Figuring torque from kv and esc

Hummina Shadeeba · Apr 18, 2022

If I have a 55kv motor and an esc that will do 140 amps what torque is possible from the shaft?

Please show ur math. I get lost on the radians part.

DogDipstick · Apr 18, 2022

What is the nM/Amp of the motor?

If you do not have this figure, you will have to use a controlled prony dynometer to figure this number. Cannot calculate without. (You need an RPM number) .

(Tachometer, strobe,).

Power output in SI units may be calculated as follows:

Rotary power (in newton-meters per second, N·m/s) = 2π × the distance from the center-line of the drum (the friction device) to the point of measurement (in meters, m) × rotational speed (in revolutions per second) × measured force (in newtons, N).

Or in English units:

Rotary power (in pound-feet per second, lbf·ft/s) = 2π × distance from center-line of the drum (the friction device) to the point of measurement (in feet, ft) × rotational speed (in revolutions per second) × measured force (in pounds, lbf).

https://en.wikipedia.org/wiki/Prony_brake

A substantial pre-load is then applied to the ends of the band, so that each spring balance has an initial and identical reading. When the engine is running, the frictional force between the drum and the band will increase the force reading on one balance and decrease it on the other. The difference between the two readings multiplied by the radius of the driven drum is equal to the torque. If the engine speed is measured with a tachometer, the brake horsepower is easily calculated.

You can have a large motor and a small motor with the same Kv constant. The large motor will be more powerful than the small motor. So there is no way to use Kv to tell you how powerful your motor is.

K M is the motor ( SIZE) constant
In SI units, the motor constant is expressed in newton metres per square root watt

Ke = back EMF constant

If:
Kt=(N*M)/A (torque constant)
Ke=V/(rad/sec) (Back EMF)

Then
Kt=Ke=1/Kv
( newton meter per amp) (kT)

T =kT * I

In this equation, T is torque, Kt is the torque constant, and I is current. Kt has units of Newton-meters per Amp.
Kt × Kv = 1352
Kt = 1352 ÷ Kv

.....multiply the product (NM*rad/sec) by 1352.4 to get the equivalent in (inch ounces*rpm). 1352.4 is a conversion factor and is not a magic number that only applies to electric motors. It is made up of the conversion of:
Newtons to ounces
Meters to inches
radians to revolutions
seconds to minutes

Lets apply this to your eq. 55kV, 140A. So the 1352/55 = 24.6 nM/Amp. You have 140A.

24.6(nM per amp) x 140(A) = 3,441.45 oz-in (17.92 lb-foot FORCE) / 140A.

Remember, 1 N-M/sec = 1 Watt... So... 1 newton meter/second = 1V*1A
140 watts at 1 volt (~55RPM) with 140 amps = 24.32nM/A.. = ~18 lb-foot FORCE

In SI units, the motor constant is expressed in newton metres per square root watt

However many RPM this is, figures your power and tork. IF the motor turned 100RPM, this would mean you put 0.3hp (250w) down..... @ 1000RPM, this would mean you put 3.4 horsepower down (2550w). At 10,000 RPM, this would mean you put down 34.1 horsepower. ( 25,000w ~) . You must know the RPM. To figure the power. (voltage? matters.)

Newton Per Ampere Per Meter (N/A-m) is a unit in the category of Magnetic field strength. It is also known as newton/ampere-meter. Newton Per Ampere Per Meter (N/A-m) has a dimension of MT-2I-1 where M is mass, T is time, and I is electric current. It essentially the same as the corresponding standard SI unit T.

How to calculate torque of motor:

Torque is nothing but a momentary force developed at the time of force is applied to the motor. The unit of torque is N.m (Newton-meter). In other words, Torque T(N.m) is equal to the ratio between the electrical power P(W) in watts to the acceleration.

A pound-foot (lbf⋅ft) is a unit of torque representing one pound of force acting at a perpendicular distance of one foot from a pivot point. Conversely one pound-foot is the moment about an axis that applies one pound-force at a radius of one foot.

