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Calculating lead screw TPI based on motor torque

Calculating lead screw TPI based on motor torque

Postby MachiningBob » Tue Apr 12, 2011 9:26 pm

Ok, so I'm fooling around...dreaming about lead screws on roton.com and I figured I better break out the math.

The lead screw I have my eye on is the 1/2" Hi-Lead 0.5"/rev or effective TPI of 2.

I have 425oz-in motors in bi-polar parallel setup.

So I take the calculations of converting that into lb-in and I get 26.5625/lb-in.

Assuming a gantry weight of 50lbs...my equation looks like:

x = in/rev

x = (26.5626 * 6.2831854) / 50

x = 3.3379 in/rev

Assuming maximum efficiency and no slop.

According to engineering data I should be able to get 66% efficiency and a plastic nuts are apparently 10-20% more efficient than bronze. Not sure I'm even going to factor that. What I will do is assume I'm going to get 50% efficiency so ???

3.3379 * 0.5 = 1.66895 and divide that by 3 (for slop and safety) and I get 0.5563167 in/rev

Am I in the zone?

To check my work on .5 in-rev lead screw...I do it backwards...

(50 * 0.5) / 6.2831854 = 3.98 lbs/in = 63.68 oz-in

Right?

So my motors are oversized (at their best) by 425 / 63.68 = 6.67 times :!:

That seems good. What am I missing? Does the router work suddenly make it seem like the load is 500lbs?
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Re: Calculating lead screw TPI based on motor torque

Postby Awesomeness » Tue Apr 12, 2011 10:21 pm

What is the 6.2831854 number?

What do you mean by your motors are "oversized"? Are you trying to calculate acceleration against inertia?

The motors' output is a curve - and a curve that drops off really fast as the RPMs go up. Your calculations here are based on the maximum torque, which occurs when the machine is not moving, or moving very slowly ("slowly" depends on your motor's torque curve).

The capabilities of your system depend on the voltage, current, turns per inch of the motors, torque curve of the motors, mass of the axis (e.g. gantry for x) and the ideal cutting speed or RPM you'll be working at.
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Re: Calculating lead screw TPI based on motor torque

Postby Beermkr » Wed Apr 13, 2011 1:25 am

Awesomeness wrote:What is the 6.2831854 number?


2Pi

R/
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Re: Calculating lead screw TPI based on motor torque

Postby MachiningBob » Wed Apr 13, 2011 2:45 pm

Awesomeness wrote:What is the 6.2831854 number?


What Beermkr said. 2pi. I was grabbing that from the buildyourcnc.com link on torque motion.

http://buildyourcnc.com/torquemotion.aspx

Awesomeness wrote:What do you mean by your motors are "oversized"? Are you trying to calculate acceleration against inertia?


More or less. Yes. I want to be able to apply sufficient force to stop the gantry in motion or move it at rest. "Oversized" in the respect that the motors would be more than able to handle the things I'm not thinking of or can't easily calculate...like resistance of the bearings, friction from me over tightening the gantry against the rails, etc.

Awesomeness wrote:The motors' output is a curve - and a curve that drops off really fast as the RPMs go up. Your calculations here are based on the maximum torque, which occurs when the machine is not moving, or moving very slowly ("slowly" depends on your motor's torque curve).


I'm using a bi-polar parallel configuration which I'm told should give me pretty good/stable torque through most of the curve and if I use an effective 2TPI lead screw and 128 or even 256 microstep I should be able to get speed and precision.

Awesomeness wrote:The capabilities of your system depend on the voltage, current, turns per inch of the motors, torque curve of the motors, mass of the axis (e.g. gantry for x) and the ideal cutting speed or RPM you'll be working at.


Right. I think I'm there. 36VDC at 9.6ish amps. For the 425 oz-in motors I should be able to meet peak and mean voltage and current. I realize things won't be perfect and everything is rough estimates, vendors exaggerate about specs, etc. I was just thinking I have enough gravy in my torque output to drive this lead screw. I was also thinking on the Z axis that I might choose a lead screw up to 3-4 effective TPI for more mechanical advantage since I am directly working against gravity. So 2 TPI for the x and y since I'm sliding things around and 3-4 TPI for the z axis since I'm lifting and lowering.

Regarding ideal cutting speed and RPM...I was hoping this configuration would give me options for IPM and the router I chose claims 8-24k rpm.
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Re: Calculating lead screw TPI based on motor torque

Postby Awesomeness » Wed Apr 13, 2011 4:15 pm

Ok, I see what Patrick was doing there, though I question why. That calculation is fairly meaningless by itself, and totally meaningless out of the context of a specific machine.

Keeping the axis moving is the easiest job the motors have, so calculating how much torque it takes to do it is not useful. You followed the calculations correctly, but didn't really discover anything about your machine in the process. (I'd never seen that article of Patrick's before, and I'm going to have to email him and tell him to change or remove it.)

Newton's First Law of Motion states that "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force". In other words, once the gantry is moving, the motors would be doing nothing in an ideal case. In our case, they must do a little work, to combat friction and the cutting forces (and gravity on the z-axis).

From here you need to use the good old F=MA, or Force = Mass * Acceleration, if you want to really calculate these things out. In a frictionless world, a mouse could push a mountain, with a tiny force, but the acceleration would be so slow that it would take forever. (You also have to account for energy in the system. Inertial energy is I=(1/2)MV^2, so it's ultimately "how much energy can your motors put out" that determines acceleration.)

