# Fatigue Life Analysis of Cylindrical Roller Bearings Considering Elastohydrodynamic Lubrications
## 5 Bearing Fatigue Life Test
### Comparison Between Fatigue Life Test Results and Model Calculation Results  
To verify the accuracy of the theoretical model, this study conducted a comparative analysis of bearing fatigue test results. The calculated bearing life (\(\text{L}_{\text{De}}\)) obtained using the De Mul model (without considering lubrication effects), the theoretical model considering lubrication correction (\(\text{L}_{\text{E}}\)), and the fatigue test results (\(\text{L}_{\text{S}}\)) were compared. The test results are presented in Table 10.  
An analysis of Table 10 reveals that discrepancies exist between the model calculation results and the actual experimental data, with theoretical model predictions generally overestimating experimental fatigue life. The fatigue life of test bearings exhibits substantial variability, which primarily stems from the inherent stochastic nature of material fatigue. Even bearings with identical structures, dimensions, and manufacturing processes still demonstrate significant discrepancies in service life under equivalent operating conditions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **De Mul Model/r** & **The Model Presented in This Study/r** & **Test Result/r** & **Deviation 1/\%** & **Deviation 2/\%** \\ \hline No. 1 & \(1.72\times 10^{8}\) & \(1.47\times 10^{8}\) & \(1.40\times 10^{8}\) & \(18.7\) & \(5.2\) \\ No. 2 & \(1.72\times 10^{8}\) & \(1.47\times 10^{8}\) & \(1.52\times 10^{8}\) & \(11.6\) & \(-3.1\) \\ No. 3 & \(1.72\times 10^{8}\) & \(1.47\times 10^{8}\) & \(1.57\times 10^{8}\) & \(8.8\) & \(-6.4\) \\ No. 4 & \(1.72\times 10^{8}\) & \(1.47\times 10^{8}\) & \(1.38\times 10^{8}\) & \(19.5\) & \(6.1\) \\ No. 5 & \(1.99\times 10^{7}\) & \(1.62\times 10^{7}\) & \(1.57\times 10^{7}\) & \(20.7\) & \(2.7\) \\ No. 6 & \(1.99\times 10^{7}\) & \(1.62\times 10^{7}\) & \(1.49\times 10^{7}\) & \(25.1\) & \(8.0\) \\ No. 7 & \(1.99\times 10^{7}\) & \(1.62\times 10^{7}\) & \(1.78\times 10^{7}\) & \(10.6\) & \(9.7\) \\ No. 8 & \(1.99\times 10^{7}\) & \(1.62\times 10^{7}\) & \(2.22\times 10^{7}\) & \(-11.7\) & \(-38.3\) \\ \hline \hline \end{tabular}  
Notes: deviation\(1=[(\text{L}_{\text{De}}-\text{L}_{\text{S}})/\text{L}_{\text{S}}]\cdot 100\%\); deviation\(2=[(\text{L}_{\text{E}}-\text{L}_{\text{S}})/\text{L}_{\text{S}}]\cdot 100\%\).  
\end{table} 
Table 10: Comparison of bearing fatigue life calculation results. Figure 15: Photographs of the failed components. (**a**) A spalling phenomenon occurred on the roller. (**b**) Slippage of the bearing inner ring was observed. (**c**) A slight indentation was observed on the bearing outer ring. (**d**) Spalling occurred on the bearing inner ring. A comparative analysis after eliminating abnormal data shows that the measured average life under light-load conditions reaches 1.4715 \(\times\) 10\({}^{8}\) revolutions, while under heavy-load conditions, it reduces to 1.617 \(\times\) 10\({}^{7}\) revolutions. The De Mul model demonstrates an average error of 16.4% compared with experimental results, whereas the lubrication-considered model shows a reduced average error of 5.88%. These deviation values confirm that the bearing life prediction model based on the De Mul model exhibits insufficient prediction accuracy due to inadequate consideration of the influencing factors. An analysis of Tables 8 and 9 indicates that bearing No. 1, No. 5, and No. 6 exhibited fatigue flaking and microcracking phenomena in their components post-testing, with their failure modes classified as fatigue failures. Therefore, these three sets of experimental results were selected as validation benchmarks for the established fatigue life prediction model. As shown in Table 10, when lubrication was not considered, the test results of bearing No. 1 exhibited an 18.7% deviation from model calculations, while incorporating the effects of lubrication factors reduced this error to 5.2%, representing a reduction of 12.9 percentage points; for specimen No.