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Retraction Force Calculator

Formula

To calculate the retraction force:

$RF = P \left(\frac{\pi Dp^2}{4} - \frac{\pi Dr^2}{4}\right)$

Where:

$RF$ is the retraction force in pounds-force (lbf)
$P$ is the pressure between the piston and rod in pounds per square inch (psi)
$Dp$ is the diameter of the piston in inches
$Dr$ is the diameter of the rod in inches

What is Retraction Force?

A retraction force is the total force required to retract a pneumatic cylinder with a piston and rod. It is calculated by subtracting the area of the rod from the area of the piston and then multiplying by the pressure. This force is crucial for the proper functioning of pneumatic systems.

Example Calculation 1

Let's assume the following values:

Pressure ( $P$ ) = 100 psi
Diameter of the Piston ( $Dp$ ) = 4 inches
Diameter of the Rod ( $Dr$ ) = 1 inch

Using the formula:

$RF = 100 \left(\frac{\pi \times 4^2}{4} - \frac{\pi \times 1^2}{4}\right) = 100 \left(\frac{16\pi}{4} - \frac{1\pi}{4}\right) = 100 \left(4\pi - 0.25\pi\right) = 100 \times 3.75\pi \approx 1178.10$

The retraction force is approximately 1178.10 lbf.

Example Calculation 2

Let's assume the following values:

Pressure ( $P$ ) = 150 psi
Diameter of the Piston ( $Dp$ ) = 5 inches
Diameter of the Rod ( $Dr$ ) = 2 inches

Using the formula:

$RF = 150 \left(\frac{\pi \times 5^2}{4} - \frac{\pi \times 2^2}{4}\right) = 150 \left(\frac{25\pi}{4} - \frac{4\pi}{4}\right) = 150 \left(6.25\pi - 1\pi\right) = 150 \times 5.25\pi \approx 2471.24$

The retraction force is approximately 2471.24 lbf.