板金属冲压成形快速模拟算法研究
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摘要
在汽车开发过程中，车身模具的开发周期在整个研发周期中占有重要比重。为了缩短模具的开发周期，板料成形的模拟软件被普遍应用到模具开发过程中。板料成形的模拟算法按照理论基础可以分为两种：一类是基于增量理论；另一种是基于全量理论。前者计算精度较高，但计算时间过长；后者以一步逆成形算法为代表，计算速度很快，但计算精度较低。因此，本文在大变形弹塑性理论基础上，提出改进型梯度法对一步逆成形算法的求解过程做改进研究；并深化研究，将一步正成形思想发展完善成具有一定工程实用性的仿真模拟算法，最后提出兼顾计算精度和计算效率的基于拟全量理论的多步正成形算法。研究内容简述如下：
(1)、在一步逆成形算法框架下，提出一种改进型梯度法用于Newton-Raphson迭代计算，取代以往基于方程组求解的迭代算法。该方法从有限元分析中由单元形状改变量引起的单元失衡力入手，不断优化节点位置坐标来降低整个板料的失衡力。在每个迭代步上，先计算由扰动小量引起的节点失衡力梯度，再利用值域归一法计算节点坐标修改量，最后沿失衡力梯度下降方向，以修改量为步长修改初始坯料上节点坐标。为了避免不相关节点处失衡力向量的重复计算，将摄动方法的局部修正思想引入到迭代求解过程中。
(2)、以一步逆成形算法理论为基础，初步完成具有一定工程实用性的的一步正成形模拟算法。先利用基于映射关系和面积坐标的二次映射法，初步得到一步正成形的空间初始解。再基于全量理论，利用针对空间坐标修改方案的改进型梯度方法，对初始解做失衡力平衡迭代修正，迭代过程中利用接触判断与修正方法保证被修改后的节点始终贴合在模具表面上。较比一步逆成形算法来说，一步正成形算法的求解过程更加符合零件的成形过程，已知初始平板料的厚度来推导成形后最终构形的厚度，可以有效的计算出规则的初始坯料在成形后的形状。由于一步成形正算法解决了一步成形逆算法的一些根本的缺陷，使求解精度得以提高。
(3)、在基于全量理论的一步正成形算法基础上，引入增量理论思想，提出多步正成形算法。通过在初始板料和最终构形之间增加若干个中间步构形，来引入加载历史的影响，进一步提高了模拟精度；构建出中间构形基准面，并以基准面为基础提出简化修正计算方案，简化了计算过程。
(4)、设计了方盒件多行程实验方案，采用电腐蚀方法在初始坯料上刻上圆形网格，进行了10mm，20mm，30mm，40mm，50mm五个不同行程的方盒件成形实验。利用光学方法测量网格变形量并推算出网格应变量，使用超声测厚仪测量板料不同行程的厚度变化量。通过几种不同算法在计算精度和计算效率上的对比，证明了多步正成形算法的有效性。最后，应用多步正成形算法模拟实际汽车冲压件，从多步正算法的模拟结果、Dynaform增量法的模拟结果和试验件测量结果对比来看，多步正成形能够高效、准确地预示出成形结果。同时也证明了多步正成形算法具有实际应用性。
In the process of automobile development, the cycle of development of autobodydies is important in the total cycle of development. The simulation software for metalsheet forming is universally applied in the process of the development of dies, inorder to shorten the cycle of development of dies. The simulation method for metalsheet forming can be divided into two kinds according to theoretical basis: One kindis based on incremental theory; another is based on deformation theory. Thecalculation accuracy of the former is higher, but the computation time is too long；Thelatter is represented by one step forming inverse algorithm, computing speed quickly,but poor precision. Therefore, the improvement research is done on the solutionprocesses of one step forming inverse algorithm using the modified gradient methodbased on large deformation elastoplastic theory; to deepen the study, the idea of onestep forming positive algorithm based on deformation theory is developed to be asimulation algorithm which has certain engineering practicability, and finallymulti-step forming positive algorithm which gives considerations to both calculationaccuracy and computational efficiency is proposed. The research content is briefly asfollows:
1、In the frame of one step forming inverse algorithm, the improved gradient methodis proposed for iterative computations, and replacing the previous iteration algorithmbased on solving the equations. This method commences from the elementunbalanced force which generated from variations of element shape in the finiteelement analysis. The norm of the unbalanced force is defined to measure theunbalanced force situation in the blank. On each iteration step, firstly the unbalancedforce gradients generated from small disturbances can be calculated. Secondly theintelligence modifier optimization method is used to calculate the node coordinatesmodifier. Finally along the unbalanced force gradient descent direction, thecoordinates of the node on the initial blank is modified. To avoid the repeated computation of the unbalanced force vector on irrelevant nodes, the idea of localmodification from perturbation theory is introduced into the iteration process.
