基于FBG的行星齿轮箱内齿圈齿根应变动态检测方法研究

通过分析FBG传感器的传感模型与耦合理论,提出了一种基于FBG传感器的行星齿轮箱内齿圈齿根应变动态检测方法。对宽带光源、传感光路、光电转换、信号解调以及数据采集等模块进行集成,搭建了内齿圈齿根应变动态检测系统,并利用该系统对不同负载工况下的行星齿轮箱进行了多次实验数据采集。结果表明:应用该系统能够实现对行星齿轮箱内齿圈齿根应变动态检测,同时,采集的数据与理论分析相吻合,能够为后续行星齿轮箱啮合状态监测与故障诊断工作提供参考。     

封闭差动行星齿轮箱动态均载性能试验研究

针对同时具有太阳轮浮动、柔性销轴和柔性内齿圈三种均载方法的封闭差动行星齿轮箱进行试验研究,探索多种均载措施的封闭差动行星传动均载性能的特点。测试行星传动的差动级内齿圈齿根弯曲应力和封闭级的太阳轮齿根弯曲应力,根据齿向方向和圆周方向上各个通道应变测试结果提出均载系数的数据处理方法。得到每个被测轮齿最大均载系数,研究行星齿轮箱动态均载系数随工况载荷的变化趋势。分析并统计封闭级和差动级不同载荷下的平均均载系数及其标准差,并与某航空发动机主齿轮箱的理论分析均载系数进行对比。结果表明封闭级均载性能优于差动级,载荷越大两级均载性能越好,具有这三种均载方法的行星系统较采用单种均载措施的传动均载性能好,为封闭差动行星齿轮的均载设计提供了依据。     

基于光纤光栅的直齿圆柱齿轮应力修正系数优化

利用光纤光栅传感器截面直径小的优势,将光纤光栅粘贴在直齿圆柱齿轮齿根过渡曲线处,测量弯曲应力将会得到比较好的测量效果。文中利用光纤光栅传感器测量了直齿圆柱齿轮弯曲应力,并对直齿圆柱齿轮弯曲应力解析计算的应力修正系数进行了优化。首先根据弹性理论的两个平面假设,提出在齿根表面一点上沿齿宽方向应力与该点至端面的距离有关,并且沿齿宽方向应力与弯曲应力的比值,在齿宽方向上服从指数函数变化规律;然后利用光纤光栅传感器,测量直齿圆柱齿轮弯曲应力;最后根据光纤光栅测量,优化直齿圆柱齿轮弯曲应力解析计算的应力修正系数。研究结果表明,直齿圆柱齿轮弯曲应力解析计算的应力修正系数取值偏大,比测量得到的应力修正系数大21.8%。直齿圆柱齿轮是最常见的传动装置基本零件,基于光纤光栅测量对直齿圆柱齿轮弯曲应力修正系数进行优化,可提高直齿圆柱齿轮强度设计的可靠性。     

光纤光栅应变传感在扭振测量中的应用

为了实现对大型旋转机械扭振的准确测量,提出了一种基于光纤布拉格光栅(Fiber Bragg Grating,FBG)应变的扭振测量方法。首先,根据旋转机械轴系的扭振产生机理以及光纤光栅传感技术,建立了扭振与光纤光栅的应变传递模型,进而设计了光纤光栅应变传感器。接着,搭建了静、动态实验平台,对该传感器进行了静、动态标定实验。最后,在机械运行状态下,对该传感器进行了动态扭振测试实验。标定实验结果表明:在线性区间内,该传感器的灵敏度为12.464με/Nm,线性相关系数为0.9987,迟滞误差为3.02%,重复性误差为1.23%;在动态响应实验中,响应时间为0.171s(±5%),超调量为67.81%。动态测试实验结果表明:该传感器能检测出与已知加载特征一致的扭振信号。因此,基本满足对扭振测量的稳定可靠、精度高、抗电磁干扰等要求。     

行星齿轮传动设计中行星轮齿根径向间隙值的配置

当内齿轮齿顶与行星轮齿根发生过渡曲线干涉时,仍保持行星轮齿根径向间隙为标准值,对提高行星齿轮传动机构的运动精度和平稳性有一定作用。提出了实现上述要求的内齿轮齿顶修缘方法。     

FBG传感器应变标定方法

为了提高光纤光栅应变传感器测量精度,针对光纤光栅传感器工程应用情况,提出了一种光纤布拉格光栅(fiber bragg grating,简称FBG)传感器应变特性标定方法。通过理论分析和实验标定了封装式光纤光栅应变传感器的灵敏度系数,对传感器理论与实验灵敏度系数误差进行了分析。实验结果表明,该方法简单、易行,用于光纤光栅传感器使用前的标定,可以提高基于光栅光栅传感器的测量精度和准确性。同时,该方法为光纤光栅传感器的工程推广应用奠定了基础。     

