• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.04a
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• pp.435-440
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• 2001

In this study, torsional and lateral vibrations of a gear box transmission system were analyzed theoretically using some mathematical models and examined to determine the causes of its excessive vibrations. As the results, it was found there exist possibility of resonance between gear mesh frequencies and lateral vibration mode of the transmission shaft during the third shifting mode operation. In order to avoid this resonance, we proposed changing the arrangement of gears on the transmission shaft. The measured vibration levels of the improved gear box were dramatically reduced. These results may be helpful to design a machine tool gear box with low noise and vibration.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2001.05a
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• pp.692-695
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• 2001

The EMFG(Extended Mark Flow Graph) is not only a powerful tool to. designing the discrete-event system conceptually or specifically but also a good representation tool for implementing the system directly. We present a transitions-firing process and automatic changes of the number of marks in each box as a firing determination algorithm with the incident matrix and the state transition equation. The convenient analysis and design of a system as well as Computer Aided Design is possible because the operations of an EMFG ran be represented in the mathematical analysis with ease.

• Research in Mathematical Education
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• v.11 no.3
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• pp.209-218
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• 2007

The purpose of this study is to create an interactive tool Geometry Player for geometric explorations. In designing this software, we referred to van Hiele's geometric learning theory of and Duval's cognitive comprehension theory of geometric figures. With Geometry Player, it is easy to construct and manipulate dynamic geometric figures. Teachers can easily present the dynamic process of geometric figures in class, and students can use it as a leaning tool to construct geometric concepts by themselves. It is hoped that Geometry Player can be a useful assistant for teachers and a nice partner for students. A brief introduction to Geometry Player and some application examples are included in this paper.

• Journal of Industrial Technology
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• v.14
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• pp.109-117
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• 1994

To satisfy the requirement for the precision and productivity of machine tools, we need the technique to predict the surface roughness of workpiece under various cutting conditions. The surface roughness is mainly influenced by the ideal roughness i. e., the roughness by feeding quantity and geometry of the tool. In this paper, the surface roughness is divided into three zones and the mathematical models of the three zones are obtained, in consideration of the feeding conditions and tool geometry. Using the mathematical models, we developed a program to calculate the maximum feeding quantity satisfying the required surface roughness of the workpiece. The program is used to calculate the maximum feed for two kinds of the bites used under the real cutting condition.

• Research in Mathematical Education
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• v.18 no.2
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• pp.103-128
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• 2014

This paper presents the Global van Hiele (GVH) questionnaire as a tool for mapping knowledge and understanding of plane and solid geometry. The questionnaire facilitates identification of the respondents' mastery of the first three levels of thinking according to van Hiele theory with regard to key geometrical topics. Teacher-educators can apply this questionnaire for checking preliminary knowledge of mathematics teaching candidates or pre-service teachers. Moreover, it can be used when planning a course or granting exemption from studying in basic geometry courses. The questionnaire can also serve high school mathematics teachers who are interested in exposing their students to multiple-choice questions in geometry.

• The Mathematical Education
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• v.56 no.1
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• pp.81-100
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• 2017

The concept of variable is a big idea to develop algebraic thinking. Variable has multiple meanings such as the unknown, a tool for generalization, and the relationship between varying quantities. In this study we analyzed in what ways the meanings of variable were presented in the current elementary mathematics textbooks and workbooks. The results showed that the most frequent meaning of variable was 'the unknown', 'a tool for generalization', and 'the relationship between varying quantities' in order. A close look at the results revealed that the same symbol was often used in representing different values of variable as the unknown. In taking variable as a tool for generalization, questions to provoke generalization were sometimes included not in the textbooks but in the teachers' manuals. The main focus in dealing with variable as the relationship between varying quantities was on finding out the dependent values compared to the independent ones. Building on these results, this study is expected to suggest implications for how to deal with variable concept in elementary mathematics instructional materials.

• Journal of Korea Multimedia Society
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• v.1 no.2
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• pp.224-238
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• 1998

The EMFG (Extended Mark Flow Graph) is not only a powerful tool for designing the discrete-event system conceptually or specifically but also a good representation tool for implementing the system directly. But it is difficult to design or analyze the system because the impossibility of mathematical analysis results from some complicated representation of the EMFG. In this paper, therefore we redefined EMFG representations to provide the possibility of mathematical analysis, and employed an output inhibit are of a transition, which makes possible the adequate representations for the indescribable parts. We also solved trouble parts in the circuit translations of the EMFG and proposed the circuit translation method by using the mathematical formula. Finally, we compared the conventional EMFG with the redefined EMFG, and we designed a 0101 detecter with the redefined EMFG and translated it to the corresponding circuit.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.17 no.4
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• pp.95-103
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• 2008

Diamond core drills are applied to drill difficult-to-cut materials. This paper proposes basic understanding of ceramic drilling mechanics and characteristics of main factors affecting tool life, tool wear, cutting force, and chipping thickness. In contrast to conventional drilling, the core drilling process make deep grooves on the workpiece. One difficulty of it is the evacuation of chips from the drilled groove. As the drilling depth increases, an increased amount of chips tend to cluster together and clog the groove. Eventually severe wear develops and diamond grits are separated from the drill body. To relieve the clogging problem and to evacuate chips from the groove easily, the helical drilling process is applied for the core drilling process. To analyze drilling characteristics and derive optimal drilling conditions, tool life, tool wear, cutting force, and chipping thickness are quantified through the monitoring system and the Taguchi method. Mathematical models for the tool life and chipping thickness are derived from the response surface method. Optimal drilling database has been constructed through the experimental models.

• Research in Mathematical Education
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• v.26 no.3
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• pp.167-202
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• 2023

A central problem of mathematics teaching worldwide is probably the insufficient adaptive handling of tasks-especially in computational practice phases and modeling tasks. All students in a classroom must often work on the same tasks. In the process, the high-achieving students are often underchallenged, and the low-achieving ones are overchallenged. This publication uses different modeling of the tennis serve as an example to show a possible solution to the problem and develops and discusses one adaptive task each for middle school, high school, and college using three mathematical models of the tennis serve each time. From model to model within the task, the complexity of the modeling increases, the mathematical or physical demands on the students increase, and the new modeling leads to more realistic results. The proposed models offer the possibility to address heterogeneous learning groups by their arrangement in the surface structure of the so-called parallel adaptive task and to stimulate adaptive mathematics teaching on the instructional topic of mathematical modeling. Models A through C are suitable for middle school instruction, models C through E for high school, and models E through G for college. The models are classified in the specific modeling cycle and its extension by a digital tool model, and individual modeling steps are explained. The advantages of the presented models regarding teaching and learning mathematical modeling are elaborated. In addition, we report our first teaching experiences with the developed parallel adaptive tasks.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.993-996
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• 2005

High speed machining(HSM) technique is widely used in the appliance, automobile part and mold industries, which has many advantages such as good quality, low cost and rapid machining time. but it also has problems like tool break, smooth tool path, and so on. In particular, small size end mill is easy to break, so it must be changed before interrupting operation. Generally, the tool life of small size end mill is effected by the milling conditions whose evaluated parameters are spindle, feedrate, and width of cut. The experiments are carried out by full factorial design of experiments using and orthogonal array. This paper shows optimal combination and mathematical model for tool life, and the analysis of variance(ANOVA) is employed to analyze the main effects and the interactions of these milling parameters and the second-order polynomial regression model with three independent variables is estimated to predict tool life by multiple regression analysis.