Frozen-in birefringence and anisotropic shrinkage in optical moldings: I. Theory and simulation scheme

An unconditionally stable upwinding scheme was proposed to improve the efficiency of the viscoelastic simulation in molding of optical products using a CV/FEM/FDM technique. A significant computation time saving was achieved due to an elimination of subdivision of the time step as required in the conventional numerical scheme. The approach was applied to simulate the flow-induced birefringence and anisotropic shrinkage in disk moldings using a nonlinear viscoelastic constitutive equation, orientation functions and equation of state. The two-dimensional triangular finite element meshes were used in the disk cavity and the one-dimensional tubular elements were utilized in the delivery system. Good agreement was shown between the simulated pressure traces and flow birefringence in the molding using the unconditionally stable upwinding scheme of the present study and the conventional numerical scheme of the earlier study. In addition, an algorithm for simulation of the thermal stresses and birefringence in moldings using linear viscoelastic and photoviscoelastic constitutive equations was presented by combining constrained and free quenching approaches. The proposed numerical scheme for viscoelastic simulation of injection molding is more suitable for future commercial applications.     

Theoretical and experimental studies of anisotropic shrinkage in injection moldings of various polyesters

A novel approach to predict anisotropic shrinkage of slow crystallizing polymers in injection moldings was proposed, using the flow‐induced crystallization, frozen‐in molecular orientation, elastic recovery, and PVT equation of state. In the present study, three different polyesters, polyethylene terephthalate, polybutylene terephthalate, and polyethylene‐2,6‐naphthalate (PEN), are used. The anisotropic thermal expansion and compressibility affected by the frozen‐in orientation function and the elastic recovery that was not frozen during moldings were introduced to obtain the in‐plane anisotropic shrinkages. The frozen‐in orientation function was calculated from the amorphous contribution based on the frozen‐in and intrinsic amorphous birefringence and crystalline contribution based on the crystalline orientation function determined from the elastic recovery and intrinsic crystalline birefringence. To model the elastic recovery and frozen‐in stresses related to birefringence during molding process, a nonlinear viscoelastic constitutive equation was used with the temperature‐dependent viscosity and relaxation time. Occurrence of the flow‐induced crystallization was introduced through the elevation of melting temperature affected by entropy production during flow of the viscoelastic melt. Kinetics of the crystallization was modeled using Nakamura and Hoffman‐Lauritzen equations with the rate constant affected by the elevated melting temperature. Numerous injection molding runs were carried out by varying the packing time, packing pressure, flow rate, melt and mold temperature, and anisotropic shrinkage of moldings were measured. The experimental results were compared with the simulated data and found in a fair agreement. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 3526–3544, 2006     

Modeling and experimental study of birefringence in injection molding of semicrystalline polymers

The prediction of birefringence developed in injection moldings is very important in order to satisfy required specification of molded products. A novel approach for the numerical simulation of the flow-induced crystallization and frozen-in birefringence in moldings of semicrystalline polymers was proposed. The approach was based on the calculation of elastic recovery that becomes frozen when the flow-induced crystallization occurred. The flow effect on the equilibrium melting temperature elevation due to the entropy reduction between the oriented and unoriented melts was incorporated to model crystallization. To find the entropy reduction and the frozen-in elastic recovery during crystallization, a non-linear viscoelastic constitutive equation was used. From the ultimate elastic recovery the crystalline orientation function was calculated. The crystalline and amorphous contributions to the overall birefringence were obtained from the crystalline orientation function and the flow birefringence, respectively. The birefringence profiles were measured and predicted in moldings of polypropylenes of different molecular weights obtained at various melt temperatures, injection speeds, holding times and mold temperatures. The resulting predictions were in fair agreement with corresponding experimental data.     

Numerical Simulation for Injection Molding with a Rapidly Heated Mold,Part II: Birefringence Prediction

In the accompanying paper, Part I, the advantages of the rapid thermal response (RTR) molding process were investigated for thin-wall-mold filling by employing coupled analysis of flow and heat transfer. Besides the complete filling of the cavity, frozen-in molecular orientation is another major quality issue in thin wall molding. The frozen-in orientation causes residual stress and birefringence, and potential part distortion. The present work focuses on the prediction and visualization of birefringence in RTR-molded parts. To calculate birefringence, flow-induced residual stress is computed first and the stress-optical law is then applied. The simulation results show that the amount of molecular orientation, residual stress, and birefringence level considerably decrease in the RTR-molding process. The effect of the mold temperature on the level of birefringence was also studied and predicted birefringence patterns were compared with experimental results for a thin-walled rectangular strip. Both predicted and experimental patterns of birefringence are in agreement on the observation that the birefringence level diminishes significantly when the mold temperature is raised to above the glass transition temperature.     

