Modeling of Fixed Displacement Swash Plate Compressor: A Mathematical Approach towards Calculation of Shaft Torque and Volumetric Efficiency

Rapid advent of mobile air conditioning industry has witnessed a wide use of fixed displacement swash plate compressor due to its small size, compact structure and light weight. An accurate prediction of volumetric efficiency and power of compressor at early stages of design serves as a very useful information for designer. No work regarding the power and volumetric efficiency prediction for double headed fixed displacement swash plate compressor is reported in the existing literature. This paper presents a mathematical model for a double acting fixed displacement swash plate compressor with the objective of evaluating the shaft torque and volumetric efficiency of compressor. Shaft torque, in turn is a measure of compressor power. The geometrical description of swash plate yields a kinematic model to obtain the piston displacement as an explicit function of angle of rotation of shaft. A methodology is presented to evaluate in cylinder gas pressures as a function of angle of rotation of shaft. This kinematic model is further extended to present a dynamic analysis of compressor which yields variation of torque with rotation angle of shaft. The trend is plotted and validated with experimental data. A brief discussion on sources of volumetric inefficiencies in reciprocating compressors is presented and a novel method to model the volumetric efficiency is presented which relates the volumetric efficiency of compressor to rotational speed of shaft. An analytical formula based on experimental data is established which can serve as a time honored method to estimate volumetric efficiency of compressor at early stages of design.