复杂件等离子熔积成形过程有限元及无网格法模拟
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摘要
等离子熔积成形具有能量密度高、加热速度快、成材范围广、冶金质量好、制件尺寸大及设备运行成本低等优点。但成形中高能量等离子束移动热源，会导致零件内温度分布不均匀和表面明显的阶梯效应。因此，如何对成形系统的温度进行有效控制和优化，减少制件由于热应力导致的热裂纹，提高成形性与成品率，是该技术实用化的关键。
论文在有限元ANSYS软件系统的基础上，考虑移动热源和三维增材成形特点，基于热力耦合数学物理模型，开发了随热源和热边界移动的单元逐步激活与加载的等离子熔积制造APDL程序，系统地模拟研究了热辐射效应和工艺参数对高温合金薄壁件成形过程温度场的影响，综合比较了循环水逐步淹没基板、基板下火炉预热与基板中循环水冷三种温度控制系统。模拟所得合适工艺参数为：熔积电压为30V，电流为70A，扫描速度为0.008m／s，冷却水流速为1.6m／s，送粉速度为0.627g／s，基板材料为Q235B。论文首次明确指出高能束成形多余能量主要通过基板以热传导方式转移，辐射与对流造成的热损失只占总量的5％左右，最后提出了成形前基于零件几何外形的基板局部预热与成形开始后基板中水冷却的等离子熔积成形复合温控方案。论文进一步研究了汽车翼子板模具(包括凸模和凹模)等离子熔积制造过程的温度场分布及其变化规律，详细评估了三种扫描路径对成形温度的影响，结果表明：与平行Z字式和交叉Z字式相比，内外回形式扫描成形中零件的温度及其梯度较低，温度场分布较均匀。在以上模拟计算工作的基础上，开展成形试验，成功制造出高温合金复杂双扭涡轮件和叶片样件。
在以上等离子熔积成形的有限元分析中，为了保证模拟计算精度和收敛性，采用了六面体网格并尽量规则、均匀和细密。然而，零件本身及其与基板过渡区的四面体网格扭曲变形严重，不但给网格划分带来了极大困难，大大增加了分析计算工作量，而且严重影响了有限元法的求解速度、精度、稳定性及收敛性。为此，本文提出采用对节点分布免疫的新型无网格法模拟等离子熔积三维复杂零件成形过程的温度场与应力应变场。与有限元法相比，无网格法只需域内的节点信息构造目标函数，从而避免了因单元网格严重扭曲造成的求解问题。
论文基于广义变分原理与G空间理论，在无网格NS-PIM和ES-PIM法理论模型的基础上，采用广义光滑梯度技术修正协调梯度场，提出并建立了三维复杂形状零件的增量动态非线性温度场和应力应变场的数学模型，并依此开发了相应的无网格法程序系统。大量复杂问题的分析结果表明：在同一种节点分布条件下，所开发的无网格软件可获得“准”精确的系统刚度，其数值解精度、收敛性及稳定性均高于传统的有限单元法结果，并且在极不规则的节点分布条件下仍能给出满意的数值精度。此外，论文首次系统地研究和比较了NS-PIM、ES-PIM、FEM与EFG和MLPG法的计算成本和效率。研究结果表明：论文开发的无网格程序的计算效率远高于经典无网格EFG、MLPG法以及标准的FEM。
鉴于目前尚无成熟的无网格法计算力学软件，论文基于面向过程的程序设计思想开发了复杂形状零件非线性温度及应力应变场分析的无网格程序系统，初步建立了一套温度及热应力场的程序设计体系，着重论述了该程序的实现过程及其主要模块功能，并给出了核心功能模块的源代码。最后对复杂双扭涡轮件成形冷却过程的非线性温度场与应力应变场进行了数值模拟分析，与实测结果基本一致，表明该软件系统在分析三维复杂件非线性温度场与热应力场的可行性与正确性。论文的研究结果为等离子熔积成形复杂三维金属零件的工艺优化与设计提供了科学依据。
The plasma deposition manufacturing(PDM) technology has the features of higherenergy density, rapid heating and solidification, widely-used materials, better metallurgicalquality, larger-dimensioned parts and lower cost of equipments. In the process ofmanufacturing, the excess energy due to the continuous heat input of plasma arc cumulatesrapidly, which usually induces the uneven temperature field and severe staircase effect thatis one of the most significant manifestations of part inaccuracy in liquid-based rapidtooling. Therefore, the key problem of advancing this technology into commercial marketis to control the temperature field, to reduce the hot crackability induced by thermal stressand to improve the formability and yield of metal pans. For the purpose of full scientificevidence to optimizing technical design, the nonlinear transient temperature and thermalstress fields of complicated parts are simulated in this thesis through both the finiteelement method(FEM) and meshfree methods.
