Theory and Method of Optimum Path Forming for Sheet Metal

Ideal forming results will be achieved if the sheet metal is formed along an optimum forming path. Such a path can be realized by multi-point forming technique. On the basis of the theory of the ideal forming path (or minimum plastic work path), the concept of an optimum forming path is proposed in this paper. The forming path can be described by the initial configuration, objective configuration and a series of intermediate configurations. According to the deformation theory and constitutive equation in ideal path forming, a finite element method to calculate the initial configuration is set up. The functional to determinate intermediate configurations is introduced and the numerical method to solve the configuration is presented. Based on the method presented in the paper, multi-step multi-point forming tests for sheet metal are designed. The test results demonstrate that when the sheet is deformed along an approximate optimum forming path, the maximum deformation curvature for the sphere objective shape and saddle objective shape are 11%∼40% and 15%∼50% greater than those of a sheet deformed along a common path respectively.

DEPENDENCE OF PREDICTION MODEL OF FORMING LIMIT STRAINS ON FORMING METHOD AND MECHANICAL PROPERTIES OF SHEET METALS

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Meshfree Method Numerical Simulation of Sheet Metal Forming Process

Metal forming plays an important role in manufacturing industry and is widely applied in industries.The tradi- tional finite element method(FEM)numerical simulation is commonly used to predict metal forming process.Conventional finite element analysis of metal forming processes often breaks down due to severe mesh distortion,therefore time-consuming remeshing is necessary.Meshfree methods have been developed since 1977 and can avoid this problem.This new generation of computational methods reduces time-consuming model generation and refinement effort,and its shape function has higher order connectivity than FEM’s.In this paper the velocity shape functions are developed from a reproducing kernel approximation that satisfies consistency conditions and is used to analyze metal tension rigid viscoplastic deforming and Magnesium Alloy(MB 15)sheet superplastic ten- sion forming.A meshfree method metal forming modeling program is set up,the partition of unity method is used to compute the integrations in weak form equations and penalty method is used to impose the essential boundary condition exactly.Metal forming examples,such as sheet metal superplastic tension forming and metal rigid viscoplastic tension forming,are analyzed to demon- strate the performance of mesh free method.

Rapid Springback Compensation for Age Forming Based on Quasi Newton Method

Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mmx750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment （DA） method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method （0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively）. In following experimental verification, mold contour for another integrated panel with 400 ram^380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel＇s design contour is less than 1 mm. Finally, the iterations with different mesh sizes （40 mm, 35 mm, 30 mm, 25 mm, 20 mm） in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear fimctions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel. It only takes 50% iterations compared to that of DA. The proposed method can serve a faster mold contour compensation method for sheet metal forming.

DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

Single-point incremental forming （SPIF） is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method（FEM） model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters＇ impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.

Forming Mechanism of Gaseous Defect in Ti-48Al-2Cr-2Nb Exhaust Valves Formed with Permanent Mold Centrifugal Casting Method

A method combining theoretical analysis with experiment is adopted and the flowing process of Ti-48A1-2Cr-2Nb alloy melt poured in a permanent mould during the centrifugal casting process has been analyzed. A mathematical model of the filling process is established and the forming mechanism of internal gaseous defect is summarized. The results of calculation show that the melt fills the mould with varying cross-section area and inclined angle. The filling speed of the cross-section is a function of filling time. The cross-section area is directly proportional to the filling speed and the inclined angle is inversely proportional to the filling speed at a given rotating speed of the platform. Both of them changes more obvious near the mould entrance. The gaseous defect can be formed in several ways and the centrifugal field has an important influence on the formation of the defect. In addition, the filling process in centrifugal field has been verified by wax experiments and the theoretical analysis are consistent with experimental results.

Flexural and eigen-buckling analysis of steel-concrete partially composite plates using weak form quadrature element method

Flexural and eigen-buckling analyses for rectangular steel-concrete partially composite plates(PCPs)with interlayer slip under simply supported and clamped boundary conditions are conducted using the weak form quadrature element method(QEM).Both of the derivatives and integrals in the variational description of a problem to be solved are directly evaluated by the aid of identical numerical interpolation points in the weak form QEM.The effectiveness of the presented numerical model is validated by comparing numerical results of the weak form QEM with those from FEM or analytic solution.It can be observed that only one quadrature element is fully competent for flexural and eigen-buckling analysis of a rectangular partially composite plate with shear connection stiffness commonly used.The numerical integration order of quadrature element can be adjusted neatly to meet the convergence requirement.The quadrature element model presented here is an effective and promising tool for further analysis of steel-concrete PCPs under more general circumstances.Parametric studies on the shear connection stiffness and length-width ratio of the plate are also presented.It is shown that the flexural deflections and the critical buckling loads of PCPs are significantly affected by the shear connection stiffness when its value is within a certain range.

Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.

A SURFACE DEFECT PREDICTION METHOD FOR METAL FORMING PROBLEM

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COMPLEX INNER PRODUCT AVERAGING METHOD FOR CALCULATING NORMAL FORM OF ODE

This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.

