﻿ 非均布变包角可倾瓦轴承性能分析
 舰船科学技术  2016, Vol. 38 Issue (12): 74-78,109 PDF

CHEN Tao, SHAO Gang, YE Sheng-jian
The 703 Research Institute of CSIC, Harbin 150036, China
Abstract: To meet the heavy load, low-speed and other abnormal operating conditions demand for the tilting-pad bearing, a non-uniform change pad-angle tilting-pad bearing is presented. The hydrodynamic lubrication model for the tilting-pad bearing is established, which includes the oil film thickness equation, Reynolds equation, energy equation, viscosity-temperature equation, heat conduction equation and pad tilting torque balance equation. With numerical methods, the model is solved and the static characteristics of the tilting-pad bearing are obtained. The influences of the distribution location of pad pivot and the tilting pad-angle on the lubrication performances of the bearing are studied in detail. The results show that, the smaller bearing pivot angle, the higher the bearing capacity; the minimum film thickness decreases as the tilting pad-angle decreasing, but the maximum film pressure also decreases.
Key words: tilting-pad bearings     reynolds equation     hydrodynamic lubrication model     numerical methods
0 引 言

1 非均布变包角径向可倾瓦轴承润滑模型

 图 1 非均布变包角可倾瓦轴承结构形式 Fig. 1 The structure of non-uniform change pad-angle tilting-pad bearing

 图 2 可倾瓦轴承坐标示意图 Fig. 2 ThePlotter ofTilting-pad bearing
1.1 油膜厚度方程及无量纲方程

 $H = {H_0} + {{\pi}} \left( {{\varphi _i},{\lambda _i}} \right) + \vartheta \left( {{\varphi _i},{\lambda _i}} \right)\text{，}$ (1)
 \begin{aligned} {H_0} = & 1-{\nu _i}\cos \left( {{\beta _i}-{\varphi _i}} \right) + {\varepsilon _i}\cos \left( {{\varphi _i}-\theta } \right)+\\ & {\delta _i}\sin \left( {{\beta _i}-{\varphi _i}} \right)\psi \text{。}\end{aligned} (2)

1.2 油膜压力方程及其无量纲方程

 $\frac{1}{{{r^2}}}\frac{\partial }{{\partial \phi }}(\frac{{{h^3}}}{{12\mu }}\frac{{\partial p}}{{\partial \phi }}) + \frac{\partial }{{\partial z}}(\frac{{{h^3}}}{{12\mu }}\frac{{\partial p}}{{\partial z}}) = \frac{\omega }{2}\frac{{\partial h}}{{\partial \phi }} + \frac{{\partial h}}{{\partial t}}{\text {。}}$ (3)

 $\frac{\partial }{{\partial \phi }}\left( {\frac{{{H^3}}}{{\bar \mu }}\frac{{\partial P}}{{\partial \phi }}} \right) + {\left( {\frac{D}{L}} \right)^2}\frac{\partial }{{\partial \lambda }}\left( {\frac{{{H^3}}}{{\bar \mu }}\frac{{\partial P}}{{\partial \lambda }}} \right) = 3\frac{{\partial H}}{{\partial \phi }} + 6\frac{{\partial H}}{{\partial \tau }}{\text{。}}$ (4)

1.3 油膜能量方程及其无量纲方程

 \begin{aligned} & \left. {\rho {c_v}\left[ {\left( {\frac{{\omega rh}}{2}-\frac{{{h^3}}}{{12\mu r}}\frac{{\partial p}}{{\partial \phi }}} \right)} \right]\frac{1}{r}\frac{{\partial T}}{{\partial \phi }}-\frac{{{h^3}}}{{12\mu }}\frac{{\partial p}}{{\partial z}}\frac{{\partial T}}{{\partial z}}} \right]= \\ & \quad \frac{{\mu {r^2}{\omega ^2}}}{h} + \frac{{{h^3}}}{{12\mu }}\left[ {{{\left( {\frac{1}{r}\frac{{\partial p}}{{\partial \phi }}} \right)}^2} + {{\left( {\frac{{\partial p}}{{\partial z}}} \right)}^2}} \right]-{k_t}\left( {T-{T_s}} \right){\text{。}} \end{aligned} (5)

 \begin{aligned} & \left( {H-\frac{1}{6}\frac{{{H^3}}}{{\bar \mu }}\frac{{\partial P}}{{\partial \phi }}} \right)\frac{{\partial \bar T}}{{\partial \phi }}-\frac{1}{6}{\left( {\frac{D}{L}} \right)^2}\frac{{{H^3}}}{{\bar \mu }}\frac{{\partial P}}{{\partial \lambda }}\frac{{\partial \bar T}}{{\partial \lambda }}= \\ & \!\!{T_c}\frac{{\bar \mu }}{H}\left\{ {1\!\! +\!\! \frac{{{H^4}}}{{12。{{\bar \mu }^2}}}\left[ {{{\left( {\frac{{\partial P}}{{\partial \phi }}} \right)}^2}\!\! +\!\! {{\left( {\frac{D}{L}} \right)}^2}{{\left( {\frac{{\partial P}}{{\partial \lambda }}} \right)}^2}} \right]} \right\} \!-\! {T_d}\left( {\bar T \!-\! {{\bar T}_s}} \right){\text{，}}\!\!\! \end{aligned} (6)