Extraordinary wavelength dispersion of birefringence in cellulose triacetate film with anisotropic nanopores

We examined birefringence in a stretched film of cellulose triacetate (CTA) after extraction of an immiscible component. The CTA film plasticized by di(2-ethylhexyl) adipate (DOA), which was added as the immiscible additive, exhibited negative birefringence to the same degree as the pure CTA film. Following removal of DOA from the film by immersion into methanol, the birefringence of the blend film changed dramatically from negative to positive. Moreover, the wavelength dependence also changed from ordinary to extraordinary, in which the absolute value of birefringence increases with wavelength. Scanning electron microscope (SEM) images revealed nanoscale ellipsoidal pores in the film after the extraction, suggesting that DOA was segregated and formed ellipsoidal domains in the CTA matrix during annealing and stretching. According to an optical theory for the nanoporous structure, we found that the form birefringence contributes to control of the optical properties of the CTA film. This phenomenon could be utilized in the design of high-performance optical films, such as quarter waveplate, because sign and wavelength dispersion of birefringence can be controlled even for a single component film.     

PE100管材专用料的结构与流变行为研究

对3种PE100管材专用料JHMGC100S、YGH041及P600进行了基本结构性能及毛细管流变行为、动态流变行为的研究。结果表明:190℃时,JHMGC100S的表观黏度与表观压力要高于P600和YGH041;当温度升高到230℃,3种专用料的不稳定流动现象明显改善,毛细管流变行为几乎无差别。动态流变研究表明:在低频下,JHMGC100S的复数黏度要高于其他两种专用料;在高频下,JHMGC100S的复数黏度介于其他两种专用料之间。在低频下,JHMGC100S的储能模量高于YGH041和P600;在高频下,JHMGC100S与YGH041的储能模量接近均,高于P600的储能模量。     

基于Moldflow/MPI的UPS电源壳体注塑成型分析

运用Moldflow/MPI模块对UPS电源壳体注塑成型过程进行了数值模拟分析,预测了熔体充模过程中的型腔压力分布、温度分布、锁模力大小、体积收缩率及翘曲变形;根据分析结果,提出了工艺优化方案,从而缩短模具设计制造周期。     

Effects of processing conditions on birefringence development in injection molded parts. II. Experimental measurement

The birefringence of injection molded parts was measured using a digital photoelasticity system, which combines a digital image analysis technique and the half-fringe photoelasticity (HFP) method The effects of processing conditions, including melt temperature, mold temperature, filling time and packing pressure, on the birefringence development in the molded parts were investigated. It was found that temperature and pressure are the two dominant factors that determine the birefringence development in the parts during the molding process. Frozen-in birefringence of the molded parts decreases with increasing melt temperature, mold temperature and injection speed. Birefringence of the parts also increases with increased packing pressure, especially around the gate area. Numerical simulations using the Leonov viscoelastic fluid model predict similar dependence of birefringence of parts on processing conditions. Simulated results are also consistent with measured values.     

Computer Filling Simulation of Injection Molding Based on 3D Surface Model

Computer simulation packages have been successful in predicting filling behavior in extremely complicated geometries, and most of the current numerical solutions are based on a hybrid finite-element/finite-difference scheme and the middle-plane model. This imported model causes some inconvenience during applications. This study introduces surface model as the datum plane, instead of the traditional middle-plane model and additional boundary conditions in the gapwise direction are employed to keep the flows in the surfaces at the same section coordinative. The simulation presented here is compared with the experimental results obtained with instrumented test mold and C-Mold results. It is demonstrated that the present formulation is well suited to handle cavities generated directly by mold design process with computer aided design (CAD) tools.     

Simulation of injection–compression‐molding process. II. Influence of process characteristics on part shrinkage

A numerical algorithm is developed to simulate the injection–compression molding (ICM) process. A Hele–Shaw fluid‐flow model combined with a modified control‐volume/finite‐element method is implemented to predict the melt‐front advancement and the distributions of pressure, temperature, and flow velocity dynamically during the injection melt filling, compression melt filling, and postfilling stages of the entire process. Part volumetric shrinkage was then investigated by tracing the thermal–mechanical history of the polymer melt via a path display in the pressure–volume–temperature (PVT) diagram during the entire process. Influence of the process parameters including compression speed, switch time from injection to compression, compression stroke, and part thickness on part shrinkage were understood through simulations of a disk part. The simulated results were also compared with those required by conventional injection molding (CIM). It was found that ICM not only shows a significant effect on reducing part shrinkage but also provides much more uniform shrinkage within the whole part as compared with CIM. Although using a higher switch time, lower compression speed, and higher compression stroke may result in a lower molding pressure, however, they do not show an apparent effect on part shrinkage once the compression pressure is the same in the compression‐holding stage. However, using a lower switch time, higher compression speed, and lower compression stroke under the same compression pressure in the postfilling stage will result in an improvement in shrinkage reduction due to the melt‐temperature effect introduced in the end of the filling stage. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 1640–1654, 2000     

