考虑多体承载啮合斜齿行星齿轮动载特性分析

斜齿行星传动在高速重载场合中应用越来越广泛,其动载特性研究对减振降噪具有重要意义。正确地描述行星齿轮系统的啮合刚度和啮合误差是进行动力学分析的前提,为此,紧密结合齿轮几何分析与力学分析,提出行星齿轮承载接触分析技术,获得各齿轮副的耦合时变啮合刚度,并计算其啮合冲击力,为行星齿轮动力学深入分析奠定基础;其次,应用集中参数法建立考虑齿轮副安装误差、刚度激励及啮合冲击激励的斜齿行星传动啮合型弯-扭-轴动力学模型,采用数值法求解系统的动载特性。表明：考虑啮合冲击激励时,随转速的增加动载荷增加更为明显;共振转速附近,啮合冲击对动态啮合力的影响较小;安装误差特别是中心距误差是引起各齿轮副啮合刚度不同的主要原因,其进一步导致了系统的共振转速变多;行星轮浮动可以明显降低共振转速处的动载荷,由于各外（内）齿轮副刚度的不同,随转速的增加行星轮浮动使得部分齿轮副的动态啮合力明显降低。     

考虑振动的内啮合齿轮副润滑特性分析

为探究动载荷作用下行星齿轮的热弹流润滑特性,综合考虑变位系数和时变啮合刚度的影响,基于动力学理论,建立行星齿轮系统的动力学模型,分析振动与静载荷作用下变位齿轮系统的热弹流润滑特性.研究表明:与其它传动类型相比,采用正传动时,行星齿轮与内齿轮啮合时的润滑效果最佳,轮齿间可以形成较厚的润滑油膜,轮齿间的摩擦系数、油膜的最高...     

考虑摩擦的磨损和修形齿轮啮合刚度计算

研究齿面偏差对齿轮啮合刚度的影响,对准确获得齿轮系统动态特性具有重要意义。本文基于改进能量法,提出了一个求解考虑齿面摩擦的直齿轮啮合刚度的完整模型。该模型通过齿廓的参数方程,实现考虑齿轮加工刀具圆角半径和齿面偏差对齿轮单齿啮合刚度的影响;通过齿形误差带来的齿间间隙和轮齿加载变形量的关系,求解出双齿啮合区齿轮副总刚度。分析了磨损齿轮和修形齿轮的啮合刚度、齿间载荷分配系数和传递误差。结果表明：齿面非均匀磨损量会显著降低双齿啮合区刚度并降低重合度,轻载条件下尤为严重;修形齿轮载荷大于修形设计载荷值时,修形效果不明显,而载荷小于修形设计载荷值时,可能出现刚度不足、重合度减小和加载传动误差显著增大等问题。     

斜齿圆柱齿轮传动的固有振动特征

在综合考虑斜齿轮啮合刚度、轮辐弯扭刚度以及传动轴－轴承支承刚度的基础上,建立了斜齿轮副的耦合振动模型,介绍了系统刚度的计算方法,分析了系统的固有振动特征及其螺旋角的影响,实例分析结果表明：螺旋角不仅引起斜齿轮复杂的耦合振动,而且它的变化将会造成斜齿轮轴向、扭摆共振频率比较大的改变,而对径向共振频率的影响不大;斜齿轮的径向和扭转共振会造成齿轮很大的动载荷,而轴向共振的这种影响则不显著。     

人字齿轮系统齿根动应力计算与对比试验

为了准确地计算人字齿轮的齿根动应力,建立了考虑误差激励、时变啮合刚度激励、啮入冲击激励和齿侧间隙影响的人字齿轮传动系统十二自由度啮合型弯-扭-轴耦合动力学模型,提出考虑实时动载荷对齿间载荷分配系数影响的齿根动应力计算方法．以某船用人字齿轮副为实例进行的仿真计算结果表明:随着外载荷和输入转速的增加,人字齿轮传动系统齿根动应力最大值均呈增加趋势;由于齿侧间隙的存在,随着外载荷增加,齿根动应力的相对波动趋势经历了先减小后增大的过程．试验数据与数值仿真基本吻合,较准确地反映了齿根动应力的波动趋势．     

