# Fatigue Life Analysis of Cylindrical Roller Bearings Considering Elastohydrodynamic Lubrications
## 4 Result Calculation and Analysis  
This study mainly analyzes the support bearings on the main shaft of an SFW250-8/850 horizontal hydraulic generator [27] (located at the left end of the main shaft of the generator). The schematic diagram of the generator structure is shown in Figure 5.  
The relevant parameters for this cylindrical roller bearing are shown in Table 2.  
Taking the cylindrical roller bearing as the research object, the relevant working condition parameters of the bearing in the horizontal hydraulic generator are selected according to GB/T 7894-2023 [28], and the working condition parameters of the bearing are shown in Tables 3 and 4.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Constants and Exponents** & **0.1 \textless{} C\textless{} 0.4** & **0.4 \textless{} C \textless{} 1** & **1 \textless{} C \textless{} 4** \\ \hline \(\alpha_{1}\) & 0.054381 & 0.19087 & 0.071739 \\ \(\alpha_{2}\) & 0.83 & 0.83 & 0.83 \\ \(\alpha_{3}\) & 1/3 & 1/3 & 1/3 \\ \(\alpha_{4}\) & \(-9.3\) & \(-9.3\) & \(-9.3\) \\ \(\mathrm{c}_{1}\) & 2.5671 & 2.5671 & 2.5671 \\ \(\mathrm{c}_{2}\) & 2.2649 & 1.9987 & 1.9987 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Values of the constants and exponents.  
The primary objective of this study is to investigate the influence of elastohydrodynamic lubrication conditions on bearing contact load distribution and ultimately on bearing fatigue life, with the radial clearance set to zero. To rigorously validate the reliability of the proposed theoretical model, the modified reference rating life of cylindrical roller bearings under general loading conditions is calculated according to ISO/TS 16281:2008 [29; 30; 31]. The computational results from the [PERSON]'s quasi-static model for cylindrical roller bearings [32] are compared with those derived from the theoretical model proposed herein.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Units** & **Numeric Value** \\ \hline Load F\({}_{\text{r}}\) & KN & 240 \\ Rotate speed N & r/min & 900 \\ Rotate speed N & r/min & 900 \\ Lubricant dynamic viscosity \(\eta\) & Pa-s & 0.19 \\ Lubricating oil kinematic viscosity \(\
u\) & m\({}^{2}\)/s & \(2.2\times 10^{-4}\) \\ Lubricating oil kinematic viscosity \(\
u\) & m\({}^{2}\)/s & \(2.2\times 10^{-4}\) \\ Lubricating oil density \(\rho\) & kg/m\({}^{3}\) & 884 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Severe-load operating parameters.  
Figure 5: Generator structure diagram.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Units** & **Numeric Value** \\ \hline Bearing outer diameter D & mm & 260 \\ Bearing bore d & mm & 120 \\ Outer ring raceway diameter D\({}_{\text{o}}\) & mm & 230 \\ Inner ring raceway diameter D\({}_{\text{i}}\) & mm & 154 \\ Cylindrical roller diameter D\({}_{\text{b}}\) & mm & 38 \\ Bearing pitch diameter D\({}_{\text{d}}\) & mm & 193 \\ Number of cylindrical rollers Z & & 14 \\ Bearing width B & mm & 55 \\ Effective length of cylindrical rollers l & mm & 36 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of cylindrical roller bearings.  
In [PERSON]'s quasi-static model for contact load analysis, the mechanism exclusively accounts for rolling element centrifugal forces while neglecting the dynamic lubrication effects between rollers and races. Furthermore, this model confines load generation to geometric approach quantities exceeding zero between the rolling elements and raceways. To simplify the boundary conditions, the analysis is restricted to bearing component motion in the \(\mathrm{x_{i}O_{i}z_{i}}\) plane under unidirectional pure radial loading.