Help picking a gear to match my rack/setup

[LSX]

I'm building a new gantry with 3:1 belt reduction on the X and Y axis's and 620-oz steppers from candcnc. I plan to run a 20° pressure angle with 20 pitch rack. I'm not a expert with gears but know enough to get me by, I'm looking for help on picking a good match.
there are gears that have from anywhere 15 teeth to 40 teeth and gear pitch dia from .75 to 2" My understanding is the more teeth trying to contact the rack causes more ware but more accurate, and less teeth more chance of backlash less ware, like I said I'm no expert just looking for some help on gear selection any help would be greatly appreciated!

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[Jim Dawson]

This may help you decide, with a 0.75 Pitch Diameter gear, the carriage will travel 2.3562 inches per gear revolution (pi times PD). Then divide by your 3:1 belt reduction 2.6252/3= 0.7854 inches per motor revolution. Then divide by 200 steps per revolution so 0.7854/200 = 0.0039 inches per step. It will be fast, but not very accurate at 200 steps. You can calculate for other steps

At 2 inch PD it would move 2.0944 per motor revolution or 0.0105 inches per step at 200 steps / rev.

Just based on those numbers you might concider going as small as possible on the PD.

Most of the rack and pinion drives I have seen have small PD gears.

[LSX]

Thanks! Do you think I would see any advantage going to a 16 pitch rack? vs the 20?

[Jim Dawson]

Racks normally come in 14 1/2° and 20° pressure angle. The 14 1/2° are a bit smoother in operation so that would be a good choice. In that case you would also have to use a 14 1/2° gear.

[metalfixer]

Boston Gear has some helpful information, page 311 of the catalog.
Rotary Drives Catalog | Gearing Bearings Couplings | Boston Gear Literature

[Torchhead]

I'm building a new gantry with 3:1 belt reduction on the X and Y axis's and 620-oz steppers from candcnc. I plan to run a 20° pressure angle with 20 pitch rack. I'm not a expert with gears but know enough to get me by, I'm looking for help on picking a good match.
there are gears that have from anywhere 15 teeth to 40 teeth and gear pitch dia from .75 to 2" My understanding is the more teeth trying to contact the rack causes more ware but more accurate, and less teeth more chance of backlash less ware, like I said I'm no expert just looking for some help on gear selection any help would be greatly appreciated!

Easy question: Your best ratio for stepper on a plasma is one that give syou 1" of linear motion for one motor revolution. So a 1" DP diameter pinion moves 3.1416 inches per rev so a 3:1 belt reduction gets you into the majic ratio. Forget the number of teeth. Its all about the diameter (DP) of the gear. (like a wheel running on a flat surface ) All you have to do is match your rack with the same pitch and pressure angle and slect the gear with the right DP (pitch diameter) . To get the gear "multiplier" you simply multiply the DP times PI

You also need to pick a gear with a bore size to match the shaft on the belt eduction .

Basically the larger they get the higher the speed per rev and the less torque it has. (speed VS torque) Torque gives you acceleration but you need enough speed so you top Cutting Speeds are at about 1/2 the max motor RPM on your system. Thus the Golder Ratio I quoted above that proves to be the best balance between speed and torque.

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