Finite Element Analysis

  The sparks people see every day in electric welding are also called arcs. If a layer of welding flux is used to cover the welding point during the welding process, the arc will be buried under the flux and cannot be seen. This welding process is called submerged arc welding. The characteristic of submerged arc welding makes the weld pool protected by the flux, with fewer impurities in the weld seam, resulting in higher welding quality. Submerged arc welding rarely uses manual operation methods, but is automatically completed by a special submerged arc welding machine, also known as submerged arc automatic welding. For Class II pressure vessel manufacturing enterprises, having a submerged arc welding machine is one of the important evaluation indicators.

  Technical Section Chief Fan Shibin and Container Workshop Director Feng Xu had both visited the petrochemical machinery to observe submerged arc welding, so they had some intuitive understanding of the working principle of submerged arc welding machines, but when it came to how they worked internally, they couldn't explain clearly.

  Lin Zhenhua, as a graduate student in mechanical engineering, was naturally very familiar with the working principle of submerged arc welding. Submerged arc welding was considered a relatively new technology at that time, but by Lin Zhenhua's time, it had become a very ordinary technology, and even a welding process textbook would have diagrams of the welding machine's principles. Zhu Tiejun casually mentioned submerged arc welding to Lin Zhenhua, originally just wanting to ask if he had heard of this technology, but unexpectedly, a few days later, Lin Zhenhua directly handed him a set of drawings for a welding machine.

  Having a blueprint does not mean that an arc welding machine can be manufactured immediately. Many related technical parameters, such as welding current, arc voltage, wire diameter, wire inclination angle, and welding speed, need to be determined through experimentation. Of course, the textbooks of later generations also have these parameter contents, but Lin Zhenhua cannot remember them so clearly. Moreover, some parameters need to be adjusted according to the actual situation in practice, different components of the welding agent, and different types of steel will affect the choice of parameters, these problems can only be solved through repeated experimentation.

  The task force was established under the leadership of Zhu Tiejun, and Lin Zhenhua's first thing to do was to give a lecture to everyone, explaining the principles and techniques of buried arc welding. The most capable group of engineers and electric welders from Hanhua Machinery Factory were all seated below listening to the lesson, including Yang Chunshan, Lin Zhenhua's future father-in-law. Zhu Tiejun also sat on the side with a notebook in his arms, taking notes. This old man, although from a military background, had a deep interest in industrial technology.

  "Kobayashi, after hearing your introduction, I feel like I have a good grasp of it. However, you said that all these parameters need to be tested, so doesn't that mean we'll have to conduct several thousand experiments?" Fan Shibin asked skeptically.

  "Several thousand experiments? When will that be done?" Welder Hao Songlin muttered.

  "Several thousand experiments are not many." Hu Yang interjected, "Mastering a technology requires several thousand experiments, which is very normal. In the past when our country introduced certain torpedo technology from the Soviet Union, in order to grasp the trajectory of the torpedoes, we actually fired several hundred torpedoes, each one costing hundreds of thousands of yuan."

  "Now that Master Hu has said so, let's start the trial. Xiao Hua, you issue a work order and we'll do it according to your requirements. With over a dozen electric welders working together, even thousands of experiments will be done quickly." Yang Chunshan said with ease, he was Lin Zhenhua's staunch supporter.

  Zhu Tiejun hesitated: "Thousands of experiments, how much money will be spent? Xiao Lin, is there a better way to do fewer experiments?"

  Lin Zhenhua sighed and said, "Well, actually, it's not necessary to do so many experiments. If we can construct a curve of parameter changes, then selecting a few nodes for experimentation would be enough."

  Zhu Tiejun asked: "Little Lin, what curve are you talking about? I don't understand. But you said how to make it like you said, what structure comes out of the curve and so on."

  Lin Zhenhua said: "To construct these curves requires some calculations, if there is a computer, then the calculations are also quite easy. But where can I get a computer now?"

  Fan Shiben clicked his tongue and said, "Let's forget about it. I've only heard that the provincial computer center has a computer that costs several hundred yuan per hour to use, and you need an introduction letter to use it. We can't afford it."

  "Xiao Lin," asked Hu Yang, "the calculation you mentioned, what knowledge is required? We don't have a computer. If we mobilize all the workers in the factory who are somewhat educated to do the calculation together, can it be done?"

