FW_Su2013_05

Uh, I'll brighten that up a little. Um, I want to talk about heat flow. We talked about heat flow in welding, but now I want to talk about heat flow and how you really solve heat flow problems in the real world. Now I did the minor for my doctoral thesis on heat and fluid flow. It of course, silver-mechanical, took courses in graduate courses in mechanical and you know, boiling water heat transfer that people were really interested in, nuclear reactor heat transfer at that time. And then I took courses over in the math department over here in building two, uh, on all the math, and you know, just go through all this mess. And it's great to give you a quiz. I could ask you to solve some partial differential equation on a quiz or something, and then you could regurgitate back to them what they had regurgitated to you, and sometimes it came out in a similar form, sometimes it didn't, but nonetheless.

But in practice as an engineer, I kind of learned that that's not how I solve heat flow problems. And I have to worry about heat flow problems all the time. And sometimes you need to do a finite element analysis, which is a lot easier to do now today than it used to be. But nonetheless, most of the time — and by most of the time I mean ninety-five percent of the time — you don't need to do the heat flow analysis. You can just do a back of the can, you can just do a back of the envelope calculation with the Fourier number.

Now the Fourier number for heat transfer, fourier's second law, which comes out of the first law — which is just the first law basically — just says if I got temperature and distance, the heat flows down the temperature gradient, and you get a steady state. And if it's Cartesian coordinates, it should be a straight line as long as the thermal conductivity just doesn't change. And the heat, fourier's first law, his J is the heat flux, is minus K DT DX if we're talking about things in one dimension, okay, just a straight line. The heat in equals the heat out, it's steady state, you get a uniform profile. And if you go to cylindrical coordinate systems, you're going to get something that has a curvature to it, okay, because your area is changing as you go out radially, right. So things do change in different coordinate systems, and there are whole textbooks that take fourier's first law.

Or fourier's second law. And the second law basically just says, well, let's have a different amount, more heat coming in than going out, and how does heat accumulate in here, and how does the temperature change with time. So fourier's first law is steady state, fourier's second law says the change in temperature with time in this little volume element here that I'm going to look at is equal to K — and you have to have the heat capacity and the density in here so you know how much you have. Obviously a foam, you can heat up a foam faster than you can a solid material of the same material, right. So you have to have a density and the heat capacity, and the gradient, or the curvature — the second derivative of temperature with distance is the curvature. So if I have heat coming in faster up here, I have to have, by fourier's first law, a steeper temperature gradient, and even if it's in Cartesian coordinates I'll get a curved line, okay, for fourier's second law. But it changes with time, it's not steady state. You look at it at a different time and things are different.

And that K over rho C sub P is defined as the thermal diffusivity, okay. This turns out just to be a diffusion equation. And that's what I took over in the math department, the mathematics of diffusion equations. They had a course on it, and there are whole books on it. And it doesn't matter, this is heat diffusion, but you can also look at this as mass diffusion, which is change in concentration with time is equal to the diffusivity, the mass diffusivity, times the square of the concentration gradient with X, okay. And if you want to write this down, you know, grad T is equal to K over rho C sub P grad squared T, okay. If you're a mathematician, you guys probably learned that by now, what a grad is, gradient. Anyway. So, and they're probably — are they teaching you how to solve these equations now, these types of equations? Isn't it fun? Okay. Well, they're teaching you, if you don't learn it by the quiz you're in trouble, that's what they're teaching you, right. So you learn how — if you don't learn how to regurgitate it, that doesn't mean you have to understand it.

Well, no one bothered to teach me that all you really need is the argument here. You can show mathematically — and they taught me over in the math department — that you can sort of do a dimensional analysis on this, and you can show that whatever solution you have, whether it's an error function solution, an exponential, a Bessel function in cylindrical coordinates, Bessel function in spherical coordinates, all these fancy things that go into these big textbooks on how to solve this in different geometries and different coordinate systems, they always will have an argument of the exponent or the Bessel function or whatever in terms of a dimensionless number, in this case called the Fourier number if we're talking about heat transfer. If it's talking about, um, mass diffusion, it's called the Fick number. And it's D, or X over the square root of DT, where D is mass diffusivity, as opposed to alpha where alpha's the thermal diffusivity.

Alpha has units — oh here it is, I got it already — of centimeters squared per second. And we already know certain things. We know that copper has very good thermal diffusivity. In fact it's about one centimeter squared per second. Aluminum is forty percent less but it's still very good thermal diffusivity. Iron is 0.1, stainless steel is 0.05, titanium is 0.05. Stainless steel and titanium are considered lousy thermal conductors as metals go. There are worse things. There are ceramics which can be 0.02 to 0.05. Insulating foams might be a hundredth, okay, or maybe even ten-to-the-minus-five. But really there's only about three orders of magnitude difference between foam insulators and something like copper, which is one of the best thermal — uh, highest thermal diffusivity of anything, turns out.

