Flywheel & Inertia — validation & limitations

What it calculates

• Flywheel sizing: required inertia, disc mass and rim/disc geometry from energy fluctuation, Cs and speed
• Limit-speed analysis on a conservative peak-stress envelope, with the governing speed margin and the total margin on yield
• Moment of inertia for 7 standard shapes with the parallel-axis theorem
• Multi-body rotational system dynamics: total reflected inertia, net torque and angular acceleration
• Motor run-up time with 50 %/90 %/100 % speed milestones and a speed–time chart
• Energy storage analysis with cross-material specific-energy comparison chart
• Rotating disc stress explorer: the exact radial, hoop and von Mises field across the radius for a bore you declare

Validation evidence — independent reference cases (2)

Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.

• Rotating bored disc stresses and limit speed

  Agrees

  Source: Timoshenko & Goodier, Theory of Elasticity, §32 (rotating uniform disc, plane stress); Shigley's Mechanical Engineering Design §3-15, Eq. 3-55

  Inputs: steel ρ 7850 kg/m³, ν 0.3, outer radius 0.4 m, bore fraction 0.25 (a 0.1 m), 3000 rpm, allowable 100 MPa

  Quantity	Reference value	Tolerance
  Bore hoop stress (= von Mises peak)	103.6247 MPa	6e-4 MPa absolute
  Max radial stress at r = √(ab) = 200 mm	28.7631 MPa	6e-4 MPa absolute
  Rim hoop stress	28.0852 MPa	6e-4 MPa absolute
  Limit speed at 100 MPa (SF)	2947.0646 rpm (0.982355)	1e-6 relative (1e-5 on SF)

  tests/golden/REF-flywheel-bored-disc.golden.test.ts

• Flywheel inertia sizing, rim hoop and arm bending, speed margin

  Agrees

  Source: Shigley's Mechanical Engineering Design 9th/10th ed. §16-12 (Eq. 16-61, 16-62) and §3-15; Timoshenko, Strength of Materials Part II (rotating ring); Timoshenko Part I / Roark & Young Table 9.2 (ring on n equal radial loads, M = (W·R/2)(1/α − cot α))

  Inputs: cast-iron rim on 8 arms (ρ 7200, σ_allow 30 MPa), 300 rpm, Cs 0.05, ΔE 5000 J, R 0.5 m, width 0.1 m

  Quantity	Reference value	Tolerance
  Required inertia I	101.321184 kg·m²	1e-6 relative
  Rim hoop stress (outer fibre)	2.595235 MPa	1e-6 relative
  Rim bending stress between arms	1.623192 MPa	1e-6 relative
  Speed margin (verdict CHECK)	2.666769	1e-6 relative

  tests/golden/REF-flywheel-sizing-rim-margin.golden.test.ts

Limitations

Not checked by this tool

• Hub interference-fit pressure, keyseats and bolt holes at the bore — The stress covers rotation only; a shrink fit is typically 2-4x the rotational value — check with /pressfit and /keys
• Burst speed (plastic collapse on ultimate strength) — The limit speed is to the allowable stress, not burst; compute burst for containment design
• Fatigue from start-stop and speed-fluctuation cycles — Not assessed; check the bore stress range with /fatigue
• Containment / guarding against fragment release — Not assessed; design the guard for the stored energy
• Balance quality and shaft critical speed — Check the balance grade with /dynamics and the shaft in /shaft
• Thermal gradients and residual (casting) stress — Not included; relevant for cast wheels and brake-type duty