一种面齿轮传动时变啮合刚度数值计算方法

准确计算时变啮合刚度是齿轮动力学研究的基础。提出了一种面齿轮传动时变啮合刚度数值计算新方法。以直齿圆柱齿轮为例,建立合理的有限元模型,得到直齿圆柱齿轮的时变啮合刚度曲线,并将其与ISO6336方法计算结果进行对比,验证了该啮合刚度计算方法的正确性及有限元模型的精确性。应用该数值计算方法,研究面齿轮传动时变啮合刚度变化规律,得到了精确的面齿轮传动时变啮合刚度曲线。研究结果为面齿轮传动的动力学分析及设计提供参考。     

An investigation on the influence of modification parameters on transmission characteristics of planetary gear system

A new gear tooth modification model of planetary gear system was established by considering the characteristics of tooth longitudinal crowning modification and tooth profile modification. Using this model, the influences of modification parameters on the time-varying mesh stiffness, transmission error, contact spots and dynamic response of the planetary gear system were analyzed through numerical analysis. The results show that tooth profile modification can effectively restrain the mesh stiffness sudden variation in the single and double tooth alternation of both the internal and external mesh pairs, and significantly decrease the transmission error fluctuation. However, longitudinal crowning modification has no marked influence on mesh stiffness sudden variation or transmission error fluctuation. The tooth profile modification can significantly reduce the sudden variation of tooth surface load during gear mesh course. Longitudinal crowning modification can make the tooth surface load evenly distributed in tooth width direction. When the external meshing pairs are modified at the tooth profile individually, the magnitude values of main response resonance peaks of internal meshing pairs have a great reduction, but those values of external meshing pairs change slightly. In the case of tooth profile modification of the internal meshing pairs, the phenomenon is reversed. By contrast with tooth profile modification, longitudinal crowning modification has little influence on the resonance peaks of internal and external meshing pairs.

     

含间隙的斜齿轮副扭振分析与试验研究

建立了科齿轮副的间隙型非线性扭振模型，其中考虑了斜齿轮副的啮合综合误差，齿侧间隙和时变啮合刚度。采用三维有限元法计算了斜齿轮副啮合刚度，用三次样条插值拟合得到时变啮合刚度函数。用数值积分方法对系统的非线性动力学微分方程进行了求解，获得了斜齿轮副在外转矩作用下受静态传动误差激励的非线性稳态强迫响应，并对系统的动态响应进行了测试，试验和理论计算结果了一致性证实了本文所提出模型和解法的正确性。     

随机风载作用下风力发电机齿轮传动系统动态可靠性分析

运用最小二乘支持向量机(Sparse least squares support vector machines,SLS-SVM)机器学习方法建立风场随机风速模型,根据随机风速模型和空气动力学理论得到随机风引起的系统外部载荷激励,建立考虑齿轮时变啮合刚度和滚动轴承时变刚度的风力发电机行星齿轮传动系统齿轮—轴承耦合动力学模型,并对动力学模型进行仿真计算,分别得到各齿轮副的动态啮合力和滚动轴承动态接触力。以此为基础,将载荷作用过程视为随机过程,推导出随机载荷作用下的等效载荷累计分布函数。根据应力—强度干涉理论建立风力发电机齿轮传动系统各齿轮和轴承的动态可靠性模型,利用二阶矩和摄动方法求出各齿轮、轴承的动态可靠性指标,并计算出动态可靠度,研究各齿轮、轴承和传动系统的动态可靠度随时间的变化规律,为风力发电机齿轮传动系统动态可靠性设计奠定了基础。     

Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach

Time-dependent mesh stiffness is a most important reason of vibration and dynamic excitation in gear sets. In this research, analytical formulas of the helical gear set and the planetary gear system are combined to calculate the time-dependent mesh stiffness of the helical planetary gear system. For this purpose, at the first step, the analytical equations are derived for the spur gear pair. Then by dividing a helical tooth into the several independent thin spur tooth slices, the helical gear pair mesh stiffness is extracted. Finally, these equations are extended to the helical planetary gear system. The suggested analytical results and those which obtained by the finite element method (FEM) are compared and are in good agreement when the helix angle is less than 15 degrees. Also, the helical planetary gear system mesh stiffness in different cases such as fixed carrier, fixed sun gear and fixed ring gears is calculated. These results show that the value of mesh frequency ratio in each case scales the mesh stiffness shapes in the rotation angle direction. In other words, mesh frequency ratio parameter determines the number of meshing period in each rotation of planets.     

