### Re: code to change the motor amp limit

Posted:

**06 Jun 2017, 21:08**As I've said before: with the same termination the KV only depends on the number of turns. Turns times KV is constant.

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Posted: **06 Jun 2017, 21:08**

As I've said before: with the same termination the KV only depends on the number of turns. Turns times KV is constant.

Posted: **06 Jun 2017, 21:13**

rew wrote:As I've said before: with the same termination the KV only depends on the number of turns. Turns times KV is constant.

I thought a few days ago we agreed that it isn't entirely turns dependent and is also affected by the KM factor of the equation.... [see quote]

rew wrote:28 May 2017, 00:47 OK. Now I get it.

Suppose I have two Y wound motors. One I rewire with thicker wire to make the end-to-end resistance 3x smaller. The second I rewire to delta. You will not be able to measure the difference between the two changed motors. Terminal resistance and KV will be identical.

A useful insight after all!

Posted: **07 Jun 2017, 05:32**

You quoted but forgot to read "with the same termination".

Posted: **07 Jun 2017, 19:17**

rew wrote:As I've said before: with the same termination the KV only depends on the number of turns. Turns times KV is constant.

To avoid circular argument I will analyze the information from a second source that agrees with your assertion, while simultaneously seeking any available scientific & mathematical proof of the validity or invalidity of the assertion...

RCGroups wrote:From RC Groups: https://www.rcgroups.com/forums/showthread.php?240993-%28Re%29winding-and-building-motors-tips-tricks-checks-tests

^Let's imagine one person believes this assertion is always true, and another person suspects this assertion can in some cases be proven false.

What is an acceptable scientific method for determining the validity of the assertion?

In situations like these, I search for any proof of impossibility of the assertion in question, and in particular, I search for proof of impossibility by contradiction.

https://en.wikipedia.org/wiki/Proof_of_impossibility wrote:https://en.wikipedia.org/wiki/Proof_of_impossibility

"A proof of impossibility, also known as negative proof, proof of an impossibility theorem, or negative result, is a proof demonstrating that a particular problem cannot be solved, or cannot be solved in general. Often proofs of impossibility have put to rest decades or centuries of work attempting to find a solution..."

...

"Proof by contradiction"

"One widely used type of impossibility proof is proof by contradiction. In this type of proof it is shown that if something, such as a solution to a particular class of equations, were possible, then two mutually contradictory things would be true, such as a number being both even and odd. The contradiction implies that the original premise is impossible."

Since I personally suspect that the assertion in question can in some cases be proven false, I will now attempt to prove the impossibility of the assertion by contradiction:

RCGroups wrote:Kv × number_winds = constant, or, in other words, Kv is inversely proportional to number of winds.

This means that Kv goes up as number of winds go down and vice versa.

rew wrote:Turns times KV is constant.

^The basis of the assertion to be proved or disproved is: Kv × number_winds = constant

Therefore (using the previous 100kv wye example):

100 Kv Wye × 28.86 winds = 2886 constant

Therefore:

X Kv Wye × (28.86 winds x (1/2)) = 2886 constant

X Kv Wye × (14.43 winds) = 2886 constant

200 Kv Wye × (14.43 winds) = 2886 constant

^Simply, according to the assertion half the number of winds is always double the kV.

In other words, in order for the assertion to be true, in every case halving the number of turns must result in a doubling of the KV.

^At this point we'll need a second source of information to prove whether this is true in every conceivable case:

MachineDesign.com wrote:From MachineDesign.com: http://www.machinedesign.com/motorsdrives/how-calculate-new-dc-motor-parameters-modified-winding

^Here we see that increasing only the cross section of a wire with identical amps and turns changes total magnetic flux generated by a coil.

By this equation, a change in total magnetic flux per amp (same number turns) should result in a change in torque per amp with an air core motor, despite the same number of turns and amps.

By extension, due to the inverse relationship between torque per amp (kt) and rpm per volt (kv), a change in torque per amp at the same number of turns should result in an inverse change in rpm per volt (kv).

