Shaft Design (`shafts`)

Shaft Design

Torsion, bending, fatigue analysis

Standards catalog

Validation: indicative · Method band: fem

Open calculator

Indicative method: Combined stress + Goodman fatigue + critical-speed screening (DIN 743 / AGMA oriented)

Assumptions

Linear elastic material behavior unless noted otherwise.
User is responsible for load combinations and load factors per the selected design code.
Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

DIN 743 / AGMA fatigue factors are partial — notch catalogs and full multi-station worksheets not complete.
Professional screening — verify critical shafts with specialized shaft software before release.

Engineering checks

Check	IND	US	EU	ISO
Combined stress utilization	implemented	—	—	—
Shaft deflection	implemented	—	—	—
Critical speed margin	implemented	—	—	—
Fatigue safety (Goodman)	implemented	—	—	—

Purpose

Analyze rotating shafts under combined bending, torsion, and axial loads using 1D FEA. Supports stepped/hollow geometry, configurable bearing supports, transverse forces, stress concentrations, fatigue screening (Marin + Goodman), FEA critical speed, and bearing reaction handoff.

Physics & theory

Power-transmitting shafts experience bending from belt/gear forces, torsion from transmitted torque, and occasional axial thrust. Stress at any section combines normal and bending stress with torsional shear; von Mises equivalent stress governs static yield checks for ductile materials.

Rotating shafts subject bending to fully reversed fatigue; torsion is typically steady. Critical (whirling) speed is estimated from FEA mass and bending stiffness (first lateral modes).

Governing equations

σ_{vm} = σ^{2} + 3 τ^{2}

S F_{static} = \frac{σ _{y}}{σ _{vm, max}}, S F_{cr} = \frac{ω _{cr}}{ω _{operating}}

Fatigue (Indicative/US):

m o d i f i e d G oo d man o n v o n M i ses a l t er na t in g / m e an co m p o n e n t s w i t h M a r in f a c t or s (S hi g l ey)

Numerical method

1D shaft FEM: Hermite beam elements (12 DOF) with axial, torsion, and biaxial bending. Stepped diameter and hollow sections via segment mesh. Pin or fixed supports at user-defined bearing positions. Lumped-mass eigen iteration for critical speed.

Inputs

Parameter	Description
`geometry`	Uniform or stepped segments (length, OD, ID)
`supports`	Bearing positions — pin (journal) or fixed
`loads`	Torque, bending moment, transverse force, axial force at stations
`stressFeatures`	Shoulder fillet, keyway, or custom Kt
`operatingRpm`	Enables fatigue and critical speed margin
`material`	E, G, density, yield, ultimate strength

Outputs

T(x), M(x), V(x), $σ_{vm} (x)$ , deflection, slope, critical speed, fatigue SF
Bearing reactions and slope utilization
Governing failure mode (static / fatigue / deflection / slope / whirling)

Design codes & checks

Indicative: von Mises static, deflection, critical speed margin, Goodman fatigue
US: AGMA 6001 interface loads (context via gear handoff)
EU: DIN 743 full worksheet — not yet implemented; use Indicative fatigue for screening

Assumptions & limitations

Linear elastic Timoshenko/Euler shaft model; no 3D fillet FEA
Kt from Peterson/Shigley approximations, not DIN 743-2 tables
Critical speed: first two lateral modes; gyroscopic/damping omitted
DIN 743 influence factors (K₁, K₂, K₃, β, K_V) not yet integrated

Verification

CI: shafts-indicative-01.json
Vitest: src/lib/machine/shafts/engine.test.ts
Engineer sign-off: validation-master-checklist.md (Machine → shafts)

Cross-module handoff

Publishes alternating/mean stress to fatigue module after calculate
Receives gear/pulley loads from upstream calculators (manual today)

References

Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 7.
Peterson, R. E. Stress Concentration Factors.
DIN 743:2012 (EU target standard — partial integration planned).

Maintainer note: Mechanics + fatigue pipeline with many derived parameters.

Shaft Design

Assumptions

Limitations

Engineering checks

Shaft Design (shafts)

Shaft Design (`shafts`)