Accurate sizing of axles and shafts is crucial in the design of mechanical systems across mining, manufacturing, and heavy equipment sectors. Whether supporting load or transmitting torque, these components must be dimensioned to handle real-world conditions without failure, deflection, or premature fatigue.
This blog explores the essential formulas and engineering principles used to determine appropriate diameters and lengths for axles and shafts.
Axles vs Shafts: Sizing Context Matters
-
Axles: Designed to support loads, mainly subjected to bending and shear.
-
Shafts: Designed to transmit power, mainly subjected to torsion and fatigue.
In most mining and heavy industry applications, combined loading is the rule, not the exception.
1. Sizing a Solid Shaft for Torsion
To calculate the minimum diameter of a shaft based on torque:
d=(16Tπτallow)1/3d = \left( \frac{16T}{πτ_{allow}} \right)^{1/3}
Where:
-
TT = Torque (Nm)
-
τallowτ_{allow} = Allowable shear stress (MPa)
-
dd = Shaft diameter (mm)
✅ Use for: Conveyor drive shafts, crusher main shafts
2. Sizing for Bending Stress in Axles
For axles exposed to pure bending:
σb=MW=32Mπd3⇒d=(32Mπσallow)1/3σ_b = \frac{M}{W} = \frac{32M}{πd^3} \Rightarrow d = \left( \frac{32M}{πσ_{allow}} \right)^{1/3}
Where:
-
MM = Bending moment
-
σallowσ_{allow} = Allowable bending stress
✅ Use for: Wheel axles in mining trucks, mobile cranes
3. Sizing Under Combined Bending and Torsion
For more realistic scenarios:
d=[16π⋅M2+(T⋅k)2σallow]1/3d = \left[ \frac{16}{π} \cdot \frac{\sqrt{M^2 + (T \cdot k)^2}}{σ_{allow}} \right]^{1/3}
Where:
-
kk = factor based on combined stress theory (often 1.5 to 2.0)
-
This approach ensures both bending and torsional limits are respected.
4. Practical Thumb Rules for Initial Estimations
Sometimes engineers use quick checks in the early design phase:
-
Transmission shaft:
dest=1.5⋅P3d_{est} = 1.5 \cdot \sqrt[3]{P}
(where PP is power in kW)
-
Axle spacing: 1.5 to 2 times the wheelbase for optimum deflection and load transfer
-
Safety factor: Use 1.5 for static loads, 2.0–2.5 for dynamic/fatigue-prone systems
Material Considerations
The selected material strength directly affects the shaft diameter. For example:
| Material | Yield Strength (MPa) | Suitable For |
|---|---|---|
| C45 / CK45 | ~550 MPa | Standard shafts and axles |
| 42CrMo4 | ~900 MPa | Heavy-duty mining shafts |
| AISI 304 SS | ~215 MPa | Corrosion-resistant use |
Mining Use Case Example
Designing a shaft for a rock crusher transmitting 45 kW at 1200 rpm:
-
Torque = 9550×Pn=358.1 Nm\frac{9550 × P}{n} = 358.1 \, \text{Nm}
-
Material: 42CrMo4, τ<sub>allow</sub> = 200 MPa
-
Calculated minimum diameter: ~38 mm, increased to 50 mm after applying safety factors and fatigue allowance
Proper sizing of axles and shafts starts with understanding real forces, continues with robust formulas, and ends with smart adjustments for fatigue, environment, and reliability. In mining and industrial design, these calculations form the backbone of mechanical safety and performance.