﻿ 弹性桨-轴系统的纵向振动传递特性研究
 舰船科学技术  2022, Vol. 44 Issue (24): 26-29    DOI: 10.3404/j.issn.1672-7649.2022.24.006 PDF

Research on longitudinal vibration transmission characteristics of elastic propeller shaft system
FENG Fu-qin
Beihai Ship Inspection Center of Guangxi Zhuang Autonomous Region, Beihai 536007, China
Abstract: In order to analyze the longitudinal vibration transmission characteristics of elastic propeller shaft system, two models of point mass propeller shaft and elastic propeller shaft are established, their transmission paths are analyzed, the response and force transmission rate of propeller shaft system of different materials at thrust bearing are compared, and the frequency matching design of elastic propeller shaft system is carried out. The conclusions are as follows: the elastic utility of the blade can modulate the transmission of longitudinal vibration. By adjusting the elastic parameters of the blade and matching the umbrella mode of the blade and the longitudinal vibration mode of the shaft system, the vibration of the shaft system can be effectively controlled..
Key words: elastic propeller shaft system     exciting force     vibration     umbrella mode
0 引　言

1 计算方法 1.1 振动方程

 $[M]\{\ddot u\}+[C]\{\dot u\}+[K]\{u\}=\{F\}。$ (1)

1.2 谐响应方程

 $\left\{ u \right\} = \left\{ {{u_{\max }}{e^{i\varphi }}} \right\}{e^{i\Omega t}}。$ (2)

 $\left\{ u \right\} =\left\{ {{u_{\max }}\left( {\cos \varphi + i\sin \varphi } \right)} \right\}{e^{i\varOmega t}} = \left( {\left\{ {{u_1}} \right\} + i\left\{ {{u_2}} \right\}} \right){e^{i\varOmega t}}。$ (3)

 $\begin{split} \left\{ F \right\} =& \left\{ {{F_{\max }}{e^{i\varphi }}} \right\}{e^{i\varphi \Omega }} = \\ &\left\{ {{F_{\max }}\left( {\cos \varphi + i\sin \varphi } \right)} \right\}{e^{i\varphi \Omega }} = \left( {\left\{ {{F_1} + i{F_2}} \right\}} \right){e^{i\varphi \Omega }} ，\\ \end{split}$ (4)

 $\begin{gathered} \left( { - {\varOmega ^2}{{M + }}\varOmega {{C + K}}} \right)\left( {\left\{ {{x_1}} \right\} + i\left\{ {{x_2}} \right\}} \right) = \left( {\left\{ {{F_1}} \right\} + i\left\{ {{F_2}} \right\}} \right)，\\ \end{gathered}$ (5)

 ${{{u}}_{\max }}{\text{ = }}\sqrt {{u_1}^2 + {u_2}^2}，$
 $\varphi {\text{ = }}\arctan \frac{{{u_1}}}{{{u_2}}} 。$
2 模型及参数设置 2.1 模型基本参数

 图 1 桨-轴系统模型 Fig. 1 Model of the propeller shaft system
2.2 模型及边界条件设置

2种形式的桨-轴系统，其前后尾轴承采用弹簧单元进行模拟，刚度各向同性均为4.6E9 N/m，不计交叉刚度，轴系旋转速度240 r/min。推力轴承均采用其中Body-ground弹簧单元进行模拟，刚度7.2E7 N/m，为弹簧一端与轴系连接，另一端设置为ground。

2.3 扫频设置

 图 2 激振力施加位置及方向图 Fig. 2 Position and direction diagram of excitation force applied
3 计算结果与分析 3.1 两种模型纵向振动传递路径

 图 3 刚性桨与弹性桨区别 Fig. 3 Difference between rigid paddle and elastic paddle

2种桨叶的具体传递路径如图4图5所示。

 图 4 质量点桨-轴系统纵向激振力的传递路径 Fig. 4 Transmission path of longitudinal excitation force of mass propeller shaft system

 图 5 弹性桨-轴系统纵向激振力的传递路径 Fig. 5 Transmission path of longitudinal excitation force of elastic propeller shaft system
3.2 桨叶弹性效应对位移传递曲线影响

 图 6 玻璃纤维桨-轴的位移传递函数图 Fig. 6 Displacement transfer function diagram of glass fiber propeller shaft system
 ${H_i} = 20 \times {\rm{lg}}\left(\left( {\frac{{\left| {{u_i}} \right|}}{{{F_0}}}} \right)/Ref\right) ({\rm{dB}})。$ (6)

3.3 桨叶弹性效应对推力轴承处位移和加速度响应影响

 图 7 推力轴承位置的位移响应对比图 Fig. 7 Displacement response comparison diagram of thrust bearing position

 图 8 推力轴承位置的加速度响应对比图 Fig. 8 Acceleration response comparison diagram of thrust bearing position
 $TDL = 20\lg ({{{u_{\rm out}}} / {{u_0}}})({\rm{dB}}) ，$ (7)
 $TAL = 20\lg ({{{a_{\rm out}}} / {{a_0}}})({\rm{dB}})。$ (8)

3.4 桨叶弹性效应对推力轴承处力传递率影响

 图 9 推力轴承位置的力传递率对比图 Fig. 9 Comparison diagram of force transfer rate at thrust bearing position
 $R = 20\lg ({{{F_{\rm out}}} \mathord{\left/ {\vphantom {{{F_{\rm out}}} {{F_{in}}}}} \right. } {{F_{in}}}})({\rm{dB}})。$ (9)

4 弹性桨-轴动力学特性匹配设计

 图 10 推力轴承位置的力传递率对比 Fig. 10 Comparison of force transfer rate at thrust bearing position

 图 11 桨叶弹性效应对力传递率的影响图 Fig. 11 Influence of blade elastic effect on force transfer rate

5 结　语

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