基于类等势场法的锻造预成形优化设计研究
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摘要
锻造是一种主要的材料成形加工方法。锻件最终成形前,往往需要进行一次或多次预成形,预成形工序数目和预成形形状设计是塑性成形工艺和模具设计的根本和难点,一直未能很好地解决。基于经验、物理模拟或数值模拟的预成形设计方法难以得到合理的预成形设计结果,从理论上研究预成形设计方法具有重要的理论和工程意义。
类等势场法作为一种新兴的非优化算法,可以用静电场中不同电压的两个导体间等势场分布模拟塑性变形过程中坯料与锻件之间最小变形路径,在三维复杂锻件的预成形设计中有广阔的应用前景。本文首次将类等势场法、工程优化算法和有限元分析方法相结合,以预锻件形状为优化对象,对三维轴对称锻件和三维复杂锻件(预成形件为三维形状)的预成形设计方法进行了系统的研究：
(1)结合类等势场法和预成形优化设计的原理,针对需要两工步模锻成形的锻件,提出了基于类等势场法进行锻造预成形多目标优化设计的方法。该方法对只需一步预成形的三维轴对称锻件或形状复杂的非轴对称锻件均适用。
(2)以典型的H型截面轴对称锻件为例,对需要两工步模锻成形的锻件进行了基于类等势场法的预成形多目标优化设计研究。首先运用静电场模拟方法获得了坯料与锻件之间的等势场分布；然后以等势线电势值和预成形件与终锻件体积比为设计变量,以锻造充填率为优化目标,对H型轴对称锻件的终锻成形过程进行了响应面分析,确定了最佳预锻件体积和合理的等势线取值范围；最后以等势线电势值为单因素设计变量,运用共轭梯度优化算法,对H型轴对称锻件进行了基于锻件变形均匀性和终锻力的多目标预成形优化设计,确定了最优预锻件形状,得到了飞边较小、变形均匀而且终锻力较小的终锻件。
(3)针对需要多工步模锻成形的三维复杂锻件,提出了基于类等势场法进行两步预成形优化设计的方法。采用反向设计法,首先结合类等势场法、响应面优化方法和有限元数值分析,确定最优预锻件形状；然后基于优化后的预锻件形状,采用纵横截面曲线方法设计合理的预制坯形状。经过两步预成形设计,可以解决三维复杂锻件终锻时容易产生折迭和不易充满的问题。
(4)以形状复杂的摆体锻件为例,对需要多工步模锻成形的三维复杂锻件进行了基于类等势场法的两步预成形优化设计研究。运用静电场模拟方法获得了坯料与摆体锻件之间的三维等势场分布,通过等势面的分布规律分析了坯料成形过程中的流动特征,判断摆体锻件可能出现的锻造缺陷；采用截面曲线放样法提取了三维静电场中等势面作为预锻件形状；基于静电场模拟结果,以等势面电势值和预锻件与终锻件体积比为设计变量,以锻造充填率为优化目标对三维复杂摆体锻件的终锻成形过程进行了响应面分析,确定了最佳预锻件形状和体积。
(5)基于优化后的摆体预锻件形状,提出了纵横截面曲线预制坯设计方法。依据坯料锻造过程中的流动规律和预锻成形缺陷分析,设计了等断面横向截面曲线和对称平面纵向截面曲线；并根据制坯和预锻成形模拟结果对截面曲线形状进行了改进,确定了合理的预制坯形状,确保材料充满预锻模锻；通过制坯和预锻两步预成形优化设计,获得了形状符合设计要求、飞边较小的无缺陷摆体锻件。
Forging is one of primary material forming processes. Generally, one or more preform processes are required before final forging. Research on the number of performs processes and preform shape design is fundamental and difficult for the plastic forming technology and die design, which has not been settled perfectly and effectively. Furthermore, it is difficult to get advisable preform shape using preform design methods based on experience, physical simulation or numerical simulation. Therefore, study on preform design method is of great theoretical significance and engineering significance.
By Quasi-equipotential Field Method which is a non-numerical optimization algorithm, the equi-potential lines generated between two conductors of different voltages show similar trends for the minimum work paths between the undeformed shape and the deformed shape. Based on this similarity, the Quasi-equipotential Field Method has the broad application prospect in preform shape optimization for complex3-D forgings. In this paper, preform shape optimization methods for3-D axisymmetric and complex forgings (with3-D preform shapes) using Quasi--equipotential Field Method, plastic finite element modeling and engineering optimization algorithm are proposed.
(1) Combing Quasi-equipotential Field Method with the principle of forging preform design optimization, a new approach to do the preform shape multi-objective optimization in two-stage die forging based on Quasi-equipotential Field Method is developed, which is effectively applied to preform design of both3-D axisymmetric forgings and non-axisymmetric complex forgings.
