修形人字齿轮振动测试试验台可行性验证

为验证封闭功率流式修形人字齿轮振动测试试验台的可行性,首先,搭建封闭功率流式人字齿轮系统振动测量试验台,依据试验台建立了包含陪试齿轮、试验齿轮以及加载扭力轴的24自由度啮合型弯-扭-轴耦合振动模型;然后,选用设计的某人字齿轮齿面三维修形的试验齿轮作为计算实例,分析了不同扭力轴刚度下,陪试齿轮对试验齿轮啮合线向相对振动加速度的影响。结果表明,在给定工况下,陪试标准齿面人字齿轮对修形人字齿轮的齿面相对振动影响为1.35%,远低于修形齿面18.2%的减振率,因此用该试验台进行人字齿轮传动系统齿面三维修形减振测试切实可行。陪试齿轮对试验齿轮振动的影响程度随着扭力轴刚度增加而增加,故试验中在满足系统强度、传动平稳及布置要求的前提下,应将扭力轴扭转刚度设计的尽量低,应最大幅度地降低扭力轴扭转刚度设计值,以减小陪试齿轮对试验齿轮振动测量的影响。     

计入齿圈柔性的直齿行星传动动力学建模

为揭示齿圈柔性对传动系统动态性能的影响,在系杆随动坐标系下建立计入齿圈柔性的直齿行星传动精细化动力学模型,建模中计入时变啮合刚度、支承刚度、陀螺效应和齿圈柔性等诸多影响因素。采用有限段单元的离散化建模方法,将连续体的柔性齿圈离散成由等效虚拟弹簧连接的刚性齿圈段,并推导齿圈段与行星轮的啮合判据。通过分析各构件间的相对位移关系及其受力,最终建立系统的运动微分方程。以三行星轮的NGW型直齿行星传动为例对其进行固有特性分析,得出系统的低阶固有频率分布及相应的振动模式,并进一步分析齿圈柔性和安装方式对系统固有特性的影响。研究结果表明,直齿行星传动的振型可归结为中心构件(太阳轮、系杆)扭转振动和中心构件平移振动两种模式,两种模式下齿圈和行星轮均做复杂平面振动;齿圈的柔性会降低系统的低阶固有频率,且其影响程度与齿圈安装方式有关,齿圈完全固定时其影响最小,径向浮动或周向转动时影响较明显。     

基于刚柔耦合的行星齿轮减速器减振降噪研究

针对某精密行星齿轮减速器的振动噪声问题,通过Romax Designer软件建立刚柔耦合动力学模型;并对减速器箱体进行模态分析,提取箱体的前六阶约束模态振型和固有频率,确定产生噪声的共振频率点;同时分析了齿轮传动误差、齿轮时变啮合刚度等激励的特性。提出通过齿轮修形降低减速器内部动态激励进而减小振动和噪声的方法,并使用LMS Virtual.lab软件对减速器进行声学响应求解。仿真结果表明,优化后减速器的振动和噪声明显降低;最后搭建了行星齿轮减速器试验台,实测噪声与仿真结果基本吻合,验证了该方法的合理性。     

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.     

国内基于功率分支技术齿轮箱的发展现状

功率分支主要是指采用行星传动、两分支与多分支传动技术。在高速或者重载或者小空间等严格工况下,通常采用基于功率分支技术的齿轮箱。从齿轮强度计算出发,对基于功率分支技术的齿轮系统进行了简化分析,发现它拥有优于常规平行轴齿轮箱的诸多特点,包括可以大大降低齿轮尺寸、提高轮系承载能力、降低齿轮节圆线速度、提高结构刚性与运转平稳性等等。根据不同轮系结构形式,对目前应用的基于功率分支技术的齿轮箱进行了分类,具体包括行星轮系、中心传动多分支轮系、多级分支轮系、人字齿/双斜齿侧分支轮系、多边边缘传动轮系。并针对每种分支轮系,进行了结构与应用分析。最后,探讨了基于功率分支技术的齿轮箱关键技术——均载技术,详细总结了目前常用的功率分支轮系的均载方法,并对采用胀紧联结套来实现均载进行了介绍。     

Model-based analysis and fault diagnosis of a compound planetary gear set with damaged sun gear

The vibration properties of compound planetary gears are more complicated than that of simple ones. This paper aims to investigate the fault properties of a compound planetary gear set in chipped sun gear conditions using model-based method. A three-dimensional lumped-parameter nonlinear dynamic model for the compound planetary gear set is established. This model considers the time-varying mesh stiffness (TVMS), the mesh phase relations, and gear chipping defects. The analytical equations are derived to quantify the TVMS reduction induced by the chipped gear based on the improved potential energy method. Further, the simulations are performed to demonstrate the fault features of sun gears with single or multiple chipped teeth in different gear stages. Moreover, the theoretical derivations are validated through the experimental signals analysis.     