基于光纤光栅法珀腔传感器的结构表面温度测量方法

针对结构表面温度测量需求,提出了一种基于光纤光栅法珀腔传感器的表面温度测量方法,通过光纤光栅和光纤法珀传感同时获取被测结构的温度、应变信息,从而补偿应变对温度的交叉敏感。本文分析了光纤光栅法珀腔的表面温度测量原理,通过仿真对传感器的主要参数进行了设计;并提出了一种基于双参数的最小均方差估计算法用于光纤光栅法珀腔传感器的信号解调;最后,对光纤光栅传感器和光纤光栅法珀腔传感器进行了温度测量对比实验。试验结果表明,光纤光栅法珀腔温度传感器在常温到400℃范围内,温度测量值的直线拟合相关系数为0.998 4,最大误差百分比为1.46%,均优于单光纤光栅温度传感器。     

风电行星轮系动态啮合特性分析

时变风载是风电增速齿轮系破坏的重要原因之一,因此对处于极端恶劣工况风电增速齿轮系动态啮合研究非常重要。以风电斜齿行星轮系为对象,考虑齿侧间隙、轴承游隙及摩擦对啮合的影响,建立了风电斜齿行星齿轮系有限元模型。采用非线性动力学方法,研究了行星齿轮与太阳轮、内齿轮啮合过程中其齿根弯曲应力的变化规律,分析了转速对其啮合冲击应力的影响。通过分析计算得出:转速增加能使齿根弯曲应力曲线提前,行星轮的冲击应力不一定会随着转速的提升而变大;齿轮箱和传动轴受到的冲击应力会随着转速的提升而变大,同时冲力应力曲线整体前移。     

轴线平行度误差对齿根变形弯曲应力的影响研究

为了研究轴线倾斜造成的装配平行度误差对齿轮啮合过程齿根弯曲变形的影响,设计并搭建了一套齿轮轴线可调节的齿轮箱实验台和完整的应变采集分析系统,并进行实验验证。基于调心滚子轴承内外圈的允许偏差,建立不同轴线偏移程度的齿轮组接触有限元模型,并进行动态仿真分析,获得啮合过程中的齿根应变应力分布曲线;通过对实验所需的不同轴线的调节方式的设计,对比了调节前后两轴角度的偏差实际值与理论值,验证了调节装置的可行性;最后,通过应变片采集卡等组成的应变采集系统,测试了不同轴线平行度误差下的齿根应变值,得到了相应的啮合应变应力分布曲线,并与仿真得到的啮合应变应力曲线进行对比,得出轴线平行度误差对齿根危险截面处弯曲变形应力的影响。     

行星齿轮内齿圈的多柔体动力学分析

以多柔体动力学理论为基础,研究了行星齿轮内齿圈在啮合过程中的动力学行为.构建了基于UG的虚拟样机模型.对系统进行了分析、计算及数值仿真,求解得到轮缘厚度系数与内齿圈应力/应变的定量关系及动应力沿内齿圈的分布规律,并对内齿圈进行了结构优化.结果表明,适当降低内齿圈的轮缘厚度系数,可有效降低振动、冲击与噪声,从而提高机构的疲劳寿命.     

Health condition identification of planetary gearboxes based on variational mode decomposition and generalized composite multi-scale symbolic dynamic entropy

This paper proposes a novel fault diagnosis method based on variational mode decomposition (VMD) and generalized composite multi-scale symbol dynamic entropy (GCMSDE) to identify the different health conditions of planetary gearboxes. First, VMD is adopted to remove the noises and highlight the fault symptoms. Second, GCMSDE is utilized to extract the fault features from the denoised vibration signals. Third, the Laplacian score (LS) approach is employed to refine the fault features. Finally, the new features are fed into Softmax regression to identify the health conditions of planetary gearboxes. The proposed method is numerically and experimentally demonstrated to be able to differentiate seven localized fault types on the sun gear, planet gear and ring gear of planetary gearboxes.     

