How do I calculate the Force produced by a pneumatic cylinder?
It is important to be able to calculate the amount of force exerted at instroke and outstroke of a pneumatic cylinder, for any given bore size and system line pressure. This is so that an appropriate cylinder can be chosen for a task at hand.
Undersizing a cylinder for a task at hand could result in the load not being moved at all and cycling problems. Oversizing can be using more compressed air, energy and space than necessary. For repetitive movements (and movements replicated across arrays), the wasted energy can be quite substantial.
Pneumatic Cylinder Maximum Force Calculation
A pneumatic cylinder consists a piston, connected to a rod, inside a cylinder body.
Figure 1. Piston Construction
In double acting cylinders, there is an inlet port and outlet port. As compressed air enters the inlet port, it exerts pressure on the side of the piston that is not connected the rod. The area of this side of the piston is wholly dependent on the bore size, and is given by the following expression: πR2, where R is radius
Working Example:
Outstroke Force Cylinder (Metric Calculation)
Since the bore size is equal to the diameter of piston, a 32mm bore cylinder has a 32mm diameter piston. Hence, the piston’s radius is 16 (half of the diameter). We can now calculate the area of the piston of a 32mm bore cylinder with the following expression: π162
The piston area side of a 32mm bore cylinder is thus: 80.4248 mm2 or 8.04 cm2. Now, the force of a pneumatic cylinder also dependent upon the gauge pressure, and is given by the following expression:
F = P x A
where F is in newtons, P is in bar, and A piston area in cm2
If the gauge pressure is 6 bar, then the force is 48.8781 newtons. In general, if the pressure is increased, then the force exerted by the same cylinder will also increase.
Instroke Force of Pneumatic Cylinder
(Metric Calculation)
For the outstroke, the force produced will be lower. This is because the area of the side of the piston connected to the rod is lower. When compressed air enters the outlet port in a double acting cylinder, it has less surface area to exert force on.
To calculate the area of the side of the piston connected to the rod, one must first calculate the area of the piston without the rod, then subtract the area of the rod from it. In order to calculate the area of the rod son piston, use the following formula:
Area of Rod-Side Piston: πR2 - πr2 ,
Where R is equal to the radius of the piston, and r is equal to the radius of the rod.
Pneumatic Cylinder Force Requirements Checklist
It is important to check whether a pneumatic cylinder is capable for fulfilling a certain job by moving a load. Use the above method to determine the theoretical force produced by the cylinder.
The Force of an Object
The force exerted by a stationary object will be determined by the mass of the object multiplied by the force of gravity (for good measure and ease of calculation, we can say 10 m/s2). If a load is 10kg, then the force exerted 100 newtons. A 32mm bore cylinder operating at 6 bar will be able to push a 45 kg load.
However, there are other factors to consider that may affect the force requirement.
1. Is the object truly stationary?
If not, then one will need to calculate the true force exerted by the load. Objects that undergo acceleration in any direction may impinge on the force exerted by the load.
2. Are there any frictional forces acting on the object?
If moving the load in a trajectory results in frictional forces applying onto the object, then the force required to the move may be greater than the calculated force.
3. Internal Friction of the Cylinder
Many of the components inside the cylinder such as the piton and rod seals, bushings, wear bands, and other seals will reduce the amount of force produced by the cylinder. Depending on the application method, additional side loading may occur, and these components will exert even greater friction.
Practicalities does not permit one to determine the true force exerted by an object for a particular application. In general, however, it is satisfactory to overengineer for the task by selecting a pneumatic cylinder that more than accounts for the force requirements.