Angular Contact Ball Research Articles

Reliability optimization design of deformation of CNC lathe spindle considering thermal effect

Angular contact ball bearings are widely used in the field of rotating machinery due to their obvious advantages such as relatively good positioning accuracy, high speed rotating performance and low cost, which have already become the most important transmission components. The heterogeneous thermal deformation caused by the high speed effect of bearing parts will lead to excessive noise and even gluing, which can further significantly reduce the machining accuracy of machine tool. Therefore, it is vital to improve the deformation resisting capability and operational reliability of the whole system. For this purpose, this paper presents a reliability model for computerized numerical control (CNC) lathe spindle by considering thermal effect. A five-degree-of-freedom quasi-static model considering thermal deformation is firstly proposed to calculate contact load and contact angle. Then the transient thermal network method is used to solve the temperature value of multi-node spindle-bearing system, and the validity of the proposed model is verified by experiments at different speeds. Next the modified first-order and second-moment method (FOSM) is used to calculate the reliability and reliability sensitivity of CNC lathe spindle deformation model considering thermal effect. Finally, the constrained nonlinear optimization method for the reliability model is proposed and applied to CNC lathe spindle. The results show that the reliability of the optimized model is significantly improved and the reliability robustness is enhanced.

Mixed lubrication of coated angular contact ball bearing considering dynamic characteristics

AbstractA mixed elastohydrodynamic lubrication (EHL) model for a coated angular contact ball bearing is developed by coupling the influence coefficients with the unified deterministic mixed EHL model. Based on the bearing quasi‐dynamics analysis, the influences of the surface roughness, coating thickness, and boundary friction coefficient on the mixed EHL performance of the coated bearing are discussed. The results reveal that high surface root‐mean‐square roughness can be detrimental to bearing lubrication performance and increase the risk of coating failures. Coating thicknesses on the order of a few microns have a limited effect on the contact load ratio, film thickness ratio, and friction coefficient while having a significant effect on the maximum surface tensile stress and interfacial shear stress, especially for high‐friction low‐speed conditions. A low‐friction self‐lubricating coating can effectively improve the tribological performance and prolong the service life of the bearing, especially in the bad lubrication state with severe asperity contacts.

A combined acoustic and dynamic model of a defective ball bearing

Due to their special characteristics, angular contact ball bearings (ACBBs) are broadly applied in various mechancial systems. The working performance of rotating machinery can be determined by the internal ACBBs. Vibration and acoustic characteristics of ACCBs in various rotating machinery are becoming increasingly significant for the high-performance mechanical systems. An in-depth recognition of acoustic characteristics of ACBB can be helpful for condition monitoring of rotating machinery. This study proposes an improved dynamic model of ACBB to consider the influences of elastic hysteresis, differential sliding friction torques, and elastohydrodynamic lubrication (EHL) rolling on the ball motion state. A modified time-dependent excitation (TDE) model is developed for describing different kinds of defects in the outer ring of ACBB. The acoustic emission models given by Sharma [8] and Patil [9] are extended to describe more degrees of freedom of ACBB. Effects of speed, load, and defect sizes on the acoustic characteristics for ACBB are investigated. Comparison results between the proposed and reported models depict the superiority of established approach here. Note that the load, speed, and defect can greatly affect the acoustic characteristics of ACBB. The results improved that this model has ability to obtain the accurate acoustic characteristics of a defective ACBB.

Research on the influence of air-gap eccentricity on the temperature field of a motorized spindle

Abstract. The air-gap state between the stator and rotor is an important indicator to measure the performance of a motorized spindle. It affects the temperature field distribution of the motorized spindle and the machining accuracy of the mechanical parts. Since the accurate thermal model is the basis of the research on the temperature field distribution of the motorized spindle, in this paper, firstly, the mechanical loss, electrical loss and magnetic loss of the motor under different air-gap eccentricities are calculated and the heat-generating power of an angular-contact ball bearing is obtained based on Harries contact theory. Secondly, the thermal model of the motorized spindle is established and the steady-state temperature field of the motorized spindle is simulated by using ANSYS, and the influence of air-gap eccentricity on the temperature field of the motorized spindle is discussed. Finally, the circumferential temperature field distribution of the motorized spindle with the air-gap eccentricity is verified by experiment. The results show that the air-gap eccentricity has a significant influence on the non-uniform temperature field of the motorized spindle.

