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.

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.

Loaded multi-tooth contact analysis and calculation for contact stress of face-gear drive with spur involute pinion

The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur involute pinion were introduced, and their relative errors are below 10%, except edge contact, which turns out that these two methods can compute contact stress of face-gear drive correctly and effectively. An agreement of the localized bearing contact stress is gotten for these two methods, making sure that the calculation results of FEM are reliable. The loaded meshing simulations of multi-tooth FEM model were developed, and the determination of the transmission error and the maximal load distribution factor of face-gear drive under torques were given. A formula for the maximal load distribution factor was proposed. By introducing the maximal load distribution factor in multi-tooth contact zone, a method for calculating the maximal contact stress in multi-tooth contact can be given. Compared to FEM, the results of these formulae are proved to be reliable, and the relative errors are below 10%.

A parametric study on the contact stress of half toroidal continuously variable transmission

The most general contact in mechanical transmission is the elliptical one. In particular, a toroidal continuously variable transmission (CVT) has an elliptical shape in the contact area under the elastohydrodynamic lubrication regime, where the shearing of the fluid subjects to high contact stress and transmits the power. Many parameters affect the contact service performance of the half toroidal CVT, which include the properties of the contacting material (Young抯 modulus), operating parameters (input torque and maximum traction coefficient) and geometrical parameters (aspect cavity ratio, curvature ratio and half cone angle of the power roller). In this paper, the contacts between the input disk, the power roller and the output disk are formulated using the classical Hertzian contact theory. Based on the formulated equations, different system parameters, which affect the maximum Hertzian stresses, are compared. The comparative results will provide some observations of the relations between the maximum Hertzian stresses and transmission ratios in the form of graphs. These graphs give useful information for designer to know the maximum Hertzian stress during operation in such systems.

Contact Stress Distribution of a Pear Cam Profile with Roller Follower Mechanism

The problem of this paper is the high contact stress at the point of contact between the cam and the follower.A pear cam and roller follower mechanism were studied and analyzed for different position of the follower and different contact compression load.The objective of this paper is to study the effect of contact compression load on the contact stress distribution of the cam profile at the point of contact.Four different positions of the follower with the cam was considered(0°,90°,180°,and 270°).The theory of circular plate was applied to derive the analytic solution of the contact stress.The numerical simulation had been done using ANSYS Ver.19.2 package to determine the contact stress,while SolidWorks software was used to investigate follower displacement,velocity,and acceleration.Four distinct values of the compression contact load,such as 3.121 N,6.242 N,9.364 N,and 12.485 N,were used in the numerical simulation.In the experiment setup,a photo-elastic technique was carried out in the field of polarized light to exhibit the stress distribution on the cam specimen.The annealed PSM-4 backalate material was used in the experiment setup.The experimental value of contact stress was checked and verified analytically and numerically at the point of contact.The innovation in this paper the use of spring-damper system which reduce the value of contact stress at the point of contact.The contact stress was maximum 2.136 MPa when the follower located at 270°with the cam,while the contact stress was minimum 1.802 MPa when the follower located at 180°at compression load 12.485 N.

CALCULATION OF CONTACT STRESS OF PLASTIC GEARS

A calculation method of contact problem of plastic gears based on three parameter model of viscoelasticity material is presented. In this calculation method, the influence of temperature upon the property of plastics is considered and an iteration process of temperature-elasticity module-friction coefficient is proposed. From the rolling contact problem of two viscoelastic cylinders with parallel axis, a set of normal-tangential contact coupled integral equations is obtained. Through numerical treatment and normal-tangential iteration, the normal contact stress,tangential stress and contact width of plastic gears are acquired.

Effect of flank angle and friction coefficient on contact stress of turbine rotor

In order to simulate the stress of turbine rotor in aeroengine, based on the ANSYS, the simplification model of the turbine rotor was built up. By applying the simplification model, the contact stress of turbine rotor was computed. The maximum contact stress appears at the chamfer below the flank, which agrees with experiment result. At the same time, the contact stress changing with the flank angle and friction coefficient was calculated, The results show that the contact stress in the flank increases slowly with the increase of flank angle; with the friction coefficient increasing, the contact stress in flank length decreases; the contact stress will not change when the friction coefficient is over 0.25.

Hybrid Method to Analyze Contact Stress Distribution on Dry Friction Interfaces

A hybrid method is established by combining photoelastic experiment and finite element analysis.The method is used to evaluate contact stress distribution on dry friction interfaces,such as the contact interfaces between shrouds of fan blades and turbine blades.The photoelastic stress frozen experiment method is used to decide the displacement boundary conditions of numerical calculation.Higher accuracy and efficiency of solving problems are improved by the method.Technical difficulty and high cost of experiment are also avoided by the method.Good agreement of the stress distribution by using the hybrid method and experiment is obtained.

