• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.10a
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• pp.135-135
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• 2003

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.507-517
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• 2004

Let (2,2,2,2) be ramification indices for the Riemann sphere. It is well known that the regular branched covering map corresponding to this, is the Weierstrass P function. Lattes [7] gives a rational function R(z)= ${\frac{z^4+{\frac{1}{2}}g2^{z}^2+{\frac{1}{16}}g{\frac{2}{2}}$ which is chaotic on ${\bar{C}}$ and is induced by the Weierstrass P function and the linear map L(z) = 2z on complex plane C. It is also known that there exist regular branched covering maps from $T^2$ onto ${\bar{C}}$ if and only if the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3), by the Riemann-Hurwitz formula. In this paper we will construct regular branched covering maps corresponding to the ramification indices (2,4,4), (2,3,6) and (3,3,3), as well as chaotic maps induced by these regular branched covering maps.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.10a
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• pp.423-427
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• 1993

An efficient 3-axis NC milling simulator is presented. The geometric simulation of milling is based on z-map structure and voxels. For the graphic simulation,dimetric projection is adopted. As a result, two faces of a voxel are exposed and they are overlapped. Visible faces are determined by using z-butter method. The simulation system is developed in IBM-PC compatible with satisfactory result.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.115-129
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• 2005

In this paper, we give a digital graph-theoretical approach of the study of digital images with relation to a simplicial complex. Thus, a digital graph $G_k$ with some k-adjacency in ${\mathbb{Z}}^n$ can be recognized by the simplicial complex spanned by $G_k$. Moreover, we demonstrate that a graphically $(k_0,\;k_1)$-continuous map $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}}^{n_1}$ can be converted into the simplicial map $S(f):S(G_{k_0}){\rightarrow}S(G_{k_1})$ with relation to combinatorial topology. Finally, if $G_{k_0}$ is not $(k_0,\;3^{n_0}-1)$-homotopy equivalent to $SC^{n_0,4}_{3^{n_0}-1}$, a graphically $(k_0,\;k_1)$-continuous map (respectively a graphically $(k_0,\;k_1)$-isomorphisim) $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}^{n_1}$ induces the group homomorphism (respectively the group isomorphisim) $S(f)_*:{\pi}_1(S(G_{k_0}),\;v_0){\rightarrow}{\pi}_1(S(G_{k_1}),\;f(v_0))$ in algebraic topology.

• 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 Korean Society of Manufacturing Technology Engineers
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• v.8 no.3
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• pp.83-91
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• 1999

In this paper, we suggest a virtual machining system that can simulate cutting forces of ball end milling at the stage of part design. Cutting forces, here, are estimated from the machanistic model that uses the concept of specific cutting farce coefficient. To this end, we need undeformed chip thickness which is used for calculating chip load. It is derived from the Z-map data of a CAD model. That is, chip load is the height difference between the cutting tool and the workpiece at an arbitrary position. The tool contact point is referred from the cutter location data. On the other hand, the workpiece height is acquired from the Z-map model of a CAD data. From the experimental verification, we can simulate machining process effectively to the slot and the side cutting of ball end mill.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.12
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• pp.86-92
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• 2002

This paper presents a new model of NC verification in NC milling using z-map. The model can describe the motion of machine tool like a real machine effectively. The model uses x, y, and z directional feed rate as well as cutting data for modeling Z-map of workpiece. The model verifies the over-cut, the under-cut and the surface topography using NC codes and cutting conditions. To investigate the performance of the model, simulation study was carried out. As the results, the model gave the geometry accuracy of workpiece, the surface topography, and the chip loads.

• Journal of the Korean Society of Industry Convergence
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• v.4 no.4
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• pp.365-369
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• 2001

This paper presented a new model of virtualized CNC milling machine. The model verifies the over cut, the under cut and the surface roughness using NC file generated from CAM and cutting condition. The model uses Z-map model to verify workpiece. In this paper, the model used the velocities of x, y and z direction and obtained a center point of a hall end mill for modeling Z-map of workpiece. To investigate the performance of the model, simulation study was carried out. As the results, the model gave geometry accuracy of workpiece, the surface roughness and the chip loads in finish cutting that can predict tool chipping. The virtualized CNC machine can he used a flat end mill, a ball end mill and a rounded end mill.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.873-876
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• 2003

Z-map model is the most widely used model for NC simulation and verification. But it has several limitations to get a high precision, to apply 5 axis machining simulation. In this paper, we tried to use quadtree for searching cutting region. Quadtree representation of two dimensional objects is performed with a tree that describes the recursive subdivision. By using these quadtree model. storage requirements were reduced. And also, recursive subdivision was processed in the boundries, so, useless computation could be reduced, too. To get more high Accuracy, we applied the supersampling method in the boundaries. The Supersampling method is the most common form of the antialiasing and usually used with polygon mesh rendering in computer graphics To verify quadtree model we compared simulated results with z-map model and enhanced z-map model

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.179-189
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• 2019

In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map $F:L{\times}L{\rightarrow}L$ is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies $F(x{\rightarrow}y,z)=x{\rightarrow}F(y,z)$ for all $x,y,z{\in}L$.