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.

Effect of nozzle inlet parameters on the dry granulation atomization process of Si_(3)N_(4) ceramic bearing balls

In this paper,the atomization characteristics of Si3N4 ceramic dry granulation affect the performance of Si3N4 ceramic bearing balls.In order to improve the dry granulation characteristics and the comprehensive performance of Si3N4 ceramic bearing balls,the atomization mechanism of the spinning nozzle used for Si3N4 dry granulation was studied in detail.The interaction between air and binder in the pressure-swirl nozzle is analyzed based on VOF method,the modified realizable k−εturbulence model is used to simulate the flow field inside and outside the pressure-swirl nozzle,the effects of nozzle inlet parameters including the number of tangential inlets and the deflection angle of tangential inlets on the binder volume fraction,velocity distribution and pressure distribution are analyzed.The results show that when the number of tangential inlets increases from 1 to 4,the swirl strength of gas–liquid two-phase in the nozzle increases,the mean diameter of air core increases from 1.51 mm to 2.01 mm,and the spray cone angle increases from 18.5◦to 26.4◦.Besides,when the deflection angle of tangential inlet increases from 0◦to 15◦,the swirl strength of gas–liquid two-phase in the nozzle with the deflection angle of tangential inlet of 10◦is the largest,and the mean diameter of air core and spray cone angle is 3.04 mm and 30.7◦,respectively.Based on the atomization experiment platform of the electric control fuel system,the mean diameter of air core and spray cone angle are measured,the micromorphology of Si3N4 particles is observed,which verifies the correctness of numerical simulation.When the Si3N4 particles are prepared by dry granulation,taking the atomization performance of nozzle into consideration,the pressure-swirl nozzle with 4 tangential inlets and 10◦deflection angle should be selected.

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.

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.

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.

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.

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.

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.

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.

Finite Element Analysis of 6300 Deep Groove Ball Bearing

Rolling bearing is widely used in mechanical support, its general components are the inner ring, outer ring, the ball, retainer etc.. Now many companies in developed countries and university in the rolling bearing as the research object, and has made great progress in design theory, the experiment method and production technology etc. We will use the finite element ANSYS to establish the model of deep groove ball bearing. Through the contact analysis, we can get the contact stress between the rings and balls, strain, contact state, penetration, sliding distance and the friction stress distribution. These values are compared to the theoretical values with Hertz theory, and they have better consistency, provide the good theoretical basis for the optimization design of rolling bearings.

NONLINEAR STABILITY OF BALANCED ROTOR DUE TO EFFECT OF BALL BEARING INTERNAL CLEARANCE

Stability and dynamic characteristics of a bail bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Flo- quet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution. The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system.

Modeling of Rolling Contact Friction of Ball Bearings at Elevated Temperature

In order to predict the rolling friction coefficient and analyze the effects of material compatibility on the friction coefficient at elevated temperature(from room temperature to 600℃),a theoretic computation model was developed based on bearing's elastic contact hysteresis and related material characteristic parameters.Some examples were carried out to verify the feasibility of the model.The research results show that the material compatibility has significant effects on rolling friction coefficient,especially the modulus of elasticity and the expansion coefficient of material,and results also show the rolling friction coefficient of the matched pair between GCr15 and Si3N4 is the smallest comparing with that between GCr15 and M50(or ASP-23,or GCr15) when making GCr15,M50,ASP-23,and Si3N4 materials as bearing's rolling balls and GCr15 material as bearing's inner and outer rings.Further research indicates that the working temperature also has played an important role in the rolling friction coefficient of the ball bearing,moreover,the friction coefficient of the matched pair of M50 and Si3N4 behaves most stably at elevated temperature.

Analysis of Rolling Contact Bearings Test Data by the Bımodal Method

Lieblein J. and Zelen A. conducted a study of the fatigue life of deep groove ball bearings. This study was based on data of 4948 bearings as obtained from 5 companies and 213 test groups. Among these data is a detailed test report #3183, lot 73, consisting of 23 failed bearings. This report states that the Weibull slope of this group is 2.23, meaning that this distribution is mono sloped. These test data were plotted by the author on a bilinear scale plane, of endurance life versus bearing number and proved to be distinctly bi sloped. This basic difference prompted a wide study resulting in several new findings and set the grounds for a new analysis method.

Research on Devices for Dividing Balls with Fluid

The methods of dividing balls equally among ball bearings to install the bearing retainer is briefly introduced in this paper, and the insufficiency of traditional methods is pointed out. A novel kind of non-contact type of dividing ball method is proposed, according to the principle theory.