A MIXED METHOD OF SOLUTION FOR CONTACT STRESSES ON ROLLER

A mixed method of solution for contact stresses on rollers was suggested by the combina- tion of similitude principle.photoelastic method,Hertz's contact theory and numerical calculation.Thus,not only the distribution regularity of axial contact pressure on roller of limited length,but also the three-dimensional solution of stresses in the contact po- sitions may be obtained.An actual example is presented in the paper.It shows that the practical damaged phenomenon in real roller is in agreement with the result of the analysis

CONTACT FRICTION ANALYSIS AND STRESS OSCILLATION SUPPRESSION WITH A SIMPLE INTERFACE ELEMENT

A simple interface element for analyzing contact friction problems is developed. Taking nodal displacements and contact stresses as unknowns, this element can simulate frictional slippage, decoupling and re-bonding of two bodies initially mating or having gaps at a common interface. The method is based on the Finite Element Method and load incremental theory. The geometric and static constraint conditions on contact surfaces are treated as additional conditions and are included in stiffness equations. This simple element has the advantages of easy implementation into standard finite element programs and fast speed for convergence as well as high accuracy for stress distribution in interface. Undesirable stress oscillations are also investigated whenever large stress gradients exist over the contact surfaces. Exact integration or the conventional Gauss integration scheme used to evaluate the interpolation function matrix of the interface element is found to be the source of the oscillations. Eigenmode analysis demonstrates that the stress behavior of an interface element can be improved by using the Newton-Cotes integration scheme. Finally, the test example of a strip footing problem is presented.

Calculating method of contact stress for non-circular gears

According to Hertz theory, the difference of contact stress for non-circular gears and equivalent gears is compared in the paper, a calculating method of contact stress for non-circular gears by using equivalent gears is researched, and computing formulas of power and rotation speed for equivalent gears are deduced. A numerical simulation of contact stress for non-circular gears has also been conducted based on the finite element method. By the comparison of fitting curves, the feasibility of using equivalent gears instead of non-circular gears to calculate the contact stress is testified.

A Spring-Layer Model for a Bi-Layered Plate-Strip with Initial Stress Through Imperfect Contact Interface

In this paper,we present our report on the forced vibration of a bi-layered plate-strip with initial stress resting on a rigid foundation induced by a time-harmonic force.The investigation is carried out according to the piecewise homogeneous body model with utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies(TLTEWISB).The materials of the body are chosen to be linearly elastic,homogeneous,and isotropic.The interface between the layers is assumed to be imperfect,and is simulated by the spring-layer model.A similar degree of imperfection on the interface is realized in the normal and tangential directions.The mathematical model for the problem under consideration is designed,and the system of the equations of motion is approximately solved by employing the finite element method(FEM).The numerical results explaining the influence of the parameter that characterizes the degree of corresponding imperfectness on the dynamic response of the plate-strip are presented.In particular,we demonstrate that the distributions of the normal stress become flat,as the normal-spring parameter increases.

Effect of crack face contact on dynamic stress intensity factors for a hole-edge crack

In order to determine the dynamic stress intensity factors(DSIFs)for a single edge crack at the center hole of a finite plate under a compressive step loading parallel to the crack,the finite element method was employed to solve the cracked plate problem.The square-root stress singularity around the crack tip was simulated by quarter point singular elements collapsed by 8-node two-dimensional isoparametric elements.The DSIFs with and without considering crack face contact situations were evaluated by using the displacement correlation technique,and the influence of contact interaction between crack surfaces on DSIFs was investigated.The numerical results show that if the contact interaction between crack surfaces is ignored,the negative mode I DSIFs may be obtained and a physically impossible interpenetration or overlap of the crack surfaces will occur.Thus the crack face contact has a significant influence on the mode I DSIFs.

STUDY ON LOADS AND CONTACT STRESSES FOR TOROIDAL DRIVE

The load distribution and calculating formulae of the contact stresses in the rotor worm and stator helical surface for toroidal drive are given. The effecting factors on contact stresses and their effects are analyzed. The results is useful for reference purposes in manufacture and design of the drive.

Modifications in the Stress Field of a Long Inclined Fault Caused by the Welded-Contact Boundary Conditions across the Interface between Two Elastic Half-Spaces

In welded-contact boundary conditions, some stress components are not required to be continuous across the boundary between two elastic half-spaces. The purpose of this note is to study the modifications in the stress field of a long inclined strike-slip, dip-slip or tensile fault caused by the welded-contact boundary conditions across the interface between two elastic half-spaces. The Poisson’s ratios of the two half-spaces do not appear in the stress field of a strike-slip fault. In the case of a dip-slip fault, the Poisson’s ratio of the half-space in which the fault lies, has a significant influence on the stress field across the interface. However, for a tensile fault, the modification in the stress field is significantly affected by the Poisson’s ratios of both the half-spaces.

