2020 Mathematical Modeling National Competition A Problem Solving Ideas

The first question: During the entire transmission process, the speed of the conveyor belt has been determined. It is necessary to consider the temperature change trend and time configured in Table 1. The temperature curve changes during this process are always continuous, and the difference is different. There is a temperature difference between the temperature zones. It is necessary to make reasonable assumptions about temperature changes in the process of solving the problem. Because the heat conduction of the object takes time, the basic stage can assume that this time period does not exist, and improvements and innovations can be mentioned later. . Given the process limit and the transportation speed, the time of the circuit board in the soldering process can be calculated, and the temperature change process can be expressed by the functional relationship. The temperature change process can be fitted by CFtool in MATLAB. As long as the expression and the restriction conditions are determined, the temperature change interval can be determined through the parameter fitting process. Determine the parameters reasonably, but the standards for each individual parameter are different, and you can judge by yourself according to the actual situation. If it can be determined that the temperature change is linear, it can also be done by Lingo. After the software process, the research on temperature can be realized through repeated control of variables. Generally speaking, there are more ways to ask first, just choose the one that suits you.

The second question: The second question and the first question are just reverse thinking. When the temperatures in different temperature zones are determined, the variables that need to be fully considered are the time during the temperature rise process at 150ºC~190ºC and the time when the temperature is greater than 217ºC. In the same way, to determine the temperature change in the temperature zone, you need to calculate the temperature time at different temperatures, because the time change from the start of the temperature zone 6 to the temperature zone 9 is only allowed in the part of 40-90 seconds, then The temperature zone between 1 and 5 can be ignored, and the following temperature zone can be described separately. The maximum allowable transmission speed is required in the question. In the case of the same distance, the shorter the passing time, the faster the speed. When we combine the distance between the temperature zones and fully consider it, we will find that the speed is also within a range. The results calculated by different software have a little error, but the error range is not large. Fitting can be performed by CFtool in MATLAB. According to the requirements of the subject, ensure that the temperature is within a reasonable range. At the same time, the welding time is always safe to achieve safe production and finally determine an optimal range. Friendly reminder: Don't correct the answer while completing the question. Affect mentality.

The third question: In order to ensure the minimum area of ​​the shadow part, that is, the speed of the transfer process in the recirculation zone is required to be fast, and the temperature increase trend is fully considered. Once the temperature increases too fast, the area will increase. (Integration principle) The area can be obtained by the basic integration method, and the expression of the shadow area can be expressed linearly, and then the temperature limit can be added to solve the maximum value. The variables in the process can be calculated by MATLAB. To solve the maximum value, the first step is to determine the range of variables, using time as the abscissa and temperature as the ordinate, determine the area of ​​the integral area to make a reasonable derivative through the expression, and calculate the best solution by the derivative method. The process of determining the time is relatively complicated, and the method of controlling variables can be used to measure its range.

Fourth question: The fourth question is based on the third question, and the third question is optimized. In order to ensure that the furnace temperature curve above 217ºC on both sides with the peak temperature as the center line should be as symmetrical as possible, and Time needs to be reasonably controlled to optimize the furnace temperature curve. At the same time, the temperature of the temperature zone and the speed of the conveyor belt need to be optimized. This process is relatively open. Different influencing factors can be optimized separately or all. Different variables need to be studied separately. Different variables have different meanings and have different effects on the results, such as the speed of temperature rise and the influence of welding quality. This aspect is a relatively open topic. If time is urgent, you can determine that a certain variable remains unchanged, but only make a fuss about one of the variables, change it, and calculate the size of the area respectively to achieve the topic requirements.

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