In the previous explanation, the RAE's reproduction test verified the hypothesis regarding the Comet crash.
To briefly summarize, the hypothesis is"Stress concentration occurred at the corners of the pressurized chamber windows and the mounting holes for the antenna, leading to progressive failure, fatigue failure, and ultimately, the aircraft disintegrating in mid-air."Met.
The results of the RAE (Royal Aeronautical Institute) replication test were:In addition to anticipating 10 million cycles of repeated loading, the development and manufacturing companies' estimates were 54,000 cycles, while actual accidents and RAE fatigue test results were less than 3000 cycles. This shows that the failure rate is orders of magnitude higher, making it extremely dangerous and not surprising that anything could happen.
This proved the hypothesis and revealed the cause of the Comet crash.
This time, we will focus on explaining stress concentration and fatigue failure, which were the causes of the Comet rocket crash.
First, let's explain in detail what stress concentration is.
応力集中
Let's explain stress concentration, which was one of the major contributing factors to the Comet crash.
You might be wondering what stress concentration is all about, so I'll give you a brief overview.
Stress concentration occurs when the cross-sectional shape of a material undergoes a rapid dimensional change (shape change), causing force to concentrate at that point.
Simply put, an example of stress concentration you can experience in everyday life is when you buy natto (fermented soybeans) or frankfurters; they almost always come with individual packets of sauce or ketchup.
When you take the sauce or ketchup out of its individual packaging, you'll likely tear the perforated part of the packaging with your hands to remove it.
The reason it cuts easily is actually thatThe abrupt shape change at the cut causes stress to concentrate even with a small force, resulting in a large force.The contents can be removed by breaking the packaging.
As you may have experienced before, stepped rods break at the stepped sections, and grooved rods break at the grooved sections, both due to stress concentration.
This stress concentration has been known since ancient times, and in machinery, measures are always taken to avoid stress concentration.
Even so, there are inevitably areas in the design where stress concentration occurs, so we take measures to minimize the degree of force concentration in those cases.
For more details on stress concentration, click here.
Naturally, this stress concentration was also occurring in the Comet.
As suggested in our previous hypothesis, the most prominent location where stress was concentrated was at the corners of the windows.
Naturally, the development and manufacturing companies were aware that stress would concentrate in areas like the corners of windows, so they had tried to address this by rounding the corners, but it seems that even that wasn't enough.
In hindsight, it appears that stress concentration occurred due to insufficient rounding of the window corners.
The next major point is fatigue failure.
Fatigue failure
The key point is fatigue failure due to repeated loading.
Simply put, fatigue failure is a phenomenon where any material or component will eventually fail after a certain number of repeated loads, even if used below its breaking strength.It will happen.
A common example is wire; you've probably experienced bending a wire repeatedly until it breaks after a certain number of bends.
Also, I think it's a common phenomenon in everyday life for things like plastic to break after repeated use.
thisIt's called fatigue failure.
Since fatigue failure can occur regardless of the material used, there are indicators for each material that show how much load and how many cycles of application will cause it to fail.
In mechanical design, the fatigue limit is an enormous number, but it refers to the load or stress that can withstand more than 10^7 cycles. This limit is used to design machines to last until the end of their lifespan.
Conversely, the lifespan and maintenance intervals of a machine are determined based on the number of fatigue failures it experiences.
For details on fatigue failure, click here.
Naturally, this has been known for some time, and Comet's development and manufacturing companies have taken it into consideration in their design and even conducted durability tests.
In hindsight, it seems that the design considerations and durability testing were insufficient.
As a result, these two became the main factors, naturallyBecause the aircraft repeatedly took off, flew, and landed with each flight, repeated pressure fluctuations due to altitude differences created stress in the pressurized cabin. This stress concentrated at the corners of the windows and the antenna holes, leading to fatigue failure, mid-air disintegration, and crash.
So, the question everyone is wondering is..."Why did the pressurized chamber fail due to fatigue, even though thorough durability testing was conducted during development?"with"Why did fatigue failure occur in the RAE test when it did not occur in the development tests?"become.
To answer this question, let's look at the differences in the durability tests of the two.
Differences between fatigue testing during development and RAE reproduction testing
First, let's look at the differences between development testing methods and RAE's reproduction testing.
First, to recap, in the RAE's reproduction test, the entire aircraft was placed in a pool, and repeated loads due to pressure differences were reproduced by adding and removing water.
Furthermore, by draining the pool water and filling the inside of the aircraft with water, they were able to recreate the expansion of the aircraft at high altitudes.
By repeating this process, the load from each flight was reproduced.
Now, let's look at what kinds of tests the development and manufacturing companies were conducting.
The test results can be summarized in the following bullet points:
1. There was no test facility large enough to accommodate the entire aircraft.The pressurized chamber was divided and subjected to durability testing.(One of the main reasons was that the pressurized chamber was constructed by dividing the engine into parts, creating them, and then gluing them together.)