The Influence of the Supporting Wheel Deflection of Large-scale Rotary Kiln on Maximum Contact Stress

The relation between the maximum contact stress ratio and deflection angle is derived from Hertz contact theory when the deflection of rotary kiln supporting wheel happens. According to the analysis of practical example, the maximum contact stress ratio within the deflection range of rotary kiln supporting wheel is listed. The contact stress will increase largely when rotary kiln supporting wheel deflects with little angle, which probably will result in accidents correlating to safety. This will provide theory conference for the design, the operating condition analysis and adjusting of the rotary kiln.

Numerical Computation of Stress Intensity Factors for Bolt-hole Corner Crack in Mechanical Joints

The three-dimensional finite element method is used to solve the problem of the quarter-elliptical comer crack of the bolt-hole in mechanical joints being subjected to remote tension. The square-root stress singularity around the corner crack front is simulated using the collapsed 20-node quarter point singular elements. The contact interaction between the bolt and the hole boundary is considered in the finite element analysis. The stress intensity factors （SIFs） along the crack front are evaluated by using the displacement correlation technique. The effects of the amount of clearance between the hole and the bolt on the SIFs are investigated. The numerical results indicate that the SIF for mode I decrease with the decreases in clearance, and in the cases of clearance being present, the corner crack is in a mix-mode, even if mode I loading is dominant.

Contact Problem in Decagonal Two-Dimensional Quasicrystal

As a new structure of solid matter quasicrystal brings profound new ideas to the traditional condensed matter physics, its elastic equations are more complicated than that of traditional crystal. A contact problem of decagonal two? dimensional quasicrystal material under the action of a rigid flat die is solved satisfactorily by introducing displacement function and using Fourier analysis and dual integral equations theory, and the analytical expressions of stress and displacement fields of the contact problem are achieved. The results show that if the contact displacement is a constant in the contact zone, the vertical contact stress has order -1/2 singularity on the edge of contact zone, which provides the important mechanics parameter for contact deformation of the quasicrystal.

沟曲率半径(密合度)对四点接触球轴承疲劳寿命影响研究

采用Romax Designer工程分析软件,应用ISO/TS 16281—2008寿命计算方法,根据经典的滚动轴承理论,对某电机轴四点接触球轴承内部载荷分布、接触应力、套圈滚道等效动态滚动元件载荷和ISO/TS16281—2008寿命等进行了大量的计算,重点研究滚道沟曲率半径对轴承内部载荷分布、接触应力、套圈滚道等效动态滚动元件载荷和ISO/TS16281—2008疲劳寿命的影响。研究结果表明,轴承型号和制造质量、载荷条件、润滑条件和可靠度等其他条件确定时,存在一个相对最优的滚道沟曲率半径(密合度);当载荷条件不同时,相应最优的滚道沟曲率半径(密合度)不同。在所研究的具体条件下,由于轴系中的2个轴承所承受的载荷不同,因而,2个轴承的最优滚道沟曲率半径(密合度)不同。研究结果可为四点接触球轴承的设计方案提供参考。

下颌All-on-4种植固定义齿不同咬合接触应力分布的有限元分析

背景:All-on-4种植固定义齿的长期修复效果与生物力学问题密切相关,其中咬合设计影响修复体各部位的应力分布,然而,国内外目前有关All-on-4种植固定义齿的生物力学研究较少且无定论。目的:分析不同咬合接触对下颌All-on-4种植固定义齿应力分布的影响。方法:建立下颌All-on-4种植固定义齿的模型,通过改变加载力的大小、方向和加载部位,设置了10种加载工况,模拟正中咬合、侧方咬合和前伸咬合,通过在不同牙位上加载模拟不同的咬合接触类型,分析比较各组模型不同加载工况中模型各部分的应力分布和最大应力值。结果与结论:①各组模型的应力分布云图基本相似,种植体应力主要集中在种植体颈部,周围骨组织的应力主要集中在种植体颈部周围,并且皮质骨的应力明显高于松质骨;基台的应力主要集中在基台与种植体和基台与上部修复体连接的部位,上部修复体中钛支架的应力主要集中在基台与钛支架连接部位,上部修复体中树脂面的应力主要集中在各加载点上;②模拟正中咬合中,末端悬臂不加载时种植体的最大Von-Mises应力值明显增大,说明下颌All-on-4种植固定义齿在正中咬合时末端悬臂区可有咬合接触;③模拟侧方咬合中,在模拟尖牙保护[牙合]工况中模型各部分的最大Von-Mises应力值明显增大;模拟平衡[牙合]工况中模型各部分的最大Von-Mises应力值较组牙功能[牙合]工况略低,说明下颌All-on-4种植固定修复在完成骨整合永久修复时,为了提高咀嚼效率,可选择组牙功能[牙合],种植术后即刻修复时可选择平衡[牙合];④模拟前伸咬合中,只在前牙区加载时模型各部分的最大Von-Mises应力值明显增大;模拟平衡[牙合]工况中,后牙区加载点在悬臂区和在悬壁区前方时模型各部分的最大Von-Mises应力值较小,说明下颌All-on-4种植固定修复义齿前伸运动的咬合接触可选择前伸平衡[牙合]。