﻿ 舰船汽轮机汽流激振时转子松动故障振动分析
 舰船科学技术  2020, Vol. 42 Issue (6): 126-131    DOI: 10.3404/j.issn.1672-7649.2020.06.025 PDF

1. 中国人民解放军91404部队，河北 秦皇岛 066000;
2. 海军工程大学 舰船高温复合材料研究所，湖北 武汉 430033

Vibration analysis of rotor loosening fault of ship steam turbine under steam flow excitation
WENG Lei1, ZHANG Lei2, LIU Dong1
1. No.91404 Unit of PLA, Qinhuangdao 066000, China;
2. Naval University of Engineering, Institute of High Temperature Structural Composite Materials for Naval Ship, Wuhan 430033, China
Abstract: Aiming at the problem of the basic looseness of the ship steam turbine unit, considering the influence of steam turbine blade tip clearance steam excitation, the rotor looseness fault analysis model under the steam flow-exciting force of the steam turbine is established. Using numerical solution method, combined with the bifurcation diagram, axial trajectory diagram, Poincare section diagram and spectrogram of system response, the effects of parameters such as rotational speed, bearing mass and mass eccentricity on the nonlinear vibration response of the system are studied. The dynamic characteristics analysis and fault diagnosis of steam turbine rotor system with loose fault under the tip clearance steam flow excitation provide some reference.
Key words: rotor     looseness fault     steam flow-exciting force     nonlinear vibration     fault diagnosis
0 引　言

1 汽流激振时转子松动动力学模型 1.1 汽轮机气流激振力模型

 ${F_{\rm{a}}} = {A_1} \cdot \delta \cdot E + {A_3} \cdot {\delta ^3} \cdot {E^3}\text{。}$ (1)

 \begin{aligned} & {A_1} = \frac{{{{(R_T^2 - R_B^2)}^2}{{\text π}} C{R_T}}}{{{{\left( {R_T^2 - R_B^2 + 2{R_T}\bar \delta } \right)}^2}}},\;\;\;{A_3} = \frac{{3{{(R_T^2 - R_B^2)}^2}{\text π} CR_T^3}}{{{{\left( {R_T^2 - R_B^2 + 2{R_T}\bar \delta } \right)}^4}}}, \\ & E = \sqrt {{x^2} + {y^2}} ,\;\;\;\;\;\;\;\;C = {V^2}\sin {\beta _1}{\rho _0}\left( {\cos {\beta _1} + \varsigma {\beta _2}} \right)\text{。} \end{aligned}

 $\left( {\begin{array}{*{20}{c}} {{F_{ax}}} \\ {{F_{ay}}} \end{array}} \right) = \left( {{A_1} \cdot \delta \cdot E + {A_3} \cdot {\delta ^3} \cdot {E^3}} \right)\left( {\begin{array}{*{20}{c}} {\cos \theta } \\ {\sin \theta } \end{array}} \right)\text{。}$ (2)

1.2 含有基础松动故障的转子系统动力学模型

 图 2 转子基础松动故障模型 Fig. 2 The rotor system with pedestal looseness fault
 ${k_{\rm{s}}} = \left\{ \begin{array}{l} {k_{{\rm{s1}}}}\;\;\;\;{y_4} > {\delta _1} \\ 0\;\;\;\;{\rm{0}} \leqslant {y_4} \leqslant {\delta _1} \\ {k_{{\rm{s2}}}}\;\;\;{y_4} < {\delta _1}{\rm{ }} \\ \end{array} \right.,\;{c_{\rm{s}}} = \left\{ \begin{array}{l} {c_{{\rm{s1}}}}\;\;\;\;{y_4} > {\delta _1} \\ 0\;\;\;\;{\rm{0}} \leqslant {y_4} \leqslant {\delta _1} \\ {c_{{\rm{s2}}}}\;\;\;{y_4} < {\delta _1}{\rm{ }} \\ \end{array} \right.\text{。}$ (3)

 \left\{ \begin{aligned} & {F_{{x_1}}} = sP{f_x}({x_1},{y_1},{{\dot x}_1},{{\dot y}_1}) \\ & {F_{{y_1}}} = sP{f_y}({x_1},{y_1},{{\dot x}_1},{{\dot y}_1}) \\ \end{aligned} \right.\text{，} (4)
 \left\{ \begin{aligned} & {F_{{x_3}}} = sP{f_x}({x_3},{y_3} - {y_4},{{\dot x}_3},{{\dot y}_3} - {{\dot y}_4}) \\ & {F_{{y_3}}} = sP{f_y}({x_3},{y_3} - {y_4},{{\dot x}_3},{{\dot y}_3} - {{\dot y}_4}) \\ \end{aligned} \right.\text{。} (5)
1.3 基础松动转子系统动力学方程

