Analysis of hydrofilm extrusion of three-dimensional shapes from round billets

A new method of die construction is proposed, which enables the exact geometrical control of die shape and ensures the initial sealing between billet and die. Using the modified method of die construction the internal metal deformation is analyzed with the aid of a special transformation combined with the upper-bound method. Based on a concept of equivalent friction factor the energy dissipation in fluid film is calculated approximately for three-dimensional hydrofilm extrusion. Computations are carried out for hydrofilm extrusion of various sections such as squares, rectangles, ellipses and clover shapes and various factors affecting the process are discussed. Experiments are performed for clover and square sections using the dies from NC manufacture based on the suggested theoretical design. A reliable sealing system is developed between punch and container. The experimental results are compared with the theoretical prediction and it is shown that the theory is in reasonable agreement with the experimental observation. Various aspects are discussed from the experiment.     

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.     

Three dimension profile extrusion simulation using meshfree method

A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of 3D profile extrusion processes. The point collocation method is a true meshfree method without the employment of a background mesh. We show that, in a point collocation approach, the implementation of program does not need the background mesh, which is a very time consuming process in a Galerkin method for integration. Among the points of the meshfree model, there is no connecting information. A mesh quality control method with mold interpenetration checking based on the Delaunay Bowyer-Watson algorithm is introduced to produce the topological relations, which enable us to show meshfree simulation results using the same procedure as in the finite element method. A C-shape profile extrusion application example is presented and compared with the finite element method to verify the proposed method.     

Modelling of extrusion force using the surface response method

Due to the complexity of bulk metal forming processes, the establishment of theoretical models for these processes is prohibitively difficult and frequently impossible. Consequently, empirical models attained by means of experimental research are habitually used to replace the theoretical models. This paper describes the application of the surface response method in an attempt to define a relationship between the maximum extrusion force and three process parameters; namely, the conical die angle γ, die land height, h and die exit diameter, d. An extensive experimental program of aluminium extrusion was undertaken in parallel with the empirical modelling. An adequacy test was made on the analysed models to determine the accuracy with which the model predicted data obtained by experimental methods.     

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.     

Propagating bias and precision errors using the perturbation method

Calculations based on measured variables are subject to some uncertainty due to errors in measurements. These measurement errors, while unavoidable, can be quantified. The usual method for determining the uncertainty in a calculated variable, given the uncertainties (or expected errors) in the measured variables that define it, involves the use of the Taylor series method. With this method, the partial derivative of the result with respect to each of the measured variables must be determined. This can be tedious and time consuming. When results are calculated by computer, another method is available that does not require partial differentiation. This alternative is known as the perturbation method.

This paper explains fow the perturbation method can be used in conjunction with the methodology for propagating measurement errors set forth in ANSI/ASME Performance Test Code 19.1-1985. The FORTRAN coding required to implement the perturbation method is also described. The program, which propagates the measurement uncertainties, is easily combined with the results calculation code and requires little or no maintenance. The code was developed to determine uncertainties associated with boiler performance calculations that were carried out as part of a test program for circulating fluidized bed combustion sponsored by the Electric Power Research Institute.     

Analysis of axisymmetric extrusion of rods by the method of weighted residuals using body-fitted coordinate transformation

The method of weighted residuals with the use of the finite difference method based on a coordinate transformation to nonorthogonal curvilinear coordinate system to fit the boundary of an arbitrary shape is proposed to determine the stresses and strains in axisymmetric extrusion of rods through continuous dies. By using the body-fitted coordinate transformation, the finite difference expressions at and adjacent to the boundary do not need any interpolation between boundaries and interior grid points. The errors defined for governing equations and boundary conditions are minimized by introducing the method of weighted residuals. The work-hardening effect is incorporated by integrating the effective strain rate along the flow line. As computational examples, four types of dies with different reductions of area are chosen. Experiments are carried out for steel and aluminum alloys at room temperature. The computed results are compared with the experimental results as well as with those by the finite element method. The extrusion load and the flow pattern computed by the present method are in excellent agreement with the experimental results and those by the finite element method.     

Determination of blank shapes for drawing irregular cups using an electrical analogue method

An electrical analogue method is introduced to determine optimum blank shapes for deep-drawing cups of irregular cross-section. Square and rectangular cups were drawn from aluminium and steel blanks having these shapes and required very little trimming. Comparison is made with other methods of developing blanks and although one empirical method gave reasonable results for rectangular cups it is concluded that the electrical analogue method is preferred; it is also applicable to irregularly shaped cups.     

From operating deflection shapes towards mode shapes using transmissibility measurements

A transmissibility measurement is the traditional way of making a frequency response measurement when the excitation force cannot be measured. It is calculated in the same way as the admittance function, or transfer function. Whereas the admittance function is the ratio of response divided by force, transmissibility is the ratio of a response divided by a reference response. It is well known that operating deflection shapes can be displayed from a set of two or more transmissibilities. The use of transmissibility functions in the field of operational modal analysis has only recently been introduced by the authors of this paper. In general the “model” obtained from transmissibility functions is only valid for the concerned operating condition and is not related to any system parameter. In this paper a new post-processing method based on transmissibility measurements is introduced that allows the estimation of the modal parameters and in particular the unscaled mode shapes. The new method is introduced and illustrated with a numerical test.     

