How the calculator works

This is a static copy of the chapter for search engines. The interactive version has animated figures, check questions, and buttons that load the example into the calculator.

ShaftLab is a small finite-element and fatigue engine written from scratch in plain JavaScript. Everything runs in your browser; nothing is sent anywhere.

The mechanics

The shaft is meshed into about 300 Euler–Bernoulli elements, cut at every step boundary, bearing, load and feature so that each element has a single well-defined cross-section. Four decoupled problems are solved on that mesh:

Problem	Unknowns per node	Gives
bending in x–y	v, θ_z	M_y(x), deflection and slope in that plane
bending in x–z	w, θ_y	M_z(x), deflection and slope
axial	u	N(x)
torsion	φ	T(x) and the twist

The two bending planes are combined vectorially afterwards. Because a round shaft has the same I about every axis, they genuinely are independent — this is not an approximation.

The fatigue engine

At every sampled section the tool works out the local diameter and bore, finds which notch (if any) is active there, computes K_t from the geometry, converts it to K_f through the Neuber notch sensitivity, builds S_e with the local k_b, and evaluates the chosen criterion. The output is a safety factor for every section, not one number for the shaft.

Where the numbers come from

Shoulder fillets and U-grooves — Peterson’s polynomial curve fits (Pilkey, Peterson’s Stress Concentration Factors), evaluated from the actual D/d and r/d.
Keyways, ring grooves, press fits — the standard design estimates (Shigley Table 7-1), because the local geometry is set by the tool or the standard rather than by you. Every one of them can be overridden.
Notch sensitivity, Marin factors, the DE criteria — Shigley, Mechanical Engineering Design, chapters 6 and 7.
Key sections — DIN 6885-1.

How it was checked

The engine reproduces Shigley’s worked Examples 7-1 to 7-3 — the four fatigue criteria on a shouldered shaft (within 0.7 %), the reactions and moment diagrams of a two-gear countershaft (exactly), and its deflections and slopes (within a few per cent, the residual being how precisely the step positions can be read off the figure). Closed-form cases — simply supported bending, twist of a uniform shaft, and the critical speed of a uniform shaft — match to better than 0.1 %.

What is deliberately not modelled

Shear deformation — Euler–Bernoulli only. Fine for L/d above about 10.
Bearing stiffness — bearings are treated as ideal simple supports, which makes the computed slopes slightly pessimistic and the critical speed slightly low.
Gyroscopic effects and damping in the critical-speed estimate.
Transverse holes are given a design K_t on the gross section rather than a net-section analysis — override it if the hole is critical.
Residual stresses, case-hardening depth profiles, welds, and finite-life (< 10⁶ cycle) design.
Buckling of long slender shafts in compression, and lateral-torsional effects.

⚠ This is a teaching and first-pass design tool. It gives you correct internal actions and a defensible fatigue estimate for the model you drew. It is not a design-code check, and for a safety-critical shaft it does not replace a proper analysis of the actual joint geometry.

💡 Your model is kept in your browser’s local storage, so it is still there when you come back. There is no server and no account.