Angular Contact Ball Bearings Research Articles

Stiffness increase in main spindles by using tapered roller bearings for aluminum cutting tests

AbstractDue to increasing demands regarding higher manufacturing accuracy and the machining of high-strength materials, the stiffness and load-carrying capacity of main spindles must be enhanced. One approach is to replace the conventionally used angular contact ball bearings, so called spindle bearings, with tapered roller bearings of the same size, which have a higher stiffness and load carrying capacity due to their larger rolling contact. In case the speed requirement is below a speed parameter $$n\cdot d_{m}=0.9\times 10^{6}$$ n · d m = 0.9 × 10 6 mm/min, the poorer speed parameter of tapered roller bearings can be compensated by a sufficiently high lubrication quantity. However, the stiffness increase by using this bearing type in main spindles has not yet been quantified in field tests. Therefore, the aim of this paper is to demonstrate the stiffness advantage of a spindle with an elastically arranged tapered roller bearing compared to a conventional spindle with angular contact ball bearings by machining tests. First, the radial load displacement characteristic of the newly developed tapered roller bearing spindle is tested in advance on an isolated test rig. In machine cutting tests, full slots are milled in an aluminum block. During the tests, the axial and radial displacements of the spindle shaft relative to the housing are measured and evaluated in radial and axial direction. These tests are repeated and compared with the conventional spindle. By varying the process parameters such as cutting depth, feed rate or rotational speed, the increased stiffness of the tapered roller bearing spindle compared to the conventional spindle is illustrated based on the measured displacements. Moreover, frequency response measurements at different speeds underpin the improved damping of the tapered roller bearing spindle. Assuming that the speed requirements are not too high and the tapered roller bearing is sufficiently lubricated, the use of this type of bearing can significantly increase the stiffness and thus the manufacturing precision in the long term for main spindles.

Dynamic reliability analysis of angular contact ball bearing based on maximum entropy quadratic fourth moment method*

ABSTRACT Bearing failure occurs when the dynamic contact stress exceeds the yield strength of the bearing material during operation. To minimise the risk of bearing failure, a new reliability theory method is proposed based on the stress-strength model of bearings, incorporating random input variables to analyse the reliability of angular contact ball bearings (ACBBs) and quantify their dynamic performance. The maximum entropy quadratic fourth moment method is used to calculate the probability distribution of maximum orthogonal shear stress-strength of bearing, and the maximum entropy principle is used to obtain the approximation of the minimum human error factors. Additionally, reliability-based sensitivity indices are derived to investigate the parametric significance of random input variables. Using B218 bearing as an example, the engineering application of this method in dynamic reliability and reliability-based sensitivity analysis is illustrated. Monte Carlo simulation is performed to verify the accuracy and effectiveness of the method to provide benchmark results. The results show that the Poisson’s ratio have a greater influence on the dynamic reliability of ACBBs than other parameters. Improving parameters such as ball diameter, raceway groove curvature radius and contact angle can also improve the reliability of bearings to some extent.

Study on Cage Stability of Solid-Lubricated Angular Contact Ball Bearings in an Ultra-Low Temperature Environment

In the ultra-low temperature environment, the material properties of the bearing change, which puts forward higher requirements for the dynamic performance of the bearing cage. The bearings operating in ultra-low temperature environments commonly use solid lubricants. This study first focused on measuring the traction coefficients of molybdenum disulfide (MoS2) solid lubricant in a nitrogen atmosphere, and the Gupta fitting model is constructed to derive the traction equation. Subsequently, the dynamic differential equation of angular contact ball bearings was established, and the stability of the bearing cage in a nitrogen environment was simulated and analyzed based on the dynamic model. The accuracy of the simulation model was verified through comparison. The results show that less than 10% of errors exist between the experimental data and the traction curve fitted by the Gupta model, and the stability of the cage is closely related to operating parameters and bearing structure parameters. Cage stability increases with axial load but decreases with radial load. The cage stability is optimal when the radial internal clearance of the bearing is approximately 0.06 mm. When other conditions remain unchanged and the ratio of the cage pocket hole gap to the cage guide surface gap is 0.2, the cage stability is the best. The research results will provide a foundation for the design and application of solid-lubricated angular contact ball bearings in ultra-low temperature environments.

