KEVOS® MAKEOS · Hydraulics
Hydraulic Cylinder Structure (Barrel, End Cap and Rod Buckling)
Is this hydraulic cylinder’s barrel thick enough, will the end cap hold the pressure, and will the rod buckle when it pushes fully extended?
Structural check of a hydraulic cylinder: barrel stresses by the thick-wall (Lamé) equations with closed ends and the von Mises stress at the bore (as the pressure cylinder tool), the least wall for your safety factor, the bore expansion under pressure (which affects the piston seal), the flat end cap thickness as a clamped plate (as the circular plate tool), the push force, and buckling of the fully extended rod by Euler or Johnson (as the column buckling tool).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Barrel | ||
| Bore | mm | Bore of the barrel. |
| Barrel wall thickness | mm | Wall thickness of the barrel. |
| Working pressure | bar | Highest working pressure. |
| Barrel yield strength | MPa | Yield strength of the barrel tube. |
| Barrel safety factor required | Safety factor against yield you require for the barrel. | |
| Elastic modulus | GPa | Elastic modulus of the barrel and rod steel. |
| Poisson’s ratio | Poisson’s ratio. | |
| End cap | ||
| End cap thickness | mm | Thickness of the flat end cap (treated as clamped at the bore). |
| End cap allowable stress | MPa | Allowable bending stress of the end cap (your design value). |
| Rod | ||
| Rod diameter | mm | Diameter of the piston rod. |
| Mount to rod end, fully extended | mm | Length from the cylinder mounting point to the rod end with the rod fully extended. |
| Effective length factor for the mounting | Effective length factor for the mounting (1 for pivoted at both ends; 2 for a fixed body with a free rod end; follow the cylinder maker’s mounting factors). | |
| Rod yield strength | MPa | Yield strength of the rod. |
| Rod buckling safety factor required | Safety factor against buckling you require for the rod. | |
Method and formulas
- Lamé at the bore: σ_θ = p (r_o² + r_i²) ÷ (r_o² − r_i²), σ_r = −p, σ_z = p r_i² ÷ (r_o² − r_i²) (closed ends); von Mises from the three (as the pressure cylinder tool); least wall found by bisection.
- Bore expansion Δd = 2 r_i [σ_θ − ν(σ_r + σ_z)] ÷ E.
- End cap (clamped plate) t = a √(0.75 p ÷ σ_a) with a = bore ÷ 2 (as the circular plate tool).
- Push force F = p π D² ÷ 4; rod buckling by Euler or Johnson with length K L_b (as the column buckling tool).
- Example: at 160 bar the barrel has a factor of 3.9142, the bore grows 32.085 µm, and the rod’s buckling factor is 8.3959.
Limitations
- Rod buckling uses a concentric load; side loads and mounting misalignment lower it.
- Welds, ports and thread roots need their own checks.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design a custom hydraulic cylinder
- Check a cylinder for a higher pressure
- Check rod buckling for a longer stroke
Who it is for
- Hydraulic engineers
- Machine designers
- Design engineers
What you get
- Barrel stresses, safety factor, least wall and bore expansion
- End cap thickness needed
- Push force and rod buckling safety factor
Interpreting the result
- Rod buckling often limits long-stroke cylinders before pressure does: a larger rod or a better mounting style helps most.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 290–294, 281–288, 3421–3425. Topic reference; no source tables or recommended settings are reproduced.
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Open the Hydraulic Cylinder Structure (Barrel, End Cap and Rod Buckling) calculator
