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 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.展开更多
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 theo...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.展开更多
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 ...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.展开更多
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...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.展开更多
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...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.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 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...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.展开更多
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 reliabilit...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.展开更多
Medical linac based imaging modalities such as portal imaging can be utilized for highly accurate measurements. An intensity-weighted centroid method for determining object center is proposed that can detect the posit...Medical linac based imaging modalities such as portal imaging can be utilized for highly accurate measurements. An intensity-weighted centroid method for determining object center is proposed that can detect the position of small object at subpixel accuracy. The principles and algorithms of the intensity-weighted centroid method are presented. Analytical results are derived for positional accuracy of a rod and a sphere in digital images, and the theoretical accuracy limits are calculated. The method was experimentally examined using phantoms with embedded ball bearings (BBs). Images of the phantoms were taken by the MV portal imager of a medical linac. The image pixel size was 0.26 mm when projected at the linac isocenter plane. The BB coordinates were calculated by applying the intensity-weighted centroid method after removing the background. The reproducibility of BB position detection was measured with 3 monitor unit (MU) exposures at various dose rates. A stationary BB, of 0.25 image contrast, showed position reproducibility in the range of 0.004 - 0.013 mm. When the method was used to measure the displacement of a moving BB, the difference between the measured and expected BB position had a standard deviation of 0.006 mm. The effect of image noise on the BB detection accuracy was measured using a phantom with multiple BBs. The overall detection accuracy, represented by standard deviation, steadily improved from 0.13 mm at 0.03 MU to 0.008 mm at 5.0 MU, and showed an inverse correlation with contrast-to-noise ratio. We demonstrated that intensity-weighted centroid method can achieve subpixel accuracy in position detection. With a linac based imaging system, precise mechanical measurement with accuracy of microns could be achieved.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
Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance ...Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial,axial and overturning moment loadings.The relation between the negative axial clearance and the contact force distribution is analyzed.The static load-carrying capacity curves are established,and the effects of the changes in negative axial clearance,curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed.The results show that,with the increase in the absolute value of negative clearance,the maximum contact load decreases first and then increases.The clearance values in the range of 0.2 mme0 mm have little effect on the static load-carrying capacity of bearing.With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle,the static load capacity of bearing decreases.展开更多
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 unde...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.展开更多
Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearing...Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearings were estimated.The Newmark-β method and Newton-Laphson method were used to solve the equations.The dynamic characteristics of rotor system were studied through the time response,the phase portrait,the Poincar?maps and the bifurcation diagrams.The results show that the system goes through the quasi-periodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions.The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases;the initial contact angle of ball bearing affects dynamic behaviors of the system obviously.The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.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
Due to the complexity of investigating deformation mechanisms in helical rolling(HR) process with traditional analytical method, it is significant to develop a 3D finite element(FE) model of HR process. The key formin...Due to the complexity of investigating deformation mechanisms in helical rolling(HR) process with traditional analytical method, it is significant to develop a 3D finite element(FE) model of HR process. The key forming conditions of cold HR of bearing steel-balls were detailedly described. Then, by taking steel-ball rolling elements of the B7008 C angular contact ball bearing as an example, a completed 3D elastic-plastic FE model of cold HR forming process was established under SIMUFACT software environment. Furthermore, the deformation characteristics in HR process were discovered, including the forming process, evolution and distribution laws of strain, stress and damage based on Lemaitre relative damage model. The results reveal that the central loosening and cavity defects in HR process may have a combined effect of large negative hydrostatic pressure(positive mean stress)caused by multi-dimensional tensile stresses, high level transverse tensile stress, and circular-alternating shear stress in cross section.展开更多
