Thread: The Relationship Between Electron Drift Velocity at Stall and Maximum Rotor Velocity in BLDC Electric Motors

1. This is probably among the most bizarre and controversial observations I've yet made regarding BLDC electric motors... & the purpose of this conversation is that some very knowledgeable folks have previously denied the truth of this tale...

I have observed that there is a direct linear relationship between changes in the maximum rotor velocity at no load rpm -- ie maximum rotor speed when there is no mechanical load applied to the rotor -- and changes in the electron drift velocity at stall in the winding of a BLDC electric motor -- ie when the rotor is mechanically held stationary.

In other words:

A=B

A = Change Factor of Electron Drift Velocity at Rotor Stall
B = Change Factor of Maximum Rotor Velocity with No Mechanical Load

For example:

Suppose I have a 100kv BLDC electric motor that has 100 "turns" copper winding per "stator tooth" and a 10 volt battery. When I apply the 10v to the 100kv motor with no mechanical load in a vacuum, the maximum rotor velocity will be 1000rpm = 10v*100kv.

Now I double the battery voltage (20v). At stall, the electron drift velocity is doubled. At maximum rotor velocity, the rotor rotation rate is doubled - 2000rpm = 20v*100kv.

Now using the original (10v) battery, I halve the length of the stator/armature copper winding -- ie half the number of "turns" -- now the motor only has 50 "turns" of the same cross section copper winding and according the the KV formula, this doubles the KV or rpm per volt of the motor to 200kv. At stall, the electron drift velocity is doubled. At maximum rotor velocity, the rotor rotation rate is doubled - 2000rpm = 10v*200kv.

In both cases -- doubling the battery voltage or halving the number of turns -- the outcome is the same: a doubling of the electron drift velocity at stall and a doubling of the maximum rotor velocity with no mechanical load.

Image Caption: The stator/armature on the right has half as many "turns" as the stator/armature on the left (and half the "conductor length"), but both wires have the same thickness or "cross section." The stator/armature on the right has double the "KV" or rpm per volt, double the "maximum rotor speed" at the same applied voltage, and double the electron drift velocity at stall at the same applied voltage.

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KV Formulas:
The "traditional" formula for describing changes in KV is as follows (no change in termination):

KN=C
K=C/N

K = kv = new kv (max rpm per volt) no load
N = turns = new # of wire turns per tooth
C = constant = original kv x original # turns

or:

D=sqrt(E/(V*N))
E=N*V*D^2
V=E/(N*D^2)
N=E/(V*D^2)

D = Change Factor of KV (rpm/v)
E = Change Factor of Conductor Resistivity (ohm-meters)
V = Change Factor of Conductor Volume (meters^3)
N = Change Factor of Conductor Resistance (ohm)

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Source: https://en.wikipedia.org/wiki/Drift_velocity

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^We can see halving the conductor length doubles the electron drift velocity... & doubling the voltage doubles the electron drift velocity... & and doubling the wire cross section has no effect on electron drift velocity... behaviors also describing changes to the maximum rotor velocity with no mechanical load (halving conductor length doubles no load rpm, and doubling voltage doubles no load rpm, and changing the thickness of the conductor has no effect on maximum rotor velocity).

-------------------

Simply when the electrons go twice as fast at stall, the rotor goes twice as fast with no mechanical load.

2.

3. Originally Posted by devin-m
This is probably among the most bizarre and controversial observations I've yet made regarding BLDC electric motors.. . .

Simply when the electrons go twice as fast at stall, the rotor goes twice as fast with no mechanical load.
You've just concluded that by reducing the number of turns, stall current goes up due to the lower copper resistance and maximum speed goes up due to reduced inductance.

That's neither bizarre nor controversial. Most ebike manufacturers advertise motors by number of turns, since ebike designers are well aware of that tradeoff. Want to go faster? Reduce the number of turns. But then watch out for overheating and efficiency losses, because currents will be higher.

4. Originally Posted by billvon
Originally Posted by devin-m
This is probably among the most bizarre and controversial observations I've yet made regarding BLDC electric motors.. . .

Simply when the electrons go twice as fast at stall, the rotor goes twice as fast with no mechanical load.
You've just concluded that by reducing the number of turns, stall current goes up due to the lower copper resistance and maximum speed goes up due to reduced inductance.

That's neither bizarre nor controversial. Most ebike manufacturers advertise motors by number of turns, since ebike designers are well aware of that tradeoff. Want to go faster? Reduce the number of turns. But then watch out for overheating and efficiency losses, because currents will be higher.
@billvon -- except doubling the battery voltage has no effect on inductance -- but it does double both the electron drift velocity at stall and maximum rotor velocity with no mechanical load.

