挤压变形力的数值分析及模拟方法研究
摘要
金属挤压已成为塑性成形领域中最重要的方法之一,其理论研究与技术开发正面临着一个重要的崭新的发展时期,基础研究与工艺创新紧密结合是推动金属挤压成形进一步发展的关键。挤压制品的组织、性能、表面质量、外形尺寸和形状精度、成材率、挤压模具的优化设计、挤压生产效率等,均与金属在挤压过程中的流动有着密切的关系。建立可靠的数学-力学模型来控制金属在挤压变形过程中的流动行为具有极为重要的理论意义,在此基础上寻求有效的挤压工艺优化设计途径是发展挤压技术、提升挤压制品质量的核心突破点。
挤压过程中金属流动行为的研究方法,可以分为解析法和实验法两大类。这些方法各自具有其他方法所不具备的特点,适用于不同的具体研究对象,但同时又都存在明显的局限性,并没有在工程实践中得到广泛的应用。长期以来,工艺设计过程中相关参数的确定主要以缺乏理论依据的经验公式为主,这成为制约挤压技术发展的主要瓶颈之一。究其原因,一是缺乏具有理论依据的数学-力学模型,将挤压过程中的变形物理参数与工艺设计几何参数有机联系起来,从而导致设计计算偏差；二是数值模拟技术在金属体积成型领域的应用水平仍不成熟,无法有效指导生产实践。本文采用理论模型与数值模拟相结合的方法针对锥形模正挤压、杯形件反挤压及镦挤复合变形过程展开研究,用具有理论依据的计算方法来代替经验公式,寻求变形物理参数和模具几何参数相互影响的本质规律。
基于经典塑性理论,应用数值计算方法,研究了挤压过程中变形物理参数与模具几何参数的解析关系,构建了具有塑性成型理论依据的数值分析模型。首先通过精确作图法得到不同摩擦边界条件下、不同变形程度的杯形件反挤压及棒材锥形模正挤压过程的多种滑移线场模型,并以该塑性力学模型为载体,求解出应力场及变形力等物理参数关于滑移线场参数的函数关系。综合应用曲线拟合、求解微分方程、迭代插值及函数求极值等数值分析方法建立了滑移线场参数与模具尺寸、挤压比等关键几何参数的解析关系。在滑移线解的基础上,用几何参数代替滑移线场参数,构建了应力场、单位变形力等变形物理参数关于几何参数的数学模型。基于模块化思想,应用简单边界条件模型通过滑移线场叠加方法建立了复杂边界条件的镦挤复合变形模型。通过纯铝挤压实验验证了杯形件反挤压数值分析模型的可靠性,研究了锥形模正挤压过程中模锥角对于变形过程的影响规律。
论述了Lagrange网格与Euler网格分别在固体与流体力学行为模拟中的应用特点,综合分析了有限元法与有限体积法在金属大变形、热变形数值模拟领域的局限性及优越性。针对棒材锥形模正挤压、杯形件反挤压进行有限元与有限体积对比模拟,分析了各物理场量对于变形过程的影响规律,研究了有限元软件DEFORM与有限体积软件MSC.SUPERFORGE在体积成形领域的适用范围。应用MSC.SUPERFORGE软件针对镦挤复合成形过程进行有限体积模拟,根据模拟结果调整工艺参数,并最终实现了工艺优化设计。
挤压过程的数值分析模型可以避免经验公式在工艺设计中的盲目性,以该模型为目标函数,可实现相关工艺参数的优化设计。符合实际变形规律的数值模拟能方法够正确反映变形物理参数与几何参数的相互影响规律,实现计算机辅助优化设计。
Extrusion is one the most important method of metal plastic forming process. The theory research and technology development of it are faced with an important new stage of development. The combination of basic theory research and technological innovation will promote the further development of metal extrusion. There are many technological factors are closely related to the material flow in extrusion, such as the product structure, properties, surface quality, dimension and shape accuracy, finished product rate, the optimization of extrusion die design and extrusion efficiency etc. It is of an extremely important theoretical significance to establish a reliable mathematical-mechanical model to control the material flow behavior in the extrusion process. On this basis, the rational and effective optimum design methods of extrusion process are the key sally port for the development of extrusion technology and improvement the quality of extruded products.
