选区激光烧结过程传热分析的高效无网格法
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摘要
增材制造是通过材料逐层堆积来实现构件无模成形的新型制造技术,近年来受到人们的广泛关注。基于无单元伽辽金法(无网格法)提出了一种可高效模拟以粉末床为主要技术特征的选区激光烧结增材制造过程的数值模拟技术。相应于材料逐层增加过程,逐层引入计算节点和背景积分单元。充分利用无单元法建立近似函数仅依赖于节点而非网格单元的优点,对远离当前加工层的区域自适应地进行"网格"粗化以减小计算规模。为进一步提高计算效率,引入稳定相容节点积分技术,大幅度减少了积分点数目。数值结果表明,所发展方法能够有效模拟选区激光烧结增材制造的热传导过程,再现温度场的演化历程。与使用通用有限元软件的模拟方法以及使用高斯积分的标准无网格法相比,该方法大幅度缩短了计算时间,显著提高了选区激光烧结过程传热分析的计算效率。
Additive manufacturing is an advanced model-free manufacturing technology by means of the layered deposition of materials and in recent years it attracts intensive attentions. Based on the element-free Galerkin method(meshfree method), a numerical technique to efficiently simulate the selective laser sintering additive manufacturing process, in which powder-bed is the main technical characteristic, is presented. Corresponding to the process of laying powder layer by layer, the computational nodes and background integration cells are introduced layer by layer. "Mesh" coarsening is adaptively employed in regions far from current manufacturing layer to reduce the scale of the computation, by making full use of the merit of the element-free method in which the construction of approximation functions only depends on nodes instead of elements of the mesh. In order to further improving the computational efficiency, the stabilized conforming nodal integration technology is introduced and the number of integration points is substantially reduced. Numerical results show that the developed method is able to effectively simulate the heat conduction in selective laser sintering additive manufacturing process and to reproduce the evolution of the thermal field. In comparison with the simulation method using general finite element analysis software and the standard meshfree method using Gauss integration, the proposed method substantially reduces the computational time and significantly improves the computational efficiency of the numerical analysis of the heat conduction in selective laser sintering process.
Additive manufacturing is an advanced model-free manufacturing technology by means of the layered deposition of materials and in recent years it attracts intensive attentions. Based on the element-free Galerkin method(meshfree method), a numerical technique to efficiently simulate the selective laser sintering additive manufacturing process, in which powder-bed is the main technical characteristic, is presented. Corresponding to the process of laying powder layer by layer, the computational nodes and background integration cells are introduced layer by layer. "Mesh" coarsening is adaptively employed in regions far from current manufacturing layer to reduce the scale of the computation, by making full use of the merit of the element-free method in which the construction of approximation functions only depends on nodes instead of elements of the mesh. In order to further improving the computational efficiency, the stabilized conforming nodal integration technology is introduced and the number of integration points is substantially reduced. Numerical results show that the developed method is able to effectively simulate the heat conduction in selective laser sintering additive manufacturing process and to reproduce the evolution of the thermal field. In comparison with the simulation method using general finite element analysis software and the standard meshfree method using Gauss integration, the proposed method substantially reduces the computational time and significantly improves the computational efficiency of the numerical analysis of the heat conduction in selective laser sintering process.
引文
[1]李涤尘,贺健康,田小永,等.增材制造:实现宏微结构一体化制造[J].机械工程学报,2013,49(6):129-135.LI Dichen,HE Jiankang,TIAN Xiaoyong,et al.Additive manufacturing:Integrated fabrication of macro/microstructures[J].Journal of Mechanical Engineering,2013,49(6):129-135.
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[6]史玉升,鲁中良,章文献,等.选择性激光熔化快速成形技术与装备[J].中国表面工程,2006,19(5):150-153.SHI Yusheng,LU Zhongliang,ZHANG Wenxian,et al.The technology and equipment of selective laser melting[J].Chinese Surface Engineering,2006,19(5):150-153.
[7]HEINL P,MüLLER L,K?RNER C,et al.Cellular Ti-6Al-4V structures with interconnected macro porosity for bone implants fabricated by selective electron beam melting[J].Acta Biomaterialia,2008,4:1536-1544.
[8]张亚玮,张述泉,王华明.激光熔化沉积定向快速凝固高温合金组织与性能[J].稀有金属材料与工程,2008,37(1):169-172.ZHANG Yawei,ZHANG Shuquan,WANG Huaming.Microstructure and mechanical properties of directional rapidly solidified Ni-base superalloy Rene95 by laser melting deposition manufacturing[J].Rare Metal Materials and Engineering,2008,37(1):169-172.
