Improved mathematical modeling for the sheet reheat phase during thermoforming

In any thermoforming process, plastic sheet heating is the most important phase as it is responsible for final part quality as well as overall process efficiency and productivity. The goal of the study reported here was to improve existing mathematical models to accurately predict the temperature profile inside a heated sheet, where the model could be used to better control the overall thermoforming process. A mathematical model with temperature dependent, variable sheet material properties including density, thermal diffusivity, specific heat, and thermal conductivity was developed and validated against experimental data. Models with constant and variable plastic sheet properties were created, simulated, and compared in Matlab. The models were validated by experiments which obtained temperature profiles at different depths within a plastic sheet by inserting thermocouples and recording temperatures. Further, the effect of sheet color on heating was investigated by considering two extreme cases: white (transparent) and black (opaque) colored sheets, and the effect of oven air temperature and velocity on sheet heating was also investigated. Results indicated that a variable properties model was needed to control sheet reheating especially with narrow forming windows, and that the heating profiles required for colored and noncolored sheets were very different. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Derivation of optimal processing parameters of polypropylene foam thermoforming by an artificial neural network

The effects of processing parameters on the thermoforming of polymeric foam sheets are highly nonlinear and fully coupled. The complex interconnection of these dominant processing parameters makes the process design a difficult task. In this study, the optimal processing parameters of polypropylene foam thermoforming are obtained by the use of an artificial neural network. Data from tests carried out on a lab‐scale thermoforming machine were used to train an artificial neural network, which serves as an inverse model of the process. The inverse model has the desired product dimensions as inputs and the corresponding processing parameters as outputs. The structure, together with the training methods, of the artificial neural network is also investigated. The feasibility of the proposed method is demonstrated by experimental manufacturing of cups with optimal geometry derived from the finite element method. Except the dimension deviation at one location, which amounts to 17.14%, deviations of the other locations are all below 3.5%. POLYM. ENG. SCI., 45:375–384, 2005. © 2005 Society of Plastics Engineers     

Rheological modeling of fracture in plug‐assisted vacuum thermoforming

The fracture of polymeric sheets is one of the practical problems occurring during plug‐assisted vacuum thermoforming. This defect can occur during both the plug‐assist and vacuum‐forming stages. This article focuses on two issues: (1) the origins of fracture creation and (2) the determination of the process parameters needed for removal of the defect. The results of our work not only lead to an understanding of the cause of this problem but also enable us to calculate the parameters that affect the fracture of polymeric sheets during plug‐assisted vacuum thermoforming. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Ranking the key parameters of immersion precipitation process and modeling the resultant membrane structural evolution

Key parameters coupling with the instantaneous nucleation concept (ie, the Big Bang analogy) was used to model immersion precipitation process. The merits of the acquired model were verified via comparing its predictions with experimental results of two well‐prepared and characterized cellulose acetate (CA) and polyacrylonitrile (PAN) membranes. A morphology predictable map, ΔPη^?1 versus ?₁, was constructed, where ΔP, η and ?₁ are osmotic pressure difference between nonsolvent and dope solution, dope viscosity and intruded nonsolvent volume fraction into the dope, respectively. The phase separation map, ΔPη^?1 (proportional with apparent system diffusivity with the unit of time^?1) versus ?₁ showed three regimes which, at least qualitatively, depicted the correct morphological evolution trends of the studied systems. Phase separation in regime one of CA membrane with the longest delayed time or lowest ΔPη^?1, led to bead‐like morphology. CA membrane with the shortest elapsed time or highest ΔPη^?1, separated to finger‐like morphology in regime three. Finally, phase separation in the intermediate regime of CA membrane, ended up to sponge‐like morphology. Phase separation time scales of the PAN membranes versus intruded nonsolvent into the dope solution were located in finger‐like region of the CA membrane, which its downward transition lowered the fingers population. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Thermodynamic modeling of the CaO-SiO2-ZrO2 system coupled with key phase diagram experiments

Thermodynamic modeling coupled with key phase diagram experiments of the ternary CaO-SiO₂-ZrO₂ system was carried out. The isothermal phase diagram of the CaO-SiO₂-ZrO₂ system at 1873 K was established by using a classical phase equilibration and quenching technique followed by EPMA phase analysis. The Gibbs energy of each phase was optimized through critical evaluation of all available thermodynamic properties and phase diagram data in literature with new experimental data. The discrepancies between experimental phase diagram data and possible errors in the existing thermodynamic data were resolved in this study.     

