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。     

重载车辆变速箱齿轮齿廓修形技术研究

利用MSC.Marc软件对变速箱齿轮副进行准静态接触有限元分析,得到不同修形方式下齿轮副传动误差、齿面接触应力变化情况.针对重载车辆行驶工况恶劣,齿轮负载变化大、可靠性要求高的特点,提出应以最大限度降低齿面接触应力峰值,且不增加齿轮系统传动误差波动为修形目标.     

内啮合斜齿轮高精度三维有限元自动建模方法

为提高内啮合斜齿轮有限元接触分析的建模速度和模型精度,提出了一种齿轮高精度三维有限元模型的自动建模方法。基于齿轮插刀齿廓方程,利用齿廓法线法,得到包括齿根过渡曲线的内、外斜齿轮端面齿廓,建立了内、外齿轮参数化粗网格有限元模型。开发了表层六面体网格剖分方法,自动识别齿面接触带单元,进行分级剖分细化,保证了有限元模型的建模精度和网格密度。进行了齿面接触分析,得到了内啮合斜齿轮的弯曲应力、接触应力、接触印痕、传动误差、时变啮合刚度和载荷分配率。粗细网格有限元模型计算结果对比分析表明,该方法提高了内啮合斜齿轮有限元建模效率和计算精度,缩短了计算时间,为快速准确的齿轮接触分析奠定了基础。     

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。     

核电循环泵行星齿轮热弹流润滑研究

核电齿轮箱的良好润滑性能是核电循环泵可靠运行的重要保障,充分考虑齿面形貌和齿廓修形等因素对内/外啮合齿轮副的影响是准确评估其润滑特性的前提。建立典型工况下核电循环泵行星传动系统斜齿轮热弹流润滑模型,首先将斜齿轮副的啮合状态几何等效为圆锥滚子的接触问题,然后考虑斜齿轮接触变形和齿廓偏差,计算得到内/外啮合齿轮副接触区域不同位置的油膜厚度、承载压力、摩擦应力和闪温等参数。考虑齿面磨合作用,采用移动平均滤波方法对未经磨合的初始形貌进行光滑处理,分析了齿面形貌对润滑行为的影响,最后采取齿廓修形改善润滑特性。结果表明：粗糙度和齿廓修形均会对润滑特性产生明显的影响,齿面粗糙形貌会造成油膜厚度减小,进而影响其润滑特性,弱化润滑油膜的承载能力;通过齿廓修形可以改善齿轮啮合边界处的几何过渡,降低该区域的应力集中和表面温度,从而明显改善啮合线终端的润滑状态。     

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。     

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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直齿锥齿轮齿廓圆弧修形

以理论渐开线直齿锥齿轮修形减振为目的,用圆弧曲线对直齿锥齿轮进行齿廓修形,以减小齿轮传动误差和啮合刚度的波动为衡量标准,同时确保载荷变化呈平稳过渡。静态计算结果表明,齿廓圆弧修形齿轮具有较好的减振效果。     

空间轴交角人字行星齿轮系统动态特性研究

空间轴交角直接影响人字行星齿轮齿面的啮合位置和动态特性,通过将空间轴交角分解到轴平面(两齿轮轴线组成的平面)和垂直平面(通过轴线且与轴平面垂直的平面),推导两个平面中轴交角造成的齿面沿啮合线的等效位移,进而分析出轴交角对齿轮啮合刚度的影响。以输入侧为原点,输出侧齿面相互远离时轴交角为正,考虑人字行星齿轮左右扭转柔性的三段式建模,构建出一种新型空间轴交角人字行星齿轮系统动力学模型,并分析行星齿轮轴交角对齿轮动态特性的影响。结果表明：垂直平面轴交角对啮合刚度和动态啮合力的影响大于轴平面轴交角;空间轴交角增大时,内外啮合刚度均明显减小,且内啮合变化程度大于外啮合齿;动态啮合力会随空间轴交角正向增加而在输入侧增大,输出侧减小,负向增加时则相反。研究结果为人字行星齿轮系统的动态性能设计与控制提供理论基础和技术支撑。     

齿面磨损对齿轮系统动态特性的影响

为研究齿面磨损对齿轮系统动态特性的影响,综合考虑齿轮齿侧间隙、传输误差、齿面磨损,采用集中参数法建立齿轮平移-扭转非线性动力学模型,分析齿轮的转速、运行次数对含有齿面磨损的齿轮传动系统动态特性的影响。结果表明:在啮合区域内,齿根处的齿面磨损量呈减小趋势,在节点处理论磨损量为零,齿顶处的齿面磨损呈增加趋势,齿面磨损量减小趋势大于增加趋势,整个过程中齿面磨损会造成啮合刚度的减小;存在齿面磨损时,过大或过小的转速都会使齿轮系统的振幅波动变大,幅值减小;当转速一定时,含有齿面磨损的系统随着运行次数的增加,振幅幅值会逐渐减小,传动的波动会加剧。     

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 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.     

