neither. Both machines will require additional support in order to react force against the translator in the direction of it motion.

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