Um, silver has about a thermal conductivity of 1.2. Thermal conductivity is different than the thermal diffusivity. And most people don't tabulate thermal diffusivity because it's a derived quantity from these three more fundamental quantities, and so usually you have to go and calculate it. The only text I know is — I put a table in the welding handbook, because we're always dealing in welding with transient heat flow problems. And so, um, Steve will tell you, I don't like to solve equations or go do finite element analyses myself. But it turns out I can just take the Fourier number up here, and I can solve ninety-five percent of all problems that I'm faced with — I'm talking about real engineering problems, not some homework problem — with this simple little formula of the Fourier number.

And Einstein, I think, was the first one who proved that mathematically, you always get an argument that's going to be X over the square root of the diffusivity times time. If you look at centimeter squared per second — if this is centimeter squared per second, this is time in seconds, this is the square root of centimeter squared which is centimeters, and so the whole thing's dimensionless. It's a dimensionless number. If you're a chemical engineer, they love to study dimensionless numbers when they're doing their fluid flow and things. It turns out, their fluid flow and heat flow — turns out that there is also a diffusivity for, um, not just thermal and mass, there's a diffusivity for viscosity. But because you have convection in fluids, it gets really messy, and it's called the Navier-Stokes equation, okay, it's got a lot more terms to it. But it's basically just looking how shear stresses diffuse through the system, okay, in fluid flow. And there are whole courses on Navier-Stokes equation.

But in fact, all you really need to know in heat flow most — ninety-five percent of the time — is whether you're infinitely thick, sufficiently thin that you end up with something where there's not very large temperature gradients, or you're somewhere in between. And it turns out it's only five percent of the time that you're somewhere in between where you have to go and do the fancier analysis, okay. If you are infinitely thick — turns out for a Fourier number of one, uh, you're basically in the situation where the distance the heat travels divided by the speed at which it travels, if you will, is similar ratio. And so if these are the boundaries of my system, one edge here and one edge here and the heat is flowing through here, I'm actually starting to — the heat is starting to go from one surface and start to accumulate on the other surface if I'm near a Fourier number of one. And so if I really want to know anything with any real precision, I sort of need to solve the whole equation. But that involves solving a differential equation. That's something you give to a graduate student, that's not something that a faculty member does, okay. You graduate beyond that.

Anyway, in a thick film situation or a thick solution, basically the thing is so thick that the heat coming in doesn't get anywhere near the other edge, okay. And so you can just treat it as an infinitely thick solution. And you can use this number to figure out approximately what the distance the heat flows into the material. If it's something that's a Fourier number of a tenth, basically the heat started to accumulate on this other surface and starts to flatten out the gradient, slows down the heat transfer into the material because the gradient — fourier's first law says that's the rate of heat coming into the material. Here it's a very steep gradient, okay. When you first put a cold thing into an oven, the heat going in is very rapid. As it starts to warm up, the heat going in decreases over time because the gradient at the interface, at the surface, decreases over time.

Now you do have to worry about different geometries, and so you can talk about convergent heat flow and divergent heat flow. In convergent heat flow, I'm heating on the outside of a surface and I have a smaller surface on the inside, so I might be heating the outside of a tube. And that means that I actually will heat up faster because I'm getting a smaller area to accumulate the heat in. Divergent heat flow, I'm heating on the inside of a tube for example, or a sphere. And now I have to heat up a greater mass out here. The area is decreasing as one over R here, it's increasing as one over R. In a sphere it's decreasing as one over r squared and here it's increasing as one over r squared. So there's convergent — if you're in a planar situation you have this, but convergent will be faster heating and divergent will be slower heating. And these are sort of, in most cases, maybe a factor of two difference. But in a lot of cases I don't even care about a factor of two. I just want to know, did I heat all the way through, or did I not, barely touch the surface, okay.

And to give you some examples of what you can get out of this. If I want to think and calculate what the width of the heat affected zone in steel should be from an arc weld — if I say, well, the width is going to be something on the order of the square root of alpha T, and the interaction time for the heat source as it's traveling along — remember, we had this thing from, I showed you the kind of fancy heat flow analysis tells you that you have this temperature field due to a traveling point heat source. And if I want to say, well, the size of the arc weld pool is about one centimeter long because one's a convenient number, and I say that the interaction time is one centimeter divided by the velocity — a typical arc weld might be going at half a centimeter per second — and I have for steel 0.1 centimeters squared per second, times 2, the square root of 2 is about 4 right. If I multiply 0.4 times 4, I get 0.16. This is in centimeters, but I'm going to convert everything to millimeters in my mind, if you follow what I'm doing, okay.

So the width of the heat affected zone in steel should be something on the order of four millimeters for a typical arc weld. So I'll pass this around. Anybody know what four millimeters is? About 3/16 of an inch, a little under, right. So look at that heat affected zone — it's about 3/16 of an inch, right. Well, there it is. I mean, if I want to know if the heat affected zone is one millimeter or 10 millimeters, I can go through a simple little analysis like this. All I had to do was figure out my interaction time and take fourier's law, and I come up with a number that's reasonably close.

