A hydraulic cylinder has to overcome a force of 12,600 pounds on the extend stroke and 9,375 pounds on the return stroke. The maximum system pressure available is 2200 PSIG. What is the smallest diameter cylinder required to overcome the load and what is the maximum diameter rod the cylinder can have?
To determine the smallest diameter cylinder required to overcome the load, we can use the formula for hydraulic cylinder force:
Force = Pressure x Area
Let's start by calculating the area required to overcome the load on the extend stroke:
Force_ext = 12,600 pounds
Pressure = 2,200 PSIG
We need to convert the pressure from PSIG to PSI (pounds per square inch) by subtracting atmospheric pressure, which is roughly 14.7 PSI:
Pressure_ext = 2,200 - 14.7 = 2,185.3 PSI
Let's substitute these values into the formula:
Force_ext = Pressure_ext x Area_ext
Solving for the area:
Area_ext = Force_ext / Pressure_ext
Area_ext = 12,600 / 2,185.3 = 5.76 square inches (approximately)
Now, we can calculate the diameter using the formula for the area of a circle:
Area = π x (Diameter^2) / 4
Solving for the diameter:
Diameter_ext = sqrt((4 x Area_ext) / π) = sqrt((4 x 5.76) / π) = sqrt(23.04 / π) ≈ 2.72 inches
Therefore, the smallest diameter cylinder required to overcome the load on the extend stroke is approximately 2.72 inches.
Next, let's calculate the maximum diameter rod the cylinder can have. The area of the rod will be smaller since it needs to fit inside the cylinder. We can calculate the area of the rod using the same formula:
Area_rod = Force_return / Pressure
Force_return = 9,375 pounds
Substituting the values:
Area_rod = 9,375 / 2,185.3 ≈ 4.29 square inches
Again, using the formula for the area of a circle, we can find the maximum diameter of the rod:
Diameter_rod = sqrt((4 x Area_rod) / π) = sqrt((4 x 4.29) / π) = sqrt(17.16 / π) ≈ 2.08 inches
Therefore, the maximum diameter rod the cylinder can have is approximately 2.08 inches.
To determine the smallest diameter cylinder required to overcome the load, we can use the formula for force exerted by a hydraulic cylinder:
Force = Pressure × Area
We know that the force on the extend stroke is 12,600 pounds and the maximum system pressure is 2200 PSIG. Rearranging the formula, we can solve for the required cylinder area:
Area = Force / Pressure
For the extend stroke:
Area_extend = 12,600 pounds / 2200 PSIG
Similarly, for the return stroke with a force of 9,375 pounds:
Area_return = 9,375 pounds / 2200 PSIG
To find the smallest diameter cylinder, we need to consider the maximum of these two areas:
Area_smallest = max(Area_extend, Area_return)
Once we have the smallest area, we can calculate the diameter of the cylinder using the formula:
Diameter = 2 × √(Area_smallest / π)
Next, to determine the maximum diameter rod the cylinder can have, we need to account for the available system pressure and the smallest diameter cylinder. The maximum rod diameter can be calculated using the formula:
Rod diameter = Cylinder diameter - 2 × (Cylinder wall thickness)
Since the cylinder wall thickness depends on the specific cylinder design and the operating pressure, you may need to consult the cylinder manufacturer or refer to industry standards to determine an appropriate value for the wall thickness.
By following these steps, you can calculate the smallest diameter cylinder required to overcome the load and the maximum diameter rod the cylinder can have.