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.

Measured dynamic load distribution within the in situ axlebox bearing of high-speed trains under polygonal wheel–rail excitation

The dynamic load distribution within in-service axlebox bearings of high-speed trains is crucial for the fatigue reliability assessment and forward design of axlebox bearings. This paper presents an in situ measurement of the dynamic load distribution in the four rows of two axlebox bearings on a bogie wheelset of a high-speed train under polygonal wheel–rail excitation. The measurement employed an improved strain-based method to measure the dynamic radial load distribution of roller bearings. The four rows of two axlebox bearings on a wheelset exhibited different ranges of loaded zones and different means of distributed loads. Besides, the mean value and standard deviation of measured roller–raceway contact loads showed non-monotonic variations with the frequency of wheel–rail excitation. The fatigue life of the four bearing rows under polygonal wheel–rail excitation was quantitatively predicted by compiling the measured roller–raceway contact load spectra of the most loaded position and considering the load spectra as input.

Research on the Influence of Raceway Waviness on the Vibration Characteristics of Deep Groove Ball Bearings

The dynamics model of a 2-degree-of-freedom deep groove ball bearing is established by incorporating the raceway surface waviness model comprising multiple sinusoidal functions superposition.The model is solved using the fourth-order Runge-Kutta method to obtain the vibration characteristics including displacement,velocity,acceleration,and frequency of the bearing.Validation of the model is accomplished through comparison with theoretical vibration frequencies.The influence of the amplitude of waviness of the inner and outer ring raceway surfaces of deep groove ball bearings on the vibration displacement,peak-to-peak vibration displacement and root-mean-square vibration acceleration is analyzed,and the results show that as the amplitude of the inner and outer ring raceway surfaces waviness increases,all the vibration characteristic indexes increase,indicating that the vibration amplitude of the bearings as well as the energy of the waviness-induced shock waveforms increase with the increase of the amplitude of the waviness.

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.

Vibration-based bearing fault diagnosis of high-speed trains:A literature review

Due to the advantages of comfort and safety,high-speed trains are gradually becoming the mainstream public transport in China.Since the operating speed and mileage of high-speed trains have achieved rapid growth,it is more and more urgent to ensure their reliability and safety.As an important component in the bogies of highspeed trains,the health state of the bearing directly affects the operational safety of the trains.It is therefore necessary to diagnoze the faults of bearings in the bogies of high-speed trains as early as possible.In this paper,the bearing fault diagnostic methods for high-speed trains have been systematically summarized with their challenges and perspectives.First,it briefly introduces the structure of bearings in the bogies as well as the fault characteristic frequencies.Then,a brief review of the research on vibration-based signal processing methods and machine learning methods has been provided.Finally,the challenges and future developments of vibrationbased bearing fault diagnostic methods for high-speed trains have been analyzed.

Dynamic Stability Analysis of Cages in High-Speed Oil-Lubricated Angular Contact Ball Bearings

To investigate the cage stability of high-speed oil-lubricated angular contact ball bearings, a dynamic model of cages is developed on the basis of Gupta’s and Meeks’ work. The model can simulate the cage motion under oil lubrication with all six degrees of freedom. Particularly, the model introduces oil-film damping and hysteresis damping, and deals with the collision contact as imperfect elastic contact. In addition, the effects of inner ring rotational speed, the ratio of pocket clearance to guiding clearance and applied load on the cage stability are investigated by simulating the cage motion with the model. The results can provide a theoretical basis for the design of ball bearing parameters.

Dynamic Analysis of Flexible Cage of High-speed Angular Contact Ball Bearing

A dynamics formula was established for the flexible cage of high-speed angular contact ball bearing. A modified Craig-Bampton component mode synthetic method was used to establish the formula with regard to the flexibility of cage and based on a dynamic analysis of angular contact ball bearing,and a rigid-flexible multi-body dynamic analysis program was developed using ADAMS,which is verified by a computation example of Gupta. The results show that it's not likely to keep the rotation smoothness of cage when the ratio of pocket clearance to guiding clearance and the ratio of radial load to axial load become too large or too small. By comparison,the flexible cage runs more smoothly than the rigid cage.

Model of Rotation Accuracy of High-Speed Spindles on Ball Bearings

For the purpose to improve a design quality of high-speed spindle units, we have developed mathematical models and software to simulate a rotation accuracy of spindles running on ball bearings. In order to better understand the mechanics of ball bearings, the dynamic interaction of ball bearings and spindle unit, and the influence of the bearing imperfections on the spindle rotation accuracy, we have carried out computer aided analysis and experimental studies. When doing this, we have found that the spindle rotation accuracy can vary drastically with rotational speed. The influence of bearing preload has a secondary importance. Comparison of the results of these studies has demonstrated adequacy of the models developed to the real spindle units.