RCGroups wrote:Kv × number_winds = constant, or, in other words, Kv is inversely proportional to number of winds.

This means that Kv goes up as number of winds go down and vice versa.

rew wrote:Turns times KV is constant.

By extension, a change in rpm per volt (kv) at the same number of turns conflicts with the original assertion, and therefore implies proof of impossibility of the assertion by contradiction.

Posted: **08 Jun 2017, 06:39**

Hi,

You are now progressing to valid scientific methods. Good.

Many people do not understand when a formula is applicable. So when I give them that the voltage across red led is 2V at 20mA, and I ask them to calculate the current limiting resistor for a 5V system, they will plug the given numbers into Ohms law and calculate R= 2V/.02A = 100 Ohms. Or 5V/0.02A = 250 Ohms.

What I THINK is happening is that in the article you quoted this guy fell into this trap and confused A cross section of the wire with A cross section of the LOOP that the wire makes.

Case in point, the flux depends on the number of electrons wizzing around. If it is 1A going around 10 times or 10A going around 1 time does not matter. Especially in an air-coil, the magnetic flux spreads out over the available area. So the flux would be inversely proportional to the area enclosed by the loops of the coil.

He still has a good grasp of the material at hand, because when asked to increase the KV he immediately draws the conclusion that the number of turns must be reduced, implying the validity of the proposition that you're trying to disprove.

You are now progressing to valid scientific methods. Good.

Many people do not understand when a formula is applicable. So when I give them that the voltage across red led is 2V at 20mA, and I ask them to calculate the current limiting resistor for a 5V system, they will plug the given numbers into Ohms law and calculate R= 2V/.02A = 100 Ohms. Or 5V/0.02A = 250 Ohms.

What I THINK is happening is that in the article you quoted this guy fell into this trap and confused A cross section of the wire with A cross section of the LOOP that the wire makes.

Case in point, the flux depends on the number of electrons wizzing around. If it is 1A going around 10 times or 10A going around 1 time does not matter. Especially in an air-coil, the magnetic flux spreads out over the available area. So the flux would be inversely proportional to the area enclosed by the loops of the coil.

He still has a good grasp of the material at hand, because when asked to increase the KV he immediately draws the conclusion that the number of turns must be reduced, implying the validity of the proposition that you're trying to disprove.

Posted: **09 Jun 2017, 09:41**

At precisely no load rpm 100% duty cycle, 0 amps are flowing.

With stalled motor, dc amps is determined by Ohm's law:

I = V/R

W = IV

When:

V = 4.20000 V

R = 0.08300 ohm

Therefore:

I = 50.60249 amps

W = 212.53012 watts

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

In the above example:

-With stalled motor, 4.2V DC results in 50.60 amps & 212.53 watts

-At no load rpm @ 4.2V Peak, the gyromagnetic ratio of the spinning rotor magnets must be such that the momentum per tesla of the rotor magnet surface combined with stator geometry must generate an emf force in the windings which is equal in magnitude and opposite to 50.60 amps & 212.53 watts electrical.

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

Simply at no load rpm, gyromagnetic effect on windings must equal 212.53 watts electrical

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

If we triple the voltage to 12.6V, by ohms law then triple the amps, but 9 times the watts will flow:

151.8 amps & 1912.77 watts

^Watts change factor (9) was square of the amps change factor (3)

-At no load rpm @ 12.6V, the rpm has tripled, the gyromagnetic ratio of the spinning rotor magnets must be such that the momentum per tesla of the rotor magnet surface must generate a force in the windings which is equal in magnitude and opposite to 151.8 amps & 1912.77 watts electrical.

^In other words a tripling in rotor velocity is precisely counteracting a force whose wattage and power is 9 times greater in magnitude.

^This is interesting because, counteracting force increased at the square of the velocity, and for any moving mass, kinetic energy increases at the square of the velocity. Therefore counteracting force increased proportionally to rotor magnet kinetic energy (9x increase in kinetic energy of the magnets vs 3x increase in velocity of the magnets).

