A simplified method for analyzing mold filling dynamics Part I: Theory

A graphical method based on dimensional analysis is presented for estimating the injection pressure and clamp force required for injection molding amorphous polymers to form disk-shaped parts with a constant wall thickness. A procedure is suggested for estimating clamp force when the projected area of the mold cavity is smaller than the surface area of one side of the molded part. The results reported here are based on a numerical simulation of a power-law fluid filling a cold mold at a constant injection rate. The dimensionless bulk temperature and the ratios of the nonisothermal injection pressure (clamp force) to the isothermal injection pressure (clamp force) are given as functions of the dimensionless cooling time τ, the Brinkman number Br which characterizes viscous heating, the power-law exponent n, and a dimensionless temperature β which includes the inlet melt and mold wall temperatures and the temperature coefficient for viscosity.     

Filling of a complex-shaped mold with a viscoelastic polymer. Part II: Comparison with experimental data

An experimental program has been carried out on a reciprocating screw injection molding machine in order to establish the validity of a proposed mathematical model for the filling stage of injection molding. A cavity of complex shape with an insert and variable thickness was constructed and used in these experiments. Good agreement between predicted (through computer simulation) and observed (through short-shot experiments and transducer response) results is obtained for free surface shapes and free surface locations with time. The theoretical pressure predictions are in fairly good agreement with experiments, with the maximum deviations occurring towards the end of filling and for longer filling times. This points towards the possibility that wall solidification during filling interacts with the flow processes across the gap of the cavity and makes necessary a more detailed characterization of the heat transfer at the melt/mold interface.     

一种简捷计算磨机填充率的方法及应用

一般填充率的求得靠计算法和图表法较繁琐,笔者通过多年经验,并结合有关理论总结出 1个准确、简捷的计算磨机填充率公式,以供大家参考。 1 磨机填充率公式介绍 　　以我厂Φ 2. 2m× 6. 5m和Φ 1. 83m× 7m磨机在实际生产中的数据,利用最小二乘法可得： (1)式中：ψ──磨机中研磨体填充率,％; H──球面高度, m; D i──磨机有效内径, m。　　式 (1)能准确反应填充率与球面高度的关系。因为在实际生产中ψ的精度要求在小数点后一位数,则： (2)　　表 1为查《水泥厂工艺设计手册》中表所得的ψ值与公式 (2)计算所得的ψ值的比…     

Analysis of resin injection molding in molds with preplaced fiber mats. II: Numerical simulation and experiments of mold filling

This work presents the results of numerical simulation and experimental visualization of the mold filling process in resin injection molding with preplaced fiber mats. The mold filling experiments were conducted with various mat stacks consisting of continuous random glass fiber mats and bidirectional stitched glass fiber mats. The use of two different mat types in the mat stack created porosity and permeability variations. The effect of these permeability variations was studied by taking flow pressure measurements and observing the progress of the flow front of a non-reactive fluid filling a clear acrylic mold that contained the reinforcement mat stack. Numerical simulation corresponding to each experiment was also carried out. The numerical results were compared to the experimental measurements.     

A unified simulation of the filling and postfilling stages in injection molding. Part II: Experimental verification

The unified numerical simulation of the filling/postfilling stages of the injection-molding process described in Part I is compared in the present paper with experimental results obtained with instrumented test molds. Flush-mounted pressure traces in the delivery system as well as in the cavity are favorably compared with corresponding predictions for both an amorphous and a semicrystalline polymer. It is demonstrated that the present unified formulation is well suited to handle complicated molds where compressibility effects can become important even during the filling stage, as portions of the cavity fill and undergo a packing behavior even when other regions of the cavity are still only partially filled.     

