Numerical simulation of the filling behavior of a Non-Newtonian Fluid

A numerical model for free surface flows of non-newtonian liquids which are injected into a cavity is presented. These flows are regarded as a basic model of injection molding. Model experiments of the injection process are performed with a water-based gel. The flow equations are integrated according to the finite-volume-method. The volume of fluid method (VoF) is employed in order to describe the free surface flow of two incompressible phases, the phase interface is resolved by the method of geometric reconstruction. The Herschel-Bulkley model is used in order to describe shear-thinning behavior of the molding material and the effects of a yielding point. Different patterns of the filling flow depending on the injection parameters are evident in the experiment and the simulation. They are characterized and arranged with respect to the similarity parameters of the flow. Again, the results of the simulation are found to agree well with the experimental observations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extension of SPH to simulate non-isothermal free surface flows during the injection molding process

This article presents an extension of smoothed particle hydrodynamics (SPH) to non-isothermal free surface flows during the injection molding process. Specifically, we use the method presented by Xu and Yu, Appl. Math. Model. 48 (2017) pp. 384–409, in which the corrected kernel gradient is implemented to increase the computational accuracy and the Rusanov flux is introduced into the continuity equation to alleviate large and random pressure oscillations. To model non-isothermal free surface flows, a working SPH discretization of the temperature equation is derived. An enhanced treatment of the wall boundary is further developed, which can model arbitrary-shaped mold walls. The proposed SPH method is first validated by solving non-isothermal Couette flow and non-isothermal injection molding of a circular disc with a core and comparing the SPH results with those obtained by other numerical methods or experiments. We then extend the numerical method to non-isothermal injection molding of F-shaped and N-shaped cavities. The convergence of the method is examined with several different particle sizes. The effects of the operating conditions (e.g., injection temperature, temperature of the mold wall, and injection velocity) on the flow behavior are analyzed. All the results illustrate that the present SPH method is a powerful computational tool for simulations of non-isothermal free surface flows during the injection molding process.     

Ⅰ型拉伸试样金属注射成形多相流动的三维数值模拟

将粉末注射成形充模过程视为粘结剂、粉末和空气的三相流动过程,基于多相流理论给出金属注射成形的多相流动控制方程。根据金属注射成形的工艺特点确定多相流动控制方程的初边界条件,用多相流数值分析软件CFX对Ⅰ型拉伸试样的铁粉注射成形充模流动过程实现了三维数值模拟,分析了模腔中不同位置处粘结剂一粉末流动的速度曲线。数值模拟结果表明在Ⅰ型拉伸试样金属注射成形充模流动过程中发生过两相分离的现象,数值模拟的瞬态信息可用于金属注射成形产品缺陷的分析与控制。     

Analysis of the filling capability to the microstructures in micro-injection molding

Micro-injection molding is an important fabrication process for polymer plastics with micro-features. In micro-injection molding of products with microstructures, the ability for the polymer melt to flow into the microstructures is a crucial factor for successful molding. An analytical model in micro-injection molding is constructed in this research. It has been reported that most of the filling in microstructure is done during the packing pressure. In this analytical model, the temperature of the polymer melt near the entrance of the microstructure at the end of mold filling is estimated first. With the temperature, we can calculate the injection distance into the microstructures of the mold insert during the packing stage. The model is compared with experimental results, and shows the feasibility. The experiment uses the LIGA-like lithography process to define the micro-feature and a micro-electroforming method to form the mold insert with the replicated micro-feature. The injection distance into the microstructures predicted by this analytical model shows reasonable result as compared to the experimental measurement.     

