• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.5
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• pp.831-836
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• 1989

It was found that the effect of the friction between the roll and the workpiece on the spread ratio in flat rolling processes varies with the width-to-height ratio and the reduction in height by Tozawa, Oh and kobayashi numerically. In the present study, the barrelling profile accompanying the width spread was predicted by using the energy method proposed by Kato, which is known to be one of the most advanced method for the three dimensional analysis of the rolling process. The modified velocity field was applied to compute the width spread and the result was verified by experiments. the analysis by the energy method gave the result that the spread ratio increases with the friction factor when the width-to-height ratio is 1 and decreases when the ratio is larger then 2, being consistent with the results of Tozawa and Oh. Nevertheless the cold rolling experiment for pure aluminium showed that the spread ratio decreases with the increasing friction factor irrespective of the width-to-hight ratio.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.8
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• pp.63-72
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• 1995

Closed-die forging of spur gears with hollow cylindrical billet 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 the forging die profile. In the analysis, the deformation region has been divided into nine zones. A constant frictional stress has been assumed on the contacting surfaces. Utilizing the formulated velocity field, numerical calculations have been carried out to investigate the effects of various parameters, such as module, number of teeth and friction factor, on the forging of spur gears. Hardness and accuracy of forged gears are measured. The following results have been obtained: (1) It is verified that an axisymmetric deformation zone exists between root circle and center of gear through forged gears. (2) The average relative forging pressure is predominantly dependent on the number of teeth and increases near the final filling stage as the addendum modification coefficient increases. (3) Close agreement was found between the predicted values of forging load and those obtained from experimental results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.1
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• pp.51-61
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• 1993

A systematic approach of the energy method is proposed for analysis of axisymmetric deep drawing in which the total deforming region is divided into five sections by the geometric characteristic. The corresponding solution is found through optimization of the total energy dissipation with respect to some parameters assumed in the kinematically admissible velocity field defined over each region. The sheet blank is divided into three-or five-layers to consider the bending effect. For the evaluation of frictional energy, it is assumed that the blank holding force acts on the outer rim of the flange and that the contact pressure acting on punch shoulder or die shoulder has uniform distributions, respectively. The computed results by the present method are compared with the experiment and the computed results by the elastic-plastic finite element method for the distribution of thickness strain and the relation between the punch stroke and punch load. The results for the case of multi-layers show better agreements than for the case of a single layer in load vs. stroke relation and strain distribution. It is thus shown that the multi-layer technique can be effectively employed in analyzing axisymmetric deep drawing in connection with the energy method.

• Journal of the Korean Geotechnical Society
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• v.23 no.4
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• pp.185-197
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• 2007

Limit analysis of upper and lower bound solutions has been well developed to provide the stability numbers for shallow tunnels in cohesive soil ($c_u$ material), cohesive-frictional soil (c'-$\phi$' material) and cohesionless soil ($\phi$'material). However, an extension of these methods to relatively deep circular tunnels in the cohesionless soil has been explored rarely to date. For this reason, the closed-form analytical solutions including lower bound solution based on the stress discontinuity concept and upper bound solution based on the kinematically admissible failure mechanism were proposed for assessing tunnel collapse load in this study. Consequently, the tunnel collapse load from those solutions was compared with both the finite element analysis and the previous analytical bound solutions and shown to be in good agreement with the FE results, in particular with the FE soil elements located on the horizontal tunnel axis.