考虑随机制造误差的风力机行星齿轮系统动力学特性

为研究综合传递误差的随机波动对风力发电机齿轮传动系统动力学特性的影响,考虑齿轮时变啮合刚度、综合传递误差等因素,建立风力发电机行星齿轮传动系统纯扭转动力学模型。以随机风速引起的齿轮系统转矩波动作为行星齿轮系统的外部激励,对某1.5 MW风力发电机行星齿轮传动系统的动力学特性进行仿真分析,得到系统各响应量时域内的统计特征和齿轮副间的动态啮合力统计特征。分析表明：行星架、行星轮和太阳轮在扭转方向上的振动特性与外部载荷相关,其振动位移与外部载荷波动有相似变化的趋势;综合传递误差随机分量的离散程度对行星齿轮系统的动态特性和齿轮副间的动态啮合力有较大影响。随着综合传递误差随机分量离散程度的增加,行星架、太阳轮和行星轮在扭转方向上的振动幅值明显增加;综合传递误差随机分量的随机性使齿轮副间动态啮合力产生随机波动,随机分量离散程度越大,动态啮合力波动越明显;当随机分量的离散程度达到某一值时,齿轮啮合过程发生脱离,引发啮合冲击。     

随机内外激励对齿轮系统动态特性的影响分析

考虑时变啮合刚度、齿侧间隙等因素的影响,建立了单对齿轮系统纯扭转非线性动力学模型。将齿轮综合传递误差波动和外部载荷作为随机变量,利用数值仿真方法对系统模型进行了求解,通过统计分析得到了系统各响应量和动态啮合力的统计特征。结果表明:外部激励的随机性对齿轮系统振幅和动态啮合力的影响比综合传递误差波动随机时明显;综合传递误差及外部激励随机波动离散程度的增加会导致系统振幅和动态啮合力不稳定性加剧。     

考虑强度退化和失效相关性的风电齿轮传动系统动态可靠性分析

针对随机风作用下风力发电机齿轮传动系统失效率高的问题,研究了随机风引起的风力发电机传动系统外部风载荷以及内部由齿轮、轴承刚度及综合啮合误差等引起的内部动载荷激励,基于集中质量法建立了风电齿轮传动系统齿轮-轴承耦合动力学模型。在对模型进行仿真求解的基础上,分别求得了传动系统中各齿轮和轴承的动态接触应力-时间历程。将载荷作用过程视为随机过程,推导出随机载荷作用下的等效载荷累计分布函数,从系统层面上建立了基于应力-强度干涉理论的风力发电机齿轮传动系统动态时变可靠性模型,模型考虑了零件的失效相关性和强度退化因素,研究了失效相关性和强度退化对风电齿轮传动系统可靠度和失效率的影响规律,为风力发电机齿轮传动系统动态设计和可靠性优化设计奠定了基础。     

基于动力学的风电增速箱多级齿轮传动系统可靠性评估

针对风力发电机齿轮传动系统在变风速工况下失效率高的问题,在模拟真实风速的基础上,建立了考虑外部随机风载及内部轮齿时变啮合刚度、轴承时变刚度、综合传递误差等激励因素的风力发电机齿轮传动系统齿轮-轴承耦合动力学模型,通过对动力学模型进行仿真计算,得到了各齿轮副的动态啮合力和各支承轴承的动态接触力,并求得齿轮的使用系数、齿轮和轴承的载荷系数。在此基础上,建立了基于动力学的风电齿轮传动系统可靠性评估模型,并求得了各零件及传动系统的可靠度,较全面地评价了随机风载作用下风力发电机齿轮传动系统的可靠性,为风力发电机齿轮传动系统可靠性设计和动态优化奠定了基础。     

输入转矩对驱动桥系统动力学特性的影响

在驱动桥系统中,滚子轴承是连接轴系与壳体的关键部件,其刚度具有各向耦合性和非线性特性,且与输入转矩有关。为准确高效地分析输入转矩对驱动桥系统动力学特性的影响,基于非线性轴承理论、有限元法和模态综合方法,建立包含主减速器总成、差速器总成、轮毂总成和桥壳等部件的完整驱动桥系统动力学分析模型,根据输入转矩大小的不同,定义轻载、中载和重载三种典型工况,分别计算各工况下的非线性轴承刚度,分析轴承刚度随输入转矩大小变化的特点,对驱动桥系统进行单位谐波传动误差激励下的动力学分析,研究输入转矩对驱动桥系统动力学特性的影响,分析不同工况下准双曲面齿轮动态啮合力的频响特性。计算结果表明,驱动桥系统动力学特性随输入转矩大小变化具有一定规律,能有效指导驱动桥系统的减振降噪设计,避开危险工况。     