Investigation of Graphene Platelet-Based Dry Lubricating Film Formation in Tribological Contacts

Dry lubricants used in highly loaded rolling bearings are in the focus of current research. In previous studies, graphene platelets applied as dry lubricants on the surfaces of angular contact ball bearings demonstrated superior properties. These specific bearings, experiencing both rolling and spinning motion, create more severe conditions for dry lubricants. To gain deeper insights into the lubrication effects, micro-tribological studies were carried out on the respective film formation and running behavior effects. In the tests, a fixed steel ball slid against an oscillating counterpart under a defined load. During the measurements, the applied load and tangential forces on the ball were recorded to calculate the friction. Comparative investigations included nano-graphite particles and fullerene as dry lubricants, in addition to graphene platelets of various staple thicknesses. To increase the adhesion of the films to the surfaces, a pre-rolling process was implemented. Afterwards, the friction on the compressed films was measured. The results indicate that the pre-rolling process effectively reduces the friction of the system. After testing, the surfaces underwent analysis using laser scanning microscopy to assess the formed films, wear, and material transfer. It has been demonstrated that the pre-rolling process leads to the formation of a very thin compacted film with surface protective properties. With the ball as a counterpart, the graphene platelets generate a transfer film on the contacting surface.

Study on the Wear Characteristics of Angular Contact Ball Bearings

For the wear of rolling bearings, this paper establishes a wear model of angular contact ball bearings based on the proposed static mechanics of rolling bearings, kinematics of rolling bearings and Archard's wear theory, studies the wear of bearings, and analyses the effects of rotational speed, load and structural parameters on the wear of bearings. The results show that: the inner ring of the bearing is uniformly worn and the depth of wear is larger than the outer ring; the depth of wear of the inner ring of the bearing increases with the increase of rotational speed, the load has a certain effect on the depth of wear, the depth of wear increases with the increase of axial load; the structural parameters of the bearings have a certain effect on the wear, the depth of wear of the inner ring decreases with the increase of the radius of curvature of the internal grooves, the radius of curvature of the internal grooves has a small effect on the outer ring wear, and the selection of appropriate structural parameters can effectively reduce the wear of the bearings, the wear of the bearings can be reduced. Selection of appropriate structural parameters can effectively attenuate the wear.

Influences of external moment on the contact characteristics of angular contact ball bearings under combined loads

Angular contact ball bearings are widely used in rotating machinery. The external moment about the bearing lateral direction (i.e. the lateral moment) applied to a bearing affects the service life and performance of the bearings by influencing its internal contact characteristics. This work established a quasi-dynamic model of the ball bearing by comprehensively considering the inclination angle of the inner ring due to external lateral moment, the viscous drag, the inertial force and moment of the ball, the spin and sliding of the ball in the contact ellipse. On this basis, the operation process of angular contact ball bearings was simulated under combined radial and moment loads. The effectiveness of the model was verified experimentally, and the influences of external moments about different directions on the contact angle, slip-roll ratio, and load distribution under combined loads were analyzed. The results show that the increase in moment intensifies the spin-sliding of the rolling element. When the lateral moment and the radial load are applied together, the lateral moment can reduce the maximum load of the rolling element and causes the maximum load of the rolling element to deviate from its original position. When the lateral moment is combined with the axial and radial loads, the bearing load zone is concentrated by the rolling elements near the lateral direction. The curve of the load distribution changes from an ideal oval to a distorted oval. The research results can be used to guide the design, service life calculation, and performance evaluation of rolling bearings.

복합하중을 받는 각접촉 볼베어링을 위한 개선된 피로수명식

복합하중을 받는 각접촉 볼베어링을 위한 개선된 피로수명식

Economic tolerance design of the P2 raceway based on the quasi-static model of aerospace ball bearings

This study focused on designing the raceway tolerance of high-precision rolling bearings. After the tolerance error equivalence relationship is defined, the application of the rolling bearing error equalization effect in tolerance design is studied. First, a five-degree of freedom quasi-static model was established for angular contact ball bearings. The waviness was included in the manufacturing error, and the radial and axial runouts of the bearing inner ring were calculated. Second, the error homogenization effect of the rolling bearing was studied, and the error homogenization coefficient was defined. The results of the study demonstrated that the bearing rotary accuracy was higher than the raceway error by an order of magnitude. Third, the manufacturing error range of each precision grade of the rolling bearing raceway was obtained by investigating errors of the equalization coefficient. Finally, the specific value of the raceway tolerance of P2 rolling bearings was obtained.

