How to Calculate the Force Applied by a Pneumatic Cylinder

Pneumatic cylinders or actuators are used for mechanical movements. These movements are employed every day in assembly lines and automated machinery. One advantage air cylinders have over hydraulic cylinders is the use of flow restrictors and pressure regulators, which can help with precision air adjustments.

Instructions

1. Understand there are two positions to an air cylinder, fully extended and fully retracted. When an air cylinder extends, it will generally apply more force than in the retraction movement. The reason for this difference of force is the diameter of the air cylinder's stroke rod. The stroke rod attaches to any device the cylinder is moving. Since the rod is attached to the force plate, the diameter or surface area of the rod must be deducted from the total area of the plate. It is the area of the force plate combined with the air pressure, delivered to the cylinder, that gives the final applied force.

2. Calculate the applied force of an air cylinder with the following dimensions: The internal force plate is 3 inches in diameter with a stroke rod diameter of 1 inch. The applied air pressure is 100 pounds per square inch (psi).

3. Find the area of the force plate by using the formula: Area is equal to Pi times radius squared (A=Pi*R^2). Pi is equal to 3.14 and the radius of the 3-inch plate is equal to 1.5 inches. Plugging the numbers into the formula, the equation will read: A = 3.14 * (1.5)^2. The area is equal to 7.065 square inches or in^2.

4. Calculate the amount of force applied with 100 psi of air pressure. To find the result, multiply 100 psi times 7.065 in^2; the answer is 706.5 pounds of force. This is the amount of force from the air cylinder in the full extended mode.

5. Find the force for the air cylinder in the retraction mode. Find the area of the 1-inch-diameter stroke rod. By applying the formula in step 3, the area is .785 in^2. Subtract the area from the result in step 3 or find the force lost by multiplying the 100 psi times .785 in^2, which is equal to 78.5 pounds of force. Subtract 78.5 from 706.5, and the amount of force from the cylinder in a retraction mode is equal to 628 pounds of force.

Tips & Warnings

• The above calculations are for theory only; friction from worn or old cylinders may have to be taken into consideration for precise force applications. The speed of airflow may also play a factor in the force applied to an air cylinder.

References

• Millwrights and Mechanical Guide; Carl A. Nelson; 1975
• Essential of Mathematics; Russell V. Person; 1979