I'd suggest going about this an entirely different way. This article, http://pminmo.com/PMinMOwiki/index.php5 ... ical_Power , will explain how to compare two drive methods based on the torque curves for a specific motor. It doesn't calculate about the gantry, just to compare the power of drive systems. They're talking about the differences between several screws, but I think you can follow enough to figure out how to do these calculations for belts/chains, etc., too. If not, let me know.

As for the microstepping, NO, you can't just turn it up to 256. There are two reasons for this. First, every time you turn it up, you divide the torque-per-step by a similar amount (e.g. at 64 microstep, each step only has 2.45% of the rated peak holding torque). Second, it's empty, hollow resolution, for a number of lengthy reasons I won't bother explaining here. The generally accepted practice is to turn microstepping up just enough to get a resolution smaller than you need - in our case that typically means to turn it up until you get a number in the ten-thousandths per step (e.g. mine is 0.0007" per step, at 1/16th microstepping, with chain drive).

Sorry for the long post, but to really go into this, it would take a few posts as long as Patrick's.
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Re: Calculating lead screw TPI based on motor torque

Postby MachiningBob » Wed Apr 13, 2011 7:12 pm

Ok, good to know about the micro stepping. I went looking and basically it looks like it's mostly about "smoothness" but holding torque drops like a rock as it increases which is undesirable, which makes sense why when gears enter the equation things start to shape up.

Regarding the link you posted, those numbers make sense and appear to be congruent with Patrick's/buildyourcnc formula. I do like how your link shows where the efficiency rating goes in. That was very helpful.

Thank you!
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Re: Calculating lead screw TPI based on motor torque

Postby Awesomeness » Wed Apr 13, 2011 7:44 pm

That calculation is only useful to compare the torque you can get out of different drive gearing and set ups.

To truly calculate the torque you need, you would do something like this...
  1. Calculate the torque you need to meet the acceleration you want. Use 5 in/sec^2, and 100lb, as generous numbers.
  2. Calculate power (as in force*velocity) needed to do this, using the answers from steps 1 and desired velocity.
  3. Rule of thumb is to choose a motor with 140% of that calculated power, to add in safety margin.

My opnions: On the book machine, with threaded rod (NOT ACME screw) you could probably get by with like a 150 in-oz motor, because it has so much mechanical advantage that you probably run into whipping problems before the motors give out. Switching to ACME screw or chain drive will drop the RPM way down, and you can get moving much faster without running into whipping problems, but you lost all the mechanical advantage and are dependent on the motors - at that point you probably need 250 in-oz just to get by, and would be better off in the 300-350 range. A 4'x8' BlackFoot probably needs like 350 in-oz minimum, is comfortable around 400-450, and would be a waste to go over 550-600 without upgrading the spindle (you'd probably bog the spindle out first).

There are a lot of spindle considerations at work in my guesses there, though. You can't go by just drive motors until you have a spindle so powerful that it doesn't bog down when cutting at full depth and full feedrate. That would be like a 2KW spindle, which is several times more powerful than a 2.25HP wood router. At the speeds and forces that would use that, we'd also far exceed the rigidity of our DIY machines.

It's a crazy balancing game, and frankly, trying to calculate it isn't really worth your effort. Just throw 425 in-oz motors in it, which are cheap and easy to find, and call it a day. They'll probably be like 150% more powerful than you need, though nowhere near the 7x that psuedo-science formula calculated. Taking the empirically derived information at face value will give you a better all around solution than trying to work the physics to encompass all the factors at play. :ugeek:
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Re: Calculating lead screw TPI based on motor torque

Postby Awesomeness » Wed Apr 13, 2011 11:37 pm

There is an explanation of choosing motor sizes on the last two pages of this stepper motor guide.

I'm not sure what they are calculating though. They say to calculate torque needed to accelerate the gantry, but then they say to convert it to watts while they write the answer in "oz/in", then they top off the mystery by dividing by 4506. (What the hell is an "oz/in"? You'd think a STEPPER COMPANY would know that the units are "in*oz". :roll: )

I've spent like an hour trying to figure out where the hell that 4506 comes from. After you finished calculating the torque, all you needed to do in order to get to power was multiply by velocity. Instead of multiplying by velocity, they multiply by pulses/second and divide by 4506. That means 4506 must be in units of something/inch, but what that something is I have no idea. If they had just multiplied by their desired in/sec velocity, they would find that 1 oz*in^2/sec^3 equals 0.00001829 W.

I'm not entirely convinced that they know what they're talking about, especially after their invention of "oz/in" units. :o
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Re: Calculating lead screw TPI based on motor torque

Postby MachiningBob » Thu Apr 14, 2011 2:45 pm

Heh. Well, I went with the empirical wisdom for motor and driver selection at 425 oz-in. I was just really wondering how much I might be able to tweak out of it in a future upgrade.

I spent some time last night spinning on the Gecko guide. I'm not able to puzzle out the 4506 constant either. The only thing I can think of is that number must some how be able to account for a 200/1.8 degree motor and the 4506 accounts for the decline in power for an assumed microstepping value/pulse count over time. It's the only way you can get to a value of oz-in over pulse/time. *shrug* I can't find the constant anywhere else either. I suspect it's a Gecko derived/rule of thumb value. It's frustrating that they just pull a number out of apparently thin air.
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Re: Calculating lead screw TPI based on motor torque

Postby Awesomeness » Thu Apr 14, 2011 3:01 pm

Yeah, I really wish they would have given more explanation. Now I'm a bit determined to figure out what it is, just because mysteries bother me. haha
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