According to the features of moving heat source and adding material manufacture inthe PDM, The ANSYS Parametric Design Langrage(APDL) is used to develop the virtualmanufacturing process of elemental activation and load step by step following the movingheat source. This program is then used to investigate the influences of radiation andconvection, plasma power voltage(U_p), transferred arc current(I_(PO)), scanning speed ofplasma torch(v_s.), mean flow rate of cooling water in the substrate(ν_(im)) and the powderflow rate(u_p) on the transient temperature field of the superalloy thin wall. Moreover,three types of temperature control schemes, including the submerging substrate withcooling water, the preheating with a stove under the substrate and the cooling water insidesubstrate are compared and validated using above manufacturing program. Computationalresults show that the great majority of excess energy in the PDM is taken away throughthe substrate by the way of heat conduction, and about five percent of heat is released byradiation and convection. The suitable processing specifications can be obtained: U_p=30V,I_(PO)=70A,ν_s.=0.008m/s,ν_(im)=1.6m/s and u_p=0.627g/s together with Q235B as the substratematerial, and then the temperature control system of locally preheating in terms of thegeometry shape of metal part before fabrication and circulating water cooling inside the substrate at the outset of fabrication are proposed. Using the optimized process scheme,temperature distribution and its evolution principle of a car fender mould(including apunch and die mould) manufactured by the PDM are further investigated, and three typesof scanning path are evaluated in terms of hot crackability and formability. Computationalresults show that, compared with parallel Z-shaped and criss-cross Z-shaped scanningstrategies, the in-to-out scanning strategy can give much less peak temperature and itsgradient as well as much more uniform temperature distribution. Finally, a geometricallycomplicated turbine and a blade are manufactured successfully, in which the good surfacequalityand small deformation and warps are found during and after the fabrication.
It is suggested from the foregoing analysis that a regular, uniform and fine meshshould be used for accurate selection to simulate the deposition process. In addition, largeelemental deformation and distortion usually take place especially for the tetrahedrons inthe transition region between the part and substrate. This kind of integrated initial meshcan not only result in the significant increase of manpower and cost of the analysis butalso strongly deteriorate the convergence rate, accuracy and reliability of the numericalsolutions. In recent decades, meshfree methods that are not sensitive to or even immunefrom elemental mesh have been developed as the powerful alternative techniques to theFEM. Remarkable progress has been made to provide more effectively solutions forproblems, such as large deformation and dynamic propagation of cracks that cannot beefficiently solved using the traditional FEM.
Meshfree smoothed PIMs including the Node-based Smoothed PIM(NS-PIM) andthe Edge-based Smoothed PIM(ES-PIM) are developed recently by Professor Liu GR.They use the generalized gradient smoothing technique to modify the gradient fields.Based on the G space theory and the generalized variational principle, the dynamicincremental smoothed nonlinear mathematical formula of temperature and residual stressfields is established in this dissertation from conventional meshfree NS-PIM and ES-PIM.The meshfree codes are then developed to analyze three-dimensional nonlineartemperature and thermal stress fields of geometrically complicated parts. Numerousexample problems have been investigated in details using both NS-PIM and ES-PIM.They have been proven to be stable, works well with triangular and tetrahedral meshes respectively for two and three dimensions, free from volumetric locking, much moreresistant to mesh distortion, and capable of giving a close-to-exact stiffness, ultra-accurate,and even upper bound solutions compared with FEM. In the present work, thecomputational cost and efficiency are systematically investigated for methods of NS-PIM,ES-PIM, FEM, EFG and MLPG. It is indiciated that two types of meshfree methods ofNS-PIM and ES-PIM developed are much more efficient than the well-developed EFGand MLPG as well as the standard FEM.
It is well-known that, up to the present, no any meshfree software has been developed.Based on the procedure of process-oriented programming, the dynamic incrementalnonlinear meshfree in-house code has been developed using FORTRAN 90. The detailedaspects of their programming are given in Chapter 5, and some kernel subroutine codesare given for the comparison and reference. A turbine part with both complicatedgeometry and boundary conditions are then simulated based on this software. Numericalresults show that present software is very stable numerically, and the computationalconvergence, accuracy and efficiency are better than the traditional FEM using the sameset of nodes and triangular cells. This indicates that present meshfree NS-PIM andES-PIM are promising and potential to the wide applications into practical problems witharbitrarily complicated geometries and boundary conditions.
