Study on furnace temperature curve model based on least square method

Abstract

Data fitting based on the least square method was adopted. Through the analysis of relevant data, the data were divided into five sections: small temperature region 1-5, small temperature region 6, small temperature region 7, small temperature region 8-9, and small temperature region 10-11. Then the least square method can be used to fit the five formulas, and then find out their corresponding derivative function, because the heat conduction effect of the back weld furnace on the circuit board is basically fixed, so it is assumed that the heat conduction effect of different temperatures and transmission speeds is consistent. Finally, according to the derivative function, the furnace temperature curves of the five sections can be calculated. Thus, the temperature of the midpoint 3, midpoint 6, midpoint 7 and edge 8 of the small temperature zone are 109.3℃, 155.6℃, 166.8℃ and 190.4℃, respectively. Nonlinear programming is used to solve the problem. First, constraint conditions are established according to the process boundary, and the objective function can be obtained by combining the obtained temperature acceleration. The problem is transformed into a nonlinear programming problem, and the final solution can be obtained: 182°C (small temperature range 1~5), 203°C (small temperature range 6), 237°C (small temperature range 7), 254°C (small temperature range 8~9), and the maximum speed of the conveyor belt passing through the furnace is 83cm/min.