Nature of contact between polymer and mold in injection molding. Part II: Influence of mold deflection on pressure history and shrinkage

In injection molding of thermoplastic parts, high hold pressures are set during the packing phase to generate a post‐filling, which compensates the shrinkage of polymer due to its cooling. The polymer pressure in mold cavity leads to a cavity deformation due to mold and machine compliance. Then, the increase in cavity thickness can modify the post‐filling and consequently the pressure history, the volumetric shrinkage and the part mass. The first goal of this paper is to present a simple method to locally determine mold rigidities: over‐packed slabs are injected and local deflections are determined from measurements of the local residual pressure, the local in‐plane shrinkages and the plate thickness. In the studied plate mold, which can be considered as stiff compared to some industrial molds, a rigidity of more than 1 μm/MPa has been measured close to the center of the plate. The second goal of this paper is to show the influence of mold deflection on dimensional properties. If the cavity thickness is small as for our 1‐mm‐thick plate mold, considering an infinitely rigid mold cannot do realistic predictions of polymer pressure history, volumetric shrinkages and part mass. Nevertheless, in‐plane shrinkage seems to be less affected by mold deflection. It means that the additional polymer mass due to mold deflection is mainly distributed in the part thickness.     

A Brownian dynamics simulation method for analyzing particle behavior in nonuniform and alternating electric fields

A new iterative Brownian dynamics simulation (BDS) method for analyzing the diffusive behavior of particles in an alternating electric field is proposed and tested in comparison with several previous techniques, including the most widely used BDS method developed by Ermak. To evaluate the proposed method with other schemes, particle trajectories in constant, AC, nonuniform DC in DMA, and quadrupole electric fields were obtained from each algorithm with various integration time steps. It is shown that the proposed BDS method is much more accurate at predicting the mean and variance of particle position for most cases. With respect to algorithm efficiency, the new scheme is about 5–50 times more efficient than the conventional BDS method for high-frequency AC electric fields. The simulation results for a particle beam generated in a quadrupole electric field show that the selection of a suitable algorithm and the proper size of time step are important for calculating system properties related to the diffusive motion of particles. In addition, a correction to the stochastic term is suggested and its effect investigated.     

Mold filling analysis in vacuum-assisted resin transfer molding. Part II: SCRIMP based on grooves

Compared with SCRIMP based on the high-permeable medium, SCRIMP based on grooves has the advantage of a much higher mold filling rate. This paper analyzes the influences of various molding conditions on mold filling and presents models that can be used to predict the filling time and flow pattern in SCRIMP based on grooves. Mold filling experiments were carried out to investigate the effect of various factors such as the size of the groove, groove spacing, number of fiber layers and resin viscosity on mold filling. A leakage flow model was developed to simplify the simulation of the mold filling process in SCRIMP based on grooves. An “equivalent permeability” was introduced to represent the average flow capacity in the grooves. Compared with the Control Volume/Finite Element Method (CV/FEM) model, the leakage flow model greatly reduced computation time and yet provided simulation results that were in good agreement with experimental observations.     

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.     

Combustion of fly-ash carbon: Part II: Thermodynamic aspects and calorimetric experiment

Thermodynamic aspects of carbon combustion are discussed. At lower temperatures (<400°C), carbon dioxide is the dominant species in the reacting system. Thermodynamic calculations indicate that at low temperatures methane can be produced. Based on literature data, the reaction rate of methane generation is low and therefore the methane combustion represents probably only a marginal contribution to the overall energy balance. Calorimetric experiments proved that impregnation of pelletized carbon fly-ash samples by sodium and/or potassium carbonates have beneficial effect on conversion of CO to CO₂. The value of the effective heat of combustion, calculated from CO and CO₂ outlet concentrations, increased for sample modified by Na₂CO₃ by 5% and for sample modified with K₂CO₃ almost by 20%.     