Load sharing and stress analysis of single enveloping worm gearing considering transmission errors

A procedure, known as the slicing method, which has been developed earlier by the authors to estimate the load share of single enveloping (cylindrical) worm gear drives and to calculate the instantaneous tooth meshing stiffness and stresses, is extended in this study to investigate the effect of transmission error on loading and stresses. Tooth composite deflection caused by bending, shearing, contact deformation and initial separation due to profile mismatch are determined in the analysis as well as tooth stiffness variation during the course of contact of both the worm and the wheel. The elasticity theory was used to calculate fillet stresses and deformation of both the worm and wheel. Numerical examples are presented to illustrate the response of worm gear set in the presence of transmission error and under given loading conditions. The procedure was proven to be safe and reliable in rating the load capacity and useful in the design of worm gear drives with compact size and high power transmission.     

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。     

Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach

Time-dependent mesh stiffness is a most important reason of vibration and dynamic excitation in gear sets. In this research, analytical formulas of the helical gear set and the planetary gear system are combined to calculate the time-dependent mesh stiffness of the helical planetary gear system. For this purpose, at the first step, the analytical equations are derived for the spur gear pair. Then by dividing a helical tooth into the several independent thin spur tooth slices, the helical gear pair mesh stiffness is extracted. Finally, these equations are extended to the helical planetary gear system. The suggested analytical results and those which obtained by the finite element method (FEM) are compared and are in good agreement when the helix angle is less than 15 degrees. Also, the helical planetary gear system mesh stiffness in different cases such as fixed carrier, fixed sun gear and fixed ring gears is calculated. These results show that the value of mesh frequency ratio in each case scales the mesh stiffness shapes in the rotation angle direction. In other words, mesh frequency ratio parameter determines the number of meshing period in each rotation of planets.     

齿轮传动系统的动态模拟

针对齿轮副非线性振动问题展开研究,综合分析了啮合冲击激励、时变啮合刚度和误差激励对齿轮系统振动的影响。根据扭转啮合刚度定义,分别建立了无齿面缺陷和有齿面缺陷的齿轮三维接触仿真分析模型。计算了两种运行状态下,不同接触位置上的扭转啮合刚度。在进行齿轮副非线性振动的分析时,综合考虑了啮合冲击激励、时变啮合刚度和误差激励等非线性因素,建立了齿轮副非线性动力学模型,采用变步长四阶Runge-Kutta数值积分方法求解了系统的动态响应。     

复式直齿行星排行星轮轴向力研究

在车辆的传动系统中,复式直齿行星排的行星轮与行星架之间存在轴向作用力,导致止推垫圈磨损严重。分析了复式直齿行星排长行星轮轴向力的产生机理,建立了行星轮滚针轴承负荷分布与轴向力计算模型。通过仿真分析与试验研究,指出了影响行星轮轴向力的主要因素及其对轴向力的影响规律。为复式直齿行星排行星轮轴向力的研究提供了分析方法,为复式行星排的设计改进提供了依据。     

行星轮系动力学新模型及其故障响应特性研究

行星轮系中零部件多、结构复杂,建模难度大。行星轮既自转又公转,导致啮合点到固定在箱体上的传感器之间的距离时刻变化,从而产生振动传递路径时变效应,增加了振动响应的复杂性。现有的动力学模型大多针对正常情况下的行星轮系进行建模,而且未考虑振动传递路径时变效应对振动响应的影响。针对以上不足,推导了行星轮系正常、裂纹及剥落三种情况下的时变啮合刚度算法,考虑振动传递路径时变效应的影响,建立了相应的动力学模型,求解得到行星轮系正常、裂纹及剥落时的动态响应,并分析了它们的频谱特性。搭建了行星齿轮箱试验台以获取振动响应信号,与模型响应信号进行了对比分析,结果验证了动力学模型的准确性,为行星轮系的健康监测提供了理论依据。     

Experimental evaluation of friction between contacting discs for the simulation of gear contact

Instant gear contact can be simulated with contacting discs, which provides steady operating conditions and eliminates most of the dynamics and manufacturing tolerances involved in real gears, resulting in an accurately controlled contact condition. A high-pressure twin-disc test device was developed, where loading and rolling velocity can be varied continuously. It is equipped with disc bulk temperature, mean contact resistance and friction moment measurements. The test discs were grinded transversal to the disc rolling direction with proper crowning corresponding to the real gear flank properties. The test device was applied by studying the friction behaviour against the slide-to-roll ratio at different contact pressures, rolling velocities and surface roughness. The measurements were performed using mineral base oil in the range of operation conditions often used in industrial gears. In general, the measured friction coefficient behaviour correlates with earlier published results and is logical with measured bulk temperature and mean contact resistance. The limiting shear stress of the lubricant has an essential role in friction behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

