Precision Hydraulic Cylinder Engineering Formulas
Hydraulic cylinders convert pressurized fluid energy into linear mechanical force. Pascal's Law states that pressure applied to an enclosed fluid is transmitted undiminished in all directions.
1. Hydraulic Force Equations
During extension (push), the pressurized oil acts against the entire circular piston cap area. During retraction (pull), the effective area is reduced by the presence of the piston rod:
- Piston Cap Area:
A_cap = (π × D_bore²) / 4 - Rod End Annular Area:
A_annular = π × (D_bore² - D_rod²) / 4 - Push Force (lbs):
F_push = Pressure (PSI) × A_cap (in²) - Pull Force (lbs):
F_pull = Pressure (PSI) × A_annular (in²)
2. Cylinder Velocity & Cycle Time
The speed of cylinder actuation depends directly on fluid flow rate (Gallons Per Minute) delivered by the hydraulic pump:
Velocity (inches/second) = (231 × GPM) / (60 × Area)Stroke Time (seconds) = Stroke (inches) / Velocity (in/sec)
3. Theoretical Pump Power
The mechanical input horsepower required to drive a pump at a given pressure and flow is calculated as:
Horsepower (HP) = (Pressure in PSI × Flow in GPM) / 1714Tip: For real-world systems, assume 85% to 90% hydraulic efficiency (multiply required engine/motor HP by 1.15 to account for friction and piping heat losses).