Effects of different coupling models of a helical gear system on vibration characteristics

Time-varying mesh stiffness (TVMS) and the dynamic coupling between the helical gears have a great influence on the vibration characteristics of a helical gear rotor system. Considering the effects of TVMS and adopting two coupling models (lateral-torsional coupling model and lateral-torsional-axial-swing coupling model), the dynamic behavior of a helical gear system was studied. First, an analytical model was used to analyze TVMS of a helical gear pair where the helical tooth is simulated by many spur tooth slices along the direction of the tooth width and the mesh stiffness of each slice is calculated using the energy method. Then, considering the effects of the TVMS excitation, the finite element model of a helical gear rotor system was established. Gear mesh was simulated by the above-mentioned two coupling models to investigate the effects of coupling forms on the system vibration characteristics. The strain energy was used to distinguish the dominant mode and dominant shaft of a gear system in natural characteristics analysis. The results show that the full coupling model can analyze accurately the vibration characteristics of the system and the axial and swing motions cannot be ignored in vibration analysis. Finally, the effects of helix angle on TVMS and vibration responses of a helical gear system were also studied.     

Fault identification method for planetary gear based on DT-CWT threshold denoising and LE

Planetary gear is widely used in large-scale complex mechanical systems. However, because of the particularity of planetary gear transmission, serious wear and fatigue crack failures often occur in the sun gear, planet gears, and inner gear ring. In addition, every type of fault will experience different degradation processes. Improving the operation reliability of mechanical equipment through fault diagnosis of planetary gears and monitoring their degradation process is beneficial. This paper proposes a planetary gear fault identification method based on Dual-tree Complex wavelet transform (DT-CWT) threshold denoising and Laplacian eigenmaps (LE). The noise reduction processing of the original signal is achieved by the DT-CWT threshold denoising method, which takes full advantage of DT-CWT and is combined with the wavelet threshold of rigrsure principle. The original high-dimensional feature set, including the time domain features, frequency domain features, permutation entropy, and fractal box dimension of the denoised signal, is constructed from multi-angles. To solve the problems of excessively large feature dimension and the existence of redundant information, the LE algorithm is used to reduce the dimension of the original high-dimensional feature set, and the low-dimensional sensitive features are obtained. Through the above method, the effective identification of different fault states and different degradation states of the planetary gear are achieved.     

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.     

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。     

Analytical determination of mesh phase relations in general compound planetary gears

This paper systematically studies the mesh phase relations of general compound planetary gears. The mesh phase relations are described by the relative phases between mesh tooth variation functions of all gear meshes. The analysis allows for compound planetary gears having multiple mesh periods. A numbering method is proposed for accurate definition of the relative phases in a general compound planetary gear. By introducing the concepts of system-level, stage-level, and train-level relative phases, the relative phases between any two gear meshes in a compound planetary gear are calculated systematically. Important relations among these relative phases are derived. The results from this study are necessary for analytical or computational multibody studies on the static or dynamic response of general compound planetary gears.     

Vibration signal modeling of a planetary gear set with transmission path effect analysis

For a planetary gear set, the transducer-perceived vibration signal contains vibration information from multiple sources including the sun gear, planet gears, and the ring gear. All these vibration sources are subject to corresponding transmission path effects. In this paper, a comprehensive vibration signal model for a planetary gear set is proposed considering all the vibration sources and transmission path effects. Vibration sources were generated with a nonlinear two-dimensional lumped-parameter dynamic model. Transmission path effects are modeled as two parts: the part inside the gearbox to the casing and the other part along the casing to the transducer position. Given the gear sizes, the transmission path effect modeling parameters are estimated. Then the influences of different transmission paths on resultant vibration signals are analyzed. Some vibration characteristics are revealed for one healthy planetary gear set. These vibration characteristics are validated with lab experimental data in both time domain and frequency domain.     

