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.

This tutorial will teach you the fundamentals of gearbox design and implementation.  First, I will teach you about motor characteristics.  Next, I will discuss how to choose a motor and gear ratio given application requirements.  I will then provide information about choosing a gearbox, followed by an overview of the motors and gearboxes available in FRC.  Finally, I will demonstrate how to use what you learn in this tutorial in an example problem and point out extra tools and resources if you want to learn more.

This tutorial was made through the Autodesk FIRST High School Intern program.

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

(1)

 

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

(2)

 

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

Photo Credit: http://www.engin.umich.edu/group/ctm/examples/motor/motor.html