﻿ 船舶推进轴系振动对轴承承载特性的影响
 舰船科学技术  2019, Vol. 41 Issue (4): 71-75 PDF

Research on influence of ship propulsion shaft vibration to bearing bearing characteristics
ZHANG Xin-bao, WANG Ding
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Abstract: This paper takes the actual ship propulsion shafting as the research object, considers the influence of propeller excitation force magnitude and frequency, obtains the bearing state of the radial sliding bearing when the propulsion shafting vibrates, and deduces the expression of liquid film stiffness and bearing capacity of the radial sliding bearings, analyzes the effect of propulsive shaft vibration caused by propeller excitation on bearing characteristics of radial sliding bearings. The research results show that the propeller excitation force will cause the periodic fluctuating of bearing capacity and liquid film stiffness of the radial lubricated bearing. The bearing characteristics of the bearing are different under different load frequencies, and the bearing characteristics of the bearing are more fluctuating under heavy load conditions. Obviously, bearings must be properly designed to improve the bearing's bearing capacity, and thus ensure the stability of the entire propulsion shaft system.
Key words: propulsion shafting     radial sliding bearings     liquid film stiffness     bearing characteristics
0 引　言

1 Reynolds方程的求解原理

 $\frac{\partial }{{\partial x}}\left( {\frac{{{h^3}}}{\eta }\frac{{\partial p}}{{\partial x}}} \right) + \frac{\partial }{{\partial z}}\left( {\frac{{{h^3}}}{\eta }\frac{{\partial p}}{{\partial z}}} \right) = 6U\frac{{\partial h}}{{\partial x}}\text{。}$ (1)

 图 1 轴瓦平面网格划分与差商示意图 Fig. 1 Bearing shell mesh and differential quotient diagram
2 轴承承载特性分析 2.1 推进轴系振动时轴承承载力

 $\left\{ {\begin{array}{*{20}{c}} {{y_{\rm{z}}}} \\ {{\theta _z}} \\ M \\ Q \end{array}} \right\}_i^R = \left[ {\begin{array}{*{20}{c}} 1&0&0&0 \\ 0&1&0&0 \\ 0&0&1&0 \\ { - k + m{\omega ^2}}&0&0&1 \end{array}} \right]\left\{ {\begin{array}{*{20}{c}} {{y_z}} \\ {{\theta _z}} \\ M \\ Q \end{array}} \right\}_i^L,$ (2)

 $\left\{ {\begin{array}{*{20}{c}} {{y_z}} \\ {{\theta _z}} \\ M \\ Q \end{array}} \right\}_i^L = \left[ {\begin{array}{*{20}{c}} 1&{{l_i}}&{\dfrac{{{l^2}}}{{2EJ}}}&{\dfrac{{{l^3}}}{{6EJ}}} \\ 0&1&{\dfrac{l}{{EJ}}}&{\dfrac{{{l^2}}}{{2EJ}}} \\ 0&0&1&{{l_i}} \\ 0&0&0&1 \end{array}} \right]\left\{ {\begin{array}{*{20}{c}} {{y_z}} \\ {{\theta _z}} \\ M \\ Q \end{array}} \right\}_{i - 1}^R\text{。}$ (3)

 $F = {F_1} + {F_2} = {F_1} + {A_2}\sin wt,$ (4)

