• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.127-138
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• 1991

A gear forming method by cold extrusion and an analytical method with its numerical solution program based on the upper bound method were developed. In the analysis the involute curve was as a shape of die and the upper bound method was used to calculate energy dissipation rate. By this method the power requirement and optimum conditions necessary for extruding helical(spur) gear were successfully calculated. These numerical solutions are in good agreement with experimental data. In the experiment, 4-6 class helical gear of KS standard for automobile transmission was successfully manufactured.

• East Asian mathematical journal
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• v.17 no.1
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• pp.93-101
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• 2001

We give an equivalent formulation to the $Erd\"{o}s'$ conjecture on the lower bound of the greatest element in a set having distinct subset sums. On this basis we suggest a possible approach towards $ERD\"{O}S'$ conjecture. Also we reproduce L. Moser's result by means of an analytic method.

• Journal of the Korean Society of Propulsion Engineers
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• v.4 no.3
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• pp.55-63
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• 2000

Studies for tube spin forming have been implemented restrictively compared to spinning process, because of the complex of deformation mechanism. Especially there were not many studies by using FEM(Finite Element Method) for overcoming restriction of upper bound method. In this paper, the tube spinning process is analyzed to produce cylindrical body made by titanium alloy. In analysis, processing parameters was obtained by using upper bound method to consider material properties of titanium alloy and finite element analysis was implemented to investigate the flatness and the elongation of the titanium alloy workpiece by using ABAQUS code. The independent variables are ; material properties of workpiece, angles of roller, reduction of diameter. Three variables, two angles of roller and reduction of diameter are optimized by using the upper bound method. In this method, we can estimate the workable power, working force and reduction of diameter, and also the flatness and the elongation of workpiece by the finite elements analysis using ABAQUS/standard. The results indicates that these variables play a critical factors of spinning process for the titanium alloy and the optimum values of these variables.

• Geomechanics and Engineering
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• v.6 no.5
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• pp.503-515
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• 2014

On the basis of Hoek-Brown failure criterion, a numerical solution for the shape of collapsing block in the rectangular cavity subjected to seepage forces is obtained by upper bound theorem of limit analysis. The seepage forces obtained from the gradient of excess pore pressure distribution are taken as external loadings in the limit analysis, and the pore pressure is easily calculated with pore pressure coefficient. Thus the seepage force is incorporated into the upper bound analysis as a work rate of external force. The upper solution of the shape of collapsing block is derived by virtue of variational calculation. In order to verify the validity of the method proposed in the paper, the result when the pore pressure coefficient equals zero, and only hydrostatic pressure is taken into consideration, is compared with that of previous work. The results show good effectiveness in calculating the collapsing block shape subjected to seepage forces. The influence of parameters on the failure mechanisms is investigated.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.933-944
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• 2004

Packing dimension of a set is an upper bound for the packing dimensions of measures on the set. Recently the packing dimension of statistically self-similar Cantor set, which has uniform distributions for contraction ratios, was shown to be its Hausdorff dimension. We study the method to find an upper bound of packing dimensions and the upper Renyi dimensions of measures on a statistically quasi-self-similar Cantor set (its packing dimension is still unknown) which has non-uniform distributions of contraction ratios. As results, in some statistically quasi-self-similar Cantor set we show that every probability measure on it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely and it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely for almost all probability measure on it.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.9
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• pp.1364-1372
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• 1997

In this paper, the forging of helical gears has been investigated. Punch is tooth-shaped as is the die insert. The punch compresses a cylindrical billet placed in a die insert. As a consequence the material of billet flows into the tooth region. The forging has been analysed by using the upper-bound method. A kinematically admissible velocity field has been developed, wherein, an involute curve has been introduced to represent tooth profile of the gear. Numerical calculations have been carried out to investigate the effects of various parameters, such as module, number of teeth, helix angle and friction factor on the forging of helical gears. Some forging experimentswere carried out with aluminum alloy to show the validity of the analysis. Good agreement was found between the predicted values of the forging load and obtained from the experimental results.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.8 s.197
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• pp.34-40
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• 2007

In this study, focusing on reducing a load in forming helical gears, the extrusion using two-step processes for manufacturing helical gear is proposed. The process is composed of the extrusion step in which spur gear to be used as a preform in next step is formed, and the torsion step in which the preform of spur gear is formed to helical gear. Upper-bound theory for the two-step process is applied and compared with the results of experiment. The result of upper-bound solution has a good agreement with that of the experiment and the FE analysis. The newly proposed method can be used as an advanced forming technique to remarkably reduce a forming load, to prolong a tool life, and to replace the conventional forming process of helical gears. Results obtained from the extrusion using two-step processes enable the designer and manufacturer of helical gear to be more efficient in this field.

• Journal of Integrative Natural Science
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• v.9 no.1
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• pp.10-15
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• 2016

In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.

• Journal of KIISE:Software and Applications
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• v.28 no.9
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• pp.681-687
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• 2001

In order to raise a class discrimination power by combining multiple classifiers under the Bayesian decision theory, the upper bound of a Bayes error rate bounded by the conditional entropy of a class variable and decision variables obtained from training data samples should be minimized. Wang and Wong proposed a tree dependence first-order approximation scheme of a high order probability distribution composed of the class and multiple feature pattern variables for minimizing the upper bound of the Bayes error rate. This paper presents an extended high order product approximation scheme dealing with higher order dependency more than the first-order tree dependence, based on the minimization of the upper bound of the Bayes error rate. Multiple recognizers for unconstrained handwritten numerals from CENPARMI were combined by the proposed approximation scheme using the Bayesian formalism, and the high recognition rates were obtained by them.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.9A
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• pp.1401-1410
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• 1999

In this paper, we propose a fast block matching algorithm using the lower and upper bound of mean absolute difference (MAD) which is calculated at the search region overlapped with neighbor blocks. At first, we calculate the lower bound of MAD and reduce the search point by using this lower bound. In this method, we can get good prediction error performance close to full search block matching algorithm (FSBMA), but there exists some computational complexity that has to be reduced. Therefore, we further reduce the computational complexity by using pixel subsampling besides the lower and upper bound of MAD. Experimental results show that we can remarkably reduce the computational complexity with good prediction error performance close to FSBMA.