[JesseK]

Steve, I can't account for how to apply inefficiency accurately (i.e. sqrt(inefficiency) vs full inefficiency to only torque), but here's an anecdote from my season:

For our lift's acme rod, I calculated the inefficiency directly and applied it solely to torque inefficiency. I used the diameter of the acme rod and the # of inches/turn. That gave me a triangle (circumference = x, inch/turn = y) from which I then calculated the angle of the threads. The efficiency then has the form sin(angle)/[cos(angle)+sin(angle)]. Since the angle of our threads was ~45.5 degrees, the inefficiency was ~50%. Most acme rod or ball thread setups have thread angles between 25-45 degrees from what I've seen.

We modeled our threaded rod lift with this inefficiency. We used a spring force meter (is that the right term?) to accurately measure the force needed to lift the production lift with all of its inefficiencies. I then put it into an Excel spreadsheet that used Ether's equations from the minibot to calculate the time of the lift (accounting for motor acceleration, gearing, etc); the spreadsheet was fairly accurate, within 0.2 seconds of the real lift (of course, subject to human error of timing).

I'll reiterate that the inefficiencies of the gearbox & rod were only applied as a torque load on the motor (i.e. an extra subtraction of Newtons in the numerator of "D" in Ether's equations). After reading some of your analysis, I'd conjecture that it worked only because our lift was geared for torque rather than speed AND because there are major losses in the rod. Thus the raw # of torque loss was more noticable than the raw # of speed loss. I put the same types of calculations into our drive train, yet I haven't had a chance to get to the robot to test how the sim holds up to the true system.

For a worm gear setup, I presume the same method for inefficiency can be used: the diameter of the worm pinion is the X of the triangle; for "inches/turn" you'd have to use the circumference of the worm wheel as if it were a straight line, and then apply the gear ratio to it to figure it out.