Determination of the metal/die interfacial heat transfer coefficient and its application in evaluating the pressure distribution inside the casting during the high pressure die casting process

Abstract

High pressure die casting (HPDC) experiments were conducted on a 650 t cold chamber die casting machine to study the interfacial heat transfer behaviour between casting and die. A 'step shape' casting and two commercial alloys namely ADC12 and AM50 were used during the experiments. Temperature and pressure measurements were made inside the die and at the die surface. The metal/die interfacial heat transfer coefficient (IHTC) was successfully determined based on the measured temperature inside the die by solving the inverse heat transfer problem. The IHTC was then used as the boundary condition to determine the 3-D temperature field inside the casting. Based on the predicted temperature distribution, the pressure distribution inside the casting was evaluated by assuming that the transferred pressure from the plunger tip of the injection side to the casting is primarily influenced by the solid fraction of the casting. Reasonable agreement was found between the determined pressure values and the measured pressures at the die surface of the casting.     

镁合金铸造成形过程宏观／微观模拟

通过研究镁合金压铸过程中界面热,采用热传导反算法确定压铸过程的界面换热系数,研究镁合金压铸过程中工艺参数及凝固过程对铸件界面换热系数的影响规律,建立镁合金压铸过程界面换热边界条件的处理模型,以实现镁合金压铸过程中凝固过程的准确预测。通过实验研究镁合金压铸过程中凝固组织,建立了镁合金压铸过程中形核模型。采用CA方法,建立了镁合金枝晶生长模型,以实现镁合金凝固组织的预测。采用相场方法研究了镁合金枝晶生长形貌。     

Study on interfacial heat transfer coefficient at metal/die interface during high pressure die casting process of AZ91D alloy

The high pressure die casting (HPDC) process is one of the fastest growing and most efficient methods for the production of complex shape castings of magnesium and aluminum alloys in today's manufacturing industry. In this study, a high pressure die casting experiment using AZ91D magnesium alloy was conducted, and the temperature profiles inside the die were measured. By using a computer program based on solving the inverse heat problem, the metal/die interfacial heat transfer coefficient (IHTC) was calculated and studied. The results show that the IHTC between the metal and die increases right after the liquid metal is brought into the cavity by the plunger, and decreases as the solidification process of the liquid metal proceeds until the liquid metal is completely solidified, when the IHTC tends to be stable. The interfacial heat transfer coefficient shows different characteristics under different casting wall thicknesses and varies with the change of solidification behavior.     

Measurement of temperature inside die and estimation of interfacial heat transfer coefficient in squeeze casting

As an advanced near-net shape technology, squeeze casting is an excellent method for producing high integrity castings. Numerical simulation is a very effective method to optimize squeeze casting process, and the interfacial heat transfer coefficient (IHTC) is an important boundary condition in numerical simulation. Therefore, the study of the IHTC is of great significance. In the present study, experiments were conducted and a"plate shape" aluminum alloy casting was cast in H13 steel die. In order to obtain accurate temperature readings inside the die, a special temperature sensor units (TSU) was designed. Six 1 mm wide and 1 mm deep grooves were machined in the sensor unit for the placement of the thermocouples whose tips were welded to the end wall. Each groove was machined to terminate at a particular distance (1, 3, and 6 mm) from the front end of the sensor unit. Based on the temperature measurements inside the die, the interfacial heat transfer coefficient (IHTC) at the metal-die interface was determined by applying an inverse approach. The acquired data were processed by a low pass filtering method based on Fast Fourier Transform (FFT). The feature of the IHTC at the metal-die interface was discussed.     

Regularized determination of interfacial heat transfer coefficient during ZL102 solidification process

The interfacial heat transfer coefficient（IHTC） between the casting and the mould is essential to the numerical simulation as one of boundary conditions. A new inverse method was presented according to the Tikhonov regularization theory. A regularized functional was established and the regularization parameter was deduced. The functional was solved to determine the interfacial heat transfer coefficient by using the sensitivity coefficient and Newton-Raphson iteration method. The temperature measurement experiment was done to ZL102 sand mold casting, and the appropriate mathematical model of the IHTC was established. Moreover, the regularization method was used to determinate the IHTC. The results indicate that the regularization method is very efficient in overcoming the ill-posedness of the inverse heat conduction problem（IHCP）, and ensuring the accuracy and stability of the solutions.     

