Electric machine

1. An electric machine, comprising:

a first carrier having an array of electromagnetic elements;

a second carrier having electromagnetic elements defining magnetic poles, 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, 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 defining a size of the electric machine and being arranged so that the electric machine is an axial flux or radial flux machine;

the magnetic poles having a pole pitch S in mm;

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 group of inequalities A is for a size of 25 mm, the group of inequalities B is for a size of 50 mm, the group 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 electric machine is a radial flux machine, having an airgap diameter, and the size of the electric machine is the airgap diameter.

3. The electric machine of claim 2 in which the electric conductors comprise a concentrated winding.

4. The electric machine of claim 2 in which the electric conductors comprise a distributed winding.

5. The electric machine of claim 1 in which the electric machine is a rotary axial flux machine, having an average airgap diameter, and the size of the electric machine is the average airgap diameter.

6. The electric machine of claim 5 in which the electric conductors comprise a concentrated winding.

7. The electric machine of claim 5 in which the electric conductors comprise a distributed winding.

8. The electric machine of claim 1 in which the electric machine is a linear machine having a direction of translation, the first carrier has a first length in the direction of translation, the second carrier has a second length in the direction of translation, and the size of the electric machine is the first length if the first length is shorter or equal to the second length and the second length if the second length is shorter than the first length.

9. The electric machine of claim 8 in which the electric conductors comprise a concentrated winding.

10. The electric machine of claim 8 in which the electric conductors comprise a distributed winding.

11. The electric machine of claim 1 in which the first carrier comprises a stator formed of a unitary piece of magnetically susceptible material, each post comprising a portion of the stator.

12. The electric machine of claim 11 in which the stator comprises a material with no measurable creep below 20,000 psi.

13. The electrical machine of claim 11 in which the posts each have a tangential width and the stator comprises a backiron portion, the backiron portion having a thickness equal to or less than the tangential width of the posts.

14. The electrical machine of claim 11 in which the posts each have a tangential width and the stator comprises a backiron portion, the backiron portion having a thickness equal to or less than half the tangential width of the posts.

15. The electric machine of claim 1 in which the second carrier comprises:

an annular disk formed of a unitary piece of a material and defining an axis, and having an inner edge and an outer edge;

circumferentially spaced second carrier posts extending axially from the annular disk and defining second carrier slots between the second carrier posts; and

the annular disk defining holes extending between the inner edge and the outer edge.

16. The electric machine of claim 1 which electric machine has an axis defining an axial direction, the second carrier has an inner circumference and an outer circumference, the inner circumference has an inner axial length, the outer circumference has an outer axial length, and the inner axial length is not equal to the outer axial length.

17. The electric machine of claim 16 in which the inner axial length is less than the outer axial length.

18. The electric machine of claim 17 in which the second carrier has a conical shape.

19. The electric machine of claim 1 in which the electric conductors comprise anodized aluminum conductors.

20. The electric machine of claim 1 further comprising a coolant supply connected to supply cooling fluid to one or both of the first carrier and the second carrier.

21. The electric machine of claim 1 further comprising a power supply connected to supply electrical energy of at least 70 A/mm2 to the electric conductors.

22. The electric machine of claim 1 in which the second carrier comprises magnet slots and the electromagnetic elements of the second carrier comprise permanent magnets held within the magnet slots by magnetic forces.

23. The electric machine of claim 22 in which the electric conductors form single layers around the posts, measured radially outward from the posts.

24. The electric machine of claim 1 in which the airgap is from 0.001″ to 0.010″.

25. The electric machine of claim 1 in which the airgap is from 0.005″ to 0.010″.

26. The electric machine of claim 1 in which the electric machine is mounted on a robotic arm.

27. The electric machine of claim 26 in which components of the robotic arm form a housing for the electric machine that supports the first carrier and the second carrier.

28. The electric machine of claim 1 in which the electric machine is a frameless electric machine.