Kinetics of adsorption in bi-porous molecular sieves. Part II: Comparison of theory and experiment for batch systems

Experimental kinetic uptake curves for two sorbates (cis-2-butene from the gas phase and n-heptane from the liquid phase) have been measured in a variety of 5A molecular sieve pellets. Conditions were selected to fulfil either the linear isotherm approximation of the Ruckenstein⁽³⁾ model or the rectangular isotherm approximation of the preceding paper. For these systems both macropore and micropore diffusional resistances are significant and it is shown that the theoretical models provide a satisfactory interpretation of the experimental uptake curves. Time constants for both macropore and micropore diffusion, calculated by matching experimental and theoretical uptake curves, are consistent with independently measured values.     

储罐充装柴油与白油过程的静电实验

搭建储罐充装油品系统静电实验平台,实验测量镀锌金属管、金属骨架塑料软管、PVC管输油过程管道逸散电流以及采用底部管道输油、中间鹤管输油等不同充装方式时储罐内液面最大电势。实验结果表明：管道输送柴油过程中,管道导电能力越强管道内油品流动产生的静电荷越多,管道逸散电流越大;镀锌金属管道内油品开始流动,管道上静电荷即开始逸散,而PVC管内油品流动约3.5s后管道上静电荷开始逸散;输油管路中设置逸散罐可使油品中部分电荷逸散到大地,以减少储罐内静电荷输入量,可以使储罐内静电势降低约50%;储罐充装柴油过程中,中间鹤管输油比底部管道输油产生的液面最大电势小,但储罐充装白油过程则相反;储罐充装白油过程中,储罐是否接地对储罐内静电势的影响显著小于储罐充装柴油过程。研究结果对于指导充装方式、输油管道选取以及输油管路布置以降低静电危险性具有重要意义。     

Interface evolution and penetration behavior during two‐component transfer molding. Part II: Simulation and experiment

Simulation and experimental study of the pressure‐controlled sequential sandwich transfer molding of two SBR rubber compounds under isothermal condition have been carried out to obtain a two‐layered sandwich structure. One SBR compound, which is intended for the skin material, is first laid up in the cavity. Then, another SBR compound, intended for the core material, is transferred to penetrate into the skin material and to push the lay‐up to fully fill the cavity, resulting in an encapsulated skin/core sandwich structure. Two cases involving different material combinations with different viscosity ratios have been studied. The rheological interaction of the skin/core components and its effect on the penetration behavior and interface shape have been investigated. The influence of processing conditions, such as the volume fraction transferred and pressure, is discussed. The penetration and encapsulation behavior, and the interface development are found to be significantly affected by the rheological properties of the compounds and the volume fraction transferred. However, at a constant volume fraction transferred, the pressure imposed during transfer molding is found to have a little effect on the interface development. These experimental findings are in good agreement with the present predictions based on the model and simulation proposed in Part I of this study. Polym. Eng. Sci. 44:697–713, 2004. © 2004 Society of Plastics Engineers.     

Primary and secondary gas penetration during gas‐assisted injection molding. Part II: Simulation and experiment

Simulation and experimental studies have been carried out on the transient gas‐liquid interface development and gas penetration behavior during the cavity filling and gas packing stage in the gas‐assisted injection molding of a spiral tube cavity. The evolution of the gas/melt interface and the distribution of the residual wall thickness of skin melt along with the advancement of gas/melt front were investigated. Numerical simulations were implemented on a fixed mesh covering the entire cavity. The residual thickness of a polymer layer and the length of gas penetration in the moldings were calculated using both the simulation and model developed in Part I of this study and commercial software (C‐Mold). Extensive molding experiments were performed on polystyrene at different processing conditions. The obtained results on the gas bubble dynamics and penetration behaviors were compared with those predicted by the present simulation and C‐Mold, indicating the good predictive capability of the proposed model. Polym. Eng. Sci. 44:992–1002, 2004. © 2004 Society of Plastics Engineers.     