Modeling and simulation of injection molding process of polymer melt by a robust SPH method

In the present study, the injection molding process of polymer melt based on the generalized Newtonian fluid model is investigated by a robust smoothed particle hydrodynamics (SPH) method. The numerical method is proposed by introducing a Rusanov flux into the continuity equation to improve the prediction of the pressure distribution and employing a corrected kernel gradient to improve the computational accuracy. In addition, a robust treatment of solid boundary is presented and verified by the spin-down problem. The merits of the robust SPH method are firstly illustrated by 2D dam breaking flow. Then the numerical method is extended to deal with the flow phenomena related to injection molding process of polymer melt. A number of numerical examples including 2D injection moldings of a thin plate mold, a circular disc with core, a ring-shaped channel, and a S-shaped cavity, and 3D injection moldings of a Z-shaped cavity and a four-legged fork are conducted. The numerical results are in agreement with the experiments, which demonstrate that the SPH method proposed here is capable of handling with injection molding process of polymer melt in a robust manner. Moreover, the robust SPH method allows to recover the fluctuations-free pressure and velocity fields which in most cases cannot be easily obtained by the traditional SPH method.     

Eine Kennzeichnung der Regel- und Gesimsflächen

We study two classes of surfaces in euclidean 3-space, namelyruled andmolding surfaces, specialsurfaces of revolution (molding surfaces are covered by a plane curve if the plane is rolling over a torse, in particularsurfaces moulures by G.MONGE for a cylindrical torse). The main result: A connected surface hyperosculating molding surfaces in every point is contained in a ruled or in a molding surface; a connected surface hyperosculating in every point surfaces of revolution is a surface of revolution. We characterize hyperosculating molding surfaces by means of the generating torse and study finally molding surfaces having contact of higher order.     

CFD-based predictive control of melt temperature in plastic injection molding

A unique method of coupling computational fluid dynamics (CFD) to model predictive control (MPC) for controlling melt temperature in plastic injection molding is presented. The methodology is based on using CFD to generate, via open-loop testing, a temperature and input dependent system model for multi-variable control of a three-heater barrel on an injection molding machine. Results clearly show the benefit of temperature and input dependent system models for MPC control, and that CFD can be used to dramatically reduce the time associated with open-loop testing through physical experiments.     

Effect of process parameters on injection compression molding of pickup lens

The residual stresses and shrinkages of pickup lens in injection compression molding are investigated in this study. It was realized that the behavior of residual stresses in injection compression molding parts was affected by different process conditions such as melt temperature, mold temperature, compression pressure and time. Moldings under different conditions were numerically investigated to study the effects of the process conditions on the residual stresses and shrinkage of a pickup lens with large thickness variations. The mold temperature and compression were found to be the most important factors that affect the shrinkage of lens in the thickness direction, resulting in surface profile deviation. The effect of heat transfer coefficient of the mold wall used in the molding simulation was also discussed.     

Optimization of the injection molding process for short-fiber-reinforced composites

A fast and effective methodology integrating the finite-element and Taguchi methods is presented to determine the optimal design conditions of the injection molding process for short-fiber-reinforced polycarbonate composites. The finite-element-based flow simulation software, M-flow, was employed to simulate the molding process to obtain the fiber orientation distributions required. The Taguchi optimization technique was used to identify the optimal settings of injection molding parameters to maximize the shear layer thickness. The effects of four main parameters — the filling time, melt temperature, mold temperature, and injection speed — on the fiber orientation or the shear layer thickness were investigated and discussed. It is found that the dominant parameter is the filling time. The best levels of the four parameters to acquire the thickest shear layer are also identified.     

Rheology of Organodispersions of Alumina Nanopowders Used in Producing Articles from Engineering Ceramics

The rheological properties of molding suspensions of alumina nanopowder in paraffin have been studied. Powders with specific surface areas of 32 and 55 m²/g and the surface-active substances oleic acid and Hypermer LP1 were used. The Hamaker constant for alumina particles in paraffin wax was estimated. A rough calculation showed that a gel should arise in the suspensions studied. The linearly viscoelastic characteristics determined by the method of small-amplitude periodic shear (on the frequency range from 0.063 to 157 s⁻¹) confirmed this conclusion. The flow curves of the molding feedstock, determined over a broad range of shear rates (from 0.018 to 1070 s⁻¹), point to a pseudoplastic character of the flow. From the rheological studies it follows that, in manufacturing engineering ceramics by injection molding from the suspensions investigated and in designing or selecting the forming equipment, the realization of maximum high shear strains must be ensured, which will promote a qualitative filling of intricately shaped and small-size molds.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 373–390, May–June, 2005.     

