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(#65) Gears Cams Bearings Precision Fits Failure · Mechanical Engineering Made Simple

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  Welcome back, design junkies to Mechanical Engineering Made
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  simple. Today we're we're undertaking a
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  really critical deep dive into the very core of machine design.
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  We're talking about the components that control motion,
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  transmit power, and, you know, most importantly, manage all the
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  stress and longevity. That's right.
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  Gears, cams, bearings, linkages, the works.
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  A whole vocabulary. Our analysis is coming from some
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  seriously dense engineering handbooks.
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  I mean, they focus intensely on the geometry, the manufacturing,
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  and the sometimes brutal calculations you need to make
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  sure these things actually survive.
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  So our mission today is really to pull out the functional
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  essence of these parts. Yeah, and to show you why every
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  single moving part is a small hard won victory against the
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  physics of failure. What becomes immediately clear,
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  and you see it right away in the sources, is that it doesn't
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  matter if you're looking at a simple little detent or a, you
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  know, full on aerospace actuator.
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  The design is just this massive balancing act.
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  Every millimeter, every angle, every material choice has to be
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  absolutely precise. There's no room for error.
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  OK, so let's start with rotational power.
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  Let's start with gears. The fundamental language of
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  gears and 1st we have to define tooth size that really splits
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  into two major systems. Metric and US.
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  Right. In the metric world, we use
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  what's called the module, and it's actually pretty simple.
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  It's just the gears pitch diameter in millimeters divided
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  by the number of teeth, OK. Straightforward enough, but in
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  the US customary system we use the diameterial pitch.
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  And this is one that always, always trips people up.
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  OK, it's inverse. Totally inverse.
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  It's the ratio of the number of teeth per inch of pitch
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  diameter. So the physically larger the
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  gear tooth is, the smaller the diametral pitch number becomes.
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  It feels completely backwards. It does, but that's just how the
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  ratio works. And that demand for precision,
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  it flows right into the manufacturing process.
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  You can't just cut the stuff out of a block of metal, no.
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  Absolutely not. To create a gear face that can
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  withstand constant high load, you're talking about highly
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  specialized operations. You need milling then maybe
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  hobbing for spur gears, or end milling and shaping for internal
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  gears. And some things, like bevel
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  gears need their own specialized machines.
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  Exactly. And it's not just gears.
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  It's astonishing when you look at something like a standard
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  roller chain sprocket, right? They have to adhere strictly to
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  ANI standard geometry. The dimensions aren't just
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  picked, they are derived from these complex equations based on
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  the pitch, which we call P and the number of teeth N.
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  So every single curve is mathematically defined.
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  To the thousandth of an inch. I mean take 1/2 inch pix roller
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  chain. The source gives a minimum
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  seating curve value of .317 inches.
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  It's calculated down to that level because if that contact
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  point is even slightly off. You just destroy the chain.
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  You destroy the chain in the sprocket.
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  It's a rapid failure which, you know, leads us right into
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  material selection. Because the material has to
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  handle those forces. Precisely.
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  For something low speed, light load, sure.
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  You might get away with engineering plastics, acedal,
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  polycarbonate, things like that. But for any serious power
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  transmission. You immediately jump to heat
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  treated ferrous and non ferrous alloys, no question.
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  And this is where it gets really interesting because this
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  quality, both material manufacturing, it's all
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  quantified by the AGMA quality numbers, yes.
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  And this is where you get a just a profound insight into the
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  mechanical hierarchy of the world.
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  AGMA numbers define exactly how accurate your gear manufacturing
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  has to be, so. Give us an example.
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  What's the range look like? OK, think about a simple
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  agricultural bailing machine. It might be perfectly functional
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  with quality numbers between, say, 5:00 and 7:00.
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  OK. So that's pretty loose
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  tolerance. Very loose, but then you jump
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  into something sensitive like electronic instrument control
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  and guidance systems. That's a whole different ball
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  game. It is.
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  Suddenly you need quality numbers from 10 all the way up
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  to 14. The tolerance just tightens
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  massively. And what's at the very top end?
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  Well, if you were engineering something truly demanding like a
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  space navigation sextant and a Star Trekker, you need quality
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  #14 and up. The required accuracy for a
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  mechanism pointing to a star is just.
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  It's a different universe compared to 1 compacting A.
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  It shows that precision isn't just a cost factor.
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  No, it's a mission critical constraint, and that material
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  choice also dictates how you can even machine the part.