(2) Research on preform shape multi-objective optimisation in two-stage die forging based on Quasi-equipotential Field Method is conducted by the example of H-section axisymmetric part. First, electric field distribution distribution of equipotential line between the undeformed shape and the deformed shape is obtained by electrostatic field simulation method. Second, with the potential value of an equi-potential line and volume ratio of preform to final shape as the design variables, forging filling ratio as the optimization goal, response surface analysis about forging forming process of H-section axisymmetric forging is carried out. Accordingly, the optimum volume ration and the appropriate range of potential lines for the preform of is determined. Finally, with the potential value of an equi-potential line as single factor variable, preform shape multi-objective optimization design controlling deformation uniformity and deforming force for H-section axisymmetric forging is performed using the conjugate gradient optimization algorithm. Consequently, flashless final forging with complete die fill and optimum deformation uniformity and deforming force is obtained
(3) A new approach to optimize preform shape in multi-stage die forging for3-D complex forgings based on Quasi-equipotential Field Method is proposed, which is based on stepping backward method. In the first stage of preform design, optimum pre-forging shape is determined combining Quasi-equipotential Field Method, response surface optimization with finite element analysis. In the second stage, Vertical and horizontal Cross-section Curves Method is introduced to design advisable preformed blank based on the optimized pre-forging shape. The two-stage preform design method is suitable to eliminate underfill and fold which easily occur in the forming process of three dimensional complex forging.
(4) Research on preform shape optimization in multi-stage die forging for3-D complex forging part based on Quasi-equipotential Field Method is conducted by the example of pendulum mass part. First, three dimensional electric field distribution between the undeformed shape and the deformed shape is obtained by electrostatic field simulation method. The material flow characteristics in the forming process are analyzed by the distribution of three dimensional equipotential surface so that the possible defects in the forging process can be predicted. The equipotential surfaces in3-D electrostatic field are extracted as pre-forging shapes by cross section curve lofting method. Based on the electrostatic field simulation results, response surface analysis about forging forming process of3-D complex pendulum mass part is performed with the potential value of an equi-potential surface and volume ratio of preform to final shape as the design variables, forging filling ratio as the optimization goal. Consequently, the optimum shape and volume of pre-forging is determined for obtaining final forging with complete die fill.
(5) Vertical and horizontal Cross-section Curves Method is introduced to design advisable preformed blank based on the optimized pre-forging shape. The equal horizontal cross-section curve and longitudinal cross-section curve of symmetry plane are designed according to material flow characteristics and forming defects in the pre-forging process. As a consequence, the advisable preformed blank is found, ensuring pre-forging with complete die fill on the basis of finite element simulation results of the first and second preform processes. Final forging with complete die fill and without folding defect is obtained after two-stage preform forging processes,
类等势场法作为一种新兴的非优化算法,可以用静电场中不同电压的两个导体间等势场分布模拟塑性变形过程中坯料与锻件之间最小变形路径,在三维复杂锻件的预成形设计中有广阔的应用前景。本文首次将类等势场法、工程优化算法和有限元分析方法相结合,以预锻件形状为优化对象,对三维轴对称锻件和三维复杂锻件(预成形件为三维形状)的预成形设计方法进行了系统的研究：
(1)结合类等势场法和预成形优化设计的原理,针对需要两工步模锻成形的锻件,提出了基于类等势场法进行锻造预成形多目标优化设计的方法。该方法对只需一步预成形的三维轴对称锻件或形状复杂的非轴对称锻件均适用。
(2)以典型的H型截面轴对称锻件为例,对需要两工步模锻成形的锻件进行了基于类等势场法的预成形多目标优化设计研究。首先运用静电场模拟方法获得了坯料与锻件之间的等势场分布；然后以等势线电势值和预成形件与终锻件体积比为设计变量,以锻造充填率为优化目标,对H型轴对称锻件的终锻成形过程进行了响应面分析,确定了最佳预锻件体积和合理的等势线取值范围；最后以等势线电势值为单因素设计变量,运用共轭梯度优化算法,对H型轴对称锻件进行了基于锻件变形均匀性和终锻力的多目标预成形优化设计,确定了最优预锻件形状,得到了飞边较小、变形均匀而且终锻力较小的终锻件。
(3)针对需要多工步模锻成形的三维复杂锻件,提出了基于类等势场法进行两步预成形优化设计的方法。采用反向设计法,首先结合类等势场法、响应面优化方法和有限元数值分析,确定最优预锻件形状；然后基于优化后的预锻件形状,采用纵横截面曲线方法设计合理的预制坯形状。经过两步预成形设计,可以解决三维复杂锻件终锻时容易产生折迭和不易充满的问题。
(4)以形状复杂的摆体锻件为例,对需要多工步模锻成形的三维复杂锻件进行了基于类等势场法的两步预成形优化设计研究。运用静电场模拟方法获得了坯料与摆体锻件之间的三维等势场分布,通过等势面的分布规律分析了坯料成形过程中的流动特征,判断摆体锻件可能出现的锻造缺陷；采用截面曲线放样法提取了三维静电场中等势面作为预锻件形状；基于静电场模拟结果,以等势面电势值和预锻件与终锻件体积比为设计变量,以锻造充填率为优化目标对三维复杂摆体锻件的终锻成形过程进行了响应面分析,确定了最佳预锻件形状和体积。
(5)基于优化后的摆体预锻件形状,提出了纵横截面曲线预制坯设计方法。依据坯料锻造过程中的流动规律和预锻成形缺陷分析,设计了等断面横向截面曲线和对称平面纵向截面曲线；并根据制坯和预锻成形模拟结果对截面曲线形状进行了改进,确定了合理的预制坯形状,确保材料充满预锻模锻；通过制坯和预锻两步预成形优化设计,获得了形状符合设计要求、飞边较小的无缺陷摆体锻件。
Forging is one of primary material forming processes. Generally, one or more preform processes are required before final forging. Research on the number of performs processes and preform shape design is fundamental and difficult for the plastic forming technology and die design, which has not been settled perfectly and effectively. Furthermore, it is difficult to get advisable preform shape using preform design methods based on experience, physical simulation or numerical simulation. Therefore, study on preform design method is of great theoretical significance and engineering significance.
