面向植入体的多孔结构建模及激光选区熔化直接制造研究
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摘要
传统方法制造的金属植入体因为自身过重和刚度过大容易引起病人的不适,且实心的结构导致植入体-宿主骨之间无相互啮合固定,容易引起松脱,导致植入体使用寿命减少。为了获得更好生物力学性能的植入体,可以将其表面或者全部模型设计成多孔结构。虽然目前多孔结构的设计和制造／制备方法有很多,但是大多都建立在传统制造方法的基础上,随着增材制造(Additive Manufacturing, AM)技术的发展,更大设计自由度的多孔结构可以被制造出来,包括其中一些精细微小的几何特征。所以更多地考虑仿生的结构和力学参数,对植入体进行多孔化设计和制造是一项非常有意义的研究。
本文建立在激光选区熔化(Selective Laser Melting, SLM)技术的基础上,研究了基于该技术的多孔结构设计规则,提出了一种由隐函数表示的隐式曲面建构多孔单元的方法,并通过形函数控制的方法对多孔单元进行造型变换构建了空间域的多孔结构,对它们进行结构和力学参数表征,开发了多孔结构建模系统,最后通过SLM技术直接制造多孔植入体,验证了本文建立的方法和技术的可行性。主要研究内容及成果包括以下几方面：
(1)分析了SLM加工多孔结构的尺寸精度、轮廓精度和几何特征成型分辨率等几何限制,并对激光深穿透、光斑尺寸等技术约束进行了讨论；研究了通过轮廓偏移控制孔隙率的方法；对构成多孔结构的基本元素——支柱的可加工性进行了分析。建立了基于SLM技术的多孔结构设计规则。在规则指导下,可以在设计阶段对多孔结构的结构参数进行控制,使其满足SLM工艺要求,并通过控制工艺参数来提高多孔结构的可加工性。
(2)提出了一种由隐函数表示的隐式曲面建构多孔单元的方法,通过定义不同的空间实值函数可以定义不同形状和孔隙率的多孔单元。研究了隐函数在多孔单元建模中的关键技术,包括曲面边界表达模型的生成、曲面求交、曲面三角化和STL模型的提取等。该建模方法具有高效性和可控性的特点,可以与现有设计方法相结合,为多孔植入体的设计提供一种新的方法。
(3)利用有限元中六面体单元对植入体局部或者全部模型进行网格划分,通过形函数控制的方法,利用空间域中8结点六面体单元信息将参数域中母单元进行映射,插值出空间域中不规则六面体子单元。并对空间域中所有子单元的STL模型进行合并,删除重叠三角面片,使相邻子单元成为一体的连通实体,从而构建出连续的多孔植入体模型。
(4)研究了对多孔结构进行结构和力学参数表征的方法,利用直接表征法和网格表征法对结构参数进行了估测：利用Micro-CT对SLM成型的多孔钛进行结构性能测试,并通过压缩试验法计算了其弹性模量。利用表征法、有限元分析及测试得到的值对结构和力学参数分别进行计算采样,建立了P单元隐函数的系数与其对应的多孔结构的结构参数和力学参数关系的响应面模型,利用该模型可以对其结构参数和力学参数进行估测。
(5)建立在前述理论和方法的基础上,在VC++环境下结合OpenGL开发了多孔结构建模系统,并建立了与Ansys的数据接口,系统可以读入从Ansys导出的六面体和四面体单元和节点信息。建立在设计规则的基础上,利用多孔结构建模系统设计并通过SLM技术直接制造了两种典型的多孔植入体,零件成型质量较好,孔径在600-1000μm之间,弹性模量与骨骼相当,验证了本文建立的方法和技术的可行性。
The metallic implant manufactured via traditional method easily causes patients' discomfort due to its overweight and excessive stiffness; besides, due to its solid construction, there is no mutual meshing and fixation between implant and host's bone, thus it is easy to cause let-go, which shortens the service life of implants. It is able to design the surface or whole model of implant as porous structure in order to obtain the implant with better biomechanical properties. Although there are many design and manufacturing/preparing methods for porous structures, most of those methods are established on the basis of traditional manufacturing method; with the development of additive manufacturing (AM) technology, the porous structure with bigger design freedom can be manufactured, including some refined and tiny geometrical features. Therefore, more consideration on bionic structural and mechanical parameter is a significant research for porous design and manufacturing of implants.
