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The purpose of this paper is to analyze the force and basic rating life of angular contact ball bearings of RV reducer under the actual operating condition.

Force analysis of angular contact ball bearing under the actual operating condition, calculate the axial, radial load and internal load distribution, calculate the basic rating life of angular contact ball bearing under variable load conditions.

The external load has a great influence on the radial load of angular contact ball bearing, further affecting the basic rating life of angular contact ball bearing, which is a great influence on the overall life of RV reducer under the condition of high frequency and heavy load.

This paper provides important ideas for the design and manufacture of RV reducer in theory and experiment technology.

Thermal performances are key factors impacting the operation of angular contact ball bearings. Heat generation and transfer about angular contact ball bearings, however, have not been addressed thoroughly. So far, most researchers only considered the convection effect between bearing housings and air, whereas the cooling/lubrication operation parameters and configuration effect were not taken into account when analyzing the thermal behaviors of bearings. This paper aims to analyze the structural constraints of high-speed spindle, structural features of bearing, heat conduction and convection to study the heat generation and transfer of high-speed angular contact ball bearings.

Based on the generalized Ohm’s law, the thermal grid model of angular contact ball bearing of high-speed spindle was first established. Next Gauss–Seidel method was used to solve the equations group by Matlab, and the nodes temperature was calculated. Finally, the bearing temperature rise was tested, and the comparative analysis was made with the simulation results.

The results indicate that the simulation results of bearing temperature rise for the proposed model are in better agreement with the test values. So, the thermal grid model established is verified.

This paper shows an improved model on forecasting temperature rise of high-speed angular contact ball bearings. In modeling, the cooling/lubrication operation parameters and structural constraints are integrated. As a result, the bearing temperature variation can be forecasted more accurately, which may be beneficial to improve bearing operating accuracy and bearing service life.

Fix-position preloading, centrifugal force and higher temperatures cause the bearing units in angular contact ball bearings to expand, changing the contact load and affecting bearing life. This study aims to examine the effect of thermal and centrifugal expansion on the fatigue life of fix-position preloaded angular contact ball bearings in high-speed operating conditions.

The contact loads on the inner and outer bearing rings were resolved according to the thermal and centrifugal expansion factors in the quasi-static position preloading model. The pressure and frictional stress distribution were used to calculate the subsurface stress in the contact area, while the Zaretsky model was used to determine the relative fatigue life of the inner and outer bearing rings.

Under fix-position bearing preloading, thermal and centrifugal expansion significantly affected the contact load and relative fatigue life. At the same axial preload, the inner ring contact load was higher than the outer ring contact load, with a maximum difference of 132.3%. The decrease in the inner ring relative life exceeded the outer ring contact load, with a maximum difference of 7.5%, compared to the absence of thermal and centrifugal expansion.

This study revealed the influence of thermal and centrifugal expansion on the fatigue life of angular contact ball bearings in high-speed service conditions.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2023-0065/

The purpose of this paper is to clarify the relationship between fatigue life and kinematics of angular contact ball bearing. It proposes a new modeling method of spin to roll ratio based on raceway friction, which is more accurate than the traditional raceway control theory.

The uniform model of spin to roll ratio based on raceway friction in a wide speed range is proposed using quasi-statics method, which considers centrifugal force, gyroscopic moment, friction force of raceway and other influencing factors. The accuracy is considerably improved compared with the static model without increasing too much computation.

A uniform model for spin to roll ratio of angular contact ball bearing based on raceway friction is established, and quite different relationships between fatigue life and speed under two operating conditions are found.

The conclusion of this paper is based on the bearing basic fatigue life calculation theory provided by ISO/TS 16281; however, the accuracy of theory needs to be further verified.

This paper provides guidance for applying angular contact ball bearing, especially at a high speed.

This paper reveals the changing trend of fatigue life of angular contact ball bearing with the speed under different loads.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-01-2020-0030

Under fix-position preload, the high rotation speed of the angular contact ball bearing exacerbates the frictional heat generation, which causes the increase of the bearing temperature and the thermal expansion. The high rotation speed also leads to the centrifugal expansion of the bearing. Under the thermal and centrifugal effect, the structural parameters of the bearing change, affecting the mechanical properties of the bearing. The mechanical properties of the bearing determine its heat generation mechanism and thermal boundary conditions. The purpose of this paper is to study the effect of centrifugal and thermal effects on the thermo-mechanical characteristics of an angular contact ball bearing with fix-position preload.

