• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.8
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• pp.322-330
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• 2001

The stability and the leakage performance of turbo pump unit seals supported by elastic-ring ball bearings are Investigated for the Improvement of onset speed of instability(OSI). The numerical analysis of floating ring seal in consistence with its geometry and operating conditions is executed with detailed comparison of various seal types. The results show that the floating ring seal has superior performance in terms of rotordynamic salability compared to the ocher type seals while it shows slightly inferior leakage performance. To Improve the leakage performance. floating ring seal could be combined with hole Pattern damper or labyrinth seal surface.

• Transactions of the Korean Society of Automotive Engineers
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• v.9 no.5
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• pp.165-172
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• 2001

Wheel bearing units were almost exclusively used for car front wheel, where the two ball rows are directly side by side with integrated rubber seal. The seal is of important for wheel bearing units due to the adverse environmental conditions with mud and splash water. The seal of wheel bearing units was designed to have geometry with multi lips, which elastic lip contacts and deforms with bearing. The equation of reaction force for deformed lip as cantilever beam was previously used for seal lip design. But it's result was not useful because deflection of the beam differs from lip's. In this study, deformed shape of the lip was assumed to and order function which is more similar to lip deformation and made the equation for reaction force prediction. The Reaction forces from each other equations were compared with results by FEA to prove usefulness of new equation.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.333-342
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• 2007

Suppose that ${\mu}$ is a finite positive Borel measure on the unit ball $B{\subset}C^n$. The boundary of B is the unit sphere $S=\{z:{\mid}z{\mid}=1\}$. Let ${\sigma}$ be the rotation-invariant measure on S such that ${\sigma}(S)=1$. In this paper, we will show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$ where $P(z,{\zeta})$ is the Poission-Szeg$\ddot{o}$ kernel for B, then ${\mu}$ is a Carleson measure. We will also show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$, then the operator T such that T(f) = P[f] is compact as a mapping from $L^p(\sigma)$ into $L^p(B,d{\mu})$.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-667
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• 2011

A class of functions involving divided differences of the psi and tri-gamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving the ratio of two gamma functions and originating from the establishment of the best upper and lower bounds in Kershaw's double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in $\mathbb{R}^{n-1}$ and $\mathbb{R}^n$ respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.1025-1028
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• 2002

In this paper, a micro-turning lathe is introduced for micro machining of aluminum rod. To give feed motion, stepwise motion[2] actuators are used instead of the conventional inchworm mechanism. These are consisted of two Piezoelectric ceramics; one is for feeding the slider, and the other is for clamping the slider in the guide way of the body. The guide is V-form. The linearity and positional accuracy of the actuators is good enough far high precision motion. Since the system is more compact than the conventional system using three Piezoelectric ceramics, it is applicable for the micro-machine or MEMS unit. To fabricate the lathe, a small spindle unit with ball bearings of diameter of 10 millimeter is built-up on the top the slider. The motion is feed backed with miniaturized linear encoder attached each axis slider. The diamond tool bite is used for cutting tool. The machining is tried to make small diameter rod. The possible diameter that can be machined in this machine is presented as well as chip formation, surface roughness, and machinability.

• KSTLE International Journal
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• v.4 no.1
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• pp.1-7
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• 2003

A turbo pump unit provides high pressure oxygen and fuel in a space shuttle main engine (SSME). This paper focused on rotordynamics, investigating its characteristics based on a numerical simulation of turbo pump finite element model. Speeds up to 50,000 rpm are considered, as well as the special problems related to elastic-ring, seal hydrodynamic force, shroud force and clearance-excitation farce. The rotordynamic prediction shows that the elastic-ring which is inserted between the casing and the outer race of ball bearing allows far an acceptable separate margin of first critical speed. Additionally, the results show that the floating ring seal, which have a peculiar ring, adds substantial stiffness and damping to the system as well as exhibits superior performance in terms of rotordynamic stability of system compared to the plain seal.

