• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1331-1343
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• 2017

A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1523-1532
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• 1990

The objective of this study is to develope an optimized multi-facet drill (MFD). The principal factors that affect drilling performance are its geometry and the cutting conditions. In particular, the helix angle in the total twist angle of the twist drill, affects much morgen influence on the dynamic and static stiffness and on determining the characteristics of the chip disposal capacity of the drill. In this study, considering the helix angle as a major parameter, the model was developed. From this model, the deformation of transverse direction was simulated with the bending forces applied. The performance of a drill largely depends upon drilling forces. Comprehensive models for predicating the drilling thrust and torque are developed for the different drill geometries. The effects of MFD geometric parameters on thrust and torque are also deduced from the prediction models, from which an optimal drill geometry is found with the emphasis on minimum drilling forces.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.373-377
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• 2002

In the end milling operation the deflection of the cutter is an important factor affecting the accuracy of machining with implications on the selection of cutting parameters and economics of the operation. The deflection of the end mill was studied both experimentally with strain gauge, tool dynamometer, laser measuring apparatus and on a finite element model of the cutting using ANSYS software. The deflection of machining tool with various helix angles was studied with FEM simulation and experiment. ANSYS analysis performed on the finite element model of the end mill provides deflection results which agree within 15.0% with the experimental ones.

• Proceedings of the Korean Society of Crop Science Conference
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• 2017.10a
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• pp.228-228
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• 2017

• Journal of the Korean Society for Precision Engineering
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• v.19 no.2
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• pp.79-86
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• 2002

In end milling process the undeformed chip thickness and the cutting force components vary periodically with phase change of the tool. In this study, up end milling process is transformed to the equivalent oblique cutting. The varying undeformed chip thickness and the cutting force components in end milling process are replaced with the equivalent average ones. Then it can be possible to analyze the chip-tool friction and shear process in the shear plane of the end milling process by the equivalent oblique cutting system. According to this analysis, when cutting Inconel 718, 61, 64 and 55% of the total energy is consumed in the shear process with the helix angle 30$^{\circ}$, 40$^{\circ}$ and 50$^{\circ}$ respectively, and the balance is consumed in the friction process. With the helix angle of 40$^{\circ}$ the specific cutting energy consumed is smaller than with the helix angle 30$^{\circ}$ and 50$^{\circ}$.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.5
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• pp.133-138
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• 2002

The technique of high speed machining is widely studied in machining fields, because the high efficiency and accuracy in machining can be obtained in high speed machining. Unfortunately the development of tool fur high speed machining in not close behind that of machine tool. In this study, 10 types flat endmill is prepared for obtaining data according to tool shape. Especially, we concentrated in helix angle, number of cutting edge and rake angle. Cutting condition is selected for several experiments and measuring cutting farce, tool life, tool wear and chip shape according to cutting length. 3-axis cutting farces are acquired from the tool dynamometer with high natural frequency, as the conventional tool dynamometer (9257B, Kistler) has cannot measure the state of high frequency force. Particularly, we found out that the axial cutting force waveform has a good relation with tool wear features. And flow is interrupted at the beginning of cutting by the decrease of rake angle. By above results. it is suggested the endmill tool with 45$^{\circ}$helix angle, 6 cutting edge and -15$^{\circ}$rake angle is suitable for high speed machining.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.11
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• pp.88-93
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• 2000

Recently the gear design focuses on the optimal design to extract the design factors from the vehicle transmission that is required to equip the powerful, speedy and silent characteristics. In this study, we had determined modules($m_n$) and face widths (b) to sustain strengths of contact and bending. The pressure angle ($\alpha$) and the helix angle ($\beta$) also had been obtained from the constraint of a contact ratio ($\varepsilon) on helical gears. Through the optimal design algorithm suggested in this study, the design factors were calculated on vehicle transmission gears and those determined factors were able to firm a suitability of the design.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.04a
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• pp.302-307
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• 2002

In end milling process, the undeformed chip section area and cutting forces vary periodically with phase change of the tool. However, the real undeformed chip section area deviates from the geometrically ideal one owing to cutter runout and tool shape error. In this study, a method of estimating the real undeformed chip section area which reflects cutter runout and tool shape error was presented during up-end milling of Inconel 718 using measured cutting forces. The specific cutting resistance, K. and $K_t$ are defined as the radial and tangential cutting forces divided by the modified chip section area. Both of $K_r$, and $K_t$ values become smaller as the helix angle increases from $30^\circ$ to $40^\circ$ Whereas they become larder as the helix angle increases from $40^\circ$ to $50^\circ$. On the other hand, the $K_r$, and $K_t$ values show a tendency to decrease with increase of the modified chip section area and this tendency becomes distinct with smaller helix angle.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.04a
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• pp.308-313
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• 2002

In end milling process, the undeformed chip section area and cutting forces vary periodically with phase change of the tool. However, the real undeformed chip section area deviates from the geometrically ideal one owing to cutter runout and tool shape error. In this study, a method of estimating the real undeformed chip section area which reflects cutter runout and tool shape error was presented during down end-milling of Inconel 715 using measure cutting forces. Contrary to the up-end milling the value of radial specific cutting resistance, $K_r$, becomes larger as the helix angle increases from $30^{\circ}$ to $40^{\circ}$ and it shows almost same value at $50^{\circ}$ The value of tangential specific cutting resistance, $K_t$ becomes larger as the helix angle increases same as in up-end milling, the $KK_r$, and $K_t$ values show a tendency to decrease with increase of the modified chip section area and this tendency is distinct with helix angle $40^{\circ}$.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.8
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• pp.63-70
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• 2002

In end milling process, the undeformed chip section area and cutting forces vary periodically with phase change of the tool. However the real undeformed chip section area deviates from the geometrically ideal one owing to cutter runout and tool shape error. In this study, a method of estimating the real undeformed chip section area which reflects cutter runout and tool shape error was presented in up end milling process using measured cutting forces. The average specific cutting resistance, Ka is defined as the main cutting force component divided by the modified chip section area. Ka value becomes smaller as the helix angle increases from $30^circC \;to\;40\circC$. But it becomes larger as the helix angle increases from $40^\circ$to 50 . On one hand, the Ka value shows a tendency to decrease with increase of the modified chip section area and this tendency becomes distinct with smaller helix angle.