# Permeability in a DC Motor

Started by May 31, 2016
```Two motors were evaluated to find the ratio of the speed of the rotor over the speed of the electron in the coil.

ratio = speed(rotor) / speed(electron)

ratio = 8 meters per second / 10 microns per second

Some calculations show that DC electric motors rotate thousands of times faster than the electrons move in the drive current. For example, the Mabuchi RE 280RA motor has a current running electrons at a speed of 5*10^-6 meters per second and its rotor is moving at 8 meters per second. Plus or minus a big number.

The mechanical motor runs a million times faster than the speed at which an electron is flowing in its coil.

A second motor was examined: Maxon Motor: 8 meter per second rotor speed and electron speed estimated at 2.7*10^-5 meters per second. Plus or minus a big amount.

This implies that maybe the permeability of free space  (mu zero) is involved to set that ratio of speeds:

1/(mu) = 796,000 meters per Henry

Then a rotor velocity limit can be expected to be 796,000 times faster than the electron in the coil, during conditions where there is no mechanical load on the motor. That is the maximum speed for a motor but going faster makes it into a generator.

H = B/mu

H is magnetic field (units: Amps per meter, or meters per second in Continuum Science)

B is magnetic flux density (units: second^-1 or Weber per square meter, using Coulomb=area theory)

Henry is Webers per Ampere (units = 1)

1/mu = 796,000 meters

\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$

Conclusion:  It seems that the number of turns in a motor coil does not set the maximum RPM speed. The number of turns can increase the torque but not the no-load speed. The no-load speed of the motor is set by the speed of the electrons in the coil. The flux density (B) does not change the speed limit of a rotor, all flux has the same velocity amplification (H) relative to electron motion. That mechanical amplification has a factor of 1/mu.

Please check your motors for the ratio of rotor speed over electron speed, no load. Is it 796,000?
```
```On Tue, 31 May 2016 15:32:40 -0700, omnilobe wrote:

> Two motors were evaluated to find the ratio of the speed of the rotor
> over the speed of the electron in the coil.
>
> ratio = speed(rotor) / speed(electron)
>
> ratio = 8 meters per second / 10 microns per second
>
> Some calculations show that DC electric motors rotate thousands of times
> faster than the electrons move in the drive current. For example, the
> Mabuchi RE 280RA motor has a current running electrons at a speed of
> 5*10^-6 meters per second and its rotor is moving at 8 meters per
> second. Plus or minus a big number.
>
> The mechanical motor runs a million times faster than the speed at which
> an electron is flowing in its coil.
>
> A second motor was examined: Maxon Motor: 8 meter per second rotor speed
> and electron speed estimated at 2.7*10^-5 meters per second. Plus or
> minus a big amount.
>
> This implies that maybe the permeability of free space  (mu zero) is
> involved to set that ratio of speeds:
>
> 1/(mu) = 796,000 meters per Henry
>
> Then a rotor velocity limit can be expected to be 796,000 times faster
> than the electron in the coil, during conditions where there is no
> mechanical load on the motor. That is the maximum speed for a motor but
> going faster makes it into a generator.
>
> H = B/mu
>
> H is magnetic field (units: Amps per meter, or meters per second in
> Continuum Science)
>
> B is magnetic flux density (units: second^-1 or Weber per square meter,
> using Coulomb=area theory)
>
> Henry is Webers per Ampere (units = 1)
>
> 1/mu = 796,000 meters
>
> \$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
>
> Conclusion:  It seems that the number of turns in a motor coil does not
> set the maximum RPM speed. The number of turns can increase the torque
> but not the no-load speed. The no-load speed of the motor is set by the
> speed of the electrons in the coil. The flux density (B) does not change
> the speed limit of a rotor, all flux has the same velocity amplification
> (H) relative to electron motion. That mechanical amplification has a
> factor of 1/mu.
>
> Please check your motors for the ratio of rotor speed over electron
> speed, no load. Is it 796,000?

Limits on DC motor rotor speed comes from bearings burning up, brush
float (on a brushed motor) or, once you've solved that problem, the rotor
failing (or at least deforming) from centripetal acceleration.  On some
motors there's probably a secondary limit on the armature overheating
because you're exceeding the design limit on eddy current or (possibly, I
don't design motors) B-field strength in the iron.

