Digital high-efficiency print forming method and device for multi-material casting molds

Sand mold 3D printing technology based on the principle of droplet ejection has undergone rapid development in recent years and has elicited increasing attention from engineers and technicians.However,current sand mold 3D printing technology exhibits several problems,such as single-material printing molds,low manufacturing efficiency,and necessary post-process drying and heating for the manufacture of sand molds.This study proposes a novel high-efficiency print forming method and device for multi-material casting molds.The proposed method is specifically related to the integrated forming of two-way coating and printing and the shortflow manufacture of roller compaction and layered heating.These processes can realize the high-efficiency print forming of high-performance sand molds.Experimental results demonstrate that the efficiency of sand mold fabrication can be increased by 200%using the proposed two-way coating and printing method.The integrated forming method for layered heating and roller compaction presented in this study effectively shortens the manufacturing process for 3D-printed sand molds,increases sand mold strength by 63.8%,and reduces resin usage by approximately 30%.The manufacture of multi-material casting molds is demonstrated on typical wheeled cast-iron parts.This research provides theoretical guidance for the engineering application of sand mold 3D printing.

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.

Finite Element Simulation of Flexible Roll Forming with Supplemented Material Data and the Experimental Verification

Flexible roll forming is a promising manufacturing method for the production of variable cross section products. Considering the large plastic strain in this forming process which is much larger than that of uniform deformation phase of uniaxial tensile test, the widely adopted method of simulating the forming processes with non-supplemented material data from uniaxial tensile test will certainly lead to large error. To reduce this error, the material data is supplemented based on three constitutive models. Then a finite element model of a six passes flexible roll forming process is established based on the supplemented material data and the original material data from the uniaxial tensile test. The flexible roll forming experiment of a B pillar reinforcing plate is carried out to verify the proposed method. Final cross section shapes of the experimental and the simulated results are compared. It is shown that the simulation calculated with supplemented material data based on Swift model agrees well with the experimental results, while the simulation based on original material data could not predict the actual deformation accurately. The results indicate that this material supplement method is reliable and indispensible, and the simulation model can well reflect the real metal forming process. Detailed analysis of the distribution and history of plastic strain at different positions are performed. A new material data supplement method is proposed to tackle the problem which is ignored in other roll forming simulations, and thus the forming process simulation accuracy can be greatly improved.

Symmetry Classification of Partial Differential Equations Based on Wu's Method

Lie algorithm combined with differential form Wu's method is used to complete the symmetry classification of partial differential equations(PDEs)containing arbitrary parameter.This process can be reduced to solve a large system of determining equations,which seems rather difficult to solve,then the differential form Wu's method is used to decompose the determining equations into a series of equations,which are easy to solve.To illustrate the usefulness of this method,we apply it to some test problems,and the results show the performance of the present work.

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.

EFFECT OF VELOCITY ON DUCTILITY UNDER HIGH VELOCITY FORMING

The ring expansion procedures over various forming velocities are calculated with ANSYS software in order to show the effect of forming velocity on ductility of rate insensitive materials. Ring expansion procedures are simplified to one-dimensional tension by constraining the radial deformation, with element birth and death method, fracture problem of circular ring are considered. The calculated results show that for insensitive materials of 1060 aluminum and 3A21 aluminum alloy, fracture strain increases corresponding to the increase of forming velocity. This trend agrees well with experimental results, and indicates inertia is the key factor to affect ductility; With element birth and death methods, fracture problems can be solved effectively. Experimental studies on formability of tubular workpieces are also conducted, experimental results show that the formability of 1060 aluminum and 3A21 aluminum alloy under electromagnetic forming is higher than that under quasistatic forming, according to the characteristics of electromagnetic forming, the forming limit diasrams of the two materials tube are also built respectively, this is very important to promote the development of electromagnetic forming and guide the engineering practices.

PREDICTION OF MICROSTRUCTURE EVOLUTION DURING HOT EXPANDING-EXTRUSION FORMING OF RESTRAINING RINGS

A mathematic model for dynamic and static recrystallization of Mn18Cr18N steel is presented.Hot expanding extrusion forming and air cooling process of 600 MW retaining ring has been simulated by the combination of thermos coupled rigid viscoplasitic FEM with this model,and grain size distribution on cross section of ring is shown.The essential results can be provided for use of the new technique.