2. DividedTo determine how much load it would take for the pressurized chamber to fail (one-shot failure), a test was conducted applying a load twice the load experienced during flight.
3,A fatigue test was conducted by repeatedly applying loads to the divided pressurized chamber used in the second test.
4. The fatigue test involves repeatedly applying a load due to a pressure difference, a pressure of 0.6 atm (60 kPa).As a precaution, we applied double the pressure, 1.2 atm (120 kPa), every 1000 cycles.
5. To apply repeated loads to a pressurized chamberUsing compressed airThe pressurized chamber was repeatedly subjected to loads.
At first glance, the testing conducted by the development and manufacturing companies appears to be without issue. Furthermore, because it is a world first, they are even applying a load twice the actual load on the aircraft to confirm its performance as a precaution.
This aloneIt appears they conducted more stringent tests than the reproduction tests in RAE, but there's a big pitfall.That was the case.
Let's examine the mechanism by which these differences in test content led to differences in Comet's test results.
Effects of dividing the pressurized chamber for testing (finite element method)
This part gets a little technical, but I think it's interesting, so I'll try to explain it as clearly as possible so that anyone can understand.
The first major pitfall is the difference between conducting tests in segmented pressurized chambers and conducting tests using the entire aircraft (RAE).
The practice of conducting tests in divided pressurized chambers during development is neither wrong nor bad; it's a common method even today when testing large components.
However, if the test conditions are not carefully considered, the behavior of the divided parts and the completed parts can be completely different.
First, let's use a simple needle as an example to show the difference between testing it in sections and testing it as a whole.
A variation of a simple beam (a tension rod installed on a wall)
First, consider a beam (or tension rod) of length l that is fixed at both ends. A uniformly distributed load q [N/m] (which can also be thought of as pressure) is applied to it.
If you think about it normally, you can probably imagine it transforming as follows.
If it's a little hard to imagine, think of a familiar example: tension rods sold at 100-yen shops or home improvement stores.
If you install that tension rod on the wall and hang a very heavy, wet futon folded in half to the full length of the rod, you will have the same conditions as in the example problem.
Now, let me introduce a method for thinking about things in parts.
Let's consider the deformation of a simple beam by dividing it into sections.
First, let's try dividing it at the midpoint, at the position of length $ \frac{l}{2}$.
In that case, the divided A and B can be considered as shown in the following diagram.Both A and B are divided by a rod that is fixed on one side.
The deformation of A and B is simple, and they bend as shown in the following diagram.
If we consider it in terms of a futon, it would look like this:
We'll combine them to return them to their original form.
Note that at this point, A and B are continuously connected, so the deformation of the contact surfaces A and B will be equal.
This results in the same deformation as the original beam.
Well, in this example it's simple so there's not much point in dividing it and calculating, but when the shape is complex, you can easily find the deformation of the original shape by dividing it into simpler shapes, calculating each one, and then combining them.
However, while the calculation becomes simpler, the computational complexity increases.
in this wayThe method of dividing a problem into sections for calculation and testing is called the Finite Element Method (FEM).
This meansThe fundamental mechanism of all modern computer-aided engineering (CAE) is to divide extremely complex shapes into thousands or tens of thousands of elements for calculation.
Computers are excellent at performing simple calculations multiple times at extremely high speeds, so they are a very good match.
At the time of writing, I think most of you have probably seen a video on the news or somewhere similar showing the simulation results of "how saliva droplets spread when a person sneezes indoors," calculated using the supercomputer Fugaku in relation to COVID-19.
That involves fluid analysis and calculations that divide time, making it slightly complex, but the principle is exactly the same as what I've described here.
Common issues include:If you use the wrong method of division, the result will be completely different.
A simple beam deformation caused by incorrect division.
For example, let's say we divide the same needle we used earlier.
However, this time, both A and B are divided into beams (tension rods) fixed on both sides.
The deformation of each of these divided beams can be seen as follows.
Just like before, they combine back into their original shape. At this point, A and B are continuously connected, so the deformation of the contact surfaces A and B will be equal.
I think anyone can see that this kind of deformation is absolutely impossible.
Even when drying a wet futon, the tension rod will not deform into a W shape.
But all the calculations themselves are correct.
The only mistake is getting the condition of the dividing line wrong when dividing it – whether it's free or fixed.
Just one mistake can make such a big difference in the outcome.
このThe conditions under which a division occurs and when it is reunited are called boundary conditions, and they are extremely important.
In this case, since it's a simple beam (rod), anyone can easily spot the mistake. However, when you're calculating a super-complex shape divided into thousands or tens of thousands of parts, it's incredibly difficult to realize the error.
In other words, they are completely unaware that they are wrong.
ThenUltimately, the only way to determine if the boundary conditions are correct is to measure them using the actual equipment.
Judging the accuracy of the results, then and now, relies on the accumulation of painstaking tests and experiments, and on human judgment—it's extremely important (current AI can't make that judgment. Who knows what the future holds?).
However, once you understand these boundary conditions, you can quickly and accurately determine the answer by simulating or testing similar phenomena in the future.