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

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

If we triple the cross section of the windings, the resistance decreases to 0.02766ohm

With stalled motor, amps is determined by Ohm's law:

I = V/R

W = IV

When:

V = 12.60000 V

R = 0.02766 ohm <-- 1x(1/3) decrease in resistance

Therefore:

I = 455.53145 amps <-- 1x3 increase in amps

W = 5739.69631 watts <-- 1x3 increase in watts

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

^Let's assume for a moment it would be possible to change the cross section of a wire (same turns) and have no effect on kv,

it implies no load rpm will remain the same rotations per minute in both of these motors:

1912.77 watts electrical @ 12.6V dc @ stall motor

5739.69 watt electrical @ 12.6V dc @ stall motor

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

In the first 2 examples with the same resistance windings but different applied voltages (4.2V vs 12.6V), the change in kinetic energy of the rotor magnets at no load rpm was directly proportional to the change in electrical wattage which was counteracted in the windings by the rotor's gyromagnetic forces.

One could say that the increase in electrical wattage counteracted in the windings in the second example with higher voltage was directly proportional to the (1x9) increase in the kinetic energy of the magnets at the (1x3) higher no load rpm (& (1x9) increase in wattage counteracted was not directly proportional to the (1x3) increase in magnet velocity).

If the ability of the magnets to counteract electrical wattage in windings increases in direct proportion to their kinetic energy, as implied, then it implies tripling the wattage which must be counteracted (in the third example) should require tripling the kinetic energy of the energy of the rotor magnets (compared to the second example) which would require..... drumroll....

an increase factor of sqrt(3) in no load speed aka rpm per volt.

^this happens to be exactly the increase factor of KV seen in a delta retermination (which also triples electrical wattage at the same applied voltage due to 1/3rd resistance of identical wye)...

At the same no load speed as the second example (assuming wire cross section does not change kv) there doesn't seem to be any extra available kinetic energy from the rotor to counteract the decreased resistance and increased electrical wattage of a tripled cross section winding at the same applied 12.6V peak voltage, which implies proof of impossibility by contradiction of "kv x turns = constant"...

With stalled motor, dc amps is determined by Ohm's law:

I = V/R

W = IV

When:

V = 4.20000 V

R = 0.08300 ohm

Therefore:

I = 50.60249 amps

W = 212.53012 watts

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

In the above example:

-With stalled motor, 4.2V DC results in 50.60 amps & 212.53 watts

-At no load rpm @ 4.2V Peak, the gyromagnetic ratio of the spinning rotor magnets must be such that the momentum per tesla of the rotor magnet surface combined with stator geometry must generate an emf force in the windings which is equal in magnitude and opposite to 50.60 amps & 212.53 watts electrical.

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

Simply at no load rpm, gyromagnetic effect on windings must equal 212.53 watts electrical

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

If we triple the voltage to 12.6V, by ohms law then triple the amps, but 9 times the watts will flow:

151.8 amps & 1912.77 watts

^Watts change factor (9) was square of the amps change factor (3)

-At no load rpm @ 12.6V, the rpm has tripled, the gyromagnetic ratio of the spinning rotor magnets must be such that the momentum per tesla of the rotor magnet surface must generate a force in the windings which is equal in magnitude and opposite to 151.8 amps & 1912.77 watts electrical.

^In other words a tripling in rotor velocity is precisely counteracting a force whose wattage and power is 9 times greater in magnitude.

^This is interesting because, counteracting force increased at the square of the velocity, and for any moving mass, kinetic energy increases at the square of the velocity. Therefore counteracting force increased proportionally to rotor magnet kinetic energy (9x increase in kinetic energy of the magnets vs 3x increase in velocity of the magnets).

