Drive-Shaft Fatigue Strength Calculator
Screen solid and hollow drive shafts for fatigue capacity, elastic response, keyway geometry, and combined bending–torsion stress.
Engineering screening tool—verify inputs and results independently. Use at your own risk.
Mode and inputs
Select the loading model, then enter positive magnitudes in the displayed units.
Cyclic torque capacity
Section properties and screening values for the selected mode.
How to use
- Select fatigue torsion, fatigue bending, keyway, elastic torsion, elastic bending, or combined stress.
- For fatigue modes, enter local diameter in mm, material static strength in MPa, dynamic/static ratio, and Kt or Kf. Keyway mode requires a 10–200 mm nominal diameter.
- For elastic and combined modes, enter outer and inner diameters in mm. Use zero inner diameter for a solid shaft.
- Enter length in m and modulus in GPa where shown; load inputs are non-negative magnitudes in N, N·m.
- Select Calculate or edit a field to update results. Select Reset example to restore fatigue-torsion defaults.
- Interpret capacities as nominal screening limits before any additional safety factor. Stresses are nominal section values; in elastic bending, δ₂ is the M-based secondary output, not the standard F-based cantilever displacement.
- Correct any red warning before using a result. Check unit conversions and independently verify stress factors and material data.
- Do not use this model for plasticity, crack growth, multiaxial variable-amplitude fatigue, critical-speed dynamics, buckling, thermal gradients, or final safety qualification.
Worked example
1. Select Fatigue torsion. Enter dₖ = 20 mm, τ = 500 MPa, τe/τ = 0.45, and Kf = 2.2.
2. Select Calculate. The torsion section modulus is 1.57 × 10⁻⁶ m³, static torque capacity is 785.40 N·m, and cyclic torque capacity is 160.65 N·m.
3. Interpret 160.65 N·m as a nominal cyclic screening capacity under the entered endurance ratio and stress factor—not as an allowable design torque until service factors, spectrum, reliability, and safety margins are applied.
Continue in TriboSolver
Refine combined loading, stress concentration, material behavior, and load histories in TriboSolver or an independently validated shaft model.
Equations used
All loads are entered as non-negative magnitudes. Diameter symbols use D for outer diameter, d for bore diameter, and dₖ for the local fatigue-critical diameter. SI units are used internally.
Symbols: r is dynamic/static strength ratio; Kt is geometric stress concentration and Kf is fatigue stress concentration; τ, τe are static and dynamic shear strengths; Rp0.2, σe are proof/yield and dynamic normal strengths; E and G are elastic moduli; L is shaft length; M, T, F are bending moment, torque, and tip force; φ and θ are rotations; δ is transverse deflection; σᵥ is von Mises equivalent stress.
Theory and method
The fatigue modes use elastic circular-section moduli and reduce dynamic capacity by the entered concentration factor. For ductile material the fatigue factor Kf may be lower than geometric Kt; using Kt is conservative when notch sensitivity is uncertain. The dynamic/static ratio can incorporate surface, size, loading, and material endurance influences only when those effects are represented consistently in the chosen value.
Keyway dimensions follow the discrete diameter ranges below. The critical diameter subtracts the shaft keyway depth before calculating torsional section modulus. The elastic modes assume a straight, homogeneous, prismatic Euler–Bernoulli shaft with small deflection. The reported δ₂ relation uses M rather than F and is retained as a comparative M-based secondary output; it is not the standard tip-force displacement and should not be used as one. Combined stress uses distortion-energy theory from nominal bending and torsional stresses.
| Diameter range (mm) | b × h (mm) | t₁ / t₂ (mm) |
|---|---|---|
| 10–12 | 4 × 4 | 2.5 / 1.8 |
| >12–17 | 5 × 5 | 3 / 2.3 |
| >17–22 | 6 × 6 | 3.5 / 2.8 |
| >22–30 | 8 × 7 | 4 / 3.3 |
| >30–50 | 10–14 × 8–9 | 5–5.5 / 3.3–3.8 |
| >50–95 | 16–25 × 10–14 | 6–9 / 4.3–5.4 |
| >95–150 | 28–36 × 16–20 | 10–12 / 6.4–8.4 |
| >150–200 | 40–45 × 22–25 | 13–15 / 9.4–10.4 |
Assumptions and limits
Linear elasticity, circular sections, small deflection, positive magnitude inputs, no residual stress, and no interaction with axial load are assumed. Nominal stress does not resolve a notch field. Key dimensions are preliminary and require the governing standard, tolerance, hub pressure, key bearing/shear, and length checks. Do not extrapolate keyway ranges beyond 10–200 mm.
References
- DIN 6885-1, drive-type fastenings without taper action; parallel keys, keyways, and dimensional guidance.
- Budynas and Nisbett, Shigley’s Mechanical Engineering Design, shaft stress, deflection, fatigue, and stress-concentration methods.
- Roark’s Formulas for Stress and Strain, circular-section properties and beam relations.