Combat Robot Drive Train - Optimum Gear Ratio Selection

Questions and Answers about Combat Robotics
from Team Run Amok
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Optimizing Drivetrains

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:

At any given voltage, a brushed permanent magnet DC electric motor:

Generates maximum torque when held at stall (zero speed) and zero torque at maximum speed;

Consumes current (amperage) proportional to the torque produced;

Produces maximum horsepower when loaded to 1/2 its maximum (unloaded) RPM.

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:

The stall torque of the motor at the available voltage;
The diameter of the driven wheel(s);
The weight supported by the driven wheel(s); and
An educated 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 pound-foot stall torque driving a single 6" diameter tire that bears 25 pounds of weight.

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.

Maximum tire force = Weight Supported by the Wheel * Coefficient of Friction
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.
Torque Required to Generate Maximum Tire Force = Maximum Tire force * Radius of Tire
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:

1 pound-foot = 192 ounce-inch (often given for small motors)
1 pound-foot = 1.356 newton meters (metric units)

Step 3 - Calculate gear reduction needed to
generate torque required for maximum tire force

The equation is a simple one:

Gear Reduction Needed = Torque Required ÷ Motor Stall Torque

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.
Desirable Range of Gear Reduction = Gear Reduction Needed for Maximum Pushing Force * [1.5 to 2.0]
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:

What gearing provides best performance in a sprint to the center of the 40 foot arena?

What is the impact on speed and acceleration if the gearing is adjusted for a 60 amp per motor maximum current consumption?
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.

Sixteen-Foot Sprint to Arena Center

Ratio Max Amps Speed (MPH) Time (sec)

4:1 140 12.7 1.58

6:1 93 13.4 1.39

8:1 70 12.8 1.33

10:1 56 11.5 1.35

12:1 47 10.0 1.42

The table shows that for this particular robot in this particular arena:

The best ramming speed at the end of a 16 foot sprint comes with a 6:1 reduction ratio;
The quickest time for a 16 foot sprint to arena center comes with an 8:1 reduction ratio; and
Limiting current consumption to 60 amps requires a 10:1 reduction ratio that clips about 2 MPH off the best speed but still gives a quick sprint time to the arena center.

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.

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