There are a few variables you need to know in order to figure this out:
1. The friction of your linear axis.
- are you using high quality linear slides, or something else?
2. The friction of your screw.
- an acme screw has an efficiency of around 36%
- a high quality ballscrew has an efficiency of around 91%
3. The weight of your gantry.
For example, a hypothetical 10 oz-in (.63 lb-in) motor with direct (1:1) gearing to an acme screw with pitch of 0.25" will be able to exert about 5.7 pounds of force on whatever it is moving:
thrust = gear mutiple * [1 / ( [(screw lead / 2*pi) * (1 / screw efficiency)] / torque)]
thrust = 1 * [1 / ( [(0.25 / 2 * pi) * (1 / 0.36)] / 0.63)]
thrust = 5.7 pounds
(Note: if we used a 1:2 gear off the motor, we'd get double the thrust)
I imagine that for a moving gantry with no other forces acting on it, the peak load on the motor is going to occur when you want to reverse the direction of the gantry very quickly (say within 50 milliseconds). If the gantry weighs 200 pounds (75Kg), and it is moving at a speed of 6 cm/sec (roughly 140 ips), then we really want this thing to change its speed by a total of 12 cm/sec
(remember, it is reversing direction and accelerating back up to 6 cm/sec) within 50 milliseconds.
Force = mass * acceleration
So for acceleration of 0.12 m/sec / 0.050 seconds, we'd have F = 75*0.12/0.050 -- or F = 180N
180N is about 40 pounds of force (1 pound-force = 4.448 N)
So, in this case, with a 200 pound gantry we'd like to run at 140 ips and reverse direction in 50 milliseconds or better, our little 10 in-oz motor will not cut it. We'd either need to go directly to about a 100 oz-in motor, or we'd need to do a combination of the following:
1. Use a higher efficiency screw
2. Use a stronger motor
3. Decrease the pitch of the drive screw (this will slow down our gantry, too)
4. Use a lighter gantry
5. Use a different gear ratio to drive our screw (this will also be slower)
6. Relax our requirement that the gantry change directions in 50 milliseconds.
We ignored friction in all of this, but if using a good linear slide, the variance shouldn't even be worth calculating.
For just the gantry moving speed, as a separate calculation, you'd do this:
linear speed = motor rpm / gearing * screw pitch
Example: 2500 rpm motor / 1:4 gearing * 0.250 pitch
= 2500/4*0.25
= 156 inches per second
Note: In our above example, if we did use a 1:4 gear, we'd get 32.5 pounds of force at the screw. We could then think about going to a 30 oz-in motor, and get 97.5 pounds of force, which should be plenty. We'd have 156 ips gantry jog speed, and we could easily push around a 200 pound gantry.
-Chris  |