Need Verification of Torque Calculations

Other Hardware Motors, Mechanics, Power and CNC
1

I've scoured the net and have been immersed in all sorts of formulas! Below is the result of my work, and hoping there is a good math head here that can confirm (or deny) my conclusions.

I want to build an Arduino controlled stepper system to raise and lower the head on a milling machine (Sieg SX2.7/LMS 5500). I know you can buy stuff - but "just wanna do this!" :slight_smile:

The work follows: (excuse any lapses of terminology...)

A milling machine has a head that is raised and lowered by a leadscrew. The leadscrew pitch is .05" i.e it moves the head .05" per revolution of the crank. The crank is attached to the leadscrew through 2 bevel gears, so there is a bit of additional built in mechanical advantage.

Empirically I've found that it takes about 4 Lbs to move the crank up a turn or two. I'm using 5lb as the load

.05" = 1.27mm or .00127 meters
5 Lb = 2.3 Kg
Force = ma - so the force of gravity on this mass is 2.3 Kg 9.8 m/s or about 23 Newtons.

Allow 1 second for 1 turn of the screw = 1.27mm/second

I'd like to raise the head at 10 turns/second which = 12.7mm/second.
The additional lifting force (friction and other losses aside) will be 2.3 Kg * 12.7 = 29 Newtons
23N+29N = 52 Newtons total - I'll use 60N

The stepper will have a 36 groove timing pulley with PD of 35mm or r of .0175 meters
Torque at motor shaft must be 60N * .0175 = 1.05 N/m

If I attach a 72 groove timing pulley with a PD of 69 mm I should get a 2X torque multiplication
which will give 2.1 N/m at the driven shaft.

Power needed will be 60N * .0127 m/s = .76 watts

So - Minimum requirements:
2 watt 24 VDC power supply
Any steper motor with a holding torque equal or better than 1.05 N/m.

2

I don't follow your reasoning.

An easy check is to calculate the torque at the crank required to move the head up.

That would be (2.3 kg)(9.8 m/s^2)(lever arm in meters) where lever arm is the perpendicular distance from the crank rotation axis to the point where you apply the cranking force.

What is that lever arm?

3

Put the crank handle at 3 or 9 O'clock, and pull straight down with a spring scale to see how much force is required to start the head moving up, multiply that by length of crank arm from center of shaft to pulling point will give torque.
Example: 0.1 ( 10 cm) meter lever arm, 5 kgf to move = 5 * 9.81 * 0.1 = 4.9 Nm.
Or, cut the top out of an old plastic milk jug, punch 2 holes near the top for string and do this:
out9.png
Or, measure water with measuring cup, 1 liter = 1 kg, 1 cup = 1.043 lb.