 \begin{aligned} & {{\ddot X}_1} = - \frac{{{c_1}}}{{{m_1}\omega }}{{\dot X}_1} - \frac{k}{{{m_1}{\omega ^2}}}\left( {{X_1} - {X_2}} \right) + \\ & \quad \quad \quad \frac{{sP{f_x}({X_1},{Y_1},{{\dot X}_1},{{\dot Y}_1})}}{{c{m_1}{\omega ^2}}} \text{，}\\ & {{\ddot Y}_1} = - \frac{{{c_1}}}{{{m_1}\omega }}{{\dot Y}_1} - \frac{k}{{{m_1}{\omega ^2}}}\left( {{Y_1} - {Y_2}} \right) + \\ & \quad \quad \quad \frac{{sP{f_y}({X_1},{Y_1},{{\dot X}_1},{{\dot Y}_1})}}{{c{m_1}{\omega ^2}}} \text{，} \\ & {{\ddot X}_2} = - \frac{{{c_2}}}{{{m_2}\omega }}{{\dot X}_2} - \frac{k}{{{m_2}{\omega ^2}}}\left( {2{X_2} - {X_1} - {X_3}} \right) - \\ & \quad \quad \quad \frac{{{F_{ax}}}}{{c{m_2}{\omega ^2}}} + \frac{e}{c}\cos (\tau + \beta ) \text{，}\\ & {{\ddot Y}_2} = - \frac{{{c_2}}}{{{m_2}\omega }}{{\dot Y}_2} - \frac{k}{{{m_2}{\omega ^2}}}\left( {2{Y_2} - {Y_1} - {Y_3}} \right) + \\ & \quad \quad \quad \frac{{{F_{ay}}}}{{c{m_2}{\omega ^2}}} + \frac{e}{c}\sin (\tau + \beta ) - \frac{g}{{c{\omega ^2}}} \text{，} \\ & {{\ddot X}_3} = - \frac{{{c_1}}}{{{m_1}\omega }}{{\dot X}_3} - \frac{k}{{{m_1}{\omega ^2}}}\left( {{X_3} - {X_2}} \right) + \\ & \quad \quad \quad \frac{{sP{f_x}({X_3},{Y_3} - {Y_4},{{\dot X}_3},{{\dot Y}_3} - {{\dot Y}_4})}}{{c{m_1}{\omega ^2}}} \text{，} \\ & {{\ddot Y}_3} = - \frac{{{c_1}}}{{{m_1}\omega }}{{\dot Y}_3} - \frac{k}{{{m_1}{\omega ^2}}}\left( {{Y_3} - {Y_2}} \right) + \\ &\quad \quad \quad \frac{{sP{f_y}({X_3},{Y_3} - {Y_4},{{\dot X}_3},{{\dot Y}_3} - {{\dot Y}_4})}}{{c{m_1}{\omega ^2}}} - \frac{g}{{c{\omega ^2}}} \text{，} \\ & {{\ddot Y}_4} = - \frac{{{c_s}}}{{{m_3}\omega }}{{\dot Y}_4} - \frac{{{k_s}}}{{{m_3}{\omega ^2}}}{Y_4} - \\ & \quad \quad \quad \frac{{sP{f_y}({X_3},{Y_3} - {Y_4},{{\dot X}_3},{{\dot Y}_3} - {{\dot Y}_4})}}{{c{m_3}{\omega ^2}}} - \frac{g}{{c{\omega ^2}}} \text{。} \end{aligned} (6)

2 汽流激振力作用下基础松动转子系统振动特性分析

2.1 转速对系统动力学特性的影响

 图 3 系统响应 ${X_2}$ ， ${Y_4}$ 随转速 $\omega$ 变化的分岔图 Fig. 3 Bifurcation diagram of the rotor system under the change of $\omega$

 图 4 不同转速下基础松动转子系统响应图 Fig. 4 The orbit, poincaré map and frequency spectrums of the rotor system with pedestal

2.2 支座质量对系统动力学特性的影响

 图 5 汽流激振力下松动转子系统 ${X_2}$ 、 ${Y_4}$ 随转速 $\omega$ 变化的分岔图 Fig. 5 Bifurcation diagram of the rotor system under the change of $\omega$
2.3 质量偏心对系统动力学特性的影响

 图 6 e = 0.03 mm和e = 0.07 mm时松动转子系统 ${X_2}$ ， ${Y_4}$ 随转速 $\omega$ 变化的分岔图 Fig. 6 Bifurcation diagram of the rotor system under the change of $\omega$ when $e = 0.03\;{\rm mm}$ and $e = 0.07\; {\rm mm}$

 图 7 e = 0.03 mm时松动转子系统响应的轴心轨迹图、Poincaré截面图和频谱图 Fig. 7 The orbit, Poincaré map and frequency spectrums of the rotor system with pedestal when $e = 0.03\; {\rm mm}$

 图 8 $e = 0.07\;{\rm mm}$ 时松动系统响应轴心轨迹图、Poincaré截面图和频谱图 Fig. 8 The orbit, Poincaré map and frequency spectrums of the rotor system with pedestal when $e = 0.07\;{\rm mm}$
3 结　语

1）汽流激振力的存在使得松动转子系统轴心处响应的周期性运动区间变宽，且在临界转速附近的混沌区间变窄，而对支座处响应几乎没有影响。

2）随着支座质量的增加松动转子系统轴心处的响应在临界转速附近的混沌小岛由4个逐渐减小到2个，并且混沌区间变宽；在转速较低时，松动端轴承支座在竖直方向的振动响应几乎为0，在转速升高到临界转速之后的响应才有所增加。

3）质量偏心作为系统的主要参数对系统响应有很大影响，在临界转速以下对系统的响应都不是很大；但当大于临界转速时，系统 ${X_2}$ ${Y_4}$ 的响应都随着转速的增加振动幅值明显增大，甚至发生跳跃突变。特别是在质量偏心比较大的情况下，支座处位移 ${Y_4}$ 在临界转速以下的振动幅值都明显增大，由此可见质量偏心对系统的动力学具有很大的影响，因此在设计安装过程中要严格对转子进行动平衡，防止进一步加剧转子振动。

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