Study on Stiffness of Angular Contact Ball Bearing and Its Evolution Rule under Excessive Preload

There are many factors influencing the bearing stiffness variation, among which, preload has more significant effect. In addition, bearing stiffness is developing accompanying with its performance deterioration, which leads to vibration variation of bearing-rotor system. In this paper, system support stiffness model and system dynamics model of micro-turbine bearing-rotor system test rig are built to obtain the bearing stiffness identification method by model simplification based on modal theory. The identification method is validated adopting modal test. The stiffness evolution rule and rotor vibration of different stages are achieved via employing the identification method to extract bearing stiffness over the process of bearing run-to-failure. The results indicate that bearing stiffness is the main source of system support stiffness. Bearing stiffness will change during the whole life, which affects the vibration responses in time and frequency domain. Rotor stability is influenced by cage movement.

Analysis of cage slip in angular contact ball bearing considering non-Newtonian behavior of elastohydrodynamic lubrication

A dynamic model of angular contact ball bearing considering non-Newtonian behavior and interaction between balls and cage is deduced to predict cage slip. And then the cage slip are investigated and compared with measured results under different rotational speeds and axial loads to verify the proposed dynamic model of bearing. It is concluded that the results based on the non-Newtonian behavior of elastohydrodynamic lubrication is more agreement in trend with the tests than that based on the Newtonian assumption, and so the non-Newtonian behavior of elastohydrodynamic lubrication are needed in the cage slip analysis.

Nonlinear dynamic force transmissibility of a flywheel rotor supported by angular contact ball bearings

The dynamic force transmissibility (DFT) of aerospace flywheel rotor system (FRS) supported by angular contact ball bearings (ACBBs) is examined in this paper. The influence of combined loads and contact angle variation is considered in the Sjovall formula to accurately solve the load distribution and nonlinear stiffness of ACBB. Subsequently, the lateral vibration model of FRS is established by considering the nonlinear stiffness characteristics of ACBB. The DFT of the system is solved via harmonic balance method and arc length continuation, and the stability of the results is determined. Numerical integration and dynamic tests are utilized to verify the accuracy of harmonic balance results. Based on the proposed model, the effects of rotor unbalance excitation, axial preload, and rotor damping on the DFT of the system are discussed. The soft-stiff transition phenomenon is observed in terms of the varying supporting stiffness of ACBB wherein deformation is measured under axial preload. The value of rotor unbalanced mass determines the nonlinear characteristics of FRS. The results provide an important reference for dynamic performance evaluation and vibration isolation device design of aerospace FRS.

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.

An analysis of a thermally affected high-speed spindle with angular contact ball bearings

This paper discusses thermal effects on bearing stiffness, and consequently, the natural frequencies of a high-speed spindle system. Heat is generated due to friction torque at the contacts between the raceways and the balls of the angular contact ball bearings. In our experimental spindle system, the heat sources included six bearings and a built-in motor. Five-by-five bearing stiffness matrices were computed based on the thermal-mechanical parameters. The stiffness matrices were used as inputs for a finite element model generated in the ANSYS Workbench environment, in which the bearings were simulated as bushing joints, to compute frequency response numerically. The simulated results showed that the third natural frequencies decreased with increasing temperature and were in good agreement with the experimentation.

Effect of boundary position and defect shape on the mechanical properties of ball bearings

This paper presents a mechanical model of angular contact ball bearing with local and extended defects in the outer raceway and the analytical formulations of varying stiffness under combined loads are obtained. The effects of radial load and clearance on variable stiffness of the bearing at the boundary positions are analyzed. Results show that the load distribution is not necessarily continuous and the maximum and minimum stiffness of the angular contact ball bearing can be located at either of the two boundary positions or even at non-boundary position under the effect of the contact angle. Meanwhile, the effects of defect depth and loads on the mechanical properties and varying stiffness of the bearing under localized and extended defects are studied, respectively, and the mechanism of “limit depth” and “critical load” is analyzed. These results are useful for quantitative fault diagnosis and reliability analysis of rotor-bearing systems.