Comparisons of gear dynamic responses with rectangular mesh stiffness and its approximate form

The mesh stiffness is close to rectangular stiffness, and the first harmonic approximate term of rectangular stiffness is generally adopted in the nonlinear gear dynamic analysis. The differences between the rectangular stiffness and its approximate form are analyzed in detail. The frequency response and dynamic factor are calculated by a numerical method, to illustrate the dynamic characteristics of the gear nonlinear system with different mesh stiffness forms. The results show that: The trends of frequency response of gear dynamic system with rectangular stiffness and its approximate form are identical. The jump phenomena are detected in both cases. Without the effect of static transmission error, the dynamic factor with rectangular mesh stiffness is larger than that with approximate mesh stiffness. Under design power and speed condition, the result with approximate mesh stiffness function may deduce reasonless suggestions for a designer. The static transmission error will enlarge the vibration amplitude and dynamic factor when the approximate mesh stiffness is adopted, but the effects on the response of gear system with rectangular mesh stiffness are fractional. The mesh stiffness may excite the odd subharmonic resonance, and the static transmission error may excite the even sub-harmonic resonance respectively.     

考虑齿距偏差的直齿轮转子系统振动特性分析

针对工程实际中的齿轮存在齿距偏差,主要研究齿距偏差对齿轮系统振动特性的影响。考虑齿距偏差,建立了齿轮啮合刚度和传递误差模型,在此基础上,建立了通用齿轮啮合动力学模型,将该模型与转子系统有限元模型进行耦合,得到了齿轮转子系统有限元模型,分析了齿距偏差对系统振动响应的影响。研究结果表明:由于齿距偏差的存在,齿轮双齿啮合区刚度降低,无载荷传递误差增大,齿轮系统振动增大,频谱图中出现啮合频率及其高次谐波的边频带成分,这些边频带主要由主动和从动齿轮的转频及其倍频组成。减小齿距偏差和增大作用扭矩均能降低齿距偏差引起的边频带幅值。研究结果可为含齿距偏差的齿轮振动分析提供理论依据。     

随机风作用下风力发电机齿轮传动系统动载荷计算及统计分析

针对风力发电机齿轮传动系统在随机风作用下失效率高的问题,在模拟真实风速的基础上,建立考虑外部随机风载及内部齿轮时变啮合刚度、轴承时变刚度及综合传递误差等激励因素的风力发电机齿轮传动系统齿轮-轴承耦合动力学模型,通过对动力学模型进行仿真计算,得到各齿轮副的动态啮合力和各支承轴承的动态接触力。结合有限单元法和赫兹接触理论,得到关键零部件的应力时间历程,采用雨流计数法对应力时间历程进行统计分析,得到传动系统各关键零部件承受载荷的应力谱及概率分布函数。研究结果为风力发电机齿轮传动系统的动态可靠性分析和疲劳寿命预测奠定基础。     

基于线性规划法的齿轮啮合刚度与载荷分布计算的改进方法

齿轮副啮合刚度和轮齿传递载荷的周期性变化是齿轮系统产生振动的主要内部激励之一。本文提出了一种基于线性规划法计算轮副啮合刚度和载荷分布的改进方法。该方法利用造型软件Pro-E建立具有真实渐开线齿廓的齿轮实体三维模型,运用有限元软件ANSYS计算齿面柔度系数。该方法的另一优势是整个计算过程能够实现参数化。文末利用本文提出的方法计算了一对外啮合斜齿轮,计算结果证明改进方法有效。     

Influences of friction and mesh misalignment on time-varying mesh stiffness of helical gears

As one of the most important excitation sources of vibration, time-varying mesh stiffness of helical gear pairs need accurately calculated. Compared with spur gears, friction in helical gears is significant. This work for the first time presents an improved calculation method for the mesh stiffness of helical gears with effect of friction incorporated. Firstly, helical gear is sliced into number of pieces along its axis direction and each piece could be regarded as spur gear. Then forces applied to each piece including friction force are analyzed. Potential energy method is employed to develop time-varying mesh stiffness of each piece pair of both kinds of helical gears with different transverse and axial contact ratios. Furthermore, influences of various working conditions and misalignment on mesh stiffness are also investigated. Results indicate that effect brought by friction on total mesh stiffness should be not neglected. The reduction amount of stiffness increases with lower speed, heavier load and rougher surface. The stiffness difference between cases with and without friction is affected by gear geometry and mounting parameters like module, helix angle and mounting misalignment. This work provides an essential tool for comprehensive dynamics analysis with consideration of the relationship between stiffness and working conditions.     

