Shaft Analysis — validation & limitations

What it calculates

• Static von Mises yield safety factor at the most-stressed section
• Modified-Goodman fatigue safety factor with a Marin-corrected endurance limit
• Stress-concentration factors (Kt, Kf) for shoulder fillets from the Peterson/Pilkey Chart 3.11 curves, and first-iteration estimates for keyways, grooves and threads
• Timoshenko beam-FEM bending deflection of multi-segment stepped shafts, including overhangs
• Torsional shear stress and angle of twist
• First and second critical (whirling) speeds from a beam-FEM modal solve
• Palmgren–Miner cumulative damage over a user-defined load spectrum
• DIN 743:2012 proof — fatigue safety S_D and static safety S_F at every shoulder, keyway and retaining-ring groove, with K1, K2, K_F, α, n, β, ψ and the permissible amplitude shown per section
• Ten shaft materials — the steels, stainless, aluminium and titanium at their delivery standard's guaranteed minimum for the heat-treated size, the case-hardening steels at DIN 743-3's size-scaled core strength, grey cast iron at a typical value — or, beyond the standard's size table, a certified strength you enter; with Marin surface, size and reliability factors

Standards this tool applies

• DIN 6885 — Shaft fatigue check with the Kf stress-concentration factor at the keyway notch — the complementary check alongside the key strength. It does not size or check the key to DIN 6885 — that is the Shaft Keys tool. Its headline fatigue factor uses the modified-Goodman method; separately, it proves the keyway section to DIN 743 with DIN 743-2's measured keyway notch factor (one keyway per section, at the weakest place along its segment).
• DIN 743 — DIN 743:2012 fatigue and static proof at every shoulder, keyway, retaining-ring groove and plain section, with every factor shown — alongside modified-Goodman fatigue, von Mises static yield, beam-FEM deflection and critical speed. Not checked: press-fit seats, splines, cross holes, rounded grooves, threads, hollow and surface-hardened shafts.

Validation evidence — independent reference cases (1)

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.

• Marin chain with modified Goodman fatigue factor on a plain shaft

  Agrees

  Source: Shigley's Mechanical Engineering Design, 10th ed., Ch. 6-7: Eq. 6-8, 6-18, 6-19/Table 6-2, 6-20, Table 6-5, §7-4, Eq. 6-46, Eq. 5-15

  Inputs: Dia 50 x 1000 mm shaft, radial 10 kN at midspan, torque 500 N·m, 300 rpm, machined, Su 800 / Sy 600 MPa

  Quantity	Reference value	Tolerance
  sigma_a (MPa)	203.7183	1e-4 relative
  S_e (MPa)	203.7858	1e-4 relative
  Goodman n	0.958061	1e-4 relative
  static n_y	2.90203	1e-4 relative

  tests/golden/REF-shaft-goodman-marin.golden.test.ts

Limitations

Not checked by this tool

• Press-fit seats (bearing and hub fits) in the DIN 743 proof — Prove each seat separately with the DIN 743-2 press-fit notch factors; check the fit itself with /pressfit
• Splines, serrations and cross holes in the DIN 743 proof — Use the DIN 743-2 notch factors for these features; check spline flanks with the maker or DIN 5466
• Threads, rounded grooves, undercuts and surface-hardened layers in the DIN 743 proof — Outside the implemented DIN 743 scope; prove them with DIN 743-2 data, FEA or test
• Hollow shafts — Solid sections only; for a bored shaft use the hollow-section properties by hand
• Bearing stiffness in the deflection and critical speed — Supports are near-rigid; real bearing stiffness raises deflection and lowers the critical speed — use the maker's stiffness
• Torsional vibration (torsional critical speeds) — Only bending critical speeds are computed; check torsional modes of the drive train separately
• Temperatures outside -40 to 150 C (strength derating, creep) — There is no temperature input; derate the material for hot service
• Keys, hubs and bearings on the shaft — Check keys with /keys, fits with /pressfit and bearing life with /bearings