KEVOS® MAKEOS · Strength
Hollow Shaft Conversion (Brittle Material, Size, Weight, Twist)
If I make this cast-iron (brittle) shaft hollow, what outside and bore diameters keep it as strong, how much weight do I save, and does it still fit and stay stiff enough?
Conversion of a solid shaft in a brittle material to a hollow one of equal strength: the solid diameter by the maximum-normal-stress method with shock factors and the hollow outside and bore diameters for the bore ratio (as the brittle and hollow shaft tool), wall thickness, mass per metre of both, angle of twist per metre for the torque, and checks against the largest outside diameter that fits, the least wall and your twist limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bending moment | N·m | Bending moment on the shaft. |
| Torque | N·m | Torque on the shaft. |
| Shock factor, bending | Shock and fatigue factor on bending. | |
| Shock factor, torsion | Shock and fatigue factor on torsion. | |
| Allowable tensile stress | MPa | Allowable tensile stress of the brittle material. |
| Bore ratio (inside ÷ outside) | Bore diameter as a fraction of the outside diameter. | |
| Material and limits | ||
| Density | kg/m³ | Density of the shaft material. |
| Shear modulus | GPa | Shear modulus of the material (cast iron about 40 GPa). |
| Largest outside diameter that fits | mm | Largest outside diameter the bearings or housing allow. |
| Least wall thickness | mm | Thinnest wall you accept for casting or machining. |
| Largest twist | °/m | Largest angle of twist per metre you accept. |
Method and formulas
- Solid diameter D³ = 5.1 ÷ S_t × [K_m M + √((K_m M)² + (K_t T)²)]; hollow outside = B × solid with B = ∛[1 ÷ (1 − k⁴)] (as the brittle and hollow shaft tool).
- Wall = (outside − bore) ÷ 2; mass per metre = area × density.
- Twist per metre = T ÷ (G J) with J = π (D⁴ − d⁴) ÷ 32.
- Example: solid 52.311 mm or hollow 54.788/32.873 mm; the hollow shaft weighs 10.863 kg/m against 15.474 kg/m and twists 0.93022°/m.
Limitations
- Maximum-normal-stress theory for brittle materials; fatigue and stress raisers need separate checks.
- Equal strength in combined bending and torsion.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lighten a cast-iron or brittle shaft
- Check a hollow shaft fits its bearings
- Compare twist of solid and hollow shafts
Who it is for
- Design engineers
- Machine designers
- Students
What you get
- Solid and hollow diameters
- Wall, mass per metre and saving
- Twist per metre of each
Interpreting the result
- A moderate bore (k about 0.5 to 0.6) saves a quarter to a third of the weight for a small increase in diameter.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 295–303. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Hollow Shaft Conversion (Brittle Material, Size, Weight, Twist) calculator
