High-speed Angular Contact Ball Bearings Research Articles

Optimization of high-speed angular contact ball bearing for aircraft gearbox utilizing an evolutionary multi-objective algorithm, NSGA-III

We develop a program for predicting bearing performance, including the maximum contact stress, bearing power loss, minimum lubricating film thickness, static safety factor, and dynamic life, and an optimal design for high-speed angular contact ball bearings in aircraft gearboxes using optimization algorithms. A program is developed to predict bearing performance by calculating the loads and displacements of individual balls based on the bearing’s kinematic and static equilibrium equations. Next, an optimization program is developed with non-dominated sorting genetic algorithm III (NSGA-III), wherein calculated bearing performance indicators serve as constraints or objective functions. The performance of individuals within the final Pareto front is evaluated using the inter-criteria correlation (CRITIC) and weighted product methods. The optimization performances of NSGA-III and NSGA-II are compared based on their hypervolume indicators. A solution of the kinematic and static equilibrium equations under the load cases and duty cycles of real aircraft gearboxes is obtained, enhancing the prediction accuracy. Furthermore, optimization, including bearing performance metrics rarely considered in previous studies, is performed. Optimal specifications superior to reference bearings employed in aircraft gearboxes are obtained, enhancing all three objective functions or specific objective functions. The optimization performance of NSGA-III is confirmed to surpass that of conventional NSGA-II.

Dynamic characteristics of high-speed angular contact ball bearings considering the coupling of outer race waviness and local defects

This paper proposes a novel four degrees of freedom model of angular contact ball bearings (ACBBs) under high-speed effect, in order to characterize the dynamic behavior of rolling bearings with coupling waviness and local defects on the outer race in detail. Firstly, based on bearing quasi-static model, considering centrifugal force, gyroscope moment, the bearing contact stiffness is calculated. Then, the representation model of outer race waviness and the time-varying displacement excitation expression of the bearing with local defects are put forward respectively. On the basis, a dynamic model of ACBBs with coupling factors is built. Finally, the vibration characteristics of the bearing with faults are investigated, the model is verified by the existing experimental results and the influence of different parameters on the bearing dynamics is analyzed. The results show that the bearing fault characteristic frequency is unchanged when the high-speed effect is considered, but the vibration amplitude is smaller than that without the high-speed effect. With the increase of speed, the bearing fault characteristic frequency and vibration amplitude increase. When considering the coupling of outer race waviness and local defects, with the increase of the two factors, the bearing fault characteristic frequency remains unchanged but the vibration amplitude increase.

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.

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 Temperature Prediction on High-Speed Angular Contact Ball Bearings of Machine Tool Spindles Based on CNN and Informer

This study addressed the issues related to the difficulty of determining the operating status of machine tool spindle bearings due to the high rotational speeds and rapid temperature fluctuations. This paper presents an optimized model that combines Convolutional Neural Networks (CNNs) and Informer to dynamically predict the temperature rise process of bearings. Taking the H7006C angular contact ball bearing as the research object, a combination of experimental data and simulations was used to obtain the training dataset. Next, a model for predicting the temperature rise of the bearing was constructed using CNN + Informer and the structural parameters were optimized. Finally, the model’s generalization ability was then verified by predicting the bearing temperature rise process under various working conditions. The results show that the error of the simulation data source model was less than 1 °C at steady state; the temperature error of the bearing temperature rise prediction model was less than 0.5 °C at both the temperature rise and steady-state stages under variable rotational speeds and variable load conditions compared to Informer and Long Short Term Memory (LSTM) models; the maximum prediction error of the operating conditions outside the dataset was less than 0.5 °C, and the temperature rise prediction model has a high accuracy, robustness, and generalization capability.

Dynamics-Based Thermal Analysis of High-Speed Angular Contact Ball Bearings with Under-Race Lubrication

The paper mainly studied the temperature rise characteristics of under-race lubricated high-speed angular contact ball bearings under operational conditions from the perspective of dynamics. The steady-state calculation model of the bearing was established using a thermal network method in consideration of the influence factor of friction power consumption in bearing components based on a dynamic model. Following this, the steady-state change characteristics of the bearing were obtained by solving a thermal balance equation. Through this process, the influence laws of bearing rotation speed, oil supply, and environmental temperature on the friction temperature rise of the bearing were analyzed. Finally, the finite element analysis software ANSYS was employed to provide comparative verification. The results showed that the bearing temperature nonlinearly increased with the increase in inner ring rotation speed, and when it approached a certain critical value, the outer ring temperature exceeded the inner ring temperature. It had an obvious effect on controlling the temperature rise of the bearing inner ring by way of increasing the quantity and reducing the temperature of the lubricating oil supply. Comparative verification showed that the speed–temperature variation tendency from the dynamics-based thermal analysis well agrees with that of the finite element analysis.

