Measured load spectra of the bearing in high-speed train gearbox under different gear meshing conditions

The load spectrum is a crucial factor for assess-ing the fatigue reliability of in-service rolling element bear-ings in transmission systems.For a bearing in a high-speed train gearbox,a measurement technique based on strain detection of bearing outer ring was used to instrument the bearing and determine the time histories of the distributed load in the bearing under different gear meshing conditions.Accordingly,the load spectrum of the total radial load car-ried by the bearing was compiled.The mean value and class interval of the obtained load spectrum were found to vary non-monotonously with the speed and torque of gear mesh-ing,which was considered to be caused by the vibration of the shaft and the bearing cage.As the realistic service load input of bearing life assessment,the measured load spectrum under different gear meshing conditions can be used to pre-dict gearbox bearing life realistically based on the damage-equivalent principle and actual operating conditions.

Research on Instantaneous Angular Speed Signal Separation Method for Planetary Gear Fault Diagnosis

Planetary gear train is a critical transmission component in large equipment such as helicopters and wind turbines. Conducting damage perception of planetary gear trains is of great significance for the safe operation of equipment. Existing methods for damage perception of planetary gear trains mainly rely on linear vibration analysis. However, these methods based on linear vibration signal analysis face challenges such as rich vibration sources, complex signal coupling and modulation mechanisms, significant influence of transmission paths, and difficulties in separating damage information. This paper proposes a method for separating instantaneous angular speed (IAS) signals for planetary gear fault diagnosis. Firstly, this method obtains encoder pulse signals through a built-in encoder. Based on this, it calculates the IAS signals using the Hilbert transform, and obtains the time-domain synchronous average signal of the IAS of the planetary gear through time-domain synchronous averaging technology, thus realizing the fault diagnosis of the planetary gear train. Experimental results validate the effectiveness of the calculated IAS signals, demonstrating that the time-domain synchronous averaging technology can highlight impact characteristics, effectively separate and extract fault impacts, greatly reduce the testing cost of experiments, and provide an effective tool for the fault diagnosis of planetary gear trains.

Automatic Scallion Seedling Feeding Mechanism with an Asymmetrical High-order Transmission Gear Train

The current automatic scallion-transplanting machine is a complicated mechanism composed of two linkage mechanisms and two band carriers.It delivers seedlings ine ciently because of the movement limitations of the linkage mechanism.This paper proposes a new high-order non-circular gear train for an automatic scallion-seedling feeding mechanism.The proposed gear train has an asymmetrical transmission ratio;i.e.,its transmission ratio varies.This allows the mechanism’s execution component to move in a long displacement and rotate in a large rotation angle.The long displacement enables the execution component to reach the designed working position,and the large rotation angle allows it to feed a scallion in the required pose.A mathematical model for calculating the asymmetrical transmission ratio was established according to the closure requirements and the full-cycle motion of the driven gear pitch curve.Then,the parameter-design model of the new seedling-feeding mechanism was established,based on precise pose points and trajectory-shape control points.Moreover,an aided-design program was developed to obtain the parameter-solution domain of the scallion-seedling feeding mechanism.The mechanism parameters,which met the seedling-feeding function,were optimized to determine the transmission ratio,using a program and a kinematic simulation.Finally,a prototype of the mechanism was produced,and a seedling-feeding experiment was carried out.One-thousand seedlings were tested at a rate of 100 seedlings per minute,and the statistical success rate was 93.4%.Thus,the automatic scallion-seedling feeding mechanism significantly improves the e ciency of automatically transplanting scallions.

