PM Motor theory - formulae etc.

[Miles]

V: Volts

I: Current (Amps)

Io: No-load current at a given speed (Amps)

Rm: Motor resistance at a given temperature (Ohms)

Copper loss = I² x Rm

Parasitic losses = V x Io

Total losses = Copper Loss + Parasitic Losses

Watts out = Watts In - Total Losses

Efficiency = Watts Out / Watts In


Parasitic losses:

Bearing losses are proportional to RPM
Hysteresis losses are proportional to RPM
Eddy current losses are proportional to RPM²
Cooling fan losses are proportional to RPM³


Power output:

Maximum (theoretical) power output occurs at half of no-load speed.
Max. power out = V²/4Rm
Current at max. power out = V/2Rm

Maximum continuous power output is dependant on the motor's ability to dissipate heat.

Efficiency:

Maximum efficiency is achieved when Copper loss = Parasitic Losses

Efficiency at maximum power output is 50%

[Miles]

More on reducing eddy current losses, but this is for a conventional BLDC motor. Perhaps we can learn a bit by similarity.

Using knowledge of the fundamental principles that cause core losses, they can be reduced by:

• Reducing the lamination thickness. Ideally, eddy current losses are directly proportional to the square of the lamination thickness. Therefore, if lamination thickness is reduced by a factor of two, eddy current losses decrease by a factor of four.
• Increasing the resistivity of the lamination material. Eddy current losses are directly proportional to material resistivity. Adding silicon to lamination steel is the most commonly adopted approach to increasing material resistivity.
• Annealing laminations after they have been stamped or cut. This eliminates the influence of mechanical stress on core loss.
• Reducing the amplitude of the magnetic field within the material. Hysteresis losses are directly proportional to the amplitude of the magnetic field raised to a power between 1.5 and 2.5. Eddy current losses are directly proportional to the square of the magnetic field amplitude. Using this property to reduce core loss is in direct conflict with maximizing torque production. As a result, other techniques for minimizing core losses are often implemented first.
• Reducing the number of magnet poles Nm. Hysteresis losses are directly proportional to the fundamental electrical frequency. Eddy current losses are directly proportional to the square of the fundamental electrical frequency. Since the fundamental electrical frequency is Nm/2 times greater than the motor shaft speed, reducing the magnet pole count allows one to reduce core losses significantly without lowering the motor shaft speed.

[Miles]

Rotary power

The formula for rotary power is:

Power (Watts) = Torque (Nm) x Angular Velocity (radians per sec)

Angular Velocity = rpm * 2pi / 60

So:
Watts = torque (Nm) * rpm * 2pi/60 , or
Watts = torque (Nm) * rpm * 0.105

Solved for torque:
Nm = Watts * 60 / rpm / 2pi , or
Nm = 9.549 * Watts / rpm.

[avandalen]

See another list of formulas here:

http://www.avdweb.nl/solar-bike/formulas-for-power-calculations-on-ebikes-and-hub-motors.html

[ron van sommeren]

See also this formulae compilation on RCG (sticky):
http://www.rcgroups.com/forums/showthread.php?t=587549

Horses for courses
http://www.consult-g2.com/course.html

@Albert
http://www.modelbouwforum.nl (RC)

[Miles]

http://www.innovatia.com/Design_Center/ ... ronics.htm

Scroll down to Motor Control section

[Arlo1]

More on reducing eddy current losses, but this is for a conventional BLDC motor. Perhaps we can learn a bit by similarity.


• Reducing the number of magnet poles Nm. Hysteresis losses are directly proportional to the fundamental electrical frequency. Eddy current losses are directly proportional to the square of the fundamental electrical frequency. Since the fundamental electrical frequency is Nm/2 times greater than the motor shaft speed, reducing the magnet pole count allows one to reduce core losses significantly without lowering the motor shaft speed.[/list]

I know this thread is old but I have a problem with this last statement I do understand reducing the number of magnet polls helps reduce hysteresis losses but I don't see how it can change eddy current losses. Because even if you have one big magnet or 10 little ones they will all cause the same drag at speed. Imagine the piece of aluminum with a magnet sliding down it and how slow it moves. Now imagine 10 smaller magnets all 1/10 th the size sliding down the same piece of aluminum.....

[Kingfish]

With regards to motor design, the calculations for performance and losses are a good lot more complicated than listed here in this FAQ, and are in addition to the number of teeth and poles and power and rotation, minimally determined by the following factors:

• Brushed vs Brushless
• Radial vs Axial Flux
• Iron vs Ironless cores
• Number of stators and rotors in parallel or in series

For my own part during the ongoing discovery towards good AF designs... other than the basic fundamentals, not every published study agrees with the formulas specific to each geometry. The best that can be had is to encourage investigation of multiple case studies appertaining to the specific geometry until the complexion is understood well enough to determine the proper formulations which describe as best as possible the theoretical aspects, and then compare/validate the resultants against known quantities to measure the accuracy of the formulations. Relying on low-budget FEA software for accurate answers is circumspect, though it can work well enough to the model’s physicality in order to get close approximation of performance prior to prototyping.

