Air compressor displacement calculation formula

Basic Concepts of Air Compressor Displacement

Air compressor displacement (discharge volume) is a key technical parameter for assessing an air compressor’s performance. Accurate calculation and evaluation of displacement are crucial for equipment selection, system integration, and energy‑efficiency analysis.

Air compressor displacement is typically classified intoTheoretical DisplacementandActual displacementThe theoretical displacement refers to the volume of gas that a compressor draws in per unit time under ideal conditions, whereas the actual displacement is the volume of gas discharged—corrected to the suction‑state conditions—under real operating conditions. A discrepancy exists between the two, primarily determined by the compressor’s volumetric efficiency.

Theoretical Displacement Calculation Formula

The theoretical displacement is primarily determined by the compressor’s geometric dimensions and its operating speed. For reciprocating air compressors, the formula for calculating the theoretical displacement is as follows:

V_th = (π / 4) × D² × S × n × Z × 10⁻⁶

• V_th: Theoretical displacement, in cubic meters per minute (m³/min)
• D: Cylinder bore diameter, in millimeters (mm)
• S: Piston stroke, in millimeters (mm)
• n: Compressor main shaft speed, in revolutions per minute (r/min)
• Z: Number of cylinders

For rotary air compressors, the theoretical displacement depends on the geometric dimensions of the rotor’s profile and the rotor speed; the calculation principle is similar, with the theoretical displacement being the product of the geometric volume and the rotational speed.

Actual Displacement Calculation Formula

In actual operation, due to factors such as clearance volume, gas leakage, suction resistance, and gas heating, the actual displacement is invariably less than the theoretical displacement. The formula for calculating the actual displacement is:

V_act = V_th × λ

Among them,V_actFor the actual displacement (m³/min),lambdaThis is the discharge coefficient, also known as volumetric efficiency. The discharge coefficient is a value less than 1, typically determined experimentally by the manufacturer and provided in the product data. For reciprocating compressors, the discharge coefficient generally ranges from 0.65 to 0.85, while for screw compressors it is usually above 0.90.

Main factors affecting the displacement of an air compressor

Understanding the factors that affect displacement helps ensure the equipment operates efficiently during routine maintenance.

• Clearance volume: The high-pressure gas remaining in the cylinder when the piston reaches top dead center expands and occupies part of the volume before intake, thereby reducing the amount of air drawn in.
• Leakage lossGas leakage at the piston rings, valves, and rotor clearances can result in the loss of some of the gas that has already been drawn in or compressed.
• Inhalation Resistance and Heating: The resistance of the intake valve and the heating of the cylinder walls cause the temperature of the intake gas to rise and its density to decrease, thereby reducing the actual mass of gas drawn into the cylinder.
• Rotational speed variation: Fluctuations in the drive motor speed directly affect the theoretical displacement in proportion.