# Why vehicles break

I’m not sure where to start so I will start with the equation of harmonic motion, which includes many of the variables listed above. On a vehicle, such as a skateboard, there are many different vibration inputs in the environment. It is not quite white noise (equal input at all frequencies) but we can rest assured that there will be inputs that will excite almost any vibration mode the vehicle possesses. We are interested in the form that equates to acceleration, since we can directly turn acceleration into force (load).

a = -((omega)^2) * A * (sin((omega) * t)

Where a is acceleration, omega is angular velocity, A is amplitude, and t is time. Omega is stated in radians per second and is determined by the stiffness of the spring and the mass of what is oscillating. For the simple case of a rider carving on a skateboard the stiffness is the stiffness of the board (k) – how far does it deflect when a mass is put on it and the mass (m) of the rider plus whatever portion of the board is in motion when flexing the deck and trucks to carve. The frequency is how often the rider makes a complete right and complete left turn and returns to the initial spot – one cycle. I threw that in here because we will soon need it. The equation for omega is:

omega = (k / m)^0.5

The square root of k over m. I never said there wouldn’t be any math but you too can be an engineer without remembering equations that make your eyes bleed. Do what I do. Use online calculators. If at all possible use SI units because the absurdity of English units becomes readily apparent when you have to deal with pounds force and pounds mass.

Didn’t I define omega two different ways? Good question. Yes I did. There is the “natural frequency” omega defined by the stiffness of the board and the mass of the rider and there is the “actual frequency” the system is operating at. The equation of harmonic motion is for steady state motion. There is no more input and no losses (frictionless). The system will eventually settle to oscillate at it’s natural frequency in such an environment. The rider, however, provides a different input, at his comfortable carving pace. There are additional terms to evaluate motion due to an input in the real world. The amplification, q, and the damping* ratio, zeta. The math gets really messy here and isn’t all that important due to our assumption that the environment provides inputs at all frequencies. What is important to skaters is what these mean to our rides.

The damping ratio is a measure of how friction causes loss in the system. Adding plies to a deck of other materials like fiberglass will increase the damping due to the stiffness variation in the laminate. The amplification is determined by the ratio of the input frequency and the natural frequency. If they match perfectly you get very high amplification. This is that sweet spot you find when your board rebounds you perfectly into the next turn while carving. It is why it is possible to pump a board. You want a lot of amplification for a carving board and a lot of damping for a downhill board. Speed wobbles are the devastating result of too much amplification and not enough damping. Board builders know all this engineering whether they know the theory or not. Engineering is practical application and that is how they make our boards work.

There are many other inputs to our boards when we ride them. We all know the result of riding on a road with a rough surface and know that it happens at a different frequency than our carving inputs. You could use the methods above to calculate the S and n used in the carpet plots that define fatigue failure. It turns out that, like most things mechanical, fatigue is governed by superposition. If you calculate the loss of fatigue life for a number of different frequencies, the individual contributions can be summed to determine the total loss of fatigue life. That would be remarkably tedious but that is what we do in an engineering company. Fortunately, the designs of our components are close enough that we probably don’t need to subject ourselves to the boredom. However, if you have a product you have marketed that is seeing too many failures this is the way to find out why. If you don’t have an engineer available I would recommend hiring a contract engineer stress analyst. It shouldn’t take them more than a few days to work it out.

We will get to the S-n curves soon. First a word on what fatigue is. Fatigue is the failure of a part under cyclic loading due to crack growth. We look over our prized components from top to bottom – there aren’t any cracks to grow. Yes there are. There are imperfections in the material, inclusions, that are essentially cracks and behave the same. Cast metallics have many inclusions because they are poured. Plate and bars have fewer because they are rolled. Forgings have the least because they are pressed under great pressure. This is why cast parts of the same thickness will fail sooner than parts machined from bar or a forging, even when they are the same alloy.