This paper researches design rules for porous structures based on selective laser melting (SLM) technology, proposes a method that the implicit surface represented by implict functions is used to construct porous unit and then carries out modeling transformation for porous unit via shape function control method to construct porous structure in spatial domain and conducts representation of structures and mechanical parameters, develops the modeling system of porous structure, and finally directly manufactures porous implants by SLM technology to confirm the feasibility of methods and technologies established in this paper. The main research contents and results include following aspects:
(1) This paper analyzes the geometric constraints of porous structure processed via SLM, such as dimensional accuracy, outline accuracy and geometric feature molding resolution; gives a discussion on technological constraints such as laser deep penetration and spot size; studies the method that the contour offset is used to control porosity; analyzes the manufacturability of strut which is the basic element of porous structures; establishes the design rules for SLM technology based on porous structure. Under the guidance of these rules, it is able to control the structure parameters of porous structure at design stage to make it meet requirements of SLM technology, and also improve the manufacturability of porous structure through controlling technological parameters.
(2) This paper proposes a method that the implicit surface represented by implict functions is used to construct porous unit, and defines porous unit with different shapes and porosities via defining different spatial real-valued functions; researches key technologies of implicit function in modeling of porous unit, including the generation of surface boundary representation, surface intersection, surface triangularization and extraction of STL model, etc. With high efficiency and controllability, this modeling method can be combined with existing design method to provide a new method for design of porous implants.
(3) This paper makes use of hexahedral element to carry out mesh generation for partial and whole model of implant, and then utilizes information about8-node hexahedral elements in spatial domain to make mappings for standard unit in parameter domain via shape function control method, and then obtains irregular hexahedral sub-unit in spatial domain through interpolation. This paper also merges STL models of all sub-unit in the spatial domain, and deletes the overlapping triangles to make between adjacent sub-unit linked as a connecting entity, thus constructing continuous porous implant geometry.
(4) This paper also researches the method used to represent structural and mechanical parameters of porous structures, and utilizes direct representation method and mesh-based methods to estimate the structural parameter; makes use of Micro-CT to carry out structural performance tests for porous titanium manufactured by SLM technology, and calculates the elastic modulus of porous titanium via compression tests; utilizes the value obtained via representation methods, finite element analysis and tests to carry out calculation sampling respectively on the structural and mechanical parameter, establishes the coefficient of implicit function of P unit and corresponding response surface model of relationship between structural parameter and mechanical parameter of porous structure, and then makes use of this model to estimate its structural and mechanical parameters.
(5) On the basis of the above mentioned theories and methods, under VC++environment, this paper combines with OpenGL to develop modeling system of porous structure, and establishes the data interface with Ansys, through which the system can read hexahedron and tetrahedron elements and nodes files derived from Ansys. Based on design rules, this paper designs and directly manufacturers two kinds of typical porous implant by use of modeling system of porous structure and SLM technology; the implants have good forming quality with an aperture of600-1000μm, and its elastic modulus is equivalent to that of bone. All of those confirm that the methods and technologiesy established in this paper is feasible.
本文建立在激光选区熔化(Selective Laser Melting, SLM)技术的基础上,研究了基于该技术的多孔结构设计规则,提出了一种由隐函数表示的隐式曲面建构多孔单元的方法,并通过形函数控制的方法对多孔单元进行造型变换构建了空间域的多孔结构,对它们进行结构和力学参数表征,开发了多孔结构建模系统,最后通过SLM技术直接制造多孔植入体,验证了本文建立的方法和技术的可行性。主要研究内容及成果包括以下几方面：
(1)分析了SLM加工多孔结构的尺寸精度、轮廓精度和几何特征成型分辨率等几何限制,并对激光深穿透、光斑尺寸等技术约束进行了讨论；研究了通过轮廓偏移控制孔隙率的方法；对构成多孔结构的基本元素——支柱的可加工性进行了分析。建立了基于SLM技术的多孔结构设计规则。在规则指导下,可以在设计阶段对多孔结构的结构参数进行控制,使其满足SLM工艺要求,并通过控制工艺参数来提高多孔结构的可加工性。
(2)提出了一种由隐函数表示的隐式曲面建构多孔单元的方法,通过定义不同的空间实值函数可以定义不同形状和孔隙率的多孔单元。研究了隐函数在多孔单元建模中的关键技术,包括曲面边界表达模型的生成、曲面求交、曲面三角化和STL模型的提取等。该建模方法具有高效性和可控性的特点,可以与现有设计方法相结合,为多孔植入体的设计提供一种新的方法。
(3)利用有限元中六面体单元对植入体局部或者全部模型进行网格划分,通过形函数控制的方法,利用空间域中8结点六面体单元信息将参数域中母单元进行映射,插值出空间域中不规则六面体子单元。并对空间域中所有子单元的STL模型进行合并,删除重叠三角面片,使相邻子单元成为一体的连通实体,从而构建出连续的多孔植入体模型。
(4)研究了对多孔结构进行结构和力学参数表征的方法,利用直接表征法和网格表征法对结构参数进行了估测：利用Micro-CT对SLM成型的多孔钛进行结构性能测试,并通过压缩试验法计算了其弹性模量。利用表征法、有限元分析及测试得到的值对结构和力学参数分别进行计算采样,建立了P单元隐函数的系数与其对应的多孔结构的结构参数和力学参数关系的响应面模型,利用该模型可以对其结构参数和力学参数进行估测。
(5)建立在前述理论和方法的基础上,在VC++环境下结合OpenGL开发了多孔结构建模系统,并建立了与Ansys的数据接口,系统可以读入从Ansys导出的六面体和四面体单元和节点信息。建立在设计规则的基础上,利用多孔结构建模系统设计并通过SLM技术直接制造了两种典型的多孔植入体,零件成型质量较好,孔径在600-1000μm之间,弹性模量与骨骼相当,验证了本文建立的方法和技术的可行性。
