June 9, s 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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June 9, s Coils are wound on a toroidal core ( a magnetic circuit)

June 9, s Axial View: Magnets are interacting with stator current

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

June 9, s 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

June 9, s Magnet Characteristic Geometry Combination

June 9, s This graphic shows that calculation

June 9, s Nomenclature: Two more views of the machine

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

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

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

June 9, s 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:

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

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

June 9, s Now look at it from the torque point of view:

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

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

June 9, s Average Rectified Back Voltage is: Power is simply:

June 9, s So from the DC terminals this thing looks like the DC machine:

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

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

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

June 9, s 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’)

June 9, s Control Logic: Replace open loop with position measurement