Induction motor design for PWM

[Paul E. Schoen]

My project is to make a three phase AC induction motor that will be powered
from batteries by means of a PWM sine wave inverter. I have successfully
rewound a 120 VAC 1/2 HP single phase capacitor start motor into a three
phase, four pole motor that operates on about 6 VAC at 60 Hz. I also made a
simple controller with a Microchip PIC and six MOSFETs that were able to
drive the motor from a 12 VDC battery. I have several questions and invite
comments:

(1) I want to wind a motor with 6 poles on a 36 hole stator, which should
run at just under 1200 RPM at 60 Hz. Using the PWM control, I want to
increase the frequency to 180 Hz, for 3600 RPM.

(2) For the same size motor, I would expect torque to be proportional to
number of poles, so twice the poles and half the speed would be the same
horsepower. Ideally, I would like to make a motor with 12 poles, for 600
RPM, and run it at 360 Hz for 3600 RPM. I should get six times the original
HP. However, motors with more than 4 poles seem to be much larger and
heavier than two pole motors of the same HP. Can anyone explain this?

(3) How much effect does the number of slots on the rotor vs that of the
stator have on performance, and what about rotor skew? I was concerned about
this, especially when I rewound a single phase motor for three phase, but it
seems to run OK. However, I have not tested it for torque, HP, or
efficiency.

(4) I am now rewinding a motor that was originally a 120 VAC capacitor run
motor at 1120 RPM, for three phase. It has a 36 slot stator and a 48 slot
rotor, with a skew of about 150%. By this I mean that the rotor pole piece
at one end is skewed 1.5 slots on the stator. Could there be any problems
with this rewind?

(5) I have found various motor design software packages, but they are
several thousand dollars, and I don't know if they will work for my special
design.

Any comments or suggestions will be appreciated. I had hoped to find a
newsgroup more specific to motors and motion control, but this seemed the
best fit. If you know of any other, please inform me.

Thanks

--
Paul E. Schoen, President
P S Technology, Inc.
www.pstech-inc.com

 

On Fri, 1 Jul 2005 03:36:36 -0400, "Paul E. Schoen" <pstech@smart.net>
wrote:

My project is to make a three phase AC induction motor that will be powered
from batteries by means of a PWM sine wave inverter. I have successfully
rewound a 120 VAC 1/2 HP single phase capacitor start motor into a three
phase, four pole motor that operates on about 6 VAC at 60 Hz. I also made a
simple controller with a Microchip PIC and six MOSFETs that were able to
drive the motor from a 12 VDC battery. I have several questions and invite
comments:

(1) I want to wind a motor with 6 poles on a 36 hole stator, which should
run at just under 1200 RPM at 60 Hz. Using the PWM control, I want to
increase the frequency to 180 Hz, for 3600 RPM.
* OK

(2) For the same size motor, I would expect torque to be proportional to
number of poles, so twice the poles and half the speed would be the same
horsepower. Ideally, I would like to make a motor with 12 poles, for 600
RPM, and run it at 360 Hz for 3600 RPM. I should get six times the original
HP. However, motors with more than 4 poles seem to be much larger and
heavier than two pole motors of the same HP. Can anyone explain this?
*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.

(3) How much effect does the number of slots on the rotor vs that of the
stator have on performance, and what about rotor skew? I was concerned about
this, especially when I rewound a single phase motor for three phase, but it
seems to run OK. However, I have not tested it for torque, HP, or
efficiency.
* 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

(4) I am now rewinding a motor that was originally a 120 VAC capacitor run
motor at 1120 RPM, for three phase. It has a 36 slot stator and a 48 slot
rotor, with a skew of about 150%. By this I mean that the rotor pole piece
at one end is skewed 1.5 slots on the stator. Could there be any problems
with this rewind?
*No problem

(5) I have found various motor design software packages, but they are
several thousand dollars, and I don't know if they will work for my special
design
* Patient experiment can work wonders!.

Jim

 

[Larry Brasfield]

<pentagrid@yahoo.com> wrote in message
news:8u6ac15aifntrrn8kc9mjm4kjkc7n2016m@4ax.com...