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 ...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.展开更多
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
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 ...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.展开更多
The scuffing behavior of hybrid ceramic bearing lubricated with solid is greatly affected by the contact flash temperature. Formulas are dedused using Lee’s asperity flash temperature method, to calculate the flash t...The scuffing behavior of hybrid ceramic bearing lubricated with solid is greatly affected by the contact flash temperature. Formulas are dedused using Lee’s asperity flash temperature method, to calculate the flash temperature of ball bearing lubricated with solid. The maximum flash temperature is calculated for hybrid ceramic ball bearings. The results show that under given conditions, the flash temperature of inner race is higher than that of outer race, the flash temperature of the hybrid ceramic bearing is sensitive to the load, rotational speed and race curvature. The flash temperature of inner race at 20 000 r/min is 66 9% more than that that at 11 000 r/min, and with the load changing from 1.1 kN to 2 kN, the flash temperature inner race goes up to 165 7%. Very common for high speed ball bearings, when curvature coefficients of both inner and outer race change from 0 515 to 0 56, the inner race flash temperature decreases from 421 446℃ to 56 2℃.展开更多
5 heats of GCr15 bearing steel of different sulfur contents ranging from 0.009-0.092% (wt.)were smelted. The role of sulfur in bearing steel and its effect on contact fatigue properties andfracture toughness K<su...5 heats of GCr15 bearing steel of different sulfur contents ranging from 0.009-0.092% (wt.)were smelted. The role of sulfur in bearing steel and its effect on contact fatigue properties andfracture toughness K<sub>IC</sub>Were studied. It was shown that as the sulfur content increases the sulfur content dissolved in the steelsubstrate remains unchanged. The best contact fatigue property appears at the sulfur content of0.045% (wt.), and the influence of sulfur content on the fracture toughness of bearing steel is notobvious. Finally, the mechanism of the role of sulfur was investigated.展开更多
文摘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.
基金supported by National Natural Science Foundation of China (Grant No. 50935002, Grant No. 51105342)
文摘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.
基金supported by National Natural Science Foundation of China (Grant No. 50935002, Grant No. 51105342)
文摘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.
基金the National Natural Science Foundation of China (No. 51605354)the Fundamental Research Funds for the Central Universities (WUT: 2015IVA021)+1 种基金the Innovative Research Team Development Program of Ministry of Education of China (No. IRT13087)the High-end Talent Leading Program of Hubei Province (No. 201286)
文摘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.
文摘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.
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.
基金Project supported by the National Basic Research Program(973 Program)of China(No.2015CB057400)the National Natural Science Foundation of China(No.11602070)+1 种基金the China Postdoctoral Science Foundation(No.2016M590277)the Heilongjiang Postdoctoral Financial Assistance(No.LBH-Z16067)
文摘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.
文摘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.
文摘Medical linac based imaging modalities such as portal imaging can be utilized for highly accurate measurements. An intensity-weighted centroid method for determining object center is proposed that can detect the position of small object at subpixel accuracy. The principles and algorithms of the intensity-weighted centroid method are presented. Analytical results are derived for positional accuracy of a rod and a sphere in digital images, and the theoretical accuracy limits are calculated. The method was experimentally examined using phantoms with embedded ball bearings (BBs). Images of the phantoms were taken by the MV portal imager of a medical linac. The image pixel size was 0.26 mm when projected at the linac isocenter plane. The BB coordinates were calculated by applying the intensity-weighted centroid method after removing the background. The reproducibility of BB position detection was measured with 3 monitor unit (MU) exposures at various dose rates. A stationary BB, of 0.25 image contrast, showed position reproducibility in the range of 0.004 - 0.013 mm. When the method was used to measure the displacement of a moving BB, the difference between the measured and expected BB position had a standard deviation of 0.006 mm. The effect of image noise on the BB detection accuracy was measured using a phantom with multiple BBs. The overall detection accuracy, represented by standard deviation, steadily improved from 0.13 mm at 0.03 MU to 0.008 mm at 5.0 MU, and showed an inverse correlation with contrast-to-noise ratio. We demonstrated that intensity-weighted centroid method can achieve subpixel accuracy in position detection. With a linac based imaging system, precise mechanical measurement with accuracy of microns could be achieved.