Study on Thermal Characteristics of Angular Contact Ball Bearings Considering Roundness Error

To develop an angular contact ball bearing with low power consumption, a heat generation calculation model for angular contact ball bearings has been established based on bearing quasi dynamics, elastohydrodynamic lubrication theory, heat transfer theory, and Kirchhoff’s law of energy conservation, considering the effects of roundness error, bearing preload, centrifugal effect, and thermal expansion. The correctness of the model is verified through experiments. The influence of different operating conditions and roundness errors on the thermal characteristics of angular contact ball bearings is analyzed. The results of the calculation indicate that when the roundness error order is equal to the number of balls n/2 ± 2 (where n = 1, 2, 3, …), the overall heat generation of the bearing is lower than that without considering the roundness error. When the roundness error order is equal to (2n − 1)/4 ± 2 (where n = 1, 2, 3, …), the overall heat generation of the bearing is higher than that without considering the roundness error. At the same rotating speed, the overall heat generation fluctuates as the roundness error order changes, and the trend becomes more pronounced as the rotating speed increases. The maximum overall heat generation is achieved when the roundness error order equals (2n − 1)/4 times (where n = 1, 2, 3, …) the number of balls. When the roundness error order is equal to n/2 times the number of balls (where n = 1, 2, 3, …), the bearing’s overall heat generation is minimal. The variation in the total heat generated by the bearing is directly proportional to the amplitude of the roundness error. With the increase in roundness error harmonic order, the bearing integral heat generation shows a periodic change, and the change period has a mapping relationship with the number of balls.

A thermal assessment simplification exploration for the structural constraint effect on bearing temperature

Although an extensive research effort on the structural constraint role in bearing heating was done by scholars, often many researchers either neglected the sub structure effect for model simplification or considered more influencing factors to construct a complicated thermal model for higher evaluation precision. As a result, a lightweight and accurate assessment has been not available so far. Furthermore, they usually only made some basic assumptions and qualitative analyses when creating and improving the thermal predictive models to explore the heat transfer of bearings, and hence their findings usually lack sufficient theoretical supports, especially the quantitative bases. For an efficient assessment, this paper devotes to exploring how the structural constraint impact on the heat conduction of bearings, and accordingly present a more practical thermal grid to evaluate bearing heating efficiently. Firstly, the structure and installation notes of bearings were statistically analyzed. Next, a formula was constructed to implement the contrast of the heat transfer capacity between the axial and radial directions of bearing rings, and then a novel radial thermal equivalent resistance was proposed to represent the heat conduction capacity of bearing rings. We accordingly optimized the bearing node setting scheme to develop an efficient semi-empirical thermal grid for high-speed angular contact ball bearings, in which the oil-air separation and gray-box theory was also introduced to describe the heat convection in bearing cavities. Finally the improved thermal network for a motored spindle was planned to verify the above-proposed work, and the simulation results based on the current thermal models of bearings were also obtained and contrasted with the experimental values. For a further validation, the polynomial interpolation on test data, meanwhile, was performed to observe the temperature variation trend. The result of comparative analysis indicates that we show a more proper thermal assessment on bearing temperature.

Test and analysis of friction torque of double-row angular contact ball bearing under vacuum environment

PurposeThe purpose of this paper is to test and analyze the friction torque of double-row angular contact ball bearings under vacuum or ordinary pressure environment, horizontal or upright installation mode, and different rotational speeds, and to provide theoretical bases for the development of aerospace equipment.Design/methodology/approachThe experiments were carried out to investigate the effects of vacuum or ordinary pressure environment, horizontal or upright installation mode and different rotational speeds on bearing friction torque. To explore the relationship between working conditions and bearing friction torque, firstly, based on the generation source of friction torque, the test principle was determined, a test system was developed and the reliability of data was verified. Secondly, the friction torque of bearing was tested, and the values under various working conditions were obtained. Finally, this paper compared and discussed the test results.FindingsThe test results show that the friction torque value of vacuum environment horizontal installation condition is the largest at different rotational speeds, and the rotational speed has the most significant influence on the friction torque.Originality/valueThe friction torque test system of double-row angular contact ball bearing under vacuum environment was designed and built. The influence rules of vacuum or ordinary pressure environment, horizontal or upright installation mode and different rotational speeds on bearing friction torque were obtained.Peer reviewThe peer review history for this article is available at: http://dx.doi.org/10.1108/ILT-08-2023-0259

