This process applies to Brushed Permanent Magnet Direct Current motors. For brushless motors see: Brushless Motor Selection for Combat Robots.A few handy things to know about brushed permanent magnet DC motors:
When a brushed electric motor is powered but prevented from turning (stalled) it generates no counter-electromotive force and consequently will flow a great deal of current. This high current flow generates a great deal of heat that may cause rapid failure of the motor as well as associated speed controllers and batteries.
To prevent destructive motor stalling under heavy pushing conditions commonly encountered by combat robot drivetrains, it is important to select a gear reduction ratio that will supply sufficient torque to the wheels to allow them to 'break free' and spin well before motor stall torque is reached.
You'll need the following information to calculate the optimum gearing for your 'bot:
Step 1 - Calculate the maximum force the tire
can generate before it 'breaks free' and spins
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.
For our example, Maximum tire force = 25 pounds × 0.8 = 20 pounds of force. Any more force will spin the tire.
Step 2 - Calculate the torque needed
to generate maximum tire force
In the English system, torque is measured in pound-feet. One pound-foot 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.
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 × 0.25 feet = 5 pound-feet.
Torque conversion factors:
Step 3 - Calculate gear reduction needed to
generate torque required for maximum tire force
The equation is a simple one:
For our example, the motor generates 1 pound-foot of torque and we need 5 pound-feet of torque to max out the tire grip. The gear reduction required is 5 pound-feet ÷ 1 pound-foot = 5:1
Gearing the motor 5:1 will generate the torque required to maximize the pushing force available from the tire, but it will require maximum torque output from the motor - which we have already determined is available only when the motor is stalled, consuming maximum amperage, and generating potentially damaging heat. We need to add in some additional gear reduction to allow the motor to avoid stall while still supplying the needed torque.
Step 4 - Calculate additional gear reduction
needed to keep drivetrain components healthy
Electric motors have a wide range of ability to survive stalling and high amperage loading. High performance brushless model airplane motors do not take well at all to being bogged down and generally make poor drive motors for combat robots -- but they can work very well as weapon motors where they spend much of their time in their higher rev range.
As a 'rule of thumb' for the motors commonly used in robot drivetrains, look to provide 1.5 to 2.0 times the torque needed for maximum pushing power. This will allow the motor to spin the tire freely if the robot is prevented from moving and keep the motor speed high enough to reduce the current consumption to a reasonable level.
For our example, the range of desirable gear reduction ranges from (5 * 1.5) = 7.5:1 to (5 * 2.0) = 10:1.
Selection of a ratio within that range can depend on gearbox availability and on the size of the arena; larger arenas may make the higher speed available from lesser reduction ratios more desirable, while smaller arenas favor the greater acceleration available from greater reduction ratios.
A tool to help you in your calculations
Now that you know the theory you can make good use of the Team Tentacle Torque Calculator. The calculator offers automated calculation of the effects of gear ratios on speed, acceleration, battery selection, and amperage draw for a large list of common robot drive motors -- or you can enter the critical values for motors of your own choosing. Consult the help system within the calculator for specific tips on its use.
Adjusting gearing for special conditions
The 'optimum' gearing allows the motors to produce their full output power without 'bogging' and consuming excessive current. While that is 'optimum' for the motors, the gearing may not provide adequate acceleration to achieve the best speed in small arenas or in cases where available current must be limited to the capacity of specific speed controllers. Adjustments to the 'optimum' gear reduction may be needed in these conditions.
Here is an example of adjustments made to the gearing of a 120 pound spinner-weaponed robot powered by a pair of AmpFlow F30-150 motors powering 6" diameter wheels. The builder was considering use of electronic speed controllers with a maximum current capacity of 60 amps in an arena 40 feet across. The questions are:
The Tentacle calculator shows that a 4:1 gear reduction provides tire breakaway at 140 amps -- very close to the 'optimum' tire breakaway of 147 amps. Clicking the 'Acceleration Calculator' tab and setting the 'Arena Size' to 16 feet (front edge of robot to center of 40 foot arena) shows a top speed at that distance of 12.7 MPH in an elapsed time of 1.58 seconds. Repeating that analysis for greater gear reduction ratios gives us the following table.
The table shows that for this particular robot in this particular arena:
Note: for a 32 foot 'across the arena' dash, the 'optimum' 4:1 reduction ratio provides the best top speed, but opportunities for such a long ramming run are infrequent.
Copyright 2012 by Mark Joerger -- all rights reserved.