Design of Vegetable Pot Seedling Pick‑up Mechanism with Planetary Gear Train

It has been challenging to design seedling pick-up mechanism based on given key points and trajectories,because it involves dimensional synthesis and rod length optimization.In this paper,the dimensional synthesis of seedling pickup mechanism with planetary gear train was studied based on the data of given key points and the trajectory of the endpoint of seedling pick-up mechanism.Given the positions and orientations requirements of the five key points,the study first conducted a dimensional synthesis of the linkage size and center of rotation.The next steps were to select a reasonable solution and optimize the data values based on the ideal seedling trajectory.The link motion was driven by the planetary gear train of the two-stage gear.Four pitch curves of noncircular gears were obtained by calculating and distributing the transmission ratio according to the data.For the pitch curve with two convex points,the tooth profile design method of incomplete noncircular gear was applied.The seedling pick-up mechanism was tested by a virtual prototype and a physical prototype designed with the obtained parameter values.The results were consistent with the theoretical design requirements,confirming that the mechanism meets the expected requirements for picking seedlings up.This paper presents a new design method of vegetable pot seedling pick-up mechanism for an automatic vegetable transplanter.

Translational - torsional coupled model based nonlinear dynamic analysis of an NGW planetary gear train

This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains.

Bifurcation and chaos study on transverse-torsional coupled 2K-H planetary gear train with multiple clearances

A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.

Super-harmonic resonance of gear transmission system under stick-slip vibration in high-speed train

This work deals with super-harmonic responses and the stabilities of a gear transmission system of a high-speed train under the stick-slip oscillation of the wheel-set.The dynamic model of the system is developed with consideration on the factors including the time-varying system stiffness,the transmission error,the tooth backlash and the self-excited excitation of the wheel-set.The frequency-response equation of the system at super-harmonic resonance is obtained by the multiple scales method,and the stabilities of the system are analyzed using the perturbation theory.Complex nonlinear behaviors of the system including multi-valued solutions,jump phenomenon,hardening stiffness are found.The effects of the equivalent damping and the loads of the system under the stick-slip oscillation are analyzed.It shows that the change of the load can obviously influence the resonance frequency of the system and have little effect on the steady-state response amplitude of the system.The damping of the system has a negative effect,opposite to the load.The synthetic damping of the system composed of meshing damping and equivalent damping may be less than zero when the wheel-set has a large slippage,and the system loses its stability owing to the Hopf bifurcation.Analytical results are validated by numerical simulations.

Design and Experiment of Non-circular Combined Gear Train Beating-up Mechanism

The most important performance of a beating-up mechanism is that the dwelling time of the sley must ensure the completion of the weft insertion. To meet this requirement, a new non-circular combined gear train beating-up mechanism which is composed of two-stage planetary gear trains is proposed. The first-stage is a Fourier planetary gear train and the second-stage is a non-circular planetary gear train. For designing of this new mechanism, the ideal kinematic equations of the sley are constructed first. Then the kinematic model of the first-stage Fourier planetary gear train is established and the reverse solution for the pitch curves of the second-stage non-circular gears is deduced. With a computer-aided design program, the influences of several important parameters on the pitch curves of the second-stage non-circular gears are analyzed, and a set of preferable structural parameters are obtained. Finally, a test bed of this mechanism is developed and the experimental results show that this new beating-up mechanism can achieve the designed dwelling time, namely it can meet the requirements of beating-up process.

Stability of motion state and bifurcation properties of planetary gear train

A nonlinear lateral-torsional coupled vibration model of a planetary gear system was established by taking transmission errors,time varying meshing stiffness and multiple gear backlashes into account.The bifurcation diagram of the system's motion state with rotational speed of sun gear was conducted through four steps.As a bifurcation parameter,the effect of rotational speed on the bifurcation properties of the system was assessed.The study results reveal that periodic motion is the main motion state of planetary gear train in low speed region when ns<2 350 r/min,but chaos motion state is dominant in high speed region when ns>2 350 r/min,The way of periodic motion to chaos is doubling bifurcation.There are two kinds of unstable modes and nine unstable regions in the speed region when 1 000 r/min<ns<3 000 r/min.

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.

Efficiency Evaluation of Continuously Variable Transmissions Including a Planetary Gear Train

With their advantages, continuously variable transmissions have gained more popularity in the last decade by their use in mechanical transmission systems. The present paper aims to analysis the efficiency of the transmission based on the mechanical efficiency of the planetary gear train integrated in such transmission. In this analysis, we consider the mechanical efficiency of the transmission has been determined considering how the efficiency of the CVT members changes as a function of the operating conditions. The efficiency of the planetary gear train as a function of the configuration, speeds in his three input/output shafts, and also with respect to the power flow type. Results are compared with those obtained from other methods performance evaluation of the transmission, available in the literature.