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

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

If we triple the cross section of the windings, the resistance decreases to 0.02766ohm

With stalled motor, amps is determined by Ohm's law:

I = V/R

W = IV

When:

V = 12.60000 V

R = 0.02766 ohm <-- 1x(1/3) decrease in resistance

Therefore:

I = 455.53145 amps <-- 1x3 increase in amps

W = 5739.69631 watts <-- 1x3 increase in watts

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

^Let's assume for a moment it would be possible to change the cross section of a wire (same turns) and have no effect on kv,

it implies no load rpm will remain the same rotations per minute in both of these motors:

1912.77 watts electrical @ 12.6V dc @ stall motor

5739.69 watt electrical @ 12.6V dc @ stall motor

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

In the first 2 examples with the same resistance windings but different applied voltages (4.2V vs 12.6V), the change in kinetic energy of the rotor magnets at no load rpm was directly proportional to the change in electrical wattage which was counteracted in the windings by the rotor's gyromagnetic forces.

One could say that the increase in electrical wattage counteracted in the windings in the second example with higher voltage was directly proportional to the (1x9) increase in the kinetic energy of the magnets at the (1x3) higher no load rpm (& (1x9) increase in wattage counteracted was not directly proportional to the (1x3) increase in magnet velocity).

If the ability of the magnets to counteract electrical wattage in windings increases in direct proportion to their kinetic energy, as implied, then it implies tripling the wattage which must be counteracted (in the third example) should require tripling the kinetic energy of the energy of the rotor magnets (compared to the second example) which would require..... drumroll....

an increase factor of sqrt(3) in no load speed aka rpm per volt.

^this happens to be exactly the increase factor of KV seen in a delta retermination (which also triples electrical wattage at the same applied voltage due to 1/3rd resistance of identical wye)...

At the same no load speed as the second example (assuming wire cross section does not change kv) there doesn't seem to be any extra available kinetic energy from the rotor to counteract the decreased resistance and increased electrical wattage of a tripled cross section winding at the same applied 12.6V peak voltage, which implies proof of impossibility by contradiction of "kv x turns = constant"...

rew wrote:28 May 2017, 00:47 OK. Now I get it.

Suppose I have two Y wound motors. One I rewire with thicker wire to make the end-to-end resistance 3x smaller. The second I rewire to delta. You will not be able to measure the difference between the two changed motors. Terminal resistance and KV will be identical.

A useful insight after all!

Posted: **09 Jun 2017, 20:07**

The back EMF has NOTHING to do with 50 Amps and 200 Watts. As long as it adds up to that 4.2V (whereever that comes from) it is ok.devin wrote:-At no load rpm @ 4.2V Peak, the gyromagnetic ratio of the spinning rotor magnets must be such that the momentum per tesla of the rotor magnet surface combined with stator geometry must generate an emf force in the windings which is equal in magnitude and opposite to 50.60 amps & 212.53 watts electrical.

Posted: **09 Jun 2017, 20:44**

rew wrote:The back EMF has NOTHING to do with 50 Amps and 200 Watts. As long as it adds up to that 4.2V (whereever that comes from) it is ok.

yes the gyromagnetic ratio ( https://en.wikipedia.org/wiki/Gyromagnetic_ratio ) of the rotor magnets -- the ratio of the cumulative magnetic moment in newton meters per tesla ( https://en.wikipedia.org/wiki/Magnetic_moment ) of all the rotor magnets per quantity of cumulative angular momentum of the same rotor magnets in radians per second per newton meter per tesla.

^From this, in SI units one could derive a related gyromagnetic ratio -- kinetic energy per newton meter per tesla of the rotor magnets in joules per newton meter per tesla.

Posted: **10 Jun 2017, 04:18**

A 3 tooth wye air core motor with optical sensors has 3 solenoids.

KV testing is performed with a 4.2V DC source, commutation timing is achieved via optical sensors, and effective voltage to motor is 4.2V directly from the DC source with no PWM, revealing a 100kv motor constant.