A study of metal/die interfacial heat transfer behavior of vacuum die cast pure copper

High pressure die casting copper is used to produce rotors for induction motors to improve efficiency. Experiments were carried out for a special "step-shape" casting with different step thicknesses. Based on the measured temperature inside the die, the interfacial heat transfer coefficient(IHTC) at the metal/die interface during vacuum die casting was evaluated by solving the inverse problem. The IHTC peak value was 4.5×10~3-11×10~3 W·m~(-2)·K~(-1) under the basic operation condition. The influences of casting pressure, fast shot speed, pouring temperature and initial die surface temperature on the IHTC peak values were investigated. Results show that a greater casting pressure and faster shot speed could only increase the IHTC peak values at the location close to the ingate. An increase of pouring temperature and/or initial die surface temperature significantly increases the IHTC peak values.     

Interfacial heat transfer behavior at metal/die in finger-plated casting during high pressure die casting process

Heat transfer at the metal-die interface has a great influence on the solidification process and casting structure. As thin-wall components are extensively produced by high pressure die casting process(HPDC), the B390 alloy finger-plate casting was cast against an H13 steel die on a cold-chamber HPDC machine. The interfacial heat transfer behavior at different positions of the die was carefully studied using an inverse approach based on the temperature measurements inside the die. Furthermore, the filling process and the solidification rate in different finger-plates were also given to explain the distribution of interfacial heat flux(q) and interfacial heat transfer coefficient(h). Measurement results at the side of sprue indicates that qmax and hmax could reach 9.2 MW·m~(-2) and 64.3 kW ·m~(-2)·K~(-1), respectively. The simulation of melt flow in the die reveals that the thinnest(T_1) finger plate could accelerate the melt flow from 50 m·s~(-1) to 110 m·s~(-1). Due to this high velocity, the interfacial heat flux at the end of T_1 could firstly reach a highest value 7.92 MW·m~(-2) among the ends of T_n(n=2,3,4,5). In addition, the q_(max) and h_(max) values of T_2, T_4 and T_5 finger-plates increase with the increasing thickness of the finger plate. Finally, at the rapid decreasing stage of interfacial heat transfer coefficient(h), the decreasing rate of h has an exponential relationship with the increasing rate of solid fraction(f).     

压铸过程中铸件-铸型界面换热系数与铸件凝固速率的关系

在实际压铸实验的基础上,求解了铸件一铸型界面换热系数h与铸件凝固速率v的关系.结果表明,二者呈线性变化关系:h=kh-v·v+ω(其中,斜率kh-v为铸型初始表面温度及铸件厚度的函数,ω为常数);通过线性拟合确定kh-v和ω值,从而确立换热系数与铸件凝固速率的关系.这种关系同时适用于镁合金AM50和铝合金ADC12.     

Effect of different processing parameters on interfacial heat-transfer behavior in high-pressure die-casting process

Vacuum die casting can reduce the “air entrapment” phenomenon during casting process. Based on the temperature measurements at metal–die interface with different processing parameters, such as slow shot speed (V_L), high shot speed (V_H), pouring temperature (T_p) and initial die temperature (T_m), inverse method was developed to determine the interfacial heat transfer coefficient (IHTC). The results indicate that a closer contact between the casting and die could be achieved when the vacuum system is used. It is found that the vacuum could strongly increase the values of IHTC and decrease the grain size in castings. The IHTC could have a higher peak value with increasing the T_p from 680 to 720 °C or the V_L from 0.1 to 0.4 m/s. In addition, the influence of the V_H and T_m on IHTC could be negligible.     

Characterization and Modeling Study on Interfacial Heat Transfer Behavior and Solidified Microstructure of Die Cast Magnesium AlloysEI北大核心CSCD

Magnesium alloys are widely used in various fields because of their outstanding properties. High-pressure die casting (HPDC) is one of the primary manufacturing methods of magnesium alloys. During the HPDC process, the solidification manner of casting is highly dependent on the heat transfer behavior at metal-die interface, which directly affects the solidified microstructure evolution, defect distribution and mechanical properties of the cast products. As common solidified microstructures of die cast magnesium alloys, the externally solidified crystals (ESCs), divorced eutectics and primary dendrites have important influences on the final performance of castings. Therefore, investigations on the interfacial heat transfer behavior and the solidified microstructures of magnesium alloys have considerable significance on the optimization of die-casting process and the prediction of casting quality. In this paper, recent research progress on theoretical simulation and experimental characterization of the heat transfer behaviors and the solidified microstructures of die cast magnesium alloys was systematically presented. The contents include: (1) A boundary-condition model developed based on the interfacial heat transfer coefficients (IHTCs), which could precisely simulate the boundary condition at the metal-die interface during solidification process. Accordingly, the IHTCs can be divided into four stages, namely the initial increasing stage, the high value maintaining stage, the fast decreasing stage and the low value maintaining stage. (2) A numerical model developed to simulate and predict the flow patterns of the externally solidified crystals (ESCs) in the shot sleeve during mold filling process, together with discussion on the influence of the ESCs distribution on the defect bands of die cast magnesium alloys. (3) Nucleation and growth models of the primary alpha-Mg phases developed by considering the ESCs in the shot sleeve. (4) Nucleation and growth models of the divorced eutectic phase, which can be used to simulate the microstructure evolution of die cast magnesium alloys. (5) The 3D morphology and orientation selection of magnesium alloy dendrite. It was found that magnesium alloy dendrite exhibits an eighteen-primary branch pattern in 3D, with six growing along < 11(2)over bar0 > in the basal plane and the other twelve along < 11(2)over bar3 > in non-basal planes. Accordingly, an anisotropy growth function was developed and coupled into the phase field model to achieve the 3D simulation of magnesium alloy dendrite.     

