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How to calculate gear ratio of planetary gearbox?

2024-02-26 15:16:24

The gear ratio of a planetary gearbox is a crucial parameter that determines the relationship between the input and output speeds of the system. This essay aims to provide a detailed guide on how to calculate the gear ratio of a planetary gearbox. By understanding the components and principles of planetary gear systems, you can accurately determine the gear ratio.

Understanding Planetary Gear Systems

  • Definition and Function

    A planetary gear system consists of a central sun gear, multiple planet gears, and an outer ring gear. The sun gear is driven by the input, while the ring gear is connected to the output. The planet gears, mounted on a carrier, mesh with both the sun and ring gears. This arrangement allows for torque transmission and speed reduction or increase, depending on the configuration.

  • Components and Terminology

    To accurately calculate the gear ratio, it is essential to understand the components and terminology of a planetary gear system. These include the number of teeth on each gear, the pitch diameter, gear module, and the concept of the gear train.


Calculating the Gear Ratio of a Planetary Gearbox

First, it is necessary to determine the gear configuration of the planetary gearbox, which can be mainly divided into the following categories:

  • Simple Planetary: The sun gear is the input, the ring gear is the output, and the planet gears are stationary.
  • Compound Planetary: The planet gears are the input, the sun gear is the output, and the ring gear is stationary.
  • Complex Planetary: Both the sun gear and planet gears can act as inputs or outputs, while the ring gear remains stationary.

Next you need to calculate the number of teeth on the sun, planet and ring gears. These values are usually given in the gearbox specifications or can be physically calculated if necessary.

To calculate the gear ratio, use the following formula:

Gear ratio = (number of ring gear teeth + number of sun gear teeth) / number of sun gear teeth

Example Calculation

Suppose there is a simple planetary gear with the following specifications:

Number of sun gear teeth: 20

Number of teeth on each planetary gear: 30

Number of teeth of ring gear: 60

After using the gear ratio formula, the following results are obtained:

Gear ratio = (60 + 20) / 20 = 4

The gear ratio of this planetary gearbox is 4:1, meaning that for every revolution of the sun gear, the ring gear completes four revolutions.


Calculating the gear ratio of a planetary gearbox is essential for understanding the speed relationship between the input and output. By following a systematic approach and considering the gear configuration and number of teeth on each gear, you can accurately determine the gear ratio. This knowledge enables informed decision-making in various industries, including automotive, robotics, and industrial equipment.

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