# Understanding Motor and Gearbox Design

Why Spend Time Choosing the Right Motor and Gearbox?
Choosing the correct combination of a motor and a gearbox for a given application is very important, both in the FIRST Robotics Competition (FRC) and in actual engineering projects. Without appropriate motor-gearbox combos, your team will find that your robot does not function as quickly and effectively as intended, and may have a tendency to burn out motors.

Prerequisites
A basic understanding of physics – e.g. force, torque, power, and gear systems
A willingness to learn
Step 1: Motor Characteristics

There are several important characteristics of motors that provide information about a motor and its capabilities. They are the motor’s output torque, its current draw, its output speed, its power, and its efficiency, each of which I will discuss in turn. These characteristics are interdependent and can all be derived from four values: the motor’s stall torque, stall current, free current, and free speed.

Torque
A motor’s output torque is the amount of force with which its output shaft can rotate. If too much torque is applied to a motor, its output shaft will stall, or stop turning. Other motor characteristics are commonly written as a function of torque. It is usually measured in N-m when metric units are required and oz-in when English units are required.

Current Draw
The motor’s current draw is the amount of electrical current the motor draws at any given load. As the load on the motor (the torque) increases, the amount of current that the motor draws increases linearly. This relationship can be written as

 Symbol Name Units Description I Current Amps (A) The amount of current drawn by the motor Istall Stall current Amps (A) The amount of current drawn when the motor is stalled Ifree Free Current Amps (A) The amount of current drawn when the motor has no load placed upon it τstall Stall Torque Newton Meters (N-m) The amount of torque required to stall the motor τ Torque Newton Meters (N-m) The amount of torque applied to the motor output shaft

Speed

The motor’s output speed is the rotational velocity at which the output shaft spins. As the load on the motor increases, the output speed decreases linearly. This relationship can be written as

 Symbol Name Units Description ω Speed Rounds per Minute (rpm) The rotational velocity of the motor’s output shaft ωfree Free Speed Rounds per Minute (rpm) The speed at which the motor spins when it has no load place upon it τstall Stall Torque Newton Meters (N-m) The amount of torque required to stall the motor, or prevent its output shaft from rotating τ Torque Newton Meters (N-m) The amount of torque applied to the motor output shaft

Step 2: Motor Characteristics (continued)

Power

A motor’s power is the rate at which the motor can do work. It is essentially a measurement of how fast a motor can get a job done. Its value in watts is given by the equation

 Symbol Name Units Description P Power Watts (W) The amount of power supplied by the motor τ Torque Newton Meters (N-m) The amount of torque applied to the motor output shaft ω Speed Rounds per Minute (rpm) The rotational velocity of the motor’s output shaft

Efficiency

Motor efficiency is a measurement of how much of the electrical energy put into a motor is converted to mechanical energy. Much of the remaining energy is converted into heat, which can cause a motor to burn out if it is operated at a torque/rpm where its efficiency is very low. Efficiency is given by the equation

 Symbol Name Units Description η Efficiency Percentage (%) The percentage of electrical energy input into the motor that is converted to useful mechanical energy Pout Power Output Watts (W) The motor’s output power at a given torque and speed Pin Power Input Watts (W) The amount of electrical power supplied to the motor I Current Amps (A) The amount of current drawn by the motor V Voltage Volts (V) The voltage at which the motor operates