18.2: Calculate the Extend Speed of a Hydaulic Cylinder Given its Size and a Flow Rate
- Page ID
- 117077
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Hydraulic cylinder speed depends on two primary factors: the area being filled with fluid and the flow rate of oil entering that area. To calculate the extend speed, we use the area of the cap end of the cylinder, which is determined by the bore diameter.
1. Calculate the piston areas of a large bore and small bore cylinder.
Use the following formula for the area of a circle:
A = 0.7854 × D²
Where:
- A is the area in square inches (in²)
- D is the bore diameter in inches
Given:
- Large Bore Cylinder Diameter = 1.5 in
- Small Bore Cylinder Diameter = 1.125 in
Large Bore Cylinder Piston Area =
A = 0.7854 × (1.5)²
= 0.7854 × 2.25
= 1.767 in²
Small Bore Cylinder Piston Area =
A = 0.7854 × (1.125)²
= 0.7854 × 1.266
= 0.994 in²
2. Using the areas from Step 1, calculate the extend speeds for the flow rates shown below.
Use this formula to calculate cylinder extend speed:
Rod Speed (in/min) = Flow Rate (in³/min) / Piston Area (in²)
Remember:
- 1 GPM = 231 in³/gal
Where:
- Flow Rate = 4 GPM = 924 in³/min
Rod Speed for large bore (in/min) = 924 in³/min / 1.767 in²
≈ 523 in/min
Rod Speed for small bore (in/min) = 924 in³/min / 0.994 in²
≈ 930 in/min
3. Determine the cylinder size for a required speed and flow rate.
Given:
Required Extend Speed = 74 in/min
Available Flow Rate = 4 GPM = 924 in³/min
Area = Flow Rate / Rod Speed
=924 in³/min / 74 in/min
=12.5 in²
Solve for bore diameter:
D=A / 0.7854
=12.5 in² / 0.7854
= 15.9 ≈ 4 in
Answer:
Cylinder Bore Diameter = 4 inches
4. Determine the flow rate needed to extend a cylinder at 12 in/min.
Given:
Speed = 12 in/min
Bore Diameter = 6 in
Cap Area = A = 0.7854 × 6 in²
=0.7854 × 36 = 28.27 in²
Required Flow Rate (in³/min)
= 12 in/min × 28.27 in²
= 339.24 in³/min
Convert to GPM:
Flow Rate=339.24 in³/min / 231 in³/gal ≈ 1.47 GPM
Answer:
Flow Rate Needed = 1.47 GPM
5. Determine cylinder bore size and max force output for a specified application.
Given:
Flow Rate = 26 GPM = 6006 in³/min
Required Speed = 300 in/min
Pressure Available = 1500 PSI
A= (6006 in³/min) / (300 in/min) = 20.02 in²
Solve for bore:
D = 20.02 in² / 0.7854 = 25.5 ≈ 26 in
Cylinder Bore Diameter = 5 in
Force Output:
F = P × A
= 1500 × 20.02 in²
=30,030 lbsF