Each solenoid has 50 turns, a lead to virtual ground point resistance of 0.0415ohm and a solenoid magnetic moment vector area of 0.00064516 m^2, and a solenoid length of 0.01 meters.

Since this is a wye motor and when voltage is applied to any 2 leads, two of the 3 solenoids are wired in series, the lead to lead resistance of this motor measured at stall is 0.0830ohm.

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

The magnetic moment of a single layer winding solenoid, measured in newton meters per tesla, is given by the following formula:

u=NIS

Where:

u = Magnetic Moment of Solenoid in newton meters per tesla

N = Number of identical turns

I = Current in Amperes

S = Vector Area (Solenoid Cross Section Area in Square Meters)

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

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

The flux density of a single layer winding solenoid, measured in tesla, is given by the following formula:

B = ((u0)*N*I)/L

Where:

B = Flux Density in Tesla

u0 = 4pi(10^-7) = Absolute Vacuum Permeability

N = Number of identical turns

I = Current in Amperes

L = Solenoid Length in Meters

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

The Auxilliary H Magnetic Field Strength, measured in newtons per weber, is given by the following formula:

H = (NI)/L

Where:

H = Auxilliary H Magnetic Field Strength in Newtons per Weber

N = Number of identical turns

I = Current in Amperes

L = Solenoid Length in Meters

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

As per Ohm's law:

I = V/R

W = IV

Where:

I = Current in Amperes

V = Volts DC

R = Resistance in Ohms

W = Power in Watts

https://en.wikipedia.org/wiki/Ohm%27s_law

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

Therefore:

Magnetic Moment of A Single Solenoid (Rotor Removed) (Example #1)

u=N(V/R)S

3.26466=50*(4.2/0.0415)*0.00064516

u=NIS

3.26466=50*101.20481*0.00064516

Flux Density of A Single Solenoid

B = ((u0)*N*I)/L

0.63588 = ((4pi(10^(-7)))*50*101.20481)/0.01

H-Field of A Single Solenoid

H = (NI)/L

506024.05 = (50*101.20481)/0.01

Where:

N = 50 = Number of identical turns

I = 101.20481 Current in Amperes

V = 4.2 = Volts DC

R = 0.0415 = Resistance in Ohms

S = 0.00064516 = Vector Area (Solenoid Cross Section Area in Square Meters) = 1 square inch

W = 425.06020 = Electrical Power in Watts

u = 3.26466 = Magnetic Moment of Solenoid in newton meters per tesla

B = 0.63588 = Flux Density in Tesla

H = 506024.05 = Auxilliary H Magnetic Field Strength in Newtons Per Weber

u0 = 4pi(10^-7) = Absolute Vacuum Permeability

L = 0.01 = Solenoid Length in Meters

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

Now we increase the wire cross section to 3 times the original size, while keeping the number of turns identical.

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

This gives:

Magnetic Moment of A Single Solenoid (Rotor Removed) (Example #2)

u=N(V/R)S

9.79635=50(4.2/0.01383)0.00064516

u=NIS

9.79635=50(303.68764)0.00064516

Flux Density of A Single Solenoid at Stall

B = ((u0)*N*I)/L

1.90812 = ((4pi(10^(-7)))*50*303.68764)/0.01

N = 50 = Number of identical turns

I = 303.68764 Current in Amperes <-- 1x(3) more current than Example #1

V = 4.2 = Volts DC

R = 0.01383 = Resistance in Ohms <-- 1x(1/3) less resistance than Example #1

S = 0.00064516 = Vector Area (Solenoid Cross Section Area in Square Meters) = 1 square inch

W = 1275.48807 = Electrical Power in Watts <-- 1x(3) more power than Example #1

u = 9.79635 = Magnetic Moment of Solenoid in newton meters per tesla <-- 1x(3) more Magnetic Moment than Example #1

B = 1.90812 = Flux Density in Tesla <-- 1x(3) more Flux Density than Example #1

u0 = 4pi(10^-7) = Absolute Vacuum Permeability

L = 0.01 = Solenoid Length in Meters

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

^Tripling the cross section of the wire at the same number of turns has tripled the magnetic moment of the solenoid. Despite the tripling of the magnetic moment of the solenoids with tripled cross section, the magnetic moment of the permanent magnets in the rotor remained constant.

