Quantitative Damage Detection for Planetary Gear Sets Based on Physical Models

Planetary gear set is the critical component in helicopter transmission train, and an important problem in condition monitoring and health management of planetary gear set is quantitative damage detection. In order to resolve this problem, an approach based on physical models is presented to detect damage quantitatively in planetary gear set. A particular emphasis is put on a feature generation and selection method, which is used for sun gear tooth breakage damage detection quantitatively in planetary gear box of helicopter transmission system. In this feature generation procedure, the pure torsional dynamical models of 2K-H planetary gear set is established for healthy case and sun gear tooth-breakage case. Then, a feature based on the spectrum of simulation signals of the dynamical models is generated. Aiming at selecting the best feature suitable for quantitative damage detection, a two-sample Z-test procedure is used to analyze the performance of features on damage evolution tracing. A feature named SR, which had better performance in tracking damage, is proposed to detect damage in planetary gear set. Meanwhile, the sun gear tooth-chipped seeded experiments with different severity are designed to validate the method above, and then the test vibration signal is picked up and used for damage detection. With the results of several experiments for quantitative damage detection, the feasibility and the effect of this approach are verified. The proposed method can supply an effective tool for degradation state identification in condition monitoring and health management of helicopter transmission system.

OPTIMIZATION OF THE METHOD OF SELECTING THE TOOTH NUMBER SERIES IN A SET OF CHANGE GEARS Part Ⅱ The Rules for Permuting the DBL’s of the First Order and Their Intercalated Sets

The problem in practice of determining the proper combination of Zi in a set of changegears may be abstracted to the problem of finding the proper combination and permutation ofthe elements ai,i+1 of the set A1 to give maximum M-d. Some results to find optimal combina-tions of the elements of the set A1 have been reported in part I. In this part, some rules forpermuting these elements are introduced. By means of these rules, three kinds of intercalated setsof A1 have been found, namely: （1） Sets with an even left wing, （2） Sets with coincidence of bothwings, and （3） Sets with circulated elements.

Mathematical Model and Geometrical Model of Double Pitch ZN-type Worm Gear Set Based on Generation Mechanism

The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set（e.g., ZN, ZA, or ZK）. The research of forming mechanism and three-dimensional modeling method for the double pitch worm gear set is not enough. So there are some difficulties in mathematical model deducing and geometry modeling of double pitch ZN-type worm gear set based on generation mechanism. In order to establish the mathematical model and the precise geometric model of double pitch ZN-type worm gear set, the structural characteristics and generation mechanism of the double pitch ZN-type worm gear set are investigated. Mathematical model of the ZN-type worm gear set is derived based on its generation mechanism and the theory of gearing. According to the mathematical model of the worm gear set which has been developed, a geometry modeling method of the double pitch ZN-type worm and worm gear is presented. Furthermore, a geometrical precision calculate method is proposed to evaluate the geometrical quality of the double pitch worm gear set. As a result, the maximum error is less than 6′10–4 mm in magnitude, thus the model of the double pitch ZN-type worm gear set is available to meet the requirements of finite element analysis and engineering application. The derived mathematical model and the proposed geometrical modeling method are helpful to guiding the design, manufacture and contact analysis of the worm gear set.

Influence of Setting Error of Tool on Tooth Profile and Contact Point of Face Gear Drive

In order to analyze the influence of setting error of tool on both tooth profile and contact characteristic of orthogonal face gear drive,the coordinate systems with and without setting error are established.Moreover,the equations of tooth profile and contact points of face gear drive are derived by envelope principle.According to the equations,the change of tooth profile and the contact points position on face gear are analyzed.The tooth surface and contact points are obtained by numerical simulation.Results show that the tooth profile and contact characteristic of face gear drive are not sensitive to the setting error of tool.

