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主管单位 中华人民共和国
工业和信息化部
主办单位 哈尔滨工业大学 主编 冷劲松 国际刊号ISSN 0367-6234 国内刊号CN 23-1235/T

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引用本文:李小彭,徐金池,潘五九,牟佳信,王琳琳,杨泽敏,闻邦椿.含齿面分形啮合刚度的齿轮传动系统动力学[J].哈尔滨工业大学学报,2019,51(7):56-62.DOI:10.11918/j.issn.0367-6234.201807077
LI Xiaopeng,XU Jinchi,PAN Wujiu,MU Jiaxin,WANG Linlin,YANG Zemin,WEN Bangchun.Dynamics of gear transmission system with fractal meshing stiffness on tooth surface[J].Journal of Harbin Institute of Technology,2019,51(7):56-62.DOI:10.11918/j.issn.0367-6234.201807077
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含齿面分形啮合刚度的齿轮传动系统动力学
李小彭1,徐金池1,潘五九2,牟佳信3,王琳琳1,杨泽敏1,闻邦椿1
(1. 东北大学 机械工程与自动化学院, 沈阳 110819;2. 沈阳航空航天大学 机电工程学院, 沈阳 110136; 3. 沈阳发动机研究所, 航空发动机动力传输航空科技重点实验室(中国航发)沈阳 110015)
摘要:
为研究考虑齿面分形特性的时变啮合刚度对齿轮-轴承系统的影响,用分形理论描述齿轮轮廓,采用Weber-Banaschek公式计算和分析不同分形维数D对齿轮时变啮合刚度的影响,将不同分形维数D下的刚度代入计及滑动轴承非线性油膜力、综合传递误差及齿侧间隙等因素的齿轮-轴承系统中,分析不同分形维数D下的刚度对系统动力学特性的影响. 采用Runge-Kutta法求解系统动力学微分方程,得到系统响应的相图、Poincaré截面图、时域图、分岔图以及三维频谱图等. 结果表明:随着分形维数D的增大,时变啮合刚度波动降低,系统趋于更加稳定的周期运动;相比含随机扰动的刚度,齿轮-轴承系统对于考虑齿面分形特性的齿轮啮合刚度的变化更加敏感,更能表现因齿廓变化导致的系统响应的变化;随着阻尼比的增大,系统会趋于相对稳定的单周期运动.
关键词:  齿轮  分形理论  时变啮合刚度  轴承  动力学特性
DOI:10.11918/j.issn.0367-6234.201807077
分类号:TH132.41
文献标识码:A
基金项目:中央高校基本科研业务专项资金(N170302001); 国家自然科学基金(2,1)
Dynamics of gear transmission system with fractal meshing stiffness on tooth surface
LI Xiaopeng1,XU Jinchi1,PAN Wujiu2,MU Jiaxin3,WANG Linlin1,YANG Zemin1,WEN Bangchun1
(1. School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China; 2. School of Mechatronics Engineering, Shenyang Aerospace University, Shenyang 110136, China; 3. Shenyang Engine Research Institute, Key Laboratory of Power Transmission Technology on Aero-engine (Aero Engine Corporation of China), Shenyang 110015, China)
Abstract:
The influence of time-varying meshing stiffness on the gear bearing considering the fractal characteristics of the tooth surface is studied. Firstly, the profile of gear is described by the fractal theory, and the Weber-Banaschek formula is used to calculate and analyze the influence of different fractal dimension D on the time-varying mesh stiffness, and the stiffness of different fractal dimension D is taken into the gear bearing system with the factors such as the nonlinear oil film force of the sliding bearing, the comprehensive transmission error and the backlash, etc. The influence of stiffness of different fractal dimension D on the dynamic characteristics of the system is analyzed. The dynamic differential equation is solved by Runge-Kutta method. The phase diagrams, the Poincaré diagrams, the time domain diagrams, the bifurcation diagrams and the three-dimensional spectrum diagrams of the response of the system are obtained. The results show that with the increase of fractal dimension D, the fluctuation of time-varying meshing stiffness decreases, and the system tends to more stable periodic motion; Compared with the stiffness of random disturbance, the gear bearing system is more sensitive to the change of gear meshing stiffness considering the fractal characteristics of the tooth surface, and it can better show the change of system response due to the change of tooth profile; With the increase of damping ratio, the system will tend to relatively stable single cycle motion.
Key words:  gear  fractal theory  time-varying meshing stiffness  bearing  dynamic characteristics

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