基于牛顿冷却定律的炉温曲线优化模型  

Optimal Model of Furnace Temperature Curve Based on Newton’s Law of Cooling

作　　者：熊欢欢 秦政 秦诗童 李明奇[4] XIONG Huanhuan;QIN Zheng;QIN Shitong;LI Mingqi(School of Optoelectronic Science and Engineering,University of Electronic Science and Technology of China,Chengdu 611731,China;School of Information and Communication Engineering,University of Electronic Science and Technology of China,Chengdu 611731,China;Glasgow College,University of Electronic Science and Technology of China,Chengdu 611731,China;School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]电子科技大学光电科学与工程学院,成都611731 [2]电子科技大学信息与通信工程学院,成都611731 [3]电子科技大学格拉斯哥学院,成都611731 [4]电子科技大学数学科学学院,成都611731

出　　处：《实验科学与技术》2022年第2期9-14,共6页Experiment Science and Technology

基　　金：电子科技大学研究生精品课程建设项目(JPKC20192-39);国家自然科学基金(U2030205)。

摘　　要：针对回焊炉加热电路板的炉温曲线优化问题,利用牛顿冷却定律和热传导规律,建立热传递模型和优化搜索模型。首先将整个加热过程分为3个区域,并分别建立对应模型。对于小温区,利用已知实验数据和最小二乘法求出时间参数;对于间隙区,先用热传导方程得到间隙区温度分布规律后求出时间常数;对于冷却区,采用多项式拟合的方法进行描述。然后,针对不同的制程界限建立相应的优化目标,采用蒙特卡洛模拟方法,并用变步长搜索算法加速搜索过程,得到相应条件下的最优炉温曲线。Aiming at the optimization of the furnace temperature curve when the reflow oven heats circuit boards,the heat transfer model and the optimization search model are established based on Newton’s law of cooling and law of heat conduction.First dividing the entire heating process into three areas.In the separated heating zone,the given experimental data and the least square method are applied to find the time parameters.In the gap zone,first using the heat conduction equation to obtain the pattern of temperature distribution in the gap area,and then obtaining the time constant.In the cooling zone,a polynomial fitting method is used to compute equations.Then,for different process limits,the corresponding optimization goals are established.The Monte Carlo simulation method and the variable step size algorithm are used to accelerate the search process,and the optimal furnace temperature curve under the corresponding conditions is obtained.

关 键 词：炉温曲线 牛顿冷却定律 目标优化模型 蒙特卡洛模拟 

分 类 号：O141[理学—数学]