﻿ 往复泵运动机构磨损对振动特性的影响分析
 舰船科学技术  2017, Vol. 39 Issue (1): 51-55 PDF

Reciprocating bilge pump crank-link mechanism vibration analysis with joint clearance
XIA Jiang-min, ZHANG Zhen-hai, YU Xiang, ZHU Shi-jian
Ship and Power Engineering Institute, Naval University of Engineering, Wuhan 430033, China
Abstract: The wear of reciprocating pump mechanism is the main factor affecting the performance of the reciprocating pump. It is important to study the vibration characteristics caused by the wear of the moving mechanism, which is very important for the fault diagnosis and condition monitoring of the equipment. As the components of the reciprocating pump more complex structure, only rely on vibration data analysis of signal processing methods is difficult to accurately analyze and determine the performance of equipment. Based on the mechanism analysis of the effect of the wear of the moving pair on the vibration characteristics, the contact state and the separation state model of the moving pair at the crank connecting rod were established, and the numerical calculation method was used to analyze the effect of the wear condition.The kinematics, dynamics and vibration characteristics of the bilge pump are analyzed. The influence of the wear clearance on the vibration performance of the bilge pump is analyzed. It is found that the existence of the wear gap has a great influence on the bilge pump 's motion characteristics and vibration characteristics.
Key words: reciprocating pump     running gear wear     clearance     vibration
0 引言

1 往复泵力学模型分析

 图 1 往复泵传动系统示意图 Fig. 1 Reciprocating bilge pump drive system
2 运动机构磨损数学模型分析

2.1 连杆动力学方程

 图 2 曲柄连杆机构受力分析 Fig. 2 Crank mechanism mechanical analysis
 ${m_2}{\ddot x_{{c_2}}} = F_{12}^n\cos \theta- F_{12}^t\sin \theta + F_{32}^x{,}$ (1)
 ${m_2}{\ddot y_{{c_2}}} = F_{12}^n\sin \theta + F_{12}^t\cos \theta- F_{32}^y- {m_2}g{。}$ (2)

B 点取矩，由动量矩守恒定理有：

 $\begin{array}{l} {J_B}\ddot \beta = F_{12}^t[{L_2}\cos \left( {\beta- \theta } \right) + {R_A}]- F_{12}^n{L_2}\sin \left( {\beta- \theta } \right)+\\ \quad\quad\quad {m_2}g{L_{{c_2}}}\cos \beta + {m_2}{{\ddot x}_B}{L_{{c_2}}}\sin \beta \end{array}$ (3)

 ${x_{{c_2}}} = {x_B}- {L_{{c_2}}}\cos \beta{,}$ (4)
 ${y_{{c_2}}} = {L_{{c_2}}}\sin \beta{。}$ (5)

 ${\ddot x_{{c_2}}} = {\ddot x_B}- {\dot \beta ^2}{L_{{c_2}}}\cos \beta + \ddot \beta {L_{{c_2}}}\sin \beta {,}$ (6)
 ${\ddot y_{{c_2}}} =- {\dot \beta ^2}{L_{{c_2}}}\sin \beta- \ddot \beta {L_{{c_2}}}\cos \beta {,}$ (7)

 ${d_x} = {L_1}\cos \alpha- {L_2}\cos \beta- {x_B}{,}$ (8)
 ${d_y} = {L_1}\sin \alpha- {L_2}\sin \beta {,}$ (9)

 $v_{12}^t = {\dot d_y}\cos \theta- {\dot d_x} + \sin \theta \left( {\dot \alpha- \dot \beta } \right){r_A}{,}$ (10)
 $v_{12}^n = {\dot d_y}\sin \theta + {\dot d_x}\cos \theta {。}$ (11)

σ=d-δ

 $\mu \left( \sigma \right)\text{=}\left\{ \begin{matrix} 1, & \sigma \ge 0, \\ 0, & \sigma ＜0, \\ \end{matrix} \right.$

 $F_{12}^n = \left( {K{\rm{\sigma }} + {C_n}v_{12}^n} \right)\mu \left( {\rm{\sigma }} \right){,}$ (12)
 $F_{12}^t =- \left( {fsign\left( {v_{12}^t} \right)} \right)F_{12}^n + {C_t}v_{12}^t)\mu \left( {\rm{\sigma }} \right){,}$ (13)