Forming limit predictions with the perturbation method using stress potential functions of polycrystal viscoplasticity

Plastic potentials of polycrystalline materials are calculated for plane stress states using viscoplastic crystallographic slips and the Taylor approach. The derivation process of these potentials and their development during large plastic deformation of textured aluminium sheets are discussed. These potentials are then used to predict the forming limits of sheet metals. The approach employed was that of the perturbation technique developed by Dudzinski and Molinari [Int. J. Solids Struct. 27, 601 (1991)]. The perturbation method is analytic if Hill-type yield potentials are used. Therefore, to facilitate the use of the polycrystal plastic potentials in the perturbation approach, the polycrystal stress potentials were approximated locally at the loading point by Hill-ellipsoids. In this way even the development of anisotropy during stretching could be taken into account. The effect of initial texture as well as the changes in the anisotropy during deformation are discussed. It has been found that the development of anisotropy influences strongly the predicted limit strains in the vicinity of equibiaxial stretching.     

Complex surface modeling using perturbation functions

Freeforms synthesized by means of perturbation functions are considered. A special feature of the freeforms based on the scalar perturbation functions and the method of their visualization is that the time of geometrical processing and the amount of data required for modeling the surface do not depend on its geometry. The freeforms based on the analytical perturbation functions have an advantage of spline representation of surfaces, that is, a high degree of smoothness, and an advantage of arbitrary form for a small number of perturbation functions.     

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.     

Transverse vibration of completely-free elliptic and circular plates using orthogonal polynomials in the Rayleigh-Ritz method

The Rayleigh-Ritz method using characteristic orthogonal polynomials has been applied to study the problem of transverse vibration of completely-free elliptic and circular plates of uniform thickness. A sequence of successive approximations has been generated to work out the frequencies and mode shapes. The process is continued until at least the first four frequencies converge to five significant digits. It has been found that the results agree completely with the known results for a circular plate. A comparison has also been made with some known experimental and theoretical results for an elliptic plate.     

Effects of partial-grooving on the performance of spiral groove bearings: analysis using a perturbation method

The perturbation method has been extended to investigate the effects of partial-grooving on the performance of spiral-grooved spherical and conical bearings. A ‘partial-grooving ratio’ (PGR), which has a value of 0 for a fully-grooved bearing and a value of 1 for a plain bearing, has been introduced to represent the degree of partial-grooving. It has been found that the load capacity and stiffness of a bearing are not significantly affected by partial-grooving as long as the value of PGR is below 0.2. When PGR increases above 0.2, the axial load capacity and axial stiffness will decrease sharply whereas improvements in radial load capacity and radial stiffness may be achieved. The study has also revealed that radial stability of a bearing is improved by partial-grooving, provided PGR is not too large. However, a bearing becomes inherently radially unstable if the bearing gap is not completely filled with lubricant, regardless of it being fully or partially grooved.     

Statistical confidence using minimum rank perturbation theory

In this paper, the effect of measurement noise on damage detection performance of the minimum rank perturbation theory is investigated. Closed-form solutions for the sensitivity of the minimum rank perturbation theory damage vectors and calculated stiffness perturbations with respect to errors in the measured modes shapes or frequency response functions are developed. This sensitivity allows one to establish confidence in damage existence, location and extent assessment. The use of this information in interpreting damage detection results is discussed in the context of an experimental study.     

Three-dimensional morphing of similar shapes using a template mesh

Shape morphing is the process of transforming a source shape into a target shape, through a series of intermediate shapes. There are two important problems to be considered in three-dimensional shape morphing: conforming mesh generation and path interpolation. In this paper, a novel approach in which a template mesh is mapped directly to the target mesh is proposed for the efficient treatment of the conforming mesh generation problem. Our mapping technique is based on a shape deformation method using an implicit function and the well-known mesh smoothing scheme, so the implementation of the method is very simple and robust. After mapping the source mesh to the target mesh, i.e., after obtaining a consistent mesh parameterization of the two shapes, the intermediate shapes are obtained by linear interpolation of the modified Laplacian coordinates of the source and target meshes. We demonstrate many examples of morphing between various shapes, including a model of the human head, a head sculpture model, and models of the human body in different poses to show the validity and effectiveness of the proposed method.     

等温挤压的实现方式与控制算法

提出了一种使挤压液压机实行等温挤压的双闭环串级控制方案和控制算法，讨论了串级策略的设计要点，给出了仿真实例     

铝型材挤压过程的一种数值模拟方法

通过优化几何模型,采用有限元法与有限体积法相结合,并在有限体积模拟阶段进行分步计算模拟的方法,成功地进行了一薄壁大挤压比铝型材挤压过程的数值模拟,获得了型材挤压过程中的材料流动速度、应力、应变和温度分布图,并对其结果进行讨论.