摘要
多点成形（Multi-point forming，简称 MPF）是三维曲面板类件柔性成
形的新技术，与传统的模具成形相比在许多方面占有优势，例如可实现无
模成形、优化变形路径、小设备成形大型件等等，因而有着良好的应用前
景；但在其成形过程中也易于产生一些缺陷，如压痕和起皱等。这些缺陷
影响工件的外观和内在质量，从而制约多点成形技术的实用化和进一步推
广应用。目前，CAE 技术逐渐成为现代设计流程的核心和现代设计的聚焦
点。因此，有必要对多点成形过程进行数值模拟，预测可能出现的成形缺
陷，探讨合适的工艺参数，消除或减轻缺陷，从而提高成形质量和成形效
率。
多点成形过程从力学观点来看属于几何、物理、边界条件三重非线性
和边界条件非连续性的复杂问题，而有限元方法是目前进行非线性分析的
最强有力的工具。本文选用动态显式有限元算法对薄板多点成形过程进行
数值模拟研究，为多点成形工艺的确定以及成形性的判断提供了依据，同
时对多点成形技术的发展和完善起到重要的推动作用。
本文的主要研究内容与结论如下：
1）有限元数值模拟方法的探讨
基于连续介质力学的理论，探讨了利用中心差分法使动力方程求解显
式化的过程，并对质量矩阵和阻尼矩阵的计算进行了研究；利用振动理论
的基本原理论述了临界时间步长的估算方法，保证了中心差分计算的稳定
性；引用了基于流动理论的本构方程和基于罚函数方法及库仑摩擦规律处
理多点不连续接触边界条件。
2）具有压边功能，且使用弹性介质的多点成形有限元模型的建立
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吉林大学硕士研究生学位论文
合理的有限元模型是进行有限元数值模拟计算的重要前提，本文探讨
了使用弹性介质的压边多点成形过程有限元模型建立时的若干问题，如空
间有限元离散化、有限单元的选择、材料模型的选择、边界条件等，为正
确建立多点成形有限元模型提供了原则和依据。
3）压边多点成形过程中起皱及拉裂成形缺陷的数值模拟研究
采用压边功能可实现薄板三维曲面零件的多点成形。本文从压边力和
压边间隙两种压边控制方式对压边多点成形过程进行了模拟，准确地反映
了成形工件的实际变形状态，并就不同的压边条件、板料厚度以及材质等
工艺参数对多点成形过程中起皱和拉裂现象的影响进行了数值模拟研究，
成功地运用成形极限图对拉裂现象进行了判断，判断结果与实验结果一致，
进一步说明了选择适当的工艺参数可以抑制或减少成形缺陷的产生，同时
为多点成形工艺、成形性能的分析和研究提供了依据。
4）使用弹性介质的压边多点成形过程中压痕的数值模拟研究
使用弹性介质可实现薄板三维曲面零件的无压痕多点成形。本文对使
用弹性介质和无弹性介质的多点成形过程进行了对比，指出使用弹性介质
时在满足成形精度的前提下可以明显改善工件的成形质量，并通过对不同
厚度和弹性模量的弹性介质对压痕的抑制作用进行了对比分析，探讨了最
佳的弹性介质参数。模拟结果表明：压痕深度随着弹性介质的厚度和弹性
模量的增加而减小，但当弹性介质较薄时，即使选择大弹性模量，对压痕
的防止并无太大效果。因此，选择合适的弹性介质是消除多点成形压痕缺
陷的关键。
Multi-point forming (MPF) is a flexible manufacturing technology for
three-dimensional surface part of thin sheet metal. Relative to the traditional
stamping technique, the MPF has more advantages, such as forming instead of
solid dies, optimum deformed path and using the MPF press to form large parts.
Therefore, the MPF technology can be applied extensively in many fields.
However in the process of multi-point forming, dimple and wrinkle are the
main defects which influence the forming ability and quality of the parts and
limit the development of the multi-point forming technology. At the present day
CAE is becoming the focus of modern design processes. So the numerical
simulation is carried out to analyze the multi-point forming process, and
predicts the possible defects. The different models and parameters are discussed
and compared in details; finally the best model which deform well is suggested
for the forming process. According to the simulations, those defects can be
restrained or even eliminated, so that the forming quality of the parts and
efficacy can be improved.
MPF process concerns nonlinear fields on geometry, physics, and
boundary, as well as complex discontinuous boundary problem. Nowadays the
finite element method (FEM) is a cogent tool to deal with the nonlinear
problems. In this paper, dynamic explicit algorithm FEM is successfully used to
analyze the MPF process of thin sheet metal. It provides an effective means for
optimizing the technique design and judging forming ability and quality of the
parts. Also it promotes the development of the MPF technology.
The main contents and results are as follows:
67
吉林大学硕士研究生学位论文
1) Research on the numerical simulation using finite element method
Based on the continuum mechanics theory, dynamic explicit algorithm
using centre difference method is studied including how to compute mass
matrix and damp matrix. According to the oscillation theory, critical time step is
discussed to assure the computing stabilization using centre difference method.
Furthermore, the constitution equation on the basis of the flow rule is
formulated in this thesis, and penalized function method and coulomb’s law of
friction are adopted to deal with the discontinuous boundary problem.
2) Building finite element model for MPF process
The reasonable finite element model is constructed for MPF process with
blank-holder device and elastic medium, such as spatial discretization for
multi-point process, the choice of finite element unit, the choice of material
pattern, boundary condition etc, have a great influence on the numerical
simulation. It provides the principles and basis for the correct finite element
model of MPF process.
3) Numerical simulation on the wrinkle and crack during the MPF process
with blanker-holder device
MPF technique with blank-holder device can be applied to three
dimensional surface parts. In this thesis, both blank-holder force and
blank-holder clearance controlling means are considered to simulate the MPF
process, which can reflect the real deformation well. The influence of the
different parameters, such as blank-holder condition, thickness of blank sheet
and material pattern on the wrinkle and the crack is analyzed. FLD is used to
judge the crack on the multi-point forming process successfully. The prediction
of crack accords with the experiment ones, which shows choosing the proper
parameters can eliminate or restrain the defects, and also benefits the MPF
technique and the shaping analysis.
4) Numerical simulation on the dimple during the MPF process using
elastic medium technique
MPF process with the elastic medium can be applied to the forming of
three dimensional surface part of thin sheet metal and be considered as
deformation with no dimples. In this thesis, the numerical simulation between
68
Abstract
using the elastic medium a
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