 $\frac{{\partial {{\bar T}_b}}}{{\partial \bar r}}\left| {_{\bar r = 1}} \right. =-\frac{{{\kappa _1}}}{{{k_{exc}}}}R({\bar T_b}\left| {_{\bar r = 1}} \right.-\bar T)\text{，}$

 $\frac{{\partial {{\bar T}_b}}}{{\partial \bar r}}\left| {_{\phi = {\phi _1}}} \right. =-\frac{{{\kappa _2}}}{{{k_{exc}}}}R\left( {{{\bar T}_b}\left| {_{\phi = {\phi _1}}} \right.-{{\bar T}_{bath}}} \right)\text{，}$

 $\frac{{\partial {{\bar T}_b}}}{{\partial \bar r}}\left| {_{\phi = {\phi _2}}} \right. =-\frac{{{\kappa _3}}}{{{k_{exc}}}}R({\bar T_b}\left| {_{\phi = {\phi _2}}} \right.-{\bar T_{bath}})\text{，}$

 $\frac{{\partial {{\bar T}_b}}}{{\partial \lambda }}\left| {_{\lambda = 1}} \right. =-\frac{{{\kappa _4}}}{{{k_{exc}}}}R({\bar T_b}\left| {_{\lambda = 1}} \right.-{\bar T_{bath}})\text{，}$

 $\frac{{\partial {{\bar T}_b}}}{{\partial \bar r}}\left| {_{\bar r = {{\bar R}_{ep}}}} \right. =-\frac{{{\kappa _5}}}{{{k_{exc}}}}R({\bar T_b}\left| {_{\bar r = {{\bar R}_{ep}}}} \right.-{\bar T_{bath}})\text{，}$

1.6 瓦块力矩平衡方程及其无量纲方程

 ${M_i} = \int_{-L/2}^{{\kern 1pt} L/2} {\int_{{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\phi _{{\rm{i}}2}}}^{{\kern 1pt} {\kern 1pt} {\phi _{{\rm{i}}1}}} {p\sin ({\beta _i}-{\phi _i})} } {r^2}{\rm d}\phi {\rm d}z = 0\text{，}$ (10)

 \begin{aligned} {{\bar M}_i} =& \int_{-1}^{ 1} {\int_{{\phi _{i2}}}^{{\phi _{i1}}} {P\sin ({\beta _i}-{\phi _i})} } {\rm d}\phi {\rm d}\lambda= \\ & {M_i}/({\mu _0}\omega {r^2}L{\psi ^{-2}}) = 0 \text{。}\end{aligned} (11)
1.7 数值求解步骤

1）输入轴承结构的基本尺寸及运行工作参数；

2）对压力与温度求解区域进行有限差分网格划分，并确定差分网格节点坐标及有限元节点信息；

3）利用式（1）和式（2），根据给定偏心率ε0、轴承偏位角θ0 及瓦块摆角δ0 计算油膜厚度H

4）初定油膜温度场，计算出油膜中各节点的粘度值；

5）求解雷诺方程式（3）获得压力分布；

6）初定瓦块瓦面温度分布，由解能量方程式（5）确定油膜温度分布；

7）判断温度是否满足收敛要求，重复步骤 4～步骤 6 过程，直至满足精度为止；

8）计算力矩，确定瓦块摆角，重复步骤 3～步骤 8 过程使得力矩满足一定的精度；

9）求承载能力，修正偏位角，重复步骤 3～步骤 9 过程直至满足载荷精度为止；

10）计算轴承静特性，包括无量纲最小油膜厚度Hmin、载荷系数ζ、流量、摩擦阻力系数、功耗等性能参数；

11）分别取位移与速度的小扰动，计算轴承的动力特性系数；

12）输出结果，并结束。

2 算例分析

2.1 瓦块支点位置分布对轴承性能影响

1）承载能力

 图 3 最小油膜厚度随承载系数的变化关系 Fig. 3 The variation between minimum film thickness and load coefficient

2）油膜压力分布

 图 4 瓦 2 瓦周向油膜压力分布 Fig. 4 The circumferential film pressure distribution on Pad 2#

 图 5 瓦 1 瓦面上的油膜压力分布 Fig. 5 The film pressure distribution on Pad 1#

 图 6 载荷系数随偏心率的变化关系 Fig. 6 The variation between load coefficient and eccentricity ratio
2.2 瓦块包角大小对轴承润滑性能影响

1）载荷系数与轴颈偏心率

2）承载能力及最小油膜厚度

 图 7 最小油膜厚度随载荷系数的变化关系 Fig. 7 The variation between minimum film thickness and load coefficient

 图 8 周向油膜压力的分布曲线 Fig. 8 The circumferential film pressure distribution curves

3）压力分布

3 结 语

1）提出了非均布变包角可倾瓦轴承结构，并构建了非均布变包角径向可倾瓦轴承的流体动力润滑模型，包括轴承油膜厚度方程、Reynolds 方程、能量方程、粘温方程以及瓦块热传导方程和瓦块力矩平衡方程。

2）采用数值方法，求解获得了一组非均布变包角径向可倾瓦轴承的静态特性，以此分析了瓦块支点位置分布和瓦块包角大小对轴承润滑性能影响。

3）研究结果表明瓦块支点位置的改变对油膜压力分布有一定的影响，轴承在较小的支点夹角下承载能力较高；小包角的可倾瓦轴承的最小油膜厚度较小，但油膜压力的最大值会有所降低。