Optimum gearing
From Combat Robot
A few things handy to know about permanent magnet DC motors:
- They generate their maximum torque at zero speed (stall torque);
- The amperage drawn is proportional to torque;
- Maximum horsepower comes at 1/2 the maximum (unloaded) RPM;
Motors, speed controllers, and batteries all eventually fail if the motor is held at full-power stall for very long, so it is a very good idea to make certain that the gear ratio you select for your 'bot provides enough torque to the tires to allow them to spin rather than stall if the 'bot cannot move.
You'll need the following information to calculate the optimum gearing for your 'bot:
- Stall torque of the motor at the voltage you're running;
- Diameter of the driven wheel(s);
- Weight supported by the driven wheel(s);
- A guess about the relative 'stickiness' of the tire and the arena surface (coefficient of friction)
For demonstration purposes, let's calculate gearing for a motor with 1 foot/pound stall torque driving a single 6" diameter tire that bears 25 pounds of weight.
Step 1 -- The maximum force a tire can generate is dependent on the weight bearing down on the tire and the traction of the tire/arena pairing. With a rubber tire and a painted wood/steel surface, a reasonable estimate for this coefficient of friction is about 0.8. The formula is: Weight X Coefficient of Friction = Max Force.
For our example, Max Force = 25 pounds X 0.8 = 20 pounds of force. Any more force will spin the tire.
Step 2 -- In the English measurement system, torque is measured in foot/pounds: one foot/pound of torque acting on an axle will provide one pound of force at the surface of a tire with a radius of one foot. If the tire has a radius of 1/2 foot, the force at the surface is doubled to two pounds. Knowing the diameter (radius = diameter/2) of the tire will enable us to calculate the force at the tire's surface.
Sometimes torque for small motors is given in inch/ounces: 1 foot/pound=192 inch/ounces (12 inches per foot X 16 ounces per pound = 192).
For our example, the radius of the tire is 0.25 foot, maximum force possible at the tire surface is 20 pounds, and the torque required to generate that much force is: 20 pounds X 0.25 feet = 5 foot/pounds
Step 3 – Our motor generates 1 foot/pound of torque and we need 5 foot/pounds to max out the tire grip. However, simply maxing out the grip will result in very low slippage and still a very large consumption of amperage and generation of excess heat. A good rule of thumb is to provide 1.5 times the amount of torque needed to just start the wheel spinning, so we need 5 X 1.5 = 7.5 foot/pounds of torque at the drive axle.
Gear reduction reduces speed and increases torque in direct proportion to the gear ratio, so a 7.5:1 gear reduction will provide our needed torque at the wheel.
The Team Tentacle Torque Calculator offers an automated calculation of the effects of gear ratios on speed, battery selection, and amperage draw for specific motors. Note that this calculator makes assumptions on robot design (E.G. all-wheel drive is assumed).
See also: calculating speed
