Electric machine

1. An electric machine comprising:

a stator comprising electromagnetic elements, the stator having posts on one side and a backiron having cooling fins on an opposite side, the stator comprising a unitary piece of material including at least portions of the posts and at least portions of the cooling fins; and

a rotor arranged for rotation relative to the stator, the rotor comprising a permanent magnet carrier loaded with permanent magnets, an output ring, and bearings for supporting the rotor for rotation, the bearings located on a connecting portion of the rotor connecting the permanent magnet carrier to the output ring.

2. The electric machine of claim 1 in which the machine is an axial flux machine, the machine further comprising an additional stator, and in which the rotor is arranged between the stator and the additional stator.

3. The electric machine of claim 2 in which the bearings are preloaded by magnetic forces between the rotor and stators.

4. The electric machine of claim 2 in which the rotor has two axial sides, and the permanent magnets are on each axial side of the rotor, the permanent magnets on each axial side-polarized circumferentially, and each permanent magnet aligned axially with a respective permanent magnet on the other axial side, the-circumferential polarization of each permanent magnet being opposite to the circumferential polarization of the respective permanent magnet on the other axial side.

5. The electric machine of claim 2 in which:

the electromagnetic elements of the stator and the additional stator each include posts, with slots between the posts, one or more electric conductors in each slot, the posts of each stator having a post height in mm;

the permanent magnets of the rotor define magnetic poles, the magnetic poles having a pole pitch S in mm;

the stator, the additional stator and the rotor together defining a size of the electric machine;

the stator and the additional stator are each separated from the rotor by a corresponding airgap; and

the size of the electric machine, pole pitch and post height is 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.

6. The electric machine of claim 1 in which the cooling fins are spiral cooling fins.

7. The electric machine of claim 1 in further comprising a rotor arranged on bearings for rotation between the stator and an additional stator from which the rotor is separated by airgaps, a magnetic force between the rotor and stators attracting the stators to the rotor and applying a preloading force on the bearings.

8. The electric machine of claim 7 in which the rotor has an output ring located radially inward from the permanent magnets.

9. The electric machine of claim 8 in which the bearings each have rolling elements in rolling contact with inner and outer races, the outer races being attached to the rotor.

10. The electric machine of claim 7 in which the rotor has an output ring located radially outward from the magnets.

11. The electric machine motor of claim 10 in which the bearings each have rolling elements in rolling contact with inner and outer races, the inner races being attached to the rotor.

12. The electric machine of claim 7 in which the airgaps will close by more than 50% as a result of magnetic force if the bearings are not present in the assembly.

13. The electric machine of claim 7 in which the stators and rotor will come into contact if the bearings are not present in the assembly.

14. The electric machine of claim 7 in which there are axial inward facing surfaces of a housing and the bearings have axial outward facing bearing races contacting the axial inward facing surfaces of the housing, and the axial inward facing surfaces of the housing deform under magnetic load such that the difference in position between the position of the axial inward facing surfaces and a hypothetical position of the inward facing surface if no bearings are present is greater than 0.002″.

15. The electric machine of claim 7 in which there are axial inward facing surfaces of a housing and the bearings have axial outward facing bearing races contacting the axial inward facing surfaces of the housing, and the axial inward facing surfaces of the housing deform under magnetic load such that the difference in position between the position of the axial inward facing surfaces and a hypothetical position of the inward facing surface if no magnets are present in the rotor is greater than 0.002″.

16. The electric machine of claim 7 in which the stator and the additional stator form outer portions of a housing and the outer portions are separated by a separator ring.

17. The electric machine of claim 7 further comprising:

the rotor having electromagnetic elements defining magnetic poles, the rotor being arranged to rotate relative to the two stators, the magnetic poles having a pole pitch S in mm;

respective airgaps between the stator and the additional stator and the rotor;

posts of the stator and the additional stator having a post height in mm;

the stator and the additional stator and the rotor together defining a size of the electric machine;

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.

18. The electric machine of claim 1 in which the posts have a post width in the circumferential direction, and the backiron including the fins have a height greater than 50% of the post width.

19. The electric machine of claim 1 in which the fins have tips comprising a different material than the unitary piece of material.

20. The electric machine of claim 1 in which the electric machine is an axial flux motor.

21. The electric machine of claim 20 in which the cooling fins are spiral shaped.

22. The electric machine of claim 1 further comprising:

a rotor having electromagnetic elements defining magnetic poles, the rotor being arranged to rotate relative to the stator, the magnetic poles having a pole pitch S in mm;

an airgap between the stator and the rotor;

posts of the stator having a post height in mm;

the stator and the rotor together defining a size of the electric machine;

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 100mm, 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.

23. An electric machine comprising a rotor arranged for rotation relative to one or more stators comprising electromagnetic elements, the rotor comprising a permanent magnet carrier loaded with permanent magnets, an output ring, and bearings for supporting the rotor for rotation, the bearings located on a connecting portion of the rotor connecting the permanent magnet carrier to the output ring, and in which:

the electromagnetic elements of each stator of the one or more stators include posts, with slots between the posts, one or more electric conductors in each slot, the posts of each stator having a post height in mm;

the permanent magnets of the rotor define magnetic poles, the magnetic poles having a pole pitch S in mm;

the one or more stators and the rotor together defining a size of the electric machine;

each stator is separated from the rotor by a corresponding airgap; and

the size of the electric machine, pole pitch and post height is 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.

24. The electric machine of claim 23 in which the one or more stators form outer portions of a housing and the outer portions are separated by a separator ring.

25. An electric machine comprising:

a rotor arranged on bearings for rotation between two stators from which the rotor is separated by airgaps, a magnetic force between the rotor and stators attracting the stators to the rotor and applying a preloading force on the bearings;

the rotor having electromagnetic elements defining magnetic poles, the rotor being arranged to rotate relative to the two stators, the magnetic poles having a pole pitch S in mm;

posts of the two stators having a post height in mm;

the two stators and the rotor together defining a size of the electric machine;

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.