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Step 8: 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 in FRC. 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 9: 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. We’ll try using a single BaneBots RS-550 as our starting point because of its high power, meaning it will be able to get the job done faster. In addition, it is commonly used in applications such as this, meaning that it is probably a good fit for the job in general. To make estimations easier, I made a motor curve graph for the RS-550.

First, we want to make sure that the motor won’t draw more than 40 A and blow a circuit breaker. Looking at the graph, we can visually see that it takes a load of .23 Nm for the RS-550 to draw 40 A. To ensure that the motor won’t reach this, even under heavy load, we will try designing for a current draw of 20 A. Looking at the graph again, we see that this corresponds to a torque of .115 Nm. Now, we can calculate the reduction we would need to achieve the necessary torque of 3.05 Nm.

Gear Reduction:

We have now chosen a gear reduction of 26:1, which means we can calculate the exact load our elevator motor should encounter.

Load at Motor:

Now, we can use equation (1) from “Motor Characteristics” to calculate the current we would expect the RS-550 to draw at this load:

Current Draw:

Our estimated current draw, 21.0 A, is well within our acceptable bound of 40 A. Next, we will determine the rotational velocity of the gearbox output shaft using equation (2). We will account for the 75% gearbox efficiency at this stage in the calculations.

Motor Speed:

Now we can check to see if our chosen gear ratio will allow us to achieve our desired output speed, 357rpm.

Gearbox Speed:

Finally, now that we have verified that our gear ratio satisfies our requirement, we can calculate how long it should take for the motor to raise the elevator.

Lift Time:

We have now completely verified that our RS-550 motor and 26:1 gearbox will achieve or exceed our original goals. Because real world performance is often worse than the theoretical performance, it is wise to “overdesign” these systems. Doing so also ensures that our simplifications do not cause our system to perform much worse than expected.

When you first go through this process, you may have to go through the calculations multiple times as you try different motors and gear ratios. As you gain experience, you will gain an intuition of which motors and ratios will work well for a job.

The final step in this process is to choose a gearbox. In this example, choosing the RS-550 version of Banebot’s P60 gearbox with a 26:1 reduction makes a lot of sense. Not only is it compatible with our motor, but it also has the right gear reduction and a common .5 inch keyed output shaft.

Hopefully this example problem has helped you understand the process of choosing a motor and gearbox. In addition, I hope that it has shown you how to properly apply the theory you learned earlier in this tutorial.

This section of the tutorial is meant to provide some additional resources for learning about motors and gearboxes, as well as some tools that can expedite the design process. However, DO NOT use the tools in place of understanding the theory. Instead, use them because you have verified them against your own calculations and because you understand how they work.

John V-Neun’s Design Calculator: This spreadsheet can significantly expedite the process of choosing a motor and gear ratio. However, only use it once you understand the theory behind the calculations.

A FIRST Encounter with Physics: This lesson teaches some of the fundamental physics concepts encountered in FRC. I looked at its section on motor and gearbox theory to ensure that I had all of my information right for this tutorial. However, this tutorial goes into a bit more detail than its chapter on motors and gearboxes.