Aluminum Billets Research Articles

An upper-bound solution for axisymmetric extrusion of composite rods through curved dies

The study is concerned with an analysis of forward extrusion of composite rods through curved dies. A kinematically admissible velocity field is derived by assuming proper streamlines and applying the flow function concept to each material region of plastic deformation. Two kinds of flow functions are chosen in order to compare the effect of the choice of the flow functions. The effect of work-hardening is incorporated approximately by calculating the strains at the exit of both materials. The upper-bound method is then employed to determine the extrusion pressure for various process variables. The experiments are carried out with commercially pure aluminum and copper billets for various reductions of area and cone angles at room temperature. The experimental results are then compared with the theoretical calculations. The comparison shows that the second-order flow function is in better agreement with the experimental observation both in extrusion loads and in deforming regions.

見かけの熱伝導率を用いた大型ビレットの鋳造初期シミュレーション

The computer simulation program concerned with the continuous casting of 0.5m diameter 6063 aluminum billet was completed using the steady-state difference method proposed by Adenis et al. From the measured isotherm profiles it was concluded that the ingot had not reached the steady-state in the initial 2m. In order to simulate the temperature distributions of these non-steady-state ingots using the same program, experimental formulas were proposed using the apparent thermal conductivity in the solid phase, taking the initial strong cooling effects into consideration. Three experimental results were obtained with casting velocity 0.75m/s: the thermocouple heads were inserted when the billet length was 0.6m (run a), 1.0m (run b) and 1.2m (run c), respectively. Corresponding to these experiments the following K equations were selected. run a: K=175+586×t-1/2run b: K=251-100×10-3trun c: K=230-75.3×10-3tIn run a, the heat transfer coefficient from the high temperature region of the billet surface to the cooling water was also improved to obtain good agreement with experimental data.

ALSPEN-A mathematical model for thermal stresses in direct chill casting of aluminum billets

This paper presents the mathematical model ALSPEN, in which the thermally induced strains and stresses which develop during direct chill (DC) semicontinuous casting of aluminum billets are calculated by a finite-element method. The metal is assumed to be an isotropic elasticviscoplastic material with strongly temperature-dependent properties. In the material description, the viscoplastic strain is treated in a “unified” manner, in which low-temperature (approximately) time-independent plasticity and creep at high temperatures occur as special cases. Furthermore, in the numerical time stepping procedure, all of these plastic material properties, which are present simultaneously in the solution domain as a result of the large temperature differences, are treated in a similar way. To demonstrate some of the capabilities of ALSPEN, we have modeled the casting of an AlMgSi alloy, AA6063. The material properties of this alloy have been studied in parallel with the development of the mathematical model.

Measurement of actual stress and temperature on the roll surface in rolling (3rd report. Measurement of temperature and heat flux distribution on the roll surface in cold rolling).

A temperature sensor for detecting temperature and heat flux on the roll surface in rolling has been developed. Installed in a roll surface, this sensor detects two temperatures at different depths from the roll surface by thermocouples. Surface temperature and heat flux are calculated from the two measured temperatures using the reverse calculation method for one-dimensional unsteady thermal conduction. Temperature distribution and heat flux distribution on the roll surface are measured in the cold rolling of aluminum sheets and billets. The availability of this sensing method for the investigation of thermal phenomena in rolling is discussed.

Measurement of actual stress and temperature on the roll surface during rolling. (Frictional stress distribution and pressure distribution in cold rolling).

Pressure, and frictional stress in both rolling and width directions have been measured in the cold rolling of aluminum strip and billet by a new stress sensor developed by the authors. Characteristics of the frictional stress distribution in cold rolling have been elucidated. Frictional stress in the rolling direction is almost constant from the entrance to the neutral point in the contacting arc, both in strip and billet rolling. by contrast, frictional stress in the width direction increases from the center line to the edge part and its peak lies in the central part of the contacting arc in strip rolling. However, in billet rolling, it has two peaks along the contacting arc and its value does not vary from the center line to the edge part. This may be connected with the metal flow in the width direction in billet rolling.

Measurement of actual stress and temperature on the roll surface during rolling. Measurement of temperature and heat flux distribution on the roll surface in cold rolling.

A temperature sensor for detecting temperature and heat flux on the roll surface in rolling has been developed. Installed in a roll surface, this sensor detects two temperatures at different depths from the roll surface by thermocouples. Surface temperature and heat flux are calculated from the two measured temperatures using the reverse calculation method for one-dimensional unsteady thermal conduction. Temperature distribution and heat flux distribution on the roll surface are measured in the cold rolling of aluminum sheets and billets. The availability of this sensing method for the investigation of thermal phenomena in rolling is discussed.

The Effect of Billet Location on Completely Closed Cavity Die Forging

The effect of the accuracy of location of cylindrical billets in completely closed cavity dies, on forging loads and product accuracy has been investigated. Aluminium billets with various off-centre locations were forged at room temperature on a 3000 kN hydraulic testing machine. The results indicate that inaccuracies in billet location significantly affect forging load requirements and dimensional accuracy of forgings. An energy method solution is presented to provide accurate load predictions for relatively small off-centre locations of billets.

