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(#80) Mechanical and Electrical Failure Points · Mechanical Engineering Made Simple

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  Welcome back, design junkies, to mechanical engineering made
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  simple. For this deep dive, we've got
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  something special for you, the learner.
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  We're aiming to bridge to two really critical worlds.
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  First, the physical limits of material strength.
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  You know how much of A load can something actually take before
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  it bends or breaks for good? Exactly.
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  And we're bridging that with the essential data for electrical
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  components and circuits, how current flows, what the limits
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  are, and, you know, how fast things can burnout.
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  The goal here is to find the secrets to really robust
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  electromechanical design, because you can't design a high
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  power motor mount without understanding the thermal limits
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  of the copper winding inside. And you can't size a cable
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  without knowing how the mechanical stress on its conduit
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  might degrade the insulation over, say, a decade.
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  So let's unpack the structural side.
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  First. Let's start with how materials
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  actually fail. OK, so the foundational concept
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  here is what's called the strength of materials.
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  It's really all about the relationship between an external
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  force, a load, and the internal strain or deformation that
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  results from it. We have to find exactly where
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  that point of no return is. Right, and we often hear the
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  term elasticity. That's the ability of a material
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  to snap back to its original shape once you remove the load.
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  But that ability has a very strict boundary.
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  We call it the elastic limit. Push past that even a little,
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  and you've got permanent damage. And that idea leads right into
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  yield strength, doesn't it? It does.
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  Yield strength is the maximum stress a part can handle without
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  any of that permanent deformation, and for a lot of
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  materials we figure this out using what's called the offset
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  method. Right, because some materials
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  like aluminum alloys, they don't have that sharp knee on their
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  stress strain curve. It's more of a gradual band.
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  Exactly. So for those we define yield
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  strength as the stress that results in a very specific a
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  definite 0.2% permanent set, a permanent strain.
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  Why that number? Why 0.2%?
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  It seems so specific. It is, and it's a critical
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  engineering standard. It's basically the line where
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  the material has stretched just enough that even though it
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  hasn't broken, it's now useless for any kind of precision
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  function. It's a standardized, repeatable
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  benchmark. I see so engineers all over the
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  world can use it to compare specs and guarantee reliability.
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  Precisely. Especially for things like, you
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  know, highly stressed aircraft parts or machinery that just
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  cannot afford any permanent dimensional change.
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  OK, so that's the limit for a single static load.
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  But what about when a load just sits there for a long time?
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  Or when it cycles over and over. Right, that brings up two time
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  dependent failure modes. Let's start with cold flow.
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  Cold flow. It sounds a bit strange.
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  It's insidious. It happens without any heat or
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  stress cycling. It's just a slow gradual
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  deformation under a constant load.
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  You see it a lot in non elastic materials.
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  Like soft metals or certain plastics?
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  I've heard Teflon is a classic example.
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  Teflon is a perfect example. The material basically, well, it
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  oozes out from under the pressure over time.
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  So if you're using it for a seal, that slow creep means your
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  seal is going to fail eventually, even if the pressure
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  never once changed. That's it, and that's why good
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  designers compensate for it. They'll often use spring loading
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  in the fixture to maintain a constant ceiling pressure even
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  as the material itself is slowly flowing.
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  OK, so the other time dependent failure is fatigue.
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  Now this is the one that really keeps structural engineers up at
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  night. It is this is breaking caused by
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  repeated loads, even when those loads are way way below the
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  material static yield strength. And the key concept here is the
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  fatigue endurance limit. Yes, this is the magic number.
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  It's the point where the relationship between the stress
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  and the lifespan of the part suddenly stabilizes.
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  Any load applied below this limit can in theory be applied
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  an infinite number of times without the part ever breaking.
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  So finding that limit is everything in durability
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  testing. If you design below it, you've
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  essentially built in a perpetual service life for normal
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  operation. You've got it.
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  OK, let's scale up. Let's talk about larger
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  structures like beams here. The basic mechanics all come
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  down to the conditions of equilibrium.
