Integrated simulations of structural performance,molding process,and warpage for gas‐assisted injection‐molded parts. III. Simulation of cyclic,transient variations in mold wall temperatures

Whether it is feasible to perform an integrated simulation for structural analysis, process simulation, as well as warpage calculation based on a unified CAE model for gas‐assisted injection molding (GAIM) is a great concern. In the present study, numerical algorithms based on the same CAE model used for process simulation regarding filling and packing stages were developed to simulate the cooling phase of GAIM considering the influence of the cooling system. The cycle‐averaged mold cavity surface temperature distribution within a steady cycle is first calculated based on a steady‐state approach to count for overall heat balance using three‐dimensional modified boundary element technique. The part temperature distribution and profiles, as well as the associated transient heat flux on plastic–mold interface, are then computed by a finite difference method in a decoupled manner. Finally, the difference between cycle‐averaged heat flux and transient heat flux is analyzed to obtain the cyclic, transient mold cavity surface temperatures. The analysis results for GAIM plates with semicircular gas channel design are illustrated and discussed. It was found that the difference in cycle‐averaged mold wall temperatures may be as high as 10°C and within a steady cycle, part temperatures may also vary ∼ 15°C. The conversion of gas channel into equivalent circular pipe and further simplified to two‐node elements using a line source approach not only affects the mold wall temperature calculation very slightly, but also reduces the computer time by 95%. This investigation indicates that it is feasible to achieve an integrated process simulation for GAIM under one CAE model, resulting in great computational efficiency for industrial application. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 339–351, 1999     

Simulation of a mold‐cooling process for gas‐assisted injection molded parts designed with a top rib on the gas channel

The same CAE model used for the filling and packing stage in the gas‐assisted injection molding (GAIM) process simulation was also applied to simulate the cooling phase. This was made possible by using the line source method for modeling cooling channels. The cycle‐averaged and cyclic transient mold cavity surface temperature distribution within a steady cycle was calculated using the three‐dimensional modified boundary element technique similar to that used in conventional injection molding. The analysis results for GAIM plates of a semicircular gas channel design attached with a top rib are illustrated and discussed. It was found that the difference in cycle‐averaged mold wall temperatures may be as high as 10°C, and within a steady cycle, part temperatures may also vary by about 15°C. The conversion of the gas channel into equivalent circular pipe and further simplification into two‐node elements using the line source method not only affects the mold wall temperature calculation very slightly but also reduces the computer time by 93%. This indicates that it is feasible to achieve an integrated process simulation for GAIM under one CAE model, resulting in great computational efficiency for industrial application.     

注塑模典型截面温度场的数值分析

通过二维典型截面简化模具的三维结构,建立了注塑模典型截面温度场的边界积分方程,并进行数值求解。将模具温度分为稳态和波动两部分,稳态部分是采用循环平均假设,推导出求解模具典型截面二维稳态温度场的边界积分方程。然后利用边界元法,分别对动模和定模进行传热分析,根据分型面边界相容性条件进行耦合;波动部分是在给出温度波动的微分方程后,利用有限差分法结合传热学对型腔表面温度波动进行数值求解。最后通过实例验证了文中算法的正确性与有效性。     

加热过程的滚塑模具内表面传热系数的计算

给出了2种计算加热过程的圆筒形滚塑模具内表面传热系数的方法。第一种方法是利用模具表面和内部温度的实测值通过模具内部空间的热平衡方程计算出其内表面传热系数。第二种方法是借用回转窑内物料与壁面间传热系数的理论公式来计算滚塑模具内表面的传热系数。在模具内部无粉料和装有0.21 kg粉料的情形下,分别用这2种方法计算了模具内表面瞬时的传热系数和平均的传热系数,并应用流体力学的边界层理论解释了内表面传热系数随时间的变化规律。然后将第一种方法计算所得的平均传热系数整理成努塞尔数与普朗特数的无量纲准则式N_u= 45.73 P_r ^-0.55,其适用条件为绕中心轴转动的轴向长度大于内径的圆筒形滚塑模具。结果表明,随着模具内装有粉料的体积百分比的增大,其内表面的平均传热系数减小,同时上述2种方法计算的平均传热系数也吻合得越来越好;如果粉料的体积百分比不低于62.4 %,那么第二种方法计算结果的相对误差不超过20 %。     

