A Comprehensive Analysis of Torque Terminology: Definition and Interrelation of Nominal Torque, Output Torque, and Working Torque

Torque is a fundamental concept in mechanical and power transmission systems. Motor output, gearbox specifications, and machine loads are all expressed in terms of torque, but rated torque, output torque, and operating torque do not represent exactly the same thing.

Failing to distinguish between these terms may result in an undersized gearbox, insufficient motor output, or operating conditions that exceed the allowable torque during frequent starts and stops.

This article explains the basic definition of torque, the differences between rated torque, output torque, and operating torque, and the torque conditions that should be considered when selecting a planetary gearbox.

What Is Torque?

Torque is the rotational effect of a force acting around an axis. It is usually represented by T and commonly expressed in newton-metres (Nm).

When the applied force is perpendicular to the lever arm, torque can be calculated as follows:

• T: Torque, in Nm
• F: Applied force, in N
• r: Perpendicular distance from the force to the axis of rotation, in m

For example, if a perpendicular force of 20 N is applied at a distance of 0.5 m from the axis:

Therefore, for the same applied force, a longer lever arm produces more torque. Everyday examples include pushing a door handle, tightening a bolt with a wrench, or turning a control knob.

In machinery, torque directly affects whether a motor can move the load and whether a gearbox can operate reliably over time.

What Is Rated Torque?

Rated torque is the amount of torque that a motor or gearbox can transmit continuously, or under the operating conditions specified by its manufacturer.

For a planetary gearbox, rated output torque generally depends on:

• Gearbox size and gear ratio
• Gear and bearing design
• Input and output speeds
• Lubrication and operating temperature
• Duty cycle and service-life conditions

Planetary gearboxes of different sizes and ratios may have different rated output torque values. These values are normally listed in the performance tables of the manufacturer's catalog.

Rated torque should not be interpreted as a fixed limit that applies under every operating condition. It is a specification established under defined test and operating conditions.

In addition to rated torque, gearbox selection should consider permissible peak torque, emergency-stop torque, input speed, and duty cycle.

What Is Output Torque?

Output torque is the torque transmitted at the output side of a gearbox.

A gearbox reduces output speed and increases the torque supplied by the motor according to its gear ratio. However, gears, bearings, and seals generate mechanical losses, so transmission efficiency must be included when estimating the available output torque.

If the motor torque is known, the theoretical gearbox output torque can be estimated using:

• T₂: Theoretical gearbox output torque, in Nm
• T₁: Motor output torque, in Nm
• i: Gear ratio
• η: Gearbox transmission efficiency, expressed as a decimal

For example, consider a motor with a rated torque of 1.3 Nm, a gearbox ratio of 5, and an assumed transmission efficiency of 97%:

Under these conditions, the estimated rated output torque available from the gearbox is approximately 6.3 Nm.

Transmission efficiency varies with gearbox design, number of stages, lubrication, load, and operating conditions. The efficiency specified for the actual gearbox model should be used for formal calculations.

This formula estimates the output capability available from the motor and gearbox combination. The torque actually transmitted during operation still depends on the load and the motor control conditions.

How Do You Calculate Motor Torque from Power?

If motor power and speed are known, motor torque can be estimated first. When power is expressed in kW and speed in rpm, use:

• T₁: Motor torque, in Nm
• P: Mechanical motor output power, in kW
• n: Motor speed, in rpm
• 9550: Conversion factor used with kW, rpm, and Nm

For a motor rated at 0.4 kW and 3,000 rpm:

If the motor is connected to a 5:1 planetary gearbox with 97% efficiency:

This result may differ slightly from the rated torque shown in the motor catalog because power and speed values may be rounded and actual motor characteristics can vary.

If the motor catalog provides a rated torque value directly, that value should be used in preference to a calculated estimate.

What Is Operating Torque?

In this article, operating torque refers to the torque required by the load while the machine is operating. It may also be described as load torque or application torque, depending on the manufacturer and engineering context.