Now, remember I brought in this 12, 13 inch thick weld where they had hundreds of weld passes, weighed about 10 pounds as I passed it around, right. Well that's one where they had to preheat the metal. And that was about 12 inches of steel — 12 inches, well, it's not 30 centimeters, that's 10 inches, but it's close to 30 centimeters, I'm rounding things off because it's an approximate analysis. Here's the Fourier number — x squared, the distance the heat travels, is alpha T. And if I square 30 I get 900, divide by a tenth which is alpha, the time is now 9000 seconds, which is two and a half hours. Well, that's why that weld cracked. I mean, the weld I showed you, the section of the one I showed you wasn't cracked, but they lost — you know, there's about a five million dollar loss because they'd been using this forging press for fifty years. And over time it wore out and it developed a fatigue crack and it cracked.

And people decided, okay we're gonna repair weld it. And so they brought in these good old boys welders. Well, they're good old boys welders, but they had never taken a heat flow course. They weren't welding engineers, they were welders. And they knew you were supposed to preheat the steel, and they were used to using, you know, flame torches to preheat steel, or using electric blankets to preheat the steel. But they didn't know anything about how heat flow changes when you go from one inch thick like that piece that's going around, to a piece that's 10 or 12 inches thick. And while you can heat that piece for five or ten minutes to get the heat to soak through, a piece that's 12 inches you've got to heat for two and a half hours to get the heat to soak through. So they heated for 10 or 12 minutes — that was their standard procedure — they started welding, and guess what, they're welding on unpreheated steel. And they got tremendous residual stresses, hydrogen embrittlement, and cracking.

So they decided, we'll just do it again, right. What's the definition of stupidity? Doing things over and over expecting a different result, right. Doing the same thing over and over. So they did it again, and it cracked again. Well actually it didn't crack right away — the first time, it cracked right away as it was cooling down. They heard bang, okay, and a crack propagated. The next time they actually gouged out, and they didn't make a partial penetration weld, they decided they needed a full penetration weld, which is what you actually see. And this one, it actually survived. This is — ah, it was holding together, no cracks. So they put it on the press, and the first time they loaded it, because of the significant residual stresses — they did no stress relief — wham, crack, okay. At that point they just scrapped the whole press. It's only a — well, used, it's only about a five million dollar press, um, but it's destroyed. And to buy a new one it's probably about 50 million dollars. But anyway, um, so there are a lot of problems with people not understanding heat flow and preheating and things like that. And in welding metallurgy we'll talk a little bit about preheating, which is in one of your modules you have to read.

Student: [Question — inaudible, apparently asking whether Tom is calculating the heat-affected zone width.]

Yep, our watch — approximately. Yep.

Well, it depends. I mean, first of all, I can calculate it. Just because I can doesn't mean I should. There are times when you want to know the size of the heat affected zone, for example. There are certain types of boiler steels where you actually want to use the top pass in a multi-pass weld to temper — we call it temper bead welding — temper the bottom pass. So I'm going to make some heavy section joint in some pressure vessel that I'm going to use for, let's just call it a chrome-moly steel. This is common in chrome-moly steels that you would like to have this be tempered, because the chrome-moly needs to be tempered, you'll get hard martensitic steel. So this bead will have a heat affected zone like this. Uh, I'm gonna see how long — I would draw the heat affected zone. Um, if I got some colored chalk — I used to have colored chalk. Okay, here's some colored chalk.

So in many of your heat treated steels you would like the heat affected zone around that weld, or the heat affected zone around this weld, to temper the bead underneath. Well, if the heat affected zone is too narrow, I don't temper the full bead. So what size pass can I put in? A lot of times you're limited in the size of pass in some of these pressure vessel seals because I want to have a heat affected zone that will encompass the bead underneath. I can't just pour the heat in, okay. So I'm trying to do metallurgical heat treatment with the pass above it. And then sometimes they'll put a cap pass on, okay, because these cap passes don't have anything else and they'll grind those off. Put them on and grind them off, so you've tempered everything beneath. So there's an example where I'd like to have it.

It's not just heat affected zones. You're going to see several of your homework problems — if you choose to do the problems in chapter 16 — are calculating things. For one of them, you got resistance spot welding electrodes. Yeah. Resistance spot welding electrode is copper electrode, this water cooled on the inside, got a piece of steel, and you've got another copper electrode here. And you might pass 10,000 amps through the copper electrodes for a third of a second — I don't remember what the numbers are. You know, this is copper, so you know the thermal diffusivity of one, right. And you got a third of a second. Will the cooling of the water here cool the tip before — during the time of the weld — is the water cooling effective during the time of the weld or not?

Student: [Suggests cooling happens between welds.]

Well, I went — huh, you've got the cycle between welds, and so you will actually — you definitely will cool. There's like two or three seconds between the welds, okay. But to give you a real world example, and one of the ways I use this — about 1985, they were welding galvanized steel in the automotive industry. Terrible problems. Because they used to weld non-zinc-coated steels, because they didn't care if your car rusted out in three years, you'd have to buy a new one. But after the '72 oil embargo, the goal was to have cars that had no rust for seven years. In fact, they started giving warranties to that effect, and they were starting to lose their shirts. So they actually started galvanizing the steel, putting a zinc coating on there, which is a sacrificial anode.