PIV experiments and large eddy simulations of single-loop flow fields in Rushton turbine stirred tanks

The single-loop flow fields in Rushton turbine stirred tanks with clearance C=0.15T (T is tank diameter) were investigated by using particle image velocimetry (PIV) experiments and large eddy simulation (LES) methods. The velocity and turbulent kinetic energy (TKE) were carefully measured and resolved with high resolution camera. The regions with high TKE are affected by the movement of the trailing vortices generated behind the impeller blades. The effects of both geometrical configuration and Reynolds number were discussed. It is found that the Reynolds number has little effect on the mean flow for the configuration of impeller diameter D=T/3, C=0.15T. However, the single-loop flow pattern is changed into a double-loop one if D is increased from T/3 to T/2. The LES results were compared with the PIV experiments and the laser Doppler anemometry (LDA) data in the literature. The effect of the grid was validated, and the levels of local anisotropy of turbulence near the impeller discharge regions were investigated. Both the phase-averaged and phase-resolved LES results are in good agreement with the PIV experimental data, and are better than the predictions of the k–ε model. The agreement shows that the LES method can be used to simulate the complex flow fields in stirred tanks.     

基于综合平衡法的注塑工艺参数多目标优化设计

结合正交试验法和模流分析软件Moldflow,对不同工艺条件下的汽车轮轴盖塑件成型过程进行模拟分析,运用多目标综合平衡法,对塑件成型后的体积收缩率、翘曲变形量和表面气穴3个目标值进行综合评判。通过对各成型工艺参数的极差分析和方差分析,确定熔体温度、模具温度、保压压力、冷却时间等注塑工艺参数对目标值的影响程度分,析得出最优的注塑工艺参数组合方案。生产实践证明塑件质量得到了有效的改善。     

Application of the boundary element method numerical simulations for characterization of heptode ultramicroelectrodes in SECM experiments

Quantitative analysis of the scanning electrochemical microscope (SECM) experiments with heptode ultramicroelectrodes (UME) as a probe is performed by means of the boundary element method (BEM). The method is used to calculate the amperrometric steady-state response of the heptode UME in multiple electrode working mode, including the disk-ring competition mode, within the SECM feedback mode. SECM approach curves and line scans with the heptode UME are measured and analyzed by means of numerical simulations. Simulations are performed in the 3D space, thus enabling treatment of non-symmetrical systems, which the heptodes themselves and the line scan experiments are. The approach curves and the line scans are simulated using the real heptode geometry obtained from CCD camera images. The experimental parameters are determined and adjusted as a result of simulations. In particular, the focus was made on the analysis of such system imperfections as electrode/sample tilts, electrode scan heights and heterogeneous reaction rates at the UME. It is shown how the simulations featuring the real system geometry can be used further for the analysis of the SECM line scan and imaging experiments.     

Experimental studies and molecular modelling of the stress-optical and stress-strain behaviour of poly(ethylene terephthalate). Part II: Molecular modelling of birefringence of poly(ethylene terephthalate) networks

The Monte-Carlo (MC) approach of Paper I is developed to predict the birefringence of PET. An extension of the modelling of polarisability is used that accounts for chain flexibility and for structural units containing several types of bonds. The rotational-isomeric-state (RIS) model for PET chains in melts is employed to calculate the polarisability of the terephthaloyl segment and of each of the 27 possible conformations of the five skeletal bonds of the glycol segment. These polarisabilities then enable the birefringent properties of drawn PET melts to be predicted. A method of pre-averaging the individual glycol polarisabilities that greatly reduces the length of the calculation is shown to be valid.It is found that shorter PET chains produce higher values of birefringence (Δñ) for a given deformation. This trend is due to greater proportions of the chains reaching higher conformational extensions and therefore becoming more oriented. In disagreement with Kuhn and Grün theory, Δñ is not linearly related to λ² − λ⁻¹. This non-linear behaviour is related to the non-linear behaviour of the orientation functions of the terephthaloyl and glycol segments, 〈P₂(cos ζ_ter)〉 and 〈P₂(cos ζ_gly)〉, with λ² − λ⁻¹. The non-linear behaviour of 〈P₂(cos ζ_ter)〉 with λ² − λ⁻¹ was confirmed experimentally in Paper I, where the measured values of 〈P₂(cos ζ_ter)〉 were found to be closely predicted by the present MC modelling.In the present paper, the predicted values of Δñ, calculated according to various published values of bond polarisabilities are presented and discussed. They will be used in Paper III to model the measured birefringence of drawn PET.     