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  Correct. For any static structure, we
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  really only rely on 2 fundamental conditions.
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  First, the algebraic sum of all the vertical forces has to equal
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  0. Which means in practice all the
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  forces pushing down the loads plus the beams own weight have
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  to be perfectly balanced by the upward forces from the supports
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  R1 plus R2. Exactly, and you'd be surprised
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  how often the beams own weight is overlooked or in really large
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  structures it becomes the dominant factor.
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  The second condition is about rotation, isn't it?
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  It is the algebraic sum of the moments of all those vertical
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  forces must also equal 0. When you calculate these forces,
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  you can generate something called a moment diagram.
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  And that moment diagram is the real treasure map for a
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  designer. It really is.
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  It points you to the dangerous section.
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  That's the one cross section where the internal bending
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  moment, and therefore the stress, is at its absolute
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  greatest. For a simple beam with an even
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  load, that's right in the middle, right?
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  Smack in the center and knowing that exact spot is vital because
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  that's where you need to ensure you have enough material to
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  prevent failure. Now what about impact, when a
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  load doesn't get applied gently, but just hit suddenly a shock
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  load? This is one of those great
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  counterintuitive physics facts. A sudden load, at the very
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  instant it makes contact, produces a unit stress and
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  strain that is precisely twice what the same load would produce
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  if you applied it gradually. Double the stress for the same
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  weight. No wonder shock loads are so
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  destructive. Where does all that energy go?
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  It has to dissipate somewhere. The kinetic energy of that
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  moving mass gets spread across 4 main areas.
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  The deformation of the mass itself, the deformation of the
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  structure it hits, conversion into heat and absorption by the
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  supports. So designing for shock is really
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  about designing for controlled temporary deformation.
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  It has to be. If the structure were perfectly
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  rigid, the stress would approach Infinity.
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  OK, we've covered how things break mechanically.
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  Let's switch gears completely and look at the electrical
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  world, from physical deformation to conductivity and thermal
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  breakdown. Agreed.
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  And when we talk electrical materials, we have to start with
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  copper. It's the benchmark 100% IACS
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  conductivity. And the design consequence of
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  that number is that it becomes the basis for basically all
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  thermal management in power systems.
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  Any little deviation in the copper's purity or its
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  temperature immediately throws off that fundamental calculation
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  and. When we size these conductors,
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  we use a specific unit, the circular mill, the She ML.
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  Right, which is just the cross-sectional area.
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  It's calculated as the square of the conductor's diameter in
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  thousandths of an inch. And for the really big cables?
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  We use Mcmallium where the M is just a multiplier for 1000.
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  So 1000 Mcmallium is simply 1,000,000 circular mills.
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  It's just engineering shorthand for when you're moving massive
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  amounts of power. Let's talk components resistors.
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  We usually just think about their wattage limit, how much
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  heat they can get rid of. But there's another major
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  failure mode. The maximum continuous working
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  voltage V sub West. And this is a really important
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  distinction. It's crucial a resistor can fail
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  from voltage breakdown even if it's way within its wattage
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  rating. The voltage itself, not the
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  heat, destroys the insulating properties.
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  You have to calculate V sub W. Which is the square root of the
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  power multiplied by the resistance.
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  That's the formula. So let's do a quick example.
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  A-100 Ohm resistor rated for 200 watts.
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  The absolute Max voltage you can apply is 141.4 volts.
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  Right. And if your circuit runs at a
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  higher voltage, you have to pick a physically larger resistor,
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  even if it has the same wattage rating.
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  It's about designing against two totally separate failure modes,
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  dielectric breakdown versus thermal failure.
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  Speaking of dielectric issues, the other component famous for
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  catastrophic failure is the electrolytic capacitor.
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  Oh yeah, they are notorious because they're polarized.
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  Hook one up backwards. And you will very quickly
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  release what we jokingly call the magic smoke.
