Drive Train Gear Ratio

What We Have Now

• 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.

What We Need

• 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.

What We are Going to Test

• 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)