Electric machine
An electric machine comprise a first carrier having an array of electromagnetic elements and a second carrier having electromagnetic elements defining magnetic poles, the second carrier being arranged to move relative to the first carrier. An airgap is provided between the first carrier and the second carrier. The electromagnetic elements of the first carrier include posts, with slots between the posts, one or more electric conductors in each slot, the posts of the first carrier having a post height in mm. The first carrier and the second carrier together define a size of the electric machine. The magnetic poles having a pole pitch in mm. The size of the motor, pole pitch and post height are selected to fall within a region in a space defined by size, pole pitch and post height that provides a benefit in terms of force or torque per weight per excitation level.
1. An electric machine comprising:
a first carrier having an array of electromagnetic elements;
a second carrier having electromagnetic elements defining magnetic poles, the electromagnetic elements of the second carrier comprising permanent magnets, the second carrier being arranged to move relative to the first carrier;
an airgap between the first carrier and the second carrier;
the electromagnetic elements of the first carrier including posts having a post height in mm, with slots between the posts, the slots having one or more electric conductors in each slot;
the second carrier comprising posts and at least a first retaining element for the electromagnetic elements defining magnetic poles;
the permanent magnets each having a depth and a width, the depth having a ratio relative to the width greater than 2:1;
the first carrier and the second carrier together defining a size of the electric machine;
the magnetic poles having a pole pitch S in mm; and
the size of the electric machine, pole pitch and post height being selected to fall within a region in a space defined by size, pole pitch and post height, the region being defined by either
1) a first union of:
a) a first surface defined by a first set of inequalities for a first size of electric machine;
b) a second surface defined by a second set of inequalities for a second size of electric machine; and
c) a set defined as containing all points lying on line segments having a first end point on the first surface and a second end point on the second surface;
the first set of inequalities and the second set of inequalities being respectively sets of inequalities A and B, or B and C, or C and D, in which the set of inequalities A is for a size of 25 mm, the set of inequalities B is for a size of 50 mm, the set of inequalities C is for a size of 100 mm, the set of inequalities D is for a size of 200 mm; or
2) a second union of a surface as defined by set of inequalities D and a corresponding set of all points with size greater than the surface but with pole pitch and post height corresponding to points within the surface;
where
A is selected from the group of sets of inequalities consisting of:
Set A1:
Post Height>
−1.070 * S + 2.002
for
0.572 < S < 1.189
1.175 * S + −0.667
for
1.189 < S < 2.269
13.502 * S − 28.637
for
2.269 < S < 2.500
Post Height<
−5.898 * S + 19.863
for
1.970 < S < 2.500
0.229 * S + 7.794
for
1.349 < S < 1.970
7.607 * S − 2.160
for
0.723 < S < 1.349
11.430 * S − 4.924
for
0.572 < S < 0.723
Set A2:
Post Height>
−1.340 * S + 2.305
for
0.619 < S < 1.120
1.100 * S − 0.429
for
1.120 < S < 2.074
3.830 * S − 6.082
for
2.074 < S < 2.269
Post Height<
−69.510 * S + 160.318
for
2.222 < S < 2.269
−3.430 * S + 13.492
for
1.667 < S < 2.222
2.830 * S + 3.056
for
1.133 < S < 1.667
8.650 * S − 3.545
for
0.619 < S < 1.133
Set A3:
Post Height>
−4.160 * S + 5.032
for
0.723 < S < 0.967
0.839 * S + 0.198
for
0.967 < S < 1.692
2.713 * S − 2.973
for
1.692 < S < 1.939
Post Height<
−53.233 * S + 105.506
for
1.879 < S < 1.939
−1.406 * S + 8.122
for
1.465 < S < 1.879
3.898 * S + 0.353
for
1.035 < S < 1.465
7.535 * S − 3.412
for
0.723 < S < 1.035
B is selected from the group of sets of inequalities consisting of:
Set B1:
Post Height>
0.254 * S + 0.462
for
0.319 < S < 3.667
2.665 * S + −8.380
for
3.667 < S < 5.000
Post Height<
−18.282 * S + 96.357
for
4.500 < S < 5.000