A comprehensive study on the off-diagonal coupling elements in the stiffness matrix of the angular contact ball bearing and their influence on the dynamic characteristics of the rotor system

This paper not only presents the details of the composition form and classification method of the elements in bearing stiffness matrix, but also reveals the effects of the off-diagonal stiffness items in bearing stiffness matrix on the rotor dynamic characteristics. First, the complete expression of bearing stiffness matrix is derived based on the improved model of ball bearing, and the change rules of the different categories of the stiffness elements with the rotating speeds and loads are given. Then, both the quantitative and qualitative analysis methods for the rotor-bearing systems supported by a pair of the angular contact ball bearings are presented, and the effects of the off-diagonal bearing stiffness elements on the rotor supporting stiffness and natural frequencies are given and discussed. The results show that, when the rotor system is subjected to a radial load or moment load, the additional loads from ball bearings are generated due to the off-diagonal stiffness elements in bearing stiffness matrix, and the rotor with the O-configuration has higher supporting stiffness and resonance frequencies than the rotor with the X-configuration.

Wear Analysis of Angular Contact Ball Bearing in Multiple-Bearing Spindle System Subjected to Uncertain Initial Angular Misalignment

Abstract The effects of the uncertainty of angular misalignment on the wear of angular contact ball bearings in the spindle system are investigated. The wear model of bearing raceways is derived based on the Archard model. The angular misalignment caused by mounting error is assumed to comply with normal distribution, Monte Carlo method is used to extract the angular misalignment sample. Based on the spindle system model, the spinning speed, pitch angle, and contact force of ball elements in each angular contact ball bearing are calculated. The wear depth of bearing raceways is analyzed. The results show that the uncertainty of the initial angular misalignment leads to significant dispersion of wear depth of ball bearings, but the dispersion degree is related to spindle speed, angular misalignment cases, and bearing mounting position. Increasing the spindle speed increases the wear depth but decreases the wear depth dispersion.

Tilt error correction of minitype theodolite’s vertical shaft based on angular contact ball bearings

Tilt error correction of minitype theodolite’s vertical shaft based on angular contact ball bearings

Research on Prediction of Temperature Rise of High Speed Angular Contact Ball Bearing Considering Interaction between Contact Parameters and Friction Heat

Research on Prediction of Temperature Rise of High Speed Angular Contact Ball Bearing Considering Interaction between Contact Parameters and Friction Heat

Research on comprehensive stiffness characteristics of angular contact ball bearings under multi-factor coupling condition

In order to research the dynamic performance of angular contact ball bearings of high-speed motorized spindles in detail, based on Hertz contact theory and bearing quasi-static model, considering the influence of centrifugal force, gyroscope moment and thermal effect on bearing operation, the modified quasi-static model is established to calculate the bearing contact stiffness. Then, considering the influence of temperature on the dynamic viscosity of lubricating oil, film stiffness model of bearing is also presented. On the basis, the bearing comprehensive stiffness model is proposed, and the influences of combined load and rotational speed on the bearing stiffness are investigated. The results show that as the speed increases, the radial contact stiffness increases, while the axial and angular contact stiffness decrease, the dynamic viscosity of the lubricating oil decreases, the film stiffness decreases and the comprehensive radial, axial and angular stiffness decrease. With the increase of axial load, the radial, axial and angular contact stiffness increase, the comprehensive stiffness increases. When the radial load increases, the radial, axial and angular contact stiffness decreases, while the comprehensive stiffness increases. It is found that the comprehensive stiffness considering the temperature is larger than without consideration of the temperature.

