# Gear Ratio Calculation

This page is intended to cover the calculations required to evaluate the torque and output shaft RPM for a gearbox and motor combination. To find the best motor and reduction process is often iterative or requires considering multiple configurations. These calculations apply to any reduction method whether it is gear chains, gearboxes belt drives or a combination.

### Fundamental Method

- Define the parameters of your problem
- Do a basic power calculation
- Determine the base gear ratio
- Round the ratio up to the nearest available reduction
- Note, some scenarios might result in the rounded reduction being too great in which case a compromise on the driving motor may have to be made.

- Recalculate output torque to ensure it is greater than required maximum output torque.

### Define the problem

This should be easy, list what you need out of this design, how much room you have, what motors are available, power available etc.

### Power Calculation

The first major step is to determine if the rotation rate (RPM) with a given torque is achievable with the FRC imposed restrictions. Suppose you are limited to 12V with a 30 amp breaker, the available power is the product of the current and voltage available, in this case 360 Watts. The power require is the produce of the torque and the shaft rotation rate, the rotation must be expressed in radians per second which is converted with 1 rad/s = 2*pi/60*1 RPM. An example is the output shaft is required to drive at 800 RPM with 10Nm of torque which is ~838 Watts. This example required a shaft output power much greater than the electrical power available; thus is not achievable. A compromise will either have to be made on how fast the shaft can be driven or how much it can move or push.

It should be noted that this method does not account for any losses that occur and so at least 10% of the required power should be added on to account for this.

### Determining the Base Gear Reduction ratio

- For each motor under consideration, the examine the motor performance and locate on the performance curves where the motor shaft output power is what was evaluated in the previous step. A good source of performance curves for FRC legal motors can be found here: http://motors.vex.com/.
- Depending on the more critical or the required rotation rate or torque; one should be used to evaluate the required reduction. For torque the required reduction is the ratio of the motor shaft output torque to the required torque; for rotation rate it is the opposite, the ratio of the required rotation rate to the motor rotation rate. This gives the base ratio required, however it might not be practical and so a compromise on the final output is required.
- An alternative, if feasible is to opt for a more powerful motor and and choose a desired operating condition and then derate the motor to that condition.

**Examples**

**A Gearbox to Drive a Winch to Pull up the Robot**

Suppose a system was considered with the following properties:

- Heave (robot): 40 kg
- Winch diameter: 35 mm
- Driven by a CIM motor
- Breaker: 40 Amps @12V

From the specifications above the maximum load torque can be calculated to be 13.734 Nm (= 20*9.81*0.035).

*CIM Motor data:*

CIM motor power curves

Examining the current draw plot (blue dotted), it can be determined that the motor will spin approximately 3800 RPM or 63.33 RPS or 10.080 radians per second. By examining the torque curve (solid yellow), an output torque of approximately 0.65 Nm.

By applying the the data from above the method described previously the reduction ratio is 21.129; From Vex Pro, the best suited planetary gearbox to this design problem is a 25:1