KEVOS® 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. |
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.
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