Saturday, December 7, 2019

Some Question on Stepping Motor, Gear Reduction and Microstep Driver

I'm in the planning stages of building myself a CNC machine, like most people I want it to be accurate and reasonably fast without costing a fortune.

I intend to build most of the structural components with mostly T-Slot Aluminium, the X-A-Y axis's will move using a rack & pinion. What I've learned through Google is that, a rack & pinion setup requires geared reduction of some sort and a microstep driver to achieve a balance of smooth operation and increased torque.
Most of the DIY CNC machines I've seen are using some form of belt/pulley system for the gear reduction along with microstepping. I have my reservations with this type of setup for the following reasons:

Some Question on Stepper Motors, Gear Reduction and Microstep Driver

The belt/pulley system in the link above requires additional space, components and adds complexity to the build.
I have a hard time trusting that the belts won't stretch and miss steps.
I'm cautious off backlash, on-going maintenance and their life expectancy.
Using a microstep driver will be smoother, however less accurate.

I've done a little research on this subject and would like some opinions from more knowledgeable people in this area. Rather than use a belt/pulley system, would using a stepper motor with a planetary gearbox be a viable alternative? Below are links to some NEMA 23 motors, each with vastly different ratios.

4:1 Ratio - Gear Ratio 4:1 Planetary Gearbox High Torque Nema 23 Stepper 23HS30-2804S-PG4|23HS30-2804S-PG4|Geared Stepper Motors
47:1 Ratio - Gear Ratio 47:1 Planetary Gearbox High Torque Nema 23 Stepper 23HS30-2804S-PG47|23hs22-2804s-pg15|Geared Stepper Motors

Below is an excerpt taken from the belt/pulley page which got me thinking.

The R&P system is based on a pinion with a 1" pitch circle.
The total linear distance traveled per revolution of the pinion is thus 3.14159".
With the 3:1 reduction, this means that the distance traveled per motor revolution is 3.14159 / 3, or 1.0472".
If you have a stepper with 200 steps per revolution, this means you have 200 / 1.0472" = 190.9861 steps per inch, or 0.005236" per step.
With 10x microstepping, you would have 1909.861 steps per inch, or 0.0005236" per step.

I've broken down their calculations step-by-step:

Belt/Pulley System with 10x microstepping:

3.14159 / 3 = 1.0472 (distance traveled per motor revolution)
200 / 1.0472 = 190.9861 (steps per inch)
1.0472 / 200 = 0.005236 (per step)
190.9861 * 10 = 1909.861 (steps per inch with 10x microstepping)
0.005236 / 10 = 0.0005236 (per step with 10x microstepping)

Planetary Gearbox Stepper Motor with 4:1 gear ratio and 10x microstepping:

3.14159 / 4 = 0.7853 (distance traveled per motor revolution)
200 / 0.7853 = 254.6797 (steps per inch)
0.7853 / 200 = 0.003926 (per step)
254.6797 * 10 = 2546.797 (steps per inch with 10x microstepping)
0.003926 / 10 = 0.0003926 (per step with 10x microstepping)

Planetary Gearbox Stepper Motor with 47:1 gear ratio that produces similar steps without a microstepper driver:

3.14159 / 47 = 0.0668 (distance traveled per motor revolution)
200 / 0.0668 = 2994.0119 (steps per inch)
0.0668 / 200 = 0.000334 (per step)

Considering the two motors, the 4:1 gearbox would have to be used with a microstep driver. But would it be possible to use the higher ratio 47:1 gearbox and do without the microstep driver? Or am I missing something?

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