As a test, take your cheap Mabuchi motor, oil the bearings with light oil
(20W is probably perfect, but "sewing machine oil" would work), then
attach it to a variable power supply that'll go up to twice the motor's
rated voltage.  Ramp the voltage up to 2x (or 3x or 4x) the motor's rated
voltage and observe the speed -- you'll see that it goes right up.  Keep
this up until the motor breaks.  Then disassemble, and figure out which
bit broke.

A friend of mine had a job testing brushless motors to destruction.  The
project goal was to get the most powerful motor in the smallest space.
The limit was keeping the magnets on the rotor.  They regularly exceeded
30,000 RPM.

--
Tim Wescott
Control systems, embedded software and circuit design
I'm looking for work!  See my website if you're interested
http://www.wescottdesign.com
```
```On Wednesday, June 1, 2016 at 5:41:39 AM UTC-10, Tim Wescott wrote:

> Limits on DC motor rotor speed comes from bearings burning up, brush
> float (on a brushed motor) or, once you've solved that problem, the rotor
> failing (or at least deforming) from centripetal acceleration.  On some
> motors there's probably a secondary limit on the armature overheating
> because you're exceeding the design limit on eddy current or (possibly, I
> don't design motors) B-field strength in the iron.
>
> As a test, take your cheap Mabuchi motor, oil the bearings with light oil
> (20W is probably perfect, but "sewing machine oil" would work), then
> attach it to a variable power supply that'll go up to twice the motor's
> rated voltage.  Ramp the voltage up to 2x (or 3x or 4x) the motor's rated
> voltage and observe the speed -- you'll see that it goes right up.  Keep
> this up until the motor breaks.  Then disassemble, and figure out which
> bit broke.
>
> A friend of mine had a job testing brushless motors to destruction.  The
> project goal was to get the most powerful motor in the smallest space.
> The limit was keeping the magnets on the rotor.  They regularly exceeded
> 30,000 RPM.

Hi Tim W.,

I understand that the maximum RPM is limited by a destructive event, but my point is not about that limit. I am proposing a new law of motor generators. To test it, use a low current so the motor is not destroyed. Calculate the average velocity of electrons in the armature current:

ve = I / NQA

ve = electron speed, I = current, N =electron density in copper 8*10^28/meter^3, Q is electron charge, A is area of wire

Calulate speed of a proton (vp) in an Iron magnet, relative to the orthogonal copper coil:

vp = 2 pi R omega

Law proposed

vp/ve < 797,000

where 797,000 meters = 1 / permeability of free space

Law proposed: The speed of a motor is less than 797,000 times the speed of an electron in the driving current.

That is in an ideal case where the RPMs are low enough that the motor is not damaged. The permeability of free space is Henrys per meter. Magnetic field H is amps per meter. Magnetic flux density B is Webers per square meter. using these standard terms, the Law will show that the magnetic field is a velocity:

H = meters per second = B/permeability

H = second^-1 / Henry*meter^-1

Weber = Coulomb per second = Ampere

therefore ... law under construction...
```
```On Wed, 01 Jun 2016 11:09:23 -0700, omnilobe wrote:

> On Wednesday, June 1, 2016 at 5:41:39 AM UTC-10, Tim Wescott wrote:
>
>> Limits on DC motor rotor speed comes from bearings burning up, brush
>> float (on a brushed motor) or, once you've solved that problem, the
>> rotor failing (or at least deforming) from centripetal acceleration.
>> On some motors there's probably a secondary limit on the armature
>> overheating because you're exceeding the design limit on eddy current
>> or (possibly, I don't design motors) B-field strength in the iron.
>>
>> As a test, take your cheap Mabuchi motor, oil the bearings with light
>> oil (20W is probably perfect, but "sewing machine oil" would work),
>> then attach it to a variable power supply that'll go up to twice the
>> motor's rated voltage.  Ramp the voltage up to 2x (or 3x or 4x) the
>> motor's rated voltage and observe the speed -- you'll see that it goes
>> right up.  Keep this up until the motor breaks.  Then disassemble, and
>> figure out which bit broke.
>>
>> A friend of mine had a job testing brushless motors to destruction.
>> The project goal was to get the most powerful motor in the smallest
>> space. The limit was keeping the magnets on the rotor.  They regularly
>> exceeded 30,000 RPM.