5. Originally Posted by devin-m
Originally Posted by billvon
That's neither bizarre nor controversial. Most ebike manufacturers advertise motors by number of turns, since ebike designers are well aware of that tradeoff. Want to go faster? Reduce the number of turns. But then watch out for overheating and efficiency losses, because currents will be higher.
@billvon -- except doubling the battery voltage has no effect on inductance -- but it does double both the electron drift velocity at stall and maximum rotor velocity with no mechanical load.
In stall, there is no back EMF, so the current is simply given by Ohm's law. Doubling the battery voltage then doubles the current. Easy peasy. By using "drift velocity" as a proxy for what other humans call "current" you obscure the obvious.

And doubling the voltage causing a doubling in the no-load rotor velocity is similarly neither bizarre nor controversial, although the relationship is not exact (it's correct to first order, yes, but it's not exact). Why does this surprise you so? Whenever I increase the voltage applied to a dc motor, it spins faster. I would be surprised only if this were not so.

6. Originally Posted by tk421
Originally Posted by devin-m
Originally Posted by billvon
That's neither bizarre nor controversial. Most ebike manufacturers advertise motors by number of turns, since ebike designers are well aware of that tradeoff. Want to go faster? Reduce the number of turns. But then watch out for overheating and efficiency losses, because currents will be higher.
@billvon -- except doubling the battery voltage has no effect on inductance -- but it does double both the electron drift velocity at stall and maximum rotor velocity with no mechanical load.
In stall, there is no back EMF, so the current is simply given by Ohm's law. Doubling the battery voltage then doubles the current. Easy peasy. By using "drift velocity" as a proxy for what other humans call "current" you obscure the obvious.

And doubling the voltage causing a doubling in the no-load rotor velocity is similarly neither bizarre nor controversial, although the relationship is not exact (it's correct to first order, yes, but it's not exact). Why does this surprise you so? Whenever I increase the voltage applied to a dc motor, it spins faster. I would be surprised only if this were not so.
@tk421 -- except -- doubling the cross section area of the armature winding (instead of halving turns or doubling voltage) would also double the "current" at stall according to Ohm's law -- but doubling the armature winding cross section and therefore current at stall would not affect the electron drift velocity nor would it have any effect on the rotor's maximum velocity -- which is why there is no direct relationship between stall "current" according to Ohm's law and rotor maximum velocity. For these reasons I see referring to the direct proportionality between changes in maximum rotor velocity and electron drift velocity at stall rather than current as more appropriate.

simply-- changing the cross section of the wire affects the stall current according to ohm's law, but cross section changes do not have any effect on max rpm or electron drift velocity. only changes to the winding that affect electron drift velocity -- such as conductor length and voltage changes -- have a proportional affect on maximum rotor velocity with no mechanical load.

as one can see from the following graphic, changes to conductor thickness (which do indeed affect current at stall according to ohm's law @tk421) do not change electron drift velocity (nor do they affect rotor maximum velocity):

Source: https://en.wikipedia.org/wiki/Drift_velocity

7. Originally Posted by devin-m
@tk421 -- except -- doubling the cross section area of the armature winding (instead of halving turns or doubling voltage) would also double the "current" at stall according to Ohm's law -- but doubling the armature winding cross section and therefore current at stall would not affect the electron drift velocity nor would it have any effect on the rotor's maximum velocity -- which is why there is no direct relationship between stall "current" according to Ohm's law and rotor maximum velocity. For these reasons I see referring to the direct proportionality between changes in maximum rotor velocity and electron drift velocity at stall rather than current as more appropriate.

simply-- changing the cross section of the wire affects the stall current according to ohm's law, but cross section changes do not have any effect on max rpm or electron drift velocity. only changes to the winding that affect electron drift velocity -- such as conductor length and voltage changes -- have a proportional affect on maximum rotor velocity with no mechanical load...
What I am saying is very simple. Take a motor as constructed. Drive it with a voltage under stalled conditions. Measure the current. Now double the voltage. The stall current will (approximately) double.

Now you are trying to say that cross-sectional area, etc. matter. Of course they matter in the sense that the absolute current will change, but not the proportionality.

Your claim, as originally stated, doesn't make sense (you cannot equate a linear drift velocity and a rotor's angular velocity). But it now seems that what you stated was what you really meant. In that case, your original statement is easily shown to be wrong simply on dimensional grounds, for 3 pounds can never equal 7 miles.

Only the proportionality relationship makes sense, and it isn't surprising.

If you replace "angular velocity" with "tangential velocity", that still won't save you, because I can always change the diameter of the rotor to get a variety of tangential velocities for a given fixed angular velocity.