By Quasi-equipotential Field Method which is a non-numerical optimization algorithm, the equi-potential lines generated between two conductors of different voltages show similar trends for the minimum work paths between the undeformed shape and the deformed shape. Based on this similarity, the Quasi-equipotential Field Method has the broad application prospect in preform shape optimization for complex3-D forgings. In this paper, preform shape optimization methods for3-D axisymmetric and complex forgings (with3-D preform shapes) using Quasi--equipotential Field Method, plastic finite element modeling and engineering optimization algorithm are proposed.
(1) Combing Quasi-equipotential Field Method with the principle of forging preform design optimization, a new approach to do the preform shape multi-objective optimization in two-stage die forging based on Quasi-equipotential Field Method is developed, which is effectively applied to preform design of both3-D axisymmetric forgings and non-axisymmetric complex forgings.
(2) Research on preform shape multi-objective optimisation in two-stage die forging based on Quasi-equipotential Field Method is conducted by the example of H-section axisymmetric part. First, electric field distribution distribution of equipotential line between the undeformed shape and the deformed shape is obtained by electrostatic field simulation method. Second, with the potential value of an equi-potential line and volume ratio of preform to final shape as the design variables, forging filling ratio as the optimization goal, response surface analysis about forging forming process of H-section axisymmetric forging is carried out. Accordingly, the optimum volume ration and the appropriate range of potential lines for the preform of is determined. Finally, with the potential value of an equi-potential line as single factor variable, preform shape multi-objective optimization design controlling deformation uniformity and deforming force for H-section axisymmetric forging is performed using the conjugate gradient optimization algorithm. Consequently, flashless final forging with complete die fill and optimum deformation uniformity and deforming force is obtained
(3) A new approach to optimize preform shape in multi-stage die forging for3-D complex forgings based on Quasi-equipotential Field Method is proposed, which is based on stepping backward method. In the first stage of preform design, optimum pre-forging shape is determined combining Quasi-equipotential Field Method, response surface optimization with finite element analysis. In the second stage, Vertical and horizontal Cross-section Curves Method is introduced to design advisable preformed blank based on the optimized pre-forging shape. The two-stage preform design method is suitable to eliminate underfill and fold which easily occur in the forming process of three dimensional complex forging.
(4) Research on preform shape optimization in multi-stage die forging for3-D complex forging part based on Quasi-equipotential Field Method is conducted by the example of pendulum mass part. First, three dimensional electric field distribution between the undeformed shape and the deformed shape is obtained by electrostatic field simulation method. The material flow characteristics in the forming process are analyzed by the distribution of three dimensional equipotential surface so that the possible defects in the forging process can be predicted. The equipotential surfaces in3-D electrostatic field are extracted as pre-forging shapes by cross section curve lofting method. Based on the electrostatic field simulation results, response surface analysis about forging forming process of3-D complex pendulum mass part is performed with the potential value of an equi-potential surface and volume ratio of preform to final shape as the design variables, forging filling ratio as the optimization goal. Consequently, the optimum shape and volume of pre-forging is determined for obtaining final forging with complete die fill.
(5) Vertical and horizontal Cross-section Curves Method is introduced to design advisable preformed blank based on the optimized pre-forging shape. The equal horizontal cross-section curve and longitudinal cross-section curve of symmetry plane are designed according to material flow characteristics and forming defects in the pre-forging process. As a consequence, the advisable preformed blank is found, ensuring pre-forging with complete die fill on the basis of finite element simulation results of the first and second preform processes. Final forging with complete die fill and without folding defect is obtained after two-stage preform forging processes,
引文
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