[9]张晓博,党新安,杨立军.选择性激光熔化成形过程的球化反应研究[J].激光与光电子学进展,2014,6:172-176.ZHANG Xiaobo,DANG Xinan,YANG Lijun.Study on balling phenomena in selective laser melting[J].Laser&Optoelectronics Progress,2014,6:172-176.
[10]GU D D,HAGEDORN Y C,MEINERS W,et al.Densification behavior,microstructure evolution,and wear performance of selective laser melting processed commercially pure titanium[J].Acta Materialia,2012,60(9):3849-3860.
[11]刘睿诚,杨永强,王迪.选区激光熔化成型金属零件上表面粗糙度的研究[J].激光技术,2013,37(4):425-430.LIU Ruicheng,YANG Yongqiang,WANG Di.Research of upper surface roughness of metal parts fabricated by selective laser melting[J].Laser Technology,2013,37(4):425-430.
[12]郭超,林峰,葛文君.电子束选区熔化成形316L不锈钢的工艺研究[J].机械工程学报,2014,50(21):152-158.GUO Chao,LIN Feng,GE Wenjun.Study on the fabrication process of 316L stainless steel via electron beam selective melting[J].Journal of Mechanical Engineering,2014,50(21):152-158.
[13]GOUGE M F,HEIGEL J C,MICHALERIS P.Modeling forced convection in the thermal simulation of laser cladding processes[J].The International Journal of Advanced Manufacturing Technology,2015,79(1):307-320.
[14]GOUGE M F,MICHALERIS P,PALMER T A.fixturing effects in the thermal modeling of laser cladding source of the document[J].Journal of Manufacturing Science and Engineering,2017,139(1):011001.
[15]柏久阳,王计辉,林三宝,等.电弧増材制造厚壁结构焊道间距计算策略[J].机械工程学报,2016,52(10):97-102.BAI Jiuyang,WANG Jihui,LIN Sanbao,et al.Model for multi-beads overlapping calculation in gta-additive manufacturing[J].Journal of Mechanical Engineering,2016,52(10):97-102.
[16]XIA M,GU D,YU G.Influence of hatch spacing on heat and mass transfer,thermodynamics and laser process ability during additive manufacturing of Inconel718 alloy[J].International Journal of Machine Tools&Manufacture,2016,109:147-157.
[17]田小永,曹家赫,曹毅,等.金属颗粒冷态高速微喷射增材制造工艺研究[J].机械工程学报,2016,52(3):205-212.TIAN Xiaoyong,CAO Jiahe,CAO Yi,et al.Research on the additive manufacturing process based on high-speed metal particles cold-state impact[J].Journal of Mechanical Engineering,2016,52(3):205-212.
[18]GUSAROV AV,SMUROV I.Modeling the interaction of laser radiation with powder bed at selective laser melting[J].Phys.Proc.,2010,5:381-394.
[19]GHOSH S,CHOI J.Modeling and experimental verification of transient/residual stresses and microstructure formation in multi-layer laser aided DMDprocess[J].J.Heat Transf.,2006,128(7):662-679.
[20]LI Y L,GU D D.Thermal behavior during selective laser melting of commercially pure titanium powder:numerical simulation and experimental study[J].Addit.Manuf.,2014,1:99-109.
[21]HUSSEIN A,HAO L,YAN C,R.Everson,Finite element simulation of the temperature and stress fields in single layers built without-support inselective laser melting[J].Mater.Des.,2013,52:638-647.
[22]ROBERTS I A,WANG C J,ESTERLEIN R,et al.A three dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing[J].Int.J.Mach.Tool Manu.,2009,49:916-923.
[23]姚化山,史玉升,章文献,等.金属粉末选区激光熔化成形过程温度场模拟[J].应用激光,2007,27(6):456-460.YAO Huashan,SHI Yusheng,ZHANG Wenxian,et al.Numerical simulation of the temperature field in selective laser melting[J].Applied Laser,2007,27(6):456-460.
[24]PEYRE P,AUBRY P,FABBRO R,et al.Analytical and numerical modeling of the direct metal deposition laser process[J].J.Phys.D Appl.Phys,2008,41(2):369-374.
[25]MICHALERIS P.Modeling metal deposition in heat transfer analyses of additive manufacturing processes[J].Finite Elements in Analysis and Design,2014,86:51-60.