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 NSFC(51105131)Excellent Youth Foundation of Henan Scientific Committee(124100510002)Creative Talent Foundation in University of Henan Province(2011HASTIT016)
文摘Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial,axial and overturning moment loadings.The relation between the negative axial clearance and the contact force distribution is analyzed.The static load-carrying capacity curves are established,and the effects of the changes in negative axial clearance,curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed.The results show that,with the increase in the absolute value of negative clearance,the maximum contact load decreases first and then increases.The clearance values in the range of 0.2 mme0 mm have little effect on the static load-carrying capacity of bearing.With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle,the static load capacity of bearing decreases.
文摘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.
基金Sponsored by the National Natural Science Foundation of China(Grant No. 50575054)
文摘Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearings were estimated.The Newmark-β method and Newton-Laphson method were used to solve the equations.The dynamic characteristics of rotor system were studied through the time response,the phase portrait,the Poincar?maps and the bifurcation diagrams.The results show that the system goes through the quasi-periodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions.The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases;the initial contact angle of ball bearing affects dynamic behaviors of the system obviously.The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.
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Project(2011CB706605)supported by the National Basic Research Program of ChinaProject(IRT13087)supported by the Innovative Research Team Development Program of Ministry of Education of ChinaProject(2012-86)supported by the Grant from the High-end Talent Leading Program of Hubei Province,China
文摘Due to the complexity of investigating deformation mechanisms in helical rolling(HR) process with traditional analytical method, it is significant to develop a 3D finite element(FE) model of HR process. The key forming conditions of cold HR of bearing steel-balls were detailedly described. Then, by taking steel-ball rolling elements of the B7008 C angular contact ball bearing as an example, a completed 3D elastic-plastic FE model of cold HR forming process was established under SIMUFACT software environment. Furthermore, the deformation characteristics in HR process were discovered, including the forming process, evolution and distribution laws of strain, stress and damage based on Lemaitre relative damage model. The results reveal that the central loosening and cavity defects in HR process may have a combined effect of large negative hydrostatic pressure(positive mean stress)caused by multi-dimensional tensile stresses, high level transverse tensile stress, and circular-alternating shear stress in cross section.
基金Supported by Fundamental Research Funds for Central Universities(No.FRF-TP-12-067A)
文摘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.
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 supported by the National Natural Science Foundation of China (No.50275113) and the Doctoral Science Foundation of Ministry of Education (No.20030698017)
文摘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.
文摘The scuffing behavior of hybrid ceramic bearing lubricated with solid is greatly affected by the contact flash temperature. Formulas are dedused using Lee’s asperity flash temperature method, to calculate the flash temperature of ball bearing lubricated with solid. The maximum flash temperature is calculated for hybrid ceramic ball bearings. The results show that under given conditions, the flash temperature of inner race is higher than that of outer race, the flash temperature of the hybrid ceramic bearing is sensitive to the load, rotational speed and race curvature. The flash temperature of inner race at 20 000 r/min is 66 9% more than that that at 11 000 r/min, and with the load changing from 1.1 kN to 2 kN, the flash temperature inner race goes up to 165 7%. Very common for high speed ball bearings, when curvature coefficients of both inner and outer race change from 0 515 to 0 56, the inner race flash temperature decreases from 421 446℃ to 56 2℃.
文摘5 heats of GCr15 bearing steel of different sulfur contents ranging from 0.009-0.092% (wt.)were smelted. The role of sulfur in bearing steel and its effect on contact fatigue properties andfracture toughness K<sub>IC</sub>Were studied. It was shown that as the sulfur content increases the sulfur content dissolved in the steelsubstrate remains unchanged. The best contact fatigue property appears at the sulfur content of0.045% (wt.), and the influence of sulfur content on the fracture toughness of bearing steel is notobvious. Finally, the mechanism of the role of sulfur was investigated.