• Transactions of Materials Processing
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• v.4 no.1
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• pp.59-69
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• 1995

A simple kinematically admissible velocity field is proposed to determine the final-stage extrusion load and the average extruded length in the square-die forward extrusion of regular polygonal-shaped bars from circular billets. From the proposed velocity field, the upper-bound extrusion load and the average extruded length are determined by minimizing the total power consumption with respect to four parameters. Experiments have been carried out with hard solder billets at room temperature. The theoretical predictions of the extrusion load are in good agreements with the experimental results and there is generally reason able agreement in average extruded length between theory and experiment.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.2005-2015
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• 1994

An analytical method based on the upper bound approach for the cup-bar axisymmetric combined extrusion is presented to determine the deformation zones as well as extrusion load and deformed geometry in the early stage. A new kiematically admissible velocity field is derived by the appropriate transformation of the original velocity field and applying the flow function approach. The derived velocity field is directly related to the boundary function for the plastically deforming zones and the parameter controlling the flow direction to the forward part or backward part. Experiments are carred out with the annealed aluminum 2024 at room temperature for the various area reductions. The workhardening effect is considered in the formulation as a function of the height ratio between the deformed billet and the orighinal billet to calculate the extrusion pressures. The theoretical predictions for the extrusion loads and deformed configuration are in good agreement with the experimental results.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1995.10a
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• pp.143-149
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• 1995

A simple kinematically admissible velocity field is proposed to drtermine the final-stage extrusion load and the average extruded length in the square-die forward extrusion of non-axisymmetric bars from circular billets. The proposed velocity field is applied to the square-die extrusion of trochoidal gear-shaped bars and rectangular-shaped bars, the profile function of a rectangular being approximated by using a Fourier series. Experiments have been carried out with hard solder billets at room temperature. The theoretical predictions of the extrusion load are in good agreements with the experimental results and there is generally reasonable agreements in average extruded length between theory and experiment.

• Transactions of Materials Processing
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• v.4 no.4
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• pp.390-397
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• 1995

A simple kinematically admissible velocity field is proposed to determine the final-stage extrusion load and the average extruded length in the square-die forward extrusion of non-axisymmetric bars from circular billets. The proposed velocity field is applied to the square-die extrusion of trochoidal gear-shaped bars and rectangular-shaped bars. The profile function of a rectangle is approximated by using a Fourier series. Experiments have been carried out with hard solder billets at room temperature. The theoretical predictions of the extrusion load are in good agreements with the experimental results and there is generally reasonable agreements in average extruded length between theory and experiment.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1998.03a
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• pp.210-213
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• 1998

A kinematically admissible velocity field is developed for the analysis of twisting of extruded products. The twisting of extruded product is caused by the linearly increased rotational velocity from the center on the cross-section of the workpiece at the die exit. In the analysis, the rotational velocity in angular direction is assumed by the multiplication of radial distance and angular velocity. The angular velocity is zero at the die entrance and is increased linearly by axial distance from die entrance. The increase rate of angular velocity is determined by the minimization of plastic work. The results of the analysis show that the angular velocity of the extruded product increase with the die twisting angle and the aspect ratio of product and friction condition and reduction area and show that angular velocity increases with the decreases in die length.

• Transactions of Materials Processing
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• v.7 no.4
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• pp.340-346
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• 1998

A kinematically admissible velocity field is developed for the analysis of twisting of the extruded products with elliptical shapes from round billet. The twisting of extruded product is caused by the lin-early increased rotational velocity from the center on the cross-section of the workpiece at the die exit. In the analysis the rotational velocity in angular direction is assumed by the multiplication of radial distance and angular velocity. The angular velocity is zero at the die entrance. The increase rate of angular velocity is determined by the minimization of plastic work. The results of the analysis show that the angular velocity of the extruded product in creases with the die twisting angle, the aspect ratio of product the friction condition, the reduction of area, and decreases with the die length.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1998.03a
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• pp.250-253
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• 1998

The kinematically admissible velocity 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 plane 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 zone are determined by the minimization of the plastic work and that the curvature of the extruded products increases with the eccentricity.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.03a
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• pp.130-135
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• 1997

A kinematically admissible velocity field is developed for the analysis of twisting of extruded products. The twisting of extruded product is caused by the linearly increased rotational velocity from the center on the cross-section of the workpiece at the die exit. In the analysis, the rotational velocity in angular direction is assumed by the multiplication of radial distance and angular velocity. The angular velocity is zero at the die entrance and is increased linearly by longitudinal distance from die entrance. The increase rate of angular velocity is determined by the minimization of plastic work. The results of the analysis show that the angular velocity of the extruded product changes with the aspect ratio of product and increases with the decreases in die length and in eccentricity of gravity center of the cross-section of workpiece at die entrance from that of the cross-section at the die exit.

• 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.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.