Simulation and Experimental Investigations of Material Distribution in the Sandwich Injection Molding Process

In sandwich injection molding, two polymeric materials are sequentially injected into a mold to form a multilayer product with a skin and core structure. Different properties of these polymers and their distribution in the cavity greatly affect the applications of the moldings. In an ideal situation, the core material should be entirely encapsulated in the skin material. When the flow front of the core material overtakes that of the skin material, breakthrough occurs, resulting in a defective part. The focus of this study is to determine the effect of molding parameters on the skin/core material distribution. The commercial simulation package (Moldflow) has been extensively compared with experiments. Both simulated and measured results suggest that in order to obtain the optimum encapsulated skin/core structure in the sandwich injection molded parts, it is necessary to select a proper core volume fraction and suitable processing parameters. A good agreement between simulation and experimental results indicates that the Moldflow program can be used as a valuable tool for the prediction of melt-flow behavior during the sandwich injection process.     

Comparison of numerical simulations and experiments in conical gas-solid spouted bed

Flowbehavior of gas and particles in conical spouted beds is experimentally studied and simulated using the twofluid gas-solid model with the kinetic theory of granular flow. The bed pressure drop and fountain height are measured in a conical spouted bed of 100mmI.D. at different gas velocities. The simulation results are compared with measurements of bed pressure drop and fountain height. The comparison shows that the drag coefficient model used in cylindrical beds under-predicted bed pressure drop and fountain height in conical spouted beds due to the partial weight of particles supported by the inclined side walls. It is found that the numerical results using the drag coefficient model proposed based on the conical spouted bed in this study are in good agreement with experimental data. The present study provides a useful basis for further works on the CFD simulation of conical spouted bed.     

Crystallinity and microstructure in injection moldings of isotactic polypropylenes. Part II: Simulation and experiment

The injection moldings of isotactic polypropylenes with various molecular weights were simulated using finite difference method. In the simulations, the unified crystallization model proposed in our previous paper was applied. The prediction of crystallinity and microstructure development in the moldings was based upon the crystallization kinetics and the “competing mechanisms” for introducing various microstructure layers in the moldings. Extensive injection molding experiments were carried out. The pressure traces during the molding experiments were recorded. The crystallinity distribution in the moldings was determined using differential scanning calorimetry. The measurements on the microstructure embedded in the moldings were performed, including the thickness of the highly oriented skin layer and the gapwise distribution of the spherulite sizes. The measured data for the crystallinity and microstructure in the moldings were compared with the simulated results. The effects of molecular weight and processing conditions on the development of crystallinity and microstructure in the moldings were elucidated. Theoretical predictions were found to be in a good agreement with experimental measurements.     

Population balance modeling of a microalgal culture in photobioreactors: Comparison between experiments and simulations

The growth of Scenedesmus obliquus in photobioreactors was both experimentally investigated and numerically simulated by solving a population balance equation (PBE), accounting for cell growth and division. The PBE is solved using the Finite size domain Complete set of trial functions Method Of Moments (FCMOM) and a wide range of operative conditions, namely both a batch and a continuous reactor under different light intensities, were considered in the experiments and in the numerical simulations. A thorough validation of the mathematical model was performed by comparing the experimental temporal profiles and steady‐state values of the cell density, wet weight, cell average mass, and mass distributions of the microalgal culture with the corresponding simulation results. The parameters of the distribution of division mass were identified to fit the experimental data; specifically, from the continuous reactor data, the dependence of the mean division mass from the cell average mass was obtained. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2702–2710, 2015     

CAD/CAM技术在模具设计制造中的应用

系统地介绍了应用Ｐｒｏ／ＥＮＧＩＮＥＥＲ软件进行模个设计与制造的方法。     

氧气喷射角度对煤制甲醇转化炉内速度场的影响

为了研究氧气喷射角度对煤制甲醇转化炉中速度场的影响,利用ANSYS和Fluent软件构建煤制甲醇转化炉模型,研究了氧气喷射角度在0°、8°、11°和15°时对转化炉内速度分布变化,发现氧气喷射角度在0°时,转化炉内速度梯度最小,高速区域最小且沿轴向延展,火焰最稳定,不易出现火焰淬灭现象。