Flywheel Calculator

Calculate flywheel energy storage capacity, moment of inertia, coefficient of fluctuation, and rim stress for speed regulation in rotating machinery. Design flywheels for punch presses, engines, generators, and industrial equipment.

How It Works - Flywheel Theory ▼

Kinetic Energy Storage

A flywheel stores kinetic energy in its rotating mass. The fundamental equation is:

E = (1/2) * I * omega^2

E: Kinetic energy stored (Joules)
I: Moment of inertia (kg*m^2)
omega: Angular velocity (rad/s) = RPM * pi / 30

Energy storage increases with the square of speed, making higher RPM flywheels more efficient energy stores per unit mass.

Moment of Inertia for Different Shapes

Solid Disk: I = (1/2) * m * R^2 - Simplest form, uniform mass distribution
Ring (Hollow Cylinder): I = (1/2) * m * (R_o^2 + R_i^2) - Mass concentrated at larger radius, more efficient
Spoked Flywheel: I = m * R_m^2 - Treats mass as concentrated at mean radius (R_m = (R_o + R_i)/2)

Ring and spoked designs are more efficient because placing mass at larger radius increases inertia for the same total mass.

Coefficient of Fluctuation (Cs)

The coefficient of fluctuation defines allowable speed variation:

Cs = (omega_max - omega_min) / omega_avg

This determines how much the flywheel speed can vary during energy absorption/release cycles. Lower Cs means tighter speed control but requires larger flywheel.

Precision machines: Cs = 0.002 (very tight control)
Generators/looms: Cs = 0.01
General machinery: Cs = 0.02
Punch presses: Cs = 0.05
Crushers: Cs = 0.2

Speed Regulation and Energy Fluctuation

Energy fluctuation during a cycle is related to the coefficient of fluctuation:

Delta_E = I * omega_avg^2 * Cs

This represents the energy the flywheel absorbs or releases to maintain speed within the specified limits.

To find required inertia for a given energy fluctuation:

I = Delta_E / (Cs * omega_avg^2)

Rim Stress Considerations

The rim of a spinning flywheel experiences tensile stress due to centrifugal force:

sigma = rho * v^2 = rho * (omega * R)^2

sigma: Hoop stress (Pa)
rho: Material density (kg/m^3)
v: Rim velocity (m/s)

Maximum rim velocity is typically limited to 100-150 m/s for steel, lower for cast iron. Exceeding material limits causes catastrophic failure.

Flywheel Cross-Section & Energy Storage Concept

Flywheel Calculator

Quick-Select Presets

Required Energy Fluctuation

Energy Fluctuation

Unit

Operating Speed

Average Speed

Unit

Coefficient of Fluctuation (Cs)

Flywheel Shape

Solid Disk

I = mR^2/2

Ring

I = m(Ro^2+Ri^2)/2

Spoked

I = m*Rm^2

Dimensions

Outer Diameter

Unit

Inner Diameter

Same unit as OD

Thickness / Width

Same unit as OD

Material

Material Selection

Operating Speed

Unit

Known Flywheel Properties

Moment of Inertia

Unit

Operating Speed

Unit

Speed Variation (+/-)

Unit

For Stress Check

Outer Radius

Unit

Material Density (kg/m^3)

-- kg*m^2

Moment of Inertia

Energy Storage Level --

0 100 kJ

Kinetic Energy

Energy Fluctuation

Coefficient (Cs)

Speed Range

Flywheel Mass

Angular Velocity

Rim Stress Analysis

Rim Velocity

Rim Stress

SAFE

Coefficient of Fluctuation Guidelines

Application	Cs Value	Notes
Precision machine tools	0.002	Very tight control
Generators, spinning machines	0.01	Electrical stability
Paper machines, textile looms	0.015	Product quality
General machinery	0.02	Standard industrial
Compressors, pumps	0.03	Moderate variation OK
Punch/shearing machines	0.05	Impact loads
Crushing machinery	0.2	Large variation OK

Material Properties

Material	Density	Max Rim Velocity	Yield Strength
Carbon Steel	7850 kg/m^3	150 m/s	250-400 MPa
Cast Iron	7200 kg/m^3	80 m/s	150-250 MPa
Aluminum	2700 kg/m^3	200 m/s	200-300 MPa
Titanium	4500 kg/m^3	300 m/s	800-1000 MPa
Carbon Composite	1800 kg/m^3	500+ m/s	500-1500 MPa

Key Formulas

Kinetic Energy:

E = (1/2) * I * omega^2

Energy Fluctuation:

Delta_E = I * omega_avg^2 * Cs

Required Inertia:

I = Delta_E / (Cs * omega_avg^2)

Rim Stress:

sigma = rho * (omega * R)^2