  Lin Zhenhua shook his head: "Old Hu, this calculation is not a four-operation arithmetic, I want to do a finite element analysis..."

  "What did you say? Finite element?" Hu Yang's eyes gleamed with an unusual light.

  "Uh, anyway, it's just a calculation method, whatever the name is. Lin Zhenhua hastily brushed it off, the term 'finite element' was really too difficult for Hanhua Factory people."

  Who would have thought that Hu Yang was holding on tight: "Little Lin, I once saw the concept of finite elements in a mechanical magazine, but I don't know what's going on. Can you?"

  Lin Zhenhua forced a smile and said, "I also barely know some of it, but to do even the simplest finite element analysis, you have to involve matrix operations and differential equations, I'm afraid..."

  Hu Yang turned to Zhu Tiejun and Fan Shibin, "Director Zhu, Section Chief Fan, you both know that I have a high school education, and in recent years, I've also been fond of reading books. The matrix and differential equations that Little Lin mentioned, I understand a bit. How about this? I'll take the initiative to volunteer, cooperate with Little Lin on finite element analysis, what do you think?"

  "Of course." Fan Shibin and Zhu Tiejun exchanged a glance, and immediately stated: "To say that these things were also learned when I was in college, but for more than ten or twenty years, they have not been used and have almost forgotten. I just calculated it earlier, our factory can do matrix calculations, and I estimate that one palm can calculate it. Their situation is similar to mine. If Master Hu still remembers, helping Xiaolin with this calculation would be the best."

  Zhu Tiejun stood up and said, "Alright, let's stop here for today. Master Hu, you and Xiao Lin discuss this thing called Yuan, see if you can help Xiao Lin get it done. We must do the buried arc welding. If you can reduce some experiments through calculation, that would be best. If not, we'll just have to do thousands of experiments. As long as we can get the second-class container certificate, spending some money is worth it."

  Everyone left with admiration for Lin Zhenhua, only Hu Yang stayed behind. Lin Zhenhua looked at Hu Yang and said with a worried face: "Master Hu, are you really going to do finite element analysis by hand?"

  Poplar nodded and said, "That's right, what computers can do, people can also do. However, I haven't studied finite element analysis, so I'm not quite clear about the specifics, can you tell me?"

  Lin Zhenhua said, "Hu Shifu, first tell me, to what extent do you grasp matrices and differential equations? You say you have a high school education, but these things aren't part of the high school curriculum."

  Hu Yang smiled and said, "Little Lin, I don't have any other hobbies, but I'm relatively interested in learning new things. Although I only have a high school education, I've also self-studied advanced math. To boast a bit, matrices and differential equations, ordinary problems can't stump me."

  "Alright, I'll tell you about finite element analysis," said Lin Zhenhua. "Finite element analysis is a method that replaces complex problems with simpler ones and then solves them. The core idea is to divide the solution domain of a complex problem into many small interconnected subdomains called finite elements, assume an appropriate and relatively simple approximate solution for each element, and then derive the overall solution by satisfying the conditions for the entire domain."

  Hu Yang listened attentively to Lin Zhenhua's explanation, repeating the words in his mouth as if he wanted to forcibly fill this knowledge into his brain.

  Lin Zhenhua asked with some concern after saying all this: "Master Hu, can you understand what I'm saying like this?"

  Poplar nodded: "I roughly understand, this idea should have a long history, isn't the idea of calculus like that?"

  "That's right," said Lin Zhenhua. "However, the finite element method was formally proposed in the 1960s. In just a decade or so, this method has been widely used in the Western engineering community and has almost penetrated all technical fields."

  Alas, look at us over the past decade or so, we've just been blindly muddling along, who knows how far behind the rest of the world we've fallen.

  Lin Zhenhua hastily comforted him, saying: "Master Hu, don't worry, we can still catch up now. Hasn't the Party Central Committee already proposed a scientific spring? An engineer like you who is self-taught will definitely have great use for your skills."

  "Never mind," Hu Yang waved his hand. "Xiao Lin, tell me instead, how is the finite element analysis done?"

  "Okay, let's start with a simple example..." Lin Zhenhua spread out a sheet of paper and wrote down a model for Hu Yang, then began to introduce the basic idea of finite element analysis in an orderly manner.

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