Since the magnetic moment of the permanent magnets is fixed in magnitude, the gyromagnetic ratio of the rotor magnets increases proportionally to rotor angular momentum.

In rotational systems, power is the product of the torque τ and angular velocity ω. (Source: https://en.wikipedia.org/wiki/Power_%28physics%29)

Since the gyromagnetic ratio of the rotor magnets at a particular rpm has both a mechanical torque component acting on nearby magnetic objects in proportion to their B-Field flux density, the rotor itself has a kinetic energy, and an angular momentum measured in rpm, and since power is the product of torque and angular velocity, and since the torque of a spinning rotor is proportional to its kinetic energy...

...from the magnetic moment of the permanent magnets, the magnetic properties of nearby stator and windings, the kinetic energy of the rotor and its angular velocity, we can derive the power in watts of the torque times the angular momentum of the rotating magnetic field produced by the spinning rotor magnets which is acting on the mobile charge carriers in the windings.

Since the rotating magnetic field generated by the spinning rotor magnets has a definite "available wattage" to do work on nearby magnetized objects (limited by the kinetic energy of the rotor at a particular rpm), the effect on a current in a winding caused by the spinning magnets is limited to the "available wattage" present in the spinning rotor. (Rotor torque acting on charge carriers in windings proportional to rotor kinetic energy relative to stator, angular momentum, and total magnetic moment of the permanent magnets).

If at a certain rpm the available wattage present in the rotating magnetic field of the rotor magnets' influence on mobile charge carriers in the windings is less than the opposing electrical wattage of those same mobile charge carriers in the same windings, then current present in the nearby wires cannot be reduced all the way to 0 as would be the case at no load rpm for a given applied voltage, since there is not enough available rotor wattage to counteract the winding wattage.

If in Example 1, at a particular rpm, the spinning magnetic field of the rotor has sufficient wattage to completely counteract the electrical wattage in the nearby wires, bringing current to 0 despite the 4.2V closed circuit, then this particular rpm is "no load rpm" and the rpm per applied volt is the KV.

In Example 2, when the winding cross section and electrical wattage found in the windings triples, then at the same rotor rpm which was no load rpm in Example 1, since there is no additional kinetic energy in the rotor at the same rpm as before, there is insufficient additional wattage provided by the rotating magnetic field of the rotor magnets to completely counteract the tripled electrical wattage found in the windings.

Further complicating matters is the fact that while the rotor's magnetic field is rotating, the stator's magnetic field is also rotating due to the commutations.

In example 1, at no load rpm winding current is brought down to 0 as a result of the rotational wattage of the rotating magnetic field of the rotor magnets.

In example 2, at the same rpm as was no load in example 1, the wattage in the windings is 3 times larger in magnitude than the wattage that the rotor's rotating magnetic field is exerting upon the mobile charge carriers in the windings, therefore the rotor's effect on the windings is insufficient to bring winding current to 0. Since the same RPM in example 2 is insufficient to bring current to 0 despite the 4.2V dc applied voltage, it is not no load rpm, and therefore no load RPM in example 1 and 2 must be different. Since no load rpm in example 1 and 2 must be different, and only the cross section of the wire changed, it is implied that a change in cross section of a winding wire must cause a change in KV.

KV testing is performed with a 4.2V DC source, commutation timing is achieved via optical sensors, and effective voltage to motor is 4.2V directly from the DC source with no PWM, revealing a 100kv motor constant.

Each solenoid has 50 turns, a lead to virtual ground point resistance of 0.0415ohm and a solenoid magnetic moment vector area of 0.00064516 m^2, and a solenoid length of 0.01 meters.

