行星齿轮典型断齿故障的动力学仿真

基于一种改进的行星齿轮箱集总参数模型,将断齿故障等效到时变啮合刚度中,建立了直齿行星齿轮的太阳轮断齿故障、行星轮断齿故障和内齿圈断齿故障的动力学模型。以某单级行星齿轮为研究对象,考虑扭转方向外部激励,对其正常和各断齿故障状态下的动力学模型进行求解,对内齿圈垂直振动加速度信号进行分析。研究结果表明:只考虑扭转方向的外部激励时,正常状态下内齿圈最高点处的垂直振动加速度信号频谱中幅值最高的共振峰与模态能量分布相关;在各断齿故障状态下,内齿圈垂直振动加速度的有效值均大于正常值,时域波形中可看到不同形式的冲击,包络谱中可看到对应的故障特征频率及其倍频成分。     

Quasi-Static and Dynamic Behaviors of Helical Gear System with Manufacturing Errors

Time?varying mesh stiffness(TVMS) and gear errors include short?term and long?term components are the two main internal dynamic excitations for gear transmission. The coupling relationship between the two factors is usually neglected in the traditional quasi-static and dynamic behaviors analysis of gear system. This paper investigates the influence of short?term and long?term components of manufacturing errors on quasi?static and dynamic behaviors of helical gear system considering the coupling relationship between TVMS and gear errors. The TVMS, loaded static transmission error(LSTE) and loaded composite mesh error(LCMS) are determined using an improved loaded tooth contact analysis(LTCA) model. Considering the structure of shaft, as well as the direction of power flow and bearing location, a precise generalized finite element dynamic model of helical gear system is developed, and the dynamic responses of the system are obtained by numerical integration method. The results suggest that lighter loading conditions result in smaller mesh stiffness and stronger vibration, and the corresponding resonance speeds of the system become lower. Long?term components of manufacturing errors lead to the appearance of sideband frequency components in frequency spectrum of dynamic responses. The sideband frequency components are predominant under light loading conditions. With the increase of output torque, the mesh frequency and its harmonics components tend to be enhanced relative to sideband frequency components. This study can provide effective reference for low noise design of gear transmission.     

Dynamic characteristics analysis and experimental research on a new type planetary gear apparatus with small tooth number difference

Aimed at an internal mesh planetary gear with small tooth number difference (PGSTD) reducer, this paper proposes dynamic characteristics analysis. First, static finite element (FE) analysis is performed to check the structural strength with the stress distribution in the gear teeth. Second, by means of the dynamic contact FE method, the internal dynamic excitations of teeth mesh are obtained, including mesh stiffness excitation, transmission error excitation and mesh impact excitation. According to the established model for dynamic FE modal analysis, the natural frequencies and mode shapes of the planetary gear apparatus (PGA) are calculated, and its structural dynamic response and acceleration noise are researched with the comprehensive consideration of internal and external excitations. Finally, the noise and vibration testing on the PGA is carried out by utilizing the vibration test equipment. The results confirm that the predicted values are consistent with the experimental results.     

基于包络加窗同步平均的行星齿轮箱特征提取

行星齿轮箱由于行星轮通过效应、太阳轮与行星架的旋转及时变工况,导致其振动响应存在时变传递路径及非平稳性等特点,且传统的同步平均将不能直接应用于行星齿轮箱。笔者在国外加窗同步平均的基础上提出一种能有效克服时变传递路径及非平稳性的基于包络信号角域加窗同步平均的行星齿轮箱故障特征提取方法。首先,基于谱峭度提取出行星齿轮箱振动信号的包络信号;其次,再利用计算阶比跟踪技术对包络信号进行等角度重采样,行星架每旋转一圈,选择合适的窗函数对角域信号进行多齿宽加窗截取;最后,验证齿轮啮合齿序特征,根据重排齿序对加窗信号进行重构振动分离信号,对振动分离信号进行角域同步平均,提取行星齿轮箱故障特征。行星齿轮箱故障实测信号分析表明,该方法能有效提取行星齿轮箱故障特征。     

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.     

