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.     

The use of generalised deformation boundaries for the analysis of axisymmetric extrusion through curved dies

A generalised kinematically admissible velocity field is derived for axisymmetric extrusion through curved dies by employing rigid-plastic boundaries expressed in terms of arbitrarily chosen continuous functions. The corresponding upper-bound extrusion pressure is related directly to boundary functions for the plastically deforming region when the die shape, lubrication condition and material characteristics of the billet are given. The proposed method of analysis makes it possible to predict the deformation pattern as well as extrusion pressure. In computation a third-order polynomial is chosen for the die boundary and the bounding function for the plastic region is chosen to be a fourth-order polynomial. The workhardening effect is considered in the formulation. The plastic boundaries as well as stream lines are affected by various process parameters. The theory predicts the relatively faster axial flow at the center than near the die boundary for greater friction factor even with the same die shape. The effects of area reduction and die length are also discussed in relation to extrusion pressure and deformation. Experiments are carried out for steel billets at room temperature. Deformation patterns are measured for several area reductions by the photoetching technique and the extrusion pressure is measured using a load-cell. The predicted extrusion pressure is in excellent agreement with the value computed by the finite element method. The deformation patterns agree well with the experimental observation.     

Plastic deformation analysis of strain-rate sensitive materials under plane strain conditions

The two-dimensional plane strain equation of plastic flow in accordance with the Levy-Mises constitutive relation is expressed in terms of stream functions of complex variables. Expressions for the stress, strain-rate and velocity are derived, assuming the stream function in the forms of both the summation and product of conjugate flow functions, for plastic flow in a nonlinear viscous (strain-rate sensitive) medium. The plastic states are also derived using a mixed mode solution expressed in terms of non-separable, independent conjugate complex variables. Application of the summation form solution is illustrated through the block indentation problem. Calculations are made on the effect of variation of the strain-rate sensitivity exponent on the contact stress. The predicted behavior of the contact stress suggests the possibility of the development of a specially instrumented plane strain block indentation test for the rapid determination of the strain-rate sensitivity of real materials. By reducing the results of the indentation of a perfectly plastic material it is found that the contact stress is uniform and the external load is constant. The stress on the contact surface obtained using the present analysis is identical to that available from a slip line solution to the problem.     

Modeling and simulation of polymer melts flow in the extrusion process of plastic profile with metal insert

The extrusion technology of plastic profile with metal insert is recently an advanced plastic processing method whose products keeps rising today for their excellent performance. However, the related fundamental research on polymer forming mechanism in the extrusion process of plastic profile with metal insert is lagging behind. With the development of computational fluid dynamics (CFD) theory, numerical method becomes an effective way to investigate such complex material forming problems as in the polymer extrusion process. In the present study, the mathematical model for three-dimensional non-isothermal viscous flow of the polymer melts obeying a Carreau model is developed based on the CFD theory. The Williams–Landel–Ferry equation is employed to involve the temperature dependence of material parameters. A decoupled numerical algorithm based on the penalty finite element method is conducted to predict the rheological behaviors of polymer melts within the complex flow channel. The streamline upwind/Petrov–Galerkin scheme is employed to improve the computational stability for the calculation of temperature field. Based on the theoretical model, the essential flow characteristics of polymer melts in the extrusion process of plastic profile with metal insert is investigated. The distributions of principal field variables like flow velocity, melt temperature, flow stress and pressure drop are predicted. The effects of die structure parameters including the intake angle and the distribution section length upon the melts flow patterns are further discussed. The variations of melt rheological properties versus different processing conditions like the volume flow rate and the metal insert moving velocity are also investigated. Some advice on practical processing operations of the extrusion process of plastic profile with metal insert is accordingly put forward based on the numerical results.     

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.     

An analytical solution for the spread extrusion of shaped sections

Spread extrusion could be used for manufacturing of wide profiles in the extrusion industry. In this paper a new method of design and analysis has been presented for such a problem. Special dies were designed for profiled sections such as square, rectangular, elliptical and cross shapes. These dies force the material to flow sideways and spread so as to extrude sections with wider dimensions than the initial billet or the maximum container diameter. The geometry of the deforming zone in the die was formulated and based upon that, a kinematically admissible velocity field was derived. Using this velocity, we estimated the field upper bound on extrusion power. Profile sections with different aspect ratios were investigated and the influence of other process parameters such as friction and reduction of area on the extrusion pressure were studied. Optimum die lengths for each die were calculated so as to minimize the extrusion pressure. Finite element analysis for the numerical simulation of the process was also carried out. The finite element results were also used as an aid to the design process of the extrusion dies. Dies were manufactured for different sections such as square, rectangle, and ellipse and cross shapes. Experiments were carried out to obtain data to verify the theory. Comparison of the results showed good agreement between the theoretical, numerical and experimental data. It was concluded the present method could be used to design dies for the spread extrusion of different shaped dies.     

