# Dynamic Analysis for a Reciprocating Compressor System with Clearance Fault
## 1 Introduction  
Reciprocating compressors are widely applied in the petrochemical industry and refrigeration. It often occupies a vital position in the processing system [1]. The health of the compressor is directly related to the production and economic benefits of the enterprise. Due to the severe working environment and the multiple motivating sources, faults frequently occur in the reciprocating compressor, which degrade the production efficiency and even cause serious consequences. However, the complicated structure of the reciprocating compressor makes it challenging to monitor and diagnose the faults. Therefore, the various faults' diagnostic methods and mechanism analysis have been the focus of research on reciprocating compressor systems [2; 3; 4]. So far, many researchers have investigated technologies for monitoring and diagnosing the various faults in a reciprocating compressor. Most of them pay attention to the diagnostic methods of broken valves, because valve faults are the most common in a reciprocating compressor. They presented several approaches based on a PV diagram, vibration analysis, or information entropy [5; 6; 7]. In addition, some researchers focus on automated classification of the faults in reciprocating compressors [8; 9]. However, few of them focus on the failure mechanism of the translational mechanism in the reciprocating compressor system. The translational tool consists of the critical parts of the crankshaft, linkage, crosshead, and piston assembly. Although the number of faults in these parts is less than that for the valves, it always causes more severe consequences, even causing safety accidents. Thus, fault detection and diagnosis for these parts should be concentrated on more. Compared with the valve, detecting and diagnosing faults in translational machinery is more complex because these parts are always located inside the airtight chamber. At present, the most common and effective fault diagnosis methods for these parts are based on vibration analysis. [PERSON] [10] proposed a three-stage network system to diagnose piston slap faults in reciprocating machines based on vibration signals. [PERSON] [11] developed a piston slap fault model of a reciprocating engine to investigate the vibration response induced by a slap and the relationship between the piston slap impact and the vibration. However, as the author of [11] said, the reciprocating machine vibration properties, such as the impact excitations and time-varying transfer characteristics, make it challenging to obtain a significant signature directly. Therefore, it is necessary to develop a model to compute and simulate the dynamic behaviors of the reciprocating compressor under normal and faulty conditions and investigate the relationship between faults and vibration. Recently, several models of reciprocating compressors have been established for different purposes. [PERSON] [12] proposed a dynamic model of a hermetic reciprocating compressor in on-off cycle operation to analyze the effect of the transient conditions on the mass flow rate of suction, discharge, and electrical power. [PERSON] [13] presented a comprehensive model for a semi-hermetic CO\({}_{2}\) reciprocating compressor to simulate the geometry and kinematics, the compression process, and the frictional power loss. [PERSON] [14] developed a thermodynamic model to study the effects of the parameters, including the angular speed, clearance, and pressure ratio, on the performance of the CNG reciprocating compressor. [PERSON] [15] introduced a numerical model of a reciprocating compressor in a startup and shutdown transient to investigate its performance in such transients. These models presented in the above literature are a valuable tool for analyzing or predicting a compressor's thermodynamic behavior, including the flow rate, friction loss, and so on, but they are not suitable for analysis of the vibration or fault detection and diagnosis for translational machinery. The translational mechanism of the reciprocating compressor is a crank-slider mechanism.