Analyzing Vibration Mechanism of Angular Contact Ball Bearing with Compound Faults on Inner and Outer Rings

This paper investigates a method to dynamically model compound faults on the inner and outer rings of an angular contact ball bearing as well as their effects on its dynamic behavior. Gupta’s dynamic modeling method is used to consider changes in the deformation and direction of the contact load when the ball passes through the damaged area and to develop a dynamic model of compound faults in the angular contact ball bearing. The step‐changing fourth‐order Runge–Kutta method is used to solve the dynamic compound fault model. The time‐domain signal of vibration responses in the case of a single fault in the inner and outer rings exhibited a certain periodicity, and the frequency of faults in the envelope spectrum was clear. By comparison, the periodicity of compound faults was not clear. The signals of compound faults were decomposed by the dual‐tree complex wavelet transform to identify their characteristic frequency. Errors occurred between the characteristic frequency of the theoretical fault and its simulated value. They increased with the rotational speed and decreased with an increase in axial load, whereas the influence of radial load on them was minor. For compound faults on the inner and outer rings of an angular contact ball bearing, this study provides a modeling method that can describe changes in the deformation and direction of the contact load when the ball passes through the damaged area of the inner and outer rings. The work here can provide an important foundation for fault identification in angular contact ball bearings.

White Etching Bands Formation Mechanisms Due to Rolling Contact Fatigue

White etching bands (WEBs), known as subsurface micro-structural changes in bearing steels due to cyclic stresses in rolling contacts, have been studied for decades and a number of theoretical models have been proposed to explain their formation mechanisms and predict their initiation. While many studies focus only on one subtype of WEBs, e.g. low angle bands (LAB) or high angle bands (HAB), the most recent semi-empirical model has shown to be able to predict the formation of both LAB and HAB based on observed growth patterns of ferrite grains. Following from the modelling study, this paper presents a detailed mechanistic study, showing the evolution of ferrite grains (equiaxed and elongated grains) and carbide structures in WEBs formed in inner rings of angular contact ball bearings at their different life stages through SEM, EBSD and nano-indentation analysis. The results strongly suggest both LAB and HAB initiate as equiaxed ferrite grains due to recrystallization arising from energy build-up in the initial microstructure that later develops to elongated ferrite grains due to a grain rotation/coalescence recovery mechanism induced from plastic deformation. The formation of carbide structures in LAB is associated with the transformation of equiaxed to elongated grains, where carbides nucleate at the edges of the elongated grains rather than at the equiaxed grain band edges as being previously suggested in literature. The newly proposed formation mechanism links LAB and HAB based on experimental findings from detailed inspection of gradual microstructural alteration sequence of LAB and HAB in rolling contact fatigue (RCF) tested bearings.

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.

Temperature rise characteristics for angular-contact ball bearings with oil-air lubrication based on fluid-solid conjugate heat transfer

At present, the thermal analysis of oil-air-lubricated angular-contact ball bearings uses empirical heat transfer coefficients to calculate heat transfer. This approach presents problems such as simulating the actual lubrication flow field and ignoring the internal heat conduction in the bearing ring. This paper proposes a CFD steady-state analysis model of oil-air-lubricated angular-contact ball bearings based on fluid-solid conjugate heat transfer to analyze the flow field and temperature field. A temperature rise test of oil-air-lubricated angular-contact ball bearings was carried out to verify the positive determination of the simulation analysis results. Based on a fluid-solid conjugate heat transfer steady-state analysis model, the effects of lubrication parameters, operating conditions, and rolling element materials on the temperature rise characteristics of oil-air-lubricated angular-contact ball bearings were studied. The research results provide a method for analyzing the temperature rise characteristics of oil-lubricated bearings and provide a basis for the analysis of oil-lubricated bearing life.

MANAGING TARGET COSTS AT THE DEVELOPMENT STAGE OF A PRODUCT

At the development stage of a product, target cost management has a significant effect on achievement and maintenance of product competitiveness in a given market and the desired target profit as the primary aim of production. Target cost management, i.e., target profit management, is performed by evaluating individual variations of a conceptual and preliminary design solution for a new product and by choosing the solution with the lowest development costs. The paper presents the use of Adaptive Neural Fuzzy Inference System model for managing development costs on the example of double-row angular contact ball bearings as an example of applying the above approach to market positioning in relation to competitors.