Measurement of actual stress and temperature on the roll surface in rolling. (2nd Report, Frictional stress distribution and pressure distribution in cold rolling).

Pressure, frictional stress in the rolling direction and that in the width direction have been measured in the cold rolling of aluminum strip and billet by a new stress sensor developed by the authors. Characteristics of the frictional stress distribution in cold rolling have been elucidated. Frictional stress in the rolling direction is almost constant from the entrance to the neutral point in the contacting arc, both in strip and billet rolling. On the other hand, frictional stress in the width direction increases from the centerline to the edge part and its peak lies in the central part of the contacting arc in strip rolling. However, in billet rolling, it has two peaks in the rolling direction and its value does not vary from the centerline to the edge part. This may be related with the metal flow to the width direction in billet rolling.

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.

Scrap reduction in the extrusion process: the case of an aluminium production system

The search for minimum scrap is the core problem in any aluminum product manufacturing process. This paper presents a methodology for scrap reduction in an aluminium extruding plant which produces aluminium sections from aluminium billets. The main problem under consideration is to find the different sizes of billets to be stocked to supply the total demand requirements such that the total scrap is minimized. The approach to the problem has three stages, namely: determination of all feasible billet sizes in the light of the plant limitations, determination of an optimal set of billet sizes used to produce the number of product types desired using 0–1 integer linear programming, and selection of a subset of billet sizes from the optimal set to be stocked using dynamic programming.

Mössbauer investigation of iron in aluminium—II. Al-Fe-Si samples

Mössbauer spectroscopy was used for the study of AlFeSi intermetallic compounds formed in direct chill cast (DC) aluminium billets in as cast state and after subsequent heat treatments performed between 450 and 620°C. The Mössbauer parameters of ternary compounds conceivable under such conditions, i.e. cubic and hexagonal α-(AlFeSi), β-(AlFeSi) and γ-(AlFeSi), were determined by the measurement of samples prepared directly for that purpose. Besides ternary phases Al 6Fe, Al 3Fe and Al(Fe) solid solution were also searched for in the DC billets. It was found that both the intial phase composition of the billets and the phase transformations which took place during heat treatments depended on the iron to silicon ratio of the alloy. In the Al-0.54 m% Fe-0.95 m% Si alloy, namely, only β-(AlFeSi) was found up to 575°C, while the initial Al 6Fe + cubic α-(AlFeSi) composition of the Al-0.58m% Fe-0.21 m% Si alloy changed gradually to A1 3 Fe + hexagonal α-(AlFeSi).

Determination of heat transfer coefficients during water cooling of metals

The heat transfer coefficients for various cooling methods were investigated. Copper, aluminium, and nickel billets were heated and then subjected to cooling by water spray systems and immersion in water and mixtures of water and organic agents. The temperature close to the surface was measured and used for the calculation of the heat transfer coefficient by the implicit finite difference method. The results yielded a defined relation between the heat transfer coefficient and surface temperature, thermophysical material properties, and the intensity of spray cooling or the concentration of the organic agent in the bath. Using this data, a means for analytically formulating the heat transfer coefficient was obtained, enabling easy calculation to be made of the temperature field during quenching or cooling in continuous casting.MST/154

Determination of heat transfer coefficients during water cooling of metals

AbstractThe heat transfer coefficients for various cooling methods were investigated. Copper, aluminium, and nickel billets were heated and then subjected to cooling by water spray systems and immersion in water and mixtures of water and organic agents. The temperature close to the surface was measured and used for the calculation of the heat transfer coefficient by the implicit finite difference method. The results yielded a defined relation between the heat transfer coefficient and surface temperature, thermophysical material properties, and the intensity of spray cooling or the concentration of the organic agent in the bath. Using this data, a means for analytically formulating the heat transfer coefficient was obtained, enabling easy calculation to be made of the temperature field during quenching or cooling in continuous casting.MST/154

A Study of Buckling in Upsetting by Use of Finite Element Method

To observe the fundamental characteristics of buckling in upsetting, annealed and hardened aluminium billets of circular and square cross sections were simply compressed under lubricated and restricted end conditions. Billets with a rectangular cross section were also compressed in a die which realized plane strain upsetting. The buckling distortion after a given reduction in height increased gradually with initial height/diameter (or height/width) ratio, and when the ratio reached a critical value, which usually dropped in the range between 1.5 and 2.0, the degree of buckling increased sharply. When the experimental critical ratios were compared with those calculated by the existing formulae, only qualitative agreements were obtained, i.e., larger n-value resulted in higher critical ratio. In order to simulate the buckling deformation, the rigid-plastic finite element method was used. A slight skew was given to the plane-strain upsetting model to represent the initial distortion of billet shape. It was confirmed that almost the same distorted grid as the experimental one could be obtained by FEM simulation if a proper combination of friction coefficient and the initial distortion were assumed, and that the distortion decreased with increasing friction coefficient and decreasing initial distortion. The relationship between critical height/width ratio against n-value agreed quantitatively well with the experimental results.

