• 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.4 no.3
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• pp.257-266
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• 1995

A simulation method based on upper bound method is developed in order to characterize forging characters in forging of spur gears. In this paper, utilizing a kinematically admissible velocity field and applying it to investigate the effect of inner diameter of holow billet. In the analysis, to predict the variation of inner diameter of hollw billet, neutral surface has been introduced. The neutral surface of each step is assumed as a circle and determined in order to have minimum forging energy by golden section method. By this method, the variation of inner diameter of billet during spur gear forging is successfully predicted. As a result, the selection of inner diameter of initial billet is very important to reduce the forging load.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.144-149
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• 1996

In this paper, the clamping type forging of helical gears has been investigated. Clamping type forging is an operation in which the product is constrained to extrude sideways through an orifice in the container wall. Punch is cylindrical shaped. The punch compresses a cylindrical billet placed in a die insert. As a consequence the material flows in a direction perpendicular to that of punch movement. 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, friction factor and initial height of billet on the forging of helical gears.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.04b
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• pp.183-186
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• 1995

A simulation method basee on upper bound method is developed in order to characterize forging characters in forging of spur gears. In this paer, utlizing a kinematically admissible velocity field and applying it to study the effect of inner diameter of holow billet. To predict the variation of inner diameter of hollow billet, neutal surface has been introduced into forging of hollow gears from hollow billes with flat punch. The neutral surface of each step is assumed as a circle and determined in order to have minimum forging energy by golden section method. According to the analysis, the magnitude of inner diameter of initial billet is vary important to reduce the relative pressure and forging load. And the variation of inner diameter of billet during spur gear forging is successfully predicted.

• Journal of the Korean Society of Industry Convergence
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• v.2 no.2
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• pp.187-194
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• 1999

Closed-die forging of spline was analysed using the upper bound elemental technique, Two different forging methods, denoted here as side extrusion-forging and upset forging, were proposed, The kinematically admissible velocity fields for each of the forging methods, which could express trapezoidal, rectangular and serration tooth forms, were presented. Upper bounds to forging loads and deformed configurations were predicted using the velocity fields. Theoretical results were compared with experimental ones. Experiments with lead were carried out at room temperature where grease was used as a lubricant. The present investigation revealed that analytical forging loads were reduced by using the side extrusion-forging but the upset forging could improve configuration of the final forged splines.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.653-660
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• 1986

Two uppor bound solutions, by the force balance method and by a kinematically admissible velocity field, are compared for the metal forming problems in plane strain. It is concluded that these two approaches always give identical results when the geometrical configurations of the deformation model reman the same. By detailed derivations for plastic bending of a notched bar, closed die forging, compression of a rectangular block, machining with a restricted contact tool and plane strain backward extrusion, the identity of both approaches is verified.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.45-48
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• 1997

The kinematically admissible velocity field is developed for the eccentric extrusion of circular shaped products. The curving of product in extrusion is caused by the difference of the linearly distributed longitudinal velocity on the cross-section of the workpiece at the dies exit. The results of the eccentric extrusion by upper bound analysis show that the curvature of product increases with the increase in eccentricity of gravity center of the cross-section of workpiece at dies entrance from that of the corss-section at the dies exit end. By the DEFORMTM-3D analysis, the curving of circular shaped product in extrusion is changed by the eccentricity, die land length and the die length. The result of the analysis by DEFORMTM-3D software shows that the curvature of circular shaped product increases with the eccentricity. The two analysis and one experiment show the curving phenomenon in eccentric extrusion process.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.49-52
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• 1997

The kinematically admissible velocity field is developed for the analysis of the curving of an eccentric extrusion. The curving of product in extrusion is caused by the difference of the linearly distributed longitudinal velocity on the cross-section of the workpiece at the dies exit. The result of the analysis show that the curvature of product increases with the increase in eccentricity of gravity center of the cross-section of the workpiece at the die entrance from that of the cross-section at the die exit. It also increase with the die land dimension. By the DEFORMTM-3D analysis, the curving of T-shaped product in extrusion is changed by the eccentricity, die land length and the friction constant. The result of the analysis by DEFORMTM-3D software shows that the curvature of circular shaped product increases with the eccentricity. The two analysis and one experiment show the curving phenomenon in eccentric extrusion process.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.3
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• pp.330-336
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• 1989

In analyzing the axisymmetric backward extrusion process a new method of analysis using upper-bound theorem is proposed in which the plastic zone and dead metal zone cam be predicted. Experiments are carried out with commercial aluminum. The metal flow on the meridional plane has been visualized experimentally by using the gridded specimens. It is shown that the theoretical results both in extrusion load and deformation pattern are in good agreement with the experimental results and they can be used for effective punch and die design to consider various process parameters in axisymmetric backward extrusion.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.4
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• pp.26-37
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• 1994

A kinematically admissible velocity field for the numerical analysis of closed-die forging process of spur gear is proposed. The velocity field is divided into three regions of deformation. In the analysis, the involute curve is approximated to be straight line and the upper-bound method is used to calculate energy dissipation rate. A constant frictional frictional factor has been assumed on the contacting surfaces. The effects of root diameter, number of teeth, and friction factor are determined on the relative forging pressure. The frictionless relative pressure is independent of root diameter for the same number of teeth, but increases with the number of teeth on a given root diameter. In the presence of friction, the relative forging presure increasing root diameter at the start of forging, but decreases with increasing root diameter in the processing of forging.