The value in SI units is given by multiplying the following approximate factors:

One pound (force) = 4.448 222 newtons
One foot = 0.3048 m

This gives the conversion factor:

One pound-foot = 1.35582 newton metres.

1RAD = 57.2958 degree.

1 N-M/sec = 1 Watt... So... 1 newton meter/second = 1V*1A

Since 1 N·m = 1 J, and 1 A = 1 C/s, then 1 N·m/A = 1 J·s/C = 1 V·s (same units as back EMF constant).

SI units for the torque constant are newton metres per ampere (N·m/A).

Multiply speed by torque and you get power which is volts times amps.

IN a linear motor: As per the quote: F=I/Kv

To translate this model to a rotating motor, one can simply attribute an arbitrary diameter to the motor armature e.g. 2 m and assume for simplicity that all force is applied at the outer perimeter of the rotor, giving 1 m of leverage. "

I can es-plain the influence of the Radian if you like, but that is a tork calculation. Not a power calculation.
https://en.wikipedia.org/wiki/Radian
https://www.electrical4u.net/calculator/electric-motor-torque-calculation-formula-torque-calculator-online/
https://en.wikipedia.org/wiki/Force

Here is an excellent youtube vid. If you want another explanation. From someone else.
[youtube]hUD1H5n9rF0[/youtube]

Watch this. It clearly shows the relationship of POWER = TORQUE x ANGULAR VELOCITY Explained by a professional, not me. Much clearer description.

[youtube]9eUxWdtOrik[/youtube]

I will lay out the math tomorrow when I get to the engineer Dad, when we are sitting together and have my little time. I just want to make sure the math is right. I get it wrong sometimes too. I often mess up on the units too.

Here is a good link that I went to when I wondered this. I did quote it above, most of it is seemingly easy to understand. I am sorry If i over complicate things, perhaps I will be able to lay it out clearer, and more accurately, in stages, with the math. I just need to be standing next to someone who knows absolutely the correct answer.
https://www.rcgroups.com/forums/showthread.php?344252-kt-%2A-kv-1352-%28what-units-%29

Hummina Shadeeba · Apr 18, 2022

DogDipstick said:
What is the nM/Amp of the motor?

If you do not have this figure, you will have to use a controlled prony dynometer to figure this number. Cannot calculate without.

( newton meter per amp)

Can convert from kv to kt and figure torque per amp that way.

mxlemming · Apr 18, 2022

Short answer...
Use SI units
kV to rads-¹/V
Invert it
That's your Nm/A
Multiply by amps

E.g.
55rpm/V is 55x2pi/60 is 5.76rads-¹/V
kT is 1/5.76 is 0.174Nm/A
x140A is 24Nm

That's it.

If your motor saturates, the torque will be lower.

Note... rads-¹/V = radians/(Vs) it just strangely feels more natural to write it in terms of rads-¹ (speed) and Volts

Hummina Shadeeba · Apr 18, 2022

mxlemming said:
Short answer...
Use SI units
kV to rads-¹/V
Invert it
That's your Nm/A
Multiply by amps

E.g.
55rpm/V is 55x2pi/60 is 5.76rads-¹/V
kT is 1/5.76 is 0.174Nm/A
x140A is 24Nm

That's it.

If your motor saturates, the torque will be lower.

Note... rads-¹/V = radians/(Vs) it just strangely feels more natural to write it in terms of rads-¹ (speed) and Volts

Thanks.

You think these rating are overkill? https://www.sdp-si.com/D265/PDF/D265T146.pdf
Page 22

Comparing to what I see used on bicycles the ratings here seem high
And then I don’t see how the higher speed would have such an impact reducing its rating.

mxlemming · Apr 18, 2022

The ratings in table 48 are fairly close to the level I'm driving my current ebike at, and the belts seem fine (5mhp optibelt and contitech htd5m.

