Dependence of heat transfer coefficient at quenching on diameter of cylindrical workpieces

Abstract

For computer simulation of a quenching process, the fundamental prerequisite is to have the relevant heat transfer coefficient (HTC) calculated as a function of the workpiece’s surface temperature and time respectively. In order to calculate the HTC experimental measurement of the temperature–time history (cooling curve) near the workpiece surface is necessary. In this investigation, cylindrical probes with diameters of 20, 50 and 80 mm are used. The cooling curve was always measured 1 mm below the surface of the probe. Special care has been taken to keep all other factors (e.g. design of the probes, temperature measurement, quenching conditions and calculation procedure), which can influence the calculated HTC, constant, in order to ensure that the only variable is the diameter of the probe. Assuming a radially symmetrical heat flow at the half length of the probe, the HTC was calculated using one-dimensional inverse heat conduction method. The unexpected striking result of this investigation is the fact that for the probe diameter (80 mm) the calculated HTC as a function of surface temperature does not show the film boiling phase. A plausible explanation for this effect is given, based on the critical heat flux density. The possibility of establishing a simple fixed relation (a correction factor) between the HTC and the diameter of cylinders is discussed.     

薄铝板淬火换热系数求解

针对薄铝板淬火过程,本文采用不同函数形式描述淬火换热系数,并借助ABAQUS有限元软件进行温度场和位移场模拟,得到换热系数和位移场的关系。基于试验所得翘曲位移反求换热系数,并对所选取的函数形式进行了优选。     

薄铝板淬火换热系数求解

针对薄铝板淬火过程，本文采用不同函数形式描述淬火换热系数，并借助ABAQUS有限元软件进行温度场和位移场模拟，得到换热系数和位移场的关系。基于试验所得翘曲位移反求换热系数，并对所选取的函数形式进行了优选。     

基于DEFORM反传热模型表面换热系数的确定

以7075铝合金厚板淬火过程为对象,研究DEFORM反传热模型中控制参数对表面换热系数计算和温度预测精度的影响规律。结果表明,当选择实测温度曲线上的拐点温度作为温度控制点,且表面换热系数初始值接近平均换热系数时,采用反传热模型确定的表面换热系数所预测的冷却曲线与实测曲线吻合较好。在此基础上选取合理的控制参数,并确定了7075铝合金厚板淬火过程的表面换热系数,经冷却曲线预测结果与实测值对比表明,采用DEFORM反传热模型确定的表面换热系数所预测的温度场有较高精度,可以满足工程应用需要。     

一种铝合金水冷界面换热系数反求方法的研究

针对水冷金属界面换热系数影响因素多,测量与求解难的问题,以温度场数学模型为基础,以实测温度曲线为基准,通过数值模拟迭代计算和自动寻优,实现了铝合金水冷界面换热系数随温度变化定量关系的反求.反求得到的铝合金换热系数结果表明:在浸入式水冷过程中,铝合金界面换热系数随表面温度由低到高呈现出先升后降的单峰形状特征,降低冷却水的温度会使换热系数的峰值点升高,但不会改变峰值点出现的温度范围,换热系数的最大值出现在200～230℃.金属与冷却水之间热交换的强度主要取决于界面温度,将界面温度控制在200～230℃会使强化传热效果达到最佳.     

Experimental determination of convective heat transfer coefficient in WEDM

An experimental determination method of the convective heat transfer coefficient in wire electro-discharge machining (WEDM) is introduced. A special device is developed to measure the average temperature increment of the wire after a period of short circuit discharges, and the thermal load imposed on the wire is also tracked and recorded in advance. Then, based on the thermal model of the wire, the convective coefficient can be calculated accurately. Some tuning experiments are carried out inside and outside a previously cut profile to examine the influence of the kerf on the convective coefficient. As soon as the wire cuts into the workpiece, the convective coefficient will decrease more than 30%. With this method, the effect of the coolant flushing pressure on the convective coefficient is also estimated. If the pressure is raised from 0.1 to 0.8 Mpa, the convective coefficient will increase more than 20%, and thus ameliorate the cooling condition of the WEDM process.     

