# Dynamic Analysis for a Reciprocating Compressor System with Clearance Fault
## 3 Computational Dynamic Analysis  
### Computational Simulation of the Design Model and a Typical Model  
Figure 5a displays the construction view of the design model. The commercial software MSC_ADAMS has powerful abilities in parametric modeling and can establish and solve the dynamic equations automatically. Thus, we employed ADAMS to establish the model. As shown in Figure 5a, the model consisted of two motors and a crankshaft, linkage, crosshead, piston, cylinder, cam, follower, and guide bearing. The whole parts were built with NX.UG software and imported into the ADAMS software via the Parasoid format file. After that, we finished the model in ADAMS via setting the material properties of the parts, building a kinematic pair according to the motion relationship between the parts, and creating the joint motion and the spring force. In this case, the material of the parts was set to steel,  
Figure 4: The contour of the designed cam. except for the guide bearing, for which the material was set to copper. All the kinematic pairs in the model, including the revolute joints between the crankshaft and motor shaft, between the crankshaft and linkage, between the linkage and crosshead, between the cam and the other motor shaft, and the translational joints between the crosshead and its guide, between the piston and cylinder, and between the follower and the bearing, were set to ideal joints. Table 1 provides the parametric characteristics of the model. Table 2 shows the material properties of these parts. To validate the model, a typical model of the reciprocating compressor was also established in this paper. Figure 5b displays the construction view of the typical model. The typical model had the same parametric characteristics as the design model--except for the load model, which relied on Equation (6)--and they were realized by the IF function in the ADMAS software. Equation (13) shows the IF function of the load:  
\[ \begin{array}{l}IF(MOD(time*3000,360)-38.95:\ 3086.6*(20/(740-compressor.crosshead _dx))*1.4,\ 824.6;\\ IF(MOD(time*3000,360)-180:\ 824.6,\ 824.6;\\ IF(MOD(time*3000,360)-294.2:\ 824.6*(260/(740-compressor.crosshead_dx))*1.4,\ 3086.6,3086.6 ))\ )\end{array}  \tag{13}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Characteristics** & **Value** \\ \hline Length of the crankshaft (mm) & 120 \\ Length of the linkage (mm) & 600 \\ Stroke of the piston (mm) & 240 \\ Radius of the piston (mm) & 50 \\ Pressure in the suction process (MPa) & 0.105 \\ Pressure in the discharge process (MPa) & 0.393 \\ Speed of the crankshaft (rpm) & 500 \\ Radius of the base circle of the cam (mm) & 200 \\ Stroke of the follower (mm) & 120 \\ Length of the spring(mm) & 340 \\ Stiffness coefficient of the spring (N/mm) & 20 \\ Damping coefficient of the spring (N/(mm*s)) & 0.023 \\ \multicolumn{2}{c}{Preload of the spring (N)} & 800 \\ Speed of the cam (rpm) & 500 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation characteristics. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Density (kg/mm3)** & **Young’s Modulus (N/mm2)** & **Poisson’s Ratio** \\ \hline steel & \(7.801\times 10^{-6}\) & \(2.07\times 10^{5}\) & 0.29 \\ copper & \(8.906\times 10^{-6}\) & \(1.19\times 10^{5}\) & 0.326 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material performance. Figure 5: The model of the reciprocating compressor under ADAMS: (**a**) the design model and (**b**) the typical model. where \"_compressor.crosshead_dx_\" is the measured displacement of the crosshead and piston and \"_time_\" is the time. For the rigid system, ADAMS used the modified Newton-Raphson iterative algorithm to solve the dynamic differential equation and provided four integrators (including GSTIFF, WSTIFF, DSTIFF, and CONSTANT_BDF) and three kinds of an integral formulation (including I3, SI2, and SI1).