calculatiing pinion size for rack and pinion setup

[Apples]

How do i work out what size pinion to use on a rack and pinion table setup. I will be most likely using NEMA 34's of the 470oz type i think. I will need to make the gantry to have the ability to move at least 500ipm.

How do i work it out, is it possible to do it at this speed.

I am thinking that buy having a bigger pinion the faster you go. Hopefully the NEMA 34's 470oz will have enough torque to move them at this speed.



Any opinions

Apples

[motordude]

Hello Apples.
This is pretty straightforward calculations that you will find in most engineering books about machine elements. There is no difference in strength calculations whether it is rack&pinion or pinion&gear. You have the torque of your motor and acceleration of the pinion, so the tooth load can be found from that. The teeth is then basically designed from these parameters to withstand tooth breakage and pitting. For noise reasons it is better to have a smaller module and wider+more teeth than a bigger module thinner gear.

regards
John

[ty1295]

Even with that high rate you will still need a gear box.

1 revolution of motor will be pinion diameter * PI (3.1416)

Without gear box, and 2k rpm ( max servo motor speed)

1" pinion (smallest and slowest I have found)

You will be moving at 6,283.2 inches a minute.

12:1 gear box would be nice to add.

Bigger pinion will require more gear box so keep that in mind.

[samualt]

500ipm is extremely fast. I'm trying to set mine about 100ipm.

Nema 42 Big Honking Motors:
----------------------------------------
Desired IPM (Inches Per Minute): 100
Motor RPM: 2000
Torque (oz/in): 1500
IPR (Inches Per Revolution, Assume 1" Pinion for Rack) = 1*PI = 3.14159265" per revolution
RPM Needed = Desired IPM / IPR = 31.8309887
Reduction Ratio = Motor RPM / RPM Needed = 62.83
Torque after reduction = Torque * Reduction Ratio = 94247.7795 oz/in (which really doesn't mean much as long as it isn't too low).

Actually, I may try for a reduction ratio of 40 or less. But the above will give you the basic idea. I think I'm calculating it all correctly. Once you get the Reduction ratio you can pick your gearbox or pullys/teethed-belts. For pullys just divide the number of teeth on the big gear by the number of teeth on the small gear.

72 teeth Pully/10 Teeth Pully = 7.2 Reduction Ratio (Use two sets and your in the ball park! 7.2*7.2 = 51.84 Reduction ratio)

Ummm, I could be wrong about everything here!


P.S. Did I mention that the pinion size is always going to be 1". That is the smallest you can get. Getting a larger one, considering your reduction ratio, would be insane, IMHO.