Advancing high-speed train gearbox durability:enhanced bearing load and contact stress through transition from helical to herringbone gears

High-speed trains typically utilize helical gear transmissions,which significantly impact the bearing load capacity and fatigue service performance of the gearbox bearings.This paper focuses on the gearbox bearings,establishing dynamic models for both helical gear and herringbone gear transmissions in high-speed trains.The modeling particularly emphasizes the precision of the bearings at the gearbox's pinion and gear wheels.Using this model,a comparative analysis is conducted on the bearing loads and contact stresses of the gearbox bearings under uniform-speed operation between the two gear transmissions.The findings reveal that the helical gear transmission generates axial forces leading to severe load imbalance on the bearings at both sides of the large gear,and this imbalance intensifies with the increase in train speed.Consequently,this results in a significant increase in contact stress on the bearings on one side.The adoption of herringbone gear transmission effectively suppresses axial forces,resolving the load imbalance issue and substantially reducing the contact stress on the originally biased side of the bearings.The study demonstrates that employing herringbone gear transmission can significantly enhance the service performance of high-speed train gearbox bearings,thereby extending their service life.

Research on Cavitation Characteristics and Influencing Factors of Herringbone Gear Pump

Cavitation is a common issue in pumps,causing a decrease in pump head,a fall in volumetric efficiency,and an intensification of outlet flow pulsation.It is one of the main hazards that affect the regular operation of the pump.Research on pump cavitation mainly focuses on mixed flow pumps,jet pumps,external spur gear pumps,etc.However,there are few cavitation studies on external herringbone gear pumps.In addition,pumps with different working principles significantly differ in the flow and complexity of the internal flow field.Therefore,it is urgent to study the cavitation characteristics of external herringbone gear pumps.Compared with experimentalmethods,visual research and cavitation area identification are achieved through computation fluid dynamic(CFD),and changing the boundary conditions and shape of the gear rotor is easier.The simulation yields a head error of only 0.003%under different grid numbers,and the deviation between experimental and simulation results is less than 5%.The study revealed that cavitation causes flow pulsation at the outlet,and the cavitation serious area is mainly distributed in the meshing gap and meshing area.Cavitation can be inhibited by reducing the speed,increasing the inlet pressure,and changing the helix angle can be achieved.For example,when the inlet pressure is 5 bar,the maximumgas volume fraction in themeshing area is less than 50%.These results provide a reference for optimizing the design and finding the optimal design parameters to reduce or eliminate cavitation.

Application of Isogeometric Analysis Method in Three-Dimensional Gear Contact Analysis

Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.

Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel

Although there is currently no unified standard theoretical formula for calculating the contact stress of cylindrical gears with a circular arc tooth trace(referred to as CATT gear),a mathematical model for determining the contact stress of CATT gear is essential for studying how parameters affect its contact stress and building the contact stress limit state equation for contact stress reliability analysis.In this study,a mathematical relationship between design parameters and contact stress is formulated using the KrigingMetamodel.To enhance the model’s accuracy,we propose a new hybrid algorithm that merges the genetic algorithm with the Quantum Particle Swarm optimization algorithm,leveraging the strengths of each.Additionally,the“parental inheritance+self-learning”optimization model is used to fine-tune the KrigingMetamodel’s parameters.Following this,amathematicalmodel for calculating the contact stress of Variable Hyperbolic Circular-Arc-Tooth-Trace(VH-CATT)gears using the optimized Kriging model was developed.We then examined how different gear parameters affect the VH-CATT gears’contact stress.Our simulation results show:(1)Improvements in R2,RMSE,and RMAE.R2 rose from0.9852 to 0.9974(a 1.22%increase),nearing 1,suggesting the optimized Kriging Metamodel’s global error is minimized.Meanwhile,RMSE dropped from3.9210 to 1.6492,a decline of 57.94%.The global error of the GA-IQPSO-Kriging algorithm was also reduced,with RMAE decreasing by 58.69%from 0.1823 to 0.0753,showing the algorithm’s enhanced precision.In a comparison of ten experimental groups selected randomly,the GA-IQPSO-Kriging and FEM-based contact analysis methods were used to measure contact stress.Results revealed a maximum error of 12.11667 MPA,which represents 2.85%of the real value.(2)Several factors,including the pressure angle,tooth width,modulus,and tooth line radius,are inversely related to contact stress.The descending order of their impact on the contact stress is:tooth line radius>modulus>pressure angle>tooth width.(3)Complex interactions are noted among various parameters.Specifically,when the tooth line radius interacts with parameters such as pressure angle,tooth width,and modulus,the resulting stress contour is nonlinear,showcasing amultifaceted contour plane.However,when tooth width,modulus,and pressure angle interact,the stress contour is nearly linear,and the contour plane is simpler,indicating a weaker coupling among these factors.