Structure vibration characteristics of two stage double helical tooth planetary gear trains with unequally spaced planets and stars

A computational model of two stage double helical tooth planetary gear set is employed to built the lateraltorsional coupling dynamic governing equations. Base on the dynamic equation, the free vibration properties of the system with unequally spaced planets and stars are analyzed. The vibration modes are classified into three types: star mode, planet mode, and coupling mode. For each of the modes, the relation between inherent frequency and vibration amplitude is investigated in detail by the eigenvalue and mode characteristics.

Research on global form deviations for spiral bevel gear based on latticed measurement

In order to improve the machining ac cu racy of spiral bevel gear,difference surface was adopted to characterize its gl obal form deviations quantifiably and correct its deviations.The theoretical to oth surface model of spiral bevel gear was built,and the actual tooth surface o f spiral bevel gear had been got by using latticed measurement.The equation of difference surface which can characterize the actual tooth surface deviation s was built by means of mathematical method in combination with measurement prin ciple.The quantitative mathematical relationship between the actual tooth surfa ce deviations of spiral bevel gear and the corrected values of the machine-sett ing parameters had been referred,and the theoretical correction formula of the global form deviations had been got by the least square method.Finally,the pinion of spiral bevel gear in the automobile rear axle has been set for an exam ple to account for the effectiveness of the deviation correction by use of the d ifference surface method.

基于SVM的液压机械驱动齿轮组故障诊断研究

针对液压机械驱动齿轮组故障诊断结果精准度不佳、可靠性差等问题,本文提出基于SVM的液压机械驱动齿轮组故障诊断研究。采集了液压机械驱动齿轮组振动信号,构建液压机械驱动齿轮组故障信号分离模型;运用低秩算法分离液压机械驱动齿轮箱振源信号,设计齿轮组故障信号约束条件,完成液压机械驱动齿轮组分类;根据分类结果,采用SDAE模型提取液压机械驱动齿轮组故障特征,并将提取结果输入到支持向量机内训练,其最终输出结果就是最佳诊断结果,实现基于SVM的液压机械驱动齿轮组故障诊断研究。实验结果表明,通过对该方法开展故障检测及故障诊断测试,本文方法下分类错误率不超过3.5%,验证了该方法的可行性高。

混合动力电动汽车构型优化设计方法研究

针对行星齿轮汽车结构特性与动态特性的关系,提出了混合动力汽车动力系统构型的理论设计方法.首先,将构型中所有连接分为3类,采用矩阵表示法表示这些连接,以反映系统动力学和构型的物理结构.接着,在此基础上提出了构型自动设计的矩阵表示方法,通过矩阵运算得到转速方程进而得到汽车双行星齿轮结构的各种构型.最后,通过仿真验证了该方法的有效性.结果表明,在矩阵表示方法的支持下,可以通过计算机自动完成最优构型的选择,避免了人工计算和比较,节省了大量的精力和时间.

Development and experimental validation of a novel hybrid powertrain with dual planetary gear sets for transit bus applications

Given that energy conservation and environmental protection are two important goals for the automotive industry, the application of a hybrid electric powertrain can improve vehicle energy efficiency while decreasing fuel consumption and engine emissions. Planetary gear-based power-split hybrid powertrains have become widely used in passenger vehicles, but remain rarely employed on transit buses. This study proposes a novel hybrid powertrain based on two planetary gear sets(CHS) and presents its operating principles along with development of a control strategy for the powertrain. The CHS hybrid powertrain operates in electric mode when the driving power demand is low, and changes to a hybrid electric mode according to the power-split principle of the planetary gear set. To validate the feasibility of the designed CHS hybrid powertrain, a prototype transit bus equipped with the designed hybrid powertrain system was built, and the operating characteristics of the system were analyzed through a performance test conducted on a chassis dynamometer. Compared with a conventional powertrain, the CHS hybrid powertrain can reduce fuel consumption by 39%. Thus, the CHS hybrid powertrain is a good solution for heavy-duty applications such as hybrid transit buses because of its simple structure and excellent fuel efficiency.