EFFECT OF BURNING METHOD ON THE FORMING PROCESSES OF PORTLAND CEMENT CLINKER

The forming temperature of Clinker melt underdifferent burning conditions has been studied by appearance examination and thermal shrinker determination, and the viscosity of melt has been discussed by studying the coordination number of Al^(3+) and Fe^(3+) in cement clinker burned by different method with x^- ray fluorescence analysis and Moss- bauer spectroscopy. The results show that the clin- ker melt under rapid burning may come into exis- tence at lower temperature and It's viscosity is lower. So the forming processes of clinker may be different at rapid burning from ordinary burning. They are probably an important factor to promote the formation of clinker burned at lower temperature with rapid burning method.

Properties of SiC Particulate Preforms Based on Different Pore-forming Agents and Bonding Methods for Making SiC/Al Composites

The preforms with high SiC volume fraction （〉50%） were successfully fabricated by two bonding methods. Moreover, the dimensional change, compressive strength, and microstructure of SiC preforms were investigated, and the bonding mechanism among SiC particulates in preforms was also discussed. Results show that, after heating to 1 100 ~C and holding for 2 h, a uniform and interconnected structure in the SiC preforms can be obtained by using starch, stearic acid, and graphite respectively as the pore-forming agents, which benefits the subsequent infiltration by the molten metals. More neck-like-jointing among SiC particulate by using graphite as the pore-forming agent improves the dimensional accuracy and compressive strength of the preform. Besides, the properties of the preforms by the binder bonding are better than those by the oxidation bonding, which is mainly because the mixed neck-like-jointing and binder at high temperature provide effective bonding together.

Model-element Analytic Method for Plastic Forming of Material

MEM(model element method) is proposed to resolve the present difficulties and problems in CAE about plastic forming of material.There are four advantages when MEM is integrated with FEM(finite element method) and UBM(upper boundary element method).First,it can make full use of their own advantages and overcome their own disadvantages;second,it can analyse material plastic fluid expediently;third,it can optimize design;finally,it can improve technological content and application effect of CAE software.Based on introducing the principle of MEM briefly,features and applications of MEM are pointed out.In conclusion,a new analysis method for plastic forming comes forth.

A New Curve Fitting Method for Forming Limit Experimental Data

The forming limit curve （FLC） can be obtained by means of curve fitting the limit strain points of different strain paths. The theory of percent regression analysis is applied to the curve fitting of forming limit experimental data.Forecast intervals of FLC percentiles can be calculated. Thus reliability and confidence level can be considered. The theoretical method to get the limits of limit strain points distributing region is presented, and the FLC position can be adjusted according to practical requirement. Method for establishing FLC with high reliability using small samples is presented at the same time. This method can make full use of the current experimental data and the previous data.Compared with the traditional method that can only use current experimental data, fewer specimens are required in the present method to obtain the same precision and the result is more accurate with the same number of specimens.

Application research on metal rheological forming of reproducing kernel partial method

The meshless method is a new numerical technology presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The process of cylinder compression was analyzed by using rigid-plastic meshless variational principle and programming reproducing kernel partial method(RKPM),the influence of node number,weight functions and size factor on the solution was discussed and the suitable range of size factor was obtained.Compared with the finite element method(FEM),the feasibility and validity of the method were verified,which proves a good supplement of FEM in this field and provides a good guidance for the application of meshless in actual engineering.

CFD-Based Method of Determining Form Factor k for Different Ship Types and Different Drafts

The value of form factor k at different drafts is important in predicting full-scale total resistance and speed for different types of ships. In the ITTC community, most organizations predict form factor k using a low-speed model test. However, this method is problematic for ships with bulbous bows and transom. In this article, a Computational Fluid Dynamics(CFD)-based method is introduced to obtain k for different type of ships at different drafts, and a comparison is made between the CFD method and the model test. The results show that the CFD method produces reasonable k values. A grid generating method and turbulence model are briefly discussed in the context of obtaining a consistent k using CFD.

Antenna Performance Improvement in Elliptical Array Using RMI Method of Mutual Coupling Compensation

The number of wireless electronic gadgets used in mobile communication, vehicle collision avoidance system, compact radars, etc. is extremely increasing at a rapid rate. Thus, the characteristics of the antennas involved in these gadgets are to be designed very stringently so as to avoid interferences & coupling and to improve compatibility, susceptibility, etc. Compact smart antenna with improved performance is highly essential to meet this challenging scenario. Mutual coupling between various elements of an array is one of the main factors which can be considered for improvement of performance of the antenna. Influence of mutual coupling on performance of the antenna is considered in this paper and various techniques to minimize this effect are presented. Effect of mutual coupling on radiation characteristics of the antenna can be compensated employing various methods like Conventional Mutual Impedance (CMI), Receiving Mutual Impedance (RMI). Analysis is presented as comparison between the two methods for different number of elements in the array. Analysis is also presented for different geometries of the array like circular and elliptical for improved performance. The results show performance improvement in the proposed array for parameters like SNR and Speed of convergence.

Application in metal rheological forming of element-free Galerkin method

The element-free method is a new numerical technique presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The element-free Galerkin method(EFGM) was applied for the solution to plastic large deformation.The simulation of metal rheological forming was successfully done by programming and its results were visualized by using the plotting and data analyses software Tecplot.Then plastic strain under different stages during rheological forming and the three principal stresses at the last deformation were obtained.The example shows the feasibility of EFGM used for metal rheological forming and provides a new method for numerical simulation of rheological forming of complex parts.

ADJOINT OPERATOR METHOD AND NORMAL FORMS OF HIGHER ORDER FOR NONLINEAR DYNAMICAL SYSTEM

Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.