Improved evidence for the existence of an intermediate phase during hydration of tricalcium silicate

Tricalcium silicate (Ca₃SiO₅) with a very small particle size of approximately 50 nm has been prepared and hydrated for a very short time (5 min) by two different modes in a paste experiment, using a water/solid-ratio of 1.20, and by hydration as a suspension employing a water/solid-ratio of 4000. A phase containing uncondensed silicate monomers close to hydrogen atoms (either hydroxyl groups or water molecules) was formed in both experiments. This phase is distinct from anhydrous tricalcium silicate and from the calcium-silicate-hydrate (C-S-H) phase, commonly identified as the hydration product of tricalcium silicate. In the paste experiment, approximately 79% of silicon atoms were present in the hydrated phase containing silicate monomers as determined from ²⁹Si{¹H} CP/MAS NMR. This result is used to show that the hydrated silicate monomers are part of a separate phase and that they cannot be attributed to a hydroxylated surface of tricalcium silicate after contact with water. The phase containing hydrated silicate monomers is metastable with respect to the C-S-H phase since it transforms into the latter in a half saturated calcium hydroxide solution. These data is used to emphasize that the hydration of tricalcium silicate proceeds in two consecutive steps. In the first reaction, an intermediate phase containing hydrated silicate monomers is formed which is subsequently transformed into C-S-H as the final hydration product in the second step. The introduction of an intermediate phase in calculations of the early hydration of tricalcium silicate can explain the presence of the induction period. It is shown that heterogeneous nucleation on appropriate crystal surfaces is able to reduce the length of the induction period and thus to accelerate the reaction of tricalcium silicate with water.     

Unraveling the electric field effect on the grain-boundary migration in alumina through phase field modeling

It is experimentally demonstrated that the electric field drives the grain-boundary (GB) migration in ceramics, but this has not been interpreted mechanistically. This work develops a phase field model to study the GB migration in alumina (Al₂O₃) and validate through the comparison with previous experiments. Results show that the GBs move to the small grain domain. Under an electric field in the positive bias direction, GB migration is enhanced, whereas the migration to the small grain domain is inhibited under the electric field in the negative bias direction. The enhancement or inhibition effect becomes more pronounced with increasing the electric field. The high negative bias induces decrease in the GB migration velocity even with the migration direction altering. It is revealed that GB migrations are dominated by the competitive effect between the curvature and electric field driving forces, and an analytical expression of the critical electric field is derived.     

集装箱喷漆废水处理工艺试验研究

在实验室对集装箱喷漆废水处理工艺及主要参数进行了研究。结果表明，采用SBR生化降解-物化混凝处理喷漆废水在技术上完全可行。采用SBR法处理喷漆废水时，喷漆废水与生活污水按6：4左右的比例混合．使进水COD控制在1400—1600mg／L。在此条件下，经过24h的生物好氧处理，能将出水的COD降至150mg／L以下。之后．再投加混凝剂[V（聚铝）：V（聚丙烯酰胺）=2：1]进行混凝处理，可进一步将出水COD降到80mg／L以下，达到国家二级排放标准。     

The role of process parameters in determining wall thickness distribution in plug‐assisted thermoforming

This article describes the results of a comprehensive investigation to determine the link between process parameters and observed wall thickness output for the plug‐assisted thermoforming process. The overall objective of the work was to systematically investigate the process parameters that may be adjusted during production to control the wall thickness distribution of parts manufactured by plug‐assisted thermoforming. The parameters investigated were the sheet temperature, plug temperature, plug speed, plug displacement, plug shape, and air pressure. As well as quantifying the effects of each parameter on the wall thickness distribution, a further aim of the work was to improve the understanding of the physical mechanisms of deformation of the sheet during the different stages of the process. The process parameters shown to have the greatest effect on experimentally determined wall thickness distribution were the plug displacement, sheet temperature, plug temperature, and plug shape. It is proposed that during the plug‐assisted thermoforming of polystyrene the temperature dependent friction between the plug and sheet surface was the most important factor in determining product wall thickness distribution, whereas heat transfer was shown to play a less important role. POLYM. ENG. SCI., 50:1923–1934, 2010. © 2010 Society of Plastics Engineers     

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution (RTD) in an impinging stream reactor, a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed. The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions. The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux, but is almost independent of gas flux. As the liquid flux and the gas flux increase, the liquid dispersion coefficient of center-to-wall decreases. The axial liquid dispersion coefficient is much larger than that of center-to-wall, which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.     