Since this is a wye motor and when voltage is applied to any 2 leads, two of the 3 solenoids are wired in series, the lead to lead resistance of this motor measured at stall is 0.0830ohm.

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

The magnetic moment of a single layer winding solenoid, measured in newton meters per tesla, is given by the following formula:

u=NIS

Where:

u = Magnetic Moment of Solenoid in newton meters per tesla

N = Number of identical turns

I = Current in Amperes

S = Vector Area (Solenoid Cross Section Area in Square Meters)

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

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

The flux density of a single layer winding solenoid, measured in tesla, is given by the following formula:

B = ((u0)*N*I)/L

Where:

B = Flux Density in Tesla

u0 = 4pi(10^-7) = Absolute Vacuum Permeability

N = Number of identical turns

I = Current in Amperes

L = Solenoid Length in Meters

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

The Auxilliary H Magnetic Field Strength, measured in newtons per weber, is given by the following formula:

H = (NI)/L

Where:

H = Auxilliary H Magnetic Field Strength in Newtons per Weber

N = Number of identical turns

I = Current in Amperes

L = Solenoid Length in Meters

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

As per Ohm's law:

I = V/R

W = IV

Where:

I = Current in Amperes

V = Volts DC

R = Resistance in Ohms

W = Power in Watts

https://en.wikipedia.org/wiki/Ohm%27s_law

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

Therefore:

Magnetic Moment of A Single Solenoid (Rotor Removed) (Example #1)

u=N(V/R)S

3.26466=50*(4.2/0.0415)*0.00064516

u=NIS

3.26466=50*101.20481*0.00064516

Flux Density of A Single Solenoid

B = ((u0)*N*I)/L

0.63588 = ((4pi(10^(-7)))*50*101.20481)/0.01

H-Field of A Single Solenoid

H = (NI)/L

506024.05 = (50*101.20481)/0.01

Where:

N = 50 = Number of identical turns

I = 101.20481 Current in Amperes

V = 4.2 = Volts DC

R = 0.0415 = Resistance in Ohms

S = 0.00064516 = Vector Area (Solenoid Cross Section Area in Square Meters) = 1 square inch

W = 425.06020 = Electrical Power in Watts

u = 3.26466 = Magnetic Moment of Solenoid in newton meters per tesla

B = 0.63588 = Flux Density in Tesla

H = 506024.05 = Auxilliary H Magnetic Field Strength in Newtons Per Weber

u0 = 4pi(10^-7) = Absolute Vacuum Permeability

L = 0.01 = Solenoid Length in Meters

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

Now we increase the wire cross section to 3 times the original size, while keeping the number of turns identical.

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

This gives:

Magnetic Moment of A Single Solenoid (Rotor Removed) (Example #2)

u=N(V/R)S

9.79635=50(4.2/0.01383)0.00064516

u=NIS

9.79635=50(303.68764)0.00064516

Flux Density of A Single Solenoid at Stall

B = ((u0)*N*I)/L

1.90812 = ((4pi(10^(-7)))*50*303.68764)/0.01

N = 50 = Number of identical turns

I = 303.68764 Current in Amperes <-- 1x(3) more current than Example #1

V = 4.2 = Volts DC

R = 0.01383 = Resistance in Ohms <-- 1x(1/3) less resistance than Example #1

S = 0.00064516 = Vector Area (Solenoid Cross Section Area in Square Meters) = 1 square inch

W = 1275.48807 = Electrical Power in Watts <-- 1x(3) more power than Example #1

u = 9.79635 = Magnetic Moment of Solenoid in newton meters per tesla <-- 1x(3) more Magnetic Moment than Example #1

B = 1.90812 = Flux Density in Tesla <-- 1x(3) more Flux Density than Example #1

u0 = 4pi(10^-7) = Absolute Vacuum Permeability

L = 0.01 = Solenoid Length in Meters

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

^Tripling the cross section of the wire at the same number of turns has tripled the magnetic moment of the solenoid. Despite the tripling of the magnetic moment of the solenoids with tripled cross section, the magnetic moment of the permanent magnets in the rotor remained constant.

