A three-dimensional model of the spray forming method

A three-dimensional model has been formulated to calculate the shape of the general preform, using vector calculus. The shape of a rod, tube, plate, or irregular preform can be calculated at given spray forming conditions. The shape of a spray-formed rod was analyzed at various spray forming conditions using the three-dimensional model. The effects of spray forming parameters, such as spray distribution parameters, angular velocity of rotation, withdrawal velocity, spray angle, and eccentric distance on rod shape, were analyzed. The most important parameters affecting the shape of rods are the spray distribution parameters and the withdrawal velocity. The dynamic evolution of rod shape with a stepwise variation of the withdrawal velocity during spray forming was investigated. The effect of a stepwise change of the withdrawal velocity was the same as that of the scanning atomizer. The calculated surface profiles were compared with those of spray-formed 7075 aluminum alloy rods prepared on a pilot scale. The calculated results for the surface profiles were in agreement with those of the spray-formed rods.     

喷射成形棒坯中沉积距离和回缩速度的选择

利用计算机数值模拟技术采用平均质量流率法建立了喷射成形空间质量流率分布和棒坯生长模型，通过讨论喷射成形空间质量流率分布得出沉积器的最佳位置hm和最佳回缩速度vo并计算了不同喷射参数对沉积坯端面形貌的影响。     

喷射成形过程中圆锭坯外形生长的数值模拟

通过多次试验后得出雾化喷嘴的雾化特性公式,在此基础上建立了一种模拟喷射成形过程中圆锭坯外形生长的数学模型.该数学模型考虑了喷射成形过程中各种工艺参数,如喷嘴的雾化参数、偏心距离、沉积盘的旋转速度和下拉速度等参数的影响.经过模拟计算,得到了锭坯生长的三维外形尺寸,与实际喷射成形制备的锭坯外形对比,二者吻合很好;采用该模型分析了不同时间下锭坯的轮廓形状、偏心距离以及下拉速度变化后的锭坯轮廓形状.综合分析得出,此数学模型可以预测在不同工艺参数下喷射成形锭坯的外形生长过程.     

Modeling of spray-formed materials: Geometrical considerations

In this article, a mathematical model is formulated to predict the evolution and final geometry of an axisymmetric billet (i.e., round) obtained using an off-axis spray arrangement. The model is formulated by calculating the shape change of a profile curve of a billet surface, based on an axisymmetric surface. On the basis of this model, a methodology to determine the “shadowing effect” coefficient is presented. The modeling results suggest that there are three distinct regions in a spray-formed billet: a base transition region, a uniform diameter region, and an upper transition region. The effects of several important processing parameters, such as the withdrawal velocity of substrate, maximum deposition rate, spray distribution coefficient, initial eccentric distance, and rotational velocity of substrate, on the shape factors (e.g., the diameter size of the uniform region and the geometry of the transition regions) are investigated. The mechanisms responsible for the formation of the three distinct regions are discussed. Finally, the model is then implemented and a methodology is formulated to establish optimal processing parameters during spray forming, paying particular attention to deposition efficiency.     

Modelling of droplet dynamic and thermal histories during spray forming—II. Effect of process parameters

A computer model has been developed to describe the in-flight dynamic and thermal histories of gas atomised droplets as a function of distance during spray forming. The model has been used to investigate the effects of the dynamic and thermal behaviour of individual gas atomised droplets and the cooling and solidification behaviour of the overall spray. The most influential parameters for a given alloy system, in order of importance, are: (i) droplet diameter and, therefore, the droplet size distribution within the spray; (ii) initial axial gas velocity at the point of atomisation and the subsequent gas velocity decay profile; (iii) melt mass flow rate; (iv) melt superheat at the point of atomisation; and (v) alloy composition. Experimental measurements of gas velocities and droplet size distributions during spray forming allow the spray solid fraction at deposition to be calculated and used in a subsequent computer model of billet heat flow to predict the billet top surface temperatures and solid fractions.     