Analysis of filling distance in cylindrical microfeatures for microinjection molding

In the injection molding of plastic components with cylindrical microfeatures, the ability for the polymer melt to flow into the microchannels is a crucial factor for successful molding. Penetration distance of the polymer melt into the microstructure depends on several factors as the melt flow rate and the cooling rate in the microfeatures, which depends on the materials and geometric dimensions. In this study, a simplified analytical model was constructed to estimate the filling distance into the cylindrical microchannels. The effects of the mold temperature, injection rate, heat transfer coefficient, and microchannel dimension on the filling distance were investigated. The filling distance decreases dramatically with respect to the decrease of the channel radius. In molding of plastic components with cylindrical microfeatures as those analyzed in this study, decrease of the part thickness could also increase the filling distance in the microfeatures.     

Control-oriented modeling of servo-pump driven injection molding machines in the filling and packing phase

Servo-valves or variable displacement pumps are typically used to control conventional hydraulic injection molding machines (IMMs). Recent developments in electrical drive technology allow to utilize servo-motor driven pumps instead, which is beneficial due to their higher energy efficiency. Their dynamic behavior, however, is significantly different compared to the conventional setup. Thus, currently used mathematical models and control concepts cannot be directly applied. This paper presents a computationally efficient and scalable mathematical model of the injection process for these servo-pump driven IMMs. A first-principles model of the injection machine is combined with a phenomenological model describing the injection process, i.e. the compression of the melt and the polymer flow into the mold. The proposed model is tailored to real-time applications and serves as an ideal basis for the design of model-based control strategies. The feasibility of the proposed model is demonstrated by a number of different experiments. They confirm a high model accuracy over the whole operating range for different mold geometries.     

On fat partitioning, fat covering and the union size of polygons

The complexity of the contour of the union of simple polygons with n vertices in total can be O(n²) in general. A notion of fatness for simple polygons is introduced that extends most of the existing fatness definitions. It is proved that a set of fat polygons with n vertices in total has union complexity O(n log log n), which is a generalization of a similar result for fat triangles (Matou ek et al., 1994). Applications to several basic problems in computational geometry are given, such as efficient hidden surface removal, motion planning, injection molding, and more. The result is based on a new method to partition a fat simple polygon P with n vertices into O(n) fat convex quadrilaterals, and a method to cover (but not partition) a fat convex quadrilateral with O(l) fat triangles. The maximum overlap of the triangles at any point is two, which is optimal for any exact cover of a fat simple polygon by a linear number of fat triangles.     

Influence of technological processing parameters on the properties of carbon filled thermoplastics

The effect of processing parameters of injection molding on the mechanical and tribotechnical properties of carbon plastics based on polyacetals is investigated. The copolymer of 1,3,5-trioxane with 1,3-dioxolane is used as the polymer matrix. Hydrated cellulose Ural LO-24 carbon fibers are used as the reinforcing filler. The effect of molding temperature, pressing time, and temperature of the casting mould on the properties of carbon plastics is investigated. It has been found that for improving the mechanical properties of carbon plastics it is necessary to raise the molding temperature up to 200–210°C. Prolongation of the technological cycle leads to thermal degradation of the polymer in the cylinder of a casting machine. The mould temperature only slightly affects the composite strength properties, but lower temperatures create better conditions for polymer crystallization. As a result of our investigations, the optimal processing parameters of the above carbon plastics are determined.Ukrainian State University of Chemical Technology, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 385–392, 1999.     