S-n curves are carpet plots that show a material’s resistance to fatigue. S is the local stress and n is the number of cycles – the natural frequency for the given mode multiplied by the time it experiences that mode. The S-n curve tells what number of cycles will fail the material at the given stress. The stress is determined by the applied load and the local geometry of the component. A given load, P, applied to a thin section results in a larger stress than the same load P applied to a thicker section. The stress is also dependent on the shape of the cross section (round, rectangular, octagonal, etc.) and the way the load is applied (tension, compression, shear, bending, torsion).

I will end this first installation here. To come: more about S-n curves and shock loads. If there is a topic(s) people want me to expand on I will also do that.

*The proper term is damping, not dampening. Dampening is making the board wet.

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One day ill learn what this all means lolz

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One day I’ll read all this. Lolz

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Prolly not, but that’s all good. It isn’t meant for everyone. When you write something like that you learn as much yourself as you teach. It reminds and reinforces. It forces you to think about how it applies and you gain insight you didn’t have before.

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Yeah I get it, hope someone reads it and understands it all

I have been considering using electric skateboard design as a backdrop for teaching the many new young engineers we have at work. Motor, controller, and power supply interaction as @mmaner covered in his series plus the mechanics in this one cover the vast majority of the engineering we do.

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Waiting for the “Why vehicles break for dummies” version.

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There is a summary of what matters without any math at the end of Part Deux.

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Y’all on this forum sound smart as fuck… I gotta go back to the builders forum so I can feel smart again!

All in all, I really appreciated this article. As someone who is currently a student and wants to start their own engineering business, likely in robotics, I am trying to educate myself as much as possible and despite what some people said you were able to put this in easily understandable terms as long as you spend some time and use Google to look up any terms you do not recognize. Very well written and I look forward to more of your posts.

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Our electrical engineering professor really glossed over stress tests of systems. You have given me a jumping off point for my own research.

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Never stop learning. I study something every day. I always tell young engineers you don’t become the Chief Engineer by knowing more than everyone else. You become the Chief Engineer by never being satisfied with how much you know.

And thank you. Here’s a second piece of free advice. Never start a sentence with “and”.

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It’s pretty neat to be part of a community with so many smart people involved. I am glad that this forum started so that there is and even more concentrated group of smart engineers. Too many college students do not consider what happens after college and don’t study anything themselves. Esk8 is a great way for me to constantly learn new things outside the classroom. Honestly I have learned far more from esk8 and my own research than I ever have in any lecture hall.

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I have a pretty good example of this.

The two metal brackets that secured my fairly heavy light to the nose of the deck finally broke after many many miles of riding. There was no dampening so every rattle from the road translated into wear in the metal that broke it down over time. This is cheap cast metal for you.

When I first mounted it it didn’t wiggle at all or make sound at bumps. as time went on it got looser and you could hear it begin to rattle until it shook so much I could see the light beam moving on particularly rough roads.

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If you look at the failed edge under magnification you should see something like this:

The crack growth starts at a flaw and leaves visual evidence of the crack growing due to fatigue as can be seen in the part of this photo labelled “Fatigue zone”. This has a classic signature like growth rings on a tree. When the section gets thin enough, failure is sudden.

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WOW. my brain almost blew up with so much info . I love to read and learn, i’ve been involved with esk8 for about 3.5 yrs and i love being around everyone in this forum. I don’t post as much cause i always look for knowledge that has been shared. Thank you for sharing this. Bring on all the lessons to be learned.

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Can you link this series he created ?

I’m just posting to feel smarter

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This is kind of my ideology too, always learn, always seek higher intelligence. One of my goals is to attain the Chief Engineer position in whatever company I settle down at.

Also I hated vibrations, which I just finished before I graduated (its one of our final courses as ME’s) and somehow got an A in. Hardest class I’ve ever taken. Your post brought all the pain of the last few months back to me lmao sqrt(k/m) all day man

I liked your post though, good accurate information about how all these things work. If anyone wants to become a mechanical engineer, just know that this whole post should make sense to you once you go through the four years of math and engineering courses lol

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I was hired by the department when I was a senior to grade homework. When I took Vibrations I was the grader for the class homework. Luckily by that time you know who is smart in the class and you check your work against theirs before you start grading everyone else.

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