不同重合度非圆齿轮设计及弯曲应力分析

非圆齿轮传动具有广泛的应用场景。针对非圆齿轮传动,采用齿轮啮合原理和材料力学等原理及方法,提出了大重合度非圆齿轮设计方法。探讨了非圆齿轮传动原理和节曲线构建方法,计算了其节曲线曲率半径和重合度方程。建立了不同重合度非圆齿轮轮齿时变啮合刚度与载荷分配率计算模型,推导了不同重合度非圆齿轮齿根弯曲应力方程。探讨了不同结构参数下非圆齿轮副重合度、时变啮合刚度、时变载荷分配率及齿根弯曲应力变化规律,确定了轮齿所受最大载荷位置。开展了不同重合度非圆齿轮齿根弯曲应力仿真分析和实验测量,与理论计算结果进行了对比分析,最大误差分别约为4.8%和5.9%,验证了理论方法的合理性与正确性,为大重合度非圆齿轮传动的工程应用奠定了基础。     

基于啮合特性直齿锥齿轮分支传动静力学均载分析

为了改善直齿锥齿轮分支传动系统性能,提出基于啮合特性的静态均载分析方法。通过建立考虑中心轮安装误差的单级分支系统多体齿轮齿面接触分析(MTCA)方法,获得各齿轮副初始接触间隙;计及该间隙引起的啮合偏差,采用集中参数法主要考虑中心轮的浮动特性,建立考虑其支撑变形、各齿轮扭转变形相互耦合的静力学平衡方程,获得各分支均载系数,分析了载荷、安装误差、支撑刚度等对系统均载系数的影响。结果表明,随支撑刚度、安装误差的增大,均载系数逐渐增大,轴向对正误差和偏置对正误差对均载系数的影响是等效的;随转矩的增加,均载系数逐渐减小;各分支齿轮副的几何传动误差大小反映了均载系数变化规律,即齿面初始间隙越大,承担的载荷越小。研究结果为高精度直齿锥齿轮分支系统的均载分析提供了理论参考。     

齿轮内啮合传动的重合度及载荷修正系数的计算(Ⅱ)--载荷修正系数数据表

在获得齿轮内啮合传动的齿侧间隙计算公式以后，结合齿对刚度的计算公式，推导出齿轮内啮合传动的加载重合度及载荷修正系数。通过对具有不同模数、齿数、齿数差、变位系数及载荷的齿轮内啮合传动模型的计算，发现载荷及齿数(传动比)的变化对载荷修正系数的影响较大，齿数差及变位系数的变化对载荷修正系数的影响较小，齿轮的精度对载荷修正系数的影响最大。载荷修正系数在0．30至1．00之间变化。     

Effects of dynamic transmission errors and vibration stability in helical gears

Transmission error is an important reason for instability in helical gears. A six-degree-of-freedom dynamic model coupled flexional, torsional and axial motion of a helical gear transmission system, which includes time varying mesh stiffness, bearing supporting stiffness, mesh damping and backlash, is developed, after taking into account the dynamic characteristics and vibration responses of helical gear in three dimensions. Influences of involute contact ratio, bearing supporting stiffness, mesh damping and backlash on the dynamic transmission errors and vibration stability of the helical gear system are investigated using numerical simulation technique. The effects on dynamic transmission errors and stabilities by contact ratio, supporting stiffness and mesh damping as well as gear backlash are analyzed. The intrinsic relationship between above parameters and dynamic transmission errors and stabilities for helical gear system are presented. The stable and unstable regions under different parameters are given. The results in this paper can be helpful to the dynamic and stable design of a helical gear transmission system.     

面齿轮传动分扭系统扭转振动的固有频率分析

基于集中质量法,建立了面齿轮传动分扭系统的动力学模型,模型中考虑了系统的扭转振动自由度。列出了系统的刚度矩阵和质量矩阵,求出了系统的各阶固有频率,分析了输入轴和面齿轮轴的扭转刚度以及面齿轮啮合刚度对系统固有频率的影响。结果表明,输入轴和面齿轮轴的扭转刚度对系统的高阶固有频率有较大的影响,面齿轮平均啮合刚度对系统的低阶固有频率有较大的影响。