多级行星齿轮传动静力学均载研究

建立了NGW型行星齿轮传动系统的计算模型,针对行星齿轮的制造及安装误差,运用了当量啮合误差原理,计算了系统的均载系数,并分析了不同浮动构件类型及误差对均载的影响。分析结果表明,构件的浮动可以实现均载,两个构件的联合浮动比单独浮动更有利于改善均载;齿轮的制造和装配误差对行星轮均载性能起作用,其中太阳轮误差对均载影响最大。     

内外花键间隙对行星轮系均载特性的影响分析

行星轮系的均载特性是其主要的性能指标之一.国内外多项研究指出,行星轮系中构件的浮动作用对于系统均载具有重要的影响.考虑太阳轮与输入轴的花键连接关系,模拟花键内外齿的摩擦和太阳轮的约束浮动,建立了输入轴花键对太阳轮的非线性支撑反力,以5行星轮传动系统为例,采用集中质量法计算了不同花键径向间隙下的系统均载系数,为行星轮系均载设计提供了依据.     

安装误差对封闭差动人字齿轮传动系统动态均载特性的影响

通过坐标变换推导出封闭差动人字齿轮传动系统各齿轮安装误差沿啮合线等效位移公式;基于集中参数理论,建立采用中间浮动构件的该型传动动力学模型;通过计算系统两级内外啮合均载系数,获得各齿轮安装误差与系统两级内外啮合均载系数关系曲线,进而分析齿轮安装误差对系统均载特性的影响。研究结果表明:在齿轮安装误差作用下,差动级均载系数大于封闭级;差动级内/外啮合均载系数随差动级内齿轮/太阳轮安装误差增加而增大,差动级内齿轮/太阳轮安装误差对差动级外/内啮合均载系数影响很小;封闭级均载系数随封闭级内齿轮安装误差增加而增大,封闭级太阳轮安装误差对封闭级均载系数影响很小;行星轮/星轮安装误差对差动级/封闭级均载系数影响很小;差动级均载系数对差动级中心轮安装误差位置角不敏感,封闭级中心轮安装误差位置角对封闭级均载系数影响较大。     

基于非线性动力学的行星传动均载性能研究

为研究动态下各影响因素对行星传动均载性能的影响,以2K-H行星齿轮传动系统为研究对象,综合考虑各零件的加工误差、装配误差、轮齿啮合时变刚度及间隙等因素对行星齿轮均载性能所产生的影响,建立了该系统的非线性统动力学模型。采用Newmark法求解,得到了载荷分配系数的时域历程及太阳轮和内齿圈的浮动轨迹,计算了各项误差对载荷分配系数的灵敏度,研究了零件各项误差对行星传动均载效果的影响,对行星齿轮传动的设计提供了依据。     

啮合误差对复合行星轮系动态均载特性的影响

以Ravigneaux式复合行星轮系为研究对象,基于集中参数理论,建立采用中心浮动构件的非线性动力学模型;通过计算传动系统的均载系数,获得各齿轮啮合误差与均载系数的关系曲线,进而分析安装误差和偏心误差对系统均载特性的影响。分析结果表明:行星轮的安装误差会导致行星轮出现持续的"偏载",而行星轮的偏心误差则会导致相应啮合副在运动过程中出现较大的冲击;如果合理布置行星轮的误差,使得其相对于系统的旋转中心呈辐射状对称,将能大大降低行星轮的误差对系统均载性能的影响。     

两级行星齿轮传动系统动态均载特性分析

为了研究两级行星轮系的动态均载特性,建立了两级行星轮系的平移扭转耦合动力学模型,综合考虑了时变啮合刚度、齿轮安装误差、偏心误差、齿侧间隙及级间耦合等非线性因素,推导了系统的无量纲化动力学方程。采用数值方法对方程组进行求解,对中心构件浮动形式、行星轮误差、级间耦合刚度等因素对系统动态均载特性的影响进行了分析,为两级行星轮系的动力学分析和动态均载特性的研究提供了参考,对两级行星齿轮传动系统的设计有一定的指导意义。     

啮合误差对双排并联行星齿轮传动系统静力学均载特性的影响

采用集中质量法,建立双排并联行星齿轮传动系统静力学模型,根据啮合误差原理以及各构件的静应力平衡关系,运用弹性力学分析法和简谐函数,推导出该系统静力学方程：对方程进行求解,获得行星轮均载系数计算结果,讨论偏心与安装误差对行星轮均载系数的影响。研究结果表明：双排并联行星齿轮传动系统具有较好的均载效果,系统均载系数随偏心、安装等啮合误差的增大而有微小增长,且两种误差对该系统均载系数的影响具有叠加效果。     

太阳轮支承刚度对行星齿轮系动力学均载特性的影响

建立了行星齿轮传动系统的动力学均载模型,模型中考虑了系统的综合啮合误差和时变啮合刚度。分析了太阳轮的支承刚度对行星齿轮系动力学均载的影响。计算结果表明,太阳轮的支承刚度对系统的均载影响比较大;随着支承刚度的增大,系统的均载系数增大。减小太阳轮的支承刚度,可以改善系统的均载性能。     

啮合误差及相位角对复合轮系均载特性的影响分析

以复合行星轮系为研究对象,建立了含时变啮合刚度、齿侧间隙和传递误差的复合行星传动系统平移-扭转耦合非线性动力学模型,并分析了安装误差和偏心误差及其相位角对系统均载特性的影响。结果表明,中心构件的安装误差和偏心误差对各行星轮产生均等的周期性影响;行星轮的安装误差会导致行星轮出现持续偏载,但是其偏心误差会使均载系数出现周期性变化;当行星轮的安装误差相位角朝同等方向以及分布在相啮合的行星轮对上时,均载系数较小;偏心误差分布在齿数相差较大的齿轮上时,系统均载性能较好;行星轮误差对称分布能有效降低误差对均载系数的影响。     