液压机械无级变速器机械变速机构的传动误差分析

以东方红某型号拖拉机液压机械无级变速器中的机械变速机构为研究对象,探究其传动误差随时间的变化规律,目的是减少变速器的功率损耗。利用当量啮合误差原理,建立变速器中行星齿轮组、定轴齿轮副和两者共同作用时的传动误差与时间的关系式。比较各挡位的总传动误差和行星齿轮组传动误差,得到瞬时总传动误差最大、最小的挡位以及总传动误差的主导因素。在角频率相同时,行星齿轮组传动误差和定轴齿轮副传动误差存在耦合关系。利用蒙特卡罗法,验证了研究所得规律的正确性。建立总传动误差与功率损耗的关系式,结果表明两者存在正比关系。以减小传动误差为目的,提出了减少变速器功率损耗的措施。     

基于层级有限元法的大型航空行星机构可靠性优化设计

大型航空行星机构作为多种重型航空器传动系统的基础与核心,它的可靠性水平在很大程度上制约着航空器的经济可承受性与服役安全性。将某型号重型直升机行星机构作为研究对象,以保证和提高该系统的疲劳可靠性水平为目标,利用层级有限元法计算系统全局弹性行为耦合作用下的轮齿疲劳载荷历程,并基于齿轮低周疲劳试验与最小次序统计量转化方法拟合出轮齿概率疲劳强度,为系统可靠性预测模型提供经济有效的载荷与强度输入变量。据此,建立从大型航空行星机构关键结构要素到系统可靠性指标的映射路径,提出可靠性驱动的行星机构结构尺寸多目标优化设计新方法。最后,分析了内齿圈轮缘厚度与行星架基板厚度对行星轮系疲劳可靠性的影响规律,并得到了指定型号的大型航空行星机构的轮缘与基板尺寸最佳刚度匹配结果,最大限度地发挥了核心结构要素的刚度潜力,以此平衡大型航空行星装备在可靠性与轻量化要求之间的矛盾。     

Life Distribution Transformation Model of Planetary Gear System

Planetary gear systems have been widely used in transportation, construction, metallurgy, petroleum, aviation and other industrial fields. Under the same condition of power transmission, they have a more compact structure than ordinary gear train. However, some critical parts, such as sun gear, planet gear and ring gear often suffer from fatigue and wear under the conditions of high speed and heavy load. For reliability research, in order to predict the fatigue probability life of planetary gear system, detailed kinematic and mechanical analysis for a planetary gear system is firstly completed. Meanwhile, a gear bending fatigue test is carried out at a stress level to obtain the strength information of specific gears. Then, a life distribution transformation model is established according to the order statistics theory. Transformation process is that, the life distribution of test gear is transformed to that of single tooth, and then the life distribution of single tooth can be effectively transformed to that of the planetary gear system. In addition, the effectiveness of the transformation model is finally verified by a processing method with random censoring data.     

Calculation of sliding power loss in spur gear contacts

An engineering-level calculation model for sliding power loss in spur gear contacts is presented. Teeth contact through the line of action is modelled as a constantly changing roller contact whose radius, speed, and load can be calculated from the gear geometry under the given operating conditions. The gear mesh cycle is approximated by a large number of elastohydrodynamic contacts. A constant film thickness and a Hertzian pressure distribution are assumed in each contact. The model includes non-Newtonian lubricant behaviour together with temperature and mixed lubrication effects in contact. The numerical solver is reasonably fast in evaluating effectively the sliding power loss dependence on the essential gear and lubricant parameters. The features and behaviour trends of the calculated sliding power losses have a close similarity with published results obtained from measurements and experiment-based power loss models with mineral oil. The limiting shear stress of the lubricant is observed to have an essential role in the power loss behaviour especially at high loads.     

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。     

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。     

汽车驱动桥传动效率试验台的研制及测试

研发了一种专门用于汽车驱动桥传动效率测试的试验台。使用该试验台进行测试分析,可以明确影响驱动桥传动效率的关键因素,发现各因素对驱动桥传动效率的影响规律,从而找到提高驱动桥传动效率的有效途径,这对于提高汽车动力性和燃油经济性具有十分重要的意义。该试验台采用模块化结构设计,具有安装简便、调整方便、自动化程度高的特点。该试验台采用直接转矩控制来进行转矩和转速控制,利用谐波传动和行星传动技术实现了动态加载,利用直流母线技术实现了系统功率封闭。测试结果表明:该试验台测试结果准确,完全满足驱动桥传动效率的测试要求。