比较厚板淬火换热系数反求的两种方法

在厚板淬火过程的数值模拟中,换热系数的正确求解是保证其温度场及应力场模拟结果与实际结果一致的前提。在实测冷却曲线的基础上建立了换热系数求解的两种数学模型,计算了换热系数随淬火时间关系曲线。基于ABAQUS模拟软件分析了两种模型在某特定区域温度场的实测与模拟误差。结果表明,换热系数随时间呈非均匀分布,在20～40 s之间出现换热系数峰值;一点法求解的换热系数优于两点法;两种方法计算的表面温度均出现温度回升现象,但一点法求解的表面温度回升较两点法的平缓。     

高温钢板连续喷水冷却换热系数的研究

采用有限差分法建立了高温钢板连续喷水冷却过程中一维非稳态传热条件下冷却水换热系数的计算模型,将试验测量到的数据应用该模型计算出了试验过程中冷却水与高温钢板间的换热系数[h。]分析结果表明：在流量一定的情况下,压力对换热系数的影响较明显,而在压力一定的情况下,流量对换热系数的影响较小,冷却水的换热系数随喷水密度的增加而增大,随钢板表面的温降呈先增加后减小的趋势。总结出了钢板表面温度为400～1 000 ℃,喷水密度为90～180 L/(m2·min)的条件下,喷水冷却换热系数[h]的经验计算公式。     

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.     

铝合金厚板淬火表面换热系数的离散解析求法

为了快速准确求取铝合金厚板淬火过程的换热系数,对淬火热传导过程进行分析。首先,将换热系数解析过程假设为淬火温度离散化的,并且是相邻离散点可进行迭代优化的计算过程。然后,分步解析求解了各离散温度区间的换热系数,最后完成了数据修正和仿真计算还原。结果表明,该方法获得的换热系数,可以使实验冷却曲线与计算冷却曲线较好的吻合,从而证明这种计算方法的可行性,并在文末对该方法的误差来源和特点进行了分析。     

An experimental study of heat transfer in aluminum castings during water quenching

The influence of quenching orientation and agitation conditions on heat transfer of aluminum alloys during water quenching was experimentally investigated with a test casting. The results indicate that heat transfer in water quenching of casting aluminum alloy consists of film boiling, nucleate boiling and convection stages. The highest heat transfer coefficients (HTC) are observed in the nucleate boiling, while the lowest is in the convective cooling stage. The heat transfer coefficients on the horizontal surfaces facing down during quenching are lower than those of other surfaces regardless whether the water is agitated or not. Agitation enhances heat transfer process especially when castings are at high temperatures and heat transfer process is in the film boiling stage.     

Determination of heat transfer coefficient and ceramic mold material parameters for alloy IN738LC investment castings

Investment casting molds with different numbers of shells and pre-heating temperatures were investigated in this study. The primary layer consists of colloidal silica bound ZrSiO₄ with additions of CoAl₂O₄ to achieve fine grains and to reach a good surface quality, whereas the following layers consist of mullite bound by colloidal silica. Interface temperatures (alloy/mold) that are necessary to determine heat transfer coefficients were obtained by linear extrapolation. Heat transfer coefficients in the range of 300-660 W/(m² K) were obtained. The castings were examined with regard to grain size and secondary dendrite arm spacing. Physical properties of the investment casting mold were examined by differential scanning calorimetry (DSC) and Laserflash methods for temperatures up to 1300 °C. The specific heat capacity was determined to 1.13 J/(g K), thermal diffusivity was found to be in the range of (4-5) × 10⁻⁷ m²/s and the thermal conductivity to be 1 ± 0.1 W/(m K).     

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.     

不同构造窗户的传热系数和设计应用

窗是房屋建筑中的主要围护构件之一,是建筑物得失热的主要部位。在建筑节能的研究领域内,窗户的传热系数是一个极其重要的物理量。本文探讨了不同构造窗户的传热系数及其设计运用。     

对流换热系数对熨平板焊接变形和应力的影响

采用有限元模拟不同对流换热系数下熨平板的焊后变形和应力分布,并采用塞尺和X射线法进行试验验证。结果表明:整体变形趋势为U形板呈鼓泡状,左连接板伸出端向x正向收缩变形,两侧板自由边向内收缩变形。最大变形位置出现在连接板伸出端最上端,对流换热系数为采用曲线加载时,变形误差为34.3%,系数为0.02时,误差为17.1%;不同对流散热系数对残余应力峰值影响很小,应力分布与对流换热系数为0.02时趋势一致,误差为32.6%,采用曲线加载,不考虑低应力区结果,误差为21.1%,均满足工程应用要求,证明了模拟结果的准确性。两种加载方式均满足焊接变形预测要求,在焊缝较多、应力分布复杂的情况下,应力预测建议采用曲线加载方式,反之则采用系数为0.02加载。     

