人字齿行星传动系统非线性动力学特性分析

本文对船用人字齿封闭差动行星传动系统在空载或轻载工况下出现的倍频振动问题进行了非线性动力学特性分析。根据系统中太阳轮浮动的结构特性,结合实际工况,通过考虑齿轮间隙和重力作用,采用理论研究及数值仿真方法分析了系统在空载或轻载工况下输出轴转频的倍频及其谐频的频率响应成分问题。通过分析齿轮啮合存在的3种状态,得到了变形量函数并提出了啮合力表达式。数值计算结果表明:当系统处于空载或轻载工况时,输出轴会产生输入轴的多倍频及其谐频的频率响应成分,且与行星轮数量有直接关系,当输入扭矩增大时至重载时,输出轴的倍频响应成分消失。     

行星齿轮传动系统动力学研究进展

详细评述了国内外学者对行星齿轮传动系统在动力学模型、动态响应、动载荷和均载、固有特性等方面的研究状况,介绍了2种集中参数模型用不同方法求解系统动态响应的结果,动载荷和均载的理论与试验研究,固有特性的规律及系统参数对固有特性等方面的研究成果.最后,根据行星齿轮传动系统研究的发展趋势,提出了需要进一步研究的几个问题:含摩擦力的行星齿轮动力学特性研究,复合行星齿轮动力学特性研究和齿轮系统的振动控制研究.     

渐开线花键连接的非线性动力学特性

为给花键连接磨损分析和寿命预估提供精确的数值基础,对渐开线花键的非线性动力学特性进行研究.利用集中质量模型建立具有齿侧间隙的花键连接四自由度非线性动力学方程,计算花键连接实际接触齿对数及综合时变啮合刚度,采用四阶Runge-Kutta法求解花键连接非线性动力学方程.计算结果表明:花键副啮合刚度随时间呈周期性变化,随扭矩呈分段线性分布;当系统转速为300 r/min时,系统呈简谐响应;转速为348 r/min时,系统呈两周期响应;转速为360 r/min时,系统呈5周期响应;转速为1 080 r/min时,系统进入混沌响应;花键副的动载系数也呈周期性变化,并随扭矩及齿侧间隙的的增大而增大.减小渐开线花键链接的齿侧间隙,有利于降低动态载荷,提高花键副工作的稳定性.     

行星齿轮机构弹性动力学建模

通过把行星齿轮机构划分成几个相互关联的子系统,应用牛顿第二定律,详细推导了行星齿轮的振动公式,建立了系统的旨性动力学分析模型,纠正了文献中的错误公式,为系统地研究行星齿轮机构的动态学行为和行星齿轮机构的减振奠定了理论基础。     

含齿面分形啮合刚度的齿轮传动系统动力学

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.     

行星齿轮机构弹性动力学建模

通过把行星齿轮机构划分成几个相互关联的子系统,应用牛顿第二定律,详细推导了行星齿轮的振动公式,建立了系统的弹性动力学分析模型.纠正了文献中的错误公式,为系统地研究行星齿轮机构的动力学行为和行星齿轮机构的减振奠定了理论基础.     

星型齿轮传动系统的非线性动力学分析

建立了星型齿轮传动系统的间隙型非线性动力学模型,考虑了齿轮副的啮合综合误差,齿轮的啮合间隙和时变啮合刚度。并用数值解法对系统的动力学微分方程进行求解,获得了星型齿轮传动在外扭矩作用下受齿轮副传动误差激励的非线性稳态强迫响应。以一个具有3个星轮的四自由度星型齿轮传动为例,对系统的非线性动态响应做了分析,利用时间历程、相平面、Poincar(?)映射以及 Fourier频谱阐述了多自由度间隙型非线性星型齿轮传动系统的简谐、非谐单周期、次谐波、准周期和混沌响应的动力学特性。     

同轴对转行星齿轮传动系统的固有特性

以同轴对转行星齿轮传动系统为研究对象,为揭示其固有特性,基于齿轮系统动力学和Lagrange方程建立了同轴对转系统的平移-耦合动力学模型。根据同轴对转系统的相关参数进行特征值问题的求解,得到系统的固有频率与振型矢量。分析结果表明系统存在3种不同的振动模式:定轴轮系振动模式、差动轮系振动模式和耦合振动模式。同时讨论了随着差动轮系行星轮个数的增加,系统固有频率的重根数与差动轮系行星轮个数的关系。最后分析了耦合刚度对系统振动特性的影响。     