Because of operating conditions, elastic deformation occurs between the ball and the raceway. Assuming that the surfaces of the ball and channel are absolutely smooth and the material is isotropic, quasi-static theory and thermal network method are used to establish the thermo-mechanical coupling model of the bearing, which is solved by Newton–Raphson iterative method.

The higher the rotation speed, the greater the influence of centrifugal and thermal effects on the bearing dynamic parameters, temperature rise and actual axial force. The calculation results show that the effects of thermal field on bearing dynamic parameters are more significant than the centrifugal effect. The temperature rise and actual axial force of the bearing are measured. Comparing the calculation and the experimental results, it is found that the temperature rise and the actual axial force of the bearing are closer to reality considering thermal and centrifugal effects.

In the past studies, the thermo-mechanical coupling characteristics research and experimental verification of angular contact ball bearing with fix-position preload are not concerned. Research findings of this paper provide theoretical guidance for spindle design.

This paper aims to devote to the experimental analysis and modeling on the heat generation of angular contact ball bearings under vibration.

The experiments about vibration effect on bearing temperature are implemented. To explore the causes of bearing temperature rise, the shaft-bearing system is first simplified to a forced vibration model to analyze the bearing loads in vibration. Next, the vibratory-induced additional load is proposed and the spin power loss of balls is re-derived under vibration. The vibration-induced heat is integrated into a novel forecasting model of bearing power loss. For validation, the muti-node model for angular contact ball bearings is referred to create the thermal network of spindle front bearing, and then the contrast and discussion is done.

The simulation and test results both indicate that more energy is expended and more heat is generated with vibration. And the further quantitative comparisons between simulation results and experimental values of bearing temperature demonstrate the rationality and availability of constructed model on bearing heat generation.

The vibration-induced additional load is proposed and modeled, and the novel forecasting model for heat generation for high-speed angular contact ball bearings with vibration is constructed and validated.

For 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.

First, 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.

The 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.

To 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.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2023-0180/

The purpose of this paper is to research on optimization of spindle bearing preload based on efficiency coefficient method and provide theoretical guidance for variable preload of intelligent spindle.

Based on an established thermo-mechanical coupling model of angular contact ball bearing with fix-position preload, temperature rise and axial stiffness of the bearing at different speeds and preload are analyzed, and life of the bearing is estimated by the improved L-P theory. The bearing temperature rise, axial stiffness and life data are standardized, and the preload is optimized by the efficiency coefficient method according to the requirements of operating conditions.

The optimized preload meets comprehensive requirements of the bearing temperature rise, axial stiffness and life under different operating conditions.

In the past studies, it is rarely reported that temperature rise, stiffness and life of the bearing under thermo-mechanical coupling effect are used as objective functions to optimize preload at different speeds.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2020-0205/

The 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.

The 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.

The 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.

The 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.

The peer review history for this article is available at: http://dx.doi.org/10.1108/ILT-08-2023-0259

The purpose of this study is to investigate the dynamic behavior of the ball bearing with cage broken.

By analyzing the complicated relationship and interactions among the ball bearing elements, the dynamic modelling of the ball bearing with broken cage was established, and the dynamic simulations were conducted by solving the ball bearing dynamic equations using varying-step Runge–Kutta integration.

The computational results show that there is considerable distinguishment in the dynamic characteristics between the normal cage and the broken cage of the bears. The broken cage makes the trajectory of the cage erratic, and the vibration amplitude is much bigger than that of the normal cage, which makes the motion of the cage unstable. When one of the cage lintels breaks up, the two adjacent balls will collide with each other; what is worse, this may make the balls crush because of the high amplitude of the collision force. The broken cage makes the cage-race interaction force much larger than that of the normal cage, which could promote the guiding ring and quicken the cage wear-failure.

This study can provide important ideas for the fault identification of the ball bearing with cage broken.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-01-2020-0042/