KEVOS® MAKEOS · Power Transmission
Rotor Run-Up Time (Inertia, Acceleration Time, Start Energy)
How long will this motor take to bring the rotor up to speed, how much heat goes into the motor rotor during the start, and is that within the motor’s limits?
Start-up check of a rotor driven by a motor: inertia of up to two discs and a ring on the shaft (as the mass moment of inertia tool) plus the motor rotor, run-up time from the average accelerating torque against the average load torque (as the angular acceleration torque tool), revolutions to speed, kinetic energy stored, the energy dissipated in an induction motor rotor during a direct-on-line start, and checks against the motor’s allowed start time and starts per hour.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Rotating parts | ||
| Disc 1 mass | kg | Mass of the main disc, impeller or flywheel. |
| Disc 1 diameter | mm | Outside diameter of disc 1 (treated as a solid disc). |
| Disc 2 (hub) mass | kg | Mass of a second disc or hub. |
| Disc 2 diameter | mm | Diameter of disc 2. |
| Ring mass | kg | Mass of a ring or rim (0 if none). |
| Ring outside diameter | mm | Outside diameter of the ring. |
| Ring inside diameter | mm | Inside diameter of the ring. |
| Motor rotor inertia | kg·m² | Inertia of the motor rotor (from the motor data sheet). |
| Drive | ||
| Final speed | rpm | Speed to reach. |
| Average motor torque during run-up | N·m | Average motor torque between standstill and full speed (from the speed–torque curve). |
| Average load torque during run-up | N·m | Average load torque over the same range (fans: about a third of full-load torque). |
| Allowed start time for the motor | s | Longest start time the motor can tolerate hot (from the maker; close to the locked-rotor time). |
| Starts per hour | Starts required per hour. | |
| Allowed rotor energy per hour | kJ | Rotor heat per hour the motor can dissipate (from the maker; your value). |
Method and formulas
- Solid disc J = m D² ÷ 8; ring J = m (D_o² + D_i²) ÷ 8 (as the mass moment of inertia tool).
- Run-up time t = J ω ÷ (T_m − T_L); revolutions = ω t ÷ 4π (as the angular acceleration torque tool).
- Stored energy = J ω² ÷ 2; induction rotor loss during a start ≈ J ω² ÷ 2 × T_m ÷ (T_m − T_L).
- Example: 2.3281 kg·m² reaches 1480 rpm in 4.0092 s; each start puts 37.282 kJ into the rotor.
Limitations
- Average torques; with a falling torque curve, integrate over speed for accuracy.
- Rotor loss formula assumes an induction motor started direct on line.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a motor can start a fan, centrifuge or flywheel
- Find how many starts per hour a high-inertia drive can take
- Estimate the time to reach speed
Who it is for
- Electrical engineers
- Design engineers
- Maintenance engineers
What you get
- Inertia of each part and in total
- Run-up time, revolutions and stored energy
- Rotor energy per start and per hour with checks
Interpreting the result
- Halving the load torque during the start (for example a closed damper) cuts both the time and the rotor heating.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 228–240, 2569–2580. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Rotor Run-Up Time (Inertia, Acceleration Time, Start Energy) calculator
