Determine the air consumption of a cylinder
Problem: A pneumatic system must be expanded. To estimate the costs and air consumption, also to check whether the existing compressor is still sufficient, the air consumption of the system must be determined.
The approach to calculate the air consumption is about the law of Boyle-Marriotte. Thus, the amount of air for the extension of the cylinder is as follows:
|V1 * p1 = V2 * p2 Eq.1
T1 T2If T1 ≈ T2 applies the simplification:
V1 = V2 * p2 Eq.2
|applied to the cylinder:
V1 = the sucked-in air for the compressor
p1 = pamb = pressure of the environmentV2 = stroke s * piston area A
p2 = pabs = pressure within the cylinder
QZyl. = A * s * Pabs
The single-acting cylinder retracts automatically by its return spring.
QZyl. = 2 * A * s * Pabs
The double-acting cylinder needs also compressed air to retract.
|The air consumption of a double acting cylinder is twice as large as it also requires compressed air for the retraction.|
Moreover the air-consumption within a certain time also depends on the number n of the piston strokes:
qV = QZyl * n
A common unit is liters per minute or l/min.
4A2: Determining the air-consumption of a pneumatic installation
A system should be extended by a single-acting and a double-acting cylinders. The system has an operating pressure of 8 bar. This extension operates with a clock rate of 30 per minute
Data: Single acting cylinder: diameter 20 mm, stroke 3 cm
Double acting cylinder: diameter 100 mm, stroke 10 cm
The diameter of the cylinder rod should be negligible here. Check your calculation by the diagram below.
Consumption single-acting cylinder per stroke:
Qzyl. = A * s * Pabs / Patm A = ᴫ d2 / 4 = ᴫ * 0,022m2 / 4 = 3,142 * 10-4 m2
=> QZyl. = 3,142 * 10-4 m2 * 0,03 m * 9 bar / 1 bar = 8,48 * 105 m3 = 0,0848 l
Consumption double-acting cylinder per stroke; that means extend and retract:
Qzyl. = 2 * A * s * Pabs / Patm A = ᴫ d2 / 4 = ᴫ * 0,12m2 / 4 = 7,85 * 10-3 m2
=> QZyl. = 2 * 7,85 * 10-3 m2 * 0,1 m * 9 bar / 1 bar = 14,13 l_
Proof by the diagram:
qZyl.1 ≈ 0,028 l / cm Hub ==> stroke = 3 cm ==> QZyl. ≈ 0,028 l / cm stroke * 3 cm = 0,084 l
qZyl.2 ≈ 2 * 0,7 l / cm Hub ==> stroke = 10 cm ==> QZyl. ≈ 2 * 0,7 l / cm stroke * 10 cm = 14 l
With a clock rate of 30 times a minute you can apply:
Consumption total = 30/Min * (QCyl.1 + Q.Cyl.2) = 30 /Min * (0,084 l + 14,13 l) = 426,4 l/Min