In fact, the extent to which a company possesses the know-how regarding partitioning methods and boundary conditions is a measure of its true strength that isn't visible in economics (I think this is the third time I've said this).
Therefore, if you're only shown videos of simulation results related to COVID-19, it's impossible to determine whether they match the actual phenomenon or are incorrect.
このI can't understand it unless you tell me the division method and boundary conditions.
So, just from that sneezing video, all we can tell is that "he must have done some serious calculations."
There's absolutely no problem if someone does it as a hobby using their own money, but frankly speaking, it's a problem when valuable taxpayer money and time are used just to show us videos.
Moreover, I don't know if it was well-received or not, but they were constantly running simulations under different conditions, such as on a train or inside an office.
decentFor engineers, it's common practice to conduct tests to correlate the initial simulation with the actual phenomenon before running simulations under different conditions (similar to the principle of hypothesis and verification).
Simulation results that do not correlate with actual phenomena are merely speculation and no different from playing around.
Putting that aside, this is the difference in test results (and simulations) that results from incorrect division methods and connection conditions for each divided section.
Now, let's illustrate with an extremely simple example what kind of error occurred in the division method in Comet.
Examples of erroneous results from split tests of Comet
First, because the Comet's pressurized chamber was so huge, it was made by dividing it into sections, manufacturing the parts, and then gluing them together to complete it.
I think it's safe to say that the fact that we created it in this divided form was probably fortunate (though ultimately unfortunate), as we were able to test it while it was still divided.
So, we decided to do a test before finishing it with adhesive.
Simply fix each component in place and perform the test.
If we simply add up the test results of each component, the pressurized chamber will deform as shown in the following diagram.
This is definitely wrong. With this mistake, each dividing surface (joint surface) would not deform at all.
But back then,There are no facilities to test the entire pressurized chamber, nor are there any computers, so verification is difficult.
Moreover, since the calculation itself is correct, even if there's a mistake in one of the boundary conditions, it's difficult to notice the overall error.
In the example shown in the diagram, the division is only 10 parts, but in reality, I think it would be divided into many more parts, which would increase the number of boundary conditions. If even one of those many boundary conditions is wrong, the whole thing will be messed up.
Even geniuses make mistakes, and if you don't plan and check your work based on that assumption, you'll be in big trouble.That's how it will be.
The pitfalls of the finite element method lurking all around us
The COVID-19 related sneezing simulation I mentioned earlier as a modern example is highly likely to contain similar errors.
This is because, as far as I can tell, I can't find any specific data on the boundary conditions or partitioning methods, and I don't know what kind of experiments they were paired with (were they even doing proper experiments?).
Frankly speaking, even I, the author, could create that sneeze simulation and video if I had a supercomputer, software, and enough time—it would be quite tedious, though (calculating things like oil droplets inside the engine and how the fuel mixes).
However"How do we match it with actual phenomena?"But that's extremely difficult (matching the division method and boundary conditions, and the correlation with reality).
It all starts with the question, "What exactly are we measuring in a sneeze?" (Measurement is extremely important).
However, when only videos are shown, they can appear plausible, and based on that, the government and local authorities may implement several measures.
As a result, in some cases, meaningless measures are implemented, wasting the efforts, taxes, and time of the public.
What's worse is that it's being proudly announced by RIKEN, the research institute that brings together some of Japan's top minds.
The discrepancy between this simulation and the actual phenomenon has been occurring frequently in many companies since simulations (CAE) first became popular 10 years ago.
The author is not saying that "sneezing simulations are pointless and should not be done.""When conducting simulations, always perform actual tests alongside them to determine the correlation."I'm just stating the obvious.
Rather, I hope they will implement these measures in the right way for the benefit of Japan.
I wish the Japanese mass media would at least report whether they've actually established a correlation.
If that's not possible, I'd at least like a certain national broadcasting station to investigate it.
Even a former engineer like myself can understand this, so there must be many more knowledgeable and well-known critics out there.
Tools and techniques only have meaning when they are used correctly.'S.
I'll say it again because it's extremely important:"Hypothesis and verification go together," "Simulation and experiment go together," "Experiment and measurement go together."They are absolutely necessary as a set.
Am I the only one who sees this as exactly the same thing that happened with Comet 70 years ago (a project in which a genius staked the nation's prestige)?
Learning from history and putting it into practice isIt's difficult (again).
Next time, we'll look at how the differences in the remaining exams affect the results.
To those who found this article helpful in understanding design:
Since we're on the subject, I'd like to recommend a book that's essential for mechanical design.
To be honest, the content is extremely unhelpful, but it can be used like a dictionary when you forget the details. If you read this article, you should be able to understand the content and use it effectively. It also includes commonly used standards, making it quite useful.
If you don't already own one, I highly recommend getting one, even though it's a bit pricey. However, new ones are expensive, so if you're considering buying a used one, I strongly recommend checking that the surface roughness conforms to the new JIS standard.
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