基于齿轮振动和非线性接触的动态响应理论建模  

Theoretical Modeling of Dynamic Response Characteristics of Gear Transmission System Based on Nonlinear Contact and Intrinsic Vibration

作　　者：付饶[1] 李静宇 熊奉奎 FU Rao;LI Jing-yu;XIONG Feng-kui(Department of Mechanical and Electrical Engineering,Mianyang Polytechnic,Mianyang Sichuan 621000,China;Shenyang Agricultural University,Shenyang Liaoning 110000,China;School of Mechanical Engineering,Shaanxi University of Science&Technology,Xi′an Shaanxi 710016,China)

机构地区：[1]绵阳职业技术学院机电工程系,四川绵阳621000 [2]沈阳农业大学,辽宁沈阳110000 [3]陕西科技大学机电工程学院,陕西西安710016

出　　处：《机械研究与应用》2021年第3期1-10,共10页Mechanical Research & Application

基　　金：国家重点研发计划子课题:果蔬干燥减损关键技术与装备研发(编号:2017YFD0400900);国家职业教育建筑材料工程技术专业资源库(2017-6)建设子项目:微知库课程建设(编号:Jczyk48)。

摘　　要：针对常见的齿轮传动系统动态响应特性分析模型往往忽略了单齿本征振动及齿间非线性接触的问题,文中建立了一个充分考虑单齿本征振动及齿间非线性接触的简化动态响应分析模型。建模过程中,首先基于接触特性、接触位置、惯性特性、啮合刚度和阻尼的理论计算分析,分别建立了全要素计算模型a和简化计算模型b;然后创新性的分别针对多齿传动系统A与少齿传动系统B,运用基于理论计算二次开发的Matlab和Simulink代码,并根据a和b分别进行了线性和非线性分析;最后得到6种典型的动态响应类型及其振动特性的示意图,并进行分布分析。分析结果表明:在低齿数、中低转速或高负载时,齿的本征振动对传动系统的动态响应影响不可忽略。齿的本征振动引起了非线性接触损耗和混沌运动,对齿轮传动系统的动态响应建模尤为重要。通过对a和b的响应分布和有限元分析结果进行对比,间接证明了b的正确性,同时在计算中证明b在保证分析精度的基础上,使分析效率提高了6.8%,即计算成本下降6.8%。For the common dynamic response characteristic analysis models of gear transmission systems,problems of the intrinsic vibration of single tooth and the non-linear contact between teeth are often ignored.In view of this,a simplified dynamic response analysis model that fully considers the intrinsic vibration of single tooth and the nonlinear contact between teeth is established in this paper.In the modeling process,firstly,based on the theoretical calculation and analysis of contact characteristics,contact position,inertia characteristics,meshing stiffness and damping,a full-element calculation model a and a simplified calculation model b are established respectively;and then,aiming at the multi-tooth transmission system A and the few-tooth drive system B,the linear and non-linear analysis are performed respectively according to a and b by using the Matlab and Simulink codes based on the secondary development of theoretical calculations;finally,six typical dynamic response types and schematic diagrams of their vibration characteristics are obtained,and the distribution analysis is conducted.The analysis results show that the intrinsic vibration of teeth has a non-negligible effect on the dynamic response of the transmission system when the teeth number is low,the speed is low or the load is high.The intrinsic vibration of the tooth causes nonlinear contact loss and chaotic motion,it is particularly important to model the dynamic response of the gear transmission system.By comparing the response distribution of a and b with the finite element analysis results,the correctness of b is indirectly proved,and it is proved in the calculation that the analysis efficiency of b is increased by 6.8%on the basis of ensuring the accuracy of the analysis,that is,the calculation cost are down by 6.8%.

关 键 词：齿轮传动 动态响应 齿面接触分析 本征振动 混沌运动 

分 类 号：TH132.4[机械工程—机械制造及自动化]