# Fatigue Life Analysis of Cylindrical Roller Bearings Considering Elastohydrodynamic Lubrications
## 6 Conclusions  
This study first employed the multigrid method to solve the isothermal line contact elastohydrodynamic lubrication problem and then established a quasi-static model for cylindrical roller bearings considering the effects of elastohydrodynamic lubrication based on the numerical solutions. Subsequently, the global fatigue life of cylindrical roller bearings was calculated using the modified Lundberg-Palmgren life theory, with systematic investigations into the influence of radial load, inner ring rotational speed, and lubricant viscosity parameters on bearing fatigue life. Finally, an experimental validation analysis is conducted for bearing fatigue life. The conclusions are as follows:  
1. The introduction of lubrication significantly affects bearing life. Under elastohydrodynamic lubrication conditions, even when the geometric approach quantities between rollers and bearing races in non-loaded zones are negative (indicating no direct contact), small contact loads still exist between rollers and the inner ring. The calculated contact loads are slightly greater overall than those predicted by the De Mul model (neglecting elastohydrodynamic lubrication), consequently leading to reduced computational bearing life.
2. The lubrication-modified model demonstrates significant convergence trends in the prediction deviations between calculated and measured values for bearing No. 1, No. 5, and No. 6 compared with the De Mul model (lubrication-neglected), showing an approximately 16.1% improvement (mean value) in prediction accuracy over traditional models. This confirms that lubrication enhances the alignment between computational bearing life models and actual service life.  
Under elastohydrodynamic lubrication conditions, increasing the bearing rotational speed increases the entrainment velocity between the cylindrical rollers and bearing races, while simultaneously reducing the overall fatigue life of the cylindrical roller bearings. Special attention should be paid to the effects of elastohydrodynamic lubrication on fatigue life at excessive rotational speeds.
4 Under elastohydrodynamic lubrication conditions, increasing the initial lubricant viscosity progressively decreases the overall fatigue life of cylindrical roller bearings. Particular caution is required when using high-viscosity lubricants regarding their impact on bearing fatigue life, specifically potential oil starvation phenomena and power loss.  
K.Z.: Writing--review and editing, Funding acquisition; Z.H.: Writing--review and editing, Writing--original draft; Q.L.: Data curation, Validation; R.Z.: Data curation. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation (China) (11672186) and the Shanghai association for the promotion of scientific and technological achievements (SPAT) (LM2018-5).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors would like to sincerely thank their lab mates [PERSON], [PERSON], and [PERSON] for their continuous encouragement throughout this research endeavor and for their valuable technical assistance.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.