This paper presents an improved formulation, to estimate the sliding friction torque of deep groove ball bearings (DGBBs). Running torque of rolling element bearings, is directly associated with heat generation in rotating machines. Among the components of running torque, sliding friction is a major friction source in ball bearings. For DGBBs, sliding friction is dominated by spinning and differential sliding between balls and races. This paper addresses the sliding friction torque components of DGBBs: Spinning friction, differential sliding friction due to the ball rotation, and differential sliding friction due to the ball orbital motion. An efficient and accurate computational method is proposed for the individual sliding friction sources, based on pure rolling lines in the elliptical contact area between the balls and races. The proposed method applies an updating algorithm, for estimating more accurate information about the pure rolling lines. The proposed method was validated in terms of comparison with other methods, and with the empirical formulae provided by a bearing manufacturer. Simulations were also conducted to investigate the impacts of important parameters on the sliding friction torque in DGBBs.
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Study on Thermo-mechanical Modeling and Analysis of High-speed Angular Contact Ball Bearings Under Oil-jet Lubrication Gilbert Rivera, Shinhyang Park, Chan-sik Kang, Dongjoo Kim, Seong-Wook Hong Journal of the Korean Society for Precision Engineering.2024; 41(7): 569. CrossRef
Analytical formulation for sliding friction torque in cylindrical roller bearings Gilbert Rivera, Patrick John Po, Chan-sik Kang, Seong-Wook Hong Journal of Mechanical Science and Technology.2024; 38(9): 4669. CrossRef
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Effect of Surface Roughness on the Friction Moment in a Lubricated Deep Groove Ball Bearing Harsh Kumar, Vaibhav Gupta, Velamala Bharath, Mayank Tiwari, Surajit Kumar Paul, Lokesh Agrawal, Arendra Pal Singh, Ayush Jain Lubricants.2024; 12(12): 443. CrossRef
Angular contact ball bearings (ACBBs) are widely used in rotating machinery due to their heavy load-carrying capacity and excellent accuracy in high-speed operation. However, employing an ACBB requires a careful analysis because the characteristics of the ACBB significantly depend on the operating condition. The ball-race contact condition of an ACBB is one of the most important factors that can change its properties. This study deals with the ball-race contact behavior concerning several important parameters, such as rotational speed, unloaded contact angle, and external loading. Between the ball and race under loading, an elliptical contact area is formed, in which pure rolling lines may exist. In the region other than the pure rolling lines, sliding dominates due to differential slippage in the elliptical contact area. We investigated the behavior of ball-race contact in terms of the pure rolling lines. A computational procedure was presented to determine the pure rolling lines. Through simulations, it was found that rotational speed, unloaded contact angle, axial preload, and radial load significantly affected the number and locations of pure rolling lines. The presented results are useful for investigating and estimating the sliding friction torque for ACBBs.
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Improved Formulation for Sliding Friction Torque of Deep Groove Ball Bearings Gilbert Rivera, Van-Canh Tong, Seong-Wook Hong Journal of the Korean Society for Precision Engineering.2022; 39(10): 779. CrossRef
This paper presents the characteristics of tapered roller bearings (TRBs) taking into consideration the effects of tapered roller angle error which may occur during manufacturing. To this end, a TRB model including tapered roller angle errors was developed. The effects of tapered roller angle error on the contact load distribution, bearing stiffness and fatigue life were investigated with respect to changes in the tapered roller angle error. A statistical analysis of the fatigue life of TRBs was also provided with respect to tapered roller angle error. Simulation results show that the tapered roller angle error changes the load distribution of the rollers and causes angular misalignment in TRBs, and subsequently, influences the bearing stiffness and fatigue life. The statistical analysis shows that the Weibull distribution is an acceptable method to represent the statistical fatigue life for the practical range of tapered roller angle errors.
This paper presents the effects of bearing locations on the mechanical characteristics of a multi-stepped spindle system related to bearing fatigue life, natural frequency, and static stiffness. The multi-stepped spindle is supported by a pair of tapered roller bearings (TRBs) and subjected to radial loading. To solve the equilibrium equation of the spindle system which is inherently statically-indeterminate, this study adopts an integrated shaft-bearing model, where the spindle is modelled by the finite shaft elements and the supporting TRBs are modelled by the five degrees-of-freedom TRB model developed by the authors. An iterative computational method is used to estimate the spindle deflection coupled with bearing deflections, and afterwards the bearing stiffness and internal contact loads of rolling elements are computed. The bearing fatigue life based on the ISO standard and the first natural frequency of the spindle system are evaluated with the spindle-bearing model. The influences of bearing locations on the static stiffness and natural frequency of the spindle, and the fatigue life of TRBs are rigorously investigated. The numerical results show the noticeable effects of bearing locations on the spindle system characteristics. The presented results provide a comprehensive assessment to aid for design optimization of spindle-TRB system.
The vibration analysis of flexible rotor systems supported by angular contact ball bearings is presented. Vibration analysis of rotor-ball bearing systems has often been performed via simplification of supporting bearings as linear springs with constant stiffness. In this study, an improved model of rotor-ball bearing systems was proposed. It utilizes a general bearing model based on response and time-dependent bearing characteristics. The system equations of motion were established using the finite-element method and numerically solved using the Newmark-β method. The method was used to recalculate the bearing stiffness matrices at every interval of numerical integration as a function of the instantaneous bearing displacements using a separated five-degrees-of-freedom bearing model. The method was verified via comparison with experimental data available in the literature. The extended simulations were conducted to investigate the unbalanced responses of a rotor-ball bearing system using the proposed and conventional methods. Numerical results showed a meaningful discrepancy between the vibrational responses obtained by the proposed model using the response and timedependent bearing stiffness model and the traditional constant-stiffness model.