−4.663 * S + 35.071
for
2.738 < S < 4.500
2.585 * S + 15.227
for
1.447 < S < 2.738
16.013 * S − 4.204
for
0.319 < S < 1.447
Set B2:
Post Height>
0.269 * S + 0.456
for
0.380 < S < 3.016
3.051 * S − 7.936
for
3.016 < S < 4.167
Post Height<
−14.766 * S + 66.309
for
3.667 < S < 4.167
−3.952 * S + 26.654
for
2.315 < S < 3.667
3.108 * S + 10.310
for
1.278 < S < 2.315
14.542 * S − 4.303
for
0.389 < S < 1.278
88.444 * S − 33.051
for
0.380 < S < 0.389
Set B3:
Post Height>
0.191 * S + 0.626
for
0.472 < S < 2.181
2.135 * S − 3.613
for
2.181 < S < 3.095
53.475 * S − 162.511
for
3.095 < S < 3.175
Post Height<
−5.095 * S + 23.450
for
2.222 < S < 3.175
0.805 * S + 10.339
for
1.381 < S < 2.222
10.251 * S − 2.706
for
0.572 < S < 1.381
24.420 * S − 10.810
for
0.472 < S < 0.572
C is selected from the group of sets of inequalities consisting of:
Set C1:
Post Height>
0.322 * S + 0.359
for
0.233 < S < 6.667
2.202 * S − 12.179
for
6.667 < S < 8.333
Post Height<
−25.555 * S + 219.122
for
7.778 < S < 8.333
−5.585 * S + 63.794
for
4.000 < S < 7.778
3.214 * S + 28.600
for
1.793 < S < 4.000
21.749 * S − 4.633
for
0.233 < S < 1.793
Set C2:
Post Height>
0.277 * S + 0.593
for
0.250 < S < 5.182
2.342 * S − 10.111
for
5.182 < S < 7.222
Post Height<
−13.149 * S + 101.763
for
6.111 < S < 7.222
−4.885 * S + 51.265
for
3.333 < S < 6.111
4.291 * S + 20.680
for
1.520 < S < 3.333
20.788 * S − 4.395
for
0.251 < S < 1.520
161.000 * S − 39.588
for
0.250 < S < 0.251
Set C3:
Post Height>
0.277 * S + 0.591
for
0.278 < S < 4.425
1.916 * S − 6.663
for
4.425 < S < 6.111
Post Height<
−21.337 * S + 135.438
for
5.556 < S < 6.111
−4.985 * S + 44.588
for
3.175 < S < 5.556
2.749 * S + 20.031
for
1.560 < S < 3.175
18.321 * S − 4.260
for
0.278 < S < 1.560
and
D is selected from the group of sets of inequalities consisting of:
Set D1:
Post Height>
0.257 * S + 0.327
for
0.208 < S < 7.778
1.977 * S − 13.044
for
7.778 < S < 9.444
Post Height<
−36.195 * S + 347.445
for
8.889 < S < 9.444
−5.777 * S + 77.062
for
4.833 < S < 8.889
1.950 * S + 39.718
for
2.222 < S < 4.833
20.301 * S + −1.058
for
0.389 < S < 2.222
34.481 * S + −6.574
for
0.208 < S < 0.389
Set D2:
Post Height>
0.322 * S + 0.359
for
0.233 < S < 6.667
2.202 * S + −12.179
for
6.667 < S < 8.333
Post Height<
−25.555 * S + 219.122
for
7.778 < S < 8.333
−5.585 * S + 63.794
for
4.000 < S < 7.778
3.214 * S + 28.600
for
1.793 < S < 4.000
21.749 * S + −4.633
for
0.233 < S < 1.793
Set D3:
Post Height>
0.212 * S + 0.600
for
0.264 < S < 4.833
3.017 * S + −12.960
for
4.833 < S < 6.667
Post Height<
−12.356 * S + 89.531
for
5.556 < S < 6.667
−4.551 * S + 46.170
for
3.175 < S < 5.556
3.850 * S + 19.496
for
1.502 < S < 3.175
19.751 * S + −4.387
for
0.264 < S < 1.502.
2. The electric machine of claim 1 in which the posts of the second carrier and the first retaining element are connected by a rigid connection.
3. The electric machine of claim 2 in which the posts, first retaining element and rigid connection comprise an isotropic material.
4. The electric machine of claim 2 in which the first retaining element comprises a homogenous rigid element and the posts comprise homogenous extensions of the rigid element.
5. The electric machine of claim 4 in which the permanent magnets are retained by magnetic force.
6. The electric machine of claim 4 in which the permanent magnets are tapered to narrow in a direction toward the first carrier.
7. The electric machine of claim 6 in which the posts of the second carrier are tapered to narrow in a direction away from the first carrier.
8. The electric machine of claim 7 in which the posts of the second carrier prevent the electromagnetic elements of the second carrier from moving in a direction towards the first carrier.
9. The electric machine of claim 1 in which the rigid connection comprises flux path restrictions.
10. The electric machine of claim 1 in which the ratio of magnet depth to magnet width is greater than 3:1.
11. The electric machine of claim 2 in which the ratio of magnet depth to magnet width is greater than 4:1.
12. The electric machine of claim 1 in which the second carrier comprises a homogenous rigid element, and the posts of the second carrier comprise homogenous extensions of the rigid element, the homogenous rigid element comprising flux path restrictions.