[26]DENLINGER E R,IRWIN J,MICHALERIS P.Thermomechanical modeling of additive manufacturing large parts[J].Journal of Manufacturing Science and Engineering,2014,136:061007-1-8.
[27]BELYTSCHKO T,LU Y Y,GU L.Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,37:229-256.
[28]DUARTE C A,ODEN J T.H-p clouds-an h-p meshless method[J].Numer.Methods Partial Differ.Equations,1996,12:673-705.
[29]ZHANG X.Least-Squares collocation meshless method[J].International Journal for Numerical Methods in Engineering,2001,51:1089-1100.
[30]段庆林,李锡夔.成形充填过程的任意拉格朗日-欧拉有限元与无网格自适应耦合模拟[J].机械工程学报,2007,43(7):120-127.DUAN Qinglin,LI Xikui.Simulation of injection molding process using adaptive coupled arbitrary Lagrangian-Eulerian finite element and meshfree method[J].Chinese Journal of Mechanical Engineering,2007,43(7):120-127.
[31]SONIA F M,ANTONIO H.Imposing essential boundary conditions in mesh-free methods[J].Computer Methods in Applied Mechanics&Engineering,2004,193:1257-1275.
[32]ZHU T,ATLURI S N,A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method[J].Comput.Mech,1998,21(3):211-222.
[33]DUAN Q L,WANG B B,GAO X.Quadratically consistent nodal integration for second order meshfree Galerkin methods[J].Computational Mechanics,2014,54(2):353-368.
[34]DUAN Q L,GAO X,WANG B B,et al,Consistent element-free Galerkin method[J].International Journal for Numerical Methods in Engineering,2014,99(2):79-101.
[35]WU S C,LIU G R,ZHANG H O,et al.A node-based smoothed point interpolation method(NS-PIM)for three-dimensional thermoelastic problems[J].International Journal of Thermal Sciences,2009,48(7):1367-1376.
[36]CHEN J S,WU C T,YOON S,et al.A stabilized conforming nodal integration for Galerkin mesh-free methods[J].International Journal for Numerical Methods in Engineering,2001,50:435-466.
[37]FACHINOTTI V D,ANCA A A,CARDONA A.Analytical solutions of the thermal field induced by moving double-ellipsoidal and double-elliptical heat sources in a semi-infinite body[J].International Journal for Numerical Methods in Biomedical Engineering,2011,27(4):595-607.
[38]HEIGEL J C,MICHALERIS P,REUTZEL E W.Thermo mechanical model development and validation of directed energy deposition additive manufacturing of Ti-6Al-4V[J].Additive Manufacturing,2015,5:9-19.
[39]THUMMLER F,OBERACKER R.An introduction to powder metallurgy[M].London:Cambridge University Press,1993.
[40]DAI K,SHAW L.Finite element analysis of the effect of volume shrinkage during laser densification[J].Acta Mater.,2005,53:4743-4754.
[41]LEE Y S,FARSON D F.Surface tension-powered build dimension control in laser additive manufacturing process[J].The International Journal of Advanced Manufacturing Technology,2016,85:1035-1044.
[42]蒋成保,周寿增,张茂才,等.定向凝固TbDyFe合金的取向、组织和磁致伸缩性能[J].金属学报,199834(2):164-170.JIANG Chengbao,ZHOU Shouzeng,ZHANG Maocai,et al.The preferred orientation,microstructure and magnetostostrion in directional solidified TbDyFe alloys[J].Acta Metallurgica Sinica,1998,34(2):164-170.
[2]卢秉恒,李涤尘.增材制造(3D打印)技术发展[J].机械制造与自动化,2013,42(4):1-4.LU Bingheng,LI Dichen.Development of the additive manufacturing(3D printing)technology[J].Machine Building&Automation,2013,42(4):1-4.
[3]王华明.高性能金属构件增材制造技术开启国防制造新篇章[J].国防制造技术,2013(3):5-7.WANG Huaming.A new chapter to defense manufacturing opened by additive manufacturing technology of high-performance metal components[J].Defense Manufacturing Technology,2013(3):5-7.
[4]王华明.高性能大型金属构件激光增材制造:若干材料基础问题[J].航空学报,2014,35(10):2690-2698.WANG Huaming.Material’s fundamental issues of laser additive manufacturing for high-performance large metallic components[J].Acta Aeronautica et Astronautica Sinica,2014,35(10):2690-2698.
[5]林鑫,黄卫东.高性能金属构件的激光增材制造[J].中国科学:信息科学,2015,45(9):1111-1126.LIN Xin,HUANG Weidong.Laser additive manufacturing of high performance metal components[J].Scientia Sinica(Informationis),2015,45(9):1111-1126.
