About The Vangelis’ Equation
Sometimes when I was working the night shift in the factory, I listened to Vangelis music on my headphones.
Once my professor said: “what about trying Vangelis with your machine tool?”. And, unexpectedly for him, I did it. He confessed later that he didn’t even imagine I was so “crazy” to take that seriously. I don’t know if at that time he wanted to provoke or to reprove me, or both.
So I went next to the machine and I listened there to Vangelis for the first time. I didn’t do it earlier because of my restraint towards those workers whom I respected. I have analyzed before, together with my professor, all the possible static equilibrium equations for that 5 axis milling device and nothing: it was vibrating only in some circumstances, apparently without obeying any laws. For sure, in those circumstances, something was happening that we didn’t capture in the mathematical model.
And the magnificent atmosphere induced by Vangelis suddenly brought me a vision: don’t you see or feel the tool wanting to free himself, to evade to the sky, to jump over the piece of metal? At that moment the problem was solved, it just required a huge amount of work. And I did it.
“You can’t imagine how effective your advice was, Vangelis the Greek helped me solve the problem: on one of the 5 axes there is a resistant force that, in some circumstances (the random and “unfortunate” distribution of the depth of the cut, correlated with the tool’s position) becomes a driving force and wants to blow up the German construction.”
“Be calm and modest, we are simple engineers, not geo politicians.”
The Story
This is a story about a person close to me, professor Stefan Anghel, from the Engineering University of Resita, who also led my PhD thesis. I knew him long ago, when I was a trainee engineer; at that time nobody would have thought that Mr. Anghel will leave this world so prematurely and abruptly.
When we met, we often talked, among many other things, about the bothersome mechanical failures of a high performance 5 axis numerical command machine tool from my work place (a big factory). We made a lot of hypotheses regarding the possible causes. All were logic, but when confronted with our in situ observations, we had to exclude them one by one.
At that time it happened that he asked me to work with the students as his assistant for a few hours a week and I couldn’t refuse, especially because of the fact that he invested much more time in listening and becoming involved with my work related problems; therefore I started advising some of the students on their diploma thesis. One of them was more insistent and rigorous than the others, and came to me once in the factory. Without regard to that noise and rumble, he wanted to know what a value should he admit for a certain coefficient.
Sometimes when I was working the night shift in the factory, I listened to Vangelis music on my headphones. We had a sort of glass-metal office, about 10 meters above the hall’s floor, where I kept my small and under-performing Walkman. I invited him up and said that I did’t know about his coefficient, but I would try to inspire him with something, and I had him listen to Vangelis. I think he was shocked by my approach, thinking that I did’t want to advise him on what to do. Later, he understood that the best solution is when you discover it yourself, getting inspired by something, like the Vangelis music overlapped by the factory noise. The fact is that Mr. Anghel learned about this event and, since he knew us both very well, he succeeded to harmonize us. As a result, that student had a very good and original diploma thesis, without me giving him any solution of mine.
When we met, my professor told me to be more predictable with that student, knowing more about his personal background. And politely he added: “what about trying Vangelis with your machine tool?”. And, unexpectedly for him, I did. He confessed later that he didn’t even imagine I was so “crazy” to take that seriously. I don’t know if at that time he wanted to provoke or to reprove me, or both. Later however, when we knew better, I felt he accepted my approach even if, possibly, he didn’t agree or didn’t conceive to experiment it himself (he never told me).
So I went next to the machine and I listened there Vangelis for the first time. I didn’t do it earlier because of my restraint towards those workers whom I respected. As I told you before, I have analyzed together with Mr. Anghel all the possible static equilibrium equations for that 5 axis milling device and nothing: it was vibrating only in some circumstances, apparently without obeying any laws. For sure, in those circumstances, something was happening that we didn’t capture in the mathematical model. And the magnificent atmosphere induced by Vangelis suddenly brought me a vision: don’t you see or feel the tool wanting to free himself, to evade to the sky, to jump over the piece of metal? At that moment the problem was solved, it just required a huge amount of work. And I did it.
I went soon to Mr. Anghel’s laboratory during a break and I told him:
“You can’t imagine how effective your advice was, Vangelis the Greek helped me solve the problem: on one of the 5 axes there is a resistant force that, in some circumstances (the random and “unfortunate” distribution of the depth of the cut, correlated with the tool’s position) becomes a driving force and wants to blow up the German construction.”
“Be calm and modest, we are simple engineers, not geo politicians.”
He, same as me, didn’t want to admit that the machine’s designers made this omission. It was then the moment when the communication barriers between us were falling: he begun telling me about his early childhood during WWII in a peasant family, from Bailesti, which was in those times a harmonious and hardworking community in Southern Oltenia, and about how hard he had to learn and work to become a professor in the university.
First thing we did after that was to check the “Vangelis’ equation” in situ. Mr. Anghel joked he always suspected me cheating; maybe at that moment he still doubted me. He wanted to be there to see with his own eyes how the operators were positioning the tool and the work piece, according to the forbidden areas of that equation and how the machine starts shaking and vibrating.
During the same day, a spark from his childhood ignited the present:
“Marius, you know, when I was with my father in our cart and the horses were frightened and jumped, he always mastered the reins to restrain them. We need a mechanism like my father’s reins to calm this machine.”
After a few days I gave him a reply:
“We need something to replace your father’s mastering too, and here is where I’m feeling strong.”
I learned in school about hydraulic actuation and automation, and, with such tools, imagination can do almost anything. If necessary, those teachers won’t refuse advising me, since with the automation professor I shared a common curiosity about Feigenbaum’s chaos theory, and such a thing can’t be healed for the entire life. And so I involved not only him in my “Vangelis’ equation” automation troubles, but the actuation professor too, who helped me greatly with his laboratory and knowledge.
These events opened the gates for me to my PhD thesis, after much insistence from Mr. Anghel, after we wrote and obtained together 2 patents, and after we attended in the ’90s, a Mechanisms Congress in Milan.
Despite the lack of material rewards and resources during those times, you can’t imagine how many other engineering problems benefited from our work inspired by the music of Vangelis overlapped by factory noise and by my professor’s childhood restive horses: even numerical programming optimizations, made by other colleagues, initially having nothing to do with us. We all became a horizontally self governed team and no one asked to leave the factory at the end of the work program anymore. However, the merit of the leadership was not to impede what happened “naturally”.