Establishment of Dynamic Model for Axle Box Bearing of High-Speed Trains Under Variable Speed Conditions

In this study,a dynamic model for the bearing rotor system of a high-speed train under variable speed conditions is established.In contrast to previous studies,the contact stress is simplifed in the proposed model and the compensation balance excitation caused by the rotor mass eccentricity considered.The angle iteration method is used to overcome the challenge posed by the inability to determine the roller space position during bearing rotation.The simulation results show that the model accurately describes the dynamics of bearings under varying speed profles that contain acceleration,deceleration,and speed oscillation stages.The order ratio spectrum of the bearing vibration signal indicates that both the single and multiple frequencies in the simulation results are consistent with the theoretical results.Experiments on bearings with outer and inner ring faults under various operating conditions are performed to verify the developed model.

Analysis of the Temperature Characteristics of High-speed Train Bearings Based on a Dynamics Model and Thermal Network Method

High-speed trains often use temperature sensors to monitor the motion state of bearings.However,the temperature of bearings can be affected by factors such as weather and faults.Therefore,it is necessary to analyze in detail the relationship between the bearing temperature and influencing factors.In this study,a dynamics model of the axle box bearing of high-speed trains is established.The model can obtain the contact force between the rollers and raceway and its change law when the bearing contains outer-ring,inner-ring,and rolling-element faults.Based on the model,a thermal network method is introduced to study the temperature field distribution of the axle box bearings of high-speed trains.In this model,the heat generation,conduction,and dispersion of the isothermal nodes can be solved.The results show that the temperature of the contact point between the outer-ring raceway and rolling-elements is the highest.The relationships between the node temperature and the speed,fault type,and fault size are analyzed,finding that the higher the speed,the higher the node temperature.Under different fault types,the node temperature first increases and then decreases as the fault size increases.The effectiveness of the model is demonstrated using the actual temperature data of a high-speed train.This study proposes a thermal network model that can predict the temperature of each component of the bearings on a high-speed train under various speed and fault conditions.

Simulation Analysis Module of High-speed Rail Bearings Based on Secondary Development in ADAMS

This paper develops a strong secondary development based on ADAMS feature which creates high-speed rail bearings for simulation analysis module. This thesis is in the case of non-circular pattern instructions of how to achieve rapid roller modeling, with analysis of functions and parameters required for the design of the simulation module of the high-speed rail bearing, as well as the design of dialog boxes, the environment and file structure. The specific modules is based on the secondary development language provided by ADAMS ! View. Through the menus, dialog boxes which input parameters, it can achieve high iron bearing automatic modeling, dynamic analysis and post-processing to simplify the analysis of high-speed rail bearing operations, as well as improving the high-speed rail bearing development efficiency.

Analysis of dynamic characteristics of self-aligning ball bearing

A dynamics model of the self-aligning ball bearing is proposed based on the Jones-Harris method （JHM）, and a computer program is developed to solve the equations by using the Newton-Raphson method. A parametric analysis of the centrifugal force and the gyroscopic moment, the contact loads, the contact angles, the radial deformation and the radial stiffness is carried out. The analytical results show that the applied loads and the rotational speed are two main factors that can influence the distributions of the contact loads and values of the contact angles. The centrifugal force and the gyroscopic moment increase with the increase in the rotational speed, resulting in the decrease of the inner raceway contact load and the increase of the outer raceway contact load. The outer raceway contact angle increases under the centrifugal force; on the contrary, the inner raceway contact angle decreases. Furthermore, the differences between the inner and the outer contact angles increase with the increase in the rotational speed. The higher rotational speed results in the decrease in radial stiffness for the self-aligning ball bearing, and the raceway curvature coefficient, to some extent, also influences the radial stiffness.

Quasi-static Analysis of Thrust-loaded Angular Contact Ball Bearings Part Ⅰ:Theoretical Formulation

Ball bearings play an important role in various rotating machineries,but the complicated kinematic and tribological features of ball bearings make many aspects of their operating behaviors still inconclusive.Most theoretical analyses of ball bearings up to date are based on either the hypothesis of race control or other empirical models to determine the ball motion of ball bearings,but none of these strategies can reveal and consequently employ the intrinsic coupling mechanism between the spin and the tangential traction of contacting bodies rolling upon one another.To remedy the deficiency of current analytical models for ball bearing analysis,the rolling contact theory is employed to establish an explicit link between motions and interactions within ball bearings.A differential slip model is established to precisely define the slip component due to the significant curvature of the common contact patches between the ball and inner/outer raceways.The creepage and the spin ratio are formulated to accurately define the relative rigid motion between the ball and the inner/outer raceway.Then a quasi-static analytical model is established that can accurately determine the motions of the balls and races of the ball bearing.It can also give a vivid description of the slip and traction distributions within the contact area.The analytical model can be effectively used to analyze the operational conditions and tribological features of solid-lubricated ball bearings.It can also be used optimize the construction of ball bearings for specific applications.

