﻿ 弹性流体润滑技术在船用滑动轴承的应用
 舰船科学技术  2022, Vol. 44 Issue (24): 35-38    DOI: 10.3404/j.issn.1672-7649.2022.24.008 PDF

1. 江苏海事职业技术学院，江苏 南京 211199;
2. 九江职业技术学院船舶工程学院，江西 九江 332007

Application of elastic fluid lubrication technology in the marine sliding bearings
HUI Jie1, ZUO Qian2, LIU Zhao-liang1, SUN Chang-fei1
1. Jiangsu Maritime Institute, Nanjing 211170, China;
2. Jiujiang Vocational and Technical College, Ship Engineering College, Jiujiang 332007, China
Abstract: Slide bearing is a new type of support structure, which is widely used in the important parts of ships, such as stern shaft, middle shaft, motor crankshaft, etc. The bearing capacity, maintenance efficiency, reliability and service life of the ship bearing will have an important influence on the working performance of its transmission and the main motor. Therefore, it is particularly necessary to study the elastic fluid lubrication of ship gear bearings. The analysis and study of the elastic fluid lubrication properties can help improve the reliability, carrying capacity and efficiency.
Key words: elastic fluid     sliding bearing     lubrication characteristics
0 引　言

1 船用滑动轴承润滑特性分析 1.1 经典二维Reynolds方程

 $\begin{split}\frac{\partial }{{{\partial _{{x}}}}}\left( {\frac{{\rho {{{h}}^3}}}{\eta }\frac{{\partial {{p}}}}{{{\partial _{{x}}}}}} \right) + & \frac{\partial }{{{\partial _{{y}}}}}\left( {\frac{{\rho {{{h}}^3}}}{\eta }\frac{{\partial {{p}}}}{{\partial {{y}}}}} \right) = 6\left( {{U_1} - {U_2}} \right)\frac{{\partial \left( {\rho {{h}}} \right)}}{{\partial {{x}}}} +\\ & 6\rho {{h}}\frac{\partial }{{{\partial _{{x}}}}}\left( {{U_1} + {U_2}} \right) + 12\frac{{\partial \left( {\rho {{h}}} \right)}}{{\partial {{t}}}}。\end{split}$

 $\frac{\partial }{{{\partial _{{x}}}}}\left( {\frac{{{{{h}}^3}}}{\eta }\frac{{\partial {{p}}}}{{{\partial _{{x}}}}}} \right) + \frac{\partial }{{{\partial _{{y}}}}}\left( {\frac{{{{{h}}^3}}}{\eta }\frac{{\partial {{p}}}}{{\partial {{y}}}}} \right) = 6U\frac{{\partial {{h}}}}{{\partial {{x}}}} 。$

1.2 分析模型的无量纲化

Reynolds的量化公式具有结构紧凑、模型变量小的特点，一般用于复杂结构的轴承，重点分析其主要参数对其润滑特性的影响。根据经验，一般无量纲的Reynolds方程为：

 $\frac{\partial }{{\partial \theta }}\left( {{H^3}\frac{{\partial P}}{{\partial \theta }}} \right) + {\left( {\frac{D}{L}} \right)^2}\frac{\partial }{{\partial \lambda }}\left( {{H^3}\frac{{\partial P}}{{\partial \lambda }}} \right) = \frac{{\partial H}}{{\partial \theta }} 。$
2 船用滑动轴承弹性流体润滑分析 2.1 弹性变形的计算方法

 图 1 六面体单元与坐标 Fig. 1 The hexahedral units and coordinates

 $\begin{gathered} x = \sum\limits_{i = 1}^8 {{N_i}} \left( {\xi ,\eta ,\zeta } \right){x_i}，\\ y = \sum\limits_{i = 1}^8 {{N_i}} \left( {\xi ,\eta ,\zeta } \right){y_i}，\\ z = \sum\limits_{i = 1}^8 {{N_i}} \left( {\xi ,\eta ,\zeta } \right){z_i}。\\ \end{gathered}$

 ${N_i} = \frac{1}{8}\left( {1 + {\xi _i}} \right)\left( {1 + {\eta _i}} \right)\left( {1 + {\zeta _i}} \right) 。$

2.2 轴承静特性分析

 图 2 偏位角与偏心率 Fig. 2 Deflection angle and eccentricity

 图 3 平衡半圆图 Fig. 3 Balance semicircle diagram

3 弹性流体润滑技术应用分析

3.1 温度场控制方程与边界条件

 $\begin{split}& c\rho \left( {u\frac{{\partial T}}{{\partial x}} + v\frac{{\partial T}}{{\partial y}} + w\frac{{\partial T}}{{\partial z}} + \frac{{\partial T}}{{\partial t}}} \right) = k\left( {\frac{{{\partial ^2}T}}{{\partial {x^2}}} + \frac{{{\partial ^2}T}}{{\partial {y^2}}} + \frac{{{\partial ^2}T}}{{\partial {z^2}}}} \right) - \\ &\qquad\qquad \frac{T}{\rho }\frac{{\partial \rho }}{{\partial T}}\left( {u\frac{{\partial p}}{{\partial x}} + v\frac{{\partial p}}{{\partial y}} + w\frac{{\partial p}}{{\partial z}} + \frac{{\partial p}}{{\partial t}}} \right) + \varPhi。\end{split}$

 ${c_p}\rho \left( {u\frac{{\partial p}}{{\partial x}} + v\frac{{\partial p}}{{\partial y}} + w\frac{{\partial p}}{{\partial z}}} \right) = k\frac{{{\partial ^2}T}}{{\partial {z^2}}} - \frac{T}{\rho }\frac{{\partial \rho }}{{\partial T}}\left( {u\frac{{\partial p}}{{\partial x}} + v\frac{{\partial p}}{{\partial y}}} \right) + \varPhi 。$

 $\varPhi = \eta \left[ {{{\left( {\frac{{\partial u}}{{\partial z}}} \right)}^2} + {{\left( {\frac{{\partial v}}{{\partial z}}} \right)}^2}} \right] + \left( {{U_2} - {U_1}} \right)\frac{{{\mu _c}{p_c}{A_c}}}{{{h_T}A}} \text{，}$

 $\frac{1}{{{r_b}^2}}\frac{{{\partial ^2}{T_b}}}{{\partial {\theta ^2}}} + \frac{1}{{{r_b}}}\frac{{\partial {T_b}}}{{\partial {r_b}}} + \frac{{{\partial ^2}{T_b}}}{{{\partial _{{r_b}}}^2}} + \frac{{{\partial ^2}{T_b}}}{{\partial {y^2}}} = 0 \text{，}$

 $\left\{ {\begin{array}{*{20}{l}} {{T_i} = {T_j}}，\\ {\displaystyle\int_0^{2\text{π} } {\frac{{\partial {T_j}}}{{\partial z}}{\rm{d}}\theta = 0} } 。\end{array}} \right.$

 $\left\{ {\begin{array}{*{20}{l}} {{T_b}^{inled} = {a_b} \cdot {r_b} + {b_b}}，\\ {{T_l}^{inled} = {a_l} \cdot {z^2} + {b_l} \cdot z + {c_l}} 。\end{array}} \right.$

3.2 稳态弹流润滑求解

4 结　语

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