• 한국소음진동공학회논문집
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• 제11권7호
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• pp.275-286
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• 2001

The research presents an analytical theory to calculate the characteristics of the bal bearing with waviness in its rolling elements considering the centrifugal force and gyroscopic moment of bal. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. and the waviness of rolling elements is modeled by sinusoidal function to calculate the contact force at each ball. The numerical solutions of governing equation of berating due to waviness are calculated by using the Newton-Raphson method. The accuracy of the research is validated by comparing the contact force. contact angle in case of considering the centrifugal force and gyroscopic moment of bal and the contact force and vibration frequencies in cases of considering waviness with the prior researches respectively. It investigates the stiffness, contact force. displacement and vibration frequencies of the ball bearing considering not only the centrifugal force and gyroscopic moment of ball but also the waviness of the rolling elements.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 I
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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.

• 한국기계기술학회지
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• 제13권2호
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• pp.129-135
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• 2011

Dry CVT(Continuously variable transmission) consists of a driving pulley and a driven pulley joined by rubber V-belt. Each pulley consists of a fixed flange and a movable flange. The movable flange of the driving pulley has the centrifugal roller and a ramp plate in the flange. The movable flange moves toward a fixed flange under the actuation of a centrifugal roller, as the driving pulley speed increases. The main advantages of the Dry CVT with V-belt, which has been popular in Asia, are a simple mechanism, less maintenance and low cost. The important claim which have an influence on the performance of the Dry CVT is the wear of the centrifugal roller. In this study ball type is proposed instead of roller type of movable flange to resolve claim. Also experiments are carried out for new model to evaluate performances.

• 대한기계학회논문집A
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• 제26권12호
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• pp.2636-2646
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• 2002

This research presents an analytical model to investigate vibration due to ball bearing waviness in a rotating system supported by two or more ball bearings, taking account of the centrifugal force and gyroscopic moment of the ball. The waviness of rolling elements is modeled by the sinusoidal function, and it is incorporated into the position vectors of the race curvature center. The Hertzian con tact theory is applied to calculate the elastic deflection and nonlinear contact force while the rotor has translational and angular motions. Both the centrifugal force and gyroscopic moment of the ball and the waviness of the rolling elements are included in the kinematic constraints and force equilibrium equations of a ball to derive the nonlinear governing equations of the rotor, which are solved by using the Runge-Kutta-Fehlberg algorithm to determine the new position of the rotor. The proposed model is validated by the comparison of the results of the prior researchers. This research shows that the centrifugal force and gyroscopic moment of the ball plays the important role in determining the bearing frequencies, i.e. the principal frequencies, their harmonics and the sideband frequencies resulting from the waviness of the rolling elements of ball bearing. It also shows that the bearing vibration frequencies are generated by the waviness interaction not only between the rolling elements of one ball bearing but also between those of two or more ball bearings constrained by the rotor.

• 한국정밀공학회지
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• 제29권6호
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• pp.671-679
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• 2012

This paper presents an estimation procedure for axial displacement in spindle equipped with angular contact ball bearings due to rotational speed. High-speed spindle-bearing system experiences axial displacement due to thermal expansion and rotational speed-dependent characteristics of angular contact ball bearings. This paper deals with the axial displacement caused by the rotational speed-dependent effects such as centrifugal force and gyroscopic moments. To this end, a bearing dynamic model is established that includes all the static and dynamic properties of angular contact ball bearing. An analytical formula to calculate the axial displacement based on contact angles between ball and races is derived to discuss the physics regarding the axial displacement in spindle. The proposed dynamic model is compared with a reference and a commercial program. Numerical examples are presented to show the effects of centrifugal force and gyroscopic moment on the axial displacement. The proposed model is also validated with an experimental result.

• 동력기계공학회지
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• 제17권1호
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• pp.85-90
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• 2013

Dry CVT consists of a driving pulley and a driven pulley joined by rubber V-belt. Each pulley consists of a fixed flange and a movable flange. The movable flange moves toward a fixed flange under the actuation of a centrifugal roller, as the driving pulley speed increases. The important claim which have an influence on the performance of the Dry CVT is the wear of the centrifugal roller. In this study ball type is proposed instead of roller type of movable flange to resolve the claim. Simulation is carried out for new model to verificate performance, experiments are carried out for new model to evaluate performances.

• 한국생산제조학회지
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• 제19권5호
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• pp.609-615
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• 2010

Angular contact ball bearings in a high speed spindles are under the extreme conditions, such as high temperature, big centrifugal force and thrust cutting forces. So, the assembly contacts between spindle shaft and inner ring bearings, bearing housing and outer ring of bearings are occasionally unstable at high speed revolution. Furthermore, the ball contact angle of a bearing, which influence stiffness and lifetime of bearings, are changed according to loads and rotational speed. To analyze internal forces of a bearing under high speed revolution, the ball contact are calculated using nonlinear equations in consideration of rotational speed, thrust loads and raceway form. Diameter increase of inner and outer ring by influence factors, such as internal forces to inner and outer ring, centrifugal force and temperature of inner and outer rings are calculated to establish stable state in bearing assembly in high speed spindle. Finally, contribution ratio of influence factor to assembly design tolerance of inner and outer rings are shown and the stable assembly design tolerance are proposed.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.1697-1702
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• 2004

The waterhammer has recently become more important because the pumping stations were big and the systems conveying the fluid through the large and long transmission pipelines were complex. When the pumps are started or stopped for the operation or tripped due to the power failure. the hydraulic transients occur as a result of the sudden change in velocity. In this paper, the field tests on the waterhammer by the startup, stoppage, and power failure of a centrifugal pump were carried out for Yongma transmission pumping station in Seoul. The experimental results were compared with that of the numerical calculations. in which results the procedure of controlled pump normal shut-down and the two-step closing mode of controlling the ball valve for pump emergency stop are proposed to reduce the pressure surge.

• 한국분말재료학회지
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• 제19권4호
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• pp.304-309
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• 2012

The purpose of our study was to develop the fabrication method of porous diatomite ceramics with a porosity gradient by centrifugal molding. The processing variables of centrifugal molding were derived from Stoke's law of sedimentation, which were the radius of the particles, the acceleration due to centrifugal molding and the dynamic viscosity of the slurry. And these could be controlled by ball-milling conditions, centrifugal conditions, and the addition of methyl cellulose, respectively. The effects of processing conditions on the gradient pore structure of diatomite were investigated by particle size analysis, scanning electron microscope, and mercury porosimeter.

• Tribology and Lubricants
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• 제14권2호
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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.