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.

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.

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.

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.

Bi-Modal Failure Mechanism of Rolling Contact Bearings

The theory of failure of rolling contact bearings is based on fluctuating high level loading and material fatigue. This theory is unimodal, considering only the solid components of the bearing, and ignoring the liquid phase, which is the lubricant. Bearing life is rather dispersed, reaching a ratio of 20 between the extreme values. Since this theory was established, several exceptional phenomena were detected that could not be explained by it, such as: 1) Pitting damage beyond the contact path;2) Detrimental effect of a minute quantity of water in the lubricant on bearing life. 25 ppm of water in the lubricant brought about shorter bearing life by over than 30%. The bimodal failure theory considers both solid and liquid bearing components. The damaging process of the lubricant evolves from its cavitation. During this process vapor filled cavities are formed in low pressure zones. When these cavities reach high pressure zones they implode exothermally. These implosions cause local high pressure pulses reaching 30,000 at accompanied by a temperature rise of about 2000 degrees K [1]. This paper includes cavitation erosion test results on stainless steel samples by vibratory and water tunnel test rigs. Various methods of lubricant dehydration are presented and evaluated. The main conclusion from this analysis is the use of water-free lubricants, for long life of RC bearings and more uniform service life thereof.

Bifurcation of Periodic Motion of Rigid Rotor System Supported by Angular Contact Ball Bearings

Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.

Ideal Failure Curve of Rolling Contact Bearings

The prevailing cumulative failure curves of Rolling Contact Bearings (RCB) have two main drawbacks: they begin at the origin and have a large dispersion. The purpose of this study is to develop an ideal failure curve and overcome the present drawbacks. The ideal failure curve of RC bearings is obtained by applying a water-free lubricant to the tested bearings. This eliminates the cavitation erosion from the Bimodal failure mechanism and the synergistic effect with the mechanical failure mode. This new concept considers the fatigue process involved in the failure mechanism and suggests decreasing the dispersion of bearing life.

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.

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.

Influences of preload on the friction and wear properties of high-speed instrument angular contact ball bearings

For starved-oil or solid lubrication of high-speed instrument angular contact ball bearings, friction heating and wear are the main reasons of bearing failures. This paper presents a dynamic wear simulation model to investigate the impacts of different preload methods and the changes of preload caused by wear on bearing wear life. The integral value QV of stress and sliding velocity in the contact ellipses between a ball and the inner and outer races determines friction heating and wear. The changes of QV with the friction coefficient and the wear volume under constantforce preload and fixed-position preload are analyzed. Results show that under the same initial preload, the QV decreases with an increase of the friction coefficient for both preload methods, and the latter is slightly larger. The wear of the ball and the race is equivalent to the ball diameter reduction.The QV of constant-force preload is almost not changed with a decrease of the ball diameter, but for fixed-position preload, the value decreases firstly and then increases substantially due to insufficient preload, and slipping occurs, the ball diameter is reduced by 0.025%, while the preload is reduced by 60.33%. An estimation of the bearing wear life under different preload methods requires a consideration of the changes in the wear rate of bearing parts.

Impact of lubricant traction coefficient on cage's dynamic characteristics in high-speed angular contact ball bearing

In this paper,the formulas of elasto-hydrodynamic traction coefficients of three Chinese aviation lubricating oils,4109,4106 and 4050,were obtained by a great number of elastohydrodynamic traction tests.The nonlinear dynamics differential equations of high-speed angular contact ball bearing were built on the basis of dynamic theory of rolling bearings and solved by Gear Stiff（GSTIFF） integer algorithm with variable step.The impact of lubricant traction coefficient on cage＇s dynamic characteristics in high-speed angular contact ball bearing was investigated,and Poincare map was used to analyze the impact of three types of aviation lubricating oils on the dynamic response of cage＇s mass center.And then,the period of dynamic response of cage＇s mass center and the slip ratio of cage were used to assess the stability of cage under various working conditions.The results of this paper provide the theoretical basis for the selection and application of aviation lubricating oil.

Vibration analysis of a single row angular contact ball bearing with the coupling errors including the surface roundness and waviness

Roundness and surface waviness are main manufacturing errors on the components of single row angular contact ball bearings(ACBBs).An analytical study for vibrations of the ACBBs with coupling errors including the roundness and waviness can be useful for the vibration control of the rotating machinery.However,most previous works only focused on the single error modelling method.In this paper,an improved time dependent displacement excitation(TDDE)model is proposed to consider the coupling errors including the roundness and waviness on the inner and outer races of an ACBB.The TDDE model for the roundness and waviness is established by using a combination of several sinusoidal functions.A dynamic model in the previous study is improved to consider the influences of coupling errors including the roundness and waviness.The Hertzian contact theory and Dowson’s method are adopted to calculate the bearing contact stiffness.The time-and frequency-domain vibrations for the experimental and simulation results are compared to show some model validation.The influences of roundness orders and waviness amplitudes on the vibrations of the ACBB are analysed.The obtained results show that the coupling errors including the roundness and waviness have some influence on the time-domain impulse waveform and frequency-domain spectrum characteristics of the bearing accelerations.The differences of the vibrations between the coupling errors and sing error are from 4%to 42%.This paper can provide a useful guidance for the accurate diagnosis of surface imperfections in the ACBBs.