Filling of a complex-shaped mold with a viscoelastic polymer. Part I: The mathematical model

A model for the filling stage of injection molding of viscoelastic thermoplastics in cavities of complex shape is presented. The model considers two-dimensional melt flow, with converging and diverging flow patterns induced by complex boundary shape and by the presence of an obstacle. The model is non-isothermal (with the melt loosing heat to the mold walls as it travels into the cavity) and handles a viscoelastic (following the White-Metzner model) material with properties that vary with temperature, shear rate, and pressure. The numerical method is based on finite differences, with boundary fitted curvilinear coordinates used in the mapping of the flow field (which has an arbitrary shape that evolves with time) into a time invariant rectangle. The numerical results reveal geometry-induced asymmetries in the flow and thermal fields as well as the effect of various process parameters on the pressure and temperature profiles in the cavity. The model admits variable cavity thickness, thus allowing for a treatment of the cavity thickness as a process parameter in the simulations.     

A novel network-based continuous-time representation for process scheduling: Part II. General framework

In the first part of this series of papers we presented a new network-based continuous-time representation for the short-term scheduling of batch processes, which overcomes numerous shortcomings of existing approaches. In this second part, we discuss how this representation can be extended to address aspects such as: (i) preventive maintenance activities on unary resources (e.g., processing and storage units) that were planned ahead of time; (ii) resource-constrained changeover activities on processing and shared storage units; (iii) non-instantaneous resource-constrained material transfer activities; (iv) intermediate deliveries of raw materials and shipments of finished products at predefined times; and (v) scenarios where part of the schedule is fixed because it has been programmed in the previous scheduling horizon. The proposed integrated framework can be used to address a wide variety of process scheduling problems, many of which are intractable with existing tools.     

A unified simulation of the filling and postfilling stages in injection molding. Part I: Formulation

This study employs a unified theoretical model to simulate the filling and postfilling stages of the injection-molding process. Implementation of such a model is based on a hybrid finite-element/finite-difference numerical solution of the generalized Hele-Shaw flow of a compressible viscous fluid under nonisothermal conditions. The shear viscosity of the polymeric material is represented by a Cross model for the shear-rate dependence and a WLF-type functional form for the temperature and pressure dependence, whereas the specific volume is modeled in terms of a double-domain Tait equation. The analysis also handles variable specific heat and thermal conductivity of the polymer as a function of temperature. Complex thin parts of variable thickness can be modeled and discretized by flat, triangular finite elements which may have arbitrary orientation in three-dimensional space, whereas runners and possible round pins or bosses in the part are represented as one-dimensional circular-tube elements. A control-volume scheme is employed that leads to automatic melt-front advancement during the cavity-filling stage.     

Physico-Chemical Criteria for Maximum Adhesion. Part II: A New Comprehensive Thermodynamic Analysis

In this paper, two parameters defined as the relative work of adhesion [W_A/γ_L] and the relative interfacial energy [γ_SL/γ_L] have been examined for their assumed usefulness in correlating the thermodynamic properties of the components of the system substrate/ adhesive with its practical performance (strength). It is shown that the minimum value of [γ_SL/γ_L] relevant to conditions for the maximum adhesion becomes zero only for those systems (relatively rare) for which interaction factor Φ₀ is equal to 1.0.

Several transition points were identified for boundary conditions acquired at θ = 0° and θ = 90° which can be used to predict the properties and performance of an adhesive joint. These transition points are: a_MIN—energy modulus of the system (E. M. S.), relevant to the minimum interfacial energy; a_S—E. M. S. where self-spreading of adhesive occurs; a_CRIT—E. M. S. relevant to conditions under which the thermodynamic work of adhesion becomes negative and the system exhibits a tendency for self-delaminating or has “zero-strength”; a_CF—E. M. S. beyond which the geometry of the interface at any interfacial void or boundary of the joint may be regarded as a crack tip.

It is shown that only in those systems for which Φ₀ = 1.0 can a minimum contact angle of 0° indicate a condition for the maximum strength. If Φ₀ is known, the optimum contact angle can be estimated and hence the optimum surface energy of the substrate (adjusted by surface treatment, etc.) for the maximum adhesion.