• Journal of the Korean Society for Precision Engineering
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• v.32 no.2
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• pp.117-125
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• 2015

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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.297-303
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• 2001

This research presents an analytical model to characterize the ball bearing vibration due to the waviness in a rigid rotor supported by multi-row ball bearings considering centrifugal force and gyroscopic moment of ball. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. The waviness of ball and races is modeled by the superposition of sinusoidal function and it is introduced to position vectors of race curvature center to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. The accuracy of this research is validated by comparing with the results of the prior researches. It characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing resulting from the waviness interaction.

• Journal of Wind Energy
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• v.14 no.4
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• pp.21-28
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• 2023

This study focuses on the analysis of slewing ball bearings in wind turbines. Slewing bearings have an outer diameter of several meters, and hundreds of balls are in contact with the raceway. Due to the large number of balls and raceway contact conditions, it is difficult to accurately analyze contact stresses using general analysis techniques. To analyze the contact stress of a slewing ball bearing, the sub-modeling method is applied, which is a technique that first analyzes the displacement of the entire model and then analyzes the local stress at the point of maximum displacement. In order to reduce the displacement analysis time of the entire ball bearing, the technique of replacing the ball with a nonlinear spring is adopted. The analytical agreement of the simplified model was evaluated by comparing it with a solid mesh model of the ball for three models with different spring attachment methods. It was found that for the condition where a large turnover moment is applied to the bearing, increasing the number of spring elements gives the closest results to modeling the ball with a solid mesh.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2003.11a
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• pp.324-328
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• 2003

Water-lubricated frictional characteristics of stainless steel ball bearing is not well known compared to oil-lubricated frictional characteristics. Furthermore study on friction at high temperature is rare because bearing maintenance strategy for water-lubricated or chemicals-lubricated bearings of equipment is mostly based on change of failed bearings and parts. Ball bearings and ball screw are installed on the power transmission for a developing integral reactor and these are lubricated with high temperature and high pressure chemically-controlled pure water. Bearings and power transmitting mechanical elements for an atomic reactor needs high reliability. and high performance during estimated lifetime, and it should be verified. In this paper, experimental research results of frictional characteristics of water-lubricated ball bearing as a preliminary investigation.

• Tribology and Lubricants
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• v.35 no.1
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• pp.37-43
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• 2019

This paper presents an optimization method to determine the shoulder height of an angular contact ball bearing by 3D contact analysis using nondimensional-shaped variables. The load analysis of the ball bearing is performed to calculate the internal load distributions and contact angles of each rolling element. From the results of bearing load analysis and the contact geometry between the ball and inner/outer raceway, 3D contact analyses using influence function are conducted. The nondimensional shoulder height and nondimensional load are defined to give the generalized results. The relationship between the shoulder height and radius of curvature of the shoulder under various loading conditions is investigated in order to propose a design method for the two design parameters. Using nondimensional parameters, the critical shoulder heights are optimized with loads, contact angles, and conformity ratios. We also develop contour maps of the critical shoulder height as functions of internal loads and contact angles for the different contact angles using nondimensional parameters. The results show that the dimensionless shoulder height increased as the contact angle and dimensionless load increased. Conversely, when the conformity ratio increased, the critical shoulder height decreased. Therefore, if the contact angle is reduced and the conformity ratio is increased within the allowable range, it will be an efficient design to reduce the shoulder height of ball bearings.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.05a
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• pp.433-434
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• 2012

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2003.11a
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• pp.395-401
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• 2003

In this paper, the dent printing phenomena and critical dent size which lead to premature failure of deep grooved ball bearing for automobiles are presented. The results of newly assembled test bearings showed that the ball dent size strongly affect the bearing life and inner ring raceways were the major failed parts in spite of using the dented balls. The dent printing phenomena are a root cause of premature failure, which was not reported until now. And there exist the critical ball dent size for given rolling bearings and operating conditions. So, the initial condition of tribologically mating parts should be treated as important as the failed body itself.

• Tribology and Lubricants
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• v.15 no.1
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• pp.77-82
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• 1999

The processing conditions fur the synthesis of platelet W $S_2$ lubricant powder through a solid-gas reaction were optimized. The mixture of tungsten and sulfur powders were sealed in a vacuum of 10$^{-6}$ torr, prior to heat-treating at 85$0^{\circ}C$ fur 8 days. The reaction product showed a well-developed platelet W $S_2$ powder with an average size of 3.8 ${\mu}{\textrm}{m}$. The TGA/DTA analysis of the synthesized W $S_2$ powder was performed up to 120$0^{\circ}C$ at a rate of 1$0^{\circ}C$/min in flowing air (100 ${\mu}{\textrm}{m}$/min) atmosphere. The weight loss was about 6% up to 120$0^{\circ}C$ compared to the original weight. A rapid weight loss of about 5% occurred in the temperature range of 44$0^{\circ}C$ to 66$0^{\circ}C$ and an exothermic peak observed due to the transition of W $S_2$ to W $O_3$. The synthesized W $S_2$powder was coated on the commercial deep grooved ball bearing (No. 6203) to examine the effect of W $S_2$, coating layer on the noise and endurance of the ball bearing. The level of noise obtained from W $S_2$, coated-ball bearing (56 ㏈) was higher. than the value (32 ㏈) occurred in the case of greece lubrication. The endurance of the ball-bearing assembled after the coating of W $S_2$ powder onto each part increased 50 times compared to the non-coated ball-bearing..

• Tribology and Lubricants
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• v.14 no.2
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• pp.26-34
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• 1998

This paper presents a high-speed performance analysis of ball bearings with ceramic balls under thrust loads. The sliding velocity profiles between a ball and raceways were obtained by the 3-D quasi-dynamic equations of motion including both centrifugal force and gyroscopic moment derived by vector matrix algebra. The friction at the contact areas was obtained by the Bair-Winer's non-Newtonian rheological model and the Hamrock-Dowson's central film thickness in EHL analysis. The nonlinear equations were solved by the Newton-Raphson method and the underrelaxation iterative method. The friction torques and ball behaviors with various loads, ball materials, and contact angles were predicted by this model. It was shown that the friction torque was sensitive to thrust load and contact angle, and that the friction torque and the pitch angle of the bearing with ceramic balls are smaller than those of the bearing with steel balls.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2002.10b
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• pp.303-304
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• 2002

This paper presents theoretical analysis of the NRRO(the non-repeatable run-out) for a ball bearing with geometric imperfection. This imperfection contains ball size error, ball waviness, outer race waviness and inner race waviness. The 3D dynamic analysis of a ball bearing using the Newton-Raphson method is performed to calculate the displacement of shaft center. The radial and axial NRRO are simulated, and preload and clearance effects are investigated. Preload and clearance have significant effects on radial and axial NRRO of for miniature ball bearings.