考虑多轴柔性的人字行星齿轮传动系统动态特性研究

基于有限单元法,建立了一种全自由度人字行星齿轮传动系统动力学模型.模型将时变啮合刚度、综合啮合误差和啮合相位作为动态激励,分析了太阳轮轴柔性和行星轮轴柔性对人字行星齿轮传动系统中内外啮合动态啮合力和动态传递误差的影响.结果表明:轴的柔性变形对人字齿轮行星传动系统的动态特性具有显著影响,考虑轴柔性后,人字齿轮左右两侧斜齿...     

无侧隙啮合斜齿行星传动系统动力学建模与分析

建立了一个包含无侧隙啮合、轴承间隙、时变啮合刚度、重力激励和其它外部激励的斜齿行星传动系统平移-扭转耦合动力学模型,研究了影响齿面接触状态的主要因素以及齿面接触状态对斜齿行星齿轮传动系统动态特性的影响规律。仿真结果表明,无侧隙啮合对斜齿行星传动系统的轴承力和齿面啮合力有显著的影响,无侧隙啮合与侧隙、轴承间隙密切相关,并且当行星齿轮的组件重力很大时,重力激励是造成无侧隙啮合的重要原因。     

行星架支撑方式对人字齿行星传动系统动态载荷的影响

为研究人字齿行星齿轮传动系统在不同类型行星架支撑下的接触性能,以有限元法为基础建立兆瓦级人字齿行星传动系统的动力学,分析不同行星架不同支撑方式对系统轮齿齿面啮合性能,传递误差的影响。结果表明:行星架双支撑方式提高人字齿行星传动系统的支撑刚度,动态特性,动态均载特性,降低冲击载荷。研究结果可为兆瓦级人字齿行星传动系统的研究提供一定支撑。     

轴承预紧对高速重载行星齿轮传动动态特性影响研究

为分析轴承预紧对高速重载行星齿轮传动系统动态特性的影响,建立高速重载行星齿轮传动动力学模型,考虑轴承预紧因素,分析行星销轴承预紧量对系统支撑刚度、固有频率、内外啮合副动态啮合力的影响。结果表明,行星销轴承预紧可以有效增加行星销支撑刚度;系统的固有频率随预紧先减小后增大,随游隙增大而增大;行星齿轮内外啮合副动态啮合力峰值随预紧增大而减小,随游隙增大而增大。研究结果可为优化高速重载行星齿轮传动的轴承预紧量提供支撑。     

重载工况下行星齿轮传动啮合偏载分析

为了深入研究重载行星齿轮传动多柔体变形下齿面载荷分布规律,提出一种计入结构柔性与齿轮副动态接触的行星齿轮传动耦合动力学建模方法。以某型兆瓦级风电齿轮箱行星轮系为研究对象,根据内齿圈、行星架结构及其边界特征,采用有限元缩聚理论建立内齿圈轮齿、行星架耦合点与弹性支撑之间的关联关系,利用齿轮副动态承载接触作为界面协调条件将各构件进行耦合,建立行星齿轮传动耦合动力学模型,分析了啮合偏载现象以及结构参数对啮合特性的影响。研究结果表明,作用在行星轮上的合弯矩以及行星架销轴非对称结构变形是造成啮合偏载的主要原因,系统共振会加剧啮合偏载程度;在共振区附近,齿轮动态啮合刚度与静态啮合刚度存在较大差异;增加销轴刚性、增大螺旋角可以改善啮合偏载程度,减小共振区系统振动,但在低转速区不利于系统减振,而增大行星架连接板刚性可以保持低转速区系统振动状态,同时减小共振区系统振动。     

人字齿行星齿轮传动系统振动特性研究

通过对人字齿行星齿轮传动系统多重啮合间相位关系的分析,给出了考虑啮合相位的时变啮合刚度计算公式。考虑误差激励和时变啮合刚度激励,在行星架随动坐标系中建立了人字齿行星齿轮传动系统的平移-扭转耦合动力学模型。针对两组不同啮合相位的行星齿轮传动系统,采用傅里叶级数法求解其动力学模型,得到频域解和时域解,且分析啮合相位对人字齿行星齿轮系统振动特性的影响。     

