How does shaft size affect strength?

Larger diameter gives lower endurance strength (kb decreases)

Larger diameter gives higher strength

How is a keyway accounted for in fatigue?

Using Kf = 1 + q(Kt - 1) applied to the alternating stress

By using Kt directly regardless of notch sensitivity

Practice · 5 marks

Factors affecting endurance limit of shafts

Short answer

Corrected endurance limit Se = ka kb kc kd ke kf Se' where Se' ≈0.5 Sut. Surface factor ka reduces for rough finish; size factor kb decreases with diameter; load factor kc is1 (bending),0.85 (axial),0.59 (torsion); temperature factor kd; reliability factor ke; miscellaneous kf. Fatigue stress concentration factor Kf =1+q(Kt-1).

Explain the factors that modify the endurance limit of a rotating shaft. Write the Marin equation and describe how each factor is accounted for.

The endurance limit $S_e'$ found from a standard rotating-beam test on a small polished specimen is much higher than the endurance limit of an actual shaft. The actual value is obtained using the Marin equation:

S_e = k_a\, k_b\, k_c\, k_d\, k_e\, k_f\, S_e'

where, for steels, $S_e' \approx 0.5\,S_{ut}$ (for $S_{ut} \le 1400$ MPa, with an upper limit of 700 MPa).

Modifying factors

Factor	Name	Effect
$k_a$	Surface factor	Rough surfaces (machined, hot rolled, forged) start cracks more easily than a polished one, so $k_a < 1$ . It decreases as $S_{ut}$ increases, for example $k_a = 4.51 S_{ut}^{-0.265}$ for machined steel.
$k_b$	Size factor	Larger shafts have more highly stressed volume and a flatter stress gradient, so a larger diameter gives lower strength. For $2.79 \le d \le 51$ mm, $k_b = 1.24 d^{-0.107}$ ; $k_b = 1$ for axial load.
$k_c$	Load factor	1 for bending, 0.85 for axial and 0.59 for torsion (when the tests were for bending).
$k_d$	Temperature factor	Strength falls at high temperature; $k_d = 1$ at room temperature.
$k_e$	Reliability factor	0.897 for 90 %, 0.868 for 95 %, 0.814 for 99 %, 0.753 for 99.9 %.
$k_f$	Miscellaneous factor	Corrosion, plating, residual stress, and other effects.

Stress concentration

Notches such as keyways, shoulders and grooves are included by the fatigue stress concentration factor $K_f = 1 + q(K_t - 1)$ , where $q$ is the notch sensitivity. The nominal alternating stress is multiplied by $K_f$ (or the endurance limit is divided by it).

These corrected values are used in the Soderberg or Goodman equations when designing shafts for fatigue.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Factors affecting endurance limit of shafts

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