Effects of porosity and pore size on the compressive properties of closed-cell Mg alloy foam

In our current work,AZ31 magnesium alloy foams with closed-cell were successfully fabricated by melt foaming method using Ca and CaCO3 as thickening and blowing agent,respectively.The influences of porosity and pore size on the quasi-static compressive properties of the foams were systematically investigated.The results showed that the yield strength,energy absorption capacity and ideality energy absorption efficiency were decreased with the increase in porosity.However,specimens with porosities of 60%,65%and 70%possessed similar total energy absorption capacity and ideality energy absorption efficiency.Meanwhile,experimental results showed that mean plateau strength of the foams was increased first and then decreased with increase in mean pore size.In addition,energy absorption capacities were almost the same in the initial stage,while the differences were obvious in the middle stage.From the engineering point of view,the specimens with mean pore size of 1.5 mm possess good combination of mean plateau strength and energy absorption characteristics under the present conditions.

Effect of 2D spatial variability on slope reliability: A simplified FORM analysis

To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone(deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability.

RELIABILITY ANALYSIS OF FRP LAMINATED PLATES WITH CONSIDERATION OF BOTH INITIAL IMPERFECTION AND FAILURE SEQUENCE

A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial imperfection and the strength parameters are considered as random variables. Ply-level failure probability is evaluated by the first order reliability method (FORM) together with the Tsai-Wu strength criterion and Tan criterion. Current stresses in the laminated structure are calculated by the classical lamination theory with the stiffness modified based on the last step ply failure. Probabilistically dominant ply-level failure sequences leading to overall system failure are identified, based on which the system failure probability is estimated. A numerical example is presented to demonstrate the methodology proposed. Through parameter studies it is shown that the deviation of the initial imperfection and some of the strength parameters largely influence the system reliability.

Probabilistic analysis of ultimate seismic bearing capacity of strip foundations

This paper presents a reliability analysis of the pseudo-static seismic bearing capacity of a strip foundation using the limit equilibrium theory. The first-order reliability method(FORM) is employed to calculate the reliability index. The response surface methodology(RSM) is used to assess the Hasofer e Lind reliability index and then it is optimized using a genetic algorithm(GA). The random variables used are the soil shear strength parameters and the seismic coefficients(khand kv). Two assumptions(normal and non-normal distribution) are used for the random variables. The assumption of uncorrelated variables was found to be conservative in comparison to that of negatively correlated soil shear strength parameters. The assumption of non-normal distribution for the random variables can induce a negative effect on the reliability index of the practical range of the seismic bearing capacity.

NONEXISTENCE OF POSITIVE SOLUTIONS FOR A SEMI-LINEAR EQUATION INVOLVING THE FRACTIONAL LAPLACIAN IN R^N

In this paper, we consider the semilinear equation involving the fractional Laplacian in the Euclidian space R^n：（-△）^α/2u（x） ： f（xn）u^p（x）, x ∈R^n（0.1）in the subcritical case with 1〈 p〈n＋a/n-a.Instead of carrying out direct investigations on pseudo-differential equation （0.1）, we first seek its equivalent form in an integral equation as below：u（x）=∫R^nG∞（x, y） f（yn） u^p（y）dy,where G∞（x, y） is the Green＇s function associated with the fractional Laplacian in R^n. Employing the method of moving planes in integral forms, we are able to derive the nonexistence of positive solutions for （0.2） in the subcritical case. Thanks to the equivalence, same con- clusion is true for （0.1）.

CLASSIFICATION OF POSITIVE SOLUTIONS TO ASYSTEM OF HARDY-SOBOLEV TYPE EQUATIONS

In this paper, we are concerned with the following Hardy-Sobolev type system{(-?)^(α/2) u(x) =v^q(x)/|y|^(t_2) (-?)α/2 v(x) =u^p(x)/|y|^(t_1),x =(y, z) ∈(R ~k\{0}) × R^(n-k),(0.1)where 0 < α < n, 0 < t_1, t_2 < min{α, k}, and 1 < p ≤ τ_1 :=(n+α-2t_1)/( n-α), 1 < q ≤ τ_2 :=(n+α-2 t_2)/( n-α).We first establish the equivalence of classical and weak solutions between PDE system(0.1)and the following integral equations(IE) system{u(x) =∫_( R^n) G_α(x, ξ)v^q(ξ)/|η|t^2 dξ v(x) =∫_(R^n) G_α(x, ξ)(u^p(ξ))/|η|^(t_1) dξ,(0.2)where Gα(x, ξ) =(c n,α)/(|x-ξ|^(n-α))is the Green's function of(-?)^(α/2) in R^n. Then, by the method of moving planes in the integral forms, in the critical case p = τ_1 and q = τ_2, we prove that each pair of nonnegative solutions(u, v) of(0.1) is radially symmetric and monotone decreasing about the origin in R^k and some point z0 in R^(n-k). In the subcritical case (n-t_1)/(p+1)+(n-t_2)/(q+1)> n-α,1 < p ≤ τ_1 and 1 < q ≤ τ_2, we derive the nonexistence of nontrivial nonnegative solutions for(0.1).