圆柱人字齿轮各内激励因素对齿面振动影响比例分析

为了研究圆柱人字齿轮各内激励因素对齿面振动的影响,建立同时考虑时变啮合刚度激励、轮齿线外啮入冲击激励和齿侧间隙影响的圆柱人字齿轮耦合动力学模型;针对不同的载荷和输入转速工况,分别计算啮合刚度激励、啮入冲击力激励以及齿侧间隙对圆柱齿轮系统齿面相对振动的影响程度。实例仿真计算表明,人字齿轮各内激励因素中,啮合刚度激励对振动影响占主要成分;齿侧间隙影响则是低转矩下的影响高于大转矩下的影响,高转速下的影响高于低转速下的影响,即当低速重载下,齿侧间隙非线性因素对系统影响较小。总结的各激励成分对系统振动影响比例规律,能够为后续人字齿轮齿面减振降噪优化提供更合理的设计目标。     

结构参数对三轴式内齿行星齿轮减速器动力学响应的影响

在建立弹性动力学模型的基础上,分析了轴承刚度,几何尺寸,啮合角,齿轮平均啮合刚度,内齿板质量等结构参数对具有三相内齿结构的三轴式内齿行星齿轮减速器的动力学特性的影响。研究发现:通过减小输出轴轴承的刚度、降低内齿板的质量可改善三轴式内齿行星齿轮减速器的动力学性能。     

轴承预紧力作用下的行星齿轮动态载荷研究

为分析轴承预紧量对高速重载行星齿轮传动系统接触性能影响,建立高速重载行星齿轮传动动力学模型,考虑轴承预紧量因素,分析行星销轴承预紧量对系统支撑刚度、齿面啮合性能、系统均载影响。结果表明:行星销轴承预紧量影响行星销支撑刚度、齿面啮合性能、动态均载,从负游隙到正游隙系统支撑刚度减小,齿轮副的啮合载荷最大值减小,系统的均载系数减小。研究结果可为优化高速重载行星齿轮传动的轴承预紧量提供支撑。     

多啮频激励下的多级齿轮传动分岔与冲击特性

以行星轮系+两级定轴多级齿轮传动系统为研究对象,建立含齿侧间隙、时变刚度、综合传递误差、阻尼、连接轴扭转刚度因素的多啮频激励扭转非线性动力学模型,用数值法对系统无量纲动力学方程求解,获得系统的分岔、齿面冲击、脱啮占空比、齿背接触比响应图。研究表明：系统各级传动分岔特性因多啮频激励不同步而不同步,啮频激励和连接轴扭转耦合影响各级传动的振动强度;随连接轴的扭转刚度减小其前级齿轮传动的动力特性对后级传动的影响减弱;行星轮系内外啮合结构不对称对齿面冲击、脱啮特性产生轻微影响;行星轮相位差对系统非线性动力特性无影响。     

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.     

时变位姿下行星齿轮传动系统动应力计算模型及其参数影响研究

考虑行星轮系内部非惯性和机体时变位姿外部非惯性的综合影响,推导了任意时变位姿下带有机匣的行星轮系构件运动方程,计入时变啮合刚度、啮合误差、侧隙和啮入冲击,建立了时变位姿下行星齿轮传动系统级动力学模型,并采用精细积分时程法（Precision integration method,PIM）求解得到了动态啮合力序列。根据齿间载荷分配关系进一步得到单齿啮合力序列。最后结合修正Heywood公式与Hertz公式构建了时变位姿下行星齿轮传动系统齿根弯曲动应力和接触动应力计算模型,并研究了机体平飞、滚转和筋斗位姿参数对接触动应力、弯曲动应力的影响规律。结果表明：不同时变位姿参数对弯曲、接触动应力影响显著,且对不同齿轮副影响不同,即加剧了齿轮副间承载不均;筋斗运动角速度对动应力影响比平飞加速度、滚转角速度以及筋斗回转半径对其影响复杂;机匣对动应力影响随加速度增大而增加。研究成果为时变位姿下行星齿轮传动动应力计算与高可靠性设计提供了理论依据。     