Dynamic characteristics and sensitivities analysis of a power turret gear train

The dynamic transmission characteristics and the sensitivities of the three stage idler gear system of the new NC power turret are studied in the paper. Considering the strongly nonlinear factors such as the periodically time-varying mesh stiffness, the nonlinear tooth backlash, the lump-parameter model of the gear system is developed with one rotational and two translational freedoms of each gear. The eigen-values and eigenvectors are derived and analyzed on the basis of the real modal theory. The sensitivities of natural frequencies to design parameters including supporting and meshing stiffnesses, gear masses, and moments of inertia by the direct differential method are also calculated. The results show the quantitative and qualitative impact of the parameters to the natural characteristics of the gear system. Furthermore, the periodic steady state solutions are obtained by the numerical approach based on the nonlinear model. These results are employed to gain insights into the primary controlling parameters, to forecast the severity of the dynamic response, and to assess the acceptability of the gear design.

A review on design and testing methodologies of modern freight train draft gear system

Rolling stock connection systems are key to running longer and heavier trains as they provide both the connections of vehicles and the damping,providing the longitudinal suspension of the train.This paper focuses on the evolution of both connection and stiffness damping systems.Focus is on freight rolling stock,but passenger draw gears are also examined.It was found that connection systems have evolved from the buff and chain system used in the pioneer railways of the 1800s to the modern auto-coupler connection systems that are in-service worldwide today.Refined versions of the buff and chain coupling are,however,still in use in the EU,UK,South America and India.A wide range of auto-coupler systems are currently utilised,but the AAR coupler(Janney coupler)remains the most popular.A further variation that persists is the SA3 coupler(improved Wilson coupler)which is an alternative auto-coupler design used mainly throughout the former Soviet Union.Restricting the review to auto-coupler systems allowed the paper to focus on draft gears which revealed polymer,polymer-friction,steel spring-friction,hydraulic draft gears and sliding sill cushioning systems.Along with the single compressive draft gear units balanced and floating plate configurations are also presented.Typical draft gear acceptance standards are presented along with modelling that was included to aid in presentation of the functional characteristics of draft gears.

Influence of Structural Aspects on the Generation Process in Planetary Gear Trains

Structural and rotational isomorphism in planetary Gear Trains (PGTs), is tested by Hamming number method. Symmetry in PGTs can be determined from the same Hamming matrix. Bearing of the structural property like symmetry in PGTs is studied and is used to evaluate its influence on generation of PGTs.

Method for Selecting the Optimal Solution for the Design of the Gear Train

Some researchers in mechanical engineering have developed systems for the design of gear transmission boxes, but almost no calculation methods exist for widespread synthesis. In this article, we outline methods for automatic determination of toothed helical gear trains and the selection criteria for the optimal choice of gear trains. In this work two methods were applied. As first design to use an expert system for the design and then optimize the design that is why we used Kappa PC and Catia for CAD.

The influence of AAR coupler features on estimation of in-train forces

Inadequate management of large in-train forces transferred through coupler systems of a railway train leads to running and structural failures of vehicles.Understanding these phenomena and their mitigation requires accurate estimation of relative motions and in-train forces between vehicle bodies.Previous numerical studies have ignored inertia of coupling elements and the impacts between couplers.Thus,existing models underestimate the additional dynamic variations in in-train forces.Detailed multi-body dynamic models of two AAR(Association of American Railroads)coupler systems used in passenger and freight trains are developed,incorporating coupler inertia and various slacks.Due to the modeling and simulation com-plexities involved in a full train model,with such details of coupler system,actual longitudinal train dynamics is not studied.A system comprising only two coupling units,inter-connecting two consecutive vehicles,is modeled.Considered system has been fixed at one end and an excitation force is applied at the other end,to mimic a relative force transmission through combined coupler system.Simulation results obtained from this representative system show that,noticeable influence in in-train forces are expected due to the combined effect of inertia of couplers and intermittent impacts between couplers in the slack regime.Maximum amplitude of longitudinal reaction force,transferred from draft gear housing to vehicle body,is expected to be significantly higher than that predicted using existing models of coupler system.It is also observed that the couplers and knuckles are subjected to significant longitudinal and lateral contact forces,due to the intermittent impacts between couplers.Thus,accurate estimation of draft gear reaction force and impact forces between couplers are essential to design vehicle and coupler components,respectively.