Stability Analysis of Nonlinear Models of Nose Landing Gear Shimmy

Shimmy can reduce the service life of the nose landing gear, affect ride comfort, and even cause fuselage damage leading to aircraft crashes. Taking a light aircraft as the research object, the torsional freedom of landing gear around strut axis and lateral deformation of tire are considered. Since the landing gear shimmy is a nonlinear system, a nonlinear mechanical model of the front landing gear shimmy is established. Sobol index method is proposed to analyze the influence of structural parameters on the stability region of the nose landing gear, and Routh-Huritz criterion is used to verify the reliability of the analysis results of Sobol index method. We analyse the effect of torsional stiffness of strut, caster length, rated initial tire inflation pressure, rake angle, and vertical force on the stability region of theront landing gear. And the research shows that the optimization of the torsional stiffness of the strut and the caster length of the nose landing gear should be emphasized, and the influence of vertical force on the stability region of the nose landing gear should be paid attention to.

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.

Research on Three-Dimensional Simulation of the Internal Arc Gear Skiving

Aiming at the problems that the simulation accuracy which is reduced due to the simplification of the model,a three-dimensional simulation method based on solid modeling is being proposed.By analyzing the motion relationship and positional relationship between the caries knife and the workpiece,the coordinate system of the caries machining was established.With the MATLAB software,the cutting edge model and the blade sweeping surface model of the boring cutter are sequentially established.Boolean operation is performed on the blade swept surface formed by the tooth cutter teeth with time t and the workpiece tooth geometry as well as the undeformed three-dimensional chip geometry model and the instantaneous cogging geometry model are obtained at different times.Through the compare between gear end face simulation tooth profile and the theoretical inner arc tooth profile,we verified the accuracy and rationality of the proposed method.

Time-Varying Mesh Stiffness Calculation and Dynamic Modeling of Spiral Bevel Gear with Spalling Defects

Time-varying mesh stiffness(TVMS)is a vital internal excitation source for the spiral bevel gear(SBG)transmission system.Spalling defect often causes decrease in gear mesh stiffness and changes the dynamic characteristics of the gear system,which further increases noise and vibration.This paper aims to calculate the TVMS and establish dynamic model of SBG with spalling defect.In this study,a novel analytical model based on slice method is proposed to calculate the TVMS of SBG considering spalling defect.Subsequently,the influence of spalling defect on the TVMS is studied through a numerical simulation,and the proposed analytical model is verified by a finite element model.Besides,an 8-degrees-of-freedom dynamic model is established for SBG transmission system.Incorporating the spalling defect into TVMS,the dynamic responses of spalled SBG are analyzed.The numerical results indicate that spalling defect would cause periodic impact in time domain.Finally,an experiment is designed to verify the proposed dynamic model.The experimental results show that the spalling defect makes the response characterized by periodic impact with the rotating frequency of spalled pinion.

基于UG的拖拉机齿轮传动系统仿真研究

设计了一款拖拉机复合行星齿轮的动力系统,并基于UG仿真软件,建立了齿轮参数化模型,得到了齿轮的渐开线和齿廓线,最后建立了齿轮传动系统仿真模型。齿轮传动系统可靠性实验表明:系统齿轮运动符合预期,满足设计要求,证实了系统的可靠性。

Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

通向未来的护照——美国加州圣荷塞“Gear up工程”述评

由加利福尼亚圣荷塞州立大学牵头设计实施的"通向未来的护照"项目,是美国教育部Gear up教育创新工程的一个有代表性的地方规划实施模式。本文对工程的立项背景、目标内容、运作过程和结果影响等方面进行了完整的个案研究,为我们系统地了解和借鉴整个Gear up工程的合作伙伴运作模式提供了一个比较完整的模本。

基于Gear算法的无线传感器网络路由协议研究

无线传感器网络路由协议设计与传统的无线ad hoc网络有很多不同.介绍了无线传感器网络的体系结构,分析了几种典型的路由协议,对基于位置的Gear算法路由协议进行了研究,为未来无线物联网络的建设提供了参考.