There are two kinds of main research methods about the rule of material flow in extrusion process, one is the numerical analysis method, the other is the experimental method. Those methods have its independent characteristic and can be used in specific research object. However, all of those methods have not been used widely in engineer practice for its obvious limitation. For a long time, the processing parameters in technological design calculated with empirical formula. One of reason is lack of mathematical-mechanical models with plastic theoretical basis, which can connect the physical parameters and geometrical parameters in extrusion process, the other is numerical simulation technology can not be used correctly in metal bulk forming and can not effectively guide the productive practice. In this paper, backward extrusion with cup-shaped mold, forward extrusion with cone-shaped mold and upsetting-extruding composite deformation process are researched with numerical analysis method and numerical simulation. In this way, the elemental regularity between physical parameters and geometrical parameters can be researched with numerical formula in place of empirical formula.
The analytic relationship between physical parameters and geometrical parameters was researched with numerical analysis method based on classical plastic theory. The numerical analysis model with plastic theory background was established. At first, with precise graphing method, the slip line field was researched for varying degrees deformation of backward extrusion with cup-shaped mold and forward extrusion with cone-shaped mold in different friction boundary conditions. Then, the function equation about physical parameters (deforming force, stress etc) and slip line field parameters was researched. The analytical relations about slip-line field parameters and key geometric parameters, such as die size, extrusion ratio etc, were established with curve fitting, differential equation, iterated interpolation method and extremum method. Based on slip-line solution, the numerical analysis model between physical parameters and geometrical parameters (die dimension, extrusion ratio etc) was researched. Based on modular theory, analytic model of upsetting-extruding composite deformation with complex boundary conditions were researched with superimposed slip-line field method. The numerical analysis model of backward extrusion with cup-shaped mold process was verified with experiment finaly. The influence regularity of die cone angle for the process of deformation in forward extrusion with cone-shaped mold process was investigated.
The application of the Lagrange mesh in solid behavior and Euler mesh in fluid behavior was discussed respectively. Limitations and advantages of the finite element method and finite volume method for numerical simulation of large metal deformation were investigated. Comparative simulation for backward extrusion process with cup-shaped and forward extrusion process with cone-shaped mold was studied with FEM and FVM. The influence of physical quantity for the deformation was studied at the same time. The application method of FEM with DEFORM and FVM with MSC.SUPERFORGE was also researched. Upsetting-extruding composite deformation process was simulated with MSC.SUPERFORGE and the technological parameters were adjusted based on the result of simulation. In this way, the optimum design can be realized.
Blindness of empirical formula in the technological design can be avoided with numerical analysis model. As object function, it can be used for Optimum design of extrusion. Realistic numerical simulation of deformation can be used to research the influence law between the physical parameters and geometric parameters and the realization of computer-aided optimal design.
挤压过程中金属流动行为的研究方法,可以分为解析法和实验法两大类。这些方法各自具有其他方法所不具备的特点,适用于不同的具体研究对象,但同时又都存在明显的局限性,并没有在工程实践中得到广泛的应用。长期以来,工艺设计过程中相关参数的确定主要以缺乏理论依据的经验公式为主,这成为制约挤压技术发展的主要瓶颈之一。究其原因,一是缺乏具有理论依据的数学-力学模型,将挤压过程中的变形物理参数与工艺设计几何参数有机联系起来,从而导致设计计算偏差；二是数值模拟技术在金属体积成型领域的应用水平仍不成熟,无法有效指导生产实践。本文采用理论模型与数值模拟相结合的方法针对锥形模正挤压、杯形件反挤压及镦挤复合变形过程展开研究,用具有理论依据的计算方法来代替经验公式,寻求变形物理参数和模具几何参数相互影响的本质规律。
基于经典塑性理论,应用数值计算方法,研究了挤压过程中变形物理参数与模具几何参数的解析关系,构建了具有塑性成型理论依据的数值分析模型。首先通过精确作图法得到不同摩擦边界条件下、不同变形程度的杯形件反挤压及棒材锥形模正挤压过程的多种滑移线场模型,并以该塑性力学模型为载体,求解出应力场及变形力等物理参数关于滑移线场参数的函数关系。综合应用曲线拟合、求解微分方程、迭代插值及函数求极值等数值分析方法建立了滑移线场参数与模具尺寸、挤压比等关键几何参数的解析关系。在滑移线解的基础上,用几何参数代替滑移线场参数,构建了应力场、单位变形力等变形物理参数关于几何参数的数学模型。基于模块化思想,应用简单边界条件模型通过滑移线场叠加方法建立了复杂边界条件的镦挤复合变形模型。通过纯铝挤压实验验证了杯形件反挤压数值分析模型的可靠性,研究了锥形模正挤压过程中模锥角对于变形过程的影响规律。
论述了Lagrange网格与Euler网格分别在固体与流体力学行为模拟中的应用特点,综合分析了有限元法与有限体积法在金属大变形、热变形数值模拟领域的局限性及优越性。针对棒材锥形模正挤压、杯形件反挤压进行有限元与有限体积对比模拟,分析了各物理场量对于变形过程的影响规律,研究了有限元软件DEFORM与有限体积软件MSC.SUPERFORGE在体积成形领域的适用范围。应用MSC.SUPERFORGE软件针对镦挤复合成形过程进行有限体积模拟,根据模拟结果调整工艺参数,并最终实现了工艺优化设计。
挤压过程的数值分析模型可以避免经验公式在工艺设计中的盲目性,以该模型为目标函数,可实现相关工艺参数的优化设计。符合实际变形规律的数值模拟能方法够正确反映变形物理参数与几何参数的相互影响规律,实现计算机辅助优化设计。
