Question 1

What is the coefficient of fluctuation in flywheel design?

Accepted Answer

The coefficient of fluctuation C_s = ΔN/N defines how tightly the speed is regulated relative to the mean speed N. For precision machinery C_s = 0.002–0.005; for general purposes 0.01–0.02; for punch presses 0.1–0.2. A smaller C_s requires a larger moment of inertia.

Question 2

How do you calculate the required moment of inertia for a flywheel?

Accepted Answer

Required I = ΔE / (C_s × ω²), where ΔE is the energy fluctuation per cycle derived from the torque curve, C_s is the coefficient of fluctuation, and ω is mean angular velocity. For a ring flywheel I = ½m(R²+r²); for a solid disk I = ½mR².

Question 3

How is the flywheel burst speed estimated?

Accepted Answer

Rim hoop stress σ = ρω²R² (simplified uniform thickness disk approximation). Comparing with the yield strength gives burst safety factor n = σ_y / (ρω²R²). Design typically requires n ≥ 2–3. Both outer radius R and density ρ (steel: 7850 kg/m³) are dominant parameters.

Question 4

What is the design tradeoff in flywheel sizing?

Accepted Answer

Increasing outer radius R improves moment of inertia (I ∝ R²) for a given mass, but also increases centrifugal rim stress (σ ∝ R²ω²). Increasing mass helps both I and reduces stress but adds weight and bearing loads. Typical design approach: choose R first based on envelope constraints, then determine required mass from the I requirement.

Flywheel Energy Storage & Coefficient of Fluctuation

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