基于包络加窗同步平均的行星齿轮箱特征提取

行星齿轮箱由于行星轮通过效应、太阳轮与行星架的旋转及时变工况,导致其振动响应存在时变传递路径及非平稳性等特点,且传统的同步平均将不能直接应用于行星齿轮箱。笔者在国外加窗同步平均的基础上提出一种能有效克服时变传递路径及非平稳性的基于包络信号角域加窗同步平均的行星齿轮箱故障特征提取方法。首先,基于谱峭度提取出行星齿轮箱振动信号的包络信号;其次,再利用计算阶比跟踪技术对包络信号进行等角度重采样,行星架每旋转一圈,选择合适的窗函数对角域信号进行多齿宽加窗截取;最后,验证齿轮啮合齿序特征,根据重排齿序对加窗信号进行重构振动分离信号,对振动分离信号进行角域同步平均,提取行星齿轮箱故障特征。行星齿轮箱故障实测信号分析表明,该方法能有效提取行星齿轮箱故障特征。     

基于FBG的齿根弯曲应力在线检测方法

根据国际标准化组织(international organization for standardization,简称ISO)和美国齿轮制造者协会(American gear manufacturers association,简称AGMA)关于渐开线圆柱齿轮强度的计算方法,在计算单个齿轮齿根弯曲应力时,可将轮齿简化为一悬臂梁。基于此,提出了一种齿根弯曲应力在线检测的新方法,利用光纤布拉格光栅(fiber Bragg grating,简称FBG)的应变特性和齿轮传递扭矩时轮齿产生的挠度,将齿根弯曲应力的测量转化为光栅反射波长的测量,通过对反射波长的实时解调,能够实现对运行中齿轮的齿根弯曲应力进行实时在线检测。通过对一对渐开线圆柱尼龙斜齿轮进行分析,并在1~18N·m扭矩范围进行实验,结果表明该方法能够准确测量齿根的弯曲应力,灵敏度高达70pm/MPa,线性拟合度达0.99以上,且响应速度快。利用光纤光栅准确检测齿轮运行时的齿根弯曲应力,不但能够代入实际工况实现在线检测,同时对齿轮的设计和故障诊断具有指导意义。     

基于参数反求的齿轮裂纹时变啮合刚度计算方法

基于齿根应变测试技术和优化理论提出了齿轮时变啮合刚度反求计算方法,并将其应用于齿轮故障机理研究。构建了齿根动态应力与时变啮合刚度反问题模型,并搭建齿轮裂纹故障应变测试实验台来采集齿根应变;建立了相对应的有限元模型并将计算应变与测量应变代入反问题模型,从而实现齿轮啮合刚度的反向求解。计算结果表明,相比解析法和有限元法,所提方法显著提高了求解精度并且具备更高的可靠性。建立了齿根裂纹故障的齿轮系统动力学模型,通过对动力学响应进行时域及频域分析来揭示齿轮裂纹故障机理。     

基于EEMD的行星齿轮箱齿轮裂纹损伤定位

针对行星齿轮式变速箱的齿轮裂纹损伤难以提取特征频率和定位的问题,提出基于总体平均经验模式分解(ensemble empirical mode decomposition,简称EEMD)的齿轮局部损伤频率解调分析方法。该方法在建立的齿轮局部损伤振动信号模型的基础上,分别对太阳轮、齿圈、行星轮的裂纹损伤信号进行EEMD分解和频率解调分析,通过频谱图提取齿轮的局部损伤特征频率,从而识别变速箱中裂纹损伤齿轮的位置。综合仿真分析和试验结果表明,基于EEMD的齿轮局部损伤频率解调分析方法可以有效地提取太阳轮、齿圈和行星轮的裂纹损伤特征频率,实现行星齿轮式变速箱中齿轮裂纹损伤的定位。     

Vibration condition monitoring of planetary gearbox under varying external load

The paper shows that for condition monitoring of planetary gearboxes it is important to identify the external varying load condition. In the paper, systematic consideration has been taken of the influence of many factors on the vibration signals generated by a system in which a planetary gearbox is included. These considerations give the basis for vibration signal interpretation, development of the means of condition monitoring, and for the scenario of the degradation of the planetary gearbox. Real measured vibration signals obtained in the industrial environment are processed. The signals are recorded during normal operation of the diagnosed objects, namely planetary gearboxes, which are a part of the driving system used in a bucket wheel excavator, used in lignite mines. It is found that a planetary gearbox in bad condition is more susceptible to load than a gearbox in good condition. The estimated load time traces obtained by a demodulation process of the vibration acceleration signal for a planetary gearbox in good and bad conditions are given. It has been found that the most important factor of the proper planetary gearbox condition is connected with perturbation of arm rotation, where an arm rotation gives rise to a specific vibration signal whose properties are depicted by a short-time Fourier transform (STFT) and Wigner-Ville distribution presented as a time–frequency map. The paper gives evidence that there are two dominant low-frequency causes that influence vibration signal modulation, i.e. the varying load, which comes from the nature of the bucket wheel digging process, and the arm/carrier rotation. These two causes determine the condition of the planetary gearboxes considered. Typical local faults such as cracking or breakage of a gear tooth, or local faults in rolling element bearings, have not been found in the cases considered. In real practice, local faults of planetary gearboxes have not occurred, but heavy destruction of planetary gearboxes have been noticed, which are caused by a prolonged run of a planetary gearbox at the condition of the arm run perturbation. It may be stated that the paper gives a new approach to the condition monitoring of planetary gearboxes. It has been shown that only a root cause analysis based on factors having an influence on the vibration solves the problem of planetary gearbox condition monitoring.     

