Load sharing characteristics of planetary transmissions

A nonlinear time-varying dynamic model of a planetary transmission with an arbitrary number of pinions is developed. The model includes several manufacturing errors and assembly variations, and can accommodate for any pinion spacing arrangement, tooth separations and time-varying gear mesh stiffnesses. A dynamic load sharing factor K_DLS, which is defined as the ratio of the actual dynamic load at a given gear mesh to the ideal static load, is predicted using the dynamic model. Key design parameters, assembly variations and manufacturing errors are identified, and their effects on K_DLS are quantified.     

Statistical modification analysis of helical planetary gears based on response surface method and Monte Carlo simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system's dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error(DTE) fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system's dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.     

Dynamic interaction between contact loads and tooth wear of engaged plastic gear pairs

This study investigates the interaction between the dynamic contact load and the tooth profile wear of POM and Nylon 66 plastic gear pairs. A dynamic model of a plastic gear pair is presented. This model incorporates the effects of position-varying tooth mesh stiffness, damping ratio, load sharing, tooth profile wear and temperature on the dynamic contact load. The tooth wear equation developed by Flodin and Andersson [Simulation of mild wear in spur gears. Wear 1997;207:16–23] is utilized to simulate tooth wear and tooth profile variation. The variation of the contact load generated by the cumulative tooth profile wear is simulated and examined. A computational algorithm is developed to simulate the interaction between a dynamic contact load and tooth profile wear. Numerical results demonstrate that the dynamic load histogram of an engaged plastic gear pair can change markedly due to tooth wear.     

A study on load-sharing structure of multi-stage planetary transmission system

Unequal load distribution is a crucial factor in decreasing bearing capacity and stability of the planetary transmission system. In this paper, a dynamical model of two-stage helical planetary gear transmission system is established based on lumped-parameter method and Lagrange general function. Nonlinearity of gear tooth backlash and error is taken into account. Four load-sharing structures are proposed to study the load-sharing performance. A method to calculate dynamic sensitivity of load-sharing coefficient to errors is presented that can provide a reference to component precision determination in order to make planetary system have a better load distribution. Finally, a numerical method of load-sharing performance is validated by a test. These results provide fundamental basis for multi-stage planetary gear transmission system design.     

行星齿轮传动变位参数的优化选择

为了提高NGW型行星齿轮传动的承载能力,本文对外啮合齿轮传动变位参数进行了二维优化设计,计算结果表明,合理选择变位参数可大大提高齿轮传动的承载能力.     

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.

     

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。     

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。     

含侧隙齿轮副的动载荷分析

以振动理论为基础，提出一种考虑齿轮拍击振动的齿轮动载荷的数值计算方法。建立计算动载荷的齿轮冲击模型，在模型中考虑了齿轮正、反冲击时实际的啮合刚度，并给出啮合柔度的计算方法。分析在考虑静态传递误差、啮合刚度、侧隙、摩擦力及外部扭矩变化等多种激励时，作用在轮齿上的动态载荷以及整个齿轮上的综合动态载荷的计算公式。最后通过实例分析作用在轮齿上的动态载荷、综合动态载荷变化规律以及相关激励参数对动态载荷的影响。     

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。     

转矩四分支齿轮传动系统的配齿条件研究

在高速重载传动场合越来越多的采用转矩分支传动,由于分路传递转矩,故可减小尺寸和质量,但与一般单路传动相比,其结构上存在虚约束,设计其参数时必须考虑结构约束;此外,不同配齿方案对多分支齿轮传动的均载特性影响较大,所以配齿方法的研究对保证其运动与均载具有非常重要的意义。针对转矩四分支齿轮传动系统,在考虑各支路均载的基础上建立了系统的配齿条件,提出了一种配齿计算方法,并针对某动力传输系统进行了配齿计算,结果表明,该方法得到的结果满足各种配齿要求,对其他分支齿轮传动具有普遍适用性。     

行星齿轮传动静力学均载分析

建立了2KH型行星齿轮传动系统的计算模型,从静力学角度分析了系统的均载机理。针对各构件的制造和安装误差,运用当量啮合误差的原理,计算了该系统的均载系数,并分析了各误差变化对系统均载情况的影响,以供工程应用参考。     

风力发电增速器齿轮齿廓修形有限元分析

简要介绍了齿廓修形的原理,详细介绍了齿廓修形参数的表达方式和选择原则.建立了多齿有限元接触分析模型,给出了计算齿廓修形量的方法,考察了修形前后齿间载荷分配和接触线上载荷分布情况.     

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。     

行星摆线轮齿形精确设计

根据行星摆线齿轮的形成理论,应用神经网络方法实现行星摆线轮的齿形精确设计.该方法建立了齿轮参数与齿形之间的BP神经网络非线性关系模型.仿真实验表明,采用神经网络的非线性逼近特性进行摆线轮齿形模拟设计,能精确、快速地模拟出摆线轮齿形;该方法适用于非渐开线齿轮齿形的设计.     

行星齿轮传动系统均载分析

建立了2K-H型行星齿轮传动系统的静力学计算模型,并分析了该系统的静力学均载机理。利用当量啮合误差原理,得到了当量啮合误差和载荷不均匀系数的计算公式,对比分析了各构件的制造误差和安装误差对传动系统载荷不均匀系数的影响,并从所分析的误差中得到了对系统均载性能影响最大的误差项,以便于工程实际中参考。     

行星传动动态均载特性分析

从动力学角度建立2K-H型行星传动系统的计算模型.针对各构件的制造和安装误差,运用当量啮合误差原理和动力学分析方法,推导行星传动的运动微分方程,建立系统的动力学分析模型,分析系统的动态均载特性和各误差的参数变化对系统均载特性的影响,此方法计算结果与已有试验结果十分吻合.分析结果表明,浮动太阳轮对系统的均载特性有很大的改善:装配误差和安装误差共同对系统的均载特性起作用,只减少某一个误差值达不到良好的均载效果;转速对系统的均载有较大的影响.     

封闭行星齿轮传动系统的可靠性研究

通过对封闭行星齿轮传动系统进行运动学及力学分析，结合可靠性设计和Savage等提出的单级行星齿轮传动的可靠度模型，建立了以输入构件转速和转矩为变量的构件负载与寿命关系表达式；基于系统可靠度的乘积定律，建立了典型的封闭行星齿轮传动系统的可靠度模型；结合实例，研究了负载、有效齿宽、功率分配系数等因素对系统及其零件可靠性的影响。研究表明：系统的可靠度随着功率分配系数、负载的增大而减小，随着有效齿宽的减小而减小；合理地配置齿数可使传动系统获得较大的可靠度。     

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.     

凸轮激波复式活齿传动的结构及齿形分析

提出一种新颖的大速比传动装置——凸轮激波复式滚动活齿传动装置，该传动装置由一级NGW型行星传动机构与一级凸轮激波的二齿差滚动活齿传动机构串联组成。对其传动原理、传动比及传动特性进行了分析，以此为基础设计了装置的传动结构。导出了中心内齿轮的齿形方程，给出了齿形计算示例，并进一步分析了相关参数对齿形几何性质的影响。