Quasi-static Analysis of Thrust-loaded Angular Contact Ball Bearings Part Ⅱ:Results and Discussion

Ball bearings are widely employed mechanical components characterized by high precision and quality,and usually play important roles in various rotary machines and mechanisms.Many advanced applications require a deep understanding of their various kinematic and tribological characteristics that are essential to predict the fatigue endurance,relieve the vibration and minimize the power dissipation of ball bearings in particular applications.An angular contact ball bearing under a specified operating condition is simulated with the quasi-static/creepage analytical model proposed in the preceding article.The results demonstrate that the ball bearing is a statically determinate system.That the balls spin on both inner and outer races means the ball is controlled by neither the inner nor the outer raceway.The friction between the ball and raceway renders the inner and outer contact angles unequal.The larger the coefficient of friction is,the larger the angle deviation.The tangential traction perpendicular to the rolling direction due to the spin induces a gyro-like rotation of the ball with respect to the raceway even if no inertial effects are considered.The tangential elastic compliance of contacting surfaces gives rise to locked areas within the contact patch and transforms the sliding lines from circles into spirals.The differential slip due to the close conformity of the ball and raceway makes the sliding and traction distributions asymmetric,which will influence the location of the spinning center of the ball with respect to the raceway.The quasi-static/creepage model can be used to reveal the operating behaviors of ball bearings running under steady conditions and to optimize the design of ball bearings for specific applications.

Research on the Critical Speed of a Mixed-Flow Turbocharger with Hybrid Ceramic Ball Bearing

The critical speeds for a vehicle turbocharger with hybrid ceramic ball bearing are researched. The ball bearing-rotor system produces resonance when it working in critical speed and that makes the turbocharger injury working for a long time. The calculation and analysis methods of the critical speed for the vehicle turbocharger are described. The critical speed is computed by two methods including Riccati transfer matrix and DyRoBeS finite element method for a vehicle turbocharger with hybrid ceramic ball bearing. The vibration experiment had been taken to validate the calculating result, Comparison between the results by two calculation methods and the test results show that the first critical speed differences are 6.47 % and 5.66 %, the second critical speed differences are 2.87 % and 2.94 % respectively. And then, the primary factors which influence the critical speed are analyzed, the conclusions will be helpful for the vehicle turbocharger bearing-rotor system design.

Numerical analysis of loaded stress and central displacement of deep groove ball bearing

The aim of this work is to develop a three-dimensional model of deep groove ball bearing to investigate the loaded stresses and central displacements of bearing rings. The equivalent stresses and central displacements of bearing rings are obtained based on the simulated analysis. Moreover, several parameters, such as load magnitude, raceway groove curvature radius(RGCR), thicknesses of outer and inner rings, are varied to investigate their effects on the equivalent stresses and central displacements of bearing rings. Research results provide useful guidelines for determining the design parameters.

Quasi Dynamic Calculation of Local Stiffness of Angular Contact Ball Bearings

In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular contact ball bearings were calculated using quasi dynamic calculation method. Based on the relationship of local load to contact deformation,the calculation model of local bearing stiffness was subsequently built to get radial and axial components of local stiffness. Effects of external loads on the local bearing stiffness were analyzed. The results showed that local stiffness in bearings is symmetric to the axis of radial load,and its value has a maximum on the symmetry axis along the radial load direction. External radial and axial load have different effects on local bearing stiffness.

A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.

Reliability Based Design Optimization of Aero-Engine Spindle Ball Bearings

Aero-engine spindle ball bearings work in harsh conditions which are affected by relatively complex stresses. One of the key factors which affects bearing performance is its structure. In this paper,we used reliability based design optimization method to solve the structure design problem of aero-engine spindle ball bearings.Compared with the optimization design method, the value of equivalent dynamic load using reliability optimization design method was the least by MATLAB simulation. Also the design solutions show that the optimized structure possesses higher reliability than the original solution.

Air flow patterns and noise analysis inside high speed angular contact ball bearings

The vortex formed around the rolling ball and the high pressure region formed around the ball-raceway contact zone are the principle factors that barricades the lubricant entering the bearing cavity, and further causes improper lubrication. The investigation of the air phase flow inside the bearing cavity is essential for the optimization of the oil-air two-phase lubrication method. With the revolutionary reference frame describing the bearing motion, a highly precise air phase flow model inside the angular contact ball bearing cavity was build up. Comprehensive factors such as bearing revolution, ball rotation, and cage structure were considered to investigate the influences on the air phase flow and heat transfer efficiency. The aerodynamic noise was also analyzed. The result shows that the ball spinning leads to the pressure rise and uneven pressure distribution. The air phase velocity, pressure and cage heat transfer efficiency increase as the revolving speed increases. The operating noise is largely due to the impact of the high speed external flow on the bearing. When the center of the oil-air outlet fixes near the inner ring, the aerodynamic noise is reduced. The position near the inner ring on the bigger axial side is the ideal position to fix the lubricating device for the angular contact ball bearing.