Extrusion is one the most important method of metal plastic forming process. The theory research and technology development of it are faced with an important new stage of development. The combination of basic theory research and technological innovation will promote the further development of metal extrusion. There are many technological factors are closely related to the material flow in extrusion, such as the product structure, properties, surface quality, dimension and shape accuracy, finished product rate, the optimization of extrusion die design and extrusion efficiency etc. It is of an extremely important theoretical significance to establish a reliable mathematical-mechanical model to control the material flow behavior in the extrusion process. On this basis, the rational and effective optimum design methods of extrusion process are the key sally port for the development of extrusion technology and improvement the quality of extruded products.
There are two kinds of main research methods about the rule of material flow in extrusion process, one is the numerical analysis method, the other is the experimental method. Those methods have its independent characteristic and can be used in specific research object. However, all of those methods have not been used widely in engineer practice for its obvious limitation. For a long time, the processing parameters in technological design calculated with empirical formula. One of reason is lack of mathematical-mechanical models with plastic theoretical basis, which can connect the physical parameters and geometrical parameters in extrusion process, the other is numerical simulation technology can not be used correctly in metal bulk forming and can not effectively guide the productive practice. In this paper, backward extrusion with cup-shaped mold, forward extrusion with cone-shaped mold and upsetting-extruding composite deformation process are researched with numerical analysis method and numerical simulation. In this way, the elemental regularity between physical parameters and geometrical parameters can be researched with numerical formula in place of empirical formula.
The analytic relationship between physical parameters and geometrical parameters was researched with numerical analysis method based on classical plastic theory. The numerical analysis model with plastic theory background was established. At first, with precise graphing method, the slip line field was researched for varying degrees deformation of backward extrusion with cup-shaped mold and forward extrusion with cone-shaped mold in different friction boundary conditions. Then, the function equation about physical parameters (deforming force, stress etc) and slip line field parameters was researched. The analytical relations about slip-line field parameters and key geometric parameters, such as die size, extrusion ratio etc, were established with curve fitting, differential equation, iterated interpolation method and extremum method. Based on slip-line solution, the numerical analysis model between physical parameters and geometrical parameters (die dimension, extrusion ratio etc) was researched. Based on modular theory, analytic model of upsetting-extruding composite deformation with complex boundary conditions were researched with superimposed slip-line field method. The numerical analysis model of backward extrusion with cup-shaped mold process was verified with experiment finaly. The influence regularity of die cone angle for the process of deformation in forward extrusion with cone-shaped mold process was investigated.
The application of the Lagrange mesh in solid behavior and Euler mesh in fluid behavior was discussed respectively. Limitations and advantages of the finite element method and finite volume method for numerical simulation of large metal deformation were investigated. Comparative simulation for backward extrusion process with cup-shaped and forward extrusion process with cone-shaped mold was studied with FEM and FVM. The influence of physical quantity for the deformation was studied at the same time. The application method of FEM with DEFORM and FVM with MSC.SUPERFORGE was also researched. Upsetting-extruding composite deformation process was simulated with MSC.SUPERFORGE and the technological parameters were adjusted based on the result of simulation. In this way, the optimum design can be realized.
Blindness of empirical formula in the technological design can be avoided with numerical analysis model. As object function, it can be used for Optimum design of extrusion. Realistic numerical simulation of deformation can be used to research the influence law between the physical parameters and geometric parameters and the realization of computer-aided optimal design.
引文
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