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  The electrolyte inside heats up, it boils, and the capacitor
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  physically ruptures. Sometimes the pretty explosively
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  is. There a good rule of thumb for
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  sizing them in a power supply filter.
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  Yeah, a good starting point for a standard DC power supply
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  filter is about 1000 microfarads per ampere of output current to
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  the load. That usually gives you a good
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  balance between ripple suppression and, you know, cost
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  and size. OK, let's shift to AC
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  alternating current. Here we move beyond just simple
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  resistance R and we have to introduce reactants.
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  Exactly. You have inductive reactants X
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  sub L and capacitive reactants X sub C They define how a
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  component resists a change in current flow, and together with
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  resistance they define the total circuit impedance Z sub T.
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  And there's a critical frequency point where these two reactive
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  forces. Meet the resonant frequency F
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  sub R It's the point where X sub L is precisely equal to X sub C
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  They completely cancel each other out.
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  And at that point, a circuit can behave in really extreme ways,
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  right? Huge amplifications in voltage
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  or current. Which has to be very carefully
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  designed for and finally, with AC we have to evaluate evaluate
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  the overall system efficiency using the power factor.
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  The F It's the true ower you're actually using, measured in
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  watts compared to the apparent power the voltampers.
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  In a perfect world, with a purely resistive circuit, PF is
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  1. But in the real world, as soon
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  as you add motors, Transformers, any inductive loads, that number
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  starts to drop. So what's the engineering
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  consequence of a low power factor?
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  It means the utility has to generate and deliver way more
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  apparent power than you're actually using to do work.
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  For a designer, that means you need thicker wires, bigger
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  Transformers, larger Breakers, all to handle this reactive
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  current. That's just sort of sloshing
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  back and forth, doing nothing useful.
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  And the utility companies don't like that.
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  They hate it. Many industrial sites get
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  penalized if their PF drops too low.
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  They actually have to install huge banks of capacitors just to
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  bring that number back up closer to 1.
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  OK, now let's merge these two fields.
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  Let's talk about devices that turn electrical energy into
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  mechanical motion, starting with the workhorse, the solenoid.
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  Solenoids are fascinating because they have this dual
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  current challenge. When the armature is far from
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  the coil, that's its initial state.
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  The device draws a massive inrush current.
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  Several times higher than what it needs later on.
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  Much higher, but once that armature pulls in and is fully
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  seated, the coil's inductance changes, and you only need a
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  much smaller holding current to keep it there if you let that
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  big inrush current continue. The coil is guaranteed to
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  burnout thermal overload. Absolutely.
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  So how do DC solenoids prevent this?
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  With a really clever mechanical trick.
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  It's mechanical brilliance. They build in auxiliary
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  contacts, sometimes called cut out contacts.
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  They're wired in series with a large resistor, maybe 2100 ohm
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  resistors and. When the solenoid pulls that
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  armature all the way in. The armature itself physically
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  opens those contacts, but that forces the current to go through
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  the big series resistors, which immediately drops the current
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  down to a safe holding level. That is a self regulating
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  electrical protection system that's triggered by the very
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  mechanical motion it creates. It's beautiful.
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  It is, but if that mechanism fails, you need a backup, a
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  fuse. And you can't use just any fuse.
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  No, you need a slow blow fuse. A standard one would pop
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  immediately from that required in rush current.
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  The slow blow type is designed to handle that initial surge,
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  but is rated at say 1.5 times the specified hold in current.
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  So it will blow only if the armature gets stuck open.
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  Yeah, and that destructive in rush current just keeps.
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  Flowing. That's the safety net.
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  Switching these big inductive loads, Mollenoids motors, it's
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  absolutely deadly for relay contacts because of the
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  inductive arc threat. What's happening there?
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  When you interrupt the current flowing through an inductor,
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  it's magnetic field collapses instantly.
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  That induces a massive reverse voltage transient.
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  It's a huge voltage spike and. That high voltage creates a
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  severe destructive arc across the contacts as they separate.
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  Especially with DC, there's no 0 crossing to help extinguish it.