基于自适应鲁棒控制的电动爬楼轮椅车研究

针对国内外各种电动爬楼轮椅存在的结构复杂、功能单一和控制精度不高等问题,提出一种基于自适应鲁棒控制的轮腿式多功能爬楼轮椅车方案.首先,从电动轮椅常用模式出发,按照轮腿式结构和行星齿轮组特点,设计了一种双行星轮组的轮椅机构,可以实现行驶、升降、爬楼3种功能;然后,根据爬楼轮椅工作的3个过程,建立了机器人运动学模型,得到了机构运动学求解公式;在Adams中通过模型动作编写了step函数,仿真得到机构爬楼运动轨迹,验证其满足爬楼越障所需要求;最后,设计了一种自适应鲁棒滑模控制器,得到轮椅角度和速度跟踪曲线、控制输入曲线,验证了其控制策略的合理性,为后期样机搭建奠定了基础.

基于改进蜻蜓算法的磁齿轮复合电机控制研究

针对磁齿轮复合电机双转子结构在无接触传动时出现振荡和超调的问题,提出了一种基于改进蜻蜓算法(improved dragonfly algorithm,IDA)的双闭环PI(proportional integral,比例积分)参数自整定矢量控制方法。针对DA在收敛速度和收敛精度等方面存在的不足,分别在算法寻优的前期、中期和后期引入Tent映射、改进权重系数和差分优化算法,并在其适应度函数上增加可抑制振荡和超调的惩罚项,使算法的收敛速度和收敛精度得到明显提高。采用PI、DA-PI和IDA-PI三种控制方法对磁齿轮复合电机进行控制仿真和实验,结果表明,在IDA-PI控制下电机转速的超调量和稳态误差最小,动态响应速度最快,证明了所提策略的有效性。研究结果为不同拓扑结构磁齿轮复合电机的控制提供了参考。

浅析电荷放大器的使用分析

电荷放大器广泛应用于振动、冲击、力、压力、声强等非电量电测。电荷放大器通常具有增益挡位、归一化挡位、滤波挡位和积分挡位,可以针对不同的测量需求,对其各个挡位进行合理的设置,以获得理想的测量结果。在振动冲击领域中,电荷型压电加速度计与电荷放大器配套使用,通过电荷放大器输出的电压信号来获得振动、冲击加速度量值。本文结合振动冲击领域中对电荷放大器的计量特性要求与电荷放大器使用者可能存在的一些操作现象进行讨论,阐述了电荷放大器在不同情况下使用时值得注意的事项,目的在于方便电荷放大器的使用者更加了解其计量特性。

行星齿轮系扭转非线性振动建模与运动分岔特性研究

建立行星齿轮系扭转非线性振动模型,模型中考虑了行星齿轮系各齿轮副间的时变啮合刚度、齿侧间隙以及综合传递误差等非线性因素;推导出系统的量纲一振动微分方程,采用数值积分方法研究行星齿轮的运动特性随转速以及齿侧间隙等参数的分岔特性,结合Poincaré图形分析,研究转速、啮合阻尼以及齿侧间隙等参数对系统分岔特性的影响。结果发现,随着转速的逐渐增大,系统会通过激变途径进入到混沌运动,而随着齿侧间隙的逐渐增大,系统会通过倍周期分岔途径进入到混沌。阻尼过小将会导致行星齿轮系统的稳态运动由短周期运动向复杂运动转变。齿侧间隙是影响系统运动分岔特性的重要因素,但是影响范围主要限于量纲一齿侧间隙大于3.5的大间隙区段。

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。

螺旋锥齿轮的齿面测量及机床加工参数修正

给出了Gleason制螺旋锥齿轮的理论齿面模型,用差曲面描述三坐标测量机测量得到的实际齿面到理论齿面的偏差,提出了一种利用差曲面特征参数修正机床调整参数的新方法,有效地提高了齿面几何精度。

