Library / Hydraulics, open channels and fluid power / HYD-42
Hydraulics, open channels and fluid power
Cylinder retraction speed
Speed of a double-acting cylinder as it retracts, from the flow Q into the annular rod-side chamber, the bore D and the rod diameter d.
- Ref
- HYD-42
- Rev
- v1
- Field
- Hydraulics, open channels and fluid power
- Result
- v [m/s]
During retraction, the flow enters the annular rod side, whose area is π(D² − d²)/4. The rod speed is the flow divided by that area, v = 4Q/[π(D² − d²)]. For the same flow, retraction is faster than extension because the annular area is smaller. It assumes incompressible fluid, no leakage and a free return from the cap side.
Speed of a double-acting cylinder as it retracts, from the flow Q into the annular rod-side chamber, the bore D and the rod diameter d. The fluid is incompressible, there is no leakage and the cap side returns freely.
Calculator
- Annular area, π(D² − d²)/40.00377 m²
- Extension speed for the same flow, 4Q/(π D²)0.05968 m/s
- Ratio of retraction to extension speed, D²/(D² − d²)1.333
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- 0.3 L/s into the rod side retracts the cylinder at 0.07958 m/s (79.58 mm/s), compared with 0.05968 m/s on extension.
- Retraction is 1.33 times faster than extension with the same pump flow, but the force is lower by the same ratio.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Q Flow into the rod side | 1e-6 to 0.1 m³/s | 2.653e-4 | 26.53 | 26.53 | +10% | +10 % |
| D Cylinder bore | 0.05 to 1 m | 3.826e-4 | 0.4244 | 0.424 | +10% | −21.9 % |
| d Rod diameter | 0.005 to 0.05 m | 0.05992 | 0.09794 | 0.03802 | +10% | +7.53 % |
Sweep of Rod diameter
| Rod diameter (m) | Retraction speed (m/s) |
|---|---|
| 0.005 | 0.05992 |
| 0.01063 | 0.06075 |
| 0.01625 | 0.06225 |
| 0.02188 | 0.06451 |
| 0.0275 | 0.06768 |
| 0.03313 | 0.07203 |
| 0.03875 | 0.07798 |
| 0.04438 | 0.08621 |
| 0.05 | 0.09794 |
Sweep one variable
Variables and how each one contributes
Retraction speed
What the equation gives you. Everything else feeds it.
Flow into the rod side
The flow into the annular side, in m³/s. Raises the speed in direct proportion. Raising it by 10 % (to 3.3×10−4) moves the result by +10 %, from 0.07958 to 0.08754 m/s.
Cylinder bore
The cylinder bore, in m. A larger bore lowers the speed. Raising it by 10 % (to 0.088) moves the result by −21.9 %, from 0.07958 to 0.06217 m/s.
Rod diameter
The rod diameter, in m. A thicker rod shrinks the annular area, so the speed rises. Raising it by 10 % (to 0.044) moves the result by +7.53 %, from 0.07958 to 0.08557 m/s.
Worked example with the values above
- Annular area: π(0.08² − 0.04²)/4 = 0.0037699 m².
- Divide the flow: 3×10−4 / 0.0037699.
- v = 0.079577 m/s.
Assumptions and limits
- An incompressible fluid with no leakage, except where an efficiency is given.
- Gauge pressures and steady operation, with friction and inertia not included unless stated.
Common mistakes
- Using the piston area where the annular area is needed, or the reverse.
- Mixing rev/min and rad/s.
- Forgetting back pressure on the other side of the piston.
Statistics and uncertainty
Real actuators lose force to seal friction and flow to leakage, and oil bulk modulus drops sharply with entrained air, so the stiffness and speed here are best-case figures.
Where it is used
- Sizing hydraulic cylinders, pumps and motors.
- Estimating drive speed, stiffness and natural frequency of a hydraulic actuator.
Maths you need
- Pascal’s law: pressure acts equally in all directions in a closed fluid
- Displacement: volume moved per revolution or stroke
- Bulk modulus: B, the pressure per unit volume change of the fluid