 ${F_{AX}} = \mu \left( {\rm{\sigma }} \right)\left( {- F_{12}^t\sin \theta + F_{12}^n\cos \theta } \right){,}$ (14)
 ${F_{AY}} = \mu \left( {\rm{\sigma }} \right)\left( {F_{12}^t\cos \theta + F_{12}^n\sin \theta } \right){。}$ (15)
2.2 瞬时流量和吸排压力计算 2.2.1 瞬时流量计算

 ${{\rm{x}}_B} = {L_1} + {L_2}- \left( {{L_1}\cos \alpha + {L_2}\cos \beta } \right){,}$ (16)

 $\cos \beta =\sqrt{1-{{\lambda }^{2}}{{\sin }^{2}}a}$

 $\begin{array}{l} {x_B} = {L_1}\left( {1- \cos \alpha } \right) + {L_2}\left( {1- \sqrt {1- {\lambda ^2}{{\sin }^2}\alpha } } \right),\;\\ \alpha = \omega t{。} \end{array}$ (17)

 ${{{Q}}_1} = {{A}}{{\rm{\dot x}}_B} = A{L_1}\omega \left( {\sin \alpha + \frac{{\lambda \sin 2\alpha }}{2}} \right) \approx A{L_1}\omega \sin \alpha {。}$ (18)

2.2.2 压力计算

1）吸入压力计算

 图 3 舱底泵工作原理图 Fig. 3 Bilge pump working principles
 ${E_{1- 1}} = \rho {Q_1}{Z_1} + {P_1}{Q_1}/{\text{g}} + \rho {Q_1}\mu _1^2/2{\text{g}}{。}$ (19)

 ${E_{2- 2}} = \rho {Q_1}{Z_0} + {P_a}{Q_1}/{\text{g}}{,}$ (20)

 ${E_{1- 1}} + {E_{BA}} + {E_{A1}} = {E_{2- 2}}{。}$ (21)

 ${E_{BA}} = \rho {Q_1}{h_{BA}}{,}$ (22)
 ${E_{A1}} = \rho {Q_1}{h_{A1}}{。}$ (23)

 $\rho {Z_1} + {P_1}/g + \rho \mu _1^2/2g + \rho {h_{BA}} + \rho {h_{A1}} = \rho {Z_0} + {P_a}/g{,}$ (24)

 \begin{aligned} {P_1} = & {P_a} + \rho {Z_0}g-\\ & \left( {\rho {Z_1}g + {P_1} + \rho \mu _1^2/2 + \rho {h_{BA}}g + \rho {h_{A1}}g} \right){。} \end{aligned} (25)

 ${{{P}}_1}\!=\!{{{P}}_{{a}}}\!+\!{{\rho }}{{{Z}}_0}{{g}}\!-\!{{\rho g}}\left( {{{{Z}}_1} \!+\! {{{h}}_{{阻}1}} \!+\! {{{h}}_{{{惯}}1}}\!+\! {{{K}}_{{阻}1}} \!\!+\!\! {{{K}}_{{{惯}}1}}} \right)\!-\!{{{P}}_1}\!-\!{{\rho \mu }}_1^2/2{。}$ (26)

2）压力计算

 \begin{aligned} {P_2} = &{P_c} + \rho {Z_c}g + \rho \mu _c^2/2- \rho \mu _2^2/2 + \\ &\rho g\left( {{h_{{{阻}}2}} + {h_{{{惯}}2}} + {K_{{{阻}}2}} + {K_{{{惯}}2}}} \right) \end{aligned} (27)

3）缸内综合压力

3 仿真计算

 图 4 综合压力曲线 Fig. 4 Integrated pressure curve

 图 5 活塞轴向速度曲线 Fig. 5 Velocity curve between the piston

 图 6 模态分布图 Fig. 6 Modal Distribution

 图 7 传递函数 Fig. 7 The Transfer Function

4 结语

1）通过建立舱底泵的流量和压力方程，得到了舱底泵工作时的综合压力曲线，为以后的往复式泵的压力计算提供了方法。

2）建立了运动副存在间隙情况下的接触—碰撞模型，模拟了曲柄连杆机构磨损的故障情况，为以后的磨损机体研究提供了新思路。