How Do You Calculate The Force Output Of A Pneumatic Cylinder?

Pneumatic air cylinders convert compressed air to linear energy to operate machines for various precision tasks. Their versatility has increased their use across industries, making them available in different sizes and designs. 

For pneumatic actuators to work efficiently, they need to be sized appropriately for the task. The process of sizing the unit begins with considering the speed and load requirements, in addition to the stroke length of the piston, the operating pressure, space requirements and how the unit is mounted.

Once this information is gathered, operators must calculate the force output to determine if the pressure supplied matches the cylinder type.

How To Calculate The Force Output 

Pneumatic air systems consist of a cylinder that contains a piston and a rod. The rod is attached to the piston, which supports the air pressure in the entire cylinder. When pressure is applied to the piston, it's transferred to the rod.

To ensure that the air system operates efficiently and safely, operators must calculate the force output and check that the system is sized correctly and not overloaded. Calculating the force output requires knowing the pressure and piston area, considering the piston will reduce the available space.

The mathematical calculation is F = P × A where:

F = theoretical force in Newton (theoretical because it doesn't consider friction and spring forces)

P = supply pressure measured in psi 

A = piston area in sq. inches

Finding The True Load 

Static and dynamic friction affect the force output, reducing the available space in the cylinder. Seals on the piston and rod and other internal sealing mechanisms cause friction.

Calculating the actual load capacity of a pneumatic cylinder requires accounting for friction in the system to allow for enough internal space for the system to operate effectively. For this reason, it's recommended to allow for an additional 5-10 psi input pressure to address friction, depending on the design of the cylinder and bore type.

Finding the actual load of the system requires taking friction into account; the calculation is Ff = Fp × fc where: 

Ff = friction force in-lb 

Fp = force perpendicular to the sliding surface in lb  

fc = the coefficient of friction

Calculations will differ depending on whether the cylinder is a single or double-piston. Double-acting cylinders extend and retract volumes because of the moving load on the return stroke. In this case, the piston rod must be subtracted from the piston surface area, also called the annular area.

Essential Considerations When Sizing A Cylinder

Air pressure supplied to the cylinder, connected piping and future requirements play a significant role in the sizing of the pneumatic cylinder: 

Consider Airflow And The Actual Operating Pressure

Accounting for airflow in the cylinder is necessary to estimate the correct size of various system components such as tubing, valves and filters. Calculating airflow considers the required force to move a load at a specific pressure. A good rule to remember when accounting for exact cycle speed is sizing the cylinder to handle double the load. 

Calculating the actual operating pressure in the pneumatic system accounts for pressure drops caused by flow restrictions in airlines and other devices consuming air supply in the network. For example, an air system running at 100 psi can experience a drop to 80 psi or lower at peak air usage times.

Install Correct Piping

Compressed air needs to reach the cylinder's piston at speed to build the necessary pressure to cycle the volume in the system. If piping is too small or has excessive bends and turns, airflow will be restricted, leading to slower operation and reduced power from the actuator. 

If piping is oversized, the air that needs to be pressurised will increase, slowing down the system and wasting energy.

Account For Kinetic Energy 

Kinetic energy is caused by mass moving at speed. The air cylinder absorbs kinetic energy while carrying the load in the tank, which can damage the system if there is an abrupt stop. 

Cushioning addresses problems from kinetic energy by reducing the speed of the mass. Low-energy applications operating at low speeds don't require as much cushioning. On the other hand, cylinders with a bore larger than roughly 1 inch with a stroke exceeding several inches will most likely need some kind of cushioning—for example, elastomeric bumper cushioning or an external shock absorber.

Test And Plan Ahead

Sizing a pneumatic cylinder based on mathematical calculations alone is insufficient and can lead to costly mistakes without proper testing. Changing a pneumatic system post-installation adds more expense, and it can be challenging to configure the design. For instance, a larger bore cylinder might require changing the whole system to create additional space. It's always best to test the system once calculations are complete to account for future adjustments. This will reduce unnecessary costs.

Sizing Pneumatic Cylinders Correctly 

Pneumatic air systems have the advantage of being simple and economical in design. They are durable mechanical systems, capable of running for years with limited maintenance. For this reason, air-powered systems are used for various functions in the food and beverage, packaging, and automotive sectors.

Getting the most out of pneumatic systems requires careful consideration of the cylinder's force output to ensure the system is appropriately sized for precise and optimal operation. Mathematical calculations can provide theoretical force output, but other factors such as friction, piping, and cushioning must also be accounted for.

With careful planning, manufacturers can select the correct cylinder to save energy and reduce wear to the system.