Numerical Simulation for Injection Molding with a Rapidly Heated Mold,Part I: Flow Simulation for Thin Wall Parts

The rapid thermal response (RTR) injection molding is a novel process developed to raise the mold surface temperature rapidly to the polymer melt temperature prior to the injection stage and then cool rapidly. The resulting filling process is achieved inside a hot mold cavity by prohibiting formation of frozen layer so as to enable thin wall injection molding without filling difficulty. The present work covers flow simulation of thin wall injection molding using the RTR molding process. Both 2.5-D shell analysis and 3-D solid analysis were performed, and the simulation results were compared with the prior experimental results. Coupled analysis with transient heat transfer simulation was also studied to realize more reliable thin-wall-flow estimation for the RTR molding process. The proposed coupled simulation approach based on solid elements provides reliable flow estimation by accounting for the effects of the unique thermal boundary conditions of the RTR mold.     

基于有限元离散的不规则管道几何边界红外瞬态检测识别

建立了带有不规则腐蚀内边界的管道二维瞬态传热模型,基于有限元法和共轭梯度法的导热反问题求解方法对管道内边界识别问题进行了研究,比较分析了管道外表面稳瞬态温度对内边界变化敏感程度的差异性,指出内边界瞬态检测识别比稳态检测识别更具优越性并利用数值试验进行了验证。同时,考察了测温误差、初始假设等因素对管道内边界瞬态检测识别结果的影响。在较大测温误差的情况下,采用瞬态检测条件从不同初始假设值出发都能准确地反演识别出管道内边界腐蚀后的几何形状,从而证明了算法的有效性和稳定性,表明了红外瞬态检测定量识别管道内边界的可行性。     

TRANSIENT MIXED CONVECTION ALONG A VERTICAL PLATE EMBEDDED IN POROUS MEDIA WITH INTERNAL HEAT GENERATION AND OSCILLATING TEMPERATURE

The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near the wall will be higher than the wall temperature, thus increasing buoyancy forces inside the boundary layer and consequently increasing the velocity. The increase of energy absorption term for either space or temperature dependence will decrease the velocity inside the boundary layer and increase heat transfer rates. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values for Nusselt numbers as well as local skin friction coefficient are also tabulated.     

TRANSIENT MIXED CONVECTION ALONG A VERTICAL PLATE EMBEDDED IN POROUS MEDIA WITH INTERNAL HEAT GENERATION AND OSCILLATING TEMPERATURE

The effects of oscillating plate temperature on transient mixed convection heat transfer from a porous vertical surface embedded in a saturated porous medium with internal heat generation or absorption are studied. The governing equations are transformed into dimenionless form by a set of variables and solved using the Galerkine finite element method. As the energy generation increases, the temperature near the wall will be higher than the wall temperature, thus increasing buoyancy forces inside the boundary layer and consequently increasing the velocity. The increase of energy absorption term for either space or temperature dependence will decrease the velocity inside the boundary layer and increase heat transfer rates. Different temperature and velocity profiles are drawn for different dimensionless groups. Numerical values for Nusselt numbers as well as local skin friction coefficient are also tabulated.     

Calculation of Temperature Distributions during the Solidification Stage in Ceramic Injection Molding

A finite difference procedure for calculating unsteady-state temperatures in a molded ceramic–polymer suspension during solidification is described. The method incorporates temperature-dependent thermal diffusivity and enthalpy of fusion of the polymer. An experimental method is used to assess the surface heat transfer coefficient h at the mold wall. It is found that at low injection pressures h varies with time as the molded body shrinks from the wall, but at high injection pressures h can be treated as constant throughout the solidification stage. Using an analytical method, graphical charts are produced for dimensionless temperature as a function of dimensionless time for values of Biot's modulus in the region relevant to ceramic injection molding.     