计入齿圈柔性的直齿行星传动动力学建模

为揭示齿圈柔性对传动系统动态性能的影响,在系杆随动坐标系下建立计入齿圈柔性的直齿行星传动精细化动力学模型,建模中计入时变啮合刚度、支承刚度、陀螺效应和齿圈柔性等诸多影响因素。采用有限段单元的离散化建模方法,将连续体的柔性齿圈离散成由等效虚拟弹簧连接的刚性齿圈段,并推导齿圈段与行星轮的啮合判据。通过分析各构件间的相对位移关系及其受力,最终建立系统的运动微分方程。以三行星轮的NGW型直齿行星传动为例对其进行固有特性分析,得出系统的低阶固有频率分布及相应的振动模式,并进一步分析齿圈柔性和安装方式对系统固有特性的影响。研究结果表明,直齿行星传动的振型可归结为中心构件(太阳轮、系杆)扭转振动和中心构件平移振动两种模式,两种模式下齿圈和行星轮均做复杂平面振动;齿圈的柔性会降低系统的低阶固有频率,且其影响程度与齿圈安装方式有关,齿圈完全固定时其影响最小,径向浮动或周向转动时影响较明显。     

变载荷激励下风电行星齿轮系统动力学特性

为了更准确地分析风电行星齿轮系统的动力学特性,在同时考虑风速变化和发电机电磁转矩变化引起的外部载荷激励,齿轮时变啮合刚度、轴承时变刚度以及行星齿轮啮合相位差等引起的内部激励的条件下,建立了风电行星齿轮系统的动力学模型。在此基础上,采用Runge-Kutta数值积分方法求解了某兆瓦级半直驱风电行星齿轮系统的动态响应,分析了上述激励对系统动态特性的影响规律。结果表明：外部变载荷的激励使系统的响应频率具有明显的低频成分,各构件的扭转振动位移与外部合力矩有相似的变化趋势;行星轮啮合相位差的激励使系统的结构频率成分增多且频率减小,增加了系统共振的可能性;轴承时变刚度使系统的高阶响应频率产生较大波动,增加了系统动态响应的复杂性。
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风机行星齿轮系统齿轮裂纹故障诊断

针对风力发电机实际行星齿轮系统,由于幅值及相位调制现象(各种制造误差不可避免等原因所导致)带来的故障诊断难题,搭建了含各种制造误差的动力学模型。模型考虑了出现裂纹故障以后,故障对时变啮合刚度以及传递误差的影响,通过数值求解,对比行星轮、太阳轮以及齿圈出现故障后与正常齿轮系统的包络谱结构特性,总结了故障特征频率。在风力发电机齿轮箱实验台上进行裂纹故障试验验证,结果表明所总结的故障特征频率可以作为风力发电机裂纹故障诊断及定位的依据。     

Life Distribution Transformation Model of Planetary Gear System

Planetary gear systems have been widely used in transportation, construction, metallurgy, petroleum, aviation and other industrial fields. Under the same condition of power transmission, they have a more compact structure than ordinary gear train. However, some critical parts, such as sun gear, planet gear and ring gear often suffer from fatigue and wear under the conditions of high speed and heavy load. For reliability research, in order to predict the fatigue probability life of planetary gear system, detailed kinematic and mechanical analysis for a planetary gear system is firstly completed. Meanwhile, a gear bending fatigue test is carried out at a stress level to obtain the strength information of specific gears. Then, a life distribution transformation model is established according to the order statistics theory. Transformation process is that, the life distribution of test gear is transformed to that of single tooth, and then the life distribution of single tooth can be effectively transformed to that of the planetary gear system. In addition, the effectiveness of the transformation model is finally verified by a processing method with random censoring data.     

带有柔性齿圈和行星架的直齿和斜齿行星传动的模拟

本文提供可以仿真具有变形零件的直齿和斜齿行星齿轮周转齿轮的三维静态和动态性能的模型。通过三维有限元方法得出的结构求出齿圈和行星架的变形分布。根据模型的转化技术,通过考虑到轮齿接触弹性原则,由连接齿圈结构和行星轮分块参数模型限定内齿轮元件。沿接触线导出离散的啮合刚度和当量法面偏差,并把啮合齿面位置作为随时间变化再计算它们的数值。采用约束基础技术仿真一个连接行星轮中心的行星架,用组合板块参数太阳轮／行星齿轮和沿轴装零件集成刚度,质量和惯量完善行星齿轮／周转齿轮模型。对整个啮合仿真用综合时间一分级积分框图和接触算法解相应的运动方程式。得出的一些准静态和动态的结果表明所推荐的混合模型的趋向和考虑齿圈和行星架变形的重要性。     