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.     

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.     

不锈钢管接头精密成形的工艺分析与实验研究

不锈钢管接头截面积变化大，成形和脱模困难。本文对其塑性加工工艺方案进行分析比较，并通过工艺实验，验证工艺分析结果。该零件采用温挤压成形可以获得较好的技术经济效益；一次正挤压效率高，工艺力大；正挤-镦粗复合工艺则工艺力小，但效率较低。     

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.     

温度和背压方式对等通道转角挤压过程的影响

建立了用于分析等通道转角挤压过程的热力耦合有限元模型。通过对纯钛等通道转角挤压过程的数值模拟,获得了模具及试件内部的应力、应变和温度分布。研究结果表明,等通道挤压过程中试件温度分布不均匀,在模具转角剪切部位温度最高且存在明显的温度梯度。在较高的温度条件下进行挤压,有利于降低成形压力和获得较大的变形量;接触摩擦的存在导致模具受力状况恶化及试件变形的不均匀;而带背压的挤压方式可以在有效地增加试件变形量和变形均匀性的同时降低材料产生破坏的可能性。     

A study on precision forging of spur gear forms and spline by the upper bound method

Precision forging is an important manufacturing procedure of spline and spur gear forms. It has advantages of improved strength, good tolerance, saving billet material, dispensing with the cutting, etc. In this paper, a mathematical model using an upper bound method is proposed for forging of spur gear forms and spline to investigate the plastic deformation behavior of billet within the die cavity. The material of solid billet was assumed as rigid–plastic and the shape of the tooth profile was accounted for the mathematical modeling of the kinematically admissible velocity field assumed for the plastic zone. The non-uniform velocity was employed for simulating the inhomogeneous deformation and the effect of barreling during the forging. Using the present model, various effects of forming parameter such as the friction factor, reduction, number of teeth, etc. upon the non-dimensional forging pressure, forging force and barreling of the spur gear forms and spline were analyzed systematically and the results compared with those of other researcher's analytical and experimental work. It is shown that the present modeling of the process improves knowledge of the process design performance for the precision forging of spur gear form and spline.     

A study on radial flow field for extrusion through conical dies

A generalized expression for the radial flow field for extrusion through a conical die is suggested. The upper bound to the extrusion pressure for a rigid-perfectly plastic material is obtained. Other energy methods which include solutions for work-hardening and composite billets are also obtained for the generalized radial flow field. The results are used to analyse the hydrostatic extrusion of Al, Cu and Al-Cu composite billets. The extrusion pressure and hardness distribution of the product were measured in experiments and they are compared with theoretical results.     

基于滑移线场的SiCw/6061复合材料挤压变形晶须形貌分析

为探讨挤压变形对SiCw/6061复合材料晶须形貌的影响规律,首次引入塑性变形滑移线场理论对SiCw/6061复合材料的挤压过程进行研究。通过给出典型挤压工艺的正挤压实心件及反挤压杯形件的滑移线场及速端图,分析滑移线场以及速度间断对晶须形貌的影响,并与试验所得相应晶须形貌电镜照片进行对比。研究结果表明,最大切应力将引起SiC晶须沿滑移线切线方向的转动,导致晶须取向为其初始方向与滑移线方向的合矢量;速度间断所对应的沿滑移线切向的剧烈速度变化将导致位于速度间断线两侧的SiC晶须发生折断。     

Plastic flow through conical converging dies, using a viscoplastic constitutive equation

The influence of the working speed in drawing or extrusion processes is shown when a viscoplastic constitutive equation is used and when the yield condition is replaced by a yield inequality. It is shown that the drawing (or extrusion) pressure is increased when the speed of the process or when the viscosity coefficient of the material is increased, or when the diameter of the die is decreased or when the mean yield stress of the billet is reduced. This increase is more significant for higher reduction ratios and semi-cone angles. It is shown that the optimum semi-cone angle is also dependent on the speed of the process as is the critical semi-cone angle, which corresponds to the possible formation of a dead-zone near to the die surface. The pressure on the die surface is variable and depends on the speed of the process also. From the numerical examples given it is evident that in many practical circumstances the influence of speed may be significant even for very low working speeds.     