Coupled Part and Mold Temperature Simulation for Injection Molding Based on Solid Geometry

This paper presents a coupled method that determines the interface temperatures by filling and cooling analyses simultaneously to simulate the mold and part temperature distributions for injection molding. The mold temperature is assumed to be changing and is calculated with melt together at the filling stage instead of keeping constants as is usually done in conventional methods. The mold temperature is first determined with a 3-D finite element method by specifying the heat-flow rate at the interface between mold and part. Then the finite difference approach is employed to solve the melt thermal problem to get melt temperature distributions inside the cavity and the heat-flow rate at the interface. The under-relax scheme is used to correct the boundary condition and to resolve both mold and melt thermal problems until the solutions are convergent. This method can simulate transient and multicycle problems with more complex process conditions. The simulated results agree with experimental data.     

Rotational molding of plastics: Comparison of simulation and experimental results for an axisymmetric mold

We present a validation study comparing the mold wall temperature estimates from an axisymmetric thermal finite element simulation of the rotational molding process with temperature data obtained during experiments conducted on industrial‐grade rotational molding equipment. The finite element model simulates the heat transfer processes involved in rotational molding through the end of powder deposition, and uses an Arbitrary Lagrangian Eulerian technique to track the growing molten plastic layer. The experiments were conducted with nine different operating conditions on a single axisymmetric mold shape. The simulation results for mold wall temperature agreed well with the experimental data under all of the conditions tested.     

Experimental heat transfer study on impinging,turbulent, near-critical water jets confined by an annular wall

Polycrystalline rock can be fragmented and penetrated, when hot supercritical water jets impinge on it. Knowledge about the heat transfer between supercritical water jets and the rock's surface is absolutely crucial for this drilling method called hydrothermal spallation rock drilling. The present work for the first time provides systematic heat transfer data of impinging, turbulent, near- and supercritical water jets confined by a cylindrical wall. The most striking result is the dependence of heat transfer coefficients on the surface temperature of the impingement plate: experiments at supercritical jet temperatures performed with two different calorimeter types show remarkable differences between heat transfer coefficients obtained with low surface temperatures (at high heat fluxes) and high surface temperatures (at low heat fluxes). However, the experimental data of both calorimeters could be incorporated in a single empirical correlation by accounting for the variation of individual fluid properties across the jet's thermal boundary layer.     

Optimal thermal design of compression molds for chopped-fiber composites

Because heat is convected by the motion of material in the cavity of a compression mold, the time-averaged heating load on the cavity surface is nonuniform. In rapid production of large, thin parts, this can lead to large variations in cavity surface temperature when the mold is heated by the usual uniform distribution of heating lines. In this paper, a new method is developed for optimizing the mold heating design so that this nonuniform heating requirement can be satisfied with a minimum variation in cavity surface temperature. Oil heating is considered specifically, but the method can also be used for stream or electric heat. The optimal position and power supply for each heating line in the mold is determined by combining mathematical programming techniques with an analysis of the steady temperature field in the mold. The nonuniform heating load on the cavity surface is represented by a time-averaged steady heat transfer coefficient calculated from the transient temperature distribution in a polyester sheet molding compound as it fills the mold cavity. The design method is applied to an example mold for a large flat panel. At a one-minute cycle, the optimal heating design dramatically reduces nonuniformity in cavity surface temperature compared with a conventional distribution of heating lines. The optimal design is remarkably simple, uses only conventional equipment, and involves only half the customary number of heating lines. Nevertheless, it still has sufficient flexibility to adjust for changes in cycle time without sacrificing uniformity in cavity surface temperature.     