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Study on Thermo-mechanical Modeling and Analysis of High-speed Angular Contact Ball Bearings Under Oil-jet Lubrication Gilbert Rivera, Shinhyang Park, Chan-sik Kang, Dongjoo Kim, Seong-Wook Hong Journal of the Korean Society for Precision Engineering.2024; 41(7): 569. CrossRef
Rotary tables are often used to fix and support work-pieces in machine tools. Because the deformation of the rotary table is known to significantly affect the precision in the work of the machine tool, it is very important to accurately predict the static displacements of the rotary table subjected to internal and external loads. This paper deals with modeling and experimental verification of the static displacements of a large-size rotary table supported by a thrust cylindrical roller bearing (T-CRB) and a double row cylindrical roller bearing (D-CRB). To this end, a rotary table model was developed along with the quasi-static models for T-CRB and D-CRB. The equilibrium equation of the rotary table was derived, and solved one by one in the looping manner, to overcome its statically indeterminate characteristics. The proposed modeling method was verified by means of comparing to the experimental results. Finally, an extensive simulation was carried out to investigate the deflection of the rotary table subjected to cutting forces.
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This paper presents an analysis of the stiffness and fatigue life of double-row angular contact ball bearings (D-ACBBs). To this end, a comprehensive quasi-static model was developed for D-ACBBs subjected to five degree-of-freedom (DOFs) loading and displacement. The model was verified by a commercial computational program. A rigorous numerical investigation was performed, based on the developed model regarding the effects of external load, rotational speed, axial clearance, bearing arrangement, and angular misalignment on the stiffness and fatigue life of the D-ACBB. The D-ACBB was subjected to negative axial clearance and yielded improved performance in terms of fatigue life and stiffness. The effect of angular misalignment on the bearing fatigue life was found to be significantly dependent on the amount of axial clearance. The moment stiffness of the D-ACBB in a back-to-back arrangement was higher than the face-to-face arrangement owing to the increased effective load center distance, whereas the radial stiffness and fatigue life were almost unchanged for back-to-back and face-to-face arrangements.
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Combined analysis of stiffness and fatigue life of deep groove ball bearings under interference fits, preloads and tilting moments Yi Jiang, Tianyu Zhu, Song Deng Journal of Mechanical Science and Technology.2023; 37(2): 539. CrossRef
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The stiffness characteristics analysis of the duplex angular contact ball bearings based on a comprehensive multi-degree-of-freedom mathematical model Tengfei Xu, Lihua Yang, Wei Wu, Yaoyu Han, Endian Xu, Kai Wang Applied Mathematical Modelling.2022; 106: 601. CrossRef
Characteristics of Duplex Angular Contact Ball Bearing with Combined External Loads and Angular Misalignment Tengfei Xu, Lihua Yang, Kai Wang Applied Sciences.2020; 10(17): 5756. CrossRef
Modeling of Crossed Roller Bearings Considering Roller Roundness Deformation Van-Canh Tong, Eui-Wook Jung, Seong-Wook Hong Journal of Tribology.2020;[Epub] CrossRef
Modeling of Displacements in a Large-Size Rotary Table Subjected to Loads Hyeon-Il Oh, Van-Canh Tong, Woo-Sang Park, Seong-Wook Hong Journal of the Korean Society for Precision Engineering.2018; 35(4): 443. CrossRef
Study on the Dynamic Characteristics and Fatigue Life of a Spindle-Bearing System for Large Machine Tools Hyeon-Il Oh, Sun-Woong Kwon, Woo-Sang Park, Seong-Wook Hong Journal of the Korean Society of Manufacturing Technology Engineers.2018; 27(6): 591. CrossRef
Angular misalignment has a significant effect on the characteristics of angular contact ball bearings (ACBBs). This paper presents an analysis of fatigue life for ACBBs subjected to angular misalignment. A simulation model is developed with de Mul’s bearing model and the ISO basic reference rating life model. Simulation is performed to calculate the life of the ACBBs subjected to angular misalignment. The numerical results show that angular misalignment influences the load distribution significantly, thus reducing the bearing rating life. The fatigue life of ACBBs is decreased by angular misalignment regardless of axial preload, external radial load and rotational speed. The results show that angular misalignment should be maintained at less than 1mrad for ACBBs.
This paper presents a dynamic modeling method for the indeterminate spindle-bearing system supported by multiple bearings of different types. A spindle-bearing system supported by ball and cylindrical roller bearings is considered. The de Mul’s bearing model is extended for calculating ball and cylindrical roller bearing stiffness matrices with inclusion of centrifugal force and gyroscopic moment. The dependence between spindle shaft reaction forces and bearing stiffness is effectively resolved using an iterative approach. The spindle rotor dynamics is established with the Timoshenko beam theory based finite elements. The spindle reaction forces, bearings stiffness and spindle natural frequencies are obtained with taking into account spindle radial load, ball bearing axial preload and rotational speed effects. The developed method is verified by comparing the simulation results with those from a commercial program.
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