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  Machinability is hugely affected by heat treatment.
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  I've heard that some of the high carbon steels are just a
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  nightmare to work with. They are a 4150 grade.
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  Steel is notoriously difficult to machine.
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  You have to specify tempering for steels like 4140 just to
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  make them manageable on the shop floor.
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  And all this is before the system is even running.
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  Once it is, you have to deal with the operational forces.
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  Right, which the designers have to anticipate.
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  A simple spur gear will generate tangential and radial loads, but
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  systems like helical gears or even more so, worm gearing.
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  They introduce that third dimension of.
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  Force, a massive axial load rust and the calculation for the
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  forces in a worm gear system is where things get really complex.
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  You can't just use simple geometry.
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  Not at all. Yeah, you have to factor in the
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  coefficient of dynamic friction and the system's overall
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  efficiency. And that complicates everything,
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  especially selecting the right support bearings, because that
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  friction is what converts the rotational input into a crushing
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  axial load that the bearings have to absorb day in and day
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  out. OK, calculating those continuous
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  forces is hard enough, but what about controlling the timing and
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  the specific path of a movement? That's even harder.
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  It is, and that brings us to the systems that manage selective
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  controlled movements cams. Right, so cams are what convert
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  that simple rotation into something much more complex.
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  Exactly. They're defined as mechanical
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  components that convert continuous Rotary motion into a
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  specific, you know, predetermined translating or
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  oscillating action using a follower.
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  And the absolute dictator of which Cam profile you choose.
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  It's speed. It's always speed.
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  So for low speed movement. You might use something called a
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  uniform velocity motion, but this is actually terrible
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  because when the follower hits the flat part of the Cam, it
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  goes from zero acceleration to maximum acceleration instantly.
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  It's like hitting a wall. The shock is incredible.
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  And that shock is exactly what you're trying to engineer out of
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  the system. 100% uniform acceleration and parabolic
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  motions are better for moderate speeds because they smooth out
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  that transition, but for any kind of high speed application
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  you absolutely must use cycloidal motion.
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  Why is cycloidal motion the go to for high speed?
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  Because it's the only profile that keeps the acceleration
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  curve smooth, the shape is mathematically designed to ramp
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  up and ramp down both the velocity and the acceleration
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  gradually. It prevents those massive G
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  forces from destroying the follower and, you know, the
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  mechanism itself. We see that design battle
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  against shock loads everywhere in Cam design.
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  I was reading that the slope lines defining the rise and fall
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  have to be terminated with a parabolic curve.
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  Specifically to prevent shock loads.
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  If you skip that tiny design detail, your follower mechanism
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  will literally hammer itself apart.
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  It's amazing. Now there are two main types of
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  follower systems right open track and close track.
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  Correct. You have open track cams which
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  require the follower to be held against the Cam surface by a
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  spring. Think of a standard engine valve
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  train. OK, so a spring is pushing it.
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  Back exactly, but then you have close track cams where the
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  follower actually travels inside a groove.
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  This gives you positive action. Meaning no spring is needed.
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  No spring. This is critical in
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  manufacturing machinery because if a spring breaks in an open
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  track system, the whole machine fails immediately.
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  Close track cams eliminate that specific risk.
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  But the challenge with the spring based systems, the open
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  track ones, is what happens at high speeds.
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  You get spring floating. The spring just can't keep up
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  with a Cam profile and the follower loses contact.
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  It literally floats off the surface.
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  How do you fix that? The fix is designing the spring
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  with a natural frequency below the cyclic rate of operation,
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  and often the solution is to put multiple springs in parallel.
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  That's exactly what you see in the complex valve springs of
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  high performance automotive engines.
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  And then on the total opposite end of complexity, you've got
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  the simplest Cam of all. The eccentric Cam the most
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  economical to make. It's often just a round disk
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  that's offset from its center axis.
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  You see those used for simple rise functions or actuating
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  limit switches and timing devices.
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  Yeah, but you can't run them at high speed.
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  For ultra high speed we have to look at some really advanced
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  systems like the Desmodromic system.
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  This is the system that was famously used by Mercedes-Benz
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  racing engines back in the 50s. It was.
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  It actually used a second Cam to physically force the follower
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  back down. It completely eliminated the
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  need for springs. So if you ever hear a high
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  revving 1950s Grand Prix engine, that really distinct mechanical
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  clatter. That's the sound of springs
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  being completely engineered out of existence.