单级行星齿轮非线性动力学模型与试验验证

针对单排行星直齿轮传动系统,提出了齿轮非线性啮合动态模型,模型中考虑了由中心距安装误差和传动轴弯曲变形等引起的中心距变化对啮合角、间隙和非线性啮合刚度的影响。考虑中心距变化和陀螺力矩并结合齿轮非线性啮合动态模型,建立了行星齿轮传动系统横-扭耦合非线性动力学模型。针对一个单排行星齿轮传统系统试验装置进行仿真计算和试验测试,试验对比分析了齿圈横向振动位移和内啮合均载系数。研究结果表明,仿真结果与试验结果的变化趋势基本吻合,且误差在可接受范围内,验证了笔者提出的渐开线直齿轮传动横-扭耦合非线性动力学模型和非线性动态啮合模型的正确性。     

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。     

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.

     

The meshing angular velocity and tangential contact force simulation for logarithmic spiral bevel gear based on Hertz elastic contact theory

To obtain the change tendency of output angular velocity and tangential contact force of a gear when the pinion under the step input during meshing of a new type of spiral bevel gear, which is a logarithmic spiral bevel gear, the tooth flank equation of logarithmic spiral bevel gear is deduced based on the formation mechanism of the tooth flank formation. A three-dimensional model of a pair of logarithmic spiral bevel gears whose number of teeth was 37:9, with modules being 4.5 mm, normal pressure angle being 20 degrees and spiral angle being 35 degrees were built and assembled. Based on Hertz elastic contact theory, the calculation formulas and parameters sets of contact force for conventional spiral bevel gear meshing simulation and logarithmic spiral bevel gear meshing simulation were done. Consider the dynamic simulation about meshing angular velocity and tangential contact force for conventional spiral bevel gear meshing and logarithmic spiral bevel gear meshing, respectively. Finally, by analyzing and comparing the simulation data, the results show that under the same input conditions, the fluctuation of the gear angular velocity and tangential contact force of logarithmic spiral bevel gear meshing are smaller than the conventional spiral bevel gear. That is, the transmission stationary of logarithmic spiral bevel gear meshing is superior to conventional spiral bevel gear.     

三环齿轮传动的非线性动力学模型

振动大、噪声高是三环齿轮传动存在的突出问题,线性的振动模型无法完全解释其动力学行为。在考虑输入轴和支承轴的弹性、齿轮啮合综合误差、时变啮合刚度以及齿侧间隙的情况下,建立了三环齿轮传动的弯扭耦合非线性动力学模型。采用适当的坐标变换,将线性恢复力和非线性恢复力共存的动力学方程组转化为统一的矩阵形式,并对方程进行量纲一化处理,为进一步研究三环齿轮传动的非线性动力学行为打下基础。     

Elastodynamic analysis of a gear pump. Part II: Meshing phenomena and simulation results

A non-linear lumped kineto-elastodynamic model for the prediction of the dynamic behaviour of external gear pumps is presented. It takes into account the most important phenomena involved in the operation of this kind of machines. Two main sources of noise and vibration can be considered: pressure and gear meshing. Fluid pressure distribution on gears, which is time-varying, is computed and included as a resultant external force and torque acting on the gears. Parametric excitations due to time-varying meshing stiffness, the tooth profile errors (obtained by a metrological analysis), the backlash effects between meshing teeth, the lubricant squeeze and the possibility of tooth contact on both lines of action were also included. Finally, the torsional stiffness and damping of the driving shaft and the non-linear behaviour of the hydrodynamic journal bearings were also taken into account. Model validation was carried out on the basis of experimental data concerning case accelerations and force reactions. The model can be used in order to analyse the pump dynamic behaviour and to identify the effects of modifications in design and operation parameters, in terms of vibration and dynamic forces.Part I is devoted to the calculation of the gear eccentricity in the steady-state condition as result of the balancing between mean pressure loads, mean meshing force and bearing reactions, while in Part II the meshing phenomena are fully explained and the main simulation results are presented.     

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.