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution (RTD) in an impinging stream reactor, a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed. The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions. The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux, but is almost independent of gas flux. As the liquid flux and the gas flux increase, the liquid dispersion coefficient of center-to-wall decreases. The axial liquid dispersion coefficient is much larger than that of center-to-wall, which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.     

The effects of radiation cross‐linking and process parameters on the behavior of polyamide 12 in vacuum thermoforming

Compared to amorphous thermoplastics, semi‐crystalline thermoplastics usually have a smaller processing range for thermoforming, due to their narrow temperature window for the transition from viscoelastic to viscous material behavior. On the other hand, semi‐crystalline thermoplastics offer superior properties for applications like ductility or chemical resistance. Within this article, modification of semi‐crystalline polyamide 12 by radiation cross‐linking with respect to its suitability for vacuum thermoforming as well as the effects of processing parameters and sheet thickness on the resulting strain distributions in thermoformed parts are shown. Experimental thermoforming processing studies in combination with digital image correlation measurements, thermo‐mechanical and elongational rheometry were performed to characterize the behavior of cross‐linked semi‐crystalline thermoplastics in the vacuum thermoforming process. POLYM. ENG. SCI., 2011. ©2011 Society of Plastics Engineers     

Development of a multivariable online monitoring system for the thermoforming process

The thermoforming industry has been relatively slow to embrace modern measurement technologies. As a result researchers have struggled to develop accurate thermoforming simulations as some of the key aspects of the process remain poorly understood. For the first time, this work reports the development of a prototype multivariable instrumentation system for use in thermoforming. The system contains sensors for plug force, plug displacement, air pressure and temperature, plug temperature, and sheet temperature. Initially, it was developed to fit the tooling on a laboratory thermoforming machine, but later its performance was validated by installing it on a similar industrial tool. Throughout its development, providing access for the various sensors and their cabling was the most challenging task. In testing, all of the sensors performed well and the data collected has given a powerful insight into the operation of the process. In particular, it has shown that both the air and plug temperatures stabilize at more than 80°C during the continuous thermoforming of amorphous polyethylene terephthalate (aPET) sheet at 110°C. The work also highlighted significant differences in the timing and magnitude of the cavity pressures reached in the two thermoforming machines. The prototype system has considerable potential for further development. POLYM. ENG. SCI., 54:2815–2823, 2014. © 2014 Society of Plastics Engineers     

原油分离建模中的要点分析

Aspen Plus作为一种有效的模拟计算工具在装置筹建和改造中得到了广泛地应用,Aspen Plus在已建成装置实际生产中的应用受到原油性质、操作强度的影响,建立一个和实际过程完全吻合的模型比较困难.以常减压原油分离过程为例,阐述实际建模过程涉及的要点,提供的诸多方法可用于其他油品的分离计算.     

Improved ferroelectric properties of BiFeO3-based piezoelectric ceramics through morphotropic phase boundary construction

The ceramic (1-x)BiFe_0.985Sc_0.015O₃-xBaZr_0.2Ti_0.8O₃ + 1mol% MnO₂ (x = 0.20, 0.25, 0.30, 0.35) (BFS-xBZT) was synthesized using the traditional ceramic sintering method. The components of the ceramic were determined by constructing a morphotropic phase boundary (MPB) which consists of rhombohedral (R) and tetragonal (T) phases (0.24≤ x ≤ 0.26). With the accumulation of BZT content, relax behaviors were observed by dielectric properties measurements. At the MPB, the crystal structures of the R phase and T phase change abruptly. The distortion degree of the R phase increases, and the differences between a and c of the T phase decrease. An enhanced ferroelectricity Pr of ~27.8 μC/cm² and apex piezoelectric coefficient d₃₃ of 131 ± 4 pC/N are obtained near the MPB (x = 0.25), due to the R-T phase coexistence near room temperature. The results show that BFS-xBZT ceramics could be a candidate for lead-free piezoelectric ceramics at high operating temperatures.     

