How to select gear ratio for a gear reducer?

This is the first of a multi-part series on gear reducers. In this first part we look at selecting the proper gear ratio for a gear reducer.

The information here is supplied by Bodine Electric Company.

Gear reducers are an essential part of mechanical power transmission systems, being used for speed and torque conversion. Selecting the right one for an application is a fairly straightforward process. The first step in selecting a gear reducer is to know the required torque and speed as well as the most suitable type of motor to use. Then, it can be determined if a gear reducer is needed in the particular case. If so, then the next step is to select the proper type and ratio.

A cutaway of a gear motor showing the internal worm gearing. (Image via Bodine Electric Company)

So what does a gear reducer do? The most common benefits are that they can reduce speed, multiply torque, and solve inertia mismatching issues. For instance, to take speed reduction, the amount needed will depend on the type of motor used. That’s because some motors can operate at low speeds (less than 1,000 rpm, for instance) without the need for a gear reducer, while others cannot.

For speed reduction the gear ratio is calculated using the equation:

G = N_MOTOR / N_LOAD

where G is the gear ratio, and N is the angular velocity of the motor and the load.

The way gear reducers work is that they essentially multiply the output torque of the motor. So for instance, a small motor with a gear reducer may be less expensive and smaller than a larger motor without a gear reducer producing an equal amount of torque.

To calculate the required gear ratio when torque multiplication is needed, use the equation:

G = T_LOAD / [ T_MOTOR x e_GEARS ]

where G is the gear ratio, T is torque and e is efficiency.

Another function of gear reducers is to reduce the reflected load inertia to the motor by a factor of the square of the gear ratio. For most motion applications but especially high performance ones, the ideal condition is for the reflected load inertia to equal the motor inertia.

To calculate the gear ratio when inertia matching is the main concern, take the square root of the ratio of the load inertia to the motor inertia as in the equation:

G= sqroot [ J_LOAD / J_MOTOR ]

where G is the gear ratio and J is the inertia of the motor and load.

In part 2, we’ll look at the different types of gear reducers and how to select the best one.