基于动力学的渐开线圆柱齿轮的啮合效率

提出了基于动力学的渐开线齿轮啮合效率计算模型。通过求解动力学方程获得任意啮合时刻的齿面动载荷、摩擦力和考虑到波动的表面速度,并计算瞬时输入功率和损耗功率后可得瞬时啮合效率。通过计算一个啮合周期内的总输入功和损耗功,可得到平均啮合效率。研究了不同载荷分配模型、最大修形量、转速和转矩等对啮合效率的影响。结果表明:为准确估算齿轮啮合功率损失和啮合效率,应建立较准确的载荷分配模型;对齿顶进行适当修形能有效减小双齿啮合区的摩擦损耗,从而提高齿轮传动效率;转速和转矩平均啮合效率有较大影响。     

航空高速双联斜齿圆柱齿轮行波共振的研究

本文用三维有限元方法研究了星型传动中双联斜齿圆柱齿轮结构的行波共振。根据星型传动系统计算出的作用在双联斜齿轮上的动态载荷,成功地模拟计算出了双联齿轮处于一、二和三节径前、后行波共振时的动态响应,其响应分布形态与理论分析和实验响应曲线吻合较好。数值计算结果表明,在双联齿轮传动中,由于两齿轮啮合频率的不同,将会对齿轮结构的行波共振响应产生很大影响。这一点在设计具有双联齿轮传动的系统结构时应特别值得注意。本文通过实例计算进行了比较详细的讨论。     

脂润滑齿轮齿条增程机构的动态特性

为了准确地获得脂润滑条件下齿轮齿条的动态特性,考虑齿轮齿条啮合时的结构时变啮合刚度和瞬态热弹流润滑刚度的耦合影响,建立结构-脂膜耦合啮合刚度模型,推导受摩擦影响的齿轮齿条增程机构的动力学方程.分析齿轮齿条机构及脂膜的动态特性,数值结果表明：在考虑润滑脂的瞬态热弹流效应后,轮齿的啮合总刚度比结构时变啮合刚度低;且法向啮合力越小,总刚度值越低.中心膜厚、中心压应力均具有高频波动特性,并随着当量曲率半径的增加分别呈上升与下降的趋势.最恶劣润滑状态出现在齿轮轮齿面上靠近基圆的位置,此处的脂膜温升最高,脂膜压应力最大,脂膜厚度最薄.摩擦系数在齿轮齿条传动速度较大的中间时段比起始与末端时段的低,在啮合点靠近节点位置时明显下降.     

汽车后桥主减速器非线性振动研究

以汽车后桥主减速器为研究对象,考虑了齿面摩擦、齿侧间隙以及动态传递误差等非线性因素影响,建立了8自由度准双曲面齿轮副动力学模型。通过引入齿轮副啮合线相对位移,为动力学模型缩减了一个自由度,简化了计算。利用数值计算的方法求解了无量纲化后的微分方程,得到系统稳态响应,并考查了动摩擦系数、外部载荷和轴承支承刚度对系统动力学响应的影响。结果表明,减小动摩擦系数、增加外部载荷和提高轴承支承刚度有利于提升系统的稳定性。     

负载与支承刚度对面齿轮传动系统动态特性的影响分析

为研究负载及支承刚度变化时对面齿轮传动系统动态特性的影响,建立了包含支承、齿侧间隙、时变啮合刚度、综合传动误差、阻尼和负载激励等参数的系统弯-扭耦合动力学模型,并使用PNF（Poincaré-Newton-Floquet）方法进行求解。计算结果表明,在不同的负载及支承刚度条件下,系统会出现简谐响应、次谐响应、拟周期响应及混沌响应4类稳态响应。增加负载及支承刚度能有效降低系统的动载荷,而增大支承刚度还可以减小面齿轮支承在方向与方向上的振动位移幅值差距。     

Characteristic of involute slope modification of asymmetric spur gear

The meshing characteristic of asymmetric involute spur gear was studied, the equations of the geometric shape of the asymmetric gear for both sides were deduced, and the equations of contact ratio and the key points of contact were also obtained.Meanwhile, an involute slope modification method considering the effects of static transmission errors was proposed based on the meshing properties. The characteristic of the involute slope modification was analyzed by changing different modification parameters.The mesh stiffness and synthetic mesh stiffness of unmodified and modified asymmetric spur gears were investigated. Furthermore,the spectrums of synthetic mesh stiffness under different modification parameters were compared. Research results showed that the modification parameters influence the meshing performance of gear pairs, and the proposed modification method was feasible to improve the transmission performance of gear pairs with appropriate modification parameters.     