A numerical study of fatigue life in high-speed angular contact ball bearings with thermal and centrifugal expansion

PurposeFix-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.Design/methodology/approachThe 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.FindingsUnder 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.Originality/valueThis study revealed the influence of thermal and centrifugal expansion on the fatigue life of angular contact ball bearings in high-speed service conditions.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2023-0065/

Fault dynamic model of high-speed rolling bearing by a compound displacement excitation function considering the effect of defect roughness

Most of bearing fault dynamic models use simple displacement excitation functions to characterize the fault excitations from defects, and do not consider the influence of high-speed, dynamic radial clearance and transmission path, which brings the simulation signal a big gap with the measured signal. To solve these issues, this paper proposes a compound displacement excitation function by considering the influence of defect roughness, then constructs a new fault dynamic model of high-speed angular contact ball bearing (ACBB) by using the proposed displacement excitation function and introducing the effects of high-speed, dynamic radial clearance and transmission path. The proposed ACBB fault dynamic model is numerically solved for obtaining the dynamic responses under different fault sizes and speeds, then their characteristics in time and frequency domains are analyzed. The comparative results indicate that the simulation signals generated by the proposed model are closer to the measured signals, compared with those obtained by the typical bearing fault dynamic models. Finally, the correctness and superiority of the proposed model are verified by the experiments on faulty high-speed ACBBs.

Simulation sudden oil supply in starved high-speed angular contact ball bearing

Many high-speed angular contact ball bearings work without sufficient lubrication in the contact area. A dynamic model including starved thermo-elastohydrodynamic lubrication (TEHL) was proposed to investigate starved ball bearings. For the bearings subjected to axial and radial loads, the inlet film thickness suddenly increases, the friction coefficient drops rapidly, and the ball skids severely as it passes through the low load region. When the location of the change occurs in the low load region, the degree of skidding is significantly reduced. Furthermore, the outer contact zone mainly determines whether or not to skid. Therefore starved high-speed bearings need to avoid a sudden increase in the inlet film thickness in the outer contact zone.

Modelling and Analysis of High-Speed Angular Contact Ball Bearing

Angular contact bearings are of primal importance in accommodating rotational mechanisms with high-speed characteristics. Their applications are centric to heavy axial and radial loads sustaining thrust loads to a single direction. In high-speed applications, factors such as centrifugal force, gyroscopic moments and relative displacements in various geometric features of the bearings are to be taken into consideration. This study focuses on establishing the contact angles, contact forces and spin speed for angular contact bearing to withstand varied rotational angular velocities. The forces experience a non-linear variation with respect to the body stiffness thus necessitating the involvement of numerical methods to converge at precise solutions through each juncture. The outer raceway of the bearing is accepted to be static with respect to the inner raceway as the input shaft for any application is predominantly affixed to the inner raceway of the angular contact bearing. Geometrical variations are determined under combined load conditions to simulate the natural working of the bearing at accelerated speeds. The analyses involve results for spatial parameters which are iteratively solved for each of the rolling elements in the bearing taken into concern. The spin speeds of the rolling elements are shown to dampen and exponentially increase with respect to their angular positions. The outputs manifested through this work can be utilized to accurately predict shift of salient design attributes of an angular contact bearings through low and high-speed applications.

Simulation of the load reduction process of high-speed angular contact ball bearing with coupling model of dynamics and thermo-elastohydrodynamic lubrication

The transient process can be accurately simulated using a dynamic ball bearing model. This paper proposed a dynamic model including thermo-elastohydrodynamic lubrication (TEHL) to investigate high-speed angular contact ball bearings. In this model, TEHL considering the spinning and the non-Newtonian effect was used to calculate the contact force and the friction force. The results showed that the gyroscopic moment of the ball increased in conjunction with a higher load when the axial load remained constant. Furthermore, the sliding speed and film temperature increased significantly in conjunction with a sudden decrease in the axial load from 800 N to 400 N in 3 ms due to an abrupt decline in the friction moment, while the gyroscopic moment was delayed.

