# Comparing Bol Implementation Methods in Vibration Testing for Accurate Dynamic Behavior Analysis
## 2 Materials and Methods
### Finite Element Analysis  
In this study, six methods were used to simulate bolt connections: bonded, adaptive bonded, joint, beam, screw, and fixed bolt. The six selected methods in this study represent the functions for a bolt simulation available in ANSYS and Inspire (i.e., widely used commercial software). The adaptive bonded, joint, and beam methods were provided in ANSYS, while the screw and fixed bolt methods were provided in Inspire. Particularly, the adaptive bonded and beam methods were used in previous studies, such as those that analyzed diesel engine vibrations [23], and the joint method was also frequently applied in engine vibration testing research [22]. On the other hand, the screw and fixed bolt methods were included in this study for comparative purposes although they were not widely studied. Figure 3 shows the fastening appearance of the bolts used. In addition, Figure 4 shows the application sequence of the proposed method in a flow chart. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Length [L]** & **Diameter [d]** & \begin{tabular}{c} **Head** \\ **Diameter [D]** \\ \end{tabular} & \begin{tabular}{c} **Hed** \\ **Thickness [K]** \\ \end{tabular} & \
\begin{tabular}{c} **Pitch [p]** \\ \end{tabular} &
\begin{tabular}{c} **Threaded Length [S]** \\ \end{tabular} \\ \hline Dimension (mm) & 40 & 6 & 10 & 4 & 1 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: M6 bolt dimensions. Figure 2: Structure and fastening positions of the vibration test jig for a headlamp. The bonded connection method (Figure 3a) establishes a fully bonded state by applying bonded conditions to the contact area without modeling the bolt. Contact conditions are applied to prevent deformation or slippage on all contact surfaces, ensuring a solid bond between structures. This method assumes that the entire joint area acts as a rigid body, regardless of the contact area, thus representing high bonding strength. This connection method was implemented using the \"Contacts\" tool in ANSYS Connections. The adaptive bonded connection method (Figure 3b) models bolts as line bodies, assigning contact areas and bonded conditions to connect them. To implement this, bolts are created by connecting two line bodies. These line bodies are divided into threaded and non-threaded sections for representation. At the non-threaded sections, contact conditions are applied to the upper and lower edges of the holes to simulate a weaker bonding strength. Additionally, contact conditions are applied between the line bodies and surfaces with internal threads to represent the threaded contact. This connection method was implemented using the \"Contacts\" tool in ANSYS Connections. The joint connection method (Figure 3c) models bolts as line bodies and rigidly connects them with the contact areas. Bolts were created as line bodies in the same way as in the adaptive bonded method. For contact representation, the non-threaded  
Figure 4: Implementation procedures for bolt connections. Figure 3: Implementation methods for bolt connections. sections of the line body were assigned contact conditions at the upper and lower edges. Additionally, the threaded sections were assigned contact conditions between the line body and the internal thread surfaces. This method was implemented using the \"Joint\" tool in ANSYS Connections. The beam connection method (Figure 3d) implements bolts as virtual beam elements and rigidly connects the contact areas. A notable feature of this method is that it does not require prior creation of bolt bodies. Unlike the adaptive bonded method, where bolt contacts are specified separately, the creation of beams directly serves as the bolt representation. Therefore, contact conditions are directly applied to the edge of the surface where the bolt head is fastened and the area on the lower plate where the internal threads are located. This method was implemented using the \"Beam\" tool in ANSYS Connections.