>
> Hi Tim W.,
>
> I understand that the maximum RPM is limited by a destructive event, but
> my point is not about that limit. I am proposing a new law of motor
> generators. To test it, use a low current so the motor is not destroyed.
> Calculate the average velocity of electrons in the armature current:
>
> ve = I / NQA
>
> ve = electron speed, I = current, N =electron density in copper
> 8*10^28/meter^3, Q is electron charge, A is area of wire
>
> Calulate speed of a proton (vp) in an Iron magnet, relative to the
> orthogonal copper coil:
>
> vp = 2 pi R omega
>
> R is rotor radius, omega is angular velocity, radians per second
>
> Law proposed
>
> vp/ve < 797,000
>
> where 797,000 meters = 1 / permeability of free space
>
> Law proposed: The speed of a motor is less than 797,000 times the speed
> of an electron in the driving current.
>
> That is in an ideal case where the RPMs are low enough that the motor is
> not damaged. The permeability of free space is Henrys per meter.
> Magnetic field H is amps per meter. Magnetic flux density B is Webers
> per square meter. using these standard terms, the Law will show that the
> magnetic field is a velocity:
>
> H = meters per second = B/permeability
>
> H = second^-1 / Henry*meter^-1
>
> Weber = Coulomb per second = Ampere
>
> therefore ... law under construction...

Oh, I'm sorry -- I thought you were seriously interested in something
real.

--
Tim Wescott
Control systems, embedded software and circuit design
I'm looking for work!  See my website if you're interested
http://www.wescottdesign.com
```
```On Wednesday, June 1, 2016 at 9:43:24 AM UTC-10, Tim Wescott wrote:>

Oh, I'm sorry -- I thought you were seriously interested in something  real.
>

Real motors is what I am discussing. The motors that are not damaged can be tested to prove my new Law of motor-generators. For example, for a motor with a maximum allowed RPM of 9200, run it at less than 9200 RPM so it is not damaged. Force a small current so it runs at 8000 RPM.

Calculate the velocity of the motor divided by the velocity of the electron current. The ratio of those two speeds is always below the inverse permeability. This is handled with mathematics that employ primitive units of measure: meters and seconds

B = second^-1 = magnetic flux density

H = meters per second = Magnetic field intensity

mu zero = 1 Henry per 797,000 meters

B = (mu zero) H

B/ mu zero = velocity

where B is one line of flux for one electron and one proton in a pair.
```
```On Wednesday, June 1, 2016 at 8:41:39 AM UTC-7, Tim Wescott wrote:
> On Tue, 31 May 2016 15:32:40 -0700, omnilobe wrote:
>
> > Two motors were evaluated to find the ratio of the speed of the rotor
> > over the speed of the electron in the coil.
> >
> > ratio = speed(rotor) / speed(electron)
> >
> > ratio = 8 meters per second / 10 microns per second
> >
> > Some calculations show that DC electric motors rotate thousands of times
> > faster than the electrons move in the drive current. For example, the
> > Mabuchi RE 280RA motor has a current running electrons at a speed of
> > 5*10^-6 meters per second and its rotor is moving at 8 meters per
> > second. Plus or minus a big number.
> >
> > The mechanical motor runs a million times faster than the speed at which
> > an electron is flowing in its coil.
> >
> > A second motor was examined: Maxon Motor: 8 meter per second rotor speed
> > and electron speed estimated at 2.7*10^-5 meters per second. Plus or
> > minus a big amount.
> >
> > This implies that maybe the permeability of free space  (mu zero) is
> > involved to set that ratio of speeds:
> >
> > 1/(mu) = 796,000 meters per Henry
> >
> > Then a rotor velocity limit can be expected to be 796,000 times faster
> > than the electron in the coil, during conditions where there is no
> > mechanical load on the motor. That is the maximum speed for a motor but
> > going faster makes it into a generator.
