Will the gear tooth break?

[Matt Adams]

I confess that my 'edit' about the two CIMs working on different teeth had poor logic - they're running on different teeth on the 45 tooth gear, but presumably the 13 tooth gear will have one contact point.

Since Dr. Joe seems to have a bit more confidence, from experience in this working well than I do, I want to take another swing just to see what the numbers show.

First step I think is to be a bit more conservative with the torque these gears should actually see. I'll assume that you'll design the max torque to be right around 40 Amps, which I calced out to be about 14 in-lbs from a pair of CIMs. After a 45:12 ratio, this becomes about 53.25 in-lbs.

Using this number, and the standard AGMA gear equation

Lewis Form Factor (Y) for a 14.5 degree PA gear = 0.223
Radius = 13/20 / 2 inches = 0.325 inches
Force on Tooth (Wt) = 53.25 / .325 = 163.85 lbs.
Face Width (F) = .375
Pitch (P) = 20

Stress = (Wt * P) / (F * Y)

I have this showing 38,266 PSI, or a factor of safety of 1.04 (at a megar 40,000 PSI)

I think you have a few factors to consider:

Positive Effects:

• Run time of a FIRST drive train can typically be measured in hours (relatively short).
• The impact loading on the gears in your drive train isn't too substantial.

Negative Effects:

• You could potentially apply more torque before your 40 A breakers trip if something down the line isn't geared to peak out at 40 Amps.

Another Note:

A roughly equivalent pinion in the FIRST kit drive train has a face with of 0.809 inches. This has been designed to take a single CIM motor's peak torque output with an overall reduction of (50/14 * 50/14 * 50/14) or a totally reduction of 45.5 times.

However, since you have 2 times as many motors, your face width is 2.16 times smaller, and your overall reduction is 3.75, this gear will see (14/12 = 1.16) 1.16 times more torque due to their smaller tooth count, and the kit material (assuming 100ksi yield) is 2.5 stronger than plain steel.

This means the strength of this gear, relative to the one in the drive train, based on application, is (2 * 2.16 * 3.75 * 1.16 * 2.5 = 46.98 ) about (45.5/46.98) 0.96 times as robust. However, there's presumably some factor of safety built in to the kit, so being withing 4% is probably well within their factor safety.

Hence, with average steel, I'm still going to call this border lined, but probably more above the border than below. It sounds like Travis is proposing some stronger material, which is probably the easiest fix.

Good luck,

Matt