On the evaluation of the global heat transfer coefficient in cutting

The use of numerical simulations for investigating machining processes is remarkably increasing because of the simulation cost is lower than the experiments and the possibility to analyze local variables such as pressures, strains, and temperatures is allowable. Process simulation is very hard from a computational point of view, since it frequently requires remeshing phases and very small time steps. As a consequence, the simulated cutting time is usually of the order of few milliseconds and no steady cutting conditions are generally achieved, at least as far as thermal conditions are concerned. Therefore, nowadays numerical prediction of cutting temperatures cannot be considered fully reliable. In the paper this issue was taken into account: a mixed Lagrangian-Eulerian numerical approach was utilized and the global heat transfer (film) coefficient at the tool-chip interface was derived through an inverse approach. Finally, the dependence of the film coefficient on pressure and temperature on the rake face was investigated.     

火车轮模锻成形工艺及热处理换热系数测算

为研究火车轮在模锻成形过程中内部金属流动及淬火加热、踏面淬火中的换热系数和温度变化,利用有限元软件对其模锻成形及热处理过程进行数值模拟分析,并结合黄金分割优化法对综合换热系数进行了反传热计算。结果表明:模锻过程中,辐板与上模接触区域的等效应变最大,轮辋外侧变形相对较小,踏面附近区域变形较均匀;在淬火加热过程中,换热系数随工件表面温度升高而增加,当温度在500℃以下时,换热系数随温度的升高而快速增加,500℃以后,增速缓慢,800℃时,换热系数达0.15 kW·(m^2·℃)^-1;踏面淬火时,在700℃以下,随温度下降,换热系数迅速增大,300℃时达到峰值3.1 kW·(m2·℃)^-1,在250℃以下,换热系数稍有下降,100℃时换热系数为2.5 kW·(m2·℃)^-1。     

Heat flux distributions and convective heat transfer in deep grinding

By using experimental data including the monitored temperature and power signals, combined with detailed theoretical analysis, the relationship between the undeformed grinding chip thickness and specific grinding energy has been studied and used to derive the heat flux distribution along the wheel-work contact zone. The relationship between the grinding chip thickness and specific grinding energy (SGE) has been shown to follow an exponential trend over a wide range of material removal rates. The distribution of the total grinding heat flux, q_t, along the grinding zone does not follow a simple linear form. It increases at the trailing edge with sharp gradients and then varies nearly linearly for the remainder of the contact length. The heat flux entering into the workpiece, q_w, is estimated by matching the measured and theoretical grinding temperatures, and it has been found that the square law heat flux distribution seems to give the best match, although the triangular heat flux is good enough for most cases to generate accurate temperature predictions. With the known heat flux distributions of q_t and q_w, the heat flux to the grinding fluid can then be estimated once the heat partitioning to the grinding wheel is determined by the Hahn model for a grain sliding on a workpiece. The convective heat transfer coefficient of the grinding fluid has been shown to vary along the grinding zone. An understanding of this variation is important in order to optimise the grinding fluid supply strategy, especially under deep grinding conditions when contact lengths are large. It has been demonstrated that the down grinding mode can provide a beneficial fluid supply condition, in which the fluid enters the grinding zone at the position of highest material removal where a high convective cooling function is needed.     

Inverse problem-coupled heat transfer model for steel continuous casting

An integrated approach was proposed for determining the heat transfer coefficient, which combined inverse heat transfer calculation model with temperature measurement and pin-shooting experiment. Based on the roller-layout and spray nozzle distribution, the IHTP (inverse heat transfer problem) model was developed to calculate the secondary cooling heat transfer by means of non-linear estimate method. The method transformed the inverse problem of parameter identification into solution of optimization problem using evolutionary algorithm. With the help of temperature measurement and pin-shooting experiment, the whole procedure of the model solution for identification and application in continuous casting process was given. Simulation and experiment results in plant trial confirmed the efficiency of the method used.     

6061铝合金淬火冷却过程中的表面换热系数

通过6061铝合金末端淬火测得的冷却曲线,结合有限差分法和反传热求解法,研究了6061合金固溶处理在不同冷却方式下的冷速及表面换热系数与温度的变化规律。结果表明,6061铝合金在水雾冷和喷水冷却过程中,端面冷速先增大后减小,在400℃左右达到峰值,峰值冷速约为30℃/s。6061铝合金的表面换热系数与温度呈非线性关系,其大小随着温度的降低先逐渐增大,在150～100℃范围内达最大值,然后下降;在风冷过程中,表面换热系数值先急剧增大,当温度下降到500℃后增速明显减慢。