Power Loss Analysis of an Oil-Jet Lubricated Angular Contact Ball Bearing: Theoretical and Experimental Investigations

This study presents a theoretical and experimental analysis to quantify the power losses generated by an oil jet lubricated angular contact ball bearing. The analysis is conducted for a moderate speed range (N∙dm product less than 106) and a limited applied load (<5% of the static capacity). The lubrication regime of each ball is studied through a theoretical model and varies from Iso-Viscous Rigid to Elasto-Hydrodynamic. Therefore, the hydrodynamic effects are considered in the power loss calculation. An experimental campaign is carried out and the influence of several parameters (applied load, oil injection temperature, speed, etc.) is studied. A good agreement is found between the developed model and the measurements. It is shown that the radial applied load has no influence on power losses, unlike speed and axial load. This can be explained by the load distribution and the hydrodynamic rolling contribution on the low loaded balls.

Comparative analysis of angular contact bearing stiffness calculated by Hertz contact and thermo-elastohydrodynamic lubrication

Stiffness is the key dynamic parameter of the angular contact ball bearing. This work established a dynamic bearing model based on Hertz theory and thermo-elastohydrodynamic lubrication (TEHL) and compared the contact angle, inner race position, and stiffness. In most cases, the stiffness calculated via Hertz was higher than when using TEHL. The axial stiffness values determined via the two theories were close, while the radial stiffness calculated via the Hertz theory was smaller than that determined by TEHL under light load and high speed. Considering the elastic deformation of the races and the initial contact angle, the results obtained by TEHL displayed a lower error rate in the experiment than Hertz.

A New Thermal Model of an Angular Contact Ball Bearings, in a Standard Arrangement, subjected to Radial Loads, based on State Variables and Control Volumes

A New Thermal Model of an Angular Contact Ball Bearings, in a Standard Arrangement, subjected to Radial Loads, based on State Variables and Control Volumes

Study on the effect of angular misalignment and axial preload on the mechanical properties of four-point angular contact ball bearings

Four-Point Angular Contact Ball Bearing (FPCBB) is widely used in high-speed power systems due to their capacity to withstand axial forces in two different directions, high-speed capabilities, and space-saving design. This paper presents a unified 5-degree-of-freedom quasi-static model of FPCBB, explicitly addressing the influences of axial preload and angular misalignment. Through this model, the impacts of preload and misalignment on the contact state of FPCBB are investigated. The D'Alembert principle is employed to calculate the pitch angles of balls instead of the Raceway Control Hypothesis (RCH). Furthermore, the different effects of the two preload ways on the mechanical properties of bearings under the presence of angular misalignment were comprehensively analyzed. The findings reveal that both preload and misalignment significantly affect the mechanical properties of FPCBB. Notably, under conditions of angular misalignment, the effect of fixed position preload surpasses that of constant pressure preload. These results provide valuable guidance for evaluating the performance of FPCBB in practical applications.

Angular contact ball bearing skidding mechanism analysis and diagnosis considering flexible rotor characteristics

Bearing skidding is a frequent phenomenon in rotating machinery, which causes equipment motion instability and bearing wear failure. Due to the difficulties in the manufacture of high-speed flexible rotor test rig, measurement of bearing motion parameters and complex structure of angular contact ball bearing (ACBB), which makes the research on double-piece inner ring ACBB skidding challenging. This paper studies the ACBB skidding mechanism from the aspect of rotor characteristics, and first finds the resonance skidding phenomenon. Firstly, a high-speed flexible rotor test rig is designed and built to study the ACBB skidding mechanism, and the influence of foreign matter on the bearing cage slip rate is systematically studied. Then, the bearing cage speed considering the influence of lubricating oil pollution is accurately measured based on the adaptive fractional short-time Fourier transform. Finally, bearing skidding diagnosis under variable working conditions is realized based on the deep meta-transfer learning with feature enhanced generative adversarial network and average deflection power threshold. These proposed strategies systematically solve some problems in the research field of ACBB skidding, which has high practical significance and theoretical guidance value.