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  It's the noise of pure positive mechanical action.
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  Amazing. Now when you're designing these
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  Cam profiles, there are other constraints too, right?
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  You have to look at the Contact interface.
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  Oh absolutely, the geometry is critical.
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  You have to make sure the roller radius is smaller than the
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  minimum radius of curvature along the Cam profile.
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  Otherwise you'd actually cut into the Cam itself when you're
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  manufacturing it. You'd undercut it and you also
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  have to calculate the contact stress, which we call S sub S
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  For a material like SAE 4340 steel he treated to Rockwell
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  C50, the Max allowable compressive stress is 220,000
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  PSI. £220,000 per square inch. And if your calculation exceeds
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  that stress limit, you have designed a fatigue failure
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  point. It's guaranteed to break OK.
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  Let's shift from cams to linkages, the building blocks of
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  movement. We all remember the six basic,
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  simple machines, but we're focusing on mechanisms that
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  translate motion in really ingenious ways.
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  And maybe the most dramatic is the toggle joint linkage.
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  This thing is just incredible. It's a mechanism designed
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  specifically to multiply force massively as the linkage angle
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  approaches 90°. The mechanical advantage and the
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  velocity ratio both approach Infinity.
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  That's a trick of geometry. It is the classic examples are
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  the bolt lock action of the Lucre pistol, or you know, giant
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  rock crushing machinery. Both use the toggle to generate
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  thousands of pounds of crushing force with a relatively small
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  input. Then you have the four bar
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  linkage which is just everywhere.
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  Absolutely ubiquitous, just 4 links connected by 4 pivots.
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  You see it in everything from car suspensions to construction
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  equipment. But it looks so deceptively
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  simple. It does, but mathematically its
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  action is extremely complicated. Before the 1950s, figuring out
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  the precise motion for all points was often just trial and
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  error. You'd build a prototype and see
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  what it did. It wasn't until the
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  mathematician Freudenstein developed his geometric
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  relationship that designers had a really robust mathematical
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  tool. That's right, but even then, the
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  sheer difficulty means that mathematical solutions are often
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  approximations at best. Which is why even today, high
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  speed motion analysis is so critical, you have to actually
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  film the prototype. Exactly.
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  You watch the complex actions happening at 12,000 frames per
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  second just to confirm the mechanism is performing the way
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  you thought it would. And this analysis has its own
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  defined vocabulary. You see these letters RP and S?
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  It's a kinematic vocabulary. R is for a revolute joint, which
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  is just simple rotation. P stands for a prism joint,
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  which allows sliding, and S is the sphere joint, your classic
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  ball joint. And these designations let
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  engineers define these incredibly complex 3 dimensional
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  mechanisms. They do, but then there are some
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  linkages like the RSSR linkage that just defied the standard
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  rules of kinematics. The maverick space mechanisms.
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  That's what they're called because they achieved this
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  complex non standard motion that you just can't analyze using
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  basic planar geometry. They're a class of their own.
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  All right, so all of these moving complicated parts, the
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  gears, the cams, the linkages, they all have to be supported.
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  Which brings us to Part 3, Bearings and the science of
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  precision fits. Let's start with the simplest
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  type, the plain bearing, often centered bronze.
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  And their selection comes down to one critical calculation.
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  The PV calculation the pressure velocity factor P is the
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  pressure on the projected area and V is the surface velocity
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  and designers have to balance these.
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  And this balance is everything. You can't just Max out all the
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  values. No, you can't use the maximum
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  for all three simultaneously. If you run your machine at a
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  super high velocity, you have to lower the load.
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  If you don't, the bearing material will simply melt or
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  disintegrate from the frictional heat.
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  It's a hard limit. A very hard limit.
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  For example, lead based Babbitt has a maximum PV of 35,000, but
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  PTFE fabric, a more advanced synthetic material, only has a
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  limit of 25,000. These material limitations
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  directly constrain how fast and how heavy your machinery can
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  possibly be. Then we move up to rolling
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  element bearings, your ball, roller, tapered and cylindrical
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  types. Here we're relying on
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  authoritative bodies like the Anti Friction Bearing
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  Manufacturers Association, the ABMA for standards on load
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  ratings and fatigue life. And this is where the cost of
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  miscalculation just becomes brutally clear.
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  It does. There are two critical
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  approximate rules for bearing life that every single engineer
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  has to know. The first one is this.
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  Doubling the bearing load reduces bearing life to 110th.
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  110th not half. 110th