1. June 9, 20056.11s 20051 Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.11s Design of Motors, Generators and Drive Systems June 9, 2005 J.L. Kirtley Jr. ©2005, J.L. Kirtley Jr.

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6. June 9, 20056.11s 20056 Coils are wound on a toroidal core ( a magnetic circuit)

7. June 9, 20056.11s 20057 Axial View: Magnets are interacting with stator current

8. June 9, 20056.11s 20058 Magnetic materials exhibit hysteresis For core materials you want a narrow curve But for PM materials you want a wide curve

9. June 9, 20056.11s 20059 Hard permanent magnet materials have B-H curves like this Remanent Flux density can be as high as 1.4 T Incremental permeability is like free space

10. June 9, 20056.11s 200510 Magnet Characteristic Geometry Combination

11. June 9, 20056.11s 200511 This graphic shows that calculation

12. June 9, 20056.11s 200512 Nomenclature: Two more views of the machine

13. June 9, 20056.11s 200513 This is a ‘cut’ from the radial direction (section BB)

14. June 9, 20056.11s 200514 Here is a cut through the machine (section AA) Winding goes around the core: looking at 1 turn

15. June 9, 20056.11s 200515 Voltage is induced by motion and magnetic field Induction is: Voltage induction rule: Note magnets must agree!

16. June 9, 20056.11s 200516 Single Phase Equivalent Circuit of the PM machine E a is induced (‘speed’) voltage Inductance and resistance are as expected This is just one phase of three Voltage relates to flux:

17. June 9, 20056.11s 200517 PM Brushless DC Motor is a synchronous PM machine with an inverter:

18. June 9, 20056.11s 200518 Induced voltages are: Assume we drive with balanced currents: Then converted power is: Torque must be:

19. June 9, 20056.11s 200519 Now look at it from the torque point of view:

20. June 9, 20056.11s 200520 Terminal Currents look like this: So torque is, in terms of DC side current:

21. June 9, 20056.11s 200521 VaVa VbVb VcVc V ab Rectified back voltage is max of all six line-line voltages

22. June 9, 20056.11s 200522 Average Rectified Back Voltage is: Power is simply:

23. June 9, 20056.11s 200523 So from the DC terminals this thing looks like the DC machine:

24. June 9, 20056.11s 200524 Magnets must match (north-north, south-south) for the two rotor disks. Looking at them they should look like this: End AEnd B Keyway

25. June 9, 20056.11s 200525 Need to sense position: Use a disk that looks like this

26. June 9, 20056.11s 200526 Position sensor looks at the disk: 1=‘white, 0=‘black’

27. June 9, 20056.11s 200527 Some care is required in connecting to the position sensor Vcc GND Channel 1 Channel2 (you need to figure out which of these is ‘count’ and which is ‘zero’)

28. June 9, 20056.11s 200528 Control Logic: Replace open loop with position measurement