BIZOMAT 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). |
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.
Rotating parts
What this means: Disc 1 mass
- What it is
- The mass of the main rotating disc, impeller or flywheel driven by the motor.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 1000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Disc 1 diameter
- What it is
- The outside diameter of disc 1, which the tool treats as a solid disc of even thickness.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Its inertia rises with the square of the diameter.
What this means: Disc 2 (hub) mass
- What it is
- The mass of a second disc or hub on the same shaft; zero if there is none.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 1000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Disc 2 diameter
- What it is
- The outside diameter of disc 2, which is also treated as a solid disc.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Ring mass
- What it is
- The mass of a ring or rim, such as a flywheel rim or pulley rim; zero leaves it out.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 1000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Ring outside diameter
- What it is
- The outside diameter of the ring or rim, measured across its outer edge.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Ring inside diameter
- What it is
- The inside diameter of the ring or rim; it must be smaller than the outside diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Motor rotor inertia
- What it is
- The mass moment of inertia of the motor’s own rotor, from the motor data sheet.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0 kg·m² to 10000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.05 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Inertia J, not GD² or WK²; GD² is four times J.
Drive
What this means: Final speed
- What it is
- The shaft speed the rotor must reach at the end of the run-up.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1480 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Run-up time rises in proportion to speed, and stored energy with its square.
What this means: Average motor torque during run-up
- What it is
- The average torque the motor produces from standstill to final speed, read from its speed–torque curve.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 10000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Run-up time is inertia × speed ÷ (motor torque − load torque), so more surplus torque shortens it.
What this means: Average load torque during run-up
- What it is
- The average torque the driven machine needs over the same speed range as the motor torque.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 10000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Must be less than the motor torque, or the rotor will not reach speed.
What this means: Allowed start time for the motor
- What it is
- The longest run-up time the motor can tolerate without overheating, from the motor maker.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 600 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Starts per hour
- What it is
- The number of starts per hour the duty requires, used to total the rotor heat per hour.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rotor energy per hour rises in direct proportion.
What this means: Allowed rotor energy per hour
- What it is
- The rotor heat energy per hour the motor can dissipate, from the motor maker.
- Units and format
- Enter a number in kJ: kilojoules. The form accepts 0.000001 kJ to 10000000 kJ. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 kJ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
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.
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
Starting a heavy rotor
In Inertia and Flywheels by the Numbers
What it covers: How long a motor takes to bring a heavy rotor to speed, how much energy it dissipates in its own rotor while doing so, and how start time and starts per hour are checked against the motor's limits.
Method explained here · BIZOMAT original book
Starting, stopping and braking
In Variable-Speed Drives by the Numbers
What it covers: How a drive starts a high-inertia fan compared with a direct-on-line start, where its energy goes when slowed, why short stop ramps trip drives on overvoltage, and how to size braking.
Method explained here · BIZOMAT original book
Starting, stopping and torsion
In Whirling Shafts by the Numbers
What it covers: Getting a heavy rotor up to speed: inertia, run-up time and the energy a direct-on-line start puts into a motor, resonances passed through on the way, and torsional checks of the drive.
BIZOMAT 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