Will the gear tooth break?

[Matt Adams]

Originally Posted by sanddrag

2 small CIMs, with a 12 tooth gear on each that mate with a single 45 tooth gear on a separate shaft. On the same shaft as the 45 tooth gear is a 13 tooth gear. These gears are 20 pitch, 14.5 degree pressure angle, and 3/8" face width. For now, let's say the 13 tooth gear is made out of common cold rolled steel.

Assuming a worst case scenario (motors reach stall torque/current), will the 13 tooth gear be able to withstand the force?

What calculations are used for this?

Stall Torque on Two Motors Combined = 39.3 in-lbs. [Edit: Oops... gotta be careful here. They are applying stress on different teeth. Use 19.65 in-lbs)

12:45 Ratio, so 19.65 * (45 / 12) = 73.7 in-lbs.

This 13 tooth gear has a radius of (13/20) / 2, or 0.325 inches.

Hence, the applied force is 73.7 in lbs / 0.325 lbs or 226.8 lbs.

A quick Lewis Bending Equation I'm showing says this is not fairing too well. This admittedly conservative equation is showing 0.68 factor of safety, assuming 40 kpsi yield stress on your 'common cold rolled steel'.
(Estimated Stress: 58 kpsi for 20 degree Pressure Angle. 14.5 will be roughly 20-30% weaker)

A few things to ask:

I used the stall torque of the CIMs. Is it possible for this geartrain to actually 'Lock Up'? Are you doing anything fancy that could cause locking or braking down the line in your drivetrain? If not, and your gear the drivetrain properly to ensure you don't trip breakers while pushing up against a wall, then the true peak torque on these gears will be less than what I used. (Perhaps even only 40% of the torque I used.)

A few things you can do to reduce stress on the gear:

• Increase Diameter
• Increase Face Width
• Decrease Pitch
• Increase pressure angle to 20 degrees

Also note, a quality gear bought from some place like Stock Drive Products may not be your average strength steel. 40kpsi is pretty conservative for a heat-treated gear, though I've seen some of the Martin stuff out of Mcmaster run at 30kspi out of the box.

Calcs attached (EDIT: for 20 degrees, its what I had handy) for reference.

Bottom Line:
I won't make any promises, but assuming a standard drive train setup with slipping tires right around stall current, I'd say this gear, as is, is on on the edge. I'd sleep better with 1/2" face width.

Matt