## 6 Discussion
### Effect of Preload Distribution on Tightening Performance  
In order to explore the influence of preload distributions on the tightening performance of three bolted joints with double nuts, the preload distributions of the upper and lower nuts were changed by changing the rotational angles of the nuts. The total preload was approximately 30 kN, and the preloads of the upper nut were changed to 5, 10, 15, 20, 25, and 30 kN. The discrete data points and relationship curves of tightening torques and preloads in the bolted joint installed with regular double nuts are shown in Figure 24. From the figure, it can be observed that the curve slopes in the two stages are almost the same for different preload distributions of upper and lower nuts. However, the values of preload when the tightening in the first stage is finished are different; the preload displayed here is called the transition preload (TR). The assignment of a larger preload to the upper nut requires a smaller TR to generate the same total preload during the process of tightening. This results in final tightening torques (FFTs and SFTs) in the upper and lower nuts being different, as shown in Table 5. It can be observed that as the preload assigned to the upper nut is increased, the FFT of the lower nut is decreased. Table 5 also shows the maximum final torque (MFT), which represents the degree of tightening difficulty. The MFT is the largest among these different preload distributions for the preload of 30 kN assigned to the upper nut, followed by preloads of 5, 10, 15, and 25 kN assigned to the upper nut. When a preload of 20 kN is assigned to the upper nut, the MFT is at a minimum, with very easy tightening.  
Similarly, the discrete data points and relationship curves of tightening torque and preload in the bolted joints installed with a double-thread bolt and an eccentric double nut were obtained, as shown in Figures 25 and 26, respectively. The preloads of the upper nut were also set to 5, 10, 15, 20, 25, and 30 kN in FEA. The changes in the curves during the two stages showed the same tendency as those of the regular bolted joints under different preload distributions of the upper and lower nuts. It was obvious that the slope of the curve at the second stage in the bolted joint installed with an eccentric double nut was very high, indicating more tightening difficulties for the upper nut. The FFT, SFT, and MFT for tightening of the two bolted joints at the two stages were calculated as listed in Tables 6 and 7, respectively. We can conclude that the change tendencies of FFT and SFT  
\begin{table}
\begin{tabular}{l c} \hline
**Bolted Joint** & **Index** \\ \hline Regular bolted joint & 0.1101 \\ Plain washer & 0.0935 \\ Variable-diameter nut & 0.0222 \\ Wedge-locking nut & 0.0223 \\ Wedge washer & 0.0408 \\ Regular double nuts & 0.0676 \\ Double-thread bolt connection & 0.0292 \\ Eccentric double nut & 0.0572 \\ \hline \end{tabular}
\end{table}
Table 4: Fatigue damage indexes of bolted joints.  
with increases in the preloads assigned to the upper nut were the same as those of regular bolted joints. Table 6 shows that for the double-thread bolt connection, the MFT was the largest when a preload of 5 kN was assigned to the upper nut, indicating the most difficult tightening. The MFT of 51,222 Nmm obtained when assigning a preload of 25 kN to the upper nut was the smallest. In contrast, with respect to the results of the eccentric double nut presented in Table 7, the largest MFT occurred when a preload of 30 kN was assigned to the upper nut, while the smallest value appeared when a preload of 10 kN was assigned to the upper nut. This demonstrates that for different bolted joints with double nuts, the tightening performance is greatly affected by the preload distribution applied to the upper and lower nuts.