一种求解水平连铸中瞬态界面换热系数的新方法

为有效提高温度场数值模拟的准确性，对界面换热系数的模型进行了改进和参数化，并基于这个3阶段演变模型，提出了数值模拟与优化计算相结合的反向求解方法。针对水平连铸中出现的非均匀间隙情况，获得了与位置相关的界面换热系数。算例采用了两种合金Sn-5Pb和Sn-15Pb作为算例进行计算。优化结果表明，对于两种合金3个热电偶处的模拟温度与实测值最大相对误差不超过5％。     

Determination of heat transfer coefficients by extrapolation and numerical inverse methods in squeeze casting of magnesium alloy AM60

In this work, a different wall-thickness 5-step (with thicknesses as 3, 5, 8, 12, 20 mm) casting mold was designed, and squeeze casting of magnesium alloy AM60 was performed under an applied pressure 30, 60 and 90 MPa in a hydraulic press. The casting-die interfacial heat transfer coefficients (IHTC) in the 5-step casting were determined based on thermal histories throughout the die and inside the casting which were recorded by fine type-K thermocouples. With measured temperatures, heat flux and IHTCs were evaluated using the polynomial curve fitting method and numerical inverse method. For numerical inverse method, a solution algorithm was developed based on the function specification method to solve the inverse heat conduction equations. The IHTCs curves for five steps versus time were displayed. As the applied pressures increased, the IHTC peak value of each step was increased accordingly. It can be observed that the peak IHTC value decreased as the step became thinner. Furthermore, the accuracy of these curves was analyzed by the direct modeling calculation. The results indicated that heat flux and IHTCs determined by the inverse method were more accurately than those from the extrapolated fitting method.     

Spatial interfacial heat transfer and surface characteristics during gravity casting of A356 alloy

As one of the key boundary conditions during casting solidification process, the interfacial heat transfer coefficient (IHTC) affects the temperature variation and distribution. Based on the improved nonlinear estimation method (NEM), thermal measurements near both bottom and lateral metal-mold interfaces throughout A356 gravity casting process were carried out and applied to solving the inverse heat conduction problem (IHCP). Finite element method (FEM) is employed for modeling transient thermal fields implementing a developed NEM interface program to quantify transient IHTCs. It is found that IHTCs at the lateral interface become stable after the volumetric shrinkage of casting while those of the bottom interface reach the steady period once a surface layer has solidified. The stable value of bottom IHTCs is 750 W/(m²·°C), which is approximately 3 times that at the lateral interface. Further analysis of the interplay between spatial IHTCs and observed surface morphology reveals that spatial heat transfer across casting-mold interfaces is the direct result of different interface evolution during solidification process.     

带钢热轧过程中温度演变的数值模拟和实验研究

采用三维大变形弹塑性有限元法,耦合温度场和应力、应变场,应用ABQUS软件的二次开发用户子程序模块,建立了热轧过程 中的界面换热模型,对热轧IF带钢进行了温度场的数值模拟,开发了热轧过程中的是测温技术,在实验轧机对上带钢内部温度变化进行在线测量,以测结果修正了界面换热系数模型,利用所建立的传热模型对带钢热轧过程进行了模拟计算,考虑了轧制过程压下量、初始变形温度对温度场变化的影响,结果表明模拟与实测的温度场基本吻合。     

Microstructure Simulation of Al-Cu Alloy Based on Inverse Identified Interfacial Heat Transfer Coefficient

The interfacial heat transfer coefficient (IHTC) is taken as one of the most important factors affecting the accuracy of the simulation. In the present paper, the IHTC variation with temperature was obtained by an inverse heat conduction method. Then, a 3D cellular automaton-finite element method was adopted to predict the microstructure of an Al-Cu alloy based on the identified IHTC. It was found that the IHTC was of prime importance for the precise simulation of solidification microstructure, especially in the grains distribution. In addition, the simulated results using the IHTC variation with temperature were found to exhibit a better agreement with the experimental results than those using the constant value.     