误差对行星传动系统均载特性影响分析

建立了考虑时变啮合刚度和齿侧间隙的行星轮系非线性平移扭转耦合动力学模型,分析了误差及误差相位角分布在单个或多个构件上时系统的动态均载特性变化情况。结果表明,中心构件的安装和偏心误差以及行星轮的偏心误差使均载系数周期变化;行星轮的安装误差使啮合副出现持续的偏载,且其误差相位角沿切向分布时系统的不均载现象最严重;行星轮的误差对均载系数影响最大,应尽量避免误差分布在行星轮上;误差作用在相邻行星轮上时,均载性能比作用在不相邻的行星轮或单个行星轮上好;各行星轮的误差和相位角分别相等时,其对均载系数的影响可大大降低。     

Influence of bearing stiffness on the static properties of a planetary gear system with manufacturing errors

Hybrid finite element analysis was used to analyze the influence of bearing stiffness on the static properties of a planetary gear system with manufacturing errors. The effects of changes in stiffness were similar for most of the manufacturing errors. State variables were most affected by the stiffness of the planet bearings. Floating either the sun or carrier helps to equal load sharing and minimizes the critical tooth stress. The effects of a floating sun and carrier are similar, but it is not recommended that both float, because this can induce greater critical tooth stress. Planet bearing stiffness should be optimized. Both load sharing and critical tooth stress should be considered to determine optimal bearing stiffness.     

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.     

串联型行星齿轮传动系统均载特性分析

依据串联型行星轮系统均载机理,综合考虑齿轮制造误差和安装误差、啮合刚度以及间隙浮动等因素的影响,建立了系统均载分析模型,通过计算得到了输入级与输出级的不均载系数。分析了不同齿轮精度对两级行星轮系统均载性能的影响,得出输入级对齿轮精度等级的反应比较敏感的结论,就啮合刚度及联轴器润滑条件对系统均载性能的影响做出了讨论。     

Dynamic characteristics of a planetary gear system based on contact status of the tooth surface

Studies on the planetary gear have attracted considerable attention because of its advantages, such as compactness, large torque-to-weight ratio, vibrations, and high efficiency, which have resulted in its wide applications in industry, wind turbine, national defense, and aerospace fields. We have established a novel dynamic model of the planetary gear transmission by using Newton’s theory, in which some key factors such as time-variant meshing stiffness, phase relationships, and tooth contact characteristics are considered. The influences of gear axial tipping, operating conditions, and the meshing phase on the contact characteristics and the dynamic characteristics were researched systematically. It was found that the contact area of the tooth surface was moved due to the axial gear tipping, which obviously affected the meshing stiffness. With the increase in the inclination angle of the sun gear, the meshing stiffness decreases, which produces an evident influence on the high natural frequency in the planetary transmission system. In terms of the dynamic characteristics of the system, the component of rotating frequency appeared in the dynamic meshing force of the sun gear and the planetary gear. Moreover, the floating track of the center wheel varied significantly and exhibited an oval distribution as the inclination angle of the sun gear changed. When the inclination angle of the sun gear increased, the rotating frequency component increased significantly, but the other meshing frequency components remained unchanged; meanwhile, the deformation of the floating track also increased. If the inclination angle of the sun gear changes, the vibration state of the system and the collision impact could become more serious, and the lifetime of the planetary transmission system will reduce. Furthermore, when the load was increased, we found that the gear-tooth contact zone transformed from line contact to surface contact, the meshing stiffness increased, the effect of high natural frequency on the planetary transmission system became more evident, but its low-order natural frequency remained stable. With regard to the dynamic characteristics of the system, the components of the major frequency at the external gearing remained unchanged, but the rotation frequency of the sun gear and the meshing frequency amplitude increased linearly with the increase in load. In conclusion, the variation in the meshing stiffness of the planetary gear system had minor impact on the low-order natural frequency, but had a significant impact on the high natural frequency of the planetary transmission system due to the phase variation of the gear.     

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。     

误差对精密行星传动的承载能力的影响分析

建立了基于质量—弹簧的均载计算模型,详细分析了制造、装配误差对精密行星传动承载能力的影响,并用精密行星传动装配体有限元离散模型进行了验证。分析了在强过载工况下,存在误差时精密行星传动的承载特性,找出了各种误差对均载的影响程度。     

Research on load sharing performance of wind turbine gearbox involving multiple-errors and tooth crack

The current research on wind turbine gearboxes (WTG) considering multiple-factors influence mainly focuses on dynamic response. However, load sharing performance (LSP) is also extremely important for gear transmission system reliability. In this paper, considering the comprehensive effects of manufacturing errors, assembly errors, clearance floating between stages, mesh stiffness and time-varying load, a coupled translation-torsion dynamic model for WTG was developed to study the LSP. Based on the amplitude variations of time-varying mesh stiffness caused by tooth crack, an approach is provided to introduce the tooth crack into the dynamic model. The results indicate the LSP is mostly sensitive to multiple-errors and severe tooth crack, followed by the time-varying load. The LSP of a system is periodically affected by tooth crack, and the fluctuation ranges increase with the crack growth. Furthermore, the crack of sun gear has greater influence on LSP than that of planet and ring gear.