Numerical simulation of gas-assisted injection molding using CLSVOF method

It is a typical gas-liquid two phase flow phenomenon that gas penetrates the polymer melt in gas-assisted injection molding (GAIM) process. Numerical simulation is now playing an important role in GAIM, in which the accurate simulation of moving interface is of great importance. The level set (LS) method is a popular interface tracking method, but it does not ensure naturally mass-conservation. In order to improve the mass-conservation of LS method, a coupled level-set and volume-of-fluid (CLSVOF) method with mass-correction is presented for the numerical simulations of interfacial flows in GAIM. The performance of this CLSVOF method is demonstrated by two numerical tests including the three-dimensional deformation field test and the dam break problems. Finally the CLSVOF method is employed to simulate the 3D moving interfaces in GAIM, including gas-melt interface and the melt-front interface. The influences of melt temperature and gas delay time are also analyzed detailedly. As a case study, the processes that gas penetrates the polymer melt in complex cavities are also simulated using this method, and the simulation results are in agreement with those obtained by other researchers.     

Parallel Finite Element Software Development and Performance Analysis in an Object-Oriented Programming Framework

The use of object-oriented programming techniques in the development of parallel, finite element analysis software enhances code reuse and increases efficiency during application development. In this paper, an object-oriented programming framework developed by the authors is utilized in the implementation of parallel finite element software for modeling of the resin transfer molding manufacturing process. The motivation for choosing the resin transfer molding finite element application and implementing it with the object-oriented framework is that it was originally developed and parallelized in a functional programming paradigm thus offering the possibility of direct comparisons. Discussion of the software development effort and performance results are presented and analyzed.Mathematics Subject Classifications (2000) 65M60, 65Y05.     

Optimization of TQFP molding process using neuro-fuzzy-GA approach

This paper focuses on an integrated optimization problem that involves multiple qualitative and quantitative responses in the thin quad flat pack (TQFP) molding process. A fuzzy quality loss function (FQLF) is first applied to the qualitative responses, since the molding defects cannot be simply represented by the relationship between molding conditions and mathematical models. Neural network is then used to provide a nonlinear relationship between process parameters and responses. A genetic algorithm together with exponential desirability function is employed to determine the optimal parameter setting for TQFP encapsulation. The proposed method was implemented in a semiconductor assembly factory in Taiwan. The results from this study have proved the feasibility of the proposed approach.     

Rheological Properties of Nanosized AlN Powder Suspensions for Advanced Ceramics

The rheological properties (flow curves and viscoelastic behavior) of injection molding suspensions of a plasma-processed AlN nanosized powder (nanopowder) in paraffin are investigated over a broad range of shear rates (0.07–1350 s^–1). Two viscosity plateaux are observed on the flow curves and two values of the yield stress are obtained. The lower value of the strain amplitude (0.66%), exceeding the linearity limit of periodic shear, is restricted by the rheometer resolution. The ultrasound treatment and shear deformation of suspensions affect the structure of particle packing, which is responsible for the dependence of their rheological properties on the prehistory of mechanical actions.     

Numerical Estimation of the Elastic Properties of Thin-Walled Structures Manufactured from Short-Fiber-Reinforced Thermoplastics

A model which allows us to estimate the elastic properties of thin-walled structures manufactured by injection molding is presented. The starting step is the numerical prediction of the microstructure of a short-fiber-reinforced composite developed during the filling stage of the manufacturing process. For this purpose, the Moldflow Plastic Insight^® commercial program is used. As a result of simulating the filling process, a second-rank orientation tensor characterizing the microstructure of the material is obtained. The elastic properties of the prepared material locally depend on the orientational distribution of fibers. The constitutive equation is formulated by means of orientational averaging for a given orientation tensor. The tensor of elastic material properties is computed and translated into the format for a stress-strain analysis based on the ANSYSÒ finite-element code. The numerical procedure and the convergence of results are discussed for a thin strip, a rectangular plate, and a shell of revolution. The influence of manufacturing conditions on the stress-strain state of statically loaded thin-walled elements is illustrated.