Well, um, they had problems because the zinc was alloying with the copper, creating a high resistance interface. And Ford had a spec, you had to have 2,000 welds before you had to change these copper tips because they were worn out. Why 2,000 welds? Because the robots that were making the welds would have to go for about two and a half hours between shifts until they shut down so the robot could go get coffee. Well, actually it wasn't a robot, but it's — the rest of the people, they shut down, um, after so many hours and they could do some maintenance, the other people could do maintenance, they come and change the tips. A hundred welds, that's like 10 minutes. You're going to shut down an automotive line which is turning out one car a minute, okay — five thousand dollars, ten thousand dollars profit a minute. Every minute you shut down is lost profit. So they wanted something that they only had to change the tips during the scheduled shutdown, which was like halfway through the shift, okay. That was 2,000 welds.

So Ford had a spec of 2,000 welds. When they first started using galvanized steel they were getting 100 or 200 welds before the tips were worn out. And that's why I said, you know, you got to put two, three thousand spot welds in an average automobile because you need 2,000 good ones, they're making a lot of bad ones, okay. Some of these cars go through an accident, just unzips like a piece of paper, okay, on these spot welds. So someone came in and told Chrysler in the mid '80s, said, for only fifty million dollars we will sell you a refrigeration unit that will chill the water in your copper tips, and it will improve your electrode life. No data, just, you know, oh well, obviously if you chill the tips you're going to keep them from getting this hot and blah blah, right.

Well, you get to do the calculation. I did the calculation for the guys at Chrysler and said — they said, well — I went out there, I was doing other work for them, and I went out and they said, well, this guy's trying to sell us fifty million dollars worth of refrigeration for our plant, to run chilled water through the plant, you think it'll do us any good? I said, no. And they said, why not? Well, I did fourier's law right there in front of them. They didn't have a clue. I put an equation in front of them and their eyes glazed over. And, but nonetheless, I proved that — and you'll, if you do the calculation, you can prove that during that one-third of a second, it doesn't matter whether you got water up there or not, but your point is absolutely correct, yeah, it cools it off in between the next weld, which might be two or three seconds later. So if you do the calculation, and you put in instead of a third of a second you put in three seconds, you'll find, oh yeah, I did cool the tip off in between, okay.

But I pointed out another thing. Anybody have any other idea of what the problem would be in an unair-conditioned plant with running chilled water through copper tubes?

Student: Condensation.

Exactly. How do you like it raining all on your unpainted steel? Actually it's galvanized steel, but nonetheless, how'd you like it raining on your automobile while you're trying to assemble it? And I explained to him, if you put this in, you're going to take it out a week later. Because — and they said, well, can you prove this? I said, I just did. I did the calculation. But to them that's not proof, it's just a calculation, which means nothing because — anyway. So they gave me a fifty-five thousand dollar research contract which I had to perform in three months. I didn't have time to do that so I gave most of that to one of my postdocs who was leaving to go become a professor at another university in three months. I took about ten thousand dollars of it because I had to go back to Chrysler and present this later.

We had to come up with a refrigeration unit for water coming through, you know, thing like this that was chilled water. You know how we did it? It's called a fifty-five gallon trash can, plastic trash can. We filled it with ice and water and we put a copper coil in it and ran the water through the ice water, okay, and we had chilled water, okay. It wouldn't last forever, but there's plenty of ice in the ice machines at MIT. So we actually did the test. We did some experiments, we did the calculations, and I went and convinced Pricer [Chrysler] — Chrysler — for a mere fifty-five thousand dollars I convinced them not to spend fifty million dollars on water chillers because it would do them no good. And we proved that, you know, you would not get more than 100 or 200 well, spots, on your electrodes. But I knew it from the beginning. It's easy to take that money.

Now it turns out Carl, the postdoc, he'd been one of my doctoral students, he made thirty thousand dollars in three months, okay, off that, and it was down payment for a house when he moved to his new place, okay. So it wasn't bad for him, it wasn't bad for me. We hired a bunch — and his during the summer, we hired a couple of undergraduates to do all the scutwork, you know, sitting there making welds. You know, making 5,000 welds, okay, it's really exciting. Um, but the students were happy, okay, they made ten thousand dollars over the summer. Carl made thirty thousand, you know, we had five thousand expenses, and I made ten thousand for a few trips to tell Chrysler how stupid they were, okay. Um, but it's because I knew the Fourier number, okay. But they still wanted to spend, you know — I couldn't prove it to them analytically, they wouldn't believe that.

Student: [Asks how Tom became involved with the problem / what other approaches were used.]

Well, at the time we were doing other work for them on spot welding, which is why they asked me. It turns out that there are other ways to do it well. First of all, uh, without — well, I got research money out of Detroit for ten years on this problem. When it started in 1980, they were getting about 200 spots, by 1990 they were getting about 2,000 spots. But one of the things they did, they changed some of the steel sheet surface, the galvanizing, and they went to thinner gauge of zinc. One of the more important things is they decided to do maintenance on their tips and on their equipment. One of the big problems here was, not that, um, you couldn't get a thousand if everything was aligned. But if you came in and this thing was skewed at an angle, and so you're really making contact right here, you get a real hot spot. And that was what was destroying things — if you didn't put the tips on square, okay.

