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Calculating lead screw TPI based on motor torque

Re: Calculating lead screw TPI based on motor torque

Postby derekko73 » Sun Dec 27, 2015 9:44 am

The number 4506 is calculated as follows:

746 Watts = 550 lb-ft per sec
1 Watt = 550*16*12/746 oz-in per sec.

Motor Power = Torque * Angular Velocity
= Torque * 2*pi*f = Torque * 2*pi*(Rev. per sec)

For a 200 pulses per rev. stepper motor,
Rev per sec = (Pulses Per Sec.)/200 = PPS/200

So,
Power = Torque * 2*pi*(PPS/200)
= (Torque*PPS) * (2*pi/200)
= ((Torque in oz-in * PPS) * (2*pi/200)/(550*16*12/746)) in Watts
In Geckodrive 's appnotes,
Power of motor in Watts = (Torque in oz-in)*(PPS)/4506

The number 4506 is calculated from:

(550*16*12/746)/(2*pi/200) = 4505.83

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Re: Calculating lead screw TPI based on motor torque

Postby Awesomeness » Fri Jan 08, 2016 2:00 pm

Thanks Derek!
If you don’t have time to do it right, when will you have time to do it over?
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Re: Calculating lead screw TPI based on motor torque

Postby Awesomeness » Fri Dec 30, 2016 3:04 am

I don't see how the units work out to support that. Maybe you can point out where I'm misunderstanding?

Here's how I work it out...
  1. Torque = Force x Radius, and Force = Mass x Acceleration, so Torque = Mass x Acceleration x Radius.
  2. Rotational acceleration is in radians/time^2.
  3. Torque is in units of (mass x distance x radians)/time^2. In the example of "in*oz" the oz is actual "force oz" which incorporates everything but distance.
  4. They then multiply by pulses/sec. This leaves units of (mass x distance x radians x pulses)/time^3.
  5. We need the top of that fraction to be in (mass x distance^2) unit form to be power, so we are missing a distance multiplier. (Radians x pulses) gives a psuedo-distance, since it is the distance, in pulse units, covered in that many radians of rotation.
  6. If we accept (radians x pulses) as a distance, then the units of the 4506 number must be a conversion from (radians x pulses) into a true distance unit. This means the units of 4506 itself must be (radians x pulses)/distance.

Airnocker wrote:746 Watts = 33,000 lb-ft per minute = 1 HP; 33000/2pi = 5252 * .857 = 4502

(Your stated units for horsepower are wrong. You're missing a distance. It should be 33,000 ft*lb-ft/min. I'm going to use this.)

In your example, I work out the units like this...
  1. 746 (mass x distance^2)/time^3
  2. Break down the 33,000 ft*lb-ft/min into (ft/min)*lb-ft = (velocity)*(mass*acceleration) = (distance/time)*(mass*distance/time^2) = (mass x distance^2)/time^3.
  3. 33,000 (mass x distance^2)/time^3 / 2pi radians effectively
  4. Rotational power is (torque x 2pi x RPM), in units of ((mass x distance x radians)/time^2) x 2pi x (revolutions / time) = (mass x distance x radians x (2pi * revolutions))/time^3.
  5. The (2pi * revolutions) is really a distance, because it's (2pi x revolutions x "imaginary 1 unit moment arm").
  6. Dividing by 2pi, again really (2pi x revolutions x "imaginary 1 unit moment arm"), leaves (mass x distance x radians)/time^3.
  7. This is the same as (torque x rotational speed) still, but now in units of radians/sec instead of 2pi*revolutions/sec.
  8. So this conversion unit is 1 HP = 746W = 5252 (mass * distance * radians)/time^3.

Now I can state why I don't think it works. We're in need of a 4506 conversion factor in (radians x pulses)/distance, but the 5252 is in power - either HP, Watts, or some other (mass * distance^2)/time^3 unit.

It seems to make sense when you just say "PPS is RPM further disguised", but how do the units work out then?
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Re: Calculating lead screw TPI based on motor torque

Postby airnocker » Fri Dec 30, 2016 4:07 am

That's a real timely response, there, your Awesomeness. (and you are correct, I left out a term). Happy New Year!
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Re: Calculating lead screw TPI based on motor torque

Postby Awesomeness » Fri Dec 30, 2016 4:09 am

Yeah, I found it was apparently stuck in my draft folder, so I decided to go ahead and post it.
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Re: Calculating lead screw TPI based on motor torque

Postby airnocker » Fri Dec 30, 2016 5:04 am

:-)
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