基于EEMD的行星齿轮箱齿轮裂纹损伤定位

针对行星齿轮式变速箱的齿轮裂纹损伤难以提取特征频率和定位的问题,提出基于总体平均经验模式分解(ensemble empirical mode decomposition,简称EEMD)的齿轮局部损伤频率解调分析方法。该方法在建立的齿轮局部损伤振动信号模型的基础上,分别对太阳轮、齿圈、行星轮的裂纹损伤信号进行EEMD分解和频率解调分析,通过频谱图提取齿轮的局部损伤特征频率,从而识别变速箱中裂纹损伤齿轮的位置。综合仿真分析和试验结果表明,基于EEMD的齿轮局部损伤频率解调分析方法可以有效地提取太阳轮、齿圈和行星轮的裂纹损伤特征频率,实现行星齿轮式变速箱中齿轮裂纹损伤的定位。     

M-DOF dynamic model for load sharing behavior analysis of PGT

A Multi-degree-of-freedom (M-DOF) nonlinear dynamic model for n-pinion Planetary gear train (PGT) is presented in this paper to investigate load sharing behavior of planet gears. In this dynamic model, manufacturing and assembly errors, elastic deformation and time-varying mesh stiffness are considered. Two sets of elastic compatibility equations are proposed to describe compatibility relationship between displacements, errors and elastic deformations. By means of Ishikawa formula, time-varying mesh stiffness of the gear pair is determined. The dynamic motion equations are solved with Runge-Kutta numerical integral method, which yields the displacements and deformations of each component. With the model, dynamic load sharing behavior of planet gears is evaluated. An example of 3-pinion PGT dynamic modeling is included, for which the influence of floating sun gear and adding flexible planet pin on the load sharing characteristics is analyzed.     

某型直升机行星齿轮机构弹流润滑研究

分析了某型直升机主减速器行星齿轮机构弹流润滑工况,研究了该齿轮系弹性润滑最薄弱啮合部位,计算得出了行星齿轮传动机构中齿宽、齿轮模数和压力角等齿轮参数对弹性润滑油膜厚度的影响,提出了改进直升机主减速器行星齿轮机械润滑状态的新思路和具体改进方案,结果证明增加行星轮和太阳轮的齿宽、模数和齿轮啮合角及提高润滑油粘度和粘压系数,可有效地改进齿轮润滑,减少齿面失效,提高行星齿轮传动机构的可靠性。     

基于模态叠加法的大型立式行星传动齿轮箱动力学分析及测试

根据某大型立式行星传动齿轮箱的结构和动态性能特点,建立了其直齿行星传动的平移-扭转耦合集中参数动力学模型,基于模态叠加法采用ADAMS动力学分析软件对齿轮箱的高速轴、低速轴、行星轮和太阳轮等构件进行了动力学特性分析,得到了整个传动系统的频响函数和模态频率。通过理论分析与现场测试结果进行对比,分析了该行星传动系统固有特性对齿轮箱产生的振动及噪声的影响。     

Assessing the role of plastic deformation in gear-health monitoring by precision measurement of failed gears

For constant loading and speed conditions, the principal sources of vibration excitation arising from meshing gears, characterised by the “static transmission error” (STE) excitation, are geometric deviations of the working surfaces of the teeth from equi-spaced perfect involute surfaces, and tooth/gear body elastic deformations. Changes in these two sources caused by tooth-bending-fatigue damage on one or a few teeth are manifested primarily in the rotational-harmonic content of the STE of each individual damaged gear of the meshing pair, and are most effectively detected in the time domain. The optimum number of gear rotations to be used in synchronous averaging is specified, along with how such synchronous averaging can be used to eliminate the effects of the mating gear in the case of “hunting tooth” gear pairs, and to minimise these effects otherwise. Precision measurements made on the teeth of a gear failed in a tooth-bending-fatigue test strongly suggest that whole-tooth plastic deformation—i.e. yielding, rather than changes in tooth stiffness caused by tooth-root cracks, is the principal source of detectable damage in the case of tooth bending fatigue. Such plastic deformations are geometric deviation STE contributions. Differences in gear materials, materials processing, and gear operating properties may significantly affect the amounts of such plastic deformations before tooth breakage and the operating duration between initial damage detection and tooth breakage, thereby suggesting the need for testing to determine such dependencies.     

