An analysis for extrusion of helical shapes from round billets

A method of analysis is proposed for three-dimensional extrusion of a helical shape from a round billet. It is reported that a helical shape can be made by hot extrusion through a square die. In this paper, it is suggested that a helical shape be effectively cold extruded through a continuous die with appropriate lubrication. The extrusion of helical shapes can find practical application in some useful products. However, the analytical method regarding this kind of extrusion has not been attempted so far.A kinematically admissible velocity field is derived for the extrusion model where a round billet is extruded into a twisted helical section with a long elliptic cross section. The axis of the cross section is rotating during extrusion. By assuming proper stream surfaces, the velocity field is obtained by deriving the equation of a stream line. Then, an upperbound solution is formulated for the rigid-perfectly plastic material. Computation for the upperbound pressure is carried out for various process variables such as reduction of area, friction, rotation of axis, aspect ratio of a product, die length and overall die profiles.     

Analysis of hydrofilm extrusion of elliptic shapes using perturbation method

An approximate method of solution is proposed for the hydrofilm extrusion of elliptic shapes from round billets through optimized curved dies. A modified upper-bound theorem and hydrodynamic lubrication theory are used in combination, in order to analyze metal deformation and fluid flow respectively. The fluid analysis in hydrodynamic lubrication theory is simplified by use of elliptic transformation and perturbation technique. Strain-hardening effect of billet material and viscosity variation of fluid due to pressure are taken into consideration.For several reductions of area, experiments are carried out at room temperature by using mild steel specimens and caster oil as the lubricant.The experimental extrusion pressures are in good agreement with the theoretical predictions.     

Analysis of hydrofilm extrusion through optimized curved dies

A new analysis of the hydrofilm extrusion process which includes strain-hardening effects and viscosity variation in the fluid due to pressure is developed. The upper-bound method and hydrodynamic lubrication theory are adopted for the analysis of metal forming and fluid flow respectively.Experiments were carried out at room temperature, for several reductions of area, using axisymmetric curved dies. The theoretical prediction of extrusion pressure shows good agreement with experimental measurements for mild steel using castor oil as the lubricant.     

On the equivalent friction factor in hydrofilm extrusion

Hydrofilm extrusion is a kind of hydrostatic extrusion which uses a minimum amount of oil as lubricant and pressure-transmitting medium. In hydrofilm extrusion energy dissipation in the fluid lubricant between the die and working material corresponds to sliding friction in ordinary lubricated extrusion using solid lubricants. Utilizing the upper-bound theorm, an “equivalent” friction factor is defined so that the overall frictional effect between the die and working material can be conveniently investigated in terms of geometrical parameters and press velocity. On the basis of this definition, the effects of various process parameters on the frictional characteristics in hydrofilm extrusion are discussed. It is consequently found that the dominant contribution to frictional energy dissipation is made by reduction of area and press velocity. Die length is found to have very little influence on the equivalent friction factor in so far as it is longer than billet diameter.     

Upper bound analysis of extrusion from square billets through circular and square/rectangular dies

Upper bound elemental technique (UBET) for prediction of extrusion pressure in three-dimensional forward extrusion process is presented. Using square/rectangular billets, the study of the effect of die land length has been extended for the evaluations of extrusion pressures to extrude sections such as circular, square and rectangular shaped sections with power of deformation due to ironing effect at the die land taken into account. The extrusion pressure contributions due to the die land evaluated theoretically for these shaped sections considered are found to increase with die land lengths for any given percentage reduction and also increase with increasing percentage die reductions at any given die land length. The effect of die land lengths on the extrusion pressures increases with increasing complexity of die openings geometry with rectangular section giving the highest extrusion pressure followed by circular with square section die opening, giving the least extrusion pressure for any given die reduction at any given die land lengths. The proper choice of die land length is imperative if excessive pressure buildup at the emergent section is to be avoided so as to maintain good quality and metallurgical structure of the extrudates. This paper was recommended for publication in revised form by Associate Editor Youngseog Lee Ajiboye, Joseph S. received his B.Eng, M.Eng, and PhD degrees in Mechanical Engineering from the University of Ilorin, Nigeria, in 1988, 1995 and 2006 res-pectively. Dr. Ajiboye is a lecturer in the Department of Mechanical Engineering, Uni-versity of Lagos, Nigeria. He is currently a Contract Research Scientist at KAIST Valufacture Institute of Mechanical Engineering, School of Mechanical, Aerospace & Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305 - 701, Korea. Dr. Ajiboye’s research interests include ECAE/P, determination of frictional effects in metal forming operations, upper bound and finite element in plasticity.     

压光齿圆拉刀的设计改进

由于原压光齿圆拉刀在结构设计方面不够合理因而影响了被加工工件的尺寸精度和表面质量。通过改进压光齿圆拉刀的结构设计,从而大大地提高了被加工工件的表面质量。     

Upper bound analysis of extrusion of I-section bars from square/rectangular billets through square dies

In the present study the SERR technique has been reformulated to deal with extrusion of sections with/without re-entrant corners. A comprehensive computational model has been developed for this reformulated technique. The model has been used to analyse extrusion of I-section bars and the computed results have been compared with experimental values available in literature.     