• 연구논문집
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• s.31
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• pp.77-88
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• 2001

In this paper, the critical vibration limits of a spindle unit for a high speed ball pen tip processing machine are studied. The vibration of the spindle is measured by FFT, and the influence of the vibration amplitude due to unbalance, bearing deflect, bite, and timing belts tension is analyzed. The critical vibration limits of the spindle is determined by the X, and Z directional vibrations of the spindle. Both FET and RMS values can be used to analyze the vibration characteristics of the spindle. From experimental results the limit line can be drawn for the spindle. The RMS value for the vibration limit is 3 G.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.433-442
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• 2021

Let X and X^* be a Banach space and its dual, respectively, and let B(X) and S(X) be the unit ball and unit sphere of X, respectively. In this paper, we study the relation between Modulus of n-dimensional U-convexity in X^* and normal structure in X. Some new results about fixed points of nonexpansive mapping are obtained, and some existing results are improved. Among other results, we proved: if X is a Banach space with $U^n_{X^*}(n+1)>1-{\frac{1}{n+1}}$ where n ∈ ℕ, then X has weak normal structure.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.783-800
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• 2002

Let B denote the unit ball in $C^n$, and ν the normalized Lebesgue measure on B. For $\alpha$ > -1, define $dv_\alpha$(z) ＝ $c_\alpha$$(1-\midz\mid^2)^{\alpha}$dν(z), z $\in$ B. Here $c_\alpha$ is a positive constant such that $v_\alpha$(B) ＝ 1. Let H(B) denote the space of all holomorphic functions in B. For $p\geq1$, define the Bergman-Privalov space $(AN)^{p}(v_\alpha)$ by $(AN)^{p}(v_\alpha)$ = ${f\inH(B)$ : $\int_B{log(1+\midf\mid)}^pdv_\alpha\;<\;\infty}$ In this paper we prove that a function $f\inH(B)$ is in $(AN)^{p}$$(v_\alpha)$ if and only if $(1+\midf\mid)^{-2}{log(1+\midf\mid)}^{p-2}\mid\nablaf\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case 1＜p＜$\infty$, or $(1+\midf\mid)^{-2}\midf\mid^{-1}\mid{\nabla}f\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case p ＝ 1, where $nabla$f is the gradient of f with respect to the Bergman metric on B. This is an analogous result to the characterization of the Hardy spaces by M. Stoll [18] and that of the Bergman spaces by C. Ouyang-W. Yang-R. Zhao [13].

• Journal of Welding and Joining
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• v.33 no.3
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• pp.19-24
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• 2015

Joint properties of electric control unit (ECU) module using Sn-Cu-(X)Al(Si) lead-free solder alloy were investigated for automotive electronics module. In this study, Sn-0.5Cu-0.01Al(Si) and Sn-0.5Cu-0.03Al(Si) (wt.%) lead-free alloys were fabricated as bar type by doped various weight percentages (0.01 and 0.03 wt.%) of Al(Si) alloy to Sn-0.5Cu. After fabrications of lead-free alloys, the ball-type solder alloys with a diameter of 450 um were made by rolling and punching. The melting temperatures of 0.01Al(Si) and 0.03Al(Si) were 230.2 and $230.8^{\circ}C$, respectively. To evaluation of properties of solder joint, test printed circuit board (PCB) finished with organic solderability perseveration (OSP) on Cu pad. The ball-type solders were attached to test PCB with flux and reflowed for formation of solder joint. The maximum temperature of reflow was $260^{\circ}C$ for 50s above melting temperature. And then, we measured spreadability and shear strength of two Al(Si) solder materials compared to Sn-0.7Cu solder material used in industry. And also, microstructures in solder and intermetallic compounds (IMCs) were observed. Moreover, thickness and grain size of $Cu_6Sn_5$ IMC were measured and then compared with Sn-0.7Cu. With increasing the amounts of Al(Si), the $Cu_6Sn_5$ thickness was decreased. These results show the addition of Al(Si) could suppress IMC growth and improve the reliability of solder joint.