3K-Ⅱ型直齿行星齿轮传动的固有特性

为揭示3K-Ⅱ型直齿行星齿轮传动的固有特性,建立该类传动系统在系杆随动参考坐标系下的平移-扭转耦合动力学模型.模型设定系统中每个构件均拥有3自由度,并计入各构件的支承刚度、轮齿时变啮合刚度和陀螺效应等影响因素.通过分析各构件间的相对位移关系,推导出系统的运动微分方程,进而求解其特征值问题即可获知系统的固有频率和相应振型.固有特性分析表明,3K-Ⅱ型行星齿轮传动具有与2K-H行星齿轮传动类似的三种典型振动模式,即扭转振动模式、平移振动模式和行星轮振动模式.列出三种典型振动模式下传动系统的运动特征.     

行星齿轮变速传动的弹流润滑研究

基于弹性流体动力润滑理论,针对行星齿轮变速器内齿轮主动和太阳轮主动的2种工况,分别求出行星齿轮与太阳轮啮合以及与内齿轮啮合时,沿啮合线在啮合点的最小油膜厚度。结果表明:齿轮在节点啮合的润滑情况可以体现齿轮的润滑状况;太阳轮主动的工况,行星轮与内齿轮啮合的润滑条件最差;提高润滑油的黏度可以增加齿轮润滑油膜厚度;增加齿轮压力角的方法提高齿轮油膜厚度的效果明显;提高齿轮啮合的油膜厚度对改善齿轮的润滑状态,降低齿轮的生产成本,具有实际使用价值。     

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.     

面向寿命终结阶段的机械产品设计绿色多准则优化

针对机械产品设计过程中通常考虑产品寿命终结阶段(End-of-life,EOL)报废处理过程的可拆卸性、再制造性、环保性等单个绿色质量因素影响,导致机械产品的回收拆解中可重用、回收零部件由于拆解过程费事、费力、经济性差无法回收重用或因回收重用价值不大导致零部件被直接废弃,造成严重的环境污染.从回收拆解作业效率、回收拆解...     

Study on planetary gear fault diagnosis based on entropy feature fusion of ensemble empirical mode decomposition

Because planetary gear is characterized by its small size, light weight and large transmission ratio, it is widely used in large-scale, low-speed and heavy-duty mechanical systems. Therefore, the fault diagnosis of planetary gear is a key to ensure the safe and reliable operation of such mechanical equipment. A fault diagnosis method of planetary gear based on the entropy feature fusion of ensemble empirical mode decomposition (EEMD) is proposed. The intrinsic mode functions (IMFs) with small modal aliasing are obtained by EEMD, and the original feature set is composed of various entropy features of each IMF. To address the insensitive features in the original feature set and the excessive feature dimension, kernel principal component analysis (KPCA) is used to process the original feature set. Kernel principal component extraction and feature dimension reduction are performed. The fault diagnosis of planetary gear is eventually realized by applying the extracted kernel principal components and learning vector quantization (LVQ) neural network. The experiments under different operation conditions are carried out, and the experimental results indicate that the proposed method is capable of extracting the sensitive features and recognizing the fault statuses. The overall recognition rate reaches to 96% when the motor output frequency is 45 Hz and the load is 13.5 N m, and the fault recognition rates of the normal gear, the gear with one missing tooth and the broken gear can reach to 100%. The recognition rates of different fault gears under other operation conditions also can achieve better results. Thus, the proposed method is effective for the diagnosis of planetary gear faults.     

Effects of variable loading conditions on the dynamic behaviour of planetary gear with power recirculation

Variable loads to which gearboxes are subjected are considered as one of the main sources of non-stationarity in these transmissions. In order to characterise their dynamic behaviour in such conditions, a torsional lumped parameter model of a planetary gear with power recirculation was developed. The model included time varying loading conditions and took into account the non-linearity of contact between teeth. The meshing stiffness functions were modelled using Finite Element Method and Hertzian contact theory in these conditions. Series of numerical simulations was conducted in stationary conditions, with different loading conditions. Equation of motion was solved using Newmark algorithm. Numerical results agreed with experimental results obtained from a planetary gear test bench. This test bench is composed of two similar planetary gears called test planetary gear set and reaction planetary gear set which are mounted back-to-back so that the power recirculates through the transmission. The external load was applied through an arm attached to the free reaction ring. Data Acquisition System acquired signals from accelerometers mounted on the rings and tachometer which measured instantaneous angular velocity of the carrier’s shaft. The signal processing was achieved using LMS Test.Lab software. Modulation sidebands were obtained from the ring acceleration measurements as well as a non-linear behaviour in case of variable loading resulted by a transfer of the spectral density from the fundamental mesh stiffness to its second harmonic.     