Now it turns out, halfway through the 1980s, I was being funded by General Motors, Ford, International Lead Zinc, I had kind of a little consortium actually. And I'll tell you the reason I did this. I actually in 1980, the U.S. Navy Office of Naval Research decided, okay, we got someone at MIT who's interested in welding, we have welding problems, we're going to fund him. What happened is the Reagan administration started giving them more money but no new heads, no new head count at the Office of Naval Research. So they decided, we're going to have to give out bigger research contracts. Now, we don't have that problem today. But the first place they did it was at Penn State University. They did it on sonar materials, piezoelectric ceramics. The second place was at MIT. And they gave me at the time almost a half a million dollars a year, which would be like two or three million dollar a year contract.

And I — Professor Hart, mechanical engineering, he was a new young assistant professor, I gave him his first research contract. I was going around trying to find people at MIT. I was told by ONR, we want you to find other people at MIT you can bring in to think about welding problems. And so I was going around giving away money, okay. I was still barely an associate professor, and all of a sudden I had more research money than most the full professors in the department. And I started thumbing my nose at them, okay. Uh, didn't endear me to them, but I still got tenure nonetheless. But they found — what General Motors did to me in the middle of all this — I was funded by General Motors research lab, and a guy Jamie Sue, who I have a lot of respect for — Jamie canceled the project. But it wasn't just me. He canceled all spot welding research at General Motors research because they did a study of the plants to figure out why they had problems in spot welding. And out of 39 root cause problems, they found that something like 35 of them were all maintenance issues in the plant. And the top ten were all maintenance issues. And Jamie, being a manager at General Motors research, said, why should I be spending my research money to teach them how to make better spot welds if they're not going to maintain their equipment? And he was right.

So I lost my General Motors money for six months, until Buick-Oldsmobile-Cadillac — I mean, they were in different — they reorganized all the time, but anyway, they had a — they'd, or maybe it was — anyway it was one of these car divisions, as opposed to the research division, okay. And they picked it up, because they knew they had all kinds of problems, and they wanted — they thought they liked the work I'd done and so they wanted to fund it. So they kept funding it, and Ford funded it, and International Lead Zinc funded it, and it kept on going for a while.

But let me tell you one of the things that we did. It turns out, if you think of this — I'm giving you a spot welding lecture now, which I could have given you the whole spot welding lecture thing — but so in spot welding of sheet steels, remember, this is a process invented by uh, Elihu Thompson, who had been a president of MIT, in had 380 patents, he helped co-found General Electric and stuff. They were using an angle here of about 15 degrees, okay. And that meant if your current is coming down through here, it has to come down like that. And if you just think of flow lines, the current bunches up right at the corner here, okay. That's the same thing as a stress concentration. Mathematically, it's solving Laplace's equation. I'm from MIT, I know what differential equations are.

So I would go to General Motors, and I said, well, you know, General Motors research, because they've heard of Laplace's equation, they don't know what to do with it, but they've heard of it, okay. And I said, that's the wrong angle, you should have a 45 degree angle, okay, on your electrode tips. Because now the current doesn't bunch up as much, it's less of a stress concentration for the current. And we did, we sectioned things halfway through, we did high speed infrared movies, okay, of this stuff. If I could find them, except it's probably all on VHS, I don't know if I got a VHS player anymore. But in any case, at one time it was on the website, but I think it's been lost over the years. We did high-speed movies, and you could see the hot spots just from the maldistribution of the current. And we were able, by changing just the geometry of those copper tips, to get double the life, okay.

I later found out there were companies that Ford would hire to qualify the steel from the steel suppliers. The steel suppliers had to meet 2,000 welds, right, or Ford wouldn't buy the steel from them. Well, it was hard to pass the 2,000 welds. What were they using in the plant? A 15 degree angle. What were they using to run the test? It was actually part of the Ford spec — 45 degrees, okay. 45 gave you a better electrode life, but then you go in the plant and you use the one that gives you a lousy electrode life, okay. The mathematics of this is the same thing as a stress concentration, a mechanical stress concentration. This is just an electrical current concentration. But it's all Laplace's equation, okay. So it all comes out of Ragnar Holm in electrical contacts, okay.

So how did I get off on that, I don't know, but in any case, okay. So why do you do it, how do you do it. You know, I, um, I don't know, I run into this quite as often as I used to, but I used to probably a couple of times a year have some sort of consulting project with industry. And, and maybe it's still at least once a year, maybe twice a year still. And I'll be sitting in a meeting, someone's talking about some heat flow problem, and I'll sit there, and whether I do it in my head or whether I scratch it out on a pencil and paper, I'll say, oh, this is the solution. They all look at me, well, how do you know the solution, this is a complex heat flow problem. I said, yeah, I know, but I just solved it, right. It's not that complex equation. I can do that some of those in my head, okay. X over square root of T. Sometimes I make mistakes because the square root and all that other stuff, but nonetheless, if you practice enough you can get it down. And the point is, I guess the real point of this — there's tremendous ability in being able to estimate your solution before you go off and do fancy calculations.

On thanks, so far as that goes. Okay so that's enough. That's my, you know, my secret of heat transfer. I already gave you my secret of why professors give — do a derivation for a whole hour in class, right? Why is that? They didn't have time to prepare a lecture. I told you that one before, right? I didn't tell you that? Oh, that's one of my favorites.

