## 3 Test Results and Analysis
### Vertical Compression Performance of Bearings
#### 3.1.4 Results of Vertical Stiffness  
We assumed \(\mathrm{P_{1}}\) and \(\mathrm{P_{2}}\) as the small pressure and the larger pressure in the third cycle, and gave them the values of 0.7 P and 1.3 P, respectively. We assumed \(\mathrm{Y_{1}}\) and \(\mathrm{Y_{2}}\) were the smaller displacement and the larger displacement in the third cycle, respectively. The vertical compression stiffness of all the bearings under various test cases was calculated according to Equation (7), as shown in Figures 8-10. \[\mathrm{K_{V}}=\frac{\mathrm{P_{2}}-\mathrm{P_{1}}}{\mathrm{Y_{2}}-\mathrm{Y_ {1}}} \tag{7}\]  
Figure 5: Vertical load–displacement curves under different loading frequencies: (**a**) HDRB-LSF; (**b**) TLRB; (**c**) LRB. Figure 6: Vertical load–displacement curves under different vertical pressures: (**a**) HDRB-LSF; (**b**) TLRB; (**c**) LRB. Figure 8: Vertical stiffness of HDRB-LSF. Figure 7: Vertical load–displacement curves under different pre-pressures: (**a**) HDRB-LSF; (**b**) TLRB; (c) LRB. The error of the vertical stiffness for the bearings is equal to the difference between the theoretical value and the test value divided by the theoretical value. Due to the limited length of the article, Table 4 only shows the comparison results of theoretical and experimental values of vertical stiffness when the vertical pressure is 3400 kN and the pre-pressure is 0 kN. As can be seen from Figures 8-10, under different loading cases the vertical stiffness of LRB is largest in the range between 2050 kN/m and 2450 kN/m. The vertical stiffness of HDRB-LSF takes second place within the range of 1050 kN/m and 1450 kN/m, while the vertical stiffness of TLRB is the lowest, varying from 450 kN/m and 850 kN/m. With the increase in loading frequency, the vertical stiffness of almost all bearings has an increase in different amplitude. When the loading frequency varies from 0.01 Hz to 0.02 Hz, the vertical stiffness values of the HDRB-LSF, LRB, and TLRB improve by 1.3-3.3%, about 2.7%, and 1.1-6.6%, respectively. Whereas when the loading frequency is enlarged from 0.05 Hz to 0.1 Hz, the vertical stiffness values of the HDRB-LSF, LRB, and TLRB improve by 9.1-12.1%, 3.2-4.6%, 13-19.6%. Hence, it can be concluded that the vertical stiffness of LRB is relatively stable, while that of HDRB-LSF and TLRB is sensitive to the change of loading frequency. It can be seen from the table that it is not certain whether the test value \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Loading Frequency (Hz)** & **HDRB-LSF** & **TLRB** & **LRB** \\ \hline
0.01 & 68.30 & \(-9.53\) & 1.16 \\
0.02 & 70.42 & \(-8.49\) & 3.91 \\
0.05 & 81.96 & 6.19 & 7.44 \\
0.1 & 98.88 & 22.59 & 11.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Vertical stiffness error between theoretical value and test value (%). Figure 10: Vertical stiffness of LRB. Figure 9: Vertical stiffness of TLRB. or theoretical value is more remarkable for the vertical stiffness of TLRB, while the test values of vertical stiffness for LRB and HDRB-LSF always surpass the theoretical value. Additionally, the margin of error between the test values and the theoretical values of vertical stiffness for the LRB and TLRB are small, which is basically in line with the specific design requirements. The test values of the vertical stiffness for HDRB-LSF are larger than the theoretical value, which means that it is biased towards safety in the bearing design. However, this error has exaggerated what needs to be corrected.