Comments sought on new build: A CNC Router for RC Gliders and Planes

[Jonathan]

Based on:

• 2 of RM1610-1300mm
• 55kg actuated mass

Assume:

• 10m/min feedrate
• 2m/s^2 acceleration
• 20T pulleys for 1:1 ratio, 30:N pulleys for 30:N ratio.
• Cutting force of 25N
• Not pre-loading ballscrews

Variables to select:

• Motor size
• Drive ratio

For the common 3Nm Nema 24 motors the corner speed is about 1000rpm, so lets start with 1:1 ratio and see if the torque calculated is low enough to use two of those motors. Using the script (posted here, and attached), the required torque from each motor is 0.47Nm. Up to their corner speed stepper motors output about 2/3rds of their holding torque, so 2Nm up to 1000rpm for the 3Nm motor, so since you only need 0.47Nm this system will definitely work up to 10m/min (1000rpm*10mm) plus a bit more since the torque will only drop below 0.47Nm at a fair bit more than 1000rpm, so you have a good factor of safety. You could even use 30:20T ratio and get 15m/min feedrate since the torque for these parameters is 0.78Nm, though you would need to used fixed-fixed bearings on the ballscrews to get the required critical speed.

One interesting thing to note is that if you use 30T pulleys instead of 20T, the torque required increases from 0.47Nm to 0.70Nm, so don't use bigger pulleys than necessary.

Lets try one motor driving both ballscrews:

Assume:

• 10m/min feedrate
• 2m/s^2 acceleration
• 20T pulleys for 1:1 ratio, 30:N pulleys for 30:N ratio.
  
  • One 20T pulley on each ballscrew
  • Two belts (length roughly 1/2 distance between ballscrews) with two 20T pulleys attached to motor.
  
  
• Cutting force of 25N
• Not pre-loading ballscrews

Since the system is symmetrical, we can model it as a single ballscrew with the length doubled and twice the pulley inertia. The calculated torque is 0.75Nm (or 1.09Nm with 30T pulleys). That's still within the ratings of the 3Nm motor... so no need for a Nema 34 motor (though it would clearly work, just be more expensive). If you want higher resolution, you could use 16:20 ratio (16T on motor) and the torque required is 0.55Nm.

My script also now calculates the ballscrew (nut, shaft & bearing) stiffness and the torsional stiffness of the belts. For example if we assume 100mm center distance, then for two motors the linear error due to belt compliance is 5.6um, compared to the error due to ballscrew stiffness of 0.7um. That's assuming worst case scenario - so machine operating with maximum acceleration and cutting force. If you use one motor, say the belts have about 700mm center distance then the belt stiffness goes down by a factor of 7, so it's now about the same as the torsional stiffness of the ballscrew. That sounds like a big difference, but you have to consider the stiffness of the whole system as clearly if the gantry is not terribly strong that will make a bigger difference than the belt stiffness (or lack of).

I've attached the scripts with your parameters entered for X - change the file extension from .txt to .m. The script runs in MATLAB, or GNU-octave which is free/open source and can be downloaded here. I encourage you to experiment with the numbers to get a feel for what parameters affect the torque requirements the most. You could put your numbers in for X and Z...

servo_motor_sizing_hussey_1.txtservo_motor_sizing_hussey_single_motor.txt