Thermal-mechanical fully coupled analysis of high-speed angular contact ball bearings

The thermal and mechanical properties of angular contact ball bearings are critical to their operating accuracy and service life. On the basis of the theory of dynamics and frictional heat generation, this work establishes a thermal-mechanical fully coupled model. The high-speed motion characteristics, temperature, and dynamic stiffness are analyzed, and the simulation results are compared with the theoretical calculation and experimental results. Then, the temperature and axial deformation of the bearings under different rotation speeds are analyzed, and the laws of mechanical and thermal characteristics of the bearings are obtained. Results show that an increase in the rotation speed of the inner ring causes the temperature of each component to increase, with the contact area of the balls showing the greatest increase in temperature. An increase in rotation speed also increases the axial deformation of the inner ring.

Numerical Investigation of the Heat-Fluid Characteristic inside High-Speed Angular Contact Ball Bearing Lubricated with Grease

The development of special grease makes it possible for angular contact ball bearings to operate at high speed and temperature, so, it become necessary to investigate thermal-fluid characteristics inside high-speed angular contact ball bearing lubricated with grease. In this paper, a simulation model for angular contact ball bearing was established with CFD software Fluent, the heat-fluid-solid coupling method was used to analyze the distribution and flow of grease, heat transfer, and temperature field inside the bearing chamber. The results show that, grease distribution inside bearing chamber was very inhomogeneous, most of grease was distributed on the both sides of the rolling elements along outer raceway and its flow velocity was very low, only a little grease was adhered on the surface of roll-ing elements, cage, and inner ring, its flow velocity was high; grease distribution inside bearing chamber becomes more inhomoge-neous with the increase of bearing speed; in bearing heat transfer conduction was dom-inant and grease plays a key role, convec-tion of air and grease was insignificant; affected by heat transfer condition the temperature rise of bearing components was obviously different, rolling elements have the highest temperature, the tempera-ture of inner ring was slightly lower than that of rolling elements, temperature of outer ring was the lowest. Bearing tempera-ture experiment was conducted on self-made test rig and verified the validity and accuracy of numerical simulation. The results of this study will provide some reference for lubrication design and thermal analysis of high speed angular contact ball bearing lubricated with grease.

Study on Simplified Model and Numerical Solution of High-Speed Angular Contact Ball Bearing

For the calculation model of high-speed angular contact bearing has many variables, the large root difference exists, and the Newton iterative method solving the convergence depends on the initial value problems; thus, the simplified calculation model is proposed and the algorithm is improved. Firstly, based on the nonlinear equations of variables recurrence method of the high-speed angular contact ball bearing calculation model, it is proved that the ultimate fundamental variables of calculation model are the actual inner and outer contact angles, the axial and radial deformations. According to this reason, the nonlinear equations are deformed and deduced, and the number of equations is reduced from 4Z + 2 to 2Z + 2 (Z represents the number of rolling bodies); a simplified calculation model is formed. Secondly, according to the small dependence of the artificial bee colony algorithm on the initial value, an improved artificial bee colony algorithm is proposed for the large root difference characteristics of high-speed ball bearings. The validity of the improved algorithm is verified by standard test function. The algorithm is used to solve the high-speed angular contact ball bearing calculation model. Finally, the deformations of high-speed angular contact ball bearings are compared and verified by experiments, and the results of improved algorithm show good agreement with the experiments results.

Effect of structure and assembly constraints on temperature of high-speed angular contact ball bearings with thermal network method

The thermal performances of high-speed angular contact ball bearings have not been thoroughly addressed so far. The effect of contact angle on the thermal expansion and deformation of bearings was not fully considered. Meanwhile the influence of substructures on heat exchange, especially the assembly constraints and cooling/lubrication systems significantly impacting bearing temperature were not well characterized. Again, the heat transfer of various bearing's sub sources based on different heat generation mechanisms was seldom discussed independently. In this paper, the influence of contact angle on thermal deformation was first factored into the force equilibrium of angular contact ball bearings to calculate the bearing loads and then heat generation, and the heat generation and transfer of each sub heat source were detailed. Next, the lubricant, radial/axial structural constraints and assembly relations between parts were fully analyzed in affecting bearing temperature. The heat exchange of cooling unit was modeled and the equivalent size of coolant passage was determined to facilitate the thermal estimation. On these bases, an integrated comprehensive thermal grid model for a pair of front bearings of high-speed spindle and their surroundings was developed to forecast the temperature rise of bearings. Finally, the bearing temperature variation, for the purpose of validation, was tested and compared with the corresponding numerical solutions. As a result, the bearing temperature can be better forecasted when using the developed model.

