Shafts are the backbone of mechanical power transmission in industrial machinery. In mining applications — such as crushers, conveyors, winches, and gearboxes — shafts are responsible for transferring large amounts of torque under severe conditions. That’s why understanding shaft strength calculation is essential for safe and efficient design.
This article covers the most important stress analysis techniques used in shaft design, focusing on torsional and combined load conditions encountered in heavy industry.
Key Loading Conditions in Shafts
Unlike axles, which mainly support loads, shafts primarily transmit torque. However, in real-world conditions, shafts also experience:
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Torsion (twisting)
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Bending (from self-weight, pulley force, or belt tension)
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Shear (due to keyways, gear contact points)
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Axial loads (in some applications like thrust bearings)
1. Torsional Stress Calculation (τ<sub>t</sub>)
Torsion is the dominant force in most shaft applications.
Formula:
τt=TWpτ_t = \frac{T}{W_p}
Where:
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TT = Applied torque
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WpW_p = Polar section modulus
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For solid shafts:
Wp=πd316W_p = \frac{πd^3}{16}
(Where d = shaft diameter)
This determines how much shear stress the shaft experiences during torque transfer.
2. Bending Stress Calculation (σ<sub>b</sub>)
Shafts often carry gears or pulleys, introducing bending moments due to the load position relative to supports.
Formula:
σb=MWσ_b = \frac{M}{W}
Where:
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MM = Bending moment
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WW = Section modulus for bending
3. Combined Stress: Torsion + Bending
Real-world shaft designs require evaluating combined stress conditions using:
Von Mises Equivalent Stress:
σeq=σb2+3τt2σ_{eq} = \sqrt{σ_b^2 + 3τ_t^2}
This equation accounts for both torsional and bending components, producing a single value to compare against the material yield strength.
4. Fatigue Stress Analysis
In mining, shafts are exposed to high-frequency cyclic loads, making fatigue life a critical parameter.
Key steps:
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Identify alternating vs mean loads
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Use S-N curves for the material
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Apply correction factors (surface finish, notch sensitivity, size)
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Use Goodman or Gerber criteria for safety
Example: A conveyor drive shaft operating 18 hours a day may experience millions of cycles annually, requiring a fatigue safety factor of 2.0–2.5.
5. Deflection Limits and Shaft Stiffness
While stress limits prevent failure, excessive shaft deflection can cause:
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Gear misalignment
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Bearing overload
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Vibration and noise
Deflection limit rule of thumb:
ΔL≤1300\frac{Δ}{L} ≤ \frac{1}{300}
Where:
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Δ = Maximum deflection
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L = Shaft span length
6. Keyway and Shoulder Stress Concentrations
Discontinuities such as keyways, shoulders, and steps act as stress risers. Use correction factors to increase safety margins or apply fillets to reduce localized stress.
Example from Mining Machinery
A crusher shaft transmitting 1200 Nm of torque with a 60 mm diameter:
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Torsional stress: ~22.6 MPa
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Bending moment from pulley adds ~15 MPa
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Combined stress (σeq) ~45 MPa
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Compared to material yield strength (e.g., 600 MPa for EN8), design is safe under static conditions — but fatigue must still be checked for long-term reliability.
Shaft design is about more than diameter — it’s about understanding how real-world forces interact. In mining and heavy industry, shafts must resist torsion, bending, vibration, and fatigue over years of demanding service. With proper calculations and safety margins, you ensure maximum uptime and system integrity.