2023.06.30

How to Calculate the Suitable Gear Ratio for Planetary Gearboxes?

The gear ratio of a planetary gearbox directly affects its output speed and output torque. Selecting a suitable ratio involves more than dividing the motor speed by the required output speed. The motor's rated speed, allowable maximum speed, required output torque, gearbox capacity, and operating conditions must also be considered.

This guide explains how to calculate the required planetary gearbox ratio and how to compare standard ratios using practical examples.

What Is a Planetary Gearbox Ratio?

A planetary gearbox ratio, also called a reduction ratio, represents the relationship between the gearbox input speed and output speed. It is normally expressed as i.

A higher reduction ratio produces a lower output speed at the same motor speed. After transmission efficiency is considered, it also generally provides greater torque multiplication.

Basic gear ratio formula:

Gear Ratio i = Input Speed ÷ Output Speed

i = n_in ÷ n_out

i: Gear ratio or reduction ratio
n_in: Motor or gearbox input speed
n_out: Required gearbox output speed

Planetary Gearbox Ratio Calculation Examples

Example 1: The Calculated Ratio Matches a Standard Ratio

Assume that:

Motor speed: 2,000 rpm
Required output speed: 100 rpm

The required gear ratio is:

Gear Ratio = 2,000 ÷ 100 = 20

A planetary gearbox with a 20:1 reduction ratio can therefore be considered for further evaluation.

Example 2: The Calculated Ratio Does Not Match a Standard Ratio

Assume that:

Motor rated speed: 2,000 rpm
Required output speed: 120 rpm

The calculated ratio is:

Gear Ratio = 2,000 ÷ 120 = 16.67

If the available standard ratios are 15:1 and 20:1, both options should be evaluated by comparing their output speeds, required motor speeds, and available output torque.

Option 1: Selecting a 15:1 Ratio

When the motor operates at 2,000 rpm:

Output Speed = 2,000 ÷ 15 = 133.3 rpm

To obtain the required output speed of 120 rpm, the motor speed must be adjusted to:

Required Motor Speed = 120 × 15 = 1,800 rpm

In this case, the motor does not need to exceed its rated speed of 2,000 rpm. However, it is still necessary to confirm that the 15:1 ratio can provide sufficient output torque for the application.

Option 2: Selecting a 20:1 Ratio

When the motor operates at 2,000 rpm:

Output Speed = 2,000 ÷ 20 = 100 rpm

To obtain the required output speed of 120 rpm, the motor speed must be increased to:

Required Motor Speed = 120 × 20 = 2,400 rpm

The motor must therefore be capable of operating at 2,400 rpm. The allowable input speed of the planetary gearbox must also be checked.

Should You Select a Higher or Lower Standard Ratio?

When the calculated ratio falls between two standard gearbox ratios, neither the higher nor the lower ratio is automatically the correct choice.

Comparison	Lower Reduction Ratio	Higher Reduction Ratio
Output speed	Relatively higher	Relatively lower
Torque multiplication	Relatively lower	Relatively higher
Motor speed required for the same target output speed	Lower	Higher
Main selection consideration	Confirm that the output torque is sufficient	Confirm the allowable motor and gearbox input speeds

The final decision should be based on output speed, required motor speed, output torque, and the operating limits of both the motor and gearbox.

How Does the Gear Ratio Affect Output Torque?

In addition to reducing speed, a planetary gearbox increases output torque. The theoretical output torque can be estimated with the following formula:

Output Torque = Motor Torque × Gear Ratio × Transmission Efficiency

T_out = T_in × i × η

Where:

T_out: Estimated gearbox output torque
T_in: Motor output torque
i: Gear ratio
η: Gearbox transmission efficiency

For example, assume that:

Motor output torque: 5 Nm
Gear ratio: 20:1
Estimated transmission efficiency: 95%

Output Torque = 5 × 20 × 0.95 = 95 Nm

This formula provides only an initial estimate. A complete gearbox selection must also account for load type, acceleration and deceleration, starting and stopping frequency, shock loads, load inertia, duty cycle, and the gearbox's rated and permissible peak torque.

Planetary Gearbox Ratio Selection Process

Confirm the motor's rated speed and allowable maximum speed.
Determine the application's maximum and normal operating output speeds.
Divide the motor speed by the required output speed to calculate the theoretical ratio.
Identify the closest available standard gearbox ratios.
Calculate the actual output speed for each available ratio.
Calculate the motor speed required to reach the target output speed.
Determine the required output torque and apply an appropriate safety factor.
Confirm the gearbox's rated torque, permissible peak torque, allowable input speed, and operating conditions.

Planetary Gearbox Ratio Calculator

Enter the motor rated speed and required output speed to calculate the theoretical reduction ratio and compare the adjacent standard ratios. Available ratios vary by gearbox model and series.

Planetary Gearbox Ratio Calculator

Calculate and compare adjacent standard reduction ratios

Motor Rated Speed (rpm)

Required Output Speed (rpm)

Theoretical Ratio

Adjacent Lower Ratio

Adjacent Higher Ratio

Common standard ratios for reference. Actual availability varies by model.

The calculated result provides an initial comparison based only on input and output speeds. It does not replace a complete gearbox selection. Output torque, motor speed limits, gearbox rated torque, load inertia, duty cycle, and other application conditions must still be verified.

Frequently Asked Questions

What is the formula for calculating a planetary gearbox ratio?

Divide the motor or gearbox input speed by the required output speed:

Gear Ratio = Input Speed ÷ Output Speed

What is the difference between gear ratio and reduction ratio?

In gearbox selection, the terms are often used interchangeably. A reduction ratio specifically indicates how much the gearbox reduces the input speed. For example, a 20:1 reduction ratio reduces an input speed of 2,000 rpm to a theoretical output speed of 100 rpm.

Does a higher gear ratio always provide better performance?

No. A higher ratio generally provides more torque multiplication but lowers the output speed. Reaching a specific output speed may also require the motor to operate at a higher speed. The correct ratio depends on the speed, torque, duty cycle, and operating limits of the application.

Can the closest standard ratio always be selected?

Not necessarily. When the exact calculated ratio is unavailable, the adjacent higher and lower ratios should both be evaluated. The final choice must satisfy the required output speed and torque without exceeding the motor or gearbox operating limits.

Conclusion

The theoretical ratio of a planetary gearbox can be calculated by dividing the motor speed by the required output speed. However, this calculation is only the first step in gearbox selection.

When the calculated value does not match an available standard ratio, compare the motor speed, actual output speed, and available output torque for the adjacent ratios. A suitable gearbox must achieve the required motion while keeping both the motor and gearbox within their allowable operating conditions.

Need Help Selecting a Planetary Gearbox?

Provide the motor model, required output speed, load torque, duty cycle, and mounting arrangement. GearKo can help evaluate the suitable gear ratio and planetary gearbox specifications for your application.

Contact GearKo Taiwan

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