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  That arc will literally Weld the contacts together or just
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  vaporize the metal over time. So we need robust arc
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  suppression. What are the main techniques?
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  Well, first you can use a resistor capacitor network and R
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  CS number across the contacts. The capacitor absorbs the
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  transient energy and the resistor limits the current
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  flow. OK, what's another?
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  Option You can use a verister wired across the inductive load
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  itself. It acts like a voltage clamp.
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  It immediately shunts that transient voltage, limiting it
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  to about twice the source voltage.
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  Protects everything downstream. And the third solution is
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  wonderfully physical. The magnetic blowout switch.
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  You see these in heavy DC current applications.
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  There are permanent magnets positioned right next to the
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  contacts. And when the arc forms.
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  The magnetic field puts a force on the ionized plasma of the arc
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  itself. It physically stretches it and
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  collapses it incredibly quickly. It literally blows the arc out.
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  Extends contact life dramatically.
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  Fantastic. OK, finally, let's talk motors,
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  the ultimate electromechanical machine.
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  Engineers rely on standards here like Neema frames and insulation
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  class. Yeah, Neema frames guarantee
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  mechanical interchangeability, standard mounting holes, shaft
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  heights, that sort of thing. Insulation class like say a
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  class F defines the thermal limit of the internal windings
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  and for. Class F That's 155°C.
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  It is if you go over that you rapidly degrade the insulation,
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  which leads to short circuits and, well, failure.
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  How does a motors theoretical maximum speed compared to its
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  real world performance? We calculate the synchronous
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  speed, the absolute theoretical maximum, by taking the frequency
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  in Hertz, multiplying by 1:20 and dividing by the number of
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  magnetic poles. But the actual full load speed
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  of an induction motor is always going to be lower than that.
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  Always that difference is called slip, and it's actually
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  necessary to induce current in the rotor and create torque.
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  No slip, no motor action. For any large system we also
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  have to calculate the acceleration time.
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  How long does it take the motor to get a heavy load up to speed?
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  This is critical for preventing thermal damage during startup.
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  The calculation for the time T in seconds depends on two big
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  factors, the rotating inertia, which we call WK squared, and
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  the average torque available for acceleration T sub a.
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  And there's a hard red line here that engineers have to watch out
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  for. Yes, if you're calculated
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  acceleration time is more than 20 seconds, you have to stop and
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  reconsider the whole approach. Why is that?
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  Running a standard motor at high current for that long during
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  startup just generates too much heat.
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  You'll trip thermal protection or worse, you'll permanently
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  damage the insulation. At that point you need
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  specialized motors or starters. And even with all these precise
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  calculations, engineers still sometimes go back to a very old
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  school method to verify performance.
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  The Prony Brake. It's true, despite all our
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  complex computer modeling, the Prony brake is still a valid
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  hands on way to use friction and levers to physically measure a
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  motors actual running torque and horsepower.
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  It's the ultimate reality check for the design specs.
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  It really is. So we've covered a lot of
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  ground. We've charted these essential
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  data points for material performance, from standardizing
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  failure with that 0.2% offset, to understanding why a shock
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  load double S the unit stress, and right through to managing
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  the integrity of complex systems like solenoids and motors.
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  Electromechanical engineering really is all about managing
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  that energy conversion and the stresses it creates.
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  Every single design choice is a trade off.
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  Mass versus inertia, conductivity versus thermal
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  limits, durability against cyclic fatigue.
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  A truly robust system is 1 where the electrical design fully
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  respects the mechanical limits and vice versa.
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  So considering how critically all these material constants
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  like the modulus of elasticity and the geometric properties
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  like moment of inertia factor into how long a design lasts.
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  Think about this when you're calculating the power factor
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  correction needed for a huge industrial plant.
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  What's the real world consequence if the ambient
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  temperature correction factor you used for a components Max
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  voltage rating was just slightly miscalculated?
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  How reliant are our strongest, most efficient designs in the
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  perfect constancy of environmental variables we can't
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  fully control?