## 2 Experimental Research  
### Accelerated Life Test of the Piston Rod  
In this study, an industrial two-stage, double-acting, water-cooled reciprocating compressor was modified for experimental purposes, as shown in Figure 1. The structure of reciprocating compressors involves screwing the piston rod into the crosshead, preloaded by a locknut. The compressor is driven by an electric motor, the detailed specifications of which are given in Table 1.  
Figure 1: Experimental setup. The primary objective of this experiment was to investigate the signal characteristics associated with crack initiation, subsequent crack propagation, and the ultimate failure of the piston rod under operating conditions within a compressor. To increase the efficiency of the testing process, an accelerated life test was used to induce the failure of the piston rod. The experimental modification for the piston rod accelerated fracture test is shown in Figure 2. To increase the reciprocating inertia force, the piston was replaced by a solid structure with a reciprocating inertia mass of 65 kg. Safety precautions were taken in the form of polyurethane pads attached to the piston at both the head and crankshaft ends to mitigate more serious consequences, such as a broken piston rod or the piston colliding with the block, which could damage either the piston or the cylinder. A small diameter prefabricated fracture rod was inserted between the piston rod and crosshead and threaded through the connection block (the prefabricated fracture rod thread M16 \(\times\) 1.5 and the crosshead thread M33 \(\times\) 1.5). The two ends of the prefabricated breaker bar were securely fixed to the piston rod and connecting rod, respectively, using a threaded construction. The Q235 was chosen as the material for the prefabricated fracture rod, which is characterised by a low yield strength, tending to deform plastically in areas of stress concentration. This can lead to stress concentrations in these areas, thus making cracks easier to generate for accelerated life testing. The piston, piston rod, and connecting parts were made from 40 Cr. The photograph in Figure 3 provides a visual representation of the fully assembled accelerated life-test structure. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Stroke & 0.115 m \\ Connecting rod length & 0.3 m \\ Cylinder diameter & 0.195 m \\ Piston rod diameter & 0.035 m \\ Connecting rod length & 0.3 m \\ Piston rod connection thread & M33 \(\times\) 1.5 \\ Rated speed & 740 RPM \\ Rated discharge pressure & 0.6 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Technical parameters of the reciprocating compressor. Figure 3: Photograph of the assembled accelerated life structure. Figure 2: Design of the accelerated life-test components. To determine the dimensions of the prefabricated rod, calculations based on operating loads and material fatigue properties are essential. In a reciprocating compressor, the crankshaft is driven and rotated by external forces, which are then translated into a reciprocating motion of the piston through a connecting rod mechanism; the piston rod of a compressor is subjected to cyclical alternating tensile and compressive loads during operation, as depicted in Figure 4. The crankshaft has a radius of \(r\). The motion of the connecting rod can be reduced to two masses: one moving with the centre of the crank pin and the other moving with the centre of the crosshead pin. The length of the connecting rod is \(l\), and the ratio of \(r\) to \(l\) is \(\lambda\). The reciprocating inertial force is the product of the reciprocating inertial mass and the acceleration, and its direction is always opposite to that of the acceleration. Thus, the reciprocating inertia force generated can be calculated as  
\[F_{Is}=-m_{s}a=-m_{s}r\omega^{2}(cos\theta+\lambda sin2\theta) \tag{1}\]  
where the instantaneous position of the crank is expressed as the angle \(\theta\) between the crank and the centre line of the cylinder.