A friction temperature model for dynamic bearing operation based on neural network and genetic algorithm

This study used intelligent algorithms and experimental data to investigate the dynamic temperature of bearings. A test rig was created for angular contact ball bearings to measure the temperature of two bearings precisely while independently controlling rotational speed, axial load, radial load, and grease content. The study analyzed the steady temperature of bearings under different operating conditions using a friction temperature model based on SKF bearings. The bearings temperature was computed using traditional backpropagation neural network (BPNN) and genetic algorithms (GA). The study compared the results obtained through the SKF model and the actual temperature against those produced methods. GA displayed a higher level of accuracy and robustness. Upon evaluation, it was determined that both intelligent methods are suitable for processing variable data input. This article presents an intelligent approach to computing bearing temperature using statistical data analysis, which does not require analyzing dynamics, thermodynamics, or lubrication principles. The method's ability to compute transient temperature without boundary conditions or constraints makes it highly versatile. This feature renders it a valuable tool for bearing design and temperature control.

An efficient thermal model for high-speed angular contact ball bearings based on oil-air two-phase flow and gray-box model

PurposeFor a lightweight and accurate description of bearing temperature, this paper aims to present an efficient semi-empirical model with oil–air two-phase flow and gray-box model.Design/methodology/approachFirst, the role of lubricant/coolant in bearing temperature was discussed separately, and the gray-box models on the heat convection inside a bearing cavity were also created. Next, the bearing node setting scheme was optimized. Consequently, a novel semi-empirical two-phase flow thermal grid for high-speed angular contact ball bearings was planned. With this model, the thermal network for the selected motored spindle was built, and the numerical solutions for bearing temperature rise were obtained and contrasted with the experimental values for validation. The polynomial interpolation on test data, meanwhile, was also performed to help us observe the temperature change trend. Finally, the simulations based on the current models of bearings were implemented, whose corresponding results were also compared with our research work.FindingsThe validation result indicates that the thermal prediction is more accurate and efficient when the developed semi-empirical oil–air two-phase flow model is employed to assess the thermal change of bearings. Clearly, we provide a more proper model for the thermal assessment of bearing and even spindle heating.Originality/valueTo the best of the authors’ knowledge, this paper introduced the oil–air separation and gray-box model for the first time to describe the heat exchange inside bearing cavities and accordingly presents an efficient semi-empirical oil–air two-phase flow model to evaluate the bearing temperature variation by using thermal network method.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2023-0180/

Dynamic error modeling, analysis and compensation of planar flexible multilink mechanism for high-speed precision presses considering the thermal expansion effect of sliding and angular contact ball bearings

Dynamic error modeling, analysis and compensation of planar flexible multilink mechanism for high-speed precision presses considering the thermal expansion effect of sliding and angular contact ball bearings

Nonlinear dynamic behaviors of angular contact ball bearing with waviness based on a synthetical multi-degree-of-freedom mathematical modelling

This paper proposes a synthetical multi-degree-of-freedom mathematical modelling for analyzing the dynamic characteristics of angular contact ball bearing with waviness subjected to the external load working conditions. The above multi-degree-of-freedom mathematical modelling is established based on nonlinear elastic Hertz contact theory and inner raceway control theory by employing improved Newton–Raphson iteration method; the validation of the established mathematical modelling is verified by comparing the presented results with the existing literature results. The above mathematical modelling has considered raceway waviness, ball waviness, bearing clearance, centrifugal force, gyroscopic moment, external loads, and rotating speed comprehensively. Firstly, the effects of waviness order and waviness amplitude on time-varying contact and stiffness characteristics of angular contact ball bearing are investigated systematically. Then, the influences of bearing clearance, rotating speed, axial force, radial force, and torque on the dynamic contact and stiffness characteristics of angular contact ball bearing with waviness are analyzed thoroughly. The main results show that the solution results of mathematical modelling have converged, respectively, when raceway waviness order increases to 25 and ball waviness order increases to 5; The variation tendencies of time-varying contact angle, contact force, and stiffness of angular contact ball bearing with waviness are aperiodic; The amplitudes of time-varying contact angle, contact force, and stiffness of angular contact ball bearing increase evidently with waviness amplitude increased; The bearing clearance has important influence on the contact angle and contact force of outer raceway and inner raceway, respectively; The effects of radial force and torque on contact and stiffness characteristics are consistent basically in the corresponding direction; The influences of axial force and rotating speed on the contact and stiffness characteristics are more remarkable compared with other factors. The investigations of contact and stiffness characteristics of angular contact ball bearing with waviness are helpful for the designation and manufacture of high precision angular contact ball bearing.