2.2 液膜刚度的计算

 $\left\{ {\begin{array}{*{20}{c}} {{F_x} = \displaystyle\int_{ - 1}^1 {\displaystyle\int_0^{2{\text{π}} } {{p_{ij}}\sin \left( {\theta + \varphi } \right){\rm d}\varphi {\rm d}\lambda } } }\approx\\ { \displaystyle\sum\nolimits_{i = 1}^{m + 1} {\sum\nolimits_{j = 1}^{n + 1} {{p_{ij}}\sin \left( {\theta + {\varphi _i}} \right)\Delta \varphi \Delta \lambda } } },\\ {{F_y} = \displaystyle\int_{ - 1}^1 {\int_0^{2{\text{π}} } {{p_{ij}}\cos \left( {\theta + \varphi } \right){\rm d}\varphi {\rm d}\lambda } } }\approx\\ { \displaystyle\sum\nolimits_{i = 1}^{m + 1} {\sum\nolimits_{j = 1}^{n + 1} {{p_{ij}}\cos \left( {\theta + {\varphi _i}} \right)\Delta \varphi \Delta \lambda } } }\text{。} \end{array}} \right.$ (5)

 $\left\{ {\begin{array}{*{20}{c}} {{K_{xx}} = {{\lim }_{\Delta x \to 0}}\dfrac{{\Delta {F_x}}}{{\Delta x}} = \dfrac{{\partial {F_x}}}{{\partial x}}},\\ {{K_{yx}} = {{\lim }_{\Delta x \to 0}}\dfrac{{\Delta {F_y}}}{{\Delta x}} = \dfrac{{\partial {F_y}}}{{\partial x}}},\\ {{K_{xy}} = {{\lim }_{\Delta y \to 0}}\dfrac{{\Delta {F_x}}}{{\Delta y}} = \dfrac{{\partial {F_x}}}{{\partial y}}},\\ {{K_{yy}} = {{\lim }_{\Delta y \to 0}}\dfrac{{\Delta {F_y}}}{{\Delta y}} = \dfrac{{\partial {F_y}}}{{\partial y}}}\text{。} \end{array}} \right.$ (6)

 图 2 轴承的刚度阻尼简化模型 Fig. 2 Bearing stiffness and damping simplified model

 图 3 扰动位移示意图 Fig. 3 Disturbance displacement diagram

 ${e_2} \!=\! \sqrt {O{M^2} \!+\! {{\left( {{O_1}M \!+\! \Delta x} \right)}^2}} \!=\! \sqrt {e_1^2 \!+\! \Delta {x^2} \!+\! 2\Delta x{e_1}\sin {\theta _1}} ,$ (7)

 ${\theta _2} = {\cos ^{ - 1}}\left( {OM/{e_2}} \right) = {\cos ^{ - 1}}\left( {{e_1}\cos {\theta _1}/{e_2}} \right)\text{。}$ (8)

 $\left\{ {\begin{array}{*{20}{c}} {{K_{xx}} = \dfrac{{F'_x - {F_x}}}{{\Delta x}}},\\ {{K_{yx}} = \dfrac{{F'_y - {F_y}}}{{\Delta x}}}\text{。} \end{array}} \right.$ (9)

3 算例分析

3.1 推进轴系激振力幅值的影响

 图 4 激振力幅值对轴承承载力影响 Fig. 4 The effect of exciting frequency on bearing capacity

 图 5 激振力幅值对轴承承载刚度影响 Fig. 5 The effect of exciting frequency on bearing stiffness

3.2 推进轴系激振力频率的影响

 图 6 激振力频率对轴承承载力影响 Fig. 6 The effect of exciting frequency on bearing capacity

 图 7 激振力频率对轴承承载刚度影响 Fig. 7 The effect of exciting frequency on bearing stiffness

 图 8 频率与承载力幅值关系曲线 Fig. 8 Frequency and bearing force amplitude curve
4 结　语

1）激振力幅值越大，轴承承载力及承载刚度的波动范围越大，且承载刚度的波动范围增加越明显，降低激振力的幅值大小可有效改善轴承的承载性能。

2）轴承承载力及承载刚度的波动范围随激振力频率改变而改变，部分频率范围甚至导致轴承承载失效，选择合理的运行频率，适当增加转速，可以提高轴承承载的稳定性。

3）合理设计轴承结构参数，同时提高轴承的安装精度，可以有效改善轴承的承载性能，保证推进轴系的运行稳定性。

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