In brief, unless schooled in motor design, the calculations following parameter iterations are complex and laborious. During these long hours I often humor myself with the following phase to keep my sanity in check:

“I am endeavoring, ma'am, to construct a mnemonic memory circuit using stone knives and bear skins.”

Star Trek, The City on the Edge of Forever (1967).

Believe it or not, trips to the pub help too.
Good hunting, KF

[Miles]

With regards to motor design, the calculations for performance and losses are a good lot more complicated than listed here in this FAQ

You can certainly make it more complicated.......

[bigmoose]

I was asked to comment on the pole count issue with respect to hysteresis losses. When you look at the hysteresis curve:

hysterisis.jpg (10.11 KiB) Viewed 3540 times

Note that the area inside the curve are losses. If you have twice as many poles you go through the curve twice as many times, so about twice the losses. Now if the motor is the same size, but has 1/2 the number of poles, the area inside the curves will increase though because more iron is undergoing flux reversal, also I believe the motor torque will decrease. To get the specific losses a more detailed FEA type analysis would be required.

The trends are higher speed, low pole count motor is like a low speed motor with a lot of poles. The higher the electrical speed, the faster the switching, and the need to go to more exotic and thinner laminations to control losses. Hope this helps. I did a quick Google for an overview and this white paper had some of the basics in hysteresis losses: http://www.ep2000.com/Templates/white%20papers/MagneticDipolesEP.pdf

[bigmoose]

For you guys designing motors, do you have a copy of "Brushless Permanent Magnet Motor Design" by Duane Hanselman?

http://www.scribd.com/doc/84701725/Brushless-Permanent-Magnet-Motor-Design-by-Hanselman

That is the source of my eddy current comments. Page 219

Given all of these issues, core loss prediction using relatively simple modeling mayindicate the correct trends from one motor design to the next but will not likely pro-duce accurate estimates of core losses at any given operating point.Using knowledge of the fundamental principles that cause core losses, they can bereduced by:

• Reducing the lamination thickness. Ideally, eddy current losses are directlyproportional to the square of the lamination thickness. Therefore, if lamina-tion thickness is reduced by a factor of two, eddy current losses decrease bya factor of four.

• Increasing the resistivity of the lamination material. Eddy current losses areinversely proportional to material resistivity. Adding silicon to laminationsteel is the most commonly adopted approach to increasing material resis-tivity.

• Annealing laminations after they have been stamped or cut. This eliminatesthe influence of mechanical stress on core loss.

• Reducing the amplitude of the magnetic field within the material. Hystere-sis losses are directly proportional to the amplitude of the magnetic fieldraised to a power between 1.5 and 2.5. Eddy current losses are directly pro-portional to the square of the magnetic field amplitude. Using this propertyto reduce core loss is in direct conflict with maximizing torque production.As a result, other techniques for minimizing core losses are often imple-mented first.

• Reducing the number of magnet poles Nm. Hysteresis losses are directlyproportional to the fundamental electrical frequency. Eddy current lossesare directly proportional to the square of the fundamental electrical fre-quency. Since the fundamental electrical frequency is Nm/2 times greaterthan the motor shaft speed, reducing the magnet pole count allows one toreduce core losses significantly without lowering the motor shaft speed.

[Miles]

For you guys designing motors, do you have a copy of "Brushless Permanent Magnet Motor Design" by Duane Hanselman?

http://www.scribd.com/doc/84701725/Brushless-Permanent-Magnet-Motor-Design-by-Hanselman

That is the source of my eddy current comments.

No, but I'm planning to get one...

[bigmoose]

These snap shots of pages 220 and 221 may help. The entire book is at the link provided.

book1.jpg (94.89 KiB) Viewed 2769 times

book2.jpg (85.19 KiB) Viewed 2769 times

[Miles]

These snap shots of pages 220 and 221 may help. The entire book is at the link provided.

Thanks a lot Dave.

I'd never seen it in entirety online, before now...

[Kingfish]

For you guys designing motors, do you have a copy of "Brushless Permanent Magnet Motor Design" by Duane Hanselman?

http://www.scribd.com/doc/84701725/Brushless-Permanent-Magnet-Motor-Design-by-Hanselman

<snip>

Too funny! It's right in front of me <waving it in the air>, hand-signed 2nd edition.

Seminal work that helped me understand radial flux iron-stator design such as the 9C and others.

~KF