This paper presents a method for estimating the fatigue life of crossed roller bearings (XRBs). XRBs feature a single row of rollers arranged alternately at right angles, making them ideal for applications that require high precision and a compact design. In rolling-element bearings, fatigue life is a crucial design parameter for ensuring long-term reliability and performance. However, existing fatigue life estimation models for XRBs in the literature are limited to basic rating life, with no models available for reference rating life. To address this gap, we developed a comprehensive fatigue life prediction model specifically for XRBs. We formulated a corresponding dynamic load rating to align with the values provided by bearing manufacturers and calibrated an unknown adjustment factor for XRBs using a commercial program. Additionally, a parametric study was conducted to investigate the impact of varying diametral clearance, external loads, roller dimensions, and roller profile parameters on the fatigue life of XRBs.
This study investigates the influence of operating diametral clearance on the performance of angular contact ball bearings (ACBBs). It examines critical factors affecting diametral clearance, including mounting conditions, external loads, temperature fluctuations, and rotational speeds. A novel model combining quasi-static and fit-up approaches is proposed to analyze the effects of operating diametral clearances on ACBB performance. This model incorporates key elements such as ball-race contact loads, interactions between the shaft and inner ring, interference fits between the housing and outer ring, centrifugal expansion of the rotating shaft and inner ring, and temperature-induced changes. Internal clearance variations are computed using the thick-ring theory. Simulations are conducted to predict ACBB characteristics under various fit-up conditions, including contact load distribution and stiffness, with results validated using commercial software. The study also explores the impact of various operating diametral clearances on ACBB performance under differing fitting conditions, external loads, and rotational speeds.
This paper presents an integrated thermo-mechanical model for analyzing angular contact ball bearings (ACBBs) operating under oil-jet lubrication. The proposed approach enables a comprehensive analysis of both the mechanical and thermal behavior of the ACBB system. The proposed formulation employs a quasi-static approach to accurately calculate contact loads and heat generation, taking into careful consideration variations in internal clearance resulting from factors such as surface pressure, centrifugal forces, and thermal expansion. For the thermal analysis, a refined thermal network model is utilized. The proposed thermal model incorporates a newly derived correlation for the drag coefficient under oil-jet lubrication, which is obtained through high-fidelity computational fluid dynamics simulations. The validity of the proposed model is confirmed through comparison with experimental data. Furthermore, extensive simulations are conducted to investigate the impact of bearing fit-up and thermal variations on the performance of ACBBs.
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Study on the Effects of Operating Diametral Clearance Change on the Characteristics of Angular Contact Ball Bearings Patrick John Po, Gilbert Rivera, Jin-Hyeok Sa, Seong-Wook Hong Journal of the Korean Society for Precision Engineering.2024; 41(12): 997. CrossRef
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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This paper presents an improved input shaping method to eliminate vibration during circular interpolation of a flexible 2-axis positioning system. Due to the time delay introduced by input shaping, simultaneous 2-axis positioning with circular interpolation results in a certain amount of errors from the intended track or trajectory. This study investigated the track errors associated with circular interpolation caused by input shaping for a flexible 2-axis positioning system. The following three strategies for reducing such errors were proposed: velocity reduction in circular interpolation, adjustment of the time delay between 2 axes commands, and employment of a velocity profile compensation function. Simulations were performed to discuss the pros and cons of the three proposed strategies. Experiments were also performed to validate the results. Simulation and experiments showed that the track errors due to input shaping can be sufficiently reduced by combined use of the proposed strategies.
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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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Influencia del ángulo de contacto en la cinemática y la distribución de carga de rodamientos a bolas Pello Alberdi Quevedo, Ibai Ulacia Garmendia, Aitor Arana Ostolaza, Jon Larrañaga Amilibia, Aitor Oyanguren Garcia Anales de Ingeniería Mecánica.2025;[Epub] CrossRef
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Stiffness characteristics and experimental study of angular contact ball bearings considering the influence of rotational speed Runlin Chen, Fan Xu, Gengzhou Liu, Jiakai Li, Shaodong Zhao, Xingyu Fan, Yanchao Zhang, Saisai Lv Advances in Mechanical Engineering.2024;[Epub] CrossRef
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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.
Most positioning systems experience residual vibration during operation. Such residual vibration can be eliminated or reduced to an acceptable level by using the input shaping method. However, adopting the input shaping methods typically introduces a certain amount of time-delay into a system. This study focused on the development of a delay-time adjustable input shaping method to eliminate vibration caused by repetitive motion in positioning systems. The proposed input shaping method, called the virtual mode (VM) input shaper, uses a virtual frequency parameter that adjusts delay-time and cancels residual vibration. Unlike most previous input shaping studies, this study investigated VM input shaping performance to eliminate the steady-state vibration induced by repetitive motion in positioning systems. To this end, an analytical formulation was derived and used for simulating the input shaping performance with varying dominant parameters involved in a system. Experiments were also performed to validate the proposed method.
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Data Driven Vibration Control: A Review Weiyi Yang, Shuai Li, Xin Luo IEEE/CAA Journal of Automatica Sinica.2024; 11(9): 1898. CrossRef
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Linear roller bearings are often used for linear positioning systems due to high load-carrying capacity, precision, and durability. In this paper, guide rail deformation of linear roller bearings under vertical and horizontal loads, has been experimentally investigated. An experimental system was made to measure displacement of the carriage and guide rail deformation of a bearing with varying load. Guide rail deformation inaccessible inside the carriage, was estimated by measured carriage displacement subtracted from calculated carriage displacement from a commercial program, that does not consider flexibility of guide rail and base. In addition to estimated deformation, guide rail deformation outside the bearing carriage was measured to make a complete guide rail deformation curve due to external loads. Results revealed deformations occurring in guide rail and base are significant, as to affect bearing accuracy. Thus, deformations in guide rail and base should be considered, to estimate stiffness and motion accuracy of linear roller bearing under external loading conditions.
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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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Hybrid Electric Vehicles (HEVs) are developed to be operated with two kinds of power source (Diesel Engine and Electric Motor with Rechargeable High Voltage Battery Pack). HEVs for military vehicle require high reliability to provide stable powers under serious environment such as vibration and shock. To ensure normal operation of battery pack under serious environment such as vibration and shock, the high voltage battery pack needs to have appropriate dynamic characteristics. This paper presents a design procedure for high voltage battery pack with such characteristics. An isolator design is proposed to reduce vibration and shock. Associated random vibration and shock response of the high voltage battery pack are simulated under conditions suggested by MIL specifications. Its dynamic characteristics and vibration and shock responses are validated with experiments.
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.
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