• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2647-2655
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).

• Journal of the Korean Society for Precision Engineering
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• v.29 no.6
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.181-189
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness in a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time-varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i= 1,2,3..).

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1999.06a
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• pp.119-126
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• 1999

The rolling fatigue lives (RFL) of five kinds of silicon nitride balls were investigated. Four kinds of Si$_3$N$_4$ balls were fabricated using different raw materials, sintering aids and sintering conditions, Commercially available Si3N4 ball was also studied for comparison. All the balls were finished up to the dimensional accuracy of Grade 10 defined in KS B 2001 (Steel Balls for Ball Bearings) with a size of 9.525mm. RFL tests were then conducted under the initial theoretical maximum contact stress 6.38 GPa and the spindle speed 10,000 rpm. Gear oil was provided by oiled race as lubricant. The results of RFL test indicated the prerequisitic conditions for the long rolling life of Si$_3$N$_4$ball : (1) the high density, (2) mjcrostructures consisted of small uniformly distributed grains, (3) little glassy phase in grainboundary, and (4) little crystalline phase and secondary phase that induces residual thermal stress due to the differences of thermal expansion coefficient with Si$_3$N$_4$Phase.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.564-571
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• 2003

This research investigates how characteristics of ball bearing affect non-repeatable runout(NRRO) in a HDD spindle system at elevated temperature. It shows that the elevated temperature results in the increase of bearing contact angle and the decrease of bearing deformation due to the different thermal expansion rate of the components of the HDD spindle system. The increase of contact angle at elevated temperature is so small that the variation of bearing frequencies is negligible. On the other hand, the decrease of bearing deformation at elevated temperature reduces the stiffness of ball bearing and the natural frequencies of HDD spindle system consequently, which changes the amplitude and the frequency distribution of NRRO.

• Tribology and Lubricants
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• v.15 no.2
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• pp.150-155
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• 1999

The rolling fatigue lives (RFL) of five kinds of silicon nitride balls were investigated. Four kinds of Si$_3$N$_4$balls were fabricated using different raw materials, sintering aids and sintering conditions. Commercially available Si$_3$N$_4$ball was also studied for comparison. All the balls were finished up to the dimensional accuracy of Grade 10 defined in KS B 2001 (Steel Balls fer Ball Bearings) with a size of 9.525 mm. RFL tests were then conducted under the initial theoretical maximum contact stress 6.38 GPa and the spindle speed 10,000 rpm. Gear oil was provided by oiled race as lubricant. The results of RFL test indicated the prerequisitic conditions for the long rolling life of Si$_3$N$_4$ball : (1) the high density, (2) microstructures consisted of small uniformly distributed grains, (3) little glassy phase in grainboundary, and (4) little crystalline phase and secondary phase that induces residual thermal stress due to the differences of thermal expansion coefficient with Si$_3$N$_4$phase.

• Journal of Welding and Joining
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• v.19 no.3
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• pp.311-316
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• 2001

This paper presents that the affecting factors to the solderability and initial reliability. It is the factor that the coefficient of thermal expansion between package and PCB(Printed Circuit Board), the quantity of solder paste and reflow condition, and Au thickness of the solder ball pad on polyimide tape. As the reflow soldering condition for 48 ${\mu}BGA$ is changed, it is estimated that the quantity of Au diffusion at eutectic Sn-Pb solder surface and initial bonding strength of eutectic Sn-Pb solder and lead free solder. It is the result that quantitative measurement of Au diffusion quantity is difficult, but the shear strength of eutectic Sn-Pb solder joint is 842 mN at first reflow and increases 879 mN at third reflow. The major failure mode in solder is judged solder fracture. So, Au diffusion quantity is more affected by reflow temperature than by the reflow times.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.29 no.8
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• pp.516-521
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• 2016

Mo-Cu alloys have been widely used for heat sink materials, vacuum technology, automobile, and many other applications due to their excellent physical and electric properties. Especially, Mo-Cu composites with 5 ~ 20 wt.% copper are widely used for the heavy duty service contacts due to their excellent properties like low coefficient of thermal expansion, wear resistance, high temperature strength, and prominent electrical and thermal conductivity. In most of the applications, highly-dense Mo-Cu materials with homogeneous microstructure are required for better performance. In this study, Mo-Cu alloys were prepared by PBM (planetary ball milling) and SPS (spark plasma sintering). The effect of Cu with contents of 5~20 wt.% on the microstructure and thermal properties of Mo-Cu alloys was investigated.

• Journal of the Korean Society for Precision Engineering
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• v.26 no.5
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• pp.135-141
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• 2009

The bearing clearance is influenced by shrink fit and thermal expansion during operation. The designer must take into account the reduction of clearance after installation to the interference fits, and thermal expansion must be considered. The purpose of this study is to grasp the internal clearance variation and behavior of a bearing which is a deep connected with fatigue life of bearing and performance of spindle through FEM(Finite Element Method). Finite element analysis is performed by using commercial code ANSYS according to variation of thermal condition and rotational speeds. This paper presents correct negative internal clearance according to temperature during operation. Furthermore, interrelation between thermal expansion and contraction are presented to maintain adequate contact force for three type of spindle system (HSK-A60, HSK-40E, HSK-32E). The influence of the centrifugal force and Internal clearance variation of bearing is studied to operating rotational speed.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1277-1282
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• 2008

Recently LCD panels have becom very important components for portable electronics. In the high density interconnection material, ACF's are used to connect the outer lead of the tape automated bonding to the transparent indium tin oxide electrodes of the LCD panel. ACF consists of an adhesive polymer matrix and randomly dispersed conductive balls. In this study, we analyzed Failure Mode / Mechanism of ACF which is identified Conductive ball Corrsion, Delamination, Crack and Polymer Expansion / Swelling. In ALT(Accelerated Life Test), we select primary stress factors as temperature and humidity. As time passes by, an increase of connection resistance was observed. In conclusion, we have found that high temperature / humidity affects the adhesion.