BIZOMAT MAKEOS · Mechanics
Torque to Accelerate a Rotating Load
How much torque does it take to bring this rotating load up to speed in the time allowed?
Angular acceleration, accelerating torque, total torque with friction, revolutions turned during the run-up, kinetic energy stored and the peak power at the end of acceleration for a load of known moment of inertia.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Moment of inertia of the load | kg·m² | Moment of inertia about the axis of rotation (from a mass-inertia tool or the supplier), referred to the shaft being driven. |
| Starting speed | rpm | Speed at the start. |
| Final speed | rpm | Speed at the end. |
| Acceleration time | s | Time allowed for the speed change. |
| Friction and load torque | N·m | Steady torque from friction and the load during acceleration. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Moment of inertia of the load
- What it is
- The rotating load’s resistance to a change in speed about its axis, including couplings, pulleys and anything else turning with it, referred to the shaft whose torque you want.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0.000001 kg·m² to 10000000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Accelerating torque and the energy stored rise in direct proportion.
- Get it right
- Inertia behind a gearbox appears at the input shaft divided by the ratio squared; refer every part to the same shaft before adding.
What this means: Starting speed
- What it is
- The rotational speed at the start of the speed change; zero for a start from standstill.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If this is higher than the final speed, the change is a slow-down and the torque shown is a braking torque.
What this means: Final speed
- What it is
- The rotational speed the load must reach at the end of the acceleration time. Peak power is taken at the higher of the starting and final speeds.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Accelerating torque rises in proportion to the speed change; stored energy rises with the square of speed.
What this means: Acceleration time
- What it is
- The time allowed to go from the starting speed to the final speed, with the angular acceleration taken as constant throughout.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 100000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Halving the time doubles the accelerating torque; the friction torque is unaffected.
What this means: Friction and load torque
- What it is
- The steady resisting torque present during the run-up whatever the acceleration: bearing and seal friction plus any process or gravity load on the shaft. It is added to the accelerating torque.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 100000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Refer it to the same shaft as the inertia; a torque measured after a gearbox must be divided by the ratio and the gearbox efficiency.
Method and formulas
- α = (ω₁ − ω₀) ÷ t, with ω = 2π n ÷ 60.
- Accelerating torque = J α; total torque = J α + friction torque.
- Revolutions = (n₀ + n₁) ÷ 2 × t ÷ 60; energy change = ½ J (ω₁² − ω₀²); peak power = total torque × ω₁.
- Example: 0.5 kg·m² to 1500 rpm in 2 s needs 41.27 N·m.
Limitations
- Constant acceleration; a motor’s torque varies with speed.
- Inertia must be referred to the same shaft (multiply by the speed ratio squared through gearing).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check that a motor can start a heavy rotating load
- Set an acceleration ramp on a drive
- Estimate the energy to bring a spindle or drum to speed
Who it is for
- Machine designers
- Maintenance engineers
- Automation engineers
What you get
- Angular acceleration
- Accelerating and total torque
- Revolutions and energy during run-up
Interpreting the result
- Compare the total torque with the motor’s accelerating torque across the speed range, not just its rated torque.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 176–181. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Loads on a winch drive
In Clutches and Brakes by the Numbers
What it covers: How to turn a winch's duty into the forces, torques, speeds, inertias and energies that its clutch and brakes must handle, on the shaft where each one sits.
Method explained here · BIZOMAT original book
Torque to speed up and slow down
In Inertia and Flywheels by the Numbers
What it covers: How much torque it takes to bring a rotor to speed or stop it in a given time, how many turns and how much energy that involves, and how a motor's rating compares with the torque the change needs.
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