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.     

A study on the bending stress of the hollow sun gear in a planetary gear train

Generally, planetary gear type traveling reduction gear is composed of multiple planetary gear stages and has a hollow sun gear in the last stage planetary gear. In designing reduction gear, it is important to evaluate accurately the bending stress at the tooth root of the sun gear as the sun gear is the weakest component in the reduction gear system. Although bending stress can be calculated easily using gear standard codes such as the American Gear Manufacturers Association (AGMA) and International Organization for Standardization (ISO) 6336 for almost all gears, meticulous calculation is needed for the hollow sun gear because of its low backup ratio (rim thickness divided by tooth height) and comparatively large root fillet radius. In this study, a finite element analysis (FEA) is carried out to investigate the effect of rim thickness and root fillet radius on bending stress at the tooth root of the hollow sun gear. In standard codes, bending stress at the tooth root is calculated linearly with a constant slope for the backup ratio below 1.2. However, the effect of the rim thickness on bending stress is more complex in the planetary gear system. Bending stresses calculated by FEA with various backup ratios and root filler radii are compared with the bending stresses calculated by the standard codes.     

非对称齿廓齿轮弯曲疲劳强度理论分析与试验

为提高齿轮承载能力设计齿轮两侧压力角不等的非对称渐开线新齿形,推导双压力角非对称齿廓齿轮工作齿侧与非工作齿侧的渐开线齿廓方程和齿根过渡曲线方程,通过迭代计算和优化策略提出非对称齿廓齿轮疲劳强度解析法计算公式。编制生成非对称齿轮齿廓的参数化程序,在此基础上建立非对称齿廓齿轮有限元分析模型。通过解析法对不同压力角组合的非对称齿廓齿轮弯曲应力和危险截面位置计算得出,随着工作齿侧压力角的增大齿根最大弯曲应力逐渐降低,单齿啮合区向齿顶偏移;通过对有限元模型进行计算得出的结果与解析法一致,应用最小二乘法拟合出非对称齿廓齿轮齿根弯曲应力随工作齿侧压力角变化的计算公式。采用数控电火花线切割方法加工制造非对称与标准齿廓齿轮,在高频疲劳试验机上采用双齿脉动加载方法对其进行疲劳强度试验。试验结果表明,非对称齿廓齿轮在相同寿命下比对称齿轮极限载荷提高了50%,非对称齿廓齿轮的应力值变化趋势与前两种方法是一致的。     

Crack Fault Classification for Planetary Gearbox Based on Feature Selection Technique and K-means Clustering Method

During the condition monitoring of a planetary gearbox, features are extracted from raw data for a fault diagnosis.However, different features have different sensitivity for identifying different fault types, and thus, the selection of a sensitive feature subset from an entire feature set and retaining as much of the class discriminatory information as possible has a directly effect on the accuracy of the classification results. In this paper, an improved hybrid feature selection technique(IHFST) that combines a distance evaluation technique(DET), Pearson's correlation analysis, and an ad hoc technique is proposed. In IHFST, a temporary feature subset without irrelevant features is first selected according to the distance evaluation criterion of DET, and the Pearson's correlation analysis and ad hoc technique are then employed to find and remove redundant features in the temporary feature subset, respectively, and hence,a sensitive feature subset without irrelevant or redundant features is selected from the entire feature set. Further, the k-means clustering method is applied to classify the different kinds of health conditions. The effectiveness of the proposed method was validated through several experiments carried out on a planetary gearbox with incipient cracks seeded in the tooth root of the sun gear, planet gear, and ring gear. The results show that the proposed method can successfully distinguish the different health conditions of a planetary gearbox, and achieves a better classification performance than other methods. This study proposes a sensitive feature subset selection method that achieves an obvious improvement in terms of the accuracy of the fault classification.