BIZOMAT MAKEOS · Mechanics
Flywheel Energy and Speed Fluctuation
How much energy does this flywheel give up between two speeds, and is its rim speed acceptable?
Mass moment of inertia of a disc or ring flywheel, energy released between maximum and minimum speed, coefficient of fluctuation and rim speed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Flywheel mass | kg | Mass of the rotating disc or rim (weigh it or use the CAD mass). |
| Outer diameter | mm | Outside diameter of the flywheel. |
| Inner diameter of rim (0 = solid disc) | mm | Inside diameter of a ring-shaped rim; 0 for a uniform solid disc. |
| Maximum speed | rpm | Speed before the energy is drawn (e.g. before the press stroke). |
| Minimum speed during the cycle | rpm | Lowest speed allowed during the working stroke. |
| Allowed rim speed | m/s | Rim speed limit from the flywheel maker or your design standard for the material and construction. |
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: Flywheel mass
- What it is
- The mass of the rotating disc or rim whose inertia stores the energy, by weighing or from the CAD model.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 1000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The moment of inertia and the energy released rise in proportion to the mass.
- Get it right
- Hub, spokes and shaft are not counted unless their mass is included here, and the tool treats all of it as a uniform disc or ring.
What this means: Outer diameter
- What it is
- The outside diameter of the flywheel, across the rim through the centre. It sets the inertia and the rim speed.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 800 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Inertia rises with the square of the diameter, and rim speed rises in proportion to it.
- Get it right
- Use the diameter, not the radius.
What this means: Inner diameter of rim (0 = solid disc)
- What it is
- The inside diameter of a ring-shaped rim, for a flywheel whose mass sits in a ring. Zero treats it as a uniform solid disc.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 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.
- Get it right
- It must be smaller than the outer diameter.
What this means: Maximum speed
- What it is
- The flywheel speed at the start of the energy draw, for example just before a press stroke or punch begins. The rim speed is checked at this speed.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be higher than the minimum speed.
What this means: Minimum speed during the cycle
- What it is
- The lowest speed the flywheel is allowed to fall to during the working stroke, before the motor brings it back up.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 540 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The energy released depends on the difference of the squared speeds, so a small change in this speed changes the result noticeably.
What this means: Allowed rim speed
- What it is
- The highest rim speed the flywheel is allowed to run at, from the maker or your design standard for its material and construction. The tool compares the calculated rim speed with it.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 1000 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This limit is not calculated by the tool; it must come from the maker or a stress analysis.
Method and formulas
- J = m(R² + r²) ÷ 2 (solid disc when r = 0).
- ΔE = ½J(ω₁² − ω₂²), ω = 2πn ÷ 60.
- Coefficient of fluctuation Cs = (n₁ − n₂) ÷ mean speed; rim speed = π D n₁ ÷ 60 000.
- Example: a 150 kg, 800 mm solid disc slowing from 600 to 540 rpm gives up 4,500.5 J.
Limitations
- Hub, spokes and shaft inertia are not included unless their mass is part of the entered disc.
- Rim stress depends on construction; the speed limit must come from the maker or a stress analysis.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a press or punch flywheel for one stroke
- Estimate energy stored for a cycle
- Compare rim speed with the maker’s limit
Who it is for
- Design engineers
- Maintenance engineers
- Technicians
What you get
- Mass moment of inertia
- Energy released between the two speeds
- Kinetic energy at maximum speed
- Coefficient of speed fluctuation
- Rim speed
Interpreting the result
- If the released energy is less than the work per stroke, increase inertia or allow a larger speed drop.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3000–3010, 179–186. 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
Flywheels and speed fluctuation
In Inertia and Flywheels by the Numbers
What it covers: How a flywheel carries a machine through peak loads by slowing: energy released between two speeds, the coefficient of speed fluctuation, rim speed, and the inertia a duty needs.
Method explained here · BIZOMAT original book
Flywheel energy and slowdown
In Power Presses by the Numbers
What it covers: Energy per stroke for MP-40 and AB-75, the flywheel's stored energy and slowdown, why a variable-speed press has far less energy at low speed, motor power, and a press that stalled on the bottom.
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