KEVOS® MAKEOS · Mechanics
Flywheel Rim Design (Inertia for Speed Fluctuation, Size and Stress)
What inertia does this flywheel need to hold the speed fluctuation within limits, what disc size gives it, and is the rim speed and stress safe?
Design of a flywheel as a plain annular disc: inertia needed for the energy fluctuation at the mean speed and coefficient of speed fluctuation, the inner diameter that gives that inertia at the outer diameter and width chosen, mass, the energy check by the flywheel energy method, the speed range, rim speed at the top speed, and the largest stress of a rotating disc at the top speed (as the rotating disc tool) against your safety factor.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Energy fluctuation per cycle | kJ | Largest difference in kinetic energy over the cycle (from the torque–angle diagram). |
| Mean speed | rpm | Mean running speed. |
| Coefficient of speed fluctuation | Allowed (n_max − n_min) ÷ n_mean (about 0.002 generators, 0.02–0.05 machine tools, 0.1–0.2 punches and crushers). | |
| Outer diameter | mm | Outside diameter of the flywheel. |
| Width (axial) | mm | Width of the disc or rim along the shaft. |
| Density | kg/m³ | Density (about 7200 cast iron, 7850 steel). |
| Poisson’s ratio | Poisson’s ratio. | |
| Strength (yield or tensile for cast iron) | MPa | Strength of the material for the stress check. |
| Safety factor required | Safety factor you require on the rotating stress (higher for cast iron). | |
| Largest rim speed | m/s | Largest rim speed for the material and construction (your value). |
Method and formulas
- Inertia I = ΔE ÷ (ω² C_s), ω the mean angular speed.
- Annular disc I = ρ π b (R_o⁴ − R_i⁴) ÷ 2, so R_i = [R_o⁴ − 2I ÷ (ρ π b)]^¼; mass = ρ π b (R_o² − R_i²).
- Speed range n (1 ± C_s ÷ 2); energy check ΔE = I (ω_max² − ω_min²) ÷ 2 (as the flywheel energy tool).
- Rotating disc stress at the bore at top speed: σ = (3 + ν) ÷ 4 × ρ ω² [R_o² + (1 − ν) ÷ (3 + ν) R_i²] (as the rotating disc tool).
- Example: 5 kJ at 600 rpm needs 25.33 kg·m²: a 800 mm disc 100 mm wide with a 475.8 mm bore, 233.89 kg.
Limitations
- Plain annular disc; spoked and rimmed flywheels have different inertia and stress.
- Hub, keys and bolts need their own checks.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a flywheel for a compressor, press or engine
- Check a flywheel for a higher speed
- Trade diameter against width and mass
Who it is for
- Design engineers
- Mechanical engineers
- Maintenance engineers
What you get
- Inertia needed
- Inner diameter, mass and speed range
- Rim speed, rotating stress and safety factor
Interpreting the result
- Inertia rises with the fourth power of diameter: a slightly larger diameter saves a lot of mass, until rim speed limits it.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3000–3010, 179–190. Topic reference; no source tables or recommended settings are reproduced.
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Open the Flywheel Rim Design (Inertia for Speed Fluctuation, Size and Stress) calculator