某型直升机行星齿轮机构弹流润滑研究

分析了某型直升机主减速器行星齿轮机构弹流润滑工况,研究了该齿轮系弹性润滑最薄弱啮合部位,计算得出了行星齿轮传动机构中齿宽、齿轮模数和压力角等齿轮参数对弹性润滑油膜厚度的影响,提出了改进直升机主减速器行星齿轮机械润滑状态的新思路和具体改进方案,结果证明增加行星轮和太阳轮的齿宽、模数和齿轮啮合角及提高润滑油粘度和粘压系数,可有效地改进齿轮润滑,减少齿面失效,提高行星齿轮传动机构的可靠性。     

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.     

Performances of a balanced hydraulic motor with planetary gear train

The current research of a balanced hydraulic motor focuses on the characteristics of the motor with three planet gears.References of a balanced hydraulic motor with more than three planet gears are hardly found.In order to study the characteristics of a balanced hydraulic motor with planetary gear train that includes more than three planet gears,on the basis of analysis of the structure and working principle of a balanced hydraulic motor with planetary gear train,formulas are deduced for calculating the hydraulic motor’s primary performance indexes such as displacement,unit volume displacement,flowrate fluctuation ratio,etc.Influences of the gears’ tooth number on displacement and flowrate characteristics are analyzed.In order to guarantee the reliability of sealing capability,the necessary conditions that tooth number of the sun gear and the planet gears should satisfy are discussed.Selecting large unit volume displacement and small displacement fluctuation ratio as designing objectives,a balanced hydraulic motor with three planet gears and a common gear motor are designed under the conditions of same displacement,tooth addendum coefficien and clearance coefficient.By comparing the unit volume displacement and fluctuation ratio of the two motors,it can be seen that the balanced hydraulic motor with planetary gear train has the advantages of smaller fluctuation ratio and larger unit volume displacement.The results provide theoretical basis for choosing gear tooth-number of this kind of hydraulic motor.     

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。     

齿轮故障对直齿轮副时变啮合刚度的影响研究

提出了一种基于计算机仿真的解析法,用于量化齿轮副在不同齿轮故障情况下的时变啮合刚度。齿轮故障在影响齿轮副传动的同时往往也伴随着刚度的降低,时变啮合刚度是状态监测和啮合齿轮副动态特性描述的一项重要参数,势能法是计算时变啮合刚度最常用的分析方法之一。采用势能法研究了含裂纹齿轮、断齿和齿面剥落等3种故障情况对于齿轮啮合刚度的影响。结果表明,由于齿轮故障的存在,导致了时变啮合刚度的降低,进而影响了直齿轮副的振动响应。     

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。     

钢/塑料齿轮组合行星传动的固有特性分析

建立了钢/塑料齿轮组合行星传动的纯扭转动力学模型;对8种钢/塑料齿轮组合行星传动的固有特性进行了研究,分析了组合方式对行星传动结构的固有频率、振型及模态动能的影响;研究了温度对组合行星传动一阶固有频率的影响.研究结果表明:组合方式对行星齿轮传动结构的固有特性影响显著;随着温度的升高,钢/塑料齿轮组合行星传动的固有频率下降,可能会出现温共振现象.     

钢/塑齿轮组合行星传动的振动特性

为了深入了解钢质行星齿轮传动系统引入塑料齿轮后的振动特性,建立钢/塑齿轮组合行星传动的动力学分析模型和试验模型,对SNS、SSS、SSN和NSS四种钢/塑齿轮组合行星传动的振动特性进行理论分析与试验研究,分析组合方式对行星传动振动特性的影响。数值仿真与试验研究结果表明:塑料齿轮的引入对行星齿轮传动的振动特性影响很大,显著地减小了太阳轮与行星轮和内齿圈与行星轮的啮合动载荷;有效地抑制了行星齿轮传动的齿轮啮合频带振动和高频带振动;组合方式对行星齿轮传动的振动特性影响显著,合理地采用钢/塑齿轮组合行星传动结构可以极大地降低啮合动载荷,从而有效地抑制传动系统的振动和噪声。