Drivetrain Basics

[AustinSchuh]

I feel like rerunning these numbers again, so here I am. It's been about 4 years since I ran them last, and I got numbers very similar to Paul last time.

I'm using the CIM datasheet available at http://www2.usfirst.org/2005comp/Specs/CIM.pdf

Lets assume that the torque is linear in current. It's a pretty good assumption, if you check the physics. We can then use the following data off the datasheet to get the torque at 40 Amps.

343.4 Oz-In stall at 133 Amps.
0 Oz-In free load at 2.7 Amps.

This gives us 98.3 Oz-In at 40 Amps. Which is 6.14 inch lbs.

Lets assume a coefficient of friction of about 1.2. That's not too far off for Roughtop. Assuming a 150 lb robot, our wheels will slip at 180 lbs of pushing force. Lets choose an arbitrary wheel size of 4". So, the torque at slip on the sum total of all our wheels is 360 inch-lbs.

To achieve that torque at 40 amps with 4 CIMS, we need to have a gear down of 360 / (6.14 * 4) = 14.6 to 1. Now, let's use the free speed of the motor to calculate our top speed.

5000 RPM / 60 / 14.6 * 4 * pi / 12 = 5.96 feet/sec.

Off by 10% from the 6.5 ft/sec number, which is pretty much loose change given that I probably don't know my weight or coefficient of friction that well.