Spray Deposition Behavior and Numerical Simulation of Growth of Tubular Preform in Spray Forming Process

 Analysis on the deposition behavior of spray on deposition surface was made and an optimization method for the movement parameters (u, ω) of substrate was obtained. Simultaneously, a mathematical model of growth of tubular preform, specifically aimed at the kind of atomizer that is fixed and with a tilt angle was established. By integrating the optimization method and the mathematical model, the growth process and shape of preform were simulated. The results show that the tilt angle of atomizer plays an important role on the dimensions and shapes of tubular preforms and it can provide a guidance for the development of spray forming equipment.     

Evolution of microstructure and texture in Mg-Al-Zn alloys during electron-beam and gas tungsten arc welding

The evolution of microstructure and texture in the AZ-series Mg alloys subjected to electron-beam welding and gas tungsten arc welding are examined. Electron-beam welding is demonstrated to be a promising means of welding delicate Mg plates, bars, or tubes with a thickness of up to 50 mm; gas tungsten arc welding is limited to lower-end thin Mg sheets. The grains in the fusion zone (FZ) are nearly equiaxed in shape and ∼8 μm or less in size, due to the rapid cooling rate. The as-welded FZ microhardness and tensile strength are higher than the base metals due to the smaller grain size. The weld efficiency, defined as the postweld microhardness or tensile strength at the mid-FZ region divided by that of the unwelded base metal, is around 110 to 125 pct for electron-beam welding and 97 to 110 pct for gas tungsten arc welding. There are three main texture components present in the electron-beam-welded (EBW) FZ, i.e., (with TD// ), (with ND_∧ ∼15 deg), and (with WD_∧ ∼30 deg), where TD, ND, and WD are the transverse, normal, and welding directions, respectively. The crystal growth tends to align toward the most closed-packed direction, . The texture in gas tungsten arc welded (GTAW) specimens is more diverse and complicated than the EBW counterparts, due to the limited and shallow FZ and the lower cooling rate. The cooling rates calculated by the three-dimensional (3-D) and two-dimensional (2-D) heat-transfer models are considered to be the lower and upper bounds. The cooling rate increases with decreasing Al content, increasing weld speed, and increasing distance from the weld top surface. The influences of the FZ location, welding speed, and alloy content on the resulting texture components are rationalized and discussed.     

Analysis of the spray deposition process

Net or near net shape products can be manufactured by technologies involving solidification processing, metal forming, paniculate processing, and droplet consolidation. One example of droplet consolidation is spray deposition in the Osprey^tm mode. In this process, a stream of liquid metal is atomized by an inert gas to form a spray of molten droplets; these are accelerated towards a substrate where they impinge and consolidate. An integral model for the Osprey^tm spray deposition process has been developed using established theoretical principles. Mathematical models describe the interconnected processes of droplet-gas interactions in flight and subsequent droplet consolidation on the substrate. The models predict droplet velocity and temperature as a function of flight distance, the extent of droplet solidification on arrival at the substrate, and temperature distribution in the consolidated material during deposition. This approach demonstrates the utility of modeling studies in order to establish quantitative guidelines for optimization of the process in terms of the evolution of microstructure in droplet consolidation.     

Microstructural modeling of recrystallization in deformed iron single crystals

Recrystallization kinetics in a (111)[1 0] iron single crystal deformed 70 pet by rolling were characterized experimentally at temperatures between 500°C and 600°C by means of quantitative metallography. A Laplace transform method was applied to the time-dependent global microstructural properties, volume fraction, interface area per unit volume, and the largest intercept-free length (recrystallized grain) to separate nucleation and interface migration effects from the overall recrystallization kinetics. A comprehensive nucleation and growth model was derived from analysis of the microstructural data. The model consisted of the following salient features: (a) nucleation was random and approximately site-saturated with zero incubation time at all temperatures; (b) the recrystallized grains grew three-dimensionally in the shape of prolate spheroids; and (c) interface migration rates were highly anisotropic, the grains growing at an approximately constant rate in one dimension and at a strongly decreasing rate in the other two dimensions. The present findings were compared to a similar earlier study of a deformed iron (111)[ 2] single crystal. The time dependencies of the interface migration rates were rationalized in terms of a deformation-induced, nonuniform distribution of stored energy and an orientation-dependent grain boundary mobility.     

