How can I calculate the location of Hall effect sensors for a BLDC motor according to the number of stator slots and the number of rotor poles?
What mathematical relationship is there to calculate?
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I am not a motor designer, but I have experimented with installing sensors on motors before, but only two or three times. I am not sure if there is a formula but there are some rules.
Sensors must be placed 120 electrical degrees apart from each other. Since you have 32 magnets, that is 16 pole pairs, so you have 16 electrical cycles for every full mechanical rotation of the rotor. So an electrical cycle is 360 / 16 = 22.5 degrees of mechanical rotation. So 120 electrical degrees = 7.5 mechanical degrees.
If it is not convenient to place the sensors at 7.5 degree intervals, they can instead be placed at 7.5 + N * 22.5, where N is an integer.
The first sensor should be placed so that it transitions from low to high at the positive zero crossing of the back EMF measured from phase A to B.
Based on rule 1 and 2, all of these spacings (in mechanical degrees) would be OK:
0, 7.5, 15
0, 30, 60
0, 52.5, 105
0, 75, 150
0, 97.5, 195
0, 120, 240
Since your motor has 24 slots, you have 360/24 = 15 degree spacing between slots, I think 0, 30, 60 degrees will be a good choice. You can place the sensors in the gaps between teeth. Try to center the sensors in the gaps. If the sensors are not spaced accurately, the controller will have a hard time and the motor may not run smooth.
The hardest part is figuring out where to put the first sensor. You want to place it so it toggles from low to high just as the back EMF measured from A to B crosses zero in the positive direction. This diagram may help:
Diagram may be subject to copyright. I claim fair use. I found it here: https://www.researchgate.net/figure/Hall-signal-and-Back-emf_fig1_313807594 on 7 DEC 2022.
Without knowing which winding is which on your stator I can't tell you where the first sensor should go, exactly. You may have to try several different gaps until you find the one that lines up best with the back EMF. Here is a picture showing one possible place to locate the sensors.
Good luck! Have fun experimenting.