• Proceedings of the Korean Society of Precision Engineering Conference
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• 1991.04a
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• pp.46-58
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• 1991

An upper-bound method is applied to determine the final-stage extrsuion load and the deformed configuration of extruded billet. A simple kinematically admissible velocity field for trhee-dimensional deformation at final-stage is proposed. From the proposed velocity field the upper-bound extrusion load, the velocity distribution and the configuration of extruded billet are determined byminimizing the otoal power consumption. Experiments are carried out with full-annealed commercial aluminum billets at room temperature by using different sizes of elliptic punches. The theroretical predictions both in extrusion load and deformed configuration of extruded billet are ingood agreements with the experimentalresults.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.1
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• pp.1-12
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• 1990

The study is concerned with the analysis of combined forging of non-axisymmetric shapes with inclined protrusions by UBET technique. Work hardening is considered for the given range of strain rate during the forging process. A complex shape with inclined cavities is analyzed by subdividing the workpiece into finite UBET elements for which simple velocity fields are applicable. An experimental set-up was designed and manufactured for the experiment, and experiments are carried out with lead billets. The devised set-up can be used for closed-die forging of complex shapes with protrusions in which the dies can be separated automatically for easy removal of the forged products. Based on the derived kinematically admissible velocity fields for corresponding UBET elements, general computer programs have been developed. Since the energy dissipation rate for each elemental region is provided by subprograms (Subroutine or Function), the developed program can be applied to the forging problems of various shapes. The present study has shown that the method developed can be effectively applied to forging of non-axisymmetric shapes with complicated protrusions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.3
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• pp.345-352
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• 1989

Upsetting of non-circular blocks is characterized by the three-dimensional deformation with lateral sidewise spread as well as axial bulging along thickness. A kinematically admissible velocity field for the upsetting of prismatic or non-prismatic blocks is proposed which considers the different frictional conditions at the top and bottom surfaces of a billet. From the proposed velocity field the upper-bound load and the deformed configuration are determined by minimizing the total power consumption with respect to some chosen parameters. Experiments are carried out with annealed SM 15C steel billets at room temperature for different billet shapes and frictional conditions. The theoretical predictions both in the forging load and the deformed configurations are shown to be in good agreement with the experimental observations. Therefore, the velocity field proposed in this work can be used for the prediction of forging load and deformation in upsetting of prismatic or non-prismatic blocks, considering the different frictional conditions at two flat dies.

• Transactions of Materials Processing
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• v.7 no.5
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• pp.496-504
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• 1998

The eccentric extrusion and bending process for the forming of the curved rectangular hollow tube is newly developed. Generally the bending process of hollow tube is the secondary process followed by the extrusion process of the hollow tube from the round billet. So many defects such as wrinkling and the difference of wall thickness can be happened during the secondary bending process. In order to avoid the defects the new process named as "the eccentric extrusion and bending process" is suggested and applied to the U-bending of rectangular hollow tube. In this paper the kinematically admissible velocity field between the dies surface and the internal plug boundary surface s developed for the curving velocity. By the using of this curving velocity field the curvature of extruded products can be calculated with the parameters such as eccentricity dies length friction constant aspect ratio.

• Transactions of Materials Processing
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• v.3 no.1
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• pp.23-37
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• 1994

The upper bound element technique(UBET) is used to analyze the final stage of the axisymmetric forward extrusion. Kinematically admissible velocity field involving curved surface of velocity discontinuity is assumed. The required power to arise the piping defect is obtained and is compared with Aviture's solution a the same condition. Conditions for inception of the cavity and development of the pipe are predicted. The internal radius of the pipe and critical length of billet are also determined. Experiments are carried out for extrusion with lead specimens to investigate the piping phenomena. The theoretically predicted results showed reasonably good agreement with the experimental observation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.1
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• pp.110-117
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• 1987

A new kinematically admissible velocity field for a generalized three-dimensional flow is introduced, in which the flow is bounded by an analytic die-profile function. Then, by applying the upper-bound method th the velocity field, the flow patterns as the upper-bound method are obtained. Extrusion of elliptic sections from round billets is chosen as a computational example. Computation and experiments are carried out for work-hardening material such as aluminum alloy 2024. In order to visualize the plastic flow, the grid marking technique is employed. The theoretical predictions both in extrusion load and deformed pattern are in good agreement with the experimental data.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.598-603
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• 2001

For metal forming analysis, upper-bound solution is practical method because the solution is overestimated. It is limited to determine stresses on tools by using upper-bound solution. In this study, new scheme to calculate stresses on tools based on upper bound solution is proposed. To verify the proposed scheme, plane strain drawing has been considered. The stresses on tools obtained by the proposed scheme are compared with results of rigid plastic FEM. And the stresses on tools have been determined by the proposed scheme in the forging within plane strain deformation.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.10a
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• pp.67-67
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• 2003

자동차, 항공기, 산업기계, 운반기계, 철도차량, 공작기계 등 거의 모든 산업부문에서 사용되는 베벨기어의 냉간단조 공정 및 금형 설계를 위한 해석을 수행하였다. 소성가공에 의해 생산된 베벨기어는 기계적 성질이 우수하여 동력 전달장치의 수명연장 및 신뢰성, 소형화 등을 달성할 수 있으며 생산 원가 절감의 효과가 크기 때문에 냉간 단조의 공정설계는 매우 중요하다. 베벨기어의 단조에 대한 상계해석 결과는 금형 설계 시 프레스에 필요한 단조하중을 예측할 수 있으므로 프레스의 최적성형과 안전한 금형 설계를 도모할 수 있다. 따라서 본 연구에서는 베벨기어의 냉간 단조시의 내부 동적 가용속도 장을 제시하였고 단조하중, 금속유동 등을 계산하였다. 또한 강소성 유한요소해석을 동시에 수행하여 제시한 동적 가용속도장의 적절성을 비교 검토하였다. 본 연구의 결과는 베벨기어의 적절한 냉간 단조 성형공정 및 공정설계를 위한 기초자료로 활용될 수 있을 것이다.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.6
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• pp.174-181
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• 2001

An upper bound elemental technique(UBET) has been carried out to predict the forming load, the deformation pattern and the extrude length of the lateral extrusion of a spider for the automotive universal joint. For the upper bound analysis, a kinematically admissible velocity field(KAVF) is proposed. From the proposed velocity field, the upper bound load, the deformation pattern and the average length of the extruded billets are determined by minimizing the total energy consumption rate which is a function of unknown velocities at each element. Experiments are carried out with antimony-lead billets at room temperature using the rectangular shape punch. The theoretical prediction of the forming load, the deformation pattern and the extruded length are good in agreement with the experimental results.

• Transactions of Materials Processing
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• v.7 no.2
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• pp.177-185
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• 1998

The kinematically admissible veolcity field is developed for the shapes of dead metal zone and the curving velocity distribution in the eccentric plane dies extrusion. The shape of dead metal zone is defined as the boundary surface with the maximum friction constant between the deformable zone and the rigid zone. The curving phenomenon in the eccentric lane dies is caused by the eccentricity of plane dies. The axial velocity distribution in the plane dies is divided in to the uniform velocity and the deviated velocity. The deviated velocity is linearly changed with the distance from the center of cross-section of the workpiece. The results show that the curvature of products and the shapes of the dead metal one are determined by the minimization of the plastic work and that the curvature of the extruded products increase with the eccentricity.