Hydraulic Cylinders (`hydraulics`)

Hydraulic Cylinders

Analyze actuator forces and pressure loads

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Indicative closed-form or numerical model

Assumptions

Linear elastic material behavior unless noted otherwise.
User is responsible for load combinations and load factors per the selected design code.
Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

Professional screening / indicative workspace — does not replace a licensed PE or official code compliance review.
Where specialized evaluators are not implemented, checks map solver outputs to catalog templates for orientation only.

Engineering checks

Check	IND	US	EU	ISO
Pressure utilization	implemented	—	—	—
Rod stress utilization	implemented	—	—	—

Purpose

Analyze double-acting hydraulic cylinders for rod and bore stresses, required system pressure, force output, and buckling screening of extended rod under compressive load.

Physics & theory

Hydraulic force $F = p A$ where $p$ is gauge pressure and $A$ is piston area. Annular rod-side area $A_{r} = π (D^{2} - d^{2}) /4$ for bore $D$ and rod $d$ . Retraction force uses rod-side area; extension uses full bore area.

Rod column buckling when extended follows Euler with effective length based on mounting (clevis, trunnion, foot). Seal friction and dynamic pressure drop add losses not always included in static screening. Wall hoop stress in thin cylinder: $σ_{h} = p D / (2 t)$ .

Pressure systems combine membrane stress from internal pressure with bending from weight, thermal expansion, and external loads. ASME codes distinguish sustained, occasional, and peak stress categories with different allowable limits reflecting primary vs secondary stress character.

Thin-wall theory applies when wall thickness is small compared to radius; thick-wall Lamé solutions are required for heavy-wall vessels and high-pressure cylinders.

Governing equations

F_{extend} = p \frac{π D ^{2}}{4}, F_{retract} = p \frac{π ( D ^{2} - d ^{2} )}{4}

σ_{rod} = \frac{F _{compress}}{A _{rod}}, P_{cr} = \frac{π ^{2} E I}{L _{eff}^{2}}

σ_{h} = \frac{p D}{2 t _{wall}}

Numerical method

Closed-form force, stress, and buckling equations (engine). Pressure computed from required force or force from supplied pressure. Rod buckling compared to applied compressive load during retraction/extension as configured.

Inputs

Parameter	Description
Bore $D$ , rod $d$	Cylinder geometry
Stroke, mounting	Rod effective length for buckling
Required force or pressure	Operating point
Wall thickness	Barrel hoop check
Material yield	Rod and tube allowables

Outputs

Extend/retract forces, required pressure, rod stress, hoop stress, buckling safety factor, utilization.

Design codes & checks

Indicative: Pressure and rod stress utilization
ISO: ISO 6020/6022 hydraulic cylinder dimensions (reference)

Assumptions & limitations

Steady-state static analysis; no cushioning or velocity dynamics.
Seal friction and port losses optional or omitted.
Tie-rod vs welded body stress concentrations simplified.
Does not size ports, valves, or accumulators.

Verification

CI: hydraulics-indicative-01.json
Engineer sign-off: validation-master-checklist.md

References

Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed.
ISO 6020-1:2019. Hydraulic fluid power — Mounting dimensions.
Parker Hannifin. Cylinder Design Guide.
NFPA T3.6.7. Fluid power systems — Cylinder bore sizes.
Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.

Maintainer note: Primarily equation-driven actuator calculations.

Hydraulic Cylinders

Assumptions

Limitations

Engineering checks

Hydraulic Cylinders (hydraulics)

Hydraulic Cylinders (`hydraulics`)