Marin Modification Factors⚠ unverified
Mechanical / Shafts · Compute the combined Marin endurance-limit modification factor
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| ka | ka | — | 1.0 | Surface condition factor (dimensionless) |
| kb | kb | — | 1.0 | Size factor (dimensionless) |
| kc | kc | — | 1.0 | Loading factor (dimensionless) |
| kd | kd | — | 1.0 | Temperature factor (dimensionless) |
| ke | ke | — | 1.0 | Reliability factor (dimensionless) |
| kf | kf | — | 1.0 | Miscellaneous-effects factor (dimensionless) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | k | — | Product of all Marin factors (dimensionless) |
The science & history
Understanding the Parameters
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Surface factor $k_a$ — surface finish is the usual crack origin. Ground and polished surfaces give $k_a$ near 1; as-forged, hot-rolled, or corroded surfaces drop it well below. Fitted as $k_a = a\,S_{ut}^{\,b}$ per finish.
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Size factor $k_b$ — larger shafts have more highly-stressed volume and thus more probable flaws, so $k_b < 1$ for bigger diameters. (Axial loading has $k_b = 1$ — no gradient.)
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Loading factor $k_c$ — corrects for load type relative to the rotating-bending baseline: $k_c \approx 1$ bending, $\approx 0.85$ axial, $\approx 0.59$ torsion.
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Temperature factor $k_d$ — accounts for strength change with temperature (roughly 1 near ambient, falling at high temperature where creep and strength loss set in).
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Reliability factor $k_e$ — converts the (scattered) mean endurance data to a chosen survival probability; higher required reliability → lower $k_e$ (e.g. ~0.897 at 90 %, ~0.753 at 99.9 %).
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Miscellaneous factor $k_f$ — a catch-all for stress concentration (notches, Keyway Stress Reduction), residual stresses, corrosion, plating, and fretting — often the most damaging single effect on a real shaft.
Derivation (Approaching a Proof)
The Marin equation is not derived from first principles; it is a structured empirical correction. The logic: each real-world departure from the ideal polished rotating-beam specimen degrades fatigue strength, and — assumed to act independently — their effects compound multiplicatively rather than adding:
$$S_e = k_a\,k_b\,k_c\,k_d\,k_e\,k_f \cdot S_e'.$$
Independence is the key modelling assumption: a rough surface is taken to reduce fatigue strength by the same fraction regardless of the shaft's size or temperature, so the fractions multiply. Each factor is a fitted correlation from large fatigue-test datasets (e.g. Marin's own surface-finish data), and $S_e'$ itself is estimated from the ultimate strength ($S_e' \approx 0.5\,S_{ut}$ for steels below ~1400 MPa). The product $k$ typically lands in the 0.2–0.6 range for real shafts — a sobering reminder that a polished-specimen endurance limit badly overestimates real fatigue strength.
Dimensional check. All factors are dimensionless, so $k$ is dimensionless and $S_e$ keeps the units of $S_e'$ (Pa). ✓
History and Development
The method is due to Joseph Marin (Mechanical Behavior of Engineering Materials, 1962) and is the standard fatigue-design procedure in Shigley's Mechanical Engineering Design. It operationalises Wöhler's 19th-century endurance-limit discovery for real components, feeding the modified endurance limit into the Goodman/Soderberg fatigue criteria (Shaft Fatigue Factor).
Related Concepts: Shaft Fatigue Factor, Fatigue Endurance Limit, Bolt Fatigue Endurance, Goodman Line, Keyway Stress Reduction
Notes: Full six-factor Marin product. Multiply $k$ by the specimen endurance limit $S_e' \approx 0.5\,S_{ut}$ (steel) to get the in-service $S_e$, then use Shaft Fatigue Factor. The stress-concentration effect is often carried in $k_f$ (as $1/K_f$).