【作者】 李健辉；

【导师】 李德群；

【作者基本信息】 华中科技大学 ， 材料加工工程， 2009， 博士

【摘要】 本文针对注射成型过程以及产品的特点,引入合适的假设和边界条件,建立了注射成型残余应力和翘曲变形的数学模型以及数值计算方法,开发了商业化的注射成型残余应力和翘曲变形模拟软件。本文基于粘弹性理论以及时温等效原理,提出了计算注射成型残余应力的线性热-粘弹性和热-弹性数学模型。通过引入适合于注射成型特点的基本假设,建立了线性热-粘弹性和热-弹性模型的增量格式。模型中充分考虑了保压压力历史以及温度历史对残余应力的影响,并将计算过程分为三个阶段,针对每个阶段的特点施加不同的边界条件。模型采用在时间上有限差分和在厚度方向分层处理的计算方法,提出了完整的数值解决方案。模拟结果显示,从工程角度出发,基本可以采用热-弹性模型代替热-粘弹性模型来计算残余应力,因为二者的结果比较相近。翘曲变形的模拟中,本文采用平板壳单元作为翘曲计算的有限元模型,平板壳单元由表征平面内变形的膜单元和表征垂直于平面的变形的板弯曲单元组成,通过比较几种具有代表性的膜单元和板弯曲单元,最终选用优化膜单元(Optimal TriangleMembrane Element,OPT单元)和细化离散的Mindlin三角形弯曲单元(RefinedDiscrete Kirchhoff Mindlin bending element,RDKTM单元)组成的平板壳单元。该单元具有变形模式准确、对网格质量要求低等优良特性。传统的板壳有限元分析是基于中性层模型的,而目前的注射成型模拟是基于产品的表面模型的。为了解决该问题,本文创造性地提出了基于表面模型的翘曲变形模拟方法,考虑到产品的上下表面均有网格,在本文中将单元厚度设定为产品局部厚度的一半,并通过多点约束将上下表面的位移关联起来,以使得整体结构满足经典板壳理论的Love-Kirchhoff假设。施加多点约束的普通方法有主从消元法、罚函数法以及Lagrange乘子法,由于很多注射成型产品的结构十分复杂,若采用这三种普通的多点约束方法,产品的结构响应可能会出现问题。本文提出了一种基于Lagrange乘子的消元法,该方法可保证产品的结构响应正确,且具有计算效率高、施加约束过程简单等特点。本文采用试验设计(Design of Experiment,DOE)成型了大量的产品,并采用方差分析(Analysis of Variance,ANOVA)分析了塑料熔体温度、注射速率、模具温度、保压压力、保压时间、冷却时间等6个工艺参数对注射成型产品的收缩和翘曲的影响。同时,采用模拟软件分析了与试验相同的工艺条件设置的方案,并将模拟结果与试验结果进行了详尽的对比,从而验证了残余应力与翘曲变形分析模拟软件的正确性与合理性,表明了模拟软件对提高制品质量和生产效率具有重要意义。更多还原

【Abstract】 In this thesis, concerning the characteristic of injection molding, appropriate assumptions and boundary conditions are introduced, and the mathematical models and numerical methods of residual stresses and warpage are built. Based on the presented models, commercialized simulation software of residual stresses and warpage analysis of injection molding are developed.Based on the theories of viscoelastic and time-temperature superposition, linear thermal viscoelastic model and thermal viscous elastic model are presented. By introducing appropriate assumptions, incremental formulation of linear thermo viscoelastic model and linear thermo viscous elastic model are built. In these models, the effects of the packing pressure and temperature history are taken into account adequately. The process of residual stresses computation is divided into three steps, appropriate boundary conditions are employed according to the feature of the each steps. In this model, finite difference method is used to discrete the mathematical models spatially and temporally. The simulation results show that the linear thermal viscoelastic model can be replaced by linear thermo viscous elastic model from the view of engineering, since the results of the two models are close.During warpage analysis, flat shell element is employed, which is consist of membrane element and plate bending element. By comparing several typical membrane elements and plate bending elements, the Optimal Triangle Membrane Element (OPT element) and Refined Discrete Kirchhoff Mindlin bending element (RDKTM element) are selected. The flat shell element which is consists of the selected OPT element and RDKTM element exhibits excellent performance, since it has accurate displace formulation and is insensitive to aspect ration of elements.The conventional shell finite element analysis is based on the middle surface, but present injection molding CAE is based on the surface. In order to solve this disaccord, a novel approach of warpage analysis based on surface model is presented. In this approach, the thickness of mesh is set as the half thickness of local thickness of part since meshes exist at both of the upper and bottom of the part. Multi-point Constraint (MPC) is used to handle the relationship of two corresponding nodes which distribute at upper and bottom meshes respectively. The typical algorithms for dealing with MPC equations are the master-slave elimination method, penalty function and Lagrange multiplier methods. Concerning many injection molded parts exhibit complex geometry, each of these three methods is not competent. In this thesis, the Lagrange multiplier based elimination method is presented. This method can assure the structural response of parts is correct, and it has the performance of high computational efficiency and simple implementation process.By introducing Design of Experiment (DOE), a large number of parts are manufactured. The effects of melt temperature, injection rate, mold temperature, packing pressure, packing time and cooling time on the final shrinkage and warpage of parts are analyzed using Analysis of Variance (ANOVA). The simulations based on the models presented in this thesis under the same process conditions with that of DOE is carried out, the simulation results match that of experiment basically, thereby the simulations are validated.更多还原