论文在有限元ANSYS软件系统的基础上，考虑移动热源和三维增材成形特点，基于热力耦合数学物理模型，开发了随热源和热边界移动的单元逐步激活与加载的等离子熔积制造APDL程序，系统地模拟研究了热辐射效应和工艺参数对高温合金薄壁件成形过程温度场的影响，综合比较了循环水逐步淹没基板、基板下火炉预热与基板中循环水冷三种温度控制系统。模拟所得合适工艺参数为：熔积电压为30V，电流为70A，扫描速度为0.008m／s，冷却水流速为1.6m／s，送粉速度为0.627g／s，基板材料为Q235B。论文首次明确指出高能束成形多余能量主要通过基板以热传导方式转移，辐射与对流造成的热损失只占总量的5％左右，最后提出了成形前基于零件几何外形的基板局部预热与成形开始后基板中水冷却的等离子熔积成形复合温控方案。论文进一步研究了汽车翼子板模具(包括凸模和凹模)等离子熔积制造过程的温度场分布及其变化规律，详细评估了三种扫描路径对成形温度的影响，结果表明：与平行Z字式和交叉Z字式相比，内外回形式扫描成形中零件的温度及其梯度较低，温度场分布较均匀。在以上模拟计算工作的基础上，开展成形试验，成功制造出高温合金复杂双扭涡轮件和叶片样件。
在以上等离子熔积成形的有限元分析中，为了保证模拟计算精度和收敛性，采用了六面体网格并尽量规则、均匀和细密。然而，零件本身及其与基板过渡区的四面体网格扭曲变形严重，不但给网格划分带来了极大困难，大大增加了分析计算工作量，而且严重影响了有限元法的求解速度、精度、稳定性及收敛性。为此，本文提出采用对节点分布免疫的新型无网格法模拟等离子熔积三维复杂零件成形过程的温度场与应力应变场。与有限元法相比，无网格法只需域内的节点信息构造目标函数，从而避免了因单元网格严重扭曲造成的求解问题。
论文基于广义变分原理与G空间理论，在无网格NS-PIM和ES-PIM法理论模型的基础上，采用广义光滑梯度技术修正协调梯度场，提出并建立了三维复杂形状零件的增量动态非线性温度场和应力应变场的数学模型，并依此开发了相应的无网格法程序系统。大量复杂问题的分析结果表明：在同一种节点分布条件下，所开发的无网格软件可获得“准”精确的系统刚度，其数值解精度、收敛性及稳定性均高于传统的有限单元法结果，并且在极不规则的节点分布条件下仍能给出满意的数值精度。此外，论文首次系统地研究和比较了NS-PIM、ES-PIM、FEM与EFG和MLPG法的计算成本和效率。研究结果表明：论文开发的无网格程序的计算效率远高于经典无网格EFG、MLPG法以及标准的FEM。
鉴于目前尚无成熟的无网格法计算力学软件，论文基于面向过程的程序设计思想开发了复杂形状零件非线性温度及应力应变场分析的无网格程序系统，初步建立了一套温度及热应力场的程序设计体系，着重论述了该程序的实现过程及其主要模块功能，并给出了核心功能模块的源代码。最后对复杂双扭涡轮件成形冷却过程的非线性温度场与应力应变场进行了数值模拟分析，与实测结果基本一致，表明该软件系统在分析三维复杂件非线性温度场与热应力场的可行性与正确性。论文的研究结果为等离子熔积成形复杂三维金属零件的工艺优化与设计提供了科学依据。
The plasma deposition manufacturing(PDM) technology has the features of higherenergy density, rapid heating and solidification, widely-used materials, better metallurgicalquality, larger-dimensioned parts and lower cost of equipments. In the process ofmanufacturing, the excess energy due to the continuous heat input of plasma arc cumulatesrapidly, which usually induces the uneven temperature field and severe staircase effect thatis one of the most significant manifestations of part inaccuracy in liquid-based rapidtooling. Therefore, the key problem of advancing this technology into commercial marketis to control the temperature field, to reduce the hot crackability induced by thermal stressand to improve the formability and yield of metal pans. For the purpose of full scientificevidence to optimizing technical design, the nonlinear transient temperature and thermalstress fields of complicated parts are simulated in this thesis through both the finiteelement method(FEM) and meshfree methods.
