Quote:
Originally Posted by Andrew Schreiber
Specifically, what part of my math did I do wrong? (Remember folks, I am a programmer, I do this in my spare time) I worked out what the speed of the motor at 40 amps was and based the speed off that. Is a 5.97:1 reduction too little for a 4" wheel?
|
Here's how I would design a two-speed transmission. I always try to have specific goals for my low and high gearing to "optimize" the way that I'm using the motors' mechanical power.
LOW GEAR ANALYSIS:
Goal: Be traction limited at 40A per motor
Rationale: This will let us push as hard as we can without ever popping breakers.
Assuming the load is something like 145 lbs (robot+battery+bumpers) and you are using roughtop with a static CoF ~= 1.3, the maximum amount of force that you can transfer to the ground is about 190lbs.
Assuming 4 drive motors (CIMs), and 4 inch wheels, each motor can contribute up to (190 lbs) / (4 motors) * (2 inch wheel radius) = 95 in-lb of torque before you slip your wheels.
Stall torque of a CIM is about 21.5 in-lb (at 133A). Torque at 40A is more like 6.2 in-lb. And then there's gear-train inefficiency - let's say you have a good spur gearbox for a total efficiency of 90%. Now your torque is 5.5 in-lb per motor.
So if you want to be able to push ~190lbs across the floor all the live-long day, a reduction like 95/5.5 = 17.2:1 would get the job done. When not pushing, you would expect to move at a clip of about 4.5-5 fps (I generally find that 80-85% of the "free speed" of the motor, divided by the gear ratio, gives a good top speed estimate. It is never exactly the free speed because of drag in the gear train).
HIGH GEAR ANALYSIS:
Goal: Be traction limited at 75% stall (100A per motor)
Rationale: We will be able to turn in the upper 25% of the motor power curve (since we need to skid our wheels in order to turn in a tank drive). At the same time, our max speed will be very high. We don't worry about the 40A breakers, because they won't trip unless there is a constant (> a couple seconds) heavy draw, and we will downshift if there is a need for that...
Assume all the same things as before...4 CIMs outputting 21.5 oz-in of torque and 190 lbs of total load. But now at 75% stall and 90% efficiency, we expect ~14 oz-in of torque instead of 5.5 as before. 95/14 ~= 6.8:1. We expect a top speed of about 11-12 fps.
Obviously, the goals at each design point will vary widely depending on what you are trying to do - these are only two possible criteria. For a single speed drive, you'd need to trade off between popping breakers/being traction limited and having a good degree of speed and agility.
Likewise, the missing "last step" that I would always go through would be to compare my desired ratios with those that I can easily achieve by utilizing COTS components and my teams' manufacturing capabilities. For example, a SuperShifter (with the last stage removed) can achieve ratios of 10.67:1 and 4.17:1. Coupled with a chain reduction of about 1.6:1, I get 17:1 and 6.7:1, which are pretty close to my theoretical goals using 4 inch wheels.