渐开线直齿轮的非线性振动

在齿轮传动系统内,由于运动阻尼和齿轮啮合刚度的非线性,使得齿轮振动具有非线性振动的特征。以往的研究文献,为了简化运算,都把齿轮的非线性振动问题,当做线性振动问题来处理。本文运用摄动方法求得齿轮振动的非线性渐近解,并指出它和线性振动近似解之间的差异。     

齿侧间隙优化的双圆弧谐波齿轮传动动力学分析

为了优化谐波齿轮传动齿廓结构,减小谐波齿轮传动的齿侧间隙以提高啮合性能.在谐波齿轮传动齿廓优化设计的基础上,采用三维有限元轮齿动态接触分析的方法,建立了刚轮、柔轮以及波发生器构成的轮齿接触三维有限元分析模型,通过加载和运动实现各构件间的转速和转矩的传递,对谐波齿轮的柔轮进行了啮合仿真和动力学动态仿真分析,并对传动过程中...     

Dynamic load sharing characteristics and sun gear radial orbits of double-row planetary gear train

A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.     

两级齿轮减速器非线性振动特性研究

为研究齿轮减速器中齿隙等非线性因素对系统振动特性的影响,建立了包含多齿隙的两级直齿轮减速器的8自由度非线性动力学模型.以一个两级齿轮减速器为例,利用数值方法对建立的非线性微分方程进行了求解,获得了不同参数条件下齿轮副及支撑轴振动响应中的吸引子共存现象,包括简谐与次谐吸引子共存、拟周期与简谐和次谐吸引子共存、简谐与次谐和非简谐吸引子共存、非简谐与混沌吸引子共存、混沌吸引子共存等,并分析了齿轮副的工作状态.结果表明,齿隙等非线性因素使系统的振动具有了丰富的非线性特性,且对齿轮副分离和冲击有很大影响.     

螺旋锥齿轮非线性振动特性及参数影响

引入沿啮合点法向的相对位移,建立了含间隙、时变啮合刚度和传动误差的螺旋锥齿轮传动7自由度动力学模型.运用五阶自适应Runge-Kutta方法对系统非线性振动特性和参数变化对混沌、冲击等行为的影响进行计算分析,得到冲击、非冲击的参数区间.结果表明,随着啮合频率增大、啮合刚度系数增大或啮合阻尼系数减小,系统分别经倍周期分岔、Hopf分岔两种途径进入混沌;随着载荷系数、啮合阻尼系数的增大和啮合刚度系数的减小,混沌和次谐波消减,冲击状况改善,间隙非线性的影响减弱,啮合阻尼系数变化的影响在轻载时更显著,而啮合刚度系数变化的影响在重载时更显著.     

两级人字齿行星传动系统的模态跃迁现象

根据两级人字齿行星传动系统特有的振动模态特性,分析了系统的模态跃迁现象.通过对表征局部曲率的耦合因子的分析,提出了分属不同振动模式下的固有频率模态跃迁准则,并通过具体的实例验证了准则的正确性,为系统的优化设计提供了理论依据.     

载荷分流式多级行星齿轮传动参数优化设计（“研究生论坛”稿件）

提出了一种风电增速箱用载荷分流式两级行星齿轮新型传动机构,应用转化机构法和行星齿轮传动构件速度间的普遍公式,求得了该新型传动机构的总传动比公式。研究表明,传动比随着两级行星排特性参数的取值的增加而增大,在区间[3,8]之间传动比最大取值为73。在此基础上对载荷分流三级行星传动系统的参数优化问题进行了研究。结果表明,给出的优化设计方法和得到的优化设计参数,能够显著的降低载荷分流式风电增速箱多级传动系统的体积。     

Structure vibration characteristics of two stage double helical tooth planetary gear trains with unequally spaced planets and stars

A computational model of two stage double helical tooth planetary gear set is employed to built the lateral torsional coupling dynamic governing equations. Base on the dynamic equation, the free vibration properties of the system with unequally spaced planets and stars are analyzed. The vibration modes are classified into three types: star mode, planet mode, and coupling mode. For each of the modes, the relation between inherent frequency and vibration amplitude is investigated in detail by the eigenvalue and mode characteristics.     

Dynamic load sharing behavior of transverse-torsional coupled planetary gear train with multiple clearances

A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.     

Bifurcation and chaos study on transverse-torsional coupled 2K-H planetary gear train with multiple clearances

A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.     

汽车起升机构行星减速器啮合特性模拟

齿轮传动中干涉与否和重合度的大小,是重要的啮合特性,也是评价传动质量重要指标。运用三维造型、帧幅动画等技术,完成了汽车起重机起升机构行星减速器啮合特性的三维显示模拟,直接观察了设计合理性,大大地缩短了设计周期,其有效性在１６０ｔ汽车起重机起升机构行星减速器设计中得到了充分验证。