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 und...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.展开更多
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 cause...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.展开更多
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 cont...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.展开更多
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 flexib...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.展开更多
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-D...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.展开更多
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...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.展开更多
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...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.展开更多
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 i...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.展开更多
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 ...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.展开更多
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 roun...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.展开更多
基金Supported by National Key Technology Research and Development Program of China during the 11th Five-Year Plan Period (No. JPPT-115-189)National Natural Science Foundation of China (No. 50975033)
文摘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.
基金Project(2011CB706606) supported by the National Basic Research of ChinaProject(51405375) supported by the National Natural Science Foundation of China
文摘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.
基金Sponsored by the National Basic Research Program of China (Grant No. 2013CB632305)the National Natural Science Foundation of China (GrantNo. 51275125)
文摘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.
文摘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.
基金Supported by National Natural Science Foundation of China (No.50905061)the Fundamental Research Funds for Central Universities
文摘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.
基金This work was funded by the National Natural Science Foundation of China(Nos.52175119 and 61633001).The authors are also grateful for the support of Xi’an Aerospace Propulsion Institution(China Aerospace Science and Technology Corporation).
文摘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.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.52130502 and 51875344)the Research Project of State Key Laboratory of Mechanical System and Vibration(Grant No.MSVZD202107)。
文摘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.
基金supported by the National ‘the twelfth five-year’ Projects of Science and Technology of China
文摘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.
基金financially co-supported by the National Natural Science Foundation of China(No.U1404514)Henan Outstanding Person Foundation(No.144200510020) of ChinaCollaborative Innovation Center of Major Machine Manufacturing in Liaoning,China
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.51605051,51975068)Chongqing Research Program of Basic Research and Frontier Technology(Grant No.cstc2017jcyj AX0202)。
文摘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.