> >
> > H = B/mu
> >
> > H is magnetic field (units: Amps per meter, or meters per second in
> > Continuum Science)
> >
> > B is magnetic flux density (units: second^-1 or Weber per square meter,
> > using Coulomb=area theory)
> >
> > Henry is Webers per Ampere (units = 1)
> >
> > 1/mu = 796,000 meters
> >
> > \$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
> >
> > Conclusion:  It seems that the number of turns in a motor coil does not
> > set the maximum RPM speed. The number of turns can increase the torque
> > but not the no-load speed. The no-load speed of the motor is set by the
> > speed of the electrons in the coil. The flux density (B) does not change
> > the speed limit of a rotor, all flux has the same velocity amplification
> > (H) relative to electron motion. That mechanical amplification has a
> > factor of 1/mu.
> >
> > Please check your motors for the ratio of rotor speed over electron
> > speed, no load. Is it 796,000?
>
> Limits on DC motor rotor speed comes from bearings burning up, brush
> float (on a brushed motor) or, once you've solved that problem, the rotor
> failing (or at least deforming) from centripetal acceleration.  On some
> motors there's probably a secondary limit on the armature overheating
> because you're exceeding the design limit on eddy current or (possibly, I
> don't design motors) B-field strength in the iron.
>
> As a test, take your cheap Mabuchi motor, oil the bearings with light oil
> (20W is probably perfect, but "sewing machine oil" would work), then
> attach it to a variable power supply that'll go up to twice the motor's
> rated voltage.  Ramp the voltage up to 2x (or 3x or 4x) the motor's rated
> voltage and observe the speed -- you'll see that it goes right up.  Keep
> this up until the motor breaks.  Then disassemble, and figure out which
> bit broke.
>
> A friend of mine had a job testing brushless motors to destruction.  The
> project goal was to get the most powerful motor in the smallest space.
> The limit was keeping the magnets on the rotor.  They regularly exceeded
> 30,000 RPM.

In that case, an outer-rotor brushless motor should last longer, since centripetal forces simply press the magnets harder into the rotor..?

> --
> Tim Wescott
> Control systems, embedded software and circuit design
> I'm looking for work!  See my website if you're interested
> http://www.wescottdesign.com

Michael
```
```On Wed, 01 Jun 2016 14:36:24 -0700, mrdarrett wrote:

> On Wednesday, June 1, 2016 at 8:41:39 AM UTC-7, Tim Wescott wrote:
>> On Tue, 31 May 2016 15:32:40 -0700, omnilobe wrote:
>>
>> > Two motors were evaluated to find the ratio of the speed of the rotor
>> > over the speed of the electron in the coil.
>> >
>> > ratio = speed(rotor) / speed(electron)
>> >
>> > ratio = 8 meters per second / 10 microns per second
>> >
>> > Some calculations show that DC electric motors rotate thousands of
>> > times faster than the electrons move in the drive current. For
>> > example, the Mabuchi RE 280RA motor has a current running electrons
>> > at a speed of 5*10^-6 meters per second and its rotor is moving at 8
>> > meters per second. Plus or minus a big number.
>> >
>> > The mechanical motor runs a million times faster than the speed at
>> > which an electron is flowing in its coil.
>> >
>> > A second motor was examined: Maxon Motor: 8 meter per second rotor
>> > speed and electron speed estimated at 2.7*10^-5 meters per second.
>> > Plus or minus a big amount.
>> >
>> > This implies that maybe the permeability of free space  (mu zero) is
>> > involved to set that ratio of speeds:
>> >
>> > 1/(mu) = 796,000 meters per Henry
>> >
>> > Then a rotor velocity limit can be expected to be 796,000 times
>> > faster than the electron in the coil, during conditions where there
>> > is no mechanical load on the motor. That is the maximum speed for a
>> > motor but going faster makes it into a generator.
>> >
>> > H = B/mu
>> >
>> > H is magnetic field (units: Amps per meter, or meters per second in
>> > Continuum Science)
>> >
>> > B is magnetic flux density (units: second^-1 or Weber per square
>> > meter, using Coulomb=area theory)
>> >
>> > Henry is Webers per Ampere (units = 1)
>> >
>> > 1/mu = 796,000 meters
>> >
>> > \$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
>> >
>> > Conclusion:  It seems that the number of turns in a motor coil does
>> > not set the maximum RPM speed. The number of turns can increase the
>> > torque but not the no-load speed. The no-load speed of the motor is
>> > set by the speed of the electrons in the coil. The flux density (B)
>> > does not change the speed limit of a rotor, all flux has the same
>> > velocity amplification (H) relative to electron motion. That
>> > mechanical amplification has a factor of 1/mu.