The metallic implant manufactured via traditional method easily causes patients' discomfort due to its overweight and excessive stiffness; besides, due to its solid construction, there is no mutual meshing and fixation between implant and host's bone, thus it is easy to cause let-go, which shortens the service life of implants. It is able to design the surface or whole model of implant as porous structure in order to obtain the implant with better biomechanical properties. Although there are many design and manufacturing/preparing methods for porous structures, most of those methods are established on the basis of traditional manufacturing method; with the development of additive manufacturing (AM) technology, the porous structure with bigger design freedom can be manufactured, including some refined and tiny geometrical features. Therefore, more consideration on bionic structural and mechanical parameter is a significant research for porous design and manufacturing of implants.
This paper researches design rules for porous structures based on selective laser melting (SLM) technology, proposes a method that the implicit surface represented by implict functions is used to construct porous unit and then carries out modeling transformation for porous unit via shape function control method to construct porous structure in spatial domain and conducts representation of structures and mechanical parameters, develops the modeling system of porous structure, and finally directly manufactures porous implants by SLM technology to confirm the feasibility of methods and technologies established in this paper. The main research contents and results include following aspects:
(1) This paper analyzes the geometric constraints of porous structure processed via SLM, such as dimensional accuracy, outline accuracy and geometric feature molding resolution; gives a discussion on technological constraints such as laser deep penetration and spot size; studies the method that the contour offset is used to control porosity; analyzes the manufacturability of strut which is the basic element of porous structures; establishes the design rules for SLM technology based on porous structure. Under the guidance of these rules, it is able to control the structure parameters of porous structure at design stage to make it meet requirements of SLM technology, and also improve the manufacturability of porous structure through controlling technological parameters.
(2) This paper proposes a method that the implicit surface represented by implict functions is used to construct porous unit, and defines porous unit with different shapes and porosities via defining different spatial real-valued functions; researches key technologies of implicit function in modeling of porous unit, including the generation of surface boundary representation, surface intersection, surface triangularization and extraction of STL model, etc. With high efficiency and controllability, this modeling method can be combined with existing design method to provide a new method for design of porous implants.
(3) This paper makes use of hexahedral element to carry out mesh generation for partial and whole model of implant, and then utilizes information about8-node hexahedral elements in spatial domain to make mappings for standard unit in parameter domain via shape function control method, and then obtains irregular hexahedral sub-unit in spatial domain through interpolation. This paper also merges STL models of all sub-unit in the spatial domain, and deletes the overlapping triangles to make between adjacent sub-unit linked as a connecting entity, thus constructing continuous porous implant geometry.
(4) This paper also researches the method used to represent structural and mechanical parameters of porous structures, and utilizes direct representation method and mesh-based methods to estimate the structural parameter; makes use of Micro-CT to carry out structural performance tests for porous titanium manufactured by SLM technology, and calculates the elastic modulus of porous titanium via compression tests; utilizes the value obtained via representation methods, finite element analysis and tests to carry out calculation sampling respectively on the structural and mechanical parameter, establishes the coefficient of implicit function of P unit and corresponding response surface model of relationship between structural parameter and mechanical parameter of porous structure, and then makes use of this model to estimate its structural and mechanical parameters.
(5) On the basis of the above mentioned theories and methods, under VC++environment, this paper combines with OpenGL to develop modeling system of porous structure, and establishes the data interface with Ansys, through which the system can read hexahedron and tetrahedron elements and nodes files derived from Ansys. Based on design rules, this paper designs and directly manufacturers two kinds of typical porous implant by use of modeling system of porous structure and SLM technology; the implants have good forming quality with an aperture of600-1000μm, and its elastic modulus is equivalent to that of bone. All of those confirm that the methods and technologiesy established in this paper is feasible.
引文
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