Numerical simulation of temperature distribution and solidification behaviour during spray forming

A mathematical, two-dimensional model for the analysis of the temperature and solidification behaviour in the substrate and deposit for the spray forming process of metals has been developed. Due to the irregular shape of the growing deposit, which changes with spraying time, a grid transformation method was successfully developed for the calculation of the temperature distribution and solidification front in the growing deposit. The influence of process parameters, i.e. thermal conditions of the metal spray at impact, heat transfer coefficient at the surface of the deposit and geometrical parameters, are qualitatively and quantitatively discussed.     

Microstructural and compositional transients during accelerated directional solidification of Al-4.5 wt pct Cu

The transient behavior of mushy-zone velocities, primary dendrite arm spacings, and microsegregation effects have been investigated for an Al-4.5 wt pct Cu alloy by instantaneous velocity changes in a standard Bridgman furnace. After suddenly imposed velocity changes, the mushy-zone velocities, dendrite arm spacings, and compositions exponentially adjust to new steady-state values. Good agreement was found between the transient mushy-zone positions and velocities and predictions from the theoretical model of Saitou and Hirata. The primary dendrite arm spacings appear to adjust to changed velocity conditions about as rapidly as the mushy-zone velocity adjusts. Steady-state arm spacings agree very well with corresponding steady-state data from the literature. However, the observed composition profiles in the dendrite core and the interdendritic liquid appear to adjust more slowly than the corresponding adjustment of the mushy-zone velocity and arm spacings. Our observation of the sluggish response of the compositional profiles is consistent with an estimated Lewis number of 9.4 × 10³ for the aluminum-copper system. The diffusivity of heat, thus, greatly exceeds the diffusivity of solute in this system. These results indicate that testing for the steady state during directional solidification experiments by looking for constant primary dendrite arm spacings can lead to errors, since the microsegregation profiles adjust more slowly than the spacings. It is suggested that constancy of composition also be tested for critical experiments investigating steady-state microsegregation effects.     

Numerical simulation of tube profile growth during spray forming process

Spray forming is a new type of metal material forming process,which can produce metal blanks such as billet,tube,plate etc.A mathematical model has been developed to forecast the shape evolution of tube billets during the spray forming process.The atomizer mass flux as,radial distribution coefficient bs,draw velocity and diameter of mandrel were considered in this model and the influence of different parameters such as metal flowrate,draw velocity of mandrel,diameter of mandrel on the tube’s shape change were simulated and analyzed in this paper.The simulation results obtained from this model can be provided to engineers as reference.     

Anisotropic grain growth based on the atomic adsorption model in WC-25 pct Co alloy

The process of triangular prism formation and abnormal grain growth of WC was modeled using pseudo-Monte-Carlo simulation based on atomic adsorption and the coalescence mechanism. Grains of WC evolved into a triangular prism shape due to {10 0} and {1 10} planes of fast growth rate. Coalescence of {10 0} and {1 00} planes subsequent to the anisotropic evolution was the main reason for the abnormal grain growth. The probability of coalescence computed by the Monte-Carlo method agreed well with a theoretical prediction. Experimental evaluation of the computational model was made in sintered WC-25 wt pct Co alloy. The experimental alloy was made with WC powder of different particle size, 0.8 μm and −325 mesh, respectively, and with two different sintering conditions: solid-phase sintering and liquid-phase sintering. The sample made from the coarse powder (−325 mesh) showed the same morphological characteristics as those of the original milled state, whereas the sample made from the fine powder (0.8 μm) assumed a triangular prism shape quickly during solid-phase sintering. The anisotropic growth process of the latter sample could be explained by using the adsorption and coalescence model.     

Modeling of spray-formed plates using anX-Y moving substrate

A mathematical model, incorporating the thermal component of sticking efficiency (SE _t) into the calculation of shape evolution, is formulated to predict the evolution and final geometry of plates. The plates are spray formed using a moving substrate displaced in a two-dimensional (i.e., X-Y) plane. By using this model, the effects of the substrate movement parameters, such as the acceleration, time required to complete a stroke in the reciprocal movement direction (X-axis), and the velocity in the uniform movement direction (Y-axis), on the shapes of the plates are investigated. The processing parameters are evaluated by minimizing the values of the mean-squared (MS) surface roughness. On the basis of the evaluation, the optimal combinations of processing parameters are found.     