8. Originally Posted by tk421
Originally Posted by devin-m
@tk421 -- except -- doubling the cross section area of the armature winding (instead of halving turns or doubling voltage) would also double the "current" at stall according to Ohm's law -- but doubling the armature winding cross section and therefore current at stall would not affect the electron drift velocity nor would it have any effect on the rotor's maximum velocity -- which is why there is no direct relationship between stall "current" according to Ohm's law and rotor maximum velocity. For these reasons I see referring to the direct proportionality between changes in maximum rotor velocity and electron drift velocity at stall rather than current as more appropriate.

simply-- changing the cross section of the wire affects the stall current according to ohm's law, but cross section changes do not have any effect on max rpm or electron drift velocity. only changes to the winding that affect electron drift velocity -- such as conductor length and voltage changes -- have a proportional affect on maximum rotor velocity with no mechanical load...
What I am saying is very simple. Take a motor as constructed. Drive it with a voltage under stalled conditions. Measure the current. Now double the voltage. The stall current will (approximately) double.

Now you are trying to say that cross-sectional area, etc. matter. Of course they matter in the sense that the absolute current will change, but not the proportionality.

Your claim, as originally stated, doesn't make sense (you cannot equate a linear drift velocity and a rotor's angular velocity). But it now seems that what you stated was what you really meant. In that case, your original statement is easily shown to be wrong simply on dimensional grounds, for 3 pounds can never equal 7 miles.

Only the proportionality relationship makes sense, and it isn't surprising.

If you replace "angular velocity" with "tangential velocity", that still won't save you, because I can always change the diameter of the rotor to get a variety of tangential velocities for a given fixed angular velocity.
@tk421 -- what I'm saying is what I said in the first post:

Originally Posted by devin-m
A=B

A = Change Factor of Electron Drift Velocity at Rotor Stall
B = Change Factor of Maximum Rotor Velocity with No Mechanical Load
C = Change Factor of Stall Current

@tk421 - notice i didn't say the units of measurement are equivalent, but rather the factor of change of both numerical values is always the same.

---------
Case 1: Doubling Battery Voltage

A = 2 = Change Factor of Electron Drift Velocity at Rotor Stall
B = 2 = Change Factor of Maximum Rotor Velocity with No Mechanical Load
C = 2 = Change Factor of Stall Current (as per ohm's law)

---------
Case 2: Halving "Turns" and Conductor Length

A = 2 = Change Factor of Electron Drift Velocity at Rotor Stall
B = 2 = Change Factor of Maximum Rotor Velocity with No Mechanical Load
C = 2 = Change Factor of Stall Current (as per ohm's law)

---------
Case 3: Doubling Cross Section Area of Armature Winding Conductor

A = 1 = Change Factor of Electron Drift Velocity at Rotor Stall
B = 1 = Change Factor of Maximum Rotor Velocity with No Mechanical Load
C = 2 = Change Factor of Stall Current (as per ohm's law) <--stall current doubled, but not drift velocity or max rotor velocity

^@tk421 -- in all 3 cases stall "current" is doubled, but even though stall current is doubled in case number 3, there is no effect on electron drift velocity or maximum rotor velocity. Case 3 proves there is no simple direct relationship between kv and ohm's law or stall current, and why the electron drift velocity relation to kv is more appropriate -- and also why the observation is both bizarre and controversial.

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If you wish to calculate the change factor of KV based on the change factors in resistance and volume, you can use:

D=sqrt(E/(V*N))
E=N*V*D^2
V=E/(N*D^2)
N=E/(V*D^2)

D = Change Factor of KV (rpm/v)
E = Change Factor of Conductor Resistivity (ohm-meters)
V = Change Factor of Conductor Volume (meters^3)
N = Change Factor of Conductor Resistance (ohm)

For example, using Case 2:

D=sqrt(E/(V*N))
D=sqrt(1/(0.5*0.5))

D = 2 = Change Factor of KV (rpm/v)

Using Case 3:

D=sqrt(E/(V*N))
D=sqrt(1/(2*0.5))

D = 1 = Change Factor of KV (rpm/v)

9. Case 4: Keeping Identical Copper Volume But Dividing “Turns” and Conductor Length by 1.41421... = sqrt(2) and Multiplying Cross Section Area of Armature Winding Conductor by 1.41421... = sqrt(2)

A = 1.41421... = sqrt(2) = Change Factor of Electron Drift Velocity at Rotor Stall
B = 1.41421... = sqrt(2) = Change Factor of Maximum Rotor Velocity with No Mechanical Load
C = 2 = Change Factor of Stall Current (as per ohm's law) <--stall current doubled, but not drift velocity or max rotor velocity

Using Case 4:

D=sqrt(E/(V*N))
D=sqrt(1/(1*0.5))

D = 1.41421... = sqrt(2) = Change Factor of KV (rpm/v)
E = 1 = Change Factor of Conductor Resistivity (ohm-meters)
V = 1 = Change Factor of Conductor Volume (meters^3)
N = 0.5 = 1/2 = Change Factor of Conductor Resistance (ohm)

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