在加热阶段滚塑模具内表面传热系数的两种研究方法

提出了获得电加热滚塑模具内表面传热系数的两种研究方法，这两种方法适用于模内粉料开始熔融前的加热阶段。第一种方法是首先在4种情形下测量该滚塑模具的外表面温度和模内温度，然后根据能量守恒原理建立一个传热模型，并通过该模型将这些实测的温度值转换为在这4种情形下模具的内表面传热系数。第二种方法是将实际的滚塑模具等效地简化为一个二维圆筒，将模内空气当成主相流体，粉料当成第二相流体，通过FLUENT软件的多相流模块中的Mixture模型进行仿真计算以得到模具内表面的传热系数。结果表明，这两种方法所得的结果在其中的3种情形下都吻合得很好。随着模内粉料的体积百分比的增加，模具的内表面传热系数先是快速增大，然后增大的速率变慢，在达到最大值61.2 W/（m²·K）后开始减小。当粉料的体积百分比不在58 %~74 %的范围内，由第二种方法仿真所得的模具内表面传热系数的相对误差不超过10 %。     

管内对流换热系数的瞬态测量方法

<正>1前言 直接测定对流换热系数的方法分稳态法和瞬态法,前者对实验条件要求苛刻.近年来,瞬态法倍受人们关注”-”.Hausen和Kast’‘·”相继阐述了利用周期变化的流体温度在固体壁内的传播特性确定对流换热系数的原理,即根据流体与固体温度变化之间的相位角滞后（或振幅衰减）确定对流换热系数.Roetzel‘”提出了一套适用于任意形式周期振荡流体温度的瞬态测量方法. 对实测的流体温度波Tf（t）,利用傅里叶级数分析方法把Tf＊）展开为傅里叶级数,其一次谐波正弦和余弦函数项的系数表述为 u。——一Ill（t）Slnwtdt.u。——一11’（）cosnddt（l）则一次谐波可表达为 01。“fslflO此十贝）（2）式（2）中,振幅u;一 Vu: + ug,相位角9一 arc ig（uc/us）,一次谐波的周期 P—Zt。,角速度。一。八。2 测量基础2.1 模型A——霉壁面导热热阻 忽略管壁导热热阻,管壁的能量方程为 厂dL川t一。S叮f一几）一兄凡（几一瓦）（3）若求得的管壁周期振荡温度的一次谐波为Tw（t）一u。sinnd,则流体温度超前相位角9和振幅U;分别为 .y.,o\ It【._o\“工_P_\“ 9”sfCtg WN .Ut=U。。l---- W l e -- （4）一旦实际测得相位角差贝或振幅比ff八。,即可确定对流换热系数。;.显然,当ac《a时,管外对流换热的影响甚小.当液体在管     

Fast Calculating Method and In-Mold Labeling Model for Cooling Analysis in Injection Molding

Cooling analysis with the boundary element method (BEM) forms full-matrix equations in injection molding. Computers have no ability to handle it when the element number is more than its acceptance. This paper adopts the elements incorporation method. It changes the original model from one large matrix equation to one small union matrix equation and several small block matrix equations. In this way, the calculation time is shortened considerably and the treatable number of element in cooling analysis is enhanced dramatically. In-mold labeling processing, which adds a label on part surface in the mold is a new technology, and it is becoming more and more popular. It affords the mold designer far greater latitude in the design of graphics, part shape, and the use of multiple molded components in a single molded unit. Its simulation is a new task in computer aided engineering (CAE). This paper is based on the feature that the cavity surface is always meshed into planar triangular elements, Supposing that the label and part are two plates with perfect contact, establishes a one dimensional unsteady heat transfer model under the first dissymmetry boundary for each element. Using this heat transfer model, the cooling analysis model of in-mold labeling is established.     

