An improved hydrodynamic journal bearing with the boundary slippage

Abstract

The paper presents an analysis for an infinitely wide hydrodynamic journal bearing with artificially designed boundary slippage at the stationary journal surface in the bearing inlet zone. The load-carrying capacity, friction coefficient, attitude angle, shear stress and slipping velocity distributions of the bearing are derived. The results show that the performance of the hydrodynamic journal bearing with modest and small eccentricity ratios can be significantly improved by the designed boundary slippage. When the boundary slippage is widely designed and the contact-fluid interfacial shear strength at the slipping journal surface is low, the carried load of this kind of bearing can be increased nearly by 100 % while its friction coefficient can be reduced by more than 60 %, because of the boundary slippage. The results indicate great application values of the artificial boundary slippage in this kind of hydrodynamic journal bearing.

Appendix

$$ \begin{aligned} I_{1} (\theta ) = & \int {\frac{\cos \theta - \varepsilon }{{(1 - \varepsilon \cos \theta )^{2} }}d\theta = \frac{\sin \theta }{1 - \varepsilon \cos \theta }} \\ I_{2} (\theta ) = & \int {\frac{\theta (\cos \theta - \varepsilon )}{{(1 - \varepsilon \cos \theta )^{2} }}d\theta = \frac{\theta \sin \theta }{1 - \varepsilon \cos \theta } - \frac{\ln |1 - \varepsilon \cos \theta |}{\varepsilon }} \\ I_{3} (\theta ) = & \int {\frac{\sin \theta (\cos \theta - \varepsilon )}{{(1 - \varepsilon \cos \theta )^{2} }}d\theta = \frac{{\varepsilon^{2} - 1}}{{\varepsilon^{2} (1 - \varepsilon \cos \theta )}} - \frac{\ln |1 - \varepsilon \cos \theta |}{{\varepsilon^{2} }}} \\ I_{4} (\theta ) = & \int {\frac{\sin 2\theta (\cos \theta - \varepsilon )}{{(1 - \varepsilon \cos \theta )^{2} }}d\theta = \frac{2}{{\varepsilon^{3} }}\left[ {(\varepsilon^{2} - 1)\left( {\ln\left| {\frac{1}{\varepsilon } - \cos \theta } \right| + \frac{1}{1 - \varepsilon \cos \theta }} \right) - \varepsilon \cos \theta - \ln \left| {\frac{1}{\varepsilon } - \cos \theta } \right|} \right]} \\ I_{5} (\theta ) = & \int {\frac{\sin \theta }{{(1 - \varepsilon \cos \theta )^{2} }}d\theta = \frac{1}{\varepsilon (\varepsilon \cos \theta - 1)}} \\ I_{6} (\theta ) = & \int {\frac{\theta \sin \theta }{{(1 - \varepsilon \cos \theta )^{2} }}d\theta = \frac{\theta }{\varepsilon (\varepsilon \cos \theta - 1)}} + \frac{2}{{\varepsilon \sqrt {1 - \varepsilon^{2} } }}\arctan \left[ {\left| {\sqrt {\frac{1 + \varepsilon }{1 - \varepsilon }} \tan \left( {\frac{\theta }{2}} \right)} \right|} \right] \\ I_{7} (\theta ) = & \int {\frac{{\sin^{2} \theta }}{{(1 - \varepsilon \cos \theta )^{2} }}d\theta = \frac{\sin \theta }{\varepsilon (\varepsilon \cos \theta - 1)}} + \frac{2}{{\varepsilon^{2} \sqrt {1 - \varepsilon^{2} } }}\arctan \left[ {\left| {\sqrt {\frac{1 + \varepsilon }{1 - \varepsilon }} \tan \left( {\frac{\theta }{2}} \right)} \right|} \right] - \frac{\theta }{{\varepsilon^{2} }} \\ I_{8} (\theta ) = & \int {\frac{\sin 2\theta \sin \theta }{{(1 - \varepsilon \cos \theta )^{2} }}d\theta = \frac{\sin 2\theta }{\varepsilon (\varepsilon \cos \theta - 1)}} + \frac{{8 - 4\varepsilon^{2} }}{{\varepsilon^{3} \sqrt {1 - \varepsilon^{2} } }}\arctan \left[ {\left| {\sqrt {\frac{1 + \varepsilon }{1 - \varepsilon }} \tan \left( {\frac{\theta }{2}} \right)} \right|} \right] - \frac{4\sin \theta }{{\varepsilon^{2} }} - \frac{4\theta }{{\varepsilon^{3} }} \\ \end{aligned} $$