Preliminary design

Table 3.1: Cost of active material per unit weight

Material Cost (EUR/kg)

NdFeB permanent magnets (sintered) 500

Copper 6

Iron 3

The cost of permanent magnets appearing in Table 3.1 is that of fully processed, corrosion coated with specific dimensions and already magnetized permanent magnets for the developed prototype (not mass production).

With the constraint of not exceeding a maximum flux density of about 1.8T in both the

tooth and yoke of the stator.

The permeance coefficient PC is set to the typical value of 5. The leakage flux coefficient f_LKG is assumed to be 0.85. The current density J_c of the windings is approximated to 5 A/mm². The number of strands equals 2. Every variable of the four-mentioned optimizing variables are dealt separately and iteratively with the other three variables set to a constant value. The flow chart of Figure 3.2 demonstrates the optimization process. In the first trial, EMF per turn E_pt is taken as the optimizing variable, l_c is set to 2 layers, K_ts is set to 0.5 and B_yoke is set to 1.5T. Figure 3.3 shows the efficiency, cost of active material, tooth flux density and total machine diameter as function of E_pt. It can be concluded that 0.2V/turn gives the highest efficiency of about 83.1%, active material cost of about 1180€, tooth flux density of about 0.92T and a total machine diameter of about 0.565m.

AA

Figure 3.2: Optimization design flow chart START

Given Specifications

Choice of PM Conducting and Insulating Materials

Assumption of Design Parameters B_r,J_c, f_LKG and PC

Design Process: Magnetic Circuit, Electrical Circuit, Mechanical Design and (Thermal Design)

Performance Calculations

Is Performance

Satisfactory

?

Print Design Data Sheet

STOP

No

Modify Optimizing Parameter

Yes

Assumption of Optimizing Parameters E_pt,l_c,K_ts and B_yoke

0.1 0.2 0.3 0.4 0.5

0.82 0.825 0.83

Efficiency (%)

(a)

0.1 0.2 0.3 0.4 0.5

500 1000 1500 2000 2500 3000

Cost of Active Material (€)

(b)

PM: 500€/kg Copper: 6€/kg Iron: 3€/kg

0.1 0.2 0.3 0.4 0.5

0 0.5 1 1.5 2 2.5

EMF per Turn (V/turn)

Tooth Flux Density (T)

(c)

0.1 0.2 0.3 0.4 0.5

0.2 0.4 0.6 0.8 1 1.2

EMF per Turn (V/turn)

Total Diameter (m)

(d)

Figure 3.3: (a)Efficiency, (b)cost of active material, (c)tooth flux density and (d)total diameter as function of the EMF per turn E_pt with l_c=2 layers, K_ts=0.5 and

Byoke=1.5T

With E_pt set to its optimal value of 0.2V/turn the optimizing parameter, for the second trial, is the slot conductor layers l_c, with no changes on K_ts and B_yoke. Figure 3.4 shows the efficiency, cost of active material, tooth flux density and total diameter of the machine as function of l_c. It can be noted that 5 conductor layers per slot give the highest efficiency of about 83.8%, cost of active material of about 1161€, tooth flux density of about 2.13T (will be treated by the iteration of the next parameter) and a total diameter of about 0.28m.

1 2 3 4 5 6 7

0.8 0.81 0.82 0.83 0.84

Efficiency (%)

(a)

1 2 3 4 5 6 7

1150 1160 1170 1180 1190 1200 1210 1220

Cost of Active Material (€)

(b)

PM: 500€/kg Copper: 6€/kg Iron: 3€/kg

1 2 3 4 5 6 7

0 0.5 1 1.5 2 2.5 3 3.5

Slot Conductor Layers

Tooth Flux Density (T)

(c)

1 2 3 4 5 6 7

0.2 0.4 0.6 0.8 1 1.2

Slot Conductor Layers

Total Diameter (m)

(d)

Figure 3.4: (a)Efficiency, (b)cost of active material, (c)tooth flux density and (d)total diameter as function of slot conductor layers l_c with E_pt=0.2V/turn, K_ts=0.5 and

Byoke=1.5T

In the third trial, the ratio between the width of the tooth to that of the slot K_ts is the optimizing parameter. It might vary from 0.1 up to 1. Figure 3.5 shows the efficiency, cost of active material, tooth flux density and the total diameter of the machine as function of the ratio between the width of the tooth to that of the slot. The value of the highest efficiency should not be chosen as the stator tooth flux density is saturated with 2T. A value of K_ts=0.6 gives an efficiency of about 83.7%, cost of active material of about 1163€, tooth flux density of about 1.78T and a total diameter of about 0.296m.