应用滑动轴承的风电齿轮箱行星轮系动力学建模及解耦方法

在行星轮系动力学建模中,常以非线性油膜力或线性刚度-阻尼形式考虑其对系统动力学特性的影响,前者仿真精度高但计算成本也高,后者计算效率高却忽略了油膜力和轴颈-轴套偏心量的时变性,仿真精度有限。为此,以2MW级风电齿轮箱为研究对象,建立滑动轴承时变线性刚度-阻尼模型,提出计入轴颈-轴套时变偏心量的滑动轴承附加偏心修正力计算方法;利用行星架销轴-行星轮变形协调关系,将时变线性刚度-阻尼模型与附加偏心修正力进行耦合;建立应用滑动轴承的风电齿轮箱行星轮系动力学模型,对比了工况和轴承参数对模型计算精度与系统动态响应的影响,并通过试验加以验证。研究结果表明,齿轮副动态啮合力波动会使滑动轴承刚度-阻尼系数和附加偏心修正力产生周期性变化;在稳定和瞬态工况下,提出的模型可以很好地预测系统响应,尤其是行星轮振动响应;减小滑动轴承宽径比与间隙、增大输入转矩可以改善系统均载性能。

微型行星齿轮传动设计与分析

提出一种应用于某航空发动机中空气涡轮起动机的微型行星齿轮传动设计方案,对传动系统的构型进行结构设计、参数匹配;采用有限元分析软件ANSYS对其重要零部件进行强度校核,基于正交试验法对减速器结构进行优化,为微型行星减速结构在航空发动机起动机等航空产品中的推广与应用提供理论支撑。

取秧侧向零偏移的空间轨迹再生稻分插机构设计与试验

为了解决现有空间行星轮系式分插机构在再生稻宽窄行机械化种植取秧过程中出现侧向偏移量和侧向偏转角的技术难题,本文提出一种具有局部平面轨迹特性的空间轨迹不等速行星轮系机构,并开展基于取秧口和机构回转中心位置约束下的宽窄行分插机构综合研究。构建了基于关键位姿点(取秧起始点、取秧结束点、推秧点)的空间轮系机构运动综合模型,利用关键位姿点求解机构杆长参数与空间交错轴信息,并通过优选二杆相对角位移参数实现机构传动比分配。将不完全非圆齿轮副引入空间行星轮系机构,利用间歇机构锁止弧约束行星轴,实现机构取秧过程侧向零偏移量、侧向零偏转角的平面轨迹段。通过仿真分析与机构样机试验验证了机构实际作业性能与理论设计相一致,结果表明:分插机构取秧侧向零偏移量,取秧侧向零偏转角,推秧侧向总偏移量为50.24 mm、取秧角为5.18°、推秧角为71.56°、推秧侧向角为16.26°、插秧穴口宽度为22.43 mm、轨迹高度为289.76 mm,满足预期设计要求。最后通过田间试验验证,分插机构可实现等行距取秧口和既定机构回转中心下宽行(40 cm)与窄行(20 cm)间隔机插,满足再生稻宽窄行种植要求。

三转臂式差动椭圆齿轮系分插机构的工作原理与运动分析

针对我国水稻插秧小株距密植的要求,设计一种三转臂式差动椭圆齿轮系分插机构。论述差动式椭圆齿轮系分插机构的工作原理,并通过该分插机构的示意图来阐述其工作原理和工作过程,同时通过建立运动学模型来对该机构进行运动学分析。