Heat transfer behavior of top side-pouring twin-roll casting

The interfacial heat transfer between the casting and the substrate from liquid/solid contact to solid/solid contact with pressure was investigated using a set of equipment designed according to the characteristics of the top side-pouring twin-roll casting process. The interfacial heat transfer behavior of this process consists of 4 stages: chilling, solidification shrinkage, compression and cooling. High values of the IHTC ranging from 50,000 to 90,000 W/m² °C were detected in the chilling stage, followed by a sharp decrease in solidification shrinkage stage (4000–8000 W/m² °C). Due to the pressure, which modeled the effect of rolling in twin-roll casting, the IHTC bounced back to 6000–20000 W/m² °C, according to different conditions. The influence of process variables such as pressure magnitude, compress speed, pouring temperature, surface roughness and alloy composition had been discussed. Because of the compress action, the influence of these variables performed in a different way, but it was concluded that the way to improve the contact conditions always accompanied with an increase in the IHTC.     

模具充型过程中光滑粒子流体动力学模拟(英文)

讨论了基于光滑粒子流体动力学(SPH)的压铸充型模拟的实施过程。建立了一种区分流体粒子和入流粒子的入流边界条件。对人工黏度和移动最小二乘法在处理压力振荡中的作用进行了对比。对最终模型在模拟压铸二维与三维的充型过程进行了验证。将SPH和有限差分的模拟结果与实验结果进行了对比研究。结果显示SPH与实验更为吻合,表明了SPH在描述充型过程流态方面的有效性与精度。     

Application of inverse method to estimation of boundary conditions during investment casting simulation

Inverse method was used in single crystal superalloy DD6 processing simulation during solidification. Numerical modeling coupled with experiments has been used to estimate the interface heat transfer coefficient (IHTC) between the surface of slab casting and inner mold. Calculated temperature dependent values of IHTC were obtained from a numerical solution. The calculated temperatures agreed well with the measurement of cooling profile.     

Sensitivity study of IHTC on solidification simulation for automotive casting

Abstract

Interface heat transfer coefficient values between the mould/metal interfaces need to be precisely determined in order to accurately predict the thermal histories at different locations in automotive castings. Thermo-mechanical simulations are carried out for Al–Si alloy casting processes using a commercial code. The simulation results are verified with experimental data from the literature. Sensitivity studies show that the choice of the initial value of the interface heat transfer coefficient (IHTC) between chill/metal as well as the sand mould/metal interfaces has a marked effect on the cooling curves. In addition, having chosen an initial value of the IHTC, the analyses also show differences in the solidification rate of the casting alloy near the sand/metal and chill/metal interfaces, upon further cooling. The gap formation, which results in a change in IHTC from the initial value, does not affect the cooling curves in the vicinity of the sand/metal interface due to lower thermal conductivity of sand. However it is found to have a considerable effect in the chill/metal interfacial regions due to higher thermal conductivity of the chill. Based on these studies we recommend initial IHTC values of 3000 and 7000 W m^–2 K^–1 for sand/metal and chill (steel)/metal interfaces respectively, for application in casting simulations.     

Development and application of inverse heat transfer model between liquid metal and shot sleeve in high pressure die casting process under non-shooting condition

To predict the heat transfer behavior of A380 alloy in a shot sleeve, a numerical approach(inverse method) is used and validated by high pressure die casting(HPDC) experiment under non-shooting condition. The maximum difference between the measured and calculated temperature profiles is smaller than 3 °C, which suggests that the inverse method can be used to predict the heat transfer behavior of alloys in a shot sleeve. Furthermore, the results indicate an increase in maximum interfacial heat flux density(q_(max)) and heat transfer coefficient(h_(max)) with an increase in sleeve filling ratio, especially at the pouring zone(S2 zone). In addition, the values of initial temperature(T_(IDS)) and maximum shot sleeve surface temperature(T_(simax)) at the two end zones(S2 and S10) are higher than those at the middle zone(S5). Moreover, in comparison with fluctuations in heat transfer coefficient(h) with time at the two end zones(S2 and S10), 2.4-6.5 kW ·m~(-2)·K~(-1), 3.5-12.5 kW ·m~(-2)·K~(-1), respectively, more fluctuations are found at S5 zone, 2.1-14.7 kW ·m~(-2)·K~(-1). These differences could theoretically explain the formation of the three zones: smooth pouring zone, un-smooth middle zone and smooth zone, with different morphologies in the metal log under the non-shot casting condition. Finally, our calculations also reveal that the values of q_(max) and h_(max) cast at 680 °C are smaller than those cast at 660 °C and at 700 °C.