﻿ 考虑轴承间隙影响的齿轮传动系统振动特性研究及试验验证
 舰船科学技术  2022, Vol. 44 Issue (20): 107-111    DOI: 10.3404/j.issn.1672-7649.2022.20.021 PDF

The vibration characteristics and test validation of gear drive system considering the effects of bearing clearance
WEI Wei, YANG Cheng-bin, ZHANG Ming-yu
China Coast Guard Academy, Ningbo 315800, China
Abstract: Based on the single-stage gear system supported by sliding bearings, a mathematical model of the system was established, the vibration characteristics of the system under different sliding bearing clearances were calculated theoretically, a gear-sliding bearing test bench was set up, and the vibration parameters of the gear system under different bearing clearances were tested by changing the bearings. The experimental test is consistent with the trend of theoretical calculation, which shows that increasing the sliding bearing clearance at certain times will increase the vibration of the gear system, and increasing the load torque will also increase the vibration of the gear system.
Key words: bearing clearance     gear drive system     vibration characteristics     test validation
0 引　言

1 齿轮啮合动力学模型

 图 1 齿轮系统动力学模型 Fig. 1 Coupled model of gear-bearing system

 $\left\{ \begin{gathered} {m_1}{{\ddot y}_1} + {c_{by1}}{{\dot y}_1} + {k_{by1}}{y_1} = - {m_1}g - {F_m}(t){\rm{cos}}\alpha，\\ {m_1}{{\ddot x}_1} + {c_{bx1}}{{\dot x}_1} + {k_{bx1}}{x_1} = - {F_m}(t)\sin \alpha，\\ {I_1}{{\ddot \theta }_1} = {T_{in}} - {F_m}(t){r_{b1}}，\\ \end{gathered} \right.$ (1)
 $\left\{ \begin{gathered} {m_2}{{\ddot y}_2} + {c_{by2}}{{\dot y}_2} + {k_{by2}}{y_2} = - {m_2}g + {F_m}(t){\rm{cos}}\alpha ，\\ {m_2}{{\ddot x}_2} + {c_{bx2}}{{\dot x}_2} + {k_{bx2}}{x_2} = {F_m}(t)\sin \alpha，\\ {I_2}{{\ddot \theta }_2} = - {T_{load}} + {F_m}(t){r_{b2}}。\\ \end{gathered} \right.$ (2)

2 考虑轴承间隙影响的齿轮系统振动特性分析

 $\psi = C/d。$ (3)

 $\psi = \frac{{{{(n/60)}^{4/9}}}}{{{{10}^{31/9}}}} 。$ (4)

 图 2 不同轴承间隙时系统的振动响应 Fig. 2 Vibration response of system with different bearing clearancs

3 试验验证

 图 3 不同轴承间隙下系统的振动响应（ ${T_2} = 1\;{\text{N}\cdot {\rm{m}}}$ ） Fig. 3 Vibration response of system under different bearing clearance with ${T_2} = 1\;{\text{N}\cdot {\rm{m}}}$

 图 4 不同轴承间隙下系统的振动响应（ ${T_2} = 10\;{\text{N}\cdot {\rm{m}}}$ ） Fig. 4 Vibration response of system under different bearing clearance with ${T_2} = 10\;{\text{N}\cdot {\rm{m}}}$

4 结　语

1）试验测试与理论计算的对比验证了本文建立的齿轮-滑动轴承系统模型的正确性，该模型可用于对系统振动特性的分析；

2）滑动轴承间隙对齿轮系统的振动有显著影响，轴承间隙的增加会导致支撑刚度的减小，进而使得系统振动加剧，因此为了保证齿轮系统可靠、安全的运行，轴承间隙大小应严格监测和控制；

3）负载对系统振动也有重要影响，相同参数下齿轮系统所受负载越大，系统振动幅度也越大。

 [1] 李润方, 王建军. 齿轮系统动力学[M]. 北京: 科学出版社, 1997. [2] KAHRAMAN A, SINGH R. Interactions between time-varying mesh stiffness and clearance non-linear ties in a geared system[J]. Journal of Sound and Vibration, 1991, 146(1): 135-156. DOI:10.1016/0022-460X(91)90527-Q [3] KAHRAMAN A, OZGUVEN H N, HOUSER D R, et al. Dynamic analysis of geared rotors by finite elements[J]. Journal of Mechanical Design, 1990, 114(3): 507-514. [4] 崔亚辉. 齿轮-转子-滑动轴承系统非线性动力学特性的理论和试验研究[D]. 哈尔滨: 哈尔滨工业大学, 2009: 2-6. [5] WANG J, LIM T C, Li M F. Dynamics of a hypoid gear pair considering the effects of time-varying mesh parameters and backlash nonlinearity[J]. Journal of Sound and Vibration, 2007, 308(1-2): 302-329. DOI:10.1016/j.jsv.2007.07.042 [6] 李同杰, 靳广虎, 朱如鹏, 等. 滑动轴承支撑下齿轮耦合转子系统弯扭耦合振动特性分析[J]. 中南大学学报(自然科学版), 2018, 49(3): 566-573. LI Tongjie, JIN Guanghu, ZHU Rupeng, et al. Analysis of the vibration characteristics of the bend coupling vibration of the gear coupling rotor system under the support of sliding bearings[J]. Journal of Central South University(Science and Technology), 2018, 49(3): 566-573. DOI:10.11817/j.issn.1672-7207.2018.03.008 [7] 蒋庆晶, 吴大转, 潭善光, 等. 齿轮传动多转子耦合系统振动特性研究[J]. 振动工程学报, 2010, 23(3): 254-259. JIANG Qing-jing, WU Da-zhuan, TAN Shan-guang, et al. Study on the vibration characteristics of gear drive multi-rotor coupling system[J]. Journal of Vibration Engineering, 2010, 23(3): 254-259. DOI:10.3969/j.issn.1004-4523.2010.03.004 [8] 周建星, 刘更, 马尚君. 内激励作用下齿轮箱动态响应与振动噪声分析[J]. 振动与冲击, 2011, 30(6): 234-238. ZHOU Jian-xing, LIU Geng, MA shang-jun. Vibration and noise analysis of gear transmission system[J]. Journal of Vibration and Shock, 2011, 30(6): 234-238. DOI:10.3969/j.issn.1000-3835.2011.06.047 [9] 张将, 秦训鹏, 陈浩冉. 考虑支撑间隙的齿轮系统动力学响应分析[J]. 噪声与振动控制, 2017, 37(5): 50-54+159. ZHANG Jiang, QIN Xun-peng, CHEN Hao-ran. Dynamic response analysis of gear systems with support clearance considered[J]. Noise and Vibration Control, 2017, 37(5): 50-54+159. DOI:10.3969/j.issn.1006-1355.2017.05.011 [10] 魏维, 郭文勇, 吴新跃, 等. 考虑时变轴承动力学参数的齿轮系统建模与分析[J]. 振动与冲击, 2019, 38(23): 260-266. WEI Wei, GUO Wen-yong, WU Xin-yue, et al. Gear system modeling and analysis considering time-varying bearing dynamics parameters[J]. Vibration and Shock, 2019, 38(23): 260-266. [11] 杨金福, 刘占生, 于达仁, 等. 滑动轴承非线性动态油膜力及稳定性的研究[J]. 动力工程, 2004, 24(4): 501-505. YANG Jin-fu, LIU Zhan-sheng, YU Da-ren, et al. Research on nonlinear oil film force and its stability of journal bearing[J]. Power engineering, 2004, 24(4): 501-505.