• Korean Journal of Computational Design and Engineering
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• v.8 no.4
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• pp.278-288
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• 2003

Presented in this paper is a numerical method for calculating the intersection points between Z-map vectors and the tool swept surface for circularly moving filleted-end mills. In numerically controlled(NC) machining simulation for large moulds and dies, a workpiece is frequently approximated as a set of z-axis aligned vectors, called Z-map vectors, and then the machining processes can be simulated through updating the Z-map with the intersection points. Circular motions are typically used for machining the free-form surfaces. For fast computation, we express each of intersection points with a single-variable non-linear equation and calculate the candidate interval in which the unique solution exists. Then, we prove the existence of a solution and its uniqueness in this candidate interval. Based on these properties, we can effectively apply numerical methods to finally calculate the solution of the nonlinear equation within a given precision. Experimental results are given for the case of a TV monitor and the hood of a car.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1814-1821
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• 2002

NC cutting simulation is an important factor in the development of products. The geometric modelling of cutter swept surface should be done in NC cutting simulation. A part of cutter swept surface is a ruled surface blended with silhouette curve and cutter path. Finding an intersection point between cutter swept surface and a line is one of major problems in Z-map based cutting simulation. In this paper, cutter swept surface is defined parametrically and it's intersection point with Z-map is found in an exact form. Triangular grid Z-map based 3-axis NC cutting simulation is performed.

• Korean Journal of Computational Design and Engineering
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• v.7 no.4
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• pp.219-232
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• 2002

In numerically controlled(NC) machining simulation, a Z-map has been used frequently for representing a workpiece. Since the Z-map is usually represented by a set of Z-axis aligned vectors, the machining process can be simulated through calculating the intersection points between the vectors and the surface swept by a machining tool. In this paper, we present an efficient method to calculate those intersection points when an APT-type tool moves along a linear tool path. Each of the intersection points can be expressed as the solution of a system of non-linear equations. We transform this system of equations into a single-variable equation, and calculate the candidate interval in which the unique solution exists. We prove the existence of a solution and its uniqueness in this candidate interval. Based on these characteristics, we can effectively apply numerical methods to finally calculate the solution of the non-linear equations within a given precision. The whole process of NC simulation can be achieved by updating the Z-map properly. Our method can provide more accurate results with a little more processing time, in comparison with the previous closed-form solution.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.235-239
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• 2001

Finding intersection point between a surface and a line is one of major problem in CAD/CAM. The intersection point could be found in an exact form or with numerical method. In this paper, the exact solution of the intersection point between a ruled surface which is generated by the movement of an endmill and the z-direction vector is presented. The cutter swept surface which is a ruled surface and the Z-direction vector are represented with parametric equations. With the nature of parametric equations, the geometric properties at the intersection point are easily acquired.

• Journal for History of Mathematics
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• v.15 no.2
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• pp.161-168
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• 2002

We show that if the Stone-Cech compactification of $\textit{AX}$ and the minimal basically disconnected cove. of $\beta$Χ we homeomorphic and every real $\sigma$$Z(X)^#$-ultrafilter on X has the countable intersection property, then there is a covering map from $\nu$(ΛΧ) to $\nu$Χ and every real $\sigma$$Z(X)^#$-ultrafilter on Χ has the countable intersection property if and only if there is a homeomorphism from the Hewitt realcompactification of ΛΧ to the minimal basically disconnected space of $\nu$Χ.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.5
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• pp.58-64
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• 2000

This paper proposes a method for determining optimal EDM parameters based on discharge area from the physical model of a tool electrode. Main parameters, which affect the EDM performance, are peak value of currents, pulse-on time, and pulse-off time. Such parameters are closely dependent on the discharge area in EDM process. In this paper the discharge area is estimated from the CMM scanning data to the tool electrode. The method is very useful when any geometric information to the tool electrode is not provided from tool modeler or producer. The method consists of following four steps. First a triangulation mesh is constructed from the CMM data. Secondly, the z-map is modeled from the triangulated mesh. Thirdly, the discharge area is estimated from intersection between the z-map model and a z-height plane. Finally, the machining parameters are easily calculated by some known EDM equations to the discharge area. An example is introduced to show that the machining parameters are calculated from the CMM data to a tool electrode.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.221-229
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• 2013

We show that if X is a space such that ${\beta}QF(X)=QF({\beta}X)$ and each stable $Z(X)^{\sharp}$-ultrafilter has the countable intersection property, then there is a homeomorphism $h_X:vQF(X){\rightarrow}QF(vX)$ with $r_X={\Phi}_{vX}{\circ}h_X$. Moreover, if ${\beta}QF(X)=QF({\beta}X)$ and $vE(X)=E(vX)$ or $v{\Lambda}(X)={\Lambda}(vX)$, then $vQF(X)=QF(vX)$.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.782-787
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• 1997

This paper proposes methods for pencil machining and uncut area machining. Based on Z-map represented by triangular facets, self-intersection-free offset surface is generated with K-offset method in case of ball mill and flat mill Pencil machining can elliminate overload area before main machining rough, semi-finish and finish cutting,preventing fluctuations of cutting forces in concave regions form causing bad machining condition. Low productivity is caused by uncut area which has excessive or irreguar finishing allowance. Uncut area machining has the finishing allowance keep uniformly on part surface. This paper deals with two types of uncaut area, machining detection of excessive area and user-defined area.

• Korean Journal of Remote Sensing
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• v.33 no.5_1
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• pp.469-480
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• 2017

This study aims to understand the relationship between lineaments and epicenters in Geochang region, Gyungsangnam-do, South Korea. An instrumental observation of earthquakes has been started by Korea Meteorological Administration (KMA) since 1978 and there were 6 earthquakes with magnitude ranging 2 to 2.5 in Geochang region from 1978 to 2016. Lineaments were extracted from LANDSAT 8 satellite image and shaded relief map displayed in 3-dimension using Digital Elevation Model (DEM). Then, lineament density was statistically examined by hotspot analysis. Hexagonal grids were generated to perform the analysis because hexagonal pattern expresses lineaments with less discontinuity than square girds, and the size of the grid was selected to minimize a variance of lineament density. Since hotspot analysis measures the extent of clustering with Z score, Z scores computed with lineaments' frequency ($L_f$), length ($L_d$), and intersection ($L_t$) were used to find lineament clusters in the density map. Furthermore, the Z scores were extracted from the epicenters and examined to see the relevance of each density elements to epicenters. As a result, 15 among 18 densities,recorded as 3 elements in 6 epicenters, were higher than 1.65 which is 95% of the standard normal distribution. This indicates that epicenters coincide with high density area. Especially, $L_f$ and $L_t$ had a significant relationship with epicenter, being located in upper 95% of the standard normal distribution, except for one epicenter in $L_t$. This study can be used to identify potential seismic zones by improving the accuracy of expressing lineaments' spatial distribution and analyzing relationship between lineament density and epicenter. However, additional studies in wider study area with more epicenters are recommended to promote the results.