Mathematical modeling of the dispersed phase dynamics

A vector equation of motion in the Lagrangian frame of reference is rearranged into a set of two scalar equations to determine the relative-velocity magnitude of a particle and its direction. The resulting system, written in terms of the Lamé coefficients, is solved jointly with continuum equations of motion in the Eulerian frame of reference. The method is exemplified by the flow of a heterogeneous mixture between permeable parallel walls and the flow of a heterogeneous non-Newtonian fluid over the surface of a sedimentation centrifuge rotor.Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 2, 2005, pp. 206–215.Original Russian Text Copyright © 2005 by Kholpanov, Ibyatov.     

锌精矿沸腾焙烧两个关键工艺参数的选取

锌精矿的沸腾焙烧 ,无论是氧化焙烧还是酸化焙烧 ,其工艺参数的选取对锌焙砂质量有着相当大的影响 ,并且该工艺参数与硫铁矿沸腾焙烧相比有着较大的差别。重点介绍了锌精矿沸腾焙烧两个关键参数———焙烧温度和空气过剩系数对锌焙砂质量的影响 ,以及如何正确选取这两个参数     

LSSVM过程建模中超参数选取的梯度优化算法

基于结构风险最小的最小二乘支持向量机（least squares support vector machine, LSSVM）为标准支持向量机（SVM）的约简;训练简易;性能良好。其模型精度受超参数影响;常规的网络搜索法很难搜得最佳超参数。在快速留一法的基础上;以全样本留一预测误差平方和最小化为目标;导出基于梯度的最优化算法;用以优选为LSSVM超参数;进而构建G-LSSVM模型。以柠檬酸发酵过程为算例对G-LSSVM进行检验;结果表明G-LSSVM的超参数选取耗时少;模型稳定性良好;且拟合和预报性能都优于标准SVM和神经网络。有望适用于机理不明、高度非线性、小样本的化工过程建模。     

Mathematical modeling and the estimation of parameters for the melt viscosity of polyamides

Capillary rheometry data of a range of commercial polyamide engineering materials was obtained from a mould-flow analysis material database, from which melt viscosity data was obtained at different temperatures, which made comparison of the viscosities difficult. In an attempt to make a reasonable comparison between the melt viscosities of the various polyamide materials at different temperatures, it was necessary to obtain the mathematical functions which describe the relationships between: (i) the melt viscosity and the shear rate, (ii) the melt viscosity and temperature and (iii) the melt viscosity and the combined effect of the shear rate and temperature of each of the polyamides studied. Therefore, melt viscosity was modelled as a function of shear rate at the three temperatures (275°C, 295°C and 315°C), at which the viscosities were determined. The function obtained represented smoothed versions of the experimental data, eliminating the experimental noise and enabling the generation of melt viscosity data at the six different shear rates of the original data. It was established that the melt viscosity as a function of shear rate at constant temperature, in the shear rate range 500-700 s m 1 , is incorrectly described by the Ostwald-de-Waele's model, \eta_{\rm T}={\rm f}({\dot \gamma})={\rm K}({\dot \gamma})^{({\rm n}-1)} , while the melt viscosity of the polyamides studied, as a function of temperature, is correctly described by the model \eta_{\dot \gamma}={\rm g}{(\rm T)}={\rm Pe}^{\left (\rm {QT/R}\right )} . But the response-surface melt viscosity is effectively described as a function of both shear rate and temperature by the model: \eta=\vert {\dot \gamma}\vert^{(\rm n-1)}{\rm Ae}^{(\rm ET/R)} . The parameters A, E and n are highly interrelated as they all influence the average melt viscosity. All are temperature sensitive and also, to some degree, shear sensitive.     

Some parameters of spinning poly-p-phenylene terephthalamide fibres through an air gap

The spinneret draw ratio for jets of LC solutions of PPTA (range of 1 to 10) is a basic parameter in spinning of high-strength fibres through an air gap. The strength of the fibres is a function of the conditions of intense spinneret drawing of the jets of LC solutions of PPTA and the spinning speed. Most of the sulfuric acid (solvent) passes into the spinning bath as a result of brief contact of the jet of LC PPTA solution and fibres with it during spinning. Translated from Khimicheskie Volokna, No. 2, pp. 12–14, March–April, 1998.