行星轮系动力学新模型及其故障响应特性研究

行星轮系中零部件多、结构复杂,建模难度大。行星轮既自转又公转,导致啮合点到固定在箱体上的传感器之间的距离时刻变化,从而产生振动传递路径时变效应,增加了振动响应的复杂性。现有的动力学模型大多针对正常情况下的行星轮系进行建模,而且未考虑振动传递路径时变效应对振动响应的影响。针对以上不足,推导了行星轮系正常、裂纹及剥落三种情况下的时变啮合刚度算法,考虑振动传递路径时变效应的影响,建立了相应的动力学模型,求解得到行星轮系正常、裂纹及剥落时的动态响应,并分析了它们的频谱特性。搭建了行星齿轮箱试验台以获取振动响应信号,与模型响应信号进行了对比分析,结果验证了动力学模型的准确性,为行星轮系的健康监测提供了理论依据。     

系统刚度对行星齿轮传动振动特性影响研究

为了分析齿轮啮合刚度、支承刚度对行星传动系统振动特性的影响,建立了基于人字齿行星传动的平移一扭转耦合的动力学模型.在动力学模型中,每个运动构件假定有3个自由度,同时考虑各构件的支承刚度、轮齿时变啮合刚度等影响因素.根据各构件的运动方程建立传动系统的动力学微分方程,并对其进行特征值问题求解,获取行星传动系统振动特性.     

Effects of gear modifications on the dynamic characteristics of wind turbine gearbox considering elastic support of the gearbox

The reliability and service life of wind turbines are directly influenced by the dynamic performance of the gearbox under the time-varying wind loads. The control of vibration behavior is essential for the achievement of a 20-year service life. We developed a rigid-flexible coupled dynamic model for a wind turbine gearbox. The planet carrier, the housing, and the bedplate are modelled as flexibilities while other components are assumed as rigid bodies. The actual three points elastic supporting are considered and a strip based mesh model is used to represent the engagement of the gear pairs. The effects of gear tooth modifications on the dynamics were investigated. Finally, we conducted a dynamic test for the wind turbine gearbox in the wind field. Results showed that the contact characteristics of gear pairs were improved significantly; the peak-to-peak value of transmission error of each gear pair was reduced; the amplitudes of the vibration acceleration and the structural noise of the wind turbine gearbox were lowered after suitable tooth modification.     

钢/塑齿轮组合行星传动的振动特性

为了深入了解钢质行星齿轮传动系统引入塑料齿轮后的振动特性,建立钢/塑齿轮组合行星传动的动力学分析模型和试验模型,对SNS、SSS、SSN和NSS四种钢/塑齿轮组合行星传动的振动特性进行理论分析与试验研究,分析组合方式对行星传动振动特性的影响。数值仿真与试验研究结果表明:塑料齿轮的引入对行星齿轮传动的振动特性影响很大,显著地减小了太阳轮与行星轮和内齿圈与行星轮的啮合动载荷;有效地抑制了行星齿轮传动的齿轮啮合频带振动和高频带振动;组合方式对行星齿轮传动的振动特性影响显著,合理地采用钢/塑齿轮组合行星传动结构可以极大地降低啮合动载荷,从而有效地抑制传动系统的振动和噪声。     

变速行星齿轮系统故障诊断方法

针对风力发电机行星齿轮系统变速非平稳工况,且故障信号耦合调制严重、传递路径复杂、噪声污染严重等特点,提出了基于阶次包络分析的故障诊断方法,详细阐述了方法原理和实现流程。通过对变速工况下的仿真加速度信号进行阶次包络分析,对比行星轮、太阳轮以及齿圈出现故障后与正常齿轮系统的阶次包络谱结构特性,总结了不同部件故障的特征阶次。在此基础上,通过对变速行星齿轮系统试验信号的分析表明:阶次包络分析方法能较好地抑制噪声干扰,反映故障特征清楚,且故障特征能作为变转速时行星齿轮系统故障诊断和定位的依据。