I learned this as a young first, second semester assistant professor. Um, I had been on a trip, and I was teaching a course, graduate course, on how to forge and roll and do all this other stuff. And I got in that morning and I had not — because I'd been on the trip, I really hadn't really prepared my lecture very well. And class was coming up, so I looked in the book, and here was the derivation. I said, ah, I'll just do the derivation. And all of a sudden the light went off. I said, oh, that's why professors do derivations in class.

Sure, it's a time waster. For me the time waster is telling you stories, okay. But doing a derivation on the board is less interesting than the stories, right. And the stories actually — never mind. So I justified my stories as my time waster. But at that time I swore that I would never do a derivation in class again, and I haven't. I taught thermo for years and I never did a derivation. I would always write it out on a piece of paper ahead of time and hand it out to the students and say, you're MIT students, you went through algebra in high school, you can follow this derivation even if it's a differential equation. Differential equations are just using these D's and squiggly D's and stuff in algebraic form, right. There's maybe a few other rules about the algebra, but nonetheless, you're just manipulating abstract — anyway. So I have never done a derivation in class since, okay. I hand it out and say, okay here's the — if it's not in the book, I'll hand it out and say, here's the derivation, let's talk about what it means, okay. Because that's more important. So whenever you see a professor do a derivation in class, he's just wasting time, okay. Your time and his. And most of you know it, that's why you fall asleep, right.

Okay, why don't we take a break for five minutes and come back, we're going to start late.

Student: [Question about industry investment in spot welding — "a year in a nickel a piece" inaudible.]

Yeah, I think that's right, fifty billion a year. So they spent — the U.S. automotive industry spends a lot of money on resistance spot welding — I think there's my lecture, you know — um, uh, so they spent a lot of money on resistance spot welding, billions of dollars a year. Five hundred worth of spot welding in every automobile, okay. Uh, and it to a certain extent defines a lot of the structural requirements of the car. And it's about a hundred thousand watts per square centimeter equivalent. And now we're going to go to laser and electron beam. People will say, oh well they're high heat intensity processes, they're the same, they're interchangeable. And what I'm going to do is try to contrast them and show you why they're not interchangeable, okay.

My throat plus, okay. So the first thing about these two is, with electron beam you heat with electrons, an electron beam machine. And in a laser, you're heating with photons. And you say, well, what difference does that make. Well, makes a lot of difference in a number of cases. The uh, your electron beam machine will be typically somewhere between zero and 60 kilovolts, or 100 kilovolts, or greater. And why is that? Well, turns out, if you're hitting a metal surface with electrons of less than 60 kilovolts, you can shield that with window glass, sheet metal, okay. The X-ray radiation that's coming off that is easily shielded by your vacuum chamber, okay. If you get to 100 kilovolts, or above 60 kilovolts, you get enough penetrating capability of those X-rays that you now have to add lead sheeting to the outside of your vacuum chamber, and that costs money.

And you say, okay, well, why don't they always use less than 60 kilovolts? Well, the problem is, at 60 KV — let's see, you typically need, um, something on the order — in heavier steels you need something like 10 kilowatts to make a weld. I may have mentioned that before, when I talked about the particle beam weapons and I said, oh, they had megawatts of power. I said, well, you can melt a submarine but you don't need it, you only need 10 to 100 kilowatts for most heavy section welds. Well, it turns out you don't really want more than a tenth of an ampere in your electron beam, and I'll explain why in a second. That's 6 kilowatts. So if you're doing thin sheet material, you can use zero to 60 kilovolt machines, typically 40 to 60 kilovolt machines is what most people use. And just having your part inside a vacuum system is all the radiation shielding you need for the X-rays, okay.

But if you're doing something that's half an inch thick, you don't have enough power to penetrate that when you are limited to a tenth of an amp. Well, why am I limited to a tenth of an amp? I'm limited to a tenth of an amp because, if I start looking — here's my electron gun up here, and here's my work piece, and these little electrons are shooting down here and putting their energy into the work piece. And it's all electron flow energy here, there's no — you're in a vacuum system, typically. Turns out, these things are going at essentially the speed of light. It's the relativistic, like 99 — it depends on the voltage but it's like 99 or more percent of the speed of light. And you start calculating these currents and how close these electrons are in that beam, and you find if you get up to three-tenths of an amp, the electrons are so close together they start defocusing the beam. The mutual repulsion will cause defocusing of the beam.

So there are plenty of electron beam melting furnaces out there that use three amps, but I have a spot size this big, because you don't care about the spot size if you're just trying to melt. But if you're trying to do a weld, you want a very sharp spot, and you can't focus very well above two-tenths or three-tenths of an amp. Most machines are limited to about a tenth of an amp so that you can get good focusing, the electrons are not too close together. Which means if I want to go to greater than 10 kilowatts, I typically go to 100 kilovolts in my machine to get that, because now at a tenth of an amp I can get 10 kilowatts. And in fact there are some machines — the Japanese built one at 600 kilovolts and they get 60 kilowatts, and they were doing an electron beam in four or five, six, eight inch thick steel, okay. And we'll talk about why that didn't work all that well.

