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.

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.

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.

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.

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.

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.

Valuable Impulses and Successful Models of Gearbox Development from Practice

Gears play an important role in mechanical engineering because of their moment and speed transmission possibilities. Design and optimization of a complete gearbox provide many requirements to the designer. The complex gearbox model consists of many machine elements （shafts, gears, bearings, housing, seals, and shaft-hub connections）. The gearbox must be understood as a system with interactive parts. Next to the calculation of kinematics, load capacities and life times of single elements, aspects of load distribution and efficiency and noise excitation of gearboxes become important. The wide range of knowhow needed mostly cannot be covered by a small number of engineers. The development of automated calculation routines with understandable and comprehensive results is the goal for these research projects that lead to sottware-realizing solutions for engineers to efficiently design, calculate, optimize and verify gearboxes with minimal resources in terms of calculation experts and time.

Effects of Comprehensive Eccentricity of Involute Cam on Gear Profile Deviations

The manufacturing accuracy of ultra-precision master gears signifies the technological capability of the ultra-precision gear.Currently,there is little report about the manufacturing technologies of ultra-precision master gears at home and aboard.In order to meet the requirement of grinding ultra precision master gear,the gear grinder with flat-faced wheel Y7125 is chosen as the object machine tool and the geometric model of its precision generating part,the involute cam,is established.According to the structure of the involute cam,the effective working section and its adjustable range of the cam are determined,and the mathematical expressions of the effects of comprehensive eccentricity of the involute cam on gear profile deviations are derived.According to the primary harmonic trends of the deviation curve,it is shown that gear profile form and slope deviations in different work generating sections of the involute cam are different which the latter changes with the cam eccentricity obviously.Then,the issues of extreme values and methods of error compensation are studied and the conclusion that large adjustable range is benefit to search the optimal involute-cam section which is responding to the minimum gear profile deviations is obtained.A group of examples are calculated by choosing master gears with d=120 mm and m=2-6 mm and an involute cam with base diameter djcam =117 mm.And it is found that the maximum gear profile deviation counts for no more than 5% of the cam eccentricity after error compensation.A gear-grinding experiment on the master gear with m=2 mm is conducted by choosing different sections of the involute cam and the differences of gear profile deviations then the existence of the cam eccentricity are verified.The research discloses the rule of gear profile deviations caused by the comprehensive eccentricity of the involute cam and provides the theoretical guidance and the processing methods for grinding profile of the ultra precision master gear.

COMMON DEFINITION FOR END-SURFACE CONTACT RATIO OF GEARS AND ITS APPLICATIONS

Common definition and calculating expressions of end-surface contact ratiofor all type of gears are put forward, and with calculation expressions for involute gears,micro-segments profile gears, and sine-curved profile gears being discussed. The end-surface contactratio of gears is defined as the ratio of the action angle (the rotation angle of gear from gear-into gear-out for one pair of teeth) to the rotation angle per pitch (or central angle per tooth).According to the theory of gearing, equation of the meshing line can be deduced from the toothprofiles of basic rack. Having obtained the equation of the meshing line, and being given theaddendum outline of the gears, the contact ratio can be calculated with the calculation expressions.For the involute gears, this definition has same effect as the well-known definition: ratio of thecontact line to the base pitch. This definition of contact ratio is also suitable to othernon-involute gears, such as micro-segments profile gears, sine-curved profile gears, and can givemore reliable results.

Multi-objective Optimization of a Two-Stage Helical Gearbox to Improve Efficiency and Reduce Height

The goal of this research is to look at multi-target optimization of a two-stage helical gearbox in order to determine the best key design elements for reducing gearbox height and enhancing gearbox efficiency.To do this,the method known as Taguchi and GRA(Grey Relation Analysis)were used in two stages to address the problem.The single-objective optimization problem was addressed first to close the gap between variable levels,and then the multi-objective optimization problem was solved to determine the best primary design variables.The first and second stage CWFWs(Coefficients of Wheel Face Width),ACS(Permissible Contact Stresses),and first stage gear ratio were also calculated.The study’s findings were utilized to identify the best values for five critical design aspects of a two-stage helical gearbox.

Dual cycloid gear mechanism for automobile safety pretensioners

The most conventional vehicle pretensioner system consists of an internal gear pair with involute teeth. However, it has been well known that the corresponding gear pairs are relatively weak under the situation of impact loadings. To improve this phenomenon, a new pretensioning gear system with cycloid teeth rather than the involute ones was proposed, and dual cycloidal gear mechanisms were designed for satisfying geometric constraints and dynamic loading conditions. The simulations of the prototypes were conducted by LS-DYNA program and the experiments for a prototype were performed for a dynamic model with impact loading devices. The results show that the better operation and the smoother motion are confirmed in the proposed cycloidal gear system rather than the conventional one without interferences between gear teeth under the impact of a crash.

无线传感器网络中的安全GEAR路由协议

GEAR路由是无线传感器网络中一种高效的位置和能量感知的地理路由协议,在抵御路由攻击方面有较好的特性,但是GEAR路由不能抵御虚假路由、女巫、选择性转发等攻击。针对该问题,提出了一种适合无线传感器网络特征的、基于位置密钥对引导模型的安全GEAR路由协议SGEAR,并对该协议进行了性能分析,分析显示在较小的系统开销下,SGEAR能有效抑制上述攻击及DoS攻击。

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。

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。

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。