Investigating what’s behind the “Old Truths” and general advice regarding our typical use of electric motors.
This apply to brushed and brushless motors alike, although for brushed motors I’m aware that some of the mathematical models used only work well within a narrower voltage range. The general conclusions still hold though.
I’ve stuck to dissecting the influence of winding turns and feed voltage, since those are the primary factors that we as users can influence when choosing motor and battery. The rest of the internal motor hardware is simply assumed to be “constant”.
The article is very wordy and there are many formulas presented. I’ve broken this subject into one post for each motor property. Each post, apart from the last ones, is subdivided into a short presentation, Theory, Reality Check and Conclusion.
Contents:
Introduction:
I’ve started this thread as a spin-off from another thread.
My previous statement, to the effect of “More turns => More torque, more efficiency and less Kv” stems from what’s generally accepted as the “truth” and also on the fact that the general (and good) advice is to gear down when switching to a higher Kv motor. I blame only myself for not previously having done the proper research…
Now I’ve spent some time going back to the basic physics of electric motors and compare that to reality to find out what is true.
The physics is simply an applied use of Ohm’s law, Faraday’s law, Kirchhoff’s voltage law and some other basic rules of electronics and mechanics.
For the mathematical models I’ve throughout assumed that all pieces of the motors except the windings are identical and constant. The amount of copper used for the windings is also constant (unless otherwise explicably noted).
“Reality” is represented by well proven general advice and experience as well as manufacturer’s data for the somewhat older range of Turnigy TrackStar motors. I used these motors because of the relatively exhaustive amount of data given and I run the 17.5T version myself. The full range isn’t directly comparable without caution since the motors up to 8.5T have an internal fan that the others don’t and some data lack precision. The 4.5T version can be found here.
I’m aware it’s not sufficient to have a select very few motors to make perfect conclusions set in stone, but it’s far better than having only the theories.
Some results are intriguing, to say the least…
Legend
Physics and maths go hand in hand when doing the theoretical study, so here is a legend for terms used later. Notice that there’s a difference between upper and lower case letters:
N = Number of winding turns.
R = Electrical resistance in the winding. Unit: Ω
f = Motor angular velocity, used as a variable. Unit: rad/s
f0 = Angular velocity at no load for a given voltage.
Kv = f0*π / 30*voltage. Unit: rpm/V (For brushed motors this is more voltage dependent than for BL motors. I use it as a constant though.)
V = Feed voltage, when used as a variable. Unit: V
V0 = The feed voltage, a constant.
VE = Electromotive Force. Unit: V
I = The electrical current through the motor. A variable. Unit: A
I0 = The no load current at a given voltage.
T = The torque. Unit: Nm
Ts = The stall torque.
T0 = The torque required to overcome motor friction.
P = Power. Can be electrical or mechanical. Unit: W
Pin = Electrical power drawn by the motor.
Pout = Mechanical power given off the motor axle.
Ph = Power generated as heat within the motor due to winding resistance.
Pm = Power generated as heat within the motor due to mechanical friction.
L = Load. A value from 0 to 1, often given as a percentage.
E = Power efficiency.
k[index] = used for various constants depending on the motor design
This apply to brushed and brushless motors alike, although for brushed motors I’m aware that some of the mathematical models used only work well within a narrower voltage range. The general conclusions still hold though.
I’ve stuck to dissecting the influence of winding turns and feed voltage, since those are the primary factors that we as users can influence when choosing motor and battery. The rest of the internal motor hardware is simply assumed to be “constant”.
The article is very wordy and there are many formulas presented. I’ve broken this subject into one post for each motor property. Each post, apart from the last ones, is subdivided into a short presentation, Theory, Reality Check and Conclusion.
Contents:
Code:
[B]Title Post #[/B]
Introduction, Legend 1 (This post.)
[URL=http://www.rccrawler.com/forum/electronics/530105-motor-theory-practice.html#post5178950]Motor data explained[/URL] 2
[URL=http://www.rccrawler.com/forum/electronics/530105-motor-theory-practice.html#post5178951]Kv rating[/URL] 3
[URL=http://www.rccrawler.com/forum/electronics/530105-motor-theory-practice.html#post5178952]Torque[/URL] 4
[URL=http://www.rccrawler.com/forum/electronics/530105-motor-theory-practice.html#post5178953]Power[/URL] 5
[URL=http://www.rccrawler.com/forum/electronics/530105-motor-theory-practice.html#post5178954]Heat and Power efficiency, part 1[/URL] 6
[URL="http://www.rccrawler.com/forum/electronics/530105-motor-theory-practice.html#post5178955"]Heat and Power efficiency, part 2[/URL] 7
[URL="http://www.rccrawler.com/forum/electronics/530105-motor-theory-practice.html#post5178956"]Conclusions[/URL] 8
I’ve started this thread as a spin-off from another thread.
In theory (and what seems like technically possible) John is correct, as shown below.Once inside the motor coils, the respective voltage and amperage that power is produced from doesn't matter if we keep the amp/turn and copper volume constant. The torque and power can't be changed with a different KV, low KV motors do not produce more torque. They do produce more torque per amp, but they also need higher voltage applied to get it. ...
My previous statement, to the effect of “More turns => More torque, more efficiency and less Kv” stems from what’s generally accepted as the “truth” and also on the fact that the general (and good) advice is to gear down when switching to a higher Kv motor. I blame only myself for not previously having done the proper research…
Now I’ve spent some time going back to the basic physics of electric motors and compare that to reality to find out what is true.
The physics is simply an applied use of Ohm’s law, Faraday’s law, Kirchhoff’s voltage law and some other basic rules of electronics and mechanics.
For the mathematical models I’ve throughout assumed that all pieces of the motors except the windings are identical and constant. The amount of copper used for the windings is also constant (unless otherwise explicably noted).
“Reality” is represented by well proven general advice and experience as well as manufacturer’s data for the somewhat older range of Turnigy TrackStar motors. I used these motors because of the relatively exhaustive amount of data given and I run the 17.5T version myself. The full range isn’t directly comparable without caution since the motors up to 8.5T have an internal fan that the others don’t and some data lack precision. The 4.5T version can be found here.
I’m aware it’s not sufficient to have a select very few motors to make perfect conclusions set in stone, but it’s far better than having only the theories.
Some results are intriguing, to say the least…
Legend
Physics and maths go hand in hand when doing the theoretical study, so here is a legend for terms used later. Notice that there’s a difference between upper and lower case letters:
N = Number of winding turns.
R = Electrical resistance in the winding. Unit: Ω
f = Motor angular velocity, used as a variable. Unit: rad/s
f0 = Angular velocity at no load for a given voltage.
Kv = f0*π / 30*voltage. Unit: rpm/V (For brushed motors this is more voltage dependent than for BL motors. I use it as a constant though.)
V = Feed voltage, when used as a variable. Unit: V
V0 = The feed voltage, a constant.
VE = Electromotive Force. Unit: V
I = The electrical current through the motor. A variable. Unit: A
I0 = The no load current at a given voltage.
T = The torque. Unit: Nm
Ts = The stall torque.
T0 = The torque required to overcome motor friction.
P = Power. Can be electrical or mechanical. Unit: W
Pin = Electrical power drawn by the motor.
Pout = Mechanical power given off the motor axle.
Ph = Power generated as heat within the motor due to winding resistance.
Pm = Power generated as heat within the motor due to mechanical friction.
L = Load. A value from 0 to 1, often given as a percentage.
E = Power efficiency.
k[index] = used for various constants depending on the motor design
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