Flywheel Design

Flywheel Design (flywheels)

Purpose

Size flywheels for energy storage and speed regulation by computing required moment of inertia, rim stress, and energy capacity for a specified speed fluctuation or power pulse. Used in presses, engines, and cyclic machinery.

Physics & theory

A flywheel stores kinetic energy $E=\frac{1}{2}I{\omega }^2$. For a rim-dominated disk, $I\approx m{r}^2$ where $m$ is rim mass and $r$ is mean radius. Energy change between max and min speed during a cycle is $\Delta E=\frac{1}{2}I({\omega }_{\max }^2-{\omega }_{\min }^2)$.

Coefficient of speed fluctuation $C_s=({\omega }_{\max }-{\omega }_{\min })/\omega$ links inertia to cyclic energy input/output. Rim stress from centrifugal loading approximates hoop tension $\sigma =\rho r^2{\omega }^2$ for thin rings; solid disk models use radial and tangential stress distributions.

Governing equations

Numerical method

Closed-form energy–inertia relations. Required $I$ computed from specified $\Delta E$ and speed limits. Geometry (rim thickness, width, hub bore) iterated to achieve target inertia while checking rim stress utilization against material allowable.

Inputs

Outputs

• Required moment of inertia, rim mass, stored energy, rim stress, speed fluctuation coefficient, stress utilization.

Design codes & checks

• Indicative: Rim stress utilization, energy storage capacity

Assumptions & limitations

• Axisymmetric rotation; no blade or spoke dynamic stress analysis.
• Thin-rim approximation for hoop stress; hub and spoke contributions simplified.
• No burst containment or safety guard requirements.
• Constant angular deceleration during energy release not enforced.

References

1. Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 15.
2. Spotts, M. F., & Shoup, T. E. Design of Machine Elements, 8th ed.
3. Marks' Standard Handbook for Mechanical Engineers, 12th ed.
4. Peterson, R. E. Stress Concentration Factors (rotor burst context).
5. PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
6. Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.