The required torque varies with the machine structure and operating condition. Conveyors, lifting systems, rotary tables, and robotic arms therefore require different load calculations.

Operating torque may include:

• Torque required to overcome friction
• Torque required to overcome gravity
• Acceleration and deceleration torque
• External machining or pressing forces
• Impact or shock loads

At constant speed, the drive primarily needs to overcome friction, gravity, and external loads. During acceleration or deceleration, the torque required to accelerate the inertia must also be considered.

The basic relationship for acceleration torque is:

• Tₐ: Acceleration torque, in Nm
• J: Total rotational inertia referred to the calculation shaft, in kg·m²
• α: Angular acceleration, in rad/s²

This explains why reducing the acceleration time can significantly increase peak torque, even when the machine carries the same load.

Planetary Gearbox Output Torque Example

Assume the following conditions:

• Motor power: 400 W
• Rated motor speed: 3,000 rpm
• Rated motor torque from the catalog: 1.3 Nm
• Planetary gearbox ratio: 5
• Transmission efficiency: 97%

Using the motor's catalog-rated torque:

Based on the rated motor torque, the gearbox output can provide an estimated rated output capability of approximately 6.3 Nm.

If the selected planetary gearbox has a rated output torque of 55 Nm at this ratio, the theoretical torque applied by the motor does not exceed the gearbox's rated capacity:

However, this comparison only confirms that the motor is not expected to apply more than the gearbox's rated output capacity during rated operation.

To determine whether the machine can operate correctly, the following must also be known:

• Actual operating or load torque
• Acceleration and deceleration torque
• Load inertia
• Start-stop frequency
• Duty cycle
• Impact or shock loads

A complete selection requires sufficient motor output and confirmation that both continuous and peak application requirements remain within the corresponding gearbox limits.

Relationship Between Rated, Output, and Operating Torque

These torque values should not be reduced to one general inequality. Each operating condition must be evaluated separately.

Emergency-stop torque is normally permitted only under the frequency and conditions specified by the manufacturer. It must not be treated as a continuous rated torque.

Manufacturers may use different terms and conditions for rated torque, cyclic torque, acceleration torque, maximum torque, and emergency-stop torque. Always refer to the specifications of the actual gearbox series.

How Should a Service Factor Be Used?

Start-stop frequency, daily operating time, load variation, and shock severity can all affect gearbox selection.

Some gearbox manufacturers provide a service factor for preliminary selection. The general concept is:

• Tselection: Calculated torque used for preliminary selection
• Trequired: Torque required by the application
• fs: Service factor

A higher service factor represents more demanding operating conditions and requires a gearbox with greater capacity.

Service-factor definitions and calculation methods vary between manufacturers. Start-stop frequency must not be treated as transmission efficiency, and a service factor greater than 1 must not be inserted into the output torque formula to increase the available gearbox torque.

Final selection should follow the specifications of the actual gearbox or be confirmed by the manufacturer.

Gearbox Torque Selection Checklist

1. Check the motor's rated torque, maximum torque, and rated speed.
2. Calculate the load torque required during constant-speed operation.
3. Calculate the acceleration and deceleration torque.
4. Confirm the gear ratio and transmission efficiency.
5. Calculate the torque available at the gearbox output.
6. Compare the continuous application requirement with the rated gearbox output torque.
7. Compare the acceleration requirement with the permissible gearbox peak torque.
8. Check input speed, duty cycle, load inertia, radial load, and axial load.
9. Apply the appropriate service factor according to the product specifications.
10. Confirm that emergency-stop conditions remain within the gearbox limits.

Conclusion

Rated torque, output torque, and operating torque describe the permissible capacity of the gearbox, the output capability available from the motor and gearbox combination, and the torque required by the application.

Gearbox selection cannot be based on a single torque value. Normal operating torque, acceleration torque, peak torque, duty cycle, transmission efficiency, and load inertia must all be considered.

Understanding these torque definitions helps prevent undersized gearboxes, insufficient motor output, and operating conditions that exceed permissible limits during frequent starts and stops.