Modeling of spray-formed plates using an X-Y moving substrate

A mathematical model, incorporating the thermal component of sticking efficiency (SE _t) into the calculation of shape evolution, is formulated to predict the evolution and final geometry of plates. The plates are spray formed using a moving substrate displaced in a two-dimensional (i.e., X-Y) plane. By using this model, the effects of the substrate movement parameters, such as the acceleration, time required to complete a stroke in the reciprocal movement direction (X-axis), and the velocity in the uniform movement direction (Y-axis), on the shapes of the plates are investigated. The processing parameters are evaluated by minimizing the values of the mean-squared (MS) surface roughness. On the basis of the evaluation, the optimal combinations of processing parameters are found.     

Modeling the Deposition Dynamics of a Twin-Atomizer Spray Forming System

A numerical study of the deposition dynamics of twin-atomizer spray-forming of large-diameter billets is presented with a focus on the coupled effect of the twin-atomizer scan frequency and substrate rotation frequency. The common period of the two frequencies ξ was the dominant parameter to govern the deposited droplet mass and billet shape. When ξ ≥ 10, a uniform mass distribution at the deposition surface was predicted, and the calculated shape agreed with experiments.     

Heat-transfer and solidification model of continuous slab casting: CON1D

A simple, but comprehensive model of heat transfer and solidification of the continuous casting of steel slabs is described, including phenomena in the mold and spray regions. The model includes a one-dimensional (1-D) transient finite-difference calculation of heat conduction within the solidifying steel shell coupled with two-dimensional (2-D) steady-state heat conduction within the mold wall. The model features a detailed treatment of the interfacial gap between the shell and mold, including mass and momentum balances on the solid and liquid interfacial slag layers, and the effect of oscillation marks. The model predicts the shell thickness, temperature distributions in the mold and shell, thickness of the resolidified and liquid powder layers, heat-flux profiles down the wide and narrow faces, mold water temperature rise, ideal taper of the mold walls, and other related phenomena. The important effect of the nonuniform distribution of superheat is incorporated using the results from previous three-dimensional (3-D) turbulent fluid-flow calculations within the liquid pool. The FORTRAN program CONID has a user-friendly interface and executes in less than 1 minute on a personal computer. Calibration of the model with several different experimental measurements on operating slab casters is presented along with several example applications. In particular, the model demonstrates that the increase in heat flux throughout the mold at higher casting speeds is caused by two combined effects: a thinner interfacial gap near the top of the mold and a thinner shell toward the bottom. This modeling tool can be applied to a wide range of practical problems in continuous casters.     

喷射成型锭坯形状的数值模拟研究

建立了描述喷射成型过程中沉积坯外轮廓动态生长的三维数学模型,该模型考虑了喷射成型过程中各种工艺参数的影响,这些工艺参数包括喷嘴的雾化特性值、偏心距离、沉积盘的旋转速度和下拉速度,在计算后进行数据处理得出了锭坯生长的三维外形轮廓,通过与实际喷射成型设备成形的锭坯对比,两种结果符合较好,并可用此模型来预测不同工艺条件下锭坯的外形生长轮廓。     

A thermal model of laser cladding by powder injection

A two-dimensional (2-D) finite element model is presented for laser cladding by powder injection. The model simulates the quasi-steady temperature field for the longitudinal section of a clad track. It takes into account the melting of the powder in the liquid pool and the liquid/ gas free surface shape and position, which must conform to the thermal field in order to obtain a self-consistent solution. The results for an idealized problem, where there is almost no melting of the substrate material, demonstrate the linear relationship between the laser power, the processing velocity, and the thickness of the deposited layer. The calculated clad heights agreed well with the experimental values for the conditions where a cobalt-based hard-facing alloy is clad onto mild steel with a linearly focused laser source. Formerly Postdoctoral Fellow, Ecole Polytechnique Fédérale de Lausanne