Contact finite element method for dynamic meshing characteristics analysis of continuous engaged gear drives

The dynamic meshing characteristics of gear drives have been a major concern in the design of power transmission systems as they affect vibration, acoustic noise, durability and efficiency. Gaining a more comprehensive understanding of the dynamic meshing characteristics of continuous engaged gear drives is a key to the development of power transmission systems. In this paper, a dynamic contact finite element analysis method, considering the variation of the engaged teeth pairs, the loaded elastic and contact deformations, and the sliding friction, is presented for the dynamic meshing characteristics analysis of continuous and elastic engaged gear drives. Various kinds of continuous engaged gear models under low and high speed condition are simulated and compared using the presented method. The tooth profile modification was designed based on the simulation results. Moreover, the effects of the tooth profile modification, the sliding friction and the time-varying meshing stiffness upon the dynamic meshing characteristics of continuous engaged gear drives are discussed in detail. The results show that the method is not only effective in designing and evaluating the tooth profile modification, but also in studying the dynamic meshing characteristics of continuous engaged gear drives with realistic time-varying meshing stiffness and tooth sliding friction. The present method could provide an effective tool for vibration mechanism study and dynamic design of the continuous engaged gear drives considering more influence factors.     

含误差的直齿轮的齿廓修形

依据齿轮传动载荷与轮齿变形的关系,推导出定载荷条件下,修形直齿轮静态传动误差与齿对综合修形参数的关系表达式。提出含制造误差修形齿轮修形参数的确定原则:理论设计修形齿轮的最大综合修形量应能消除含误差齿廓轮齿在啮入和啮出位置产生的几何干涉,理论设计修形齿轮的静态传动误差应保持最小的变化。给出了合制造误差修形直齿轮修形参数的计算公式,阐述了相应的确定方法。系统动态响应计算表明该方法所获得的修形齿轮具有良好的减振效果。     

直齿锥齿轮齿廓修形

根据啮合刚度和噪声之间的关系,以修形减振降噪为目的,用旋转渐开线曲线对直齿锥齿轮进行齿廓修形.以减小齿轮传动误差和啮合刚度的波动大小为衡量标准,同时确保载荷变化呈平稳过渡.静态计算结果表明,直齿锥齿轮齿廓长修形具有较好的减振效果.直齿锥齿轮采用冷精锻进行齿廓修形,显著地降低了成本,这为齿轮传动系统的修形、减振、降噪和设计提供了一种新的研究方法.     

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。     

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.     

高变位齿轮的修形及降噪分析

针对海洋钻进平台减速器高位齿轮在低速重载工况中存在啮合冲击大、齿面容易胶合以及传动噪音大等问题,选取减速箱高速级的一对齿轮副进行分析建模。在齿轮所受载荷不变的条件下,改变齿轮的齿形修形量,利用Kisssoft软件对齿轮的传动误差和瞬时加速度进行对比分析,通过ANSYS软件对齿轮修形前后的齿轮模态分析验证了齿轮修形可以减震降噪的正确性。研究结果表明:合理的修形设计能有效改善啮合质量、降低齿轮传动误差和噪音;当修行量达到26μm时,传动误差和安全系数达到最佳值,相应的齿轮噪音值最低,为低速重载齿轮修形在实际工程上的应用提供参考依据。     

基于虚拟样机技术的行星轮系的动力学仿真研究

将行星轮系扭转振动模型与虚拟样机技术结合在一起,建立力学分析模型对行星传动进行动力学仿真,考虑了行星轮系传动过程中的时变啮合刚度和齿侧间隙等因素,可较方便、准确地获得行星轮系在传动过程中的一些动态特性,为行星轮系的优化设计、寿命预测等提供了理论依据.     

Localised tooth contact analysis of single envelope worm gears with assembly errors

This paper presents the basis of loaded tooth contact analysis and predicts the influence of assembly errors on localised contact stress distribution in single enveloping (cylindrical) worm gearing during a meshing cycle. A method for loaded tooth contact analysis, geometry and kinematics of such gear pairs is developed. The method accounts for the effects of tooth composite deflection caused by bending, shearing, foundation, tooth contact deformation and initial profile separation due to assembly errors. The method includes the determination of contact lines, load and stress distribution due to assembly errors. Because of the complex geometry of worm gear teeth, the tooth bending stiffness is calculated using the slicing technique developed earlier by the authors. Classical Hertz theory is used for calculating contact stress and deformation. A computer program based on the presented method has been developed and used to study the influence of errors on mating teeth contact. It is shown that the governing factors in loaded gears with assembly error are the mesh stiffness and the amount of error which is linked to load sharing between adjacent tooth pairs. A numerical example is presented to further clarify the outlined method.