Analysis of three-dimensional extrusion of sections through curved dies by conformal transformation

A new method of analysis is proposed for the extrusion of arbitrarily shaped sections through curved die profiles. A kinematically admissible velocity field is found by deriving the equation of a stream line. Conformal transformation of a unit circle onto a section is utilized in the derivation. The upper-bound method is then applied to determine the extrusion pressure for the rigid-perfectly plastic material. The redundant work relating to the velocity discontinuities at the entrance and the exit is included in the formulation. The general formulation for an arbitrary cross section is obtained by use of conformal transformation. The upper-bound pressure for extrusion through curved die profiles is computed for a complex section with a curved boundary. Two curved die profiles widely used are chosen to compare the effects of die profiles. From the derived velocity field, the upper-bound extrusion pressures are also computed for the extrusion of regular polygons and rectangles of various aspect ratios. The effects of sectional shape, die profile and interfacial friction at the die surface are discussed.     

A new formulation for three-dimensional extrusion and its application to extrusion of clover sections

The metal flow in the extrusion process is an important factor in controlling the mechanical property of the extruded products. It is, however, difficult to predict the metal flow in three-dimensional extrusion of complicated sections due to the difficulty in representing the geometry of the die surface and in expressing the corresponding velocity field. In this study a new kinematically admissible velocity field for a generalized three-dimensional flow is derived, in which the flow is bounded by the die surface expressed by an analytic function. Then, by applying the upper-bound method to the derived velocity field, the flow pattern as well as the upper-bound extrusion pressure are obtained. As a computational example, extrusion of clover sections from round billets is chosen. A new method of die surface representation is proposed by which there is a smooth transition of die contour from the die entrance to the die exit. Computation is carried out for work-hardening materials such as aluminium and steel. The analysis takes into account the effect of product shape complexity, lubrication condition and reduction of area on extrusion pressure, average effective strain and distribution of effective strains on the cross-section of the extruded product.     

A generalized method for analysis of three-dimensional extrusion of arbitrarily-shaped sections

Despite increasing demand for and application of three-dimensional extrusion of various sections through continuous dies, so far very little work has been done by systematic and general analysis to predict the plastic flow properly. For effective die design, efficient design method and the related method of theoretical analysis are required for extrusion of complicated sections. In generalized three-dimensional extrusion of sections through continuous dies, a new method of die surface representation, using blending function and Fourier series expansion, is proposed by which smooth transitions of die contour from the die entrance to the die exit are obtained. The flow patterns as well as the upper-bound extrusion pressures are obtained on the basis of the derived velocity field. The effects of area reduction, product shape complexity, die length and frictional condition are discussed in relation to extrusion pressure, the distorted grid pattern and distribution of the final effective strain on the cross-section of the extruded billet. As computational examples for arbitrarily-shaped products rounded rectangles and ellipses are chosen for the extruded sections. Experiments are carried out for aluminum alloys at room temperature for a rounded square section and an elliptic section. 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 results.     

圆孔拉刀设计方案综合分析

结合拉刀的制造与使用,从拉刀的刃磨角度入手,对拉刀关键参数进行了优化设计,达到提高拉削表面质量、延长拉刀使用寿命的目的。     

Round-to-channel section extrusion through linearly converging die: a three-dimensional analysis

Metal flow in the extrusion process is an important factor in controlling the mechanical properties of the extruded products. It is, however, difficult to predict the metal flow in three-dimensional extrusion of sections due to the involvement of re-entrant corners. The present work is an attempt to find an upper bound solution for the extrusion of channel section from round billet through the taper die. The rigid-perfectly plastic model of the material is assumed, and the spatial elementary rigid region (SERR) technique is presented for which the kinematically admissible velocity field is found out by minimizing the plastic dissipation of power. The presented analysis allows for specification of process control parameters and their relation to extrusion load, equivalent die angle, reduction ratios and friction factor.     

Further investigation into extrusion of trocoidal gear sections considering three-dimensional plastic flow

In the present study, theoretical development proposed in previous work carried out in extrusion of clover sections in relation to a generalized die design method is presented in the extended scope for three-dimensional extrusion of trocoidal gear sections from round billets with experimental verification. Computations are carried out for clover and trocoidal gear sections. The CAD/CAM of the suggested dies is introduced for the experiments. Experiments are carried out for a clover section and a trocoidal gear section with eight teeth. Al 2024 aluminum billets were used as the working material. Half-cut specimens are used for flow visualization of the extrusion process. The theoretical predictions are in good agreement with the experimental results in extrusion load and metal flow.     