I think they're ratings for a long life expectancy (50k hours from memory is usual for belt ratings), if your willing to accept ebike service life levels (1k hours would be fairly long life) you can probably substantially overdrive them.

I've found it's very dependent on the stiffness of the rigid link between the pulleys. See my giant trance thread for my updated bracket and the extra bearing and tensioner I've added.

Hummina Shadeeba · Apr 18, 2022

mxlemming said:
The ratings in table 48 are fairly close to the level I'm driving my current ebike at, and the belts seem fine (5mhp optibelt and contitech htd5m.

I think they're ratings for a long life expectancy (50k hours from memory is usual for belt ratings), if your willing to accept while service life levels (1k hours would be fairly long life) you can probably substantially overdrive them.

I've found it's very dependent on the stiffness of the rigid link between the pulleys. See my giant trance thread for my updated bracket and the extra bearing and tensioner I've added.

What width belt u use and what torque it does? I’d like to get away with 9mm wide GT2 (5mm pitch) and using a Vesc at 140 amps peak, and with such a huge gear ratio (like 3:1 on first stage and 8:1 total) I’d think I’d be better off with such speed instead of torque and less stress but the calculator shows the opposite
Thanks for ur help.. it is a lot of help

mxlemming · Apr 19, 2022

Hummina Shadeeba said:
mxlemming said:

The ratings in table 48 are fairly close to the level I'm driving my current ebike at, and the belts seem fine (5mhp optibelt and contitech htd5m.

I think they're ratings for a long life expectancy (50k hours from memory is usual for belt ratings), if your willing to accept while service life levels (1k hours would be fairly long life) you can probably substantially overdrive them.

I've found it's very dependent on the stiffness of the rigid link between the pulleys. See my giant trance thread for my updated bracket and the extra bearing and tensioner I've added.

Click to expand...

What width belt u use and what torque it does? I’d like to get away with 9mm wide GT2 (5mm pitch) and using a Vesc at 140 amps peak, and with such a huge gear ratio (like 3:1 on first stage and 8:1 total) I’d think I’d be better off with such speed instead of torque and less stress but the calculator shows the opposite
Thanks for ur help.. it is a lot of help

I'm using a 25mm belt at (currently, offroad) about 12Nm (60kV, 80A) on the small pulley, 24 tooth. Big pulley is 148 tooth.

I imagine the 9mm belt would suffer a lot at 24Nm. But I'd also be quite surprised if that motor could really supply that torque level.

Edit:
Best way to get more power out of a belt is to use bigger pulleys. If you double the tooth count, you halve the circumferential force for the same torque AND double the teeth in mesh. It dramatically increases the practical load capacity. If you can use 36:105 instead of say 18:52 (not sure what your planning) i expect in practical terms you'd get 3 or 4x the capacity.

Another thing to look at is the optibelt drives sheet. https://www.optibelt.com/fileadmin/pdf/produkte/zahnriemen-gummi/Optibelt-TM-Rubber-Timing-Belt-Drives.pdf
Table 17 gives the nominal power for a given rpm and pulley size. You can obviously get the torque from this. It shows 2.3x the power transmission for 48 tooth as 24 tooth at 300rpm for example.

Hummina Shadeeba · Apr 25, 2022

Can you tell the max torque the motor can produce based on the stator dimensions and the max the steel can hold? The stator is 69x50.

Hummina Shadeeba · Apr 26, 2022

mxlemming said:
Hummina Shadeeba said:

mxlemming said:

I imagine the 9mm belt would suffer a lot at 24Nm. But I'd also be quite surprised if that motor could really supply that torque level.

If you can use 36:105 instead of say 18:52 (not sure what your planning) i expect in practical terms you'd get 3 or 4x the capacity.

Click to expand...

Id like to know what torque is possible out of the motor based on its dimensions but whatever it is I think it will be more than I could use at the tire with 8:1 gearing.

36:105 sounds good with the 9mm wide 5mm pitch.

Click to expand...

Figuring torque from kv and esc

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