双参平面内单级直齿圆柱齿轮系统动力特性综合分析  

Dynamic characteristic analysis of a single-stage spur gear system in two-parameter plane

作　　者：田亚平[1] 褚衍东[1,2] 饶晓波[1] TIAN Ya-ping;CHU Yan-dong;RAO Xiao-bo(School of Mechatronic Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;Key Laboratory of System Dynamics and Reliability of Rail Transport Equipment of Gansu Province,Lanzhou Jiaotong University, Lanzhou 730070,China)

机构地区：[1]兰州交通大学机电工程学院,甘肃兰州730070 [2]兰州交通大学甘肃省轨道交通装备系统动力学与可靠性重点实验室,甘肃兰州730070

出　　处：《振动工程学报》2018年第2期219-225,共7页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11262009;11462012);高等学校博士学科点专项科研基金资助项目(20136204110001);兰州市人才创新创业项目(2015-RC-3)

摘　　要：为揭示非线性直齿圆柱齿轮系统分岔、啮合冲击、脱啮和动载系数间的耦合关系,在时变啮合刚度幅值系数与无量纲频率参数平面内用PNF法和延续算法对单级齿轮系统的动力学模型求解获其周期/冲击、脱啮占空比、齿背啮合比、动载系数伪彩图。研究表明:幅值系数和频率是影响分岔、冲击、脱啮、动载系数的主要因素,随幅值系数递增系统经倍化、Hopf、激变、擦切、鞍结分岔方式由周期运动通向混沌,并导致啮合冲击、脱啮占空比和动载系数增大;混沌、拟周期运动和啮合冲击现象出现在共振频率附近,其脱啮、动载系数在该处出现极值。双参平面内综合动力特性转迁规律为齿轮结构设计参数优化提供理论参考。In order to reveal the coupling relationship among bifurcation,gear meshing impact,tooth separation,tooth back-side contact and dynamic load coefficient(DLC)of the nonlinear gear system,the pseudo color maps of the meshing impact and period,duty cycle of the mesh apart(DC 1),duty cycle of the tooth back-side contact(DC2)and DLC for a single stage gear system are obtained by Poincaré-Newton-Fouquet(PNF)and the continuation numerical calculation method in the time-varying meshing stiffness amplitude coefficient(TVMSA)and dimensionless frequency two parameters plane.Research shows that the TVMSA and resonance frequency are main factors for bifurcation,gear meshing impact and DLC of the gear system.With the increase of TVMSA,the system's periodic motion turns to chaos by the way of period-doubling,Hopf,crisis,grazing,saddle node bifurcation and the DC1,DC2 and DLC increase.Meanwhile,the chaos,quasi periodic motion and meshing impact phenomenon appear near the resonant frequency,in which the DC1,DLC reach the extreme values.The dynamic characteristics transitions laws can provide the theoretical reference for the optimization of the gear structure parameter.

关 键 词：非线性振动 单级齿轮传动系统 动力特性 PNF数值法 双参平面 

分 类 号：O322[理学—一般力学与力学基础] TH132.425[理学—力学]