• International Journal of Precision Engineering and Manufacturing
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• v.1 no.1
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• pp.111-117
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• 2000

One of the major limitations of productivity and quality in metal cutting is the machining accuracy of machine tools. The machining accuracy is affected by geometric errors, thermally-induced errors, and the deterioration of the machine tools. Geometric and thermal errors of machine tools should be measured and compensated to manufacture high quality products. In metal cutting, the machining accuracy is more affected by thermal errors than by geometric errors. This paper models the thermal errors for error analysis and develops an on-the-machine measurement system by which the volumetric errors are measured and compensated. The thermal error is modeled by means of angularity errors of a column and thermal drift error of the spindle unit which are measured by the touch probe unit with a star type styluses and a designed spherical ball artifact (SBA). Experiments show that the developed system provides a high measuring accuracy, with repeatability of $\pm$2$\mu\textrm{m}$ in X, Y and Z directions. It is believed that the developed measurement system can be also applied to the machine tools with CNC controller. In addition, machining accuracy and product quality can be also improved by using the developed measurement system when the spherical ball artifact is mounted on a modular fixture.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.1
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• pp.120-128
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• 2000

One of the major limitations of productivity and quality in metal cutting is the machining accuracy of machine tools. The machining accuracy is affected by geometric errors, thermally-induced errors, and the deterioration of the machine tools. Geometric and thermal errors of machine tools should be measured and compensated to manufacture high quality products. In metal cutting, the machining accuracy is more affected by thermal errors than by geometric errors. This paper models of the thermal errors for error analysis and develops on-the-machine measurement system by which the volumetric error are measured and compensated. The thermal error is modeled by means of angularity errors of a column and thermal drift error of the spindle unit which are measured by the touch probe unit with a star type styluses and a designed spherical ball artifact (SBA). Experiments, performed with the developed measurement system, show that the system provides a high measuring accuracy, with repeatability of $\pm$2${\mu}{\textrm}{m}$ in X, Y and Z directions. It is believed that the developed measurement system can be also applied to the machine tools with CNC controller. In addition, machining accuracy and product quality can be improved by using the developed measurement system when the spherical ball artifact is mounted on the modular fixture.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.287-304
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• 2016

In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of ${\mathbb{R}}^n$, $n{\geq}3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function H(x) is ${\beta}{\in}[1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.931-940
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• 2007

Holomorphic mean Lipschitz space is defined in the unit ball of $\mathbb{C}^n$. The membership of the space is expressed in terms of the growth of radial derivatives, which reduced to a classical result of Hardy and Littlewood when n = 1. The membership is also expressed in terms of the growth of tangential derivatives when $n{\ge}2$.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.449-457
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• 2020

We focus on the interations of the weighted Berezin transform T_α on L^p(τ), where τ is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(τ) the space of radial integrable functions played important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. Here, we introduce more properties on iterations of T_α on L¹_R(τ) and observe differences between the iterations of T_α on L1(τ) and L^p(τ) for 1 < p < ∞.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.189-202
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• 2013

On the unit ball of $\mathbb{C}^n$, the space of those holomorphic functions satisfying the mean Lipschitz condition $${\int}_0^1\;{\omega}_p(t,f)^q\frac{dt}{t^1+{\alpha}q}\;<\;{\infty}$$ is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ${\omega}_p(t,f)$ denotes the $L^p$ modulus of continuity defined in terms of the unitary transformations of $\mathbb{C}^n$.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.950-955
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• 2001

For the development of an ultra-precision CNC polishing system including on-machine measurement system, we study a corrective polishing algorithm. We analyze and test the unit removal profiles for a ball type polishing tool. Using these results we calculate dwell time distributions and residual errors for a target removal shape. We use the polishing simulation method and feed rate calculation method for the dwell time calculation. We test corrective polishing algorithm with an optical glass. The target removal shape is a sine wave that has amplitude 0.3 micro meters. We find this polishing process has a machining resolution of nanometer order and is effective for sub-micrometer order machining. This result will be used for the software development of the CNC polishing system.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.04a
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• pp.453-457
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• 2001

One of the major limitations of productivity and quality in metal cutting is the machining accuracy of machine tools. The machining accuracy is affected by geometric and thermal errors of the machine tools. In this study, the compensation device is manufactured in order to compensate thermal error of machine tools under the real-time. This paper models of the thermal errors for error analysis and develops on-the-machine measurement system by which the volumetric error are measured and compensated. The thermal error is modeled by means of angularity errors of a column and thermal drift error of the spindle unit which are measured by the touch probe unit with a star type styluses, a designed spherical ball artifact, and five gap sensors. In order to compensate thermal characteristics under several operating conditions, experiments performed with five gap sensors and manufactured compensation device on the horizontal machining center.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.735-743
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• 2001

This study was performed to evaluate the dynamic behavior of turbo pump unit. The acceptable separate margin of 1st critical speed was obtained by the use of elastic-ring inserted ball bearing, while the poor separate margin of 1$\^$st/ critical speed was appeared in the case without the elastic-ring. In addition, the results show that the stiffness and damping of plain seals gain more separate margin of 2nd critical speed. However the wear or the failure of seals could reduce the 2$\^$nd/ critical speeds near the operating speed.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.969-984
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• 2011

This paper discusses the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on the open unit ball $B_N$ of $\mathbb{C}^N$. Several analytic properties of linear fractional self-maps of $B_N$ are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.