含齿面分形啮合刚度的齿轮传动系统动力学

为研究考虑齿面分形特性的时变啮合刚度对齿轮-轴承系统的影响,用分形理论描述齿轮轮廓,采用Weber-Banaschek公式计算和分析不同分形维数D对齿轮时变啮合刚度的影响,将不同分形维数D下的刚度代入计及滑动轴承非线性油膜力、综合传递误差及齿侧间隙等因素的齿轮-轴承系统中,分析不同分形维数D下的刚度对系统动力学特性的影响.采用Runge-Kutta法求解系统动力学微分方程,得到系统响应的相图、Poincaré截面图、时域图、分岔图以及三维频谱图等.结果表明:随着分形维数D的增大,时变啮合刚度波动降低,系统趋于更加稳定的周期运动;相比含随机扰动的刚度,齿轮-轴承系统对于考虑齿面分形特性的齿轮啮合刚度的变化更加敏感,更能表现因齿廓变化导致的系统响应的变化;随着阻尼比的增大,系统会趋于相对稳定的单周期运动.     

Mesh stiffness evaluation of an internal spur gear pair with tooth profile shift

Tooth profile shift will change the thickness of gear teeth and a part of geometrical parameters of a gear pair, thus influencing its mesh stiffness and consequently the dynamic performances. In this paper, an analytical mesh stiffness calculation model for an internal gear pair in mesh considering the tooth profile shift is developed based on the potential energy principle. Geometrical representations of the tooth profile shift are firstly derived, and then fitted into the analytical tooth stiffness model of gears. This model could supply a convenient way for mesh stiffness calculation of profile shifted spur gears. Then, simulation studies are conducted based on the developed model to demonstrate the effects of tooth profile shift coefficient on the tooth compliances and the mesh stiffness of the internal spur gear pair. The results show that tooth profile shift has an obvious influence on the mean value, amplitude variation and phase of the mesh stiffness, from which it can be predicted that the dynamic response of an internal gear transmission system will be affected by the tooth profile shift.     

Dynamic load sharing characteristics and sun gear radial orbits of double-row planetary gear train

A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.     

Dynamic load sharing behavior of transverse-torsional coupled planetary gear train with multiple clearances

A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.     

曲面积分与局部有限元联合求解摆线锥齿轮非线性振动特性

针对重载啮合中动态传递误差所导致的非线性振动问题,以及如何准确预测和计算等摆线锥齿轮传动中的动态传递误差进一步改善这类齿轮系统振动特性,研究了在一定的运行速度和扭矩范围内摆线锥齿轮的动态响应特性,对摆线锥齿轮非线性振动特性提出了一种新的曲面积分与局部有限元联合求解方法,这种方法可以精确表达轮齿几何及轮齿接触力等对齿轮动力学性能有关键影响的因素;此外,所提出的方法无需将静态传递误差、时变拟合刚度和啮合频率变量等非线性因素作为外部的激励进行求解,而是从齿轮啮合的每一时步计算动态接触力以及动态传递误差,最终得出摆线锥齿轮的非线性振动特性,采用本方法可以较好地改善摆线锥齿轮的振动特性.     

柴油机正时齿轮系动力学特性分析

为了分析柴油机正时齿轮系的动力学特性以及对前端噪声的影响,建立正时齿轮系的多体动力学模型.分析考虑各齿轮负载及曲轴角速度波动时的齿轮扭转角位移、啮合齿对相对运动以及动态啮合力,并对比了不考虑曲轴角速度波动时的计算结果.结果表明,由曲轴扭振引起的角速度波动能够明显加大齿轮系的振动与冲击.凸轮轴齿轮扭转角位移的实验结果与计算结果较为一致.前端声强实验表明在1 000Hz以下,齿轮系动态特性对噪声影响较大,高频处由齿轮加工精度影响的传递误差引起的噪声较大.通过设计曲轴扭振减振器,可以改善齿轮系的啮合振动与冲击,相应地减小前端的辐射噪声.