- Our current gear reduction is 12:1 in the gearbox and 20:15 between the sprockets. This means that our overall gear ratio from the motor to the wheels is 16:1. For every 16 turns of our CIM motors, the wheels turn once. It also means that we get 16 times the motor torque at the wheels.
- From the theoretical top speed of the CIM motors and our 16:1 reduction, our current top speed should be
5310 rpm (CIM motor top speed)
* 1 minute/60 sec
* 2π radians/rotation
/(16/1) (gear ratio)
* 6.25 inches (wheel radius)
= 18.1 ft/s (pretty fast) - Our theoretical maximum pushing force (limited by the 40 Amp circuit breakers) should be
98 oz-in (CIM motor torque @ 40A current)
* 4 CIM motors
* 80% (approximate efficiency of power transmission by the gearbox and chain)
* (16/1) (gear ratio)
/ 6.25 inches (wheel radius)
=50.18 lb - We pushed against a scale with the robot and found that our maximum pushing force was 42 lb.
- The eight lbs or so of force we "lost" is because of the flat tires, the loose chains, and because the efficiency of a system like this is hard to predict. I used 80% as a ballpark, but obviously our efficiency is lower.
- To move a 150 lb robot (120 lb + battery and bumpers) up a 45º slope, we need 150/√2 ≈105lb.
- From the calculations above, we determined that we need about three times the current gear ratio we currently have, tripling the pushing force and cutting our top speed to 1/3 of what it is now.
- To triple our gear ratio, we are going to replace our sprockets to change our gear ratio. If we replace our 15 tooth sprocket with a 10 tooth sprocket, and our 20 tooth sprocket with a 40 tooth sprocket, our new gear ratio is 12:1*40/10=48:1. This is 3 times our previous gear ratio!
- From the theoretical top speed of the CIM motors and our 48:1 reduction, our current top speed should be
5310 rpm (CIM motor top speed)
* 1 minute/60 sec
* 2π radians/rotation
/(48/1) (gear ratio)
* 6.25 inches (wheel radius)
= 6.0 ft/s (not very fast) - Our theoretical maximum pushing force (limited by the 40 Amp circuit breakers) should be
98 oz-in (CIM motor torque @ 40A current)
* 4 CIM motors
* 80% (approximate efficiency of power transmission by the gearbox and chain)
* (48/1) (gear ratio)
/ 6.25 inches (wheel radius)
=150.54 lb (very strong)