• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.585-591
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• 2003

It has been widely known that geometrical or form errors of ball bearings such as ball size error, ball waviness, inner and outer race waviness due to inherent manufacturing imperfection are one of the major sources of uncontrollable non-repeatable run-out (NRRO) vibration in HDD spindle motor. NRRO in HDD is also known to be the primary cause of limiting the storage capacity of HDD. In this paper, We performed vibration analysis for NRRO a ball bearing being used in 3.5" HDD spindle motor. To theoretically estimate NRRO considering the geometrical errors of ball bearing components, a simple three degrees of freedom model was proposed and then vibration analysis for axial and radial NRRO was conducted utilizing the measured geometric imperfection of a bearing with both the waviness magnitude and phase taken into account. Effects of bearing preload and clearance on NRRO was also investigated as an effort to predict their optimum values minimizing bearing NRRO.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.810-816
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• 2001

In this paper, we theoretically analyzed the NRRO(the non-repeatable run-out) of a ball bearing with geometric imperfection. The quasi-static and dynamic analysis of a ball bearing was performed to calculate the displacement of shaft center caused by the form errors while the shaft is rotating. From consideration of the generating mechanism of NRRO, it is found that the waviness of one ball generates vibrations with nf$\sub$b/${\pm}$f$\sub$c/(where n is odd) components. Also it is confirmed that the outer race waviness of the order n = jZ${\pm}$1 generates vibration with jZf$\sub$c/ components. The form errors of ball bearing elements were precisely measured and NRRO of a ball bearing was calculated using the measured data. It is concluded that the ball bearings must has large ball number and small ball diameter to obtain low NRRO.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.7
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.978-983
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• 2014

This research proposes a method to estimate the fatigue life of solid-state drive(SSD) due to the effect of dummy solder ball under forced vibration. Mechanical jig is developed to describe the SSD in laptop computer. The jig with SSD is mounted on a shaker, and excited by a sinusoidal sweep vibration within the narrow frequency band around the first resonant frequency until the SSD fails. A finite element model of SSD is also developed to simulate the forced vibration. It shows that the solder joints at the corners of controller package are most vulnerable components and that placing dummy solder balls at those area is effective method to increase fatigue life of SSD.

• Tribology and Lubricants
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• v.33 no.4
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• pp.141-147
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• 2017

The vibration data of bearings are very useful for monitoring and determining the condition of the bearings. The defect frequencies of ball bearings have been used for monitoring there condition. However, it is not easy to verify the defect frequencies as the wear progress. Therefore there is a need for an easy method to monitor the damages of bearings in real-time and to observe the variations in vibration characteristics as the wear progress. In this study, a bearing test equipment is constructed to diagnose the damage of bearings. The friction coefficient and vibration data are measured by using a torque sensor and an acceleration sensor, and the correlation between the measured data is analyzed to diagnose the condition of the bearing. We reached the following conclusions from the results. When the ball surface, inner and outer rings of a ball bearing are damaged, the friction coefficient increases to over 0.02 with an adhesion on the surface. Moreover this damage occurs more quickly with an increase in the number of revolutions. In the vibration characteristics, the amplitude of vibration wave appears high with an increase in the friction coefficient. In the high frequency range between 1000 and 2000 Hz, a wide range of frequency components with high amplitude occurs continuously irrespective of the number of revolutions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.350.2-350
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• 2002

The purpose of this study was to present the possible use of a new standard impactor, the rubber ball (so-called, impact ball), and to assess its evaluation method as fur heavy-weight impact in multi-story residential buildings. Several experiments were carried out to investigate the effect of the impactor on noise propagation in reinforced concrete buildings. Then, the noise from the impact ball was psychoacoustically evaluated. (omitted)

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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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.

• Structural Engineering and Mechanics
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• v.83 no.5
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• pp.655-669
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• 2022

Passive vibration control devices like tuned liquid column dampers (TLCD) not only significantly reduce buildings' vibrations but also can serve as a water storage facility. The recently introduced modified form of TLCD known as tuned liquid column ball damper (TLCBD) suppressed external vibration efficiently compared to traditional TLCD. For excellent performance, the mass ratio of TLCBD should be in the range of 5% to 7%, which does not include the mass of the ball. This additional mass of the ball increases the overall structure mass. Therefore, in this paper, an effort is made to reduce the mass of TLCBD. For this purpose, a new modified version of TLCBD known as tuned liquid column hollow ball damper (TLCHBD) is proposed. The existing mathematical modeling of TLCBD is used for this new damper by updating the numerical values of the mass and mass moment of the ball. Analytically the optimal design parameters are obtained. Numerically the TLCHBD is investigated with a single degree of freedom structure under harmonic and seismic loadings. It is found that TLCHBD performance is similar to TLCBD in both loadings' cases. To validate the numerical results, an experimental study is conducted. The mass of the ball of TLCHBD is reduced by 50% compared to the ball of TLCBD. Both the arrangements are studied with a multi-degree of freedom structure under harmonic and seismic loadings using a shake table. The results of the experimental study confirm the numerical findings. It is found that the performance behavior of both the dampers is almost similar under harmonic and seismic loadings. In short, the TLCHBD is lighter in weight than TLCBD but has a similar vibration suppression ability.

• Journal of KSNVE
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• v.11 no.2
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• pp.336-345
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• 2001

This research presents a nonlinear model to analyze the ball bearing nitration due to the waviness in a rigid rotor supported by multi-row ball bearings. The waviness of a ball and each races is modeled by the superposition of sinusoidal function, and the position vectors of inner and outer groove radius center are defined with respect to the mass center of the rotor in order to consider five degrees of freedom of a general rotor-bearing system. The waviness of a ball bearing is introduced to these position vectors 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. Numerical results of this research are validated with those of prior researchers. The proposed model can calculate the translational displacement as well as the angular displacement of the rotor supported by the multi-row ball bearings with waviness. It also characterizes the nitration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing. and the sideband frequencies resulting from the waviness interaction.