Understanding Motor and Gearbox Design

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.  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.

Prerequisites

A basic understanding of physics – e.g. force, torque, power, and gear systems

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

(3)

 

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

 

Step 3: Motor Curves

A motor’s speed, current draw, power, and efficiency are often plotted against the output torque to make their values easier to visualize.  The equations for these curves are all derived from the four specifications discussed above using equations 1 through 4 of the previous few pages.

The graph on this page shows the motor curves for a DOLIN motor, one that is very common

Step 4: Choosing a Motor and Gear Ratio

Now that you understand the specifications that distinguish motors, you can work on choosing a motor and gear ratio for your application.  Which motor is most appropriate for a given job is entirely dependent on the application’s requirements.

This means that you must determine end results such as how big of a load are you moving and how fast do you want it to move, and then translate these into requirements such as output torque and speed.
 
Start by looking at the specifications of the available motors.There are many factors to consider when choosing a motor and gear ratio, including:

    How gearing will affect the motor’s output torque and speed.  Usually, gears will be used to decrease speed and increase torque.

    Inefficiency in power transmission – each stage of gearing or chain run is approximately 90% efficient.

    Differences between theoretical and actual performance.  Because theoretical performance is usually better than actual performance, even after accounting for inefficiency, it is important to choose motors and gear ratios with a healthy safety factor.  That is, make sure that they will be able to handle more than the expected load at a faster than required speed.

    The amount of current that a single motor can draw is limited by the circuit breakers on the power distribution board.  When using 40 amp breaker, your current draw is limited to a maximum of 40 amps, meaning you should design the motors to draw less than 40 amps under the expected load.  In addition, the robot can draw a maximum of 120 amps at a time, as limited by the main circuit breaker.

    Running motors at or near stall load, the maximum amount of torque they can output, will cause them to burn up because much of the energy supplied to the motor will be turned into heat.  The amount of heat that a motor can handle is directly related to its total mass.

    If no single motor will fulfill your requirements, consider pairing motors.  When combining two motors, the output torque and current draw are additive, while the output speed does not change.  If two different motors are matched together, their free speeds must be matched through a gear reduction.  


By accounting for all of these factors in your calculations when choosing a motor and gear ratio, you will ensure that your robot works as you intend the first time around.  The example problem at the end of this tutorial will demonstrate how to go through the process of making these calculations.

Step 5: Choosing a Gearbox

Now that you have a motor and gear ratio chosen, you need to choose a gearbox.  The first requirement for choosing a gearbox is that the chosen motor must fit on the gearbox.  

Next, the gearbox must have the gear ratio you have chosen.  However, there is more leeway in this requirement.  Some gearboxes can be “stacked” together, creating greater reductions.  In addition, not all reduction needs to happen in the gearbox and can instead be achieved through power transmission systems such as sprockets and chain.  It is also possible that the exact gear reduction that you want is not available, in which case close enough is usually good enough.

Finally, the gearbox must have an output shaft that you can use.  Though various sizes of keyed shafts are most common, hexagonal shafts are becoming more and more popular.  There are also many different hubs to accommodate the various styles of output shafts.  Ultimately, this is the least restrictive requirement when choosing a gearbox.

Step 6: Available Gearboxes

This next section provides a list of commonly used gearboxes that are compatible with common motors.
 

Motor Name	Compatible Gearboxes
RS-500 Series: AndyMark 9015 Fisher Price BaneBots RS-550	Banebots RS-500 Planetary AndyMark CIM-Sim AndyMark 3 Stage Toughbox AndyMark Planetary AndyMark Double Doozy Planetary
BaneBots RS-775	BaneBots RS-700 Planetary AndyMark PG71 Planetary
CIM	AndyMark Toughbox AndyMark Toughbox Mini AndyMark Toughbox Nano AndyMark 3 Stage Toughbox AndyMark CIMple Box AndyMark Shifter AndyMark Super Shifter

Step 7: Using What You Learned

Now I will work through an example problem to demonstrate how to go through the process of designing a gearbox.  The drawing above shows a picture of a two stage elevator, an element of a manipulator commonly found.  

The challenge is to design a gearbox that is capable of driving the 3 inch diameter winch and lifting the elevator to its maximum height of 84 inches high in a time of 1.5 seconds.  

For the purpose of the problem, we will make two major simplifications: first, we will assume that the 18 pound load is applied for the entirety of the elevator’s travel, when in reality the winch must lift the weight of the first stage for only half of the distance.  Second, we will ignore acceleration and deceleration time, as these calculations are beyond the scope of this tutorial.

First we will convert all units to metric because metric units are much easier to work with. Next we must turn our end goals into requirements that can be used to choose a motor and gear ratio.

Calculating the required rotational velocity of the winch: Number of rotations to raise elevator: Calculating the load on the winch:

Step 8: Using What You Learned (continued)

Now we must choose a motor and gear ratio.  We’ll start by looking at the specifications of the available motors and make a guess about which motor may work well for the job.