On Fri, 1 Jul 2005 03:36:36 -0400, "Paul E. Schoen" <pstech@smart.net
wrote:

My project is to make a three phase AC induction motor that will be powered
from batteries by means of a PWM sine wave inverter. I have successfully
rewound a 120 VAC 1/2 HP single phase capacitor start motor into a three
phase, four pole motor that operates on about 6 VAC at 60 Hz. I also made a
simple controller with a Microchip PIC and six MOSFETs that were able to
drive the motor from a 12 VDC battery. I have several questions and invite
comments:

(1) I want to wind a motor with 6 poles on a 36 hole stator, which should
run at just under 1200 RPM at 60 Hz. Using the PWM control, I want to
increase the frequency to 180 Hz, for 3600 RPM.
* OK

(2) For the same size motor, I would expect torque to be proportional to
number of poles, so twice the poles and half the speed would be the same
horsepower. Ideally, I would like to make a motor with 12 poles, for 600
RPM, and run it at 360 Hz for 3600 RPM. I should get six times the original
HP. However, motors with more than 4 poles seem to be much larger and
heavier than two pole motors of the same HP. Can anyone explain this?
*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.

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.

 

[Paul E. Schoen]

"Larry Brasfield" <donotspam_larry_brasfield@hotmail.com> wrote in message
news:%Ybxe.13$md4.2289@news.uswest.net...

pentagrid@yahoo.com> wrote in message
news:8u6ac15aifntrrn8kc9mjm4kjkc7n2016m@4ax.com...
On Fri, 1 Jul 2005 03:36:36 -0400, "Paul E. Schoen" <pstech at
smart.net
wrote:

(2) For the same size motor, I would expect torque to be proportional to
number of poles, so twice the poles and half the speed would be the same
horsepower. Ideally, I would like to make a motor with 12 poles, for 600
RPM, and run it at 360 Hz for 3600 RPM. I should get six times the
original
HP. However, motors with more than 4 poles seem to be much larger and
heavier than two pole motors of the same HP. Can anyone explain this?

*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.

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.

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 http://www.slmti.com/inm/. 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
www.pstech-inc.com

 

[Larry Brasfield]

(Posted and emailed)
"Paul E. Schoen" <pstech@smart.net> wrote in message
news:11cccc4dtbnqkd2@corp.supernews.com...

"Larry Brasfield" <donotspam_larry_brasfield@hotmail.com> wrote in message
news:%Ybxe.13$md4.2289@news.uswest.net...
pentagrid@yahoo.com> wrote in message
news:8u6ac15aifntrrn8kc9mjm4kjkc7n2016m@4ax.com...
On Fri, 1 Jul 2005 03:36:36 -0400, "Paul E. Schoen" <pstech at
smart.net
wrote:

(2) For the same size motor, I would expect torque to be proportional to
number of poles, so twice the poles and half the speed would be the same
horsepower. Ideally, I would like to make a motor with 12 poles, for 600
RPM, and run it at 360 Hz for 3600 RPM. I should get six times the original
HP. However, motors with more than 4 poles seem to be much larger and
heavier than two pole motors of the same HP. Can anyone explain this?

*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.

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.
[sig cut]
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 http://www.slmti.com/inm/. 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.

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.

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.

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

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.

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

 

On Sat, 2 Jul 2005 02:19:55 -0400, "Paul E. Schoen" <pstech@smart.net>
wrote:

"Larry Brasfield" <donotspam_larry_brasfield@hotmail.com> wrote in message
news:%Ybxe.13$md4.2289@news.uswest.net...

pentagrid@yahoo.com> wrote in message

SNIP
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.

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

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

 

[Larry Brasfield]

<pentagrid@yahoo.com> wrote in message
news:sslfc19n6qbrgprgmu1p2jstq5p6a0k6ut@4ax.com...

On Sat, 2 Jul 2005 02:19:55 -0400, "Paul E. Schoen" <pstech@smart.net
wrote:
"Larry Brasfield" <donotspam_larry_brasfield@hotmail.com> wrote in message
news:%Ybxe.13$md4.2289@news.uswest.net...

pentagrid@yahoo.com> wrote in message

SNIP
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.

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.
....
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.

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.)

I think we need to get back to fundamentals.

No objection here. That approach often sheds light.

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.

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.

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

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

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

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.

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.

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.

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.

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.

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.

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
http://www.slmti.com/inm/ ? 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.

 

On Sun, 3 Jul 2005 08:52:51 -0700, "Larry Brasfield"
<donotspam_larry_brasfield@hotmail.com> wrote:

SNIP

pentagrid@yahoo.com> wrote in message

SNIP

...
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.


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.)

**Fair comment - I should have read your post more carefully

I think we need to get back to fundamentals.


No objection here. That approach often sheds light.

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.


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.

** 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

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


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

** 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.

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


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.

** 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

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.


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.

** 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.

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.


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.

** 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.

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.

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
http://www.slmti.com/inm/ ? I believe some more fundamentals
may be necessary to understand that.

** 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