一种解决GEAR路由空洞问题的新方案

无线传感器网络中的GEAR路由协议在解决路由空洞问题时,会出现短暂路由环现象,使分组转发跳数增大,浪费更多的网络能量。基于反馈避免的思想提出一种改进的GEAR路由算法,当转发节点发现自身为空洞节点时,便向其邻节点广播hole信息,在分组转发时,邻节点将该节点标记为空洞节点,转发节点修改自身的综合代价,从而绕开该空洞节点,有效地解决短暂路由环问题。仿真结果表明:改进的路由算法能减少分组转发跳数,节省网络能量,克服了GEAR路由协议的弊端。

GEAR算法在随机轨道模型计算中的应用

本文对随机轨道模型中颗粒相常微分方程组的刚性问题进行了分析，结果表明：当采用常规算法如四阶Runge－kutta法求解方程组时，方程组的刚性是导致某些情况下计算发散或计算时间过长的原因。为此，本文将适用于求解刚性方程组的Gear算法应用于随机轨道模型的计算中，取得了良好的效果．

用Gear法求解病态的引信球转子运动常微分方程组

应用欧拉角及欧拉动力学方程、欧拉运动学方程所建立的描述引信球转子转正运动的数学模型,为强非线性的病态常微分方程组。为了准确、高效地分析球转子的运动过程,以某火炮引信球转子为例,针对不同参量和积分精度,对比地应用了Gear方法和Runge-Kutta方法,对该方程组进行了数值模拟。Gear方法比Runge-Kutta方法易于获得准确解,并且耗用机时也短。

TEST AND CONTROL SYSTEM DEVELOPMENT AND APPLICATION OF LANDING GEAR DROP TEST RIG

A control and test system of a landing gear drop test rig is developed considering the drop test specifica- tions for the ＂Seagull 300＂ multi-functional amphibious airplane. In order to realize the automation of drop test process, a servo system is proposed and programmable logic controller（PLC） technology is used. Several key technologies for measuring the horizontal load, the vertical load and the transient rotational speed are studied. According to the requirements of CCAR-23-R3, the drop test of landing gears of the ＂Seagull 300＂ airplane is accomplished. Test results show that the system has a high accuracy of data collection. The system is stable and reliable. The drop test satisfies the requirements of the drop test specifications and the results can be used as the certification of airworthiness for this kind of airplane.

基于模糊区域宽松距离的改进GEAR传感网络均衡算法

传感节点的有效选择对无线传感网络通信有着重要影响。在分析传统的GEAR传感节点分配算法基础上,提出基于模糊区域宽松距离的改进GEAR传感网络均衡算法。运用一种基于节点模糊区间划分,伴随节点运用一种宽松距离的方法进行逼近,依靠得到的模糊节点可靠性隶属度函数,完成对节点的最终选择,从而避免传统GEAR节点分配算法中单纯依靠地理位置与能量开销等先验知识进行节点选择的弊端。实验验证该方法的通信能量消耗曲线趋势要低于传统GEAR算法,能有效调节传感网络的拥塞。

GEOMETRIC MODELING OF GENERATING-MANUFACTURED SPIRAL BEVEL GEARS BASED ON CUTTING SIMULATION

A geometric modeling method for generating-manufactured spiral bevel gears（SBGs） is proposed. It consists of two steps： （1） creating a reference model by simulating the process of cutting spiral bevel gear,（2） reconstructing the final solid model by collecting data points from the reference model and fitting these points into NURBS surfaces. In this method,cutting simulation avoids abstruse mathematical theories and complex methods,thus making it convenient to obtain data points on the complex tooth surface before the gear is manufactured and efficient to increase the accuracy of the solid model. Also,the representations of tooth surfaces of the final model is unified as a NURBS surface function. The NURBS surface is continuous and smooth,thus it is available for wide applications in CAD/CAE. The experiment proves that the method can be used to establish an accurate pair of SBG models,thus providing a feasible and effective way for CAD/CAE modeling.

基于Gear算法的一个符号化仿真系统设计原理

控制系统仿真是研究控制系统不可缺少的技术手段 ,其核心问题是求微分方程组与代数方程组的联立数值解 ,即求数值积分。微分方程组的数值解法很多 ,其中Gear算法最适合控制系统仿真 ,它稳定性好 ,是一种变阶变步长的预报校正型的多步方法。基于Gear算法设计了面向框图、微分方程、状态方程对象的仿真程序 ,其输入设计为符号化的参数输入方式 ,并给出了应用实例。

Application of High-speed Solenoid Valve to the Semi-active Control of Landing Gear

To select or develop an appropriate actuator is one of the key and difficult issues in the study of semi-active controlled landing gear. Performance of the actuator may directly affect the effectiveness of semi-active control. In this article, parallel high-speed solenoid valves are chosen to be the actuators for the semi-active controlled landing gear and being studied. A nonlinear high-speed solenoid valve model is developed with the consideration of magnetic saturation characteristics and verified by test. According to the design rule of keeping the peak load as small as possible while absorbing the specified shock energy, a fuzzy PD control rule is designed. By the rule controller parameters can be self-regulated. The simulation results indicate that the semi-active control based on high-speed solenoid valve can effectively improve the control performance and reduce impact load during landing.