2、On the basis of one step forming inverse algorithm, one step forming positivealgorithm is accomplished to simulate the sheet metal forming process. The spaceinitial solution of one step forming positive algorithm is obtained preliminary usingmapping relationships and area coordinates. Then, based on deformation theory theiterative solutions are carried out in three-dimensional coordinate system by using theimproved gradient method. During iterative process the contact process is introducedto ensure that the nodes on the spatial initial solution are not separated from diesurface. Compared to the inverse approach, the simulation process of the positiveapproach is more coincident with the forming process. The thickness of the initialblank is known, and the thickness of the final shape can be derived. The stampedshape of regular sheet can be calculated effectively. As one step forming positivealgorithm can solve some fundamental flaws of one step forming inverse algorithm,the precision is improved.
3、On the basis of one step forming positive algorithm which is based on deformationtheory, introducing idea of incremental theory, the multi step forming positivealgorithm is proposed based on quasi-deformation theory. The influence of theloading history is considered by adding several intermediate shapes between theinitial blank and the final shape, and the simulation accuracy is further improved. Thebenchmark surfaces of the intermediate shapes can be built, in the basis of which theproject for the simplification of modified calculation is proposed, and the computationtime is reduced.
4、The multi-step experimental scheme of square box is designed. The circularelements are marked on the flat blank using electric corrosion method, Five squarebox experiment samples of different steps including10mm,20mm,30mm,40mm,50mm areachieved. The deformation of element is measured by the method of opticalmeasurement, and then the strain of element can be calculated. The thickness of blankin different steps is measured using ultrasonic thickness gauge. Through thecomparison among several different algorithms on calculation precision and calculation efficiency, the multi-step forming positive algorithm is proved valid.Finally, the multi-step forming positive algorithm is applied to simulate the actualautomobile stamping parts. From the comparison among the simulation results ofmulti-step forming positive algorithm, the Dynaform incremental method and theresults of experimental measurement, it is observed that the multi-step formingpositive algorithm can also predict the forming results. Meanwhile, it is proved themulti-step forming positive algorithm can be commonly used.
(1)、在一步逆成形算法框架下，提出一种改进型梯度法用于Newton-Raphson迭代计算，取代以往基于方程组求解的迭代算法。该方法从有限元分析中由单元形状改变量引起的单元失衡力入手，不断优化节点位置坐标来降低整个板料的失衡力。在每个迭代步上，先计算由扰动小量引起的节点失衡力梯度，再利用值域归一法计算节点坐标修改量，最后沿失衡力梯度下降方向，以修改量为步长修改初始坯料上节点坐标。为了避免不相关节点处失衡力向量的重复计算，将摄动方法的局部修正思想引入到迭代求解过程中。
(2)、以一步逆成形算法理论为基础，初步完成具有一定工程实用性的的一步正成形模拟算法。先利用基于映射关系和面积坐标的二次映射法，初步得到一步正成形的空间初始解。再基于全量理论，利用针对空间坐标修改方案的改进型梯度方法，对初始解做失衡力平衡迭代修正，迭代过程中利用接触判断与修正方法保证被修改后的节点始终贴合在模具表面上。较比一步逆成形算法来说，一步正成形算法的求解过程更加符合零件的成形过程，已知初始平板料的厚度来推导成形后最终构形的厚度，可以有效的计算出规则的初始坯料在成形后的形状。由于一步成形正算法解决了一步成形逆算法的一些根本的缺陷，使求解精度得以提高。
(3)、在基于全量理论的一步正成形算法基础上，引入增量理论思想，提出多步正成形算法。通过在初始板料和最终构形之间增加若干个中间步构形，来引入加载历史的影响，进一步提高了模拟精度；构建出中间构形基准面，并以基准面为基础提出简化修正计算方案，简化了计算过程。
(4)、设计了方盒件多行程实验方案，采用电腐蚀方法在初始坯料上刻上圆形网格，进行了10mm，20mm，30mm，40mm，50mm五个不同行程的方盒件成形实验。利用光学方法测量网格变形量并推算出网格应变量，使用超声测厚仪测量板料不同行程的厚度变化量。通过几种不同算法在计算精度和计算效率上的对比，证明了多步正成形算法的有效性。最后，应用多步正成形算法模拟实际汽车冲压件，从多步正算法的模拟结果、Dynaform增量法的模拟结果和试验件测量结果对比来看，多步正成形能够高效、准确地预示出成形结果。同时也证明了多步正成形算法具有实际应用性。
In the process of automobile development, the cycle of development of autobodydies is important in the total cycle of development. The simulation software for metalsheet forming is universally applied in the process of the development of dies, inorder to shorten the cycle of development of dies. The simulation method for metalsheet forming can be divided into two kinds according to theoretical basis: One kindis based on incremental theory; another is based on deformation theory. Thecalculation accuracy of the former is higher, but the computation time is too long；Thelatter is represented by one step forming inverse algorithm, computing speed quickly,but poor precision. Therefore, the improvement research is done on the solutionprocesses of one step forming inverse algorithm using the modified gradient methodbased on large deformation elastoplastic theory; to deepen the study, the idea of onestep forming positive algorithm based on deformation theory is developed to be asimulation algorithm which has certain engineering practicability, and finallymulti-step forming positive algorithm which gives considerations to both calculationaccuracy and computational efficiency is proposed. The research content is briefly asfollows:
1、In the frame of one step forming inverse algorithm, the improved gradient methodis proposed for iterative computations, and replacing the previous iteration algorithmbased on solving the equations. This method commences from the elementunbalanced force which generated from variations of element shape in the finiteelement analysis. The norm of the unbalanced force is defined to measure theunbalanced force situation in the blank. On each iteration step, firstly the unbalancedforce gradients generated from small disturbances can be calculated. Secondly theintelligence modifier optimization method is used to calculate the node coordinatesmodifier. Finally along the unbalanced force gradient descent direction, thecoordinates of the node on the initial blank is modified. To avoid the repeated computation of the unbalanced force vector on irrelevant nodes, the idea of localmodification from perturbation theory is introduced into the iteration process.
2、On the basis of one step forming inverse algorithm, one step forming positivealgorithm is accomplished to simulate the sheet metal forming process. The spaceinitial solution of one step forming positive algorithm is obtained preliminary usingmapping relationships and area coordinates. Then, based on deformation theory theiterative solutions are carried out in three-dimensional coordinate system by using theimproved gradient method. During iterative process the contact process is introducedto ensure that the nodes on the spatial initial solution are not separated from diesurface. Compared to the inverse approach, the simulation process of the positiveapproach is more coincident with the forming process. The thickness of the initialblank is known, and the thickness of the final shape can be derived. The stampedshape of regular sheet can be calculated effectively. As one step forming positivealgorithm can solve some fundamental flaws of one step forming inverse algorithm,the precision is improved.
3、On the basis of one step forming positive algorithm which is based on deformationtheory, introducing idea of incremental theory, the multi step forming positivealgorithm is proposed based on quasi-deformation theory. The influence of theloading history is considered by adding several intermediate shapes between theinitial blank and the final shape, and the simulation accuracy is further improved. Thebenchmark surfaces of the intermediate shapes can be built, in the basis of which theproject for the simplification of modified calculation is proposed, and the computationtime is reduced.
4、The multi-step experimental scheme of square box is designed. The circularelements are marked on the flat blank using electric corrosion method, Five squarebox experiment samples of different steps including10mm,20mm,30mm,40mm,50mm areachieved. The deformation of element is measured by the method of opticalmeasurement, and then the strain of element can be calculated. The thickness of blankin different steps is measured using ultrasonic thickness gauge. Through thecomparison among several different algorithms on calculation precision and calculation efficiency, the multi-step forming positive algorithm is proved valid.Finally, the multi-step forming positive algorithm is applied to simulate the actualautomobile stamping parts. From the comparison among the simulation results ofmulti-step forming positive algorithm, the Dynaform incremental method and theresults of experimental measurement, it is observed that the multi-step formingpositive algorithm can also predict the forming results. Meanwhile, it is proved themulti-step forming positive algorithm can be commonly used.
引文
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