Induction motor design for PWM

I have to disagree with that precept. For a given gap geometry, in the usual case where the gap thickness is more or less constant, for a given flux density, torque is proportional to the rate at which gap volume changes with motion, (angle for a rotary motor). If the number of poles is doubled, and the gap thickness is small compared to its dimension in the direction of motion, then the rate at which gap volume changes with motion is doubled.

Having once looked carefully at how to minimize copper losses in a motor design, I can venture an educated guess as to why more poles often results in a larger motor. As the pole count increases, for a given gap width (the dimension parallel to the shaft), the aspect ratio of the windings get worse with respect to efficiency. Since most motors, (at least ones designed with an effort to optimize power to size or weight ratio), become power limited by copper losses, that worse aspect ratio will usually mean the motor with more poles must become larger to handle the same power. But if you had a motor that had a low gap width, (meaning an aspect ratio that would improve with more poles), then it would not have to become larger to handle the same power with more poles.

--
--Larry Brasfield
email: donotspam_larry_brasfield@hotmail.com
Above views may belong only to me.

• OK

*Not true Torque is limited by maximum permissible flux density. For the same flux density, in a given frame size, HP is directly proportional to full load speed. This is slightly modified by various second order effects this but it is the basic relation. Doubling the number of poles will make little change to maximum torque so half the full load speed means roughly half the horsepower.

• If the back EMF generated within a motor is not a perfect sine wave the waveform difference results in circulating currents at harmonic frequencies. These do not produce useful torque so the efficiency drops.

This suggests the use of a sinusoidal winding distribution in an arbitrary large number of slots to achieve low flux ripple. In practice the number of slots in standard stator and rotor laminations is already chosen to keep these losses acceptably low. For minimum ripple the number of rotor slots should not be an integral multiple of the stator slot number and the rotor or the stator should be skewed by at least one slot pitch.

This is not a critical variable and even large differences will still result in a usable motor. A motor designed to run from a sine wave supply will still run (but a bit hotter!) from a square wave source

*No problem

• Patient experiment can work wonders!.

Jim

original

That seems to make sense. I know there are 3 phase 400 Hz motors for aircraft use, and they are less than 1/4 the size and 1/8 the volume of equivalent 60 Hz motors with the same number of poles (4). They run at just under 12000 RPM. You can see them at

I am impressed that a 2 HP motor is only 3.3" dia x 4.25" long. I wonder what the limits of miniaturation with higher frequencies might be. Higher RPMs may be a problem, so you would need to increase the number of poles, and thus require a somewhat larger motor. There will also be more losses in the iron as frequency increases. I think my best option is to rewind an existing 12 pole 600 RPM or 8 pole 900 RPM motor and run some tests to see where performance drops off. I'll probably post again when I have some data. Please contact me if you have any more comments or advice. I am a novice at motor design. My experience is more in the area of controls, and even that is limited. Thanks.

Paul E. Schoen

[sig cut]

One limit that I hit when designing a linear motor was that as the pole pitch becomes higher, getting a well controlled gap that was not too large in relation became very difficult. A complication in that problem is that the normal force across the gap is large and, to the extent that the flux density is gap dominated, (the usual case), that normal force increases for the parts of the gap getting smaller and decreases for the parts getting larger. So, in addition to the ordinary tolerance issues, there can be a stability issue for small gaps in comparatively large structures.

That can be controlled. If you examine the laminations in 400 Hz motors and transformers, you will find them to be much thinner than in 60 Hz equipment. Of course, scaling that thickness down with increasing frequency is one of the limitations on frequency.

I suggest an analytic approach. It's too hard to see what the tradeoffs are with just experiments.

--
--Larry Brasfield
email: donotspam_larry_brasfield@hotmail.com
Above views may belong only to me.

...

My objection was only to your claim: "Doubling the number of poles will make little change to maximum torque". If you study my first post, you will see that is what I refuted. (By implication, I might object to that last. I suggest you look into the OP's observation on that subject posted July 1.)

No objection here. That approach often sheds light.

That formulation ignores the possibility of changing flux and moving conductors, so I am skeptical of its utility, especially in a discussion about AC motors, and all the more when the excitation frequency is not fixed.

How would this apply to motors constructed with ferromagnetic structures excited by the conductors?

That's fine, as far as it goes. But I think that, for any real motors running at or above room temperature today, you will have to find a place for resistive losses when you want to talk about power limitations.

Something is missing here, then, because if I build a normal iron-based motor with some excess space for the windings, and move the windings inward or outward, you will have the power changing even as the current and back-emf stay the same.

You must be assuming a fixed frequency then. And I think you are assuming that iron losses versus frequency is a fixed relationship, ignoring the effect of lamination thickness.

How do you explain, using your above assertions, the difference in power/size ratio between commercial grade 60 Hz motors and the 400 Hz motors observed by the OP (in his post of July 1) at

? I believe some more fundamentals may be necessary to understand that.

--
--Larry Brasfield
email: donotspam_larry_brasfield@hotmail.com
Above views may belong only to me.

Clearly, as you explain there are practical considerations that reduce the dependence of power to weight ratio on speed

Nevertheless I find it hard to accept your objection to my view that full load speed is the primary factor determining power output from a fixed frame size.

I think we need to get back to fundamentals.

Firstly force on a conductor is directly related to the current carried and the total flux in which it is immersed, provided only that the flux is orthogonal to the conductor.

If located in a rotor the effective radius at which it rotates converts this into torque

The rotation speed converts this into H.P (or KW if you prefer)

Stripped of constants this is the fundamental motor relation

Neither the air gap or the iron permeablity appear in this relation - they only influence the flux density that is actually achievable in a real motor.

If we take a real motor of fixed size, rising iron losses limit the permissible maximum flux density in the iron of the rotor to a roughly constant value. This means that if you reduce the design full load speed whether by pole changing or any other method the power output drops.

Any other assumption inevitably leads to impossibly high flux densities as the speed drops.

Jim

SNIP

**Fair comment - I should have read your post more carefully ** The natural extension of this is that the time integral of the force on the conductor is the time integral of the instantaneous products of current and total flux. As I see it, this defines the force independent of both frequency and waveform. Movement of the conductor produces back EMF. Any resultant change in current is already taken into account by the time integral of the conductor current

** This is a key question and I can only plead the unashamedly weasel words "effective radius" as the answer. Unfortunately this is pretty well negated by your later comment which shows that this effective radius is almost independent of the mechanical position of the conductor within the rotor slot window.

** I assumed that you would be running at about the same current density and flux density so that power losses would be in the same ball park ** This is the killer comment. My statement is true in an air cored system or with ferromagnetic stator but fails miserably if you move the rotor conductors about within a ferromagnetic rotor slot window.

It's the same mechanism as constant volts per turn independent of the position of the windings within the window of a power transformer.

** I was assuming that the iron used was appropriate to the operating frequency i.e. higher frequency thinner lams. Overall it's optimistic because other loss mechanisms necessitate some reduction in flux density. This is a secondary effect a because a 2:1 drop in flux density is probably enough to accommodate a 10:1 increase in frequency. ** I am puzzled by this comment. My comment indicates that higher full load speed in a given frame size permits higher output power i.e higher power to weight ratio. This is is entirely consistent with the superior power to weight ratio of these high speed 400Hz motors.

Summing up - your comments have shown that the "fundamental" analysis has fatal weaknesses. However it's an interesting way of looking at the problem and stirs up a few thoughts.

Jim