• 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.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 1999년도 추계학술발표대회 논문집
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• pp.258-263
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• 1999

In this study, the numerical and experimental investigations were conducted to understand ultrasonic wave propagation and to evaluate the degree of fiber waviness in thick composites nondestructively. The path, energy and traveling time of insonified wave were predicted by adopting the ray and plane wave theories. In the analysis, the composites were assumed to have continuous fiber with sinusoidal waviness in a matrix and were modeled as stacks of infinitesimally short length off-axis elements with varying fiber orientation along the length direction. From the experiments on the specially fabricated thick composite specimens with various degrees of uniform fiber waviness, the energy distributions of received wave were obtain for the various positions of transmitter. It was observed that the energy of wave was converged to the adjacent peaks of fiber waviness. The location where maximum energy of wave was detected from the experiments showed good agreement with the location obtained from theoretical predictions. Finally, the test procedure was Proposed to evaluate fiber waviness in thick composites by considering the energy of wave and relative distance between transmitter and receiver.

• 소음진동
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• 제11권2호
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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.

• 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.

• 한국가시화정보학회지
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• 제19권3호
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• pp.69-76
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• 2021

Printed circuit heat exchanger (PCHE) is a compact heat exchanger with good heat transfer performance, high structure integrity, and reliability over a wide range of temperatures and pressures. Instead of the traditional zigzag and straight shape channel, the sinusoidal shape channel was adopted in this study to investigate the relation of thermal-hydraulic performance and waviness factors (period and amplitude). The local flow characteristics and the heat flux distribution were compared to verify the effects of period and amplitude on heat transfer performance. As the period of channel becomes shorter, the rapid change of the flow direction can produce high flow separation around the corner leading to the disturbance of the boundary layer opposite wall. The nonuniform distribution of flow velocity appeared around the corner positions can promote fluid mixing and lead to higher thermal performance. An evaluation index was used to compare the comprehensive performance of PCHE considering the Nusselt number and Fanning factor. Based on the simulation results, the optimal design parameters of PCHE channel shape were found that the channel with an equivalent bending angle of 15° offers the highest heat flux capacity.

• 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.

• 한국생산제조학회지
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• 제23권6호
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• pp.630-635
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• 2014

This study aims to develop a PZT-driven depth adjustment device with a flexure hinge and to investigate its static/dynamic characteristics. This device will be applied to rapidly and accurately trace a flat surface with slight waviness of up to several hundreds of micrometers in magnitude. One typical example is to cut a film coated on a steel plate. A depth control system composed of PMAC, PZT/PZT amplifier, flexure hinge/knife, and laser displacement sensor is implemented on a desktop three-axis machine and an actual cutting test is conducted on a steel workpiece with a sinusoidal-wavy surface. It is verified that the dynamic characteristics of the device limit the maximum cutting speed and depth precision.

• Tribology and Lubricants
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• 제29권1호
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• pp.13-18
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• 2013

Slider bearing is a widely used load-carrying element in the industry. While a large number of studies have investigated the effect of overall surface curvature, very few have considered sinusoidal surface. Recently, consideration of surface roughness/waviness or intentional wave design has been identified as an important issue in the manufacture of hard disk driver, mechanical seal, hydraulic machine, and etc. This study investigated the load-carrying capacity of a finite-width slider bearing with a wavy surface. Film thickness ratios, length-width ratio, ambient pressure, amplitude, and partial distribution were selected as the simulation parameters. The calculation results showed that the load-carrying capacity rapidly varied at small film thickness ratio, but the waviness near the area of minimum film thickness made much more influence with an increase in film thickness ratio. As the length-width ratio of bearing was increased, ambient pressure became more influential at small film thickness ratios. Furthermore a particular partial distribution of the wavy area led to higher load-carrying capacity than did the whole distribution. Consequently, the results of this study are expected to be of use in surface micro-machining of finite-width slider bearings.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 학술대회
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• pp.131-136
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• 2008

Three-dimensional characteristics of fluid flow and heat transfer around a wavy circular cylinder having sinusoidal variation in cross sectional area along the spanwise direction are numerically investigated using the immersed boundary method. The three different wavelengths of ${\pi}/4$, ${\pi}/3$ and ${\pi}/2$ and at the fixed wavy amplitude of 0.1 have been considered to investigate the effects of waviness on especially the forced convection heat transfer around a wavy cylinder when the Reynolds and Prandtl numbers are 300 and 0.71, respectively. The present computational results for a wavy cylinder are compared with those for a smooth cylinder. The time- and total surface-averaged Nusselt number for a wavy cylinder with is larger than that for a smooth cylinder, whereas that with ${\lambda}={\pi}/4$ and ${\pi}/3$ is smaller than that for a smooth cylinder. However, because the surface area exposed to heat transfer for a wavy cylinder is larger than that for a smooth cylinder, the total heat transfer rate for a wavy cylinder with different wavelengths of ${\lambda}={\pi}/4$, ${\pi}/3$ and ${\pi}/2$ is larger than that for a smooth cylinder.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.634-639
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• 2003

It has been studied the flow near a rotating disk with surface topography. The system Ekman number is assumed very small, i.e., $E[{\equiv}\frac{\nu}{{\Omega}^{\ast}L^{\ast2}}]<<1$ in which $L^{\ast}$ denotes a disk radius, ${\nu}$ kinematic viscosity of the fluid and ${\Omega}^{\ast}$ angular velocity of the basic state. Disk surface has a sinusoidal topographic variation along radial coordinate, i.e., $z={\delta}cos(2{\pi}{\omega}r)$, where ${\delta}$ and ${\omega}$ are, respectively, nondimensional amplitude and wave number of the disk surface. Analytic solutions, being useful over the parametric ranges of ${\delta}{\sim}O$( $E^{1/2}$ ) and ${\omega}{\leq}O$ ( $E^{1/2}$ ), are secured in a series-function form of Fourier-Bessel type. An asymptotic behavior, when $E{\rightarrow}0$, is clarified as : for a disk with surface roughness, in contrast to the case of a flat disk, the azimuthal velocity increases in magnitude, together with the thickening boundary layer. The radial velocity, however, decreases in magnitude as the amplitude of surface waviness increases. Consequently, the overall Ekman pumping at the edge of the boundary layer remains unchanged, maintaining the constant value equal to that of the flat disk.