Since the magnetic moment of the permanent magnets is fixed in magnitude, the gyromagnetic ratio of the rotor magnets increases proportionally to rotor angular momentum.

In rotational systems, power is the product of the torque τ and angular velocity ω. (Source: https://en.wikipedia.org/wiki/Power_%28physics%29)

Since the gyromagnetic ratio of the rotor magnets at a particular rpm has both a mechanical torque component acting on nearby magnetic objects in proportion to their B-Field flux density, the rotor itself has a kinetic energy, and an angular momentum measured in rpm, and since power is the product of torque and angular velocity, and since the torque of a spinning rotor is proportional to its kinetic energy...

...from the magnetic moment of the permanent magnets, the magnetic properties of nearby stator and windings, the kinetic energy of the rotor and its angular velocity, we can derive the power in watts of the torque times the angular momentum of the rotating magnetic field produced by the spinning rotor magnets which is acting on the mobile charge carriers in the windings.

Since the rotating magnetic field generated by the spinning rotor magnets has a definite "available wattage" to do work on nearby magnetized objects (limited by the kinetic energy of the rotor at a particular rpm), the effect on a current in a winding caused by the spinning magnets is limited to the "available wattage" present in the spinning rotor. (Rotor torque acting on charge carriers in windings proportional to rotor kinetic energy relative to stator, angular momentum, and total magnetic moment of the permanent magnets).

If at a certain rpm the available wattage present in the rotating magnetic field of the rotor magnets' influence on mobile charge carriers in the windings is less than the opposing electrical wattage of those same mobile charge carriers in the same windings, then current present in the nearby wires cannot be reduced all the way to 0 as would be the case at no load rpm for a given applied voltage, since there is not enough available rotor wattage to counteract the winding wattage.

If in Example 1, at a particular rpm, the spinning magnetic field of the rotor has sufficient wattage to completely counteract the electrical wattage in the nearby wires, bringing current to 0 despite the 4.2V closed circuit, then this particular rpm is "no load rpm" and the rpm per applied volt is the KV.

In Example 2, when the winding cross section and electrical wattage found in the windings triples, then at the same rotor rpm which was no load rpm in Example 1, since there is no additional kinetic energy in the rotor at the same rpm as before, there is insufficient additional wattage provided by the rotating magnetic field of the rotor magnets to completely counteract the tripled electrical wattage found in the windings.

Further complicating matters is the fact that while the rotor's magnetic field is rotating, the stator's magnetic field is also rotating due to the commutations.

In example 1, at no load rpm winding current is brought down to 0 as a result of the rotational wattage of the rotating magnetic field of the rotor magnets.

In example 2, at the same rpm as was no load in example 1, the wattage in the windings is 3 times larger in magnitude than the wattage that the rotor's rotating magnetic field is exerting upon the mobile charge carriers in the windings, therefore the rotor's effect on the windings is insufficient to bring winding current to 0. Since the same RPM in example 2 is insufficient to bring current to 0 despite the 4.2V dc applied voltage, it is not no load rpm, and therefore no load RPM in example 1 and 2 must be different. Since no load rpm in example 1 and 2 must be different, and only the cross section of the wire changed, it is implied that a change in cross section of a winding wire must cause a change in KV.

Posted: **10 Jun 2017, 06:21**

Who is paying me to check your homework?

Your end result is wrong, there must be something wrong with your reasoning.

I still think you're confusing the electrical power that goes into the motor, at stall being 100% losses, with something going on with the magnetic fields. You are throwing with formulas that I am unfamiliar with. I would have to study to get to know them and their limitations.

Your end result is wrong, there must be something wrong with your reasoning.

I still think you're confusing the electrical power that goes into the motor, at stall being 100% losses, with something going on with the magnetic fields. You are throwing with formulas that I am unfamiliar with. I would have to study to get to know them and their limitations.