But in fact, I have tremendous radiation at the higher voltages, which adds to the cost because I have to have extra lead sheathing. 100 kilovolts, maybe it's only an eighth of an inch, or 3/8, 3/16 of an inch of lead. Start getting to 200 kilovolt machines, and now you're talking about 3/8 of an inch of lead sheathing around the whole thing. And you got, if you have windows in the machine, it's got to be leaded glass, and it's got to be several inches thick, okay. So it just adds to the cost. But yeah —

Student: What is the major difference between an [arc weld and an electron beam weld]?

The arc weld is in a gas, in the atmosphere. I guess I should explain this. So in arc weld, we got one atmosphere of some gas, whether it's CO2, helium, argon, oxygen, whatever. And the voltage of the electrons going across there is 5 volts going across this little gas boundary layer. Here, the energy of the electron is 60,000 electron volts, or a hundred thousand electron volts. Here it's five electron volts. Here I got 100 amps of current or 200 amps of current. Here I got a tenth of an amp of current, in a vacuum. So it's still electron flow heating, but you don't have an anode voltage drop because you don't have a gas boundary layer. But you do have the work function voltage, okay.

And the energy, the kinetic energy of the electrons — mostly it's the kinetic energy of the electrons. The kinetic energy of the electrons up here, the Thompson — the KT Thompson energy — was one volt. Here it's 60,000 volts or a hundred thousand volts. Very different electrons in terms of their energy, kinetic energy. Each electron here in electron beam welding has enough energy to partially penetrate the surface. I'm going to go through that in a little bit, okay. And so you're actually depositing your heat slightly beneath the surface, okay. In arc welding it's all deposited right there on the surface. Those electrons, they can't go more than one atom deep. Now, they might get conducted away once they get in the metal, but that's metal conduction, and that's not generating anything except resistive heat which is insignificant compared to the arc key. Does that answer the question?

So for the electrons, you get finer spot size, and we're going to talk about alignment issues and all these other things that come along with these things. Remember I told you in the very first day about these different heat intensities. Once you get to laser and electron beam, you have interaction times, because you have such power densities — a million watts per square centimeter — you got to be moving fast. Are you just going to burn a hole through it? You're not going to be welding unless you travel quickly. You're traveling so quickly — remember, I got out the dollar bill and showed you the reaction time. No one can respond in the millisecond it takes to control the weld pool in an electron beam or laser weld because the thing is traveling so fast you can't respond. You can't turn the corners to follow the seam or anything else that quickly. You have to have everything automated, okay.

So it's a very, uh, energy efficient process. It's near 100 — well, calculations show it's a 99 percent energy efficient. The wall plug power in your beam — wall plug being from the gun up here, which is a hot tungsten filament in a vacuum and you're just boiling off electrons in a big electric field — that wall plug power from that electrode to here is near 100 percent efficient. In an arc it's 50 percent because you got all these hot gases going off to the side wasting energy, just heating up the welder, the guy doing the welding. The advantage is you can run an arc manually. You don't have to have a big vacuum chamber, you don't have to have automation. This is a ten thousand dollars worth of equipment to get into the arc welding business. This is a million dollars worth of equipment to get in the electron beam business.

With electron beam, you've got to have a very high production volume, or laser welding, in order to keep it busy, or you're going to need a very high value-added part. Electron beams and lasers typically are used in automotive, where you have, you know, thousands of feet of weld to make lots of parts and you can keep a machine busy. In fact, to weld the catalytic converter, the clamshell, the stainless steel clamshell, Ford one time went with out-of-vacuum electron beam. They needed six of them to take care of all the production at Ford for catalytic converters. If they had gone with gas tungsten arc welders at a much slower speed, they probably would have needed 200 arcs, okay, to do what six electron beam units could do, because of the difference in travel speed. So it's a question of the economics of the equipment.

Now in that case — we can get into it later — but Ford bought Westinghouse out of vacuum electron beam machines, where you actually generate the beam up here in a vacuum of about 10^-8 atmospheres, and you have a little aerodynamic window here, which is a continuous leak into your vacuum system, and the beam comes shooting out into the air. And it's a — the electron beam has some ability to penetrate the air, maybe — depends on the voltage, but it might penetrate a millimeter, it might penetrate five millimeters. That means your standoff distance between your work piece and the beam, before it starts to defocus in the air, because these electrons hit the atoms in the air and start scattering — you've got to have your work piece distance accurate within a few human hairs or you won't get a consistent weld. The other problem is you've got a continuous leak into your vacuum system, so the maintenance on these out-of-vacuum electron beams is horrendous.

But it turns out there was this guy in the '80s — actually started out in the '60s, I can't remember his name now — but he came from Germany, and he had sort of made a career about out-of-vacuum electron beam. And he got hired by a company in Connecticut, and they started selling these machines, and they sold some manager at Ford on these machines. And I talked to one of the guys who was the manager at the plant who had to keep these things operated, and if you just mention out-of-vacuum electron beam, he would just pull out a knife wanting to kill anyone in the area, okay. It was the biggest headache in the world to maintain the machines. They don't use them anymore, okay. But it has been done. I mean, when I worked in the mid '70s at Bethlehem Steel, we went — and I have a picture somewhere of a weld we made — I went, I flew to Pittsburgh, to Westinghouse research, and this guy made this weld for us, and you know, one pass in three-quarter inch steel, okay. You know, there are other problems with it, okay.