A computational study of die geometry and processing conditions effects on equal channel angular extrusion of a polymer

Equal channel angular extrusion (ECAE) is an efficient process to obtain enhanced microstructures via super-plastic deformation. In view of its optimisation, it is of prime importance to assess the relationships between processing conditions and material flow. More precisely, detailed knowledge of the plastic strain distribution in the extruded material in relation to the ECAE processing variables is required. The key parameters of the ECAE process are primarily die geometry, ram speed, extrusion temperature, use of back-pressure, number of extrusion sequences and processing route (e.g. rotation of the sample between successive passes). A numerical investigation was achieved to check out the influence of these parameters on the homogeneity of plastic strain distribution in the case of a conventional thermoplastic polymer. Material parameters of a phenomenological elastic viscoplastic model were deduced from compressive deformation tests at different temperatures and strain rates on high-density polyethylene (HDPE). Recommendations on tool geometry and processing conditions can then be provided, according to the numerical results.It was found that optimum ECAE die geometry is strongly material dependent. The application of a back-pressure significantly contributes to reduce the corner gap and consequently promotes the homogeneity of the plastic strain field. A slight sensitivity of plastic strain to ram speed and friction conditions was pointed out. The extrusion temperature strongly influences the magnitude of the plastic strain and has a slight effect on its homogeneity. The number of passes has a significant effect on the magnitude of the plastic strain but has a negligible influence beyond a certain temperature. The extruded material reaches a stationary strain state after few passes. The homogeneity of the plastic strain field is strongly affected by the processing route.     

Three-dimensional analysis of round-to-angle section extrusion through straight converging die

The increasing interest in the modeling of metal-forming processes in recent years has brought the development of different analytical and/or numerical technique. However, due to the complexity nature of the problem, most of the attempts are made with plain strain assumptions. Among the different techniques used, the upper bound method is a convenient tool for evaluating the rate of work in processes involving predominantly plastic deformation of rigid/perfectly plastic material. The present study is an endeavor to remodel and apply the spatial elementary rigid region technique for analyzing extrusion of angle-section bars from round billets through the linearly converging die. Optimized values of the nondimensional average extrusion pressure at various area reductions have been computed and compared with experimental results. It is observed that the proposed technique can be used effectively with adequate accuracy to predict the optimal die geometry which requires a minimal forming stress at different reduction of areas and friction conditions.     

Modeling of fretting wear evolution in rough circular contacts in partial slip

This paper presents a numerical model that maps the evolution of contact pressure and surface profile of Hertzian rough contacting bodies in fretting wear under partial slip conditions. The model was used to determine the sliding distance of the contacting surface asperities for one cycle of tangential load. The contact pressure and sliding distance were used with Archard's wear law to determine local wear at each surface asperity. Subsequently, the contact surface profile was updated due to wear. The approach developed in this study allows for implementation of simulated and/or measured real rough surfaces and study the effects of various statistical surface properties on fretting wear. The results from this investigation indicate that an elastic–perfectly plastic material model is superior to a completely elastic material model. Surface roughness of even small magnitudes is a major factor in wear calculations and cannot be neglected.     

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.     

Evaluating the effects of process parameters on maximum extrusion pressure using a new artificial neural network-based (ANN-based) partial-modeling technique

Metal extrusion process accounts for the production of the majority of industrial and domestic aluminum sections. A major limitation to the success of any extrusion operation is the capability of the particular extrusion press to meet the maximum pressure requirements for that operation. In the present work, the effects of industrial extrusion process parameters and their interactions on the resulting maximum extrusion pressure, of an industrially extruded aluminum alloy, have been studied using a newly devised ANN-based partial modeling technique. Two operating parameters (initial billet temperature and ram speed) and three geometrical parameters (extrusion ratio, profile average thickness, and number of die cavities) were investigated. The main objective for developing this modeling technique is to overcome the limitations of presently available statistical modeling tools, as foreseen by the modeling needs for a complex thermo-mechanical process such as extrusion. The main present limitations are accounting for non-linearity in the process behavior, incorporating interaction effects and a meaningful determination of the highly significant process parameters and/or interactions. These three features have been, collectively, incorporated into the present model by means of combining statistical analysis of variance into ANN and by using a partial sum of squares analysis, which we propose to call the “present factor analysis.” Normal linear regression has been also employed for comparison purposes. According to the present model, maximum extrusion pressure has shown various degree of non-linearity in behavior with respect to the different process parameters and their significant interactions. It has been found that variations in the maximum extrusion pressure are mainly a function of initial billet temperature and its interactions with other process parameters, especially the ram speed. The present ANN-based model has shown superior prediction capabilities compared to the linear model with a marginal overall prediction error value of ±2.5 %.