• Design & Manufacturing
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• 제17권1호
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• pp.33-39
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• 2023

The ball end mill is a type of cutting tool that is widely used to process complex mold shapes including aspheric surfaces. Unlike the flat end mill in which the cutting edge is formed on the cylindrical handle, the cutting edge is formed from the cylindrical handle to the hemispherical shape, which is advantageous for processing curved shapes. However, since the cutting speed continuously changes during machining due to the helix angle of the cutting edge or the machining inclination angle, it is difficult to obtain a precise machined surface. Therefore, in this paper, machining was performed while changing the helix angle of the ball end mill and the angle of the machining slope under the same cutting conditions for STD 11 material, which is widely used as a mold material. Through this, the effect of the two variables on the roughness of the machined surface was analyzed. As a result, if the helix angle was 0 degrees, it showed the best surface roughness of Ra. 0.16 ㎛. When the helix angle was 20 degrees, the best surface roughness of Ra. 0.18 ㎛ was occurred.

• 한국생산제조학회지
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• 제23권6호
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• pp.569-575
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• 2014

In this study, the effect of cutting edge geometry, such as helix and rake angles, on surface roughness in ball-end milling is investigated by using the Taguchi method. A set of experiments adopting the $L_{27}(3^{13})$ design with an orthogonal array are conducted with special WC ball-end mills having different helix and rake angles. Analysis of variance (ANOVA) is performed to analyze the effects of tool geometry and machining parameters, such as cutting speed, feed per tooth, and depth of cut, on surface roughness. The ANOVA results reveal that helix and rake angles are critical factors affecting surface roughness; the interaction of helix angle and cutting speed is also important. This research can contribute to novel cutting edge designs of ball-end mills and optimization of cutting parameters.

• 대한수학회지
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• 제54권4호
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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.

• 한국정밀공학회지
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• 제31권5호
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• pp.395-401
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• 2014

Development of five axis tool grinding machine and CAD/CAM systems increase tool design flexibility. In this research, investigated are cutting characteristics of ball-end mill with different helix angle. Special WC ball-end mills with $0^{\circ}$, $10^{\circ}$, $20^{\circ}$, $30^{\circ}$ helix angles are designed and used in various cutting tests. Machining performance according to helix angle variation is evaluated from cutting forces, surface roughness, tool wear, produced chip shape, and vibration characteristics. The ball-end mill with $10^{\circ}$ helix angle shows the best cutting performance due to appropriate chip load distribution and smooth chip flow. This research can be used for cutting edge geometry optimization and novel design of ball-end mill.

• 한국공작기계학회논문집
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• 제12권6호
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• pp.1-7
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• 2003

The experimental research was conducted to find an end mill with an ideal helix angle, which has a superior anti-vibration effect and a low machining tolerance. A conventional endmill which all low blades are $30^{\circ}$ helix angles and a different helix angle endmill which the opposite two blades are $30^{\circ}$ and the other opposites are different helix angles were studied. The cutting farce, machining tolerance and surface roughness were obtained. The AE signals appeared to have low values in up-milling rather than in down-milling. These are also appeared to have low values at low spindle revolutions rates. The cutting force values of Fxy and Fxyz were found to be increased according to the value of helix angle. In up-milling, it was difficult to find a definite tendency in machining tolerance, but in down-milling machining tolerance of the different helix angle end mill was found to be lower than that of the convention end mill. There is a definite tendency that the surface roughness gets better as the RPM increases. In down-milling, Type A($25^{\circ}$＋$30^{\circ}$) appeared to bring the most satisfactory result.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2003년도 춘계학술대회 논문집
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• pp.196-201
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• 2003

The experimental research was conducted to find an end mill with an ideal helix angle, which has a superior anti-vibration effect and a low machining-tolerance. A conventional endmill which all four blades are $30^\circ$ helix angles and a different helix angle endmill which the opposite two blades are $30^\circ$ and the other opposites are different helix angles were studied. The cutting force, machining tolerance and surface roughness were obtained. The AE signals appeared to have low values in up-milling rather than in down-milling. These are also appeared to have low values at low spindle revolutions rates. The cutting force values of Fxy and Fxyz were found to be increased according to the value of helix angle. In up-milling, it was difficult to find a definite tendency in machining tolerance, but in down-milling, machining tolerance of the different helix angle end mill was found to be lower than that of the convention end mill. There is a definite tendency that the surface roughness gets better as the RPM increases. In down-milling, Type $A(25^\circ+30^\circ)$ appeared to bring the most satisfactory result.

• 한국의류산업학회지
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• 제3권5호
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• pp.473-478
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• 2001

The newly developed cone drum twister is one of the outer surface contacting friction-twisting devices in false-twist texturing. An investigation of the drag angle for the newly developed cone drum twister texturing mechanism is reported. An analysis is given from which equations can be derived that relate to the conical angle of cone drum, wrapping angle, drag angle, and yam helix angle. Theoretical values of drag angle are calculated and discussed. It is shown that, as the helix angle and the projected wrapping angle increases, the drag angle also increases slowly until the helix angle of $40^{\circ}$ but after the helix angle of $40^{\circ}$ the drag angle increases rapidly. Furthermore the higher the projected wrapping angle and conical angle, the higher the drag angle of friction surface.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1999년도 추계학술대회 논문집 - 한국공작기계학회
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• pp.485-491
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• 1999

A burr is formed in every corner of parts as a result of machining, which produces undesirable edge geometry and influence deeply to surface quality of workpiece. Therefore these burrs must be removed certainly. The cost of removing these burrs is directly proportional to their size. Burrs have been among the most troublesome obstruction to high productivity and automation of machining processes. The proper selection of cutting condition and tool geometry will be helpful to reduce the occurrence of burrs. In paper will observe burr formation along helix angle in end milling and certificate experimentally mechanics relation of helix angle and burr formation.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.225-236
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• 2021

In this paper, we determine position vector of a line of curvature of a regular surface which is relatively normal-slant helix, with respect to Darboux frame. Then, a vector differential equation is established by means Darboux formulas, in the case of the geodesic torsion is vanishes. In terms of solution, we determine the parametric representation of a line of curvature which is relatively normal-slant helix, with respect to standard frame in Euclidean 3-space. Thereafter, we apply this result to find the position vector of a line of curvature which is isophote curve.

• 한국정밀공학회지
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• 제19권9호
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• pp.34-40
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• 2002

Machining accuracy is affected by quasi-static errors of machining center. Since machine errors have a direct influence upon both the surface finish and geometric shape of the finished workpiece, it is very important to measure the machine errors and to compensate these errors. The laser measurement method for identifying geometric errors of machine tool has the disadvantages such as high cost, long calibration time and usage of volumetric error synthesis model. Accordingly, this paper deals with analysis of the geometric errors of a machine tool using ball bar test without using complicated error synthesis model. Statistical analysis method was adopted in this paper for deriving geometric errors using hemispherical helix ball bar test. As a result of experiment, geometric errors of the vertical machining center are compensated by 88%.