0 0.2 0.4 0.6 0.8 1

0.82 0.825 0.83 0.835 0.84

Efficiency (%)

(a)

0 0.2 0.4 0.6 0.8 1

1150 1155 1160 1165 1170 1175

Cost of Active Material (€)

(b)

PM: 500€/kg Copper: 6€/kg Iron: 3€/kg

0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10 12

Tooth Width/Slot Width

Tooth Flux Density (T)

(c)

0 0.2 0.4 0.6 0.8 1

0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36

Tooth Width/Slot Width

Total Diameter (m)

(d)

Figure 3.5: (a)Efficiency, (b)cost of active material, (c)tooth flux density and (d)total diameter as function of the ratio between the width of the tooth to that of the slot

Kts with E_pt=0.2V/turn, l_c=5 layers and B_yoke=1.5T

The variable parameter, in the fourth trial, is the stator yoke flux density B_yoke with the previously treated three parameters are set to the fixed optimizing values of Ept=0.2V/turn, l_c=5 layers and K_ts=0.6. Figure 3.6 shows the efficiency, cost of active material, tooth flux density and the total diameter of the machine as function of the stator yoke flux density. A stator yoke flux density of about 1.5T yields an efficiency of about 83.7%, cost of active material of about 1163€, a constant tooth flux density of about 1.78T and a total diameter of about 0.296m.

0 0.5 1 1.5 2

0.76 0.78 0.8 0.82 0.84

Efficiency (%)

(a)

0 0.5 1 1.5 2

1100 1200 1300 1400 1500 1600 1700

Cost of Active Material (€)

(b)

PM: 500€/kg Copper: 6€/kg Iron: 3€/kg

0 0.5 1 1.5 2

0.5 1 1.5 2 2.5 3

Stator Yoke Flux Density (T)

Tooth Flux Density (T)

(c)

0 0.5 1 1.5 2

0.2 0.4 0.6 0.8

Stator Yoke Flux Density (T)

Total Diameter (m)

(d)

Figure 3.6: (a)Efficiency, (b)cost of active material, (c)tooth flux density and (d)total diameter as function of the stator yoke flux density B_yoke with E_pt=0.2V/turn, l_c=5

layers and K_ts=0.6

The optimal design parameters of the machine resulted from the preliminary design that will be the input parameters to the finite element package:

Inner radius of the stator r_s= 119.1mm. Width of the slot W_slot=23.5mm.

Height of the slot h_slot=6.1mm. Width of the tooth W_tooth=14.1mm. Height of the stator yoke h_yoke=8.3mm.

Length of the permanent magnets in the direction of magnetization l_M=10mm .

Height of the permanent magnet h_M=6mm, (2 are used).

Active length of the machine l_stk=120mm. Air gap length g=1mm.

Outer radius of the machine r_o=148mm.

Table 3.2 shows the variation of the efficiency, cost of active material, tooth flux density and total diameter of the machine with the four successive trials.

Table 3.2: Efficiency η, cost of active material C_t, tooth flux density B_t and total diameter of the machine D_t resulting from the four successive trials

Trial No.

(Optimizing variables)

T1 (E_pt=0.2,l_c=2,

Kts=0.5,B_yoke= 1.5)

T2 (E_pt=0.2,l_c=5,

Kts=0.5, B_yoke= 1.5)

T3 (E_pt=0.2,l_c=5,

Kts=0.6, B_yoke= 1.5)

T4 (E_pt=0.2,l_c=5,

Kts=0.6, B_yoke= 1.5)

η _{0.831 0.838 0.837 0.837}

Ct(€) 1180 1161 1163 1163

Bt(T) 0.92 2.13 1.78 1.78

Dt(m) 0.565 0.28 0.296 0.296

Chapter 4

Im Dokument Design, Optimization, Construction and Test of Rare-Earth Permanent-Magnet Electrical Machines with New Topology for Wind Energy Applications (Seite 63-71)