>> >
>> > Please check your motors for the ratio of rotor speed over electron
>> > speed, no load. Is it 796,000?
>>
>> Limits on DC motor rotor speed comes from bearings burning up, brush
>> float (on a brushed motor) or, once you've solved that problem, the
>> rotor failing (or at least deforming) from centripetal acceleration.
>> On some motors there's probably a secondary limit on the armature
>> overheating because you're exceeding the design limit on eddy current
>> or (possibly, I don't design motors) B-field strength in the iron.
>>
>> As a test, take your cheap Mabuchi motor, oil the bearings with light
>> oil (20W is probably perfect, but "sewing machine oil" would work),
>> then attach it to a variable power supply that'll go up to twice the
>> motor's rated voltage.  Ramp the voltage up to 2x (or 3x or 4x) the
>> motor's rated voltage and observe the speed -- you'll see that it goes
>> right up.  Keep this up until the motor breaks.  Then disassemble, and
>> figure out which bit broke.
>>
>> A friend of mine had a job testing brushless motors to destruction.
>> The project goal was to get the most powerful motor in the smallest
>> space. The limit was keeping the magnets on the rotor.  They regularly
>> exceeded 30,000 RPM.
>
>
> In that case, an outer-rotor brushless motor should last longer, since
> centripetal forces simply press the magnets harder into the rotor..?

I don't know if they tried that -- it was long before outrunners were
commonly used.  They did have rotors with titanium bands shrunk on over
the magnets -- which would fail, leaving magnet-sized inverse dimples in
the ring.

It didn't have squat to do with the ratio between electron velocity in
the wires and the rotor velocity; I know that.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

I'm looking for work -- see my website!
```
```On Wed, 1 Jun 2016 13:16:38 -0700 (PDT), omnilobe@gmail.com wrote:

>On Wednesday, June 1, 2016 at 9:43:24 AM UTC-10, Tim Wescott wrote:>
>
>Oh, I'm sorry -- I thought you were seriously interested in something  real.
>>
>
>Real motors is what I am discussing. The motors that are not damaged can be tested to prove my new Law of motor-generators. For example, for a motor with a maximum allowed RPM of 9200, run it at less than 9200 RPM so it is not damaged. Force a small current so it runs at 8000 RPM.
>
>Calculate the velocity of the motor divided by the velocity of the electron current. The ratio of those two speeds is always below the inverse permeability. This is handled with mathematics that employ primitive units of measure: meters and seconds
>
>B = second^-1 = magnetic flux density
>
>H = meters per second = Magnetic field intensity
>
>mu zero = 1 Henry per 797,000 meters
>
>B = (mu zero) H
>
>B/ mu zero = velocity
>
>where B is one line of flux for one electron and one proton in a pair.
For real DC permanent magnet motors the only thing that limits rpm is
the load on the motor. If there was no load, and the motor materials
were of infinite strength, the motor would rotate at just below the
speed of light. No matter how fast the electrons were moving in the
motor windings.
Eric
```
```On 6/1/2016 4:16 PM, omnilobe@gmail.com wrote:
> Calculate the velocity of the motor divided by the velocity of the electron current. The ratio of those two speeds is always below the inverse permeability. ...

And how is that useful?
```
```On Wednesday, June 1, 2016 at 1:28:46 PM UTC-10, Tim Wescott wrote:
> > In that case, an outer-rotor brushless motor should last longer, since
> > centripetal forces simply press the magnets harder into the rotor..?
>
> I don't know if they tried that -- it was long before outrunners were
> commonly used.  They did have rotors with titanium bands shrunk on over
> the magnets -- which would fail, leaving magnet-sized inverse dimples in
> the ring.
>
> It didn't have squat to do with the ratio between electron velocity in
> the wires and the rotor velocity; I know that.

Hi Tim, I have been reading up on motors and the websites do not discuss these electrical engineering standard variables:

H Magnetic Field Intensity

B Magnetic Flux Density

mu permeability

Magnetic motor websites have equations about voltage, current, torque, and rpm, but few even hint that a Magnetic Field Intensity is involved in a motor equation. mu is not in their equations. I am trying to put the H, B, and mu in the motor equations.

1/mu zero = 797,000 meters

That inverse permeability is profound and mysterious.
```