[6]史玉升,鲁中良,章文献,等.选择性激光熔化快速成形技术与装备[J].中国表面工程,2006,19(5):150-153.SHI Yusheng,LU Zhongliang,ZHANG Wenxian,et al.The technology and equipment of selective laser melting[J].Chinese Surface Engineering,2006,19(5):150-153.
[7]HEINL P,MüLLER L,K?RNER C,et al.Cellular Ti-6Al-4V structures with interconnected macro porosity for bone implants fabricated by selective electron beam melting[J].Acta Biomaterialia,2008,4:1536-1544.
[8]张亚玮,张述泉,王华明.激光熔化沉积定向快速凝固高温合金组织与性能[J].稀有金属材料与工程,2008,37(1):169-172.ZHANG Yawei,ZHANG Shuquan,WANG Huaming.Microstructure and mechanical properties of directional rapidly solidified Ni-base superalloy Rene95 by laser melting deposition manufacturing[J].Rare Metal Materials and Engineering,2008,37(1):169-172.
[9]张晓博,党新安,杨立军.选择性激光熔化成形过程的球化反应研究[J].激光与光电子学进展,2014,6:172-176.ZHANG Xiaobo,DANG Xinan,YANG Lijun.Study on balling phenomena in selective laser melting[J].Laser&Optoelectronics Progress,2014,6:172-176.
[10]GU D D,HAGEDORN Y C,MEINERS W,et al.Densification behavior,microstructure evolution,and wear performance of selective laser melting processed commercially pure titanium[J].Acta Materialia,2012,60(9):3849-3860.
[11]刘睿诚,杨永强,王迪.选区激光熔化成型金属零件上表面粗糙度的研究[J].激光技术,2013,37(4):425-430.LIU Ruicheng,YANG Yongqiang,WANG Di.Research of upper surface roughness of metal parts fabricated by selective laser melting[J].Laser Technology,2013,37(4):425-430.
[12]郭超,林峰,葛文君.电子束选区熔化成形316L不锈钢的工艺研究[J].机械工程学报,2014,50(21):152-158.GUO Chao,LIN Feng,GE Wenjun.Study on the fabrication process of 316L stainless steel via electron beam selective melting[J].Journal of Mechanical Engineering,2014,50(21):152-158.
[13]GOUGE M F,HEIGEL J C,MICHALERIS P.Modeling forced convection in the thermal simulation of laser cladding processes[J].The International Journal of Advanced Manufacturing Technology,2015,79(1):307-320.
[14]GOUGE M F,MICHALERIS P,PALMER T A.fixturing effects in the thermal modeling of laser cladding source of the document[J].Journal of Manufacturing Science and Engineering,2017,139(1):011001.
[15]柏久阳,王计辉,林三宝,等.电弧増材制造厚壁结构焊道间距计算策略[J].机械工程学报,2016,52(10):97-102.BAI Jiuyang,WANG Jihui,LIN Sanbao,et al.Model for multi-beads overlapping calculation in gta-additive manufacturing[J].Journal of Mechanical Engineering,2016,52(10):97-102.
[16]XIA M,GU D,YU G.Influence of hatch spacing on heat and mass transfer,thermodynamics and laser process ability during additive manufacturing of Inconel718 alloy[J].International Journal of Machine Tools&Manufacture,2016,109:147-157.
[17]田小永,曹家赫,曹毅,等.金属颗粒冷态高速微喷射增材制造工艺研究[J].机械工程学报,2016,52(3):205-212.TIAN Xiaoyong,CAO Jiahe,CAO Yi,et al.Research on the additive manufacturing process based on high-speed metal particles cold-state impact[J].Journal of Mechanical Engineering,2016,52(3):205-212.
[18]GUSAROV AV,SMUROV I.Modeling the interaction of laser radiation with powder bed at selective laser melting[J].Phys.Proc.,2010,5:381-394.
[19]GHOSH S,CHOI J.Modeling and experimental verification of transient/residual stresses and microstructure formation in multi-layer laser aided DMDprocess[J].J.Heat Transf.,2006,128(7):662-679.
[20]LI Y L,GU D D.Thermal behavior during selective laser melting of commercially pure titanium powder:numerical simulation and experimental study[J].Addit.Manuf.,2014,1:99-109.