But typically they're used in automotive — high volume, need lots of speed, you can keep them, if you feed the machine keep it busy — or aerospace, where the value added per part is huge and you can pay for an expensive machine to get a good weld. So they do have a lot more precision capability, but they're not the answer to everything, and they are expensive, okay. So it's usually aircraft or automotive. And in fact, I've seen data on lasers, and virtually 98 percent of the welding lasers are automotive or aerospace applications because of these things we're going to go through, okay.

So electron beams have tremendous penetrating capability — we're going to talk about that in the next thing. The laser heats with photons. E is equal to h nu, where h is Planck's constant, nu is the frequency. You can change that frequency to c over lambda. It turns out the wavelength of the laser is somewhere on around a micron or 10 microns, depending on whether it's a CO2 laser or YAG laser or whatever. Nonetheless, the energy at those wavelengths is something on the order of a tenth of an electron volt, not a hundred thousand electron volts like an electron beam. But there's a million-fold difference between the particles that are doing the heating.

There's also a million-fold difference in the number of particles, okay. If we got — they got one millionth of the energy, but they got the same energy in the total spot. Obviously I got to have a lot more photons, so far as that goes. But photons definitely just heat the top surface. They don't even penetrate even one atom deep. They basically interact with the electrons on the surface and are either reflected or absorbed. And we'll talk about that in a second, okay. So there is a — there's a million-fold difference in the energy of what you're hitting the surface with. And that will make a difference. We're going to go through, there's 12 different differences here. But the first one is, you have to understand, I'm using different types of particles with a million-volt difference in their energy, okay. Electron beams heat beneath the surface about a tenth of a millimeter. That's only four-thousandths of an inch, a little more than a human hair, but it can be different. So the laser, all the heat's on the surface. It doesn't even penetrate one atomic distance through the surface heating.

So my best example, by the way — did everybody get the Tuftee — must have stolen somebody's Tuftee article, when I kept it up here, anyway, did you get it? Uh, the example I give you here is actually not a welding issue, it's a heat treating issue. But there's a company in Chicago called Siaki [Sciaky]. And Sciaky is a French company originally. There's a Sciaky U.S. in Chicago now. Sciaky came to the United States about 1940 to the Philadelphia Navy Yard. They were just developing gas tungsten arc welding in the world at the time. Sciaky had the best gas tungsten arc welder. The Philadelphia Navy Yard built airplanes out of aluminum, and gas tungsten arc is a great process for welding aluminum. So the Navy brought Sciaky to the United States before the Germans took over everything. And then Sciaky kind of set up in the United States.

Well, Sciaky will sell you laser or electron beam fancy systems — million, 10 million dollars. They like to sell them to Boeing or Ford or GM or somebody, because that's where those are the industries you sell this stuff into. And so Sciaky was asked — I think it might have been Ford, but anyway one of the automotive companies wanted to harden the surfaces of crankshafts. You know, the lobes on a crank — not the crankshaft, on the camshaft, thank you. The camshafts have lobes that go spinning around and they push the valves on the engine up or down. As the camshaft is rotating, these lobes come by and they push the valve down — or it's on springs. And so they wanted to harden the surface of these lobes. So I've got a cylindrical shaft, I'm looking on it down the shaft, and it will have lobes on it like this. Um, so I'm not going to try to draw that in three dimensions, but the lobe may only be uh, three — a half an inch wide, or three-eighths, three-quarters of an inch wide, just this protruding — protrudence. And it will come along as it's rotating around, it hits the top of the valve, which usually has a cap on it, and it pushes it down against the spring, and that's how the engine gets the valves opening and closing at the right time.

Well, they wanted to heat treat this surface of the steel camshaft to make it harder. And so Sciaky built him a system — this is like 30, 35 years ago — and they were using high power lasers, which were fairly new and fairly sophisticated at the time, for an application like this. No vacuum system required, that's an advantage of lasers, okay. So you could save on the vacuum, high volume automotive, that's a big savings. So they decided to use lasers. The problem is, they always got cracking. And why do they always get cracking? It turns out, since it's all surface heating, the hottest part is right on the surface. And as you heat it up — you're not melting it, you're just trying to heat it up so you can transform the steel and then quench it to get the hardened steel. It expands. And as it expands when it's hot — what did I tell you about residual stresses? The residual stress is always reverse. So if it expands, it is in compression when it's hot, it'll be in tension when it's cold.

So they heated the surface of this lobe, ended up with very severe tensile residual stresses, and started getting surface cracks and spalling. The whole process was a disaster. Ten million dollar machine was garbage. So they switched to electron beam, and they had no problem, because electron beam actually deposits the heat about four-thousandths of an inch deep. And that meant the hottest area was just beneath the surface. That's where my tensile residual stresses were. I got compressive stresses on the very surface, okay. And they had a very successful process. In fact, they had compressive residual surface stresses, which is exactly what you want for the wear on those things. Oh, completely different results. Both high intensity processes, but because one has high energy particles and the other one doesn't, you get slightly different heating patterns. Maybe only a tenth of a — oh, maybe about four-thousandths of an inch, tenth of a millimeter difference, but it makes the world.