Axisymmetric extrusion through adaptable dies—Part 3: Minimum pressure streamlined die shapes

In Part 1 of this series of papers, six kinematically admissible velocity fields, as well as the power terms, were developed for use in upper bound models for arbitrarily shaped dies for axisymmetric extrusion. Part 2 compared the results obtained in upper bound models for the six velocity fields through a spherical die shape and demonstrated that the sine-based velocity field was the best. In this final part, the application of the sine-1 field to extrusion through streamlined dies is developed. By fixing the values of two additional constants in the radial flow flexibility function, the two surfaces of velocity discontinuity, which separate the deformation zone from the incoming and outgoing material, will have no shear. In effect, the analysis for streamlined dies can be modeled without the surface of velocity discontinuity power terms. The results for an arbitrarily curved streamlined die, as proposed by Yang and Han, using the sine-1 velocity field and the cylindrical velocity field from the work by Yang and Han are compared. It is found that the upper bound model using the sine-1 velocity field predicts lower values for the extrusion pressure. A method to determine a streamlined die shape is proposed. The method allows flexibility between the entrance and exit by the use of a Legendre polynomial series for representation of the die surface. The method is termed an adaptable die design. The adaptable die design method is used to determine streamlined die shapes, which will minimize the pressure required for the extrusion process.     

Numerical and experimental study on the three-dimensional extrusion of square section from square billet through a polynomial shaped curved die

The geometry of die profile plays a major role in reducing the extrusion pressure and ensuring the smooth flow of material. In general, the extrusion process is mostly affected by billet geometry, die geometry, and interface frictional force at the die billet geometry. In the present investigation, an analysis using three-dimensional upper bound method using fifth-order die profile function has been carried out for extrusion of square sections from square billet. The extrusion pressure and optimum die length have been computed by multivariable optimization technique. The present die shape profile is found to be superior to many other profiles. The results obtained will help in design of optimum die profile and investigation of its performance.     

Berstorff公司的几种橡胶挤出机头

当前橡胶挤出机头类型繁多,下面重点介绍德国Berstorff公司生产的几种橡胶挤出机头： 1．异型挤出机头（如用于挤出软管的机头） 该异型机头包括机头壳体、口型板及机头锁紧装置。     

Analysis of lateral extrusion of gear-like form parts

The analysis of lateral extrusion process was carried out. A three dimensional FE model was developed to analyze the effects of some important geometrical parameters such as initial billet dimensions, gap height and frictional condition on the required forging load, the material flow pattern and effective plastic strain distribution. The FE code of DEFORM-3D was employed. A series of experimental tests on commercial lead billets were carried out to verify the FE results. The simulation work has been performed by the rigid-plastic FE method. The results obtained using the numerical solutions have been compared with the experimental data for each case study in terms of required forming load and material flow pattern in different regions. Comparison between FE and experiment results showed good agreement. Both the simulation and experimental results highlight the major role of above mentioned parameters on the required forming load and material flow pattern. The results showed that the gap height has the greatest effect on the forming load and material flow. The results presented in this paper could be used as basic data in the design of the lateral extrusion process.     

Creating round focused micro-jets from rectangular nozzles

Journal of Mechanical Science and Technology - A focused jet is an axisymmetric jet of liquid surrounded by an outer coaxial gas jet. The gas jet is typically used to compress the liquid jet in the...     

A generalised CAD/CAM solution to the three-dimensional off-centric extrusion of shaped sections: analysis

In analytical method based on the upper-bound theory is proposed to investigate the three-dimensional off-centric extrusion of arbitrarily shaped sections from arbitrarily shaped billets through linearly converging and smooth curved dies. A set of generalised kinematically admissible velocity fields are derived on the assumption of Bezier-type streamlines that provide compatibility of surface representation with most CAD/CAM systems. To obtain a more realistic non-uniform metal flow, a special velocity function was also incorporated into the derived velocity fields and work hardening effect of the material considered. Based on the method presented, for a given reduction in area, material property, friction condition and off-centric positioning of the exit cross-section, predictions of the deforming grid pattern, curvature of the extruded product as well as upper-bound to the extrusion pressures may be obtained. The above procedure is highlighted and commented upon.     

Hybrid Bat & Particle Swarm Algorithm for optimization of labyrinth spillway based on half & quarter round crest shapes

Optimization is an interesting method that finds the optimal response (i.e., objective function) by searching the decision variables in the search space. The present study deals with the optimal design of a labyrinth spillway (LS) having half-round or quarter-round crest shape. For optimal the design of the spillway geometry, an evolutionary Hybrid Algorithm (HA) of Bat Algorithm (BA) and Particle Swarm Optimization (PSO) algorithm was developed. By this procedure, the worst responses of one algorithm are replaced by the best responses of the other algorithm. This HA does not get trapped in local minima and has high convergence rate concerning the optimal absolute response. Results of using HA showed that LS with half-round crest requires less concrete, compared to quarter-round crest. Moreover, the discharge capacity for LS with half-round crest was more than the quarter-round crest. The HA significantly reduced the computational time for the optimal design of LS with half-round or quarter-round crest, as compared to BA or PSO.