直接电加热滚塑工艺的传热分析

通过实验测量了直接电加热的滚塑模具在加热阶段的表面温度和模内温度以及所消耗的电能。然后根据实验数据对该滚塑工艺的加热阶段进行了传热分析,计算了有效热能和无效热能,并提出了评估该滚塑工艺的3个指标参数——热能利用率、加热每单位质量粉料所消耗的电能、加热每单位质量粉料所需的时间。结果表明,该滚塑模具的表面温度具有一定的不均匀性,不同位置处的最大温差为8 ℃。3种实验情形下的最高热能利用率为37.5 %,另外在相同的模内加热温度下,热能利用率随模内粉料质量的增大而减小。     

Numerical study of transient heat transfer performance for molten salt receiver tube

The heat transfer experimental system and mathematical model of receiver tube are established to analyze the transient heat transfer performance of molten salt with heat flux of outer wall sudden change, molten salt velocity sharp reduction, heat flux of outer wall and molten salt velocity sharp reduction at the same time. The results show that when the heat flow on the outer wall of the tube changes suddenly (sudden increase or decrease), the temperature of the molten salt in the center of the tube at the inlet section of the heat absorption tube changes less, but the temperature of the tube wall changes faster. When the molten salt velocity sharp reduction, the outlet temperature of molten salt and the outer wall temperature increase with time, but the difference of outer wall and inner wall temperature decreases at first and then increases, when t≥16.0 s, each temperature and temperature difference reach steady state. When the heat flux on the outer wall of the heat absorption tube and the molten salt flow rate in the tube are halved at the same time, the temperature of the molten salt in the center and the outlet of the tube rises first and then decreases with the passage of time. After the steady state, the two molten salt temperatures maintain a constant value and are compared with the transient state. The corresponding molten salt temperature is close to initial starting temperature. The difference of outer wall and inner wall temperature after transient stability is proportional to the heat flux of outer wall, but which is independent of molten salt velocity. The outlet temperature equation of molten salt in receiver tube after transient stability is obtained, which provides a theoretical basis for the outlet temperature control of molten salt in receiver during the transient heat transfer process.     

熔盐吸热管瞬态传热特性的数值研究

建立熔盐吸热管瞬态传热的实验台和数值计算模型,分析管外壁热通量突变、熔盐流速突减、外壁热通量和熔盐流速同时突减对吸热管瞬态传热特性的影响规律,结果表明：管外壁热通量突变（突增或突减）时,吸热管入口段的管中心熔盐温度变化较小,但其管壁温度变化较快。管内熔盐流速突减时,熔盐出口温度和管外壁温度均随时间的推移逐渐增大,而管外壁与管内壁温差随时间的推移先降低后升高,t≥16.0 s,各温度和温差基本稳定。吸热管外壁热通量和管内熔盐流速同时减半时,管中心及出口熔盐温度均随时间的推移先升高后降低,稳态后两处熔盐温度保持定值且与瞬态开始前对应熔盐温度接近。吸热管瞬态稳定后的管外壁与管内壁温差和管外壁热通量变化呈正比,与熔盐流速变化无关。得到瞬态稳定后吸热管熔盐出口温度表达式,为瞬态传热过程中吸热器熔盐出口温度控制提供理论依据。     

Gas assisted injection molding of a handle: Three‐dimensional simulation and experimental verification

Methods implemented in a three‐dimensional finite element code for the simulation of gas assisted injection molding are described, and predictions compared with the results of molding trials. The emphasis is on prediction of primary gas penetration and plastic wall thickness, including the effects of cooling during a delay before gas injection. For the latter, time dependent heat transfer coefficients at the cavity surface are used, determined in a separate analysis of transient heat conduction through the plastic and the mold tool to the circulating coolant. This shows how the initial value of 25,000 W/m²K falls by about an order of magnitude during the first few seconds of cooling, and also how values vary from cycle to cycle as steady periodic conditions are approached. For a tubular handle molded in polystyrene, with melt flow modeled by a Cross WLF model, comparisons of simulations with sectioned parts show excellent prediction of wall thickness and its variation circumferentially and in bends. The increase in wall thickness due to cooling during a gas delay is accurately modeled, as is the occurrence of a blow out. POLYM. ENG. SCI. 45:1049–1058, 2005. © 2005 Society of Plastics Engineers