A Three-Dimensional Finite Element Analysis of the Cold Forging of a Model Aluminium Connecting Rod

A fully three-dimensional elastic-plastic finite element method is used to simulate metal flow during the most complex stage of the cold forging of a model of an aluminium connecting rod. The results of the computer simulation are compared with the forging of strain-hardening aluminium billets using graphite lubrication. The analysis predicts deformation patterns and hardness distributions which have been checked by selected experiments. The experimental results show inhomogeneous deformation in various parts of the forging and noticeable variations in the formation of flash around its periphery, features which are also found in the analyses. The elastic-plastic finite element technique can thus satisfactorily be applied to three-dimensional forgings of strain-hardening material. The work described here represents one part of a continuing research programme to develop computer simulation techniques for the modelling of complex cold, warm or hot industrial forgings.

Backward Extrusion of Internally Shaped Tubes From Round Billets

An analytical method is proposed for estimating the steady-state punch pressure for three-dimensional backward extrusion (or piercing) of complicated internally shaped tubes from circular billets. A kinematically admissible velocity field is derived to formulate an upper-bound solution using velocity transformation and mapping function. The configuration of deforming boundary surfaces are determined by minimizing the extrusion power with respect to some chosen parameters. Experiments are carried out with commercially pure aluminum billets for internally shaped tubes at various reductions of area by using different sizes of shaped punches, such as square and regular hexagons. It is shown that the theoretical predictions for extrusion load are in good agreement with the experimental values.

A Refined Analytical Model for Hydrodynamic Lubrication of Cold Extrusion and Its Comparison With Experiment

In a refined analytical model for the hydrodynamic lubrication of cold extrusion, effects of viscous heating in the inlet zone and surface temperature in the work zone are included to estimate extrusion pressure for both unsteady and steady lubrication. An experimental study indicates that a hydrodynamic lubricant film may be formed by reducing friction at the start of extrusion by a secondary lubricant. Theoretical estimation of unsteady extrusion pressure is in agreement for extrusion of aluminium billets lubricated with castor oil.

An Analysis of an Electromagnetic Mold for the Continuous Casting of Nonferrous Metals

Electromagnetic molds are presently being used in the continuous casting of aluminum billets and slabs. Various theoretical models that can be used to predict electromagnetic pressure differentials and forces for this application are examined. Dimensionless pressure and force factors are first derived using a one-dimensional field model. These factors are then refined using a two-dimensional semi-infinite model. This latter model is also used to examine the effect that coil coupling has on the field strength, pressures and forces. Finally, the coupled circuit method is used to predict pressure distributions for an actual mold geometry, including the essential effect of the field shaping short-circuited turn (screen). The effect of varying the location of the inductor and screen is examined.

On the natural formulation and analysis of large deformation coupled thermomechanical problems

The paper extends previous research on the natural methodology [1], [2] to the domain of coupled thermomechanical problems under the combined action of large inelastic and elastic deformations as well as of heat exchange. Some fundamental properties of redundant natural coordinate systems of reference are studied, and the local description of the coupled thermomechanical problem is developed a priori in natural terms. Following the transition from the local to the finite element level the numerical solution of the equations governing the coupled thermomechanical problem for the discretised body undergoing finite inelastic deformations is discussed. A number of applications conclude the paper. First a purely thermal problem is investigated which is followed by the study of various physical effects on the thermomechanical response of an expanding hollow cylinder assuming plastic and viscoplastic inelastic properties of the material. Two examples taken from the metal forming practice - the heading of a steel bolt and the extrusion of an aluminium billet - are treated under the aspect of thermomechanical coupling. The paper confirms in the authors' opinion the luminous clarity of the natural approach.

Cold Forging of Hollow Cylindrical Components Having an Intermediate Flange — Ubet Analysis and Experiment

Possible cold forging operations to form hollow cylindrical Componeats having a circular intermediate flange are first proposed. The material deformation and forging pressures for these program, the basic concept of which is hased on the Unit Element Regions due first to Kudo. With the emergence of the computer revolution, the use of the Unit Element Regions was implemented as the URET program by Avitzur and others. In the present study it is assumed that the material is non-hardening, and the frictional stress over the tool-workpiece interfaces is negligible. Cold forging experiments with annealed aluminium billets or slugs are also performed to observe deformation, defect formation and working pressure. The experimental results are compared with the theoretical results which are obtained by modification of the non-hardening results to allow for the work-hardening. The coincidence is found to be fair. Finally, the relative merits and demerits among the proposed forging methods with regard to the load, unit pressure, energy and defect are discussed on the basis of the theoretical and experimental results.