Current-carrying friction in carbon coated ball bearing

In this work,we proposed a method for coating the whole surfaces of bearing balls uniformly by carbon film with a rotatable ball clamp.We studied the carbon/carbon friction with a self-designed currentcarrying ball bearing friction test system.A notable and instant friction force drop of 28%and significant carbon film wear alleviation were found when currents were applied.By using TEM-,SEM-,and EDS-analysis,special carbon stacks with a mixture of large wear particles and oxide were found in the wear areas under current applied condition.We elucidated the current-carrying friction mechanisms as follows:(1)wear particles formation;(2)wear particles charged by tribomicroplasma;(3)formation of surface passivated carbon stacks under electric force;(4)sliding between passivated carbon surfaces.This work may facilitate the development of novel solid-lubricated ball bearings and lay some foundations for current-carrying rolling friction.

Skidding and spinning investigation for dry-lubricated angular contact ball bearing under combined loads

Sliding and spinning behaviors significantly affect the performance of rolling bearings,especially for dry-lubricated bearings,micro and macro sliding may lead to increased wear of the solid lubricating film.A unified rolling contact tribology analytical model is proposed for dry-lubricated angular contact ball bearings(ACBBs)considering the extreme conditions including high combined loads and rolling contact effects.A comprehensive solution framework is proposed to ensure the robustness of the model under different loading conditions.Equilibrium equations are solved to study the effects of friction coefficients,rotating speeds,and combined loads on the skidding and spinning characteristics of the ACBB.The results show that the rolling contact effects and combined loads significantly affect the skidding and spinning performance of the ACBB.Further analysis reveals that the skidding mechanism is related to the interaction between ball kinematical motion and traction forces.The developed analytical model is proved to more accurately predict the bearing kinematical and tribological behavior as it discards the raceway control hypothesis and considers the macro/micro-slipping,creepage,and self-spinning motions of the ball,which is validated using both the existing pure axial loading dry-lubricated ACBB model and the classical Jones–Harris model.The study would provide some guidance for the structure and lubrication design of dry-lubricated ACBBs.

Multi-dimensional controllability analysis of precision ball bearing integrity

Many factors affect the integrity of precision ball bearings.In this study,the multi-dimensional controllability of precision ball bearings produced in different company brands(bearing A and bearing B)were studied and compared.The geometric errors(flatness,parallelism,roundness and cylindricity of inner and outer rings,roundness,groove and roughness of inner and outer rings)and vibration errors of bearings were analyzed.Concurrently,the residual stress,residual austenite content,element content ratio,metamorphic layer and temperature-vibration displacement coupling test were also analyzed.Based on the above analysis conclusion,the bearing fatigue life test was carried out for 2150 h.The reliability of the conclusion is proved again as follows.When the residual austenite content in the raceway of precision ball bearing is 10%,the axial residual stress is 877.4 MPa;the tangential residual stress is 488.1 MPa;the carbon content is 6%;the test temperature of bearing is the lowest;and the service life is prolonged.

Starved lubrication analysis of angular contact ball bearing based on a multi-degree-of-freedom tribo-dynamic model

When the oil supply is not adequate to maintain the ideal lubrication,angular contact ball bearing will enter into the starved lubrication regime resulting in the potential performance degradation and consequently the severe failures.To study the effects of starved lubrication on the performance of angular contact ball bearing,this paper first proposes a multi-degree-of-freedom(DOF)tribo-dynamic model by introducing five-DOF inner ring,six-DOF balls,and six-DOF cage.The model considers the starved lubrication in the ball-raceway contact and the full multi-body interactions between the bearing components.With different ball-raceway starvation degrees being analyzed,the effects of starved lubrication on the bearing tribo-dynamic performance are first revealed.By comparison,it is found that the oil film thickness,the skidding performance,and the traction forces in the ball-raceway contact are significantly influenced by the starvation degrees.It is also found that the starvation-induced change of the ball-pocket contact force is dramatical under combined loads,and the maximum contact force under this load condition increases with the increasing starvation degrees.

航空发动机高速滚珠轴承振动特性研究

Ball bearing is widely used as rotor supporting.It is a non-negligible source of vibration in aero-engines.The vibration characteristics of the highspeed ball bearing are studied in this paper.Bearing kinematics theory is applied to discuss the basic characteristics of ball bearings.The vibration factors caused by ball bearings are analyzed,and then the vibration model of ball bearings is set up.The effect of the unbalance,the ball passage vibration,the radial clearance and the surface waviness are considered.It is found that the ball passage vibration is excited by the contact force between the balls and the races.Increasing the numbers of ball can reduce the vibration amplitude.The surface waviness which is caused due to the geometric imperfection of ball bearings is considered as one of the important vibration sources of bearing systems.