行星齿轮传动系的周期运动及其稳定性

研究了间隙行星齿轮非线性传动系的周期轨道及其稳定性。针对PNF方法在求解非线性动力系统时存在的两点缺陷,即研究对象必须光滑和迭代初始点要求距离周期轨道足够近,提出了改进措施使之能够适应间隙行星齿轮传动系统的周期轨道的求解以及判稳工作。改进后的PNF方法对算例的计算结果和直接数值积分结果的吻合证明了改进措施的有效性。采用改进后的PNF方法研究了行星齿轮系统在一组给定参数下共存的周期运动,并判断了各共存周期运动的稳定性;通过延续判断不同转速下系统周期轨道的稳定性,研究了行星齿轮传动系统的周期运动状态随无量纲转速的分岔特性。结果发现,行星齿轮非线性传动系统在某些参数组合下可以共存几个稳定或者是不稳定的周期轨道;转速的变化可以使行星齿轮系统通过倍周期分岔的形式最终通往混沌。

行星齿轮传动系统动力学特性研究

运用拉格朗日方程建立了2K-H型行星轮系扭转振动动力学模型;在动坐标系中建立了2K-H型行星轮系平移-扭转耦合振动动力学模型,每个构件具有两个平移自由度和一个扭转自由度;建立了Ravingneaux型复合行星轮系在各个工况下的力学模型和数学模型,用来分析其自由振动特性,在MATLAB环境下运用GUI函数开发了齿轮传动系统动力学特性分析软件TVLab,以Ravingneaux型复合行星轮系为例,进行了动力学分析,结果表明此软件可以作为分析齿轮传动系统动力学特性的工具。

啮合误差对复合行星轮系动态均载特性的影响

以Ravigneaux式复合行星轮系为研究对象,基于集中参数理论,建立采用中心浮动构件的非线性动力学模型;通过计算传动系统的均载系数,获得各齿轮啮合误差与均载系数的关系曲线,进而分析安装误差和偏心误差对系统均载特性的影响。分析结果表明:行星轮的安装误差会导致行星轮出现持续的'偏载',而行星轮的偏心误差则会导致相应啮合副在运动过程中出现较大的冲击;如果合理布置行星轮的误差,使得其相对于系统的旋转中心呈辐射状对称,将能大大降低行星轮的误差对系统均载性能的影响。

高重合度弧齿锥齿轮加工参数设计与重合度测定

给出了高重合度弧齿锥齿轮的加工参数设计方法。利用局部综合法、轮齿接触分析(TCA)、轮齿承载接触分析(LTCA)和啮合仿真技术,通过齿面接触路径倾斜,达到了高重合度的设计目的。该设计方法不改变轮坯的几何参数,不改变大轮的加工调整参数,可在现有的机床上使用标准系列刀具加工,实用性强。给出了三种齿面接触路径倾斜度不同的设计方案,进行了啮合仿真分析与重合度测定,结果证明,用该方法可设计出重合度达2.0～3.0的高重合度弧齿锥齿轮。

基于谐波平衡法的复合行星齿轮传动系统非线性动态特性

为揭示多间隙作用下Ravigneaux型复合行星齿轮传动系统的非线性动力学行为,建立考虑时变啮合刚度、齿侧间隙与综合啮合误差的系统纯扭转强非线性动力学模型。将齿侧间隙非线性函数表达为描述函数的形式,运用谐波平衡法(Harmonic balance method,HBM)将方程组转化为非线性代数方程组,使用逆Broyden秩1法进行迭代求解,得到系统的基频稳态响应。通过改变时变啮合刚度、齿侧间隙与综合啮合误差的大小,分析参数变化对系统非线性动态特性的影响。研究发现,由于齿侧间隙的影响,系统动态特性曲线出现幅值跳跃与多值解等典型非线性特征,系统出现复杂的冲击现象;齿侧间隙、啮合刚度波动与误差波动的耦合使系统的非线性程度得以强化。基于描述函数的HBM法可用于求解更加复杂模型的基频稳态响应,为深入研究复合行星齿轮系统的动态特性提供了一种方法。