[21]HUSSEIN A,HAO L,YAN C,R.Everson,Finite element simulation of the temperature and stress fields in single layers built without-support inselective laser melting[J].Mater.Des.,2013,52:638-647.
[22]ROBERTS I A,WANG C J,ESTERLEIN R,et al.A three dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing[J].Int.J.Mach.Tool Manu.,2009,49:916-923.
[23]姚化山,史玉升,章文献,等.金属粉末选区激光熔化成形过程温度场模拟[J].应用激光,2007,27(6):456-460.YAO Huashan,SHI Yusheng,ZHANG Wenxian,et al.Numerical simulation of the temperature field in selective laser melting[J].Applied Laser,2007,27(6):456-460.
[24]PEYRE P,AUBRY P,FABBRO R,et al.Analytical and numerical modeling of the direct metal deposition laser process[J].J.Phys.D Appl.Phys,2008,41(2):369-374.
[25]MICHALERIS P.Modeling metal deposition in heat transfer analyses of additive manufacturing processes[J].Finite Elements in Analysis and Design,2014,86:51-60.
[26]DENLINGER E R,IRWIN J,MICHALERIS P.Thermomechanical modeling of additive manufacturing large parts[J].Journal of Manufacturing Science and Engineering,2014,136:061007-1-8.
[27]BELYTSCHKO T,LU Y Y,GU L.Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,37:229-256.
[28]DUARTE C A,ODEN J T.H-p clouds-an h-p meshless method[J].Numer.Methods Partial Differ.Equations,1996,12:673-705.
[29]ZHANG X.Least-Squares collocation meshless method[J].International Journal for Numerical Methods in Engineering,2001,51:1089-1100.
[30]段庆林,李锡夔.成形充填过程的任意拉格朗日-欧拉有限元与无网格自适应耦合模拟[J].机械工程学报,2007,43(7):120-127.DUAN Qinglin,LI Xikui.Simulation of injection molding process using adaptive coupled arbitrary Lagrangian-Eulerian finite element and meshfree method[J].Chinese Journal of Mechanical Engineering,2007,43(7):120-127.
[31]SONIA F M,ANTONIO H.Imposing essential boundary conditions in mesh-free methods[J].Computer Methods in Applied Mechanics&Engineering,2004,193:1257-1275.
[32]ZHU T,ATLURI S N,A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method[J].Comput.Mech,1998,21(3):211-222.
[33]DUAN Q L,WANG B B,GAO X.Quadratically consistent nodal integration for second order meshfree Galerkin methods[J].Computational Mechanics,2014,54(2):353-368.
[34]DUAN Q L,GAO X,WANG B B,et al,Consistent element-free Galerkin method[J].International Journal for Numerical Methods in Engineering,2014,99(2):79-101.
[35]WU S C,LIU G R,ZHANG H O,et al.A node-based smoothed point interpolation method(NS-PIM)for three-dimensional thermoelastic problems[J].International Journal of Thermal Sciences,2009,48(7):1367-1376.
[36]CHEN J S,WU C T,YOON S,et al.A stabilized conforming nodal integration for Galerkin mesh-free methods[J].International Journal for Numerical Methods in Engineering,2001,50:435-466.
[37]FACHINOTTI V D,ANCA A A,CARDONA A.Analytical solutions of the thermal field induced by moving double-ellipsoidal and double-elliptical heat sources in a semi-infinite body[J].International Journal for Numerical Methods in Biomedical Engineering,2011,27(4):595-607.
[38]HEIGEL J C,MICHALERIS P,REUTZEL E W.Thermo mechanical model development and validation of directed energy deposition additive manufacturing of Ti-6Al-4V[J].Additive Manufacturing,2015,5:9-19.
[39]THUMMLER F,OBERACKER R.An introduction to powder metallurgy[M].London:Cambridge University Press,1993.
[40]DAI K,SHAW L.Finite element analysis of the effect of volume shrinkage during laser densification[J].Acta Mater.,2005,53:4743-4754.
[41]LEE Y S,FARSON D F.Surface tension-powered build dimension control in laser additive manufacturing process[J].The International Journal of Advanced Manufacturing Technology,2016,85:1035-1044.
[42]蒋成保,周寿增,张茂才,等.定向凝固TbDyFe合金的取向、组织和磁致伸缩性能[J].金属学报,199834(2):164-170.JIANG Chengbao,ZHOU Shouzeng,ZHANG Maocai,et al.The preferred orientation,microstructure and magnetostostrion in directional solidified TbDyFe alloys[J].Acta Metallurgica Sinica,1998,34(2):164-170.
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