基于贝叶斯推理的沉箱式防波堤可靠性分析

Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance of structures have epistemic or aleatory uncertainties.Furthermore,sliding failure is one of the most important failure modes of caisson breakwaters.In most previous studies,for assessment purposes,uncertainties,such as wave and wave period variation,were ignored.Therefore,in this study,Bayesian reliability analysis is implemented to assess the failure probability of the sliding of Tombak port breakwater in the Persian Gulf.The mean and standard deviations were taken as random variables to consider dismissed uncertainties.For this purpose,the frst-order reliability method(FORM)and the frst principal curvature cor-rection in FORM are used to calculate the reliability index.The performances of these methods are verifed by importance sampling through Monte Carlo simulation(MCS).In addition,the reliability index sensitivities of each random variable are calculated to evaluate the importance of diferent random variables while calculating the caisson sliding.The results show that the reliability index is most sensitive to the coefcients of friction,wave height,and caisson weight(or concrete density).The sensitivity of the failure probability of each of the random variables and their uncertainties are calculated by the derivative method.Finally,the Bayesian regression is implemented to predict the statistical properties of breakwater sliding with non-informative priors,which are compared to Goda’s formulation,used in breakwater design standards.The analysis shows that the model posterior for the sliding of a caisson breakwater has a mean and standard deviation of 0.039 and 0.022,respectively.A normal quantile analysis and residual analysis are also performed to evaluate the correctness of the model responses.

An Alternative Algorithm for the Symmetry Classification of Ordinary Differential Equations

This is the first paper on symmetry classification for ordinary differential equations(ODEs)based on Wu’s method.We carry out symmetry classification of two ODEs,named the generalizations of the Kummer-Schwarz equations which involving arbitrary function.First,Lie algorithm is used to give the determining equations of symmetry for the given equations,which involving arbitrary functions.Next,differential form Wu’s method is used to decompose determining equations into a union of a series of zero sets of differential characteristic sets,which are easy to be solved relatively.Each branch of the decomposition yields a class of symmetries and associated parameters.The algorithm makes the classification become direct and systematic.Yuri Dimitrov Bozhkov,and Pammela Ramos da Conceição have used the Lie algorithm to give the symmetry classifications of the equations talked in this paper in 2020.From this paper,we can find that the differential form Wu’s method for symmetry classification of ODEs with arbitrary function(parameter)is effective,and is an alternative method.

APPLICATION OF INTEGRATION ALGORITHEMS FOR ELASTO-PLASTICITY CONSTITUTIVE MODEL FOR ANISOTROPIC SHEET MATERIALS

Two algorithms of computing stress increment by using the elasto-plasticity constitutive model are firstly formulated, which are the Euler integration method and the radial return method. Hill＇48 anisotropic yield criterion is used. The Euler integration method can not obtain more accurate computation of the stress increment as the radial return method unless enough subintervals are taken,by which the Euler integration method will take excessive computing time. Without docreasing any accuracy, the radial return method can save much time. Finally, a square cup deep drawing from NUMISHEET＇93 benchmarks is simulated with a self-developed code SheetForrn in order to investigate the accuracy and efficiency of the radial return method.

UBM STUDY ON DOUBLE-DIE IRONING PROCESS

The double-die ironing process is studied by means of UBM. The formulas of deformation load.contact stress on die surface, and tensile stress which acts on workpiece is obtained. Taking account of dirnensional accuracy, a new critical condition of limit reduction in cross section area is put forward for the flrst time. The test experiment indicats that results of theoretical analysis well accord with the actual conditions.[0]

Absolute surface form measurement of flat optics based on oblique incidence method

In this Letter, a test method based on oblique incidence is practically implemented in the interferometric measurement process. Three sets of wavefront data are achieved through cavity interference measurement with a Fizeau interferometer and one oblique incidence measurement. An iterative algorithm is applied to retrieve the absolute surface shape of the test flat. By adding two sets of measurements, the absolute surface error of the interferometer＇s reference flat can be obtained. The new method can not only calibrate the reference flat error of interferometer, but also provide the absolute measurement method for high precision optical components applied in high power laser systems.

Method of a New Iteration Scheme Combined with Kriging Model for Structural Reliability Evaluation

The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (LSF) behaves high nonlinearity, a new iteration scheme called "rotated gradient algorithm (RGA)" is proposed and combined with Kriging model to evaluate the reliability of implicit performance function. In this paper, the Kriging model is applied to approximate the real LSF first. Then the scheme of RGA, constructed in terms of gradient information of two adjacent design points obtained during the process of calculation, is used to calculate the reliability index. Numerical examples show the validity in convergence and accuracy of the proposed methodfor arbitrary nonlinear performance function.