A novel model for high-speed angular contact ball bearing by considering variable contact angles

In this study, on the basis of the various contact angles and the hybrid theory, a new mathematic model without the raceway control hypothesis is proposed for the analysis of ball bearing under the combined axial, radial and moment loads. Instead of the orthogonal decomposition method, the triangular geometric theorem and vector diagram method have been used in the force analysis of local ball to improve the computation efficiency of bearing analysis. For validation purpose, the comparative analysis of the ball-raceway contact angles and loads of ball bearing under different operation conditions obtained by the proposed model and the Jones’ model with different raceway control hypotheses has been conducted. The results show that the proposed model has a higher applicability and rationality compared to the Jones’ model, and a proper moment load can be used to improve the load distribution and service performance of ball bearing subjected to the radial load.

Effect of vibration on power loss of angular contact ball bearings

PurposeThis paper aims to devote to the experimental analysis and modeling on the heat generation of angular contact ball bearings under vibration.Design/methodology/approachThe 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.FindingsThe 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.Originality/valueThe 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.

A fault dynamic model of high-speed angular contact ball bearings

Angular contact ball bearings (ACBBs) are widely used in rotary machines especially in high-speed rotating machines because of their excellent properties. However, the traditional dynamic model of a rolling bearing is mainly applied to simulate the dynamic response at low speed, and uses the simple displacement excitation function to characterize the fault, thus its accuracy will decrease under high speed condition. Aiming at the shortcomings of the traditional model, a new high-speed fault dynamic model of ACBB is proposed by considering the influences of centrifugal force, gyroscopic moment and time-varying contact angles on the rolling element under high-speed running and using a B-spline fitting displacement excitation method to represent the fault excitation. With this model, high-speed dynamic responses under different fault sizes and rotation speeds are calculated by the Runge–Kutta method and Newton– Raphson method. Then the corresponding time and frequency domain characteristics are analyzed. From the simulation results, it can be seen that all the simulated acceleration signals of ACBBs are more in line with the actual situation than the traditional model, especially for the shape of an impulse. Finally, the effectiveness and correctness of the proposed model are verified by the experiment on aero-engine spindle bearings.

Temperature Rise Prediction of Oil-Air Lubricated Angular Contact Ball Bearings Using Artificial Neural Network

Background: Angular contact ball bearing is an important component of many high-speed rotating mechanical systems. Oil-air lubrication makes it possible for angular contact ball bearing to operate at high speed. So the lubrication state of angular contact ball bearing directly affects the performance of the mechanical systems. However, as bearing rotation speed increases, the temperature rise is still the dominant limiting factor for improving the performance and service life of angular contact ball bearings. Therefore, it is very necessary to predict the temperature rise of angular contact ball bearings lubricated with oil-air. Objective: The purpose of this study is to provide an overview of temperature calculation of bearing from many studies and patents, and propose a new prediction method for temperature rise of angular contact ball bearing. Methods: Based on the artificial neural network and genetic algorithm, a new prediction methodology for bearings temperature rise was proposed which capitalizes on the notion that the temperature rise of oil-air lubricated angular contact ball bearing is generally coupling. The influence factors of temperature rise in high-speed angular contact ball bearings were analyzed through grey relational analysis, and the key influence factors are determined. Combined with Genetic Algorithm (GA), the Artificial Neural Network (ANN) model based on these key influence factors was built up, two groups of experimental data were used to train and validate the ANN model. Results: Compared with the ANN model, the ANN-GA model has shorter training time, higher accuracy and better stability, the output of ANN-GA model shows a good agreement with the experimental data, above 92% of bearing temperature rise under varying conditions can be predicted using the ANNGA model. Conclusion: A new method was proposed to predict the temperature rise of oil-air lubricated angular contact ball bearings based on the artificial neural network and genetic algorithm. The results show that the prediction model has good accuracy, stability and robustness.

Determination of Optimum Preload Considering the Skidding and Thermal Characteristic of High-Speed Angular Contact Ball Bearing

Skidding is a typical behavior of high-speed angular contact ball bearings. Studies show that the effect of preload on bearing skidding and thermal characteristic is essential but insufficient. This paper proposed a comprehensive mathematic model to predict the skidding behavior of ball bearing, and the influences of the interactions between ball and raceways, cage and lubricant have been taken into consideration. Based on the proposed model, the bearing heating generation was calculated and the effects of skidding on bearing heating and temperature rise were analyzed. For validation proposes, a hydraulic variable preload experimental setup has been built, and the temperature rise of bearing outer rings under different preloads and speeds was collected and analyzed. The results indicated that at high speeds, the skidding has a significant negative effect on bearing temperature rise, and a proper preload can effectively prevent skidding and decrease temperature rise. Therefore, for a high-speed spindle-bearing system, an optimum preload that produced the minimum temperature rise can be obtained.