According to the features of moving heat source and adding material manufacture inthe PDM, The ANSYS Parametric Design Langrage(APDL) is used to develop the virtualmanufacturing process of elemental activation and load step by step following the movingheat source. This program is then used to investigate the influences of radiation andconvection, plasma power voltage(U_p), transferred arc current(I_(PO)), scanning speed ofplasma torch(v_s.), mean flow rate of cooling water in the substrate(ν_(im)) and the powderflow rate(u_p) on the transient temperature field of the superalloy thin wall. Moreover,three types of temperature control schemes, including the submerging substrate withcooling water, the preheating with a stove under the substrate and the cooling water insidesubstrate are compared and validated using above manufacturing program. Computationalresults show that the great majority of excess energy in the PDM is taken away throughthe substrate by the way of heat conduction, and about five percent of heat is released byradiation and convection. The suitable processing specifications can be obtained: U_p=30V,I_(PO)=70A,ν_s.=0.008m/s,ν_(im)=1.6m/s and u_p=0.627g/s together with Q235B as the substratematerial, and then the temperature control system of locally preheating in terms of thegeometry shape of metal part before fabrication and circulating water cooling inside the substrate at the outset of fabrication are proposed. Using the optimized process scheme,temperature distribution and its evolution principle of a car fender mould(including apunch and die mould) manufactured by the PDM are further investigated, and three typesof scanning path are evaluated in terms of hot crackability and formability. Computationalresults show that, compared with parallel Z-shaped and criss-cross Z-shaped scanningstrategies, the in-to-out scanning strategy can give much less peak temperature and itsgradient as well as much more uniform temperature distribution. Finally, a geometricallycomplicated turbine and a blade are manufactured successfully, in which the good surfacequalityand small deformation and warps are found during and after the fabrication.
It is suggested from the foregoing analysis that a regular, uniform and fine meshshould be used for accurate selection to simulate the deposition process. In addition, largeelemental deformation and distortion usually take place especially for the tetrahedrons inthe transition region between the part and substrate. This kind of integrated initial meshcan not only result in the significant increase of manpower and cost of the analysis butalso strongly deteriorate the convergence rate, accuracy and reliability of the numericalsolutions. In recent decades, meshfree methods that are not sensitive to or even immunefrom elemental mesh have been developed as the powerful alternative techniques to theFEM. Remarkable progress has been made to provide more effectively solutions forproblems, such as large deformation and dynamic propagation of cracks that cannot beefficiently solved using the traditional FEM.
Meshfree smoothed PIMs including the Node-based Smoothed PIM(NS-PIM) andthe Edge-based Smoothed PIM(ES-PIM) are developed recently by Professor Liu GR.They use the generalized gradient smoothing technique to modify the gradient fields.Based on the G space theory and the generalized variational principle, the dynamicincremental smoothed nonlinear mathematical formula of temperature and residual stressfields is established in this dissertation from conventional meshfree NS-PIM and ES-PIM.The meshfree codes are then developed to analyze three-dimensional nonlineartemperature and thermal stress fields of geometrically complicated parts. Numerousexample problems have been investigated in details using both NS-PIM and ES-PIM.They have been proven to be stable, works well with triangular and tetrahedral meshes respectively for two and three dimensions, free from volumetric locking, much moreresistant to mesh distortion, and capable of giving a close-to-exact stiffness, ultra-accurate,and even upper bound solutions compared with FEM. In the present work, thecomputational cost and efficiency are systematically investigated for methods of NS-PIM,ES-PIM, FEM, EFG and MLPG. It is indiciated that two types of meshfree methods ofNS-PIM and ES-PIM developed are much more efficient than the well-developed EFGand MLPG as well as the standard FEM.
It is well-known that, up to the present, no any meshfree software has been developed.Based on the procedure of process-oriented programming, the dynamic incrementalnonlinear meshfree in-house code has been developed using FORTRAN 90. The detailedaspects of their programming are given in Chapter 5, and some kernel subroutine codesare given for the comparison and reference. A turbine part with both complicatedgeometry and boundary conditions are then simulated based on this software. Numericalresults show that present software is very stable numerically, and the computationalconvergence, accuracy and efficiency are better than the traditional FEM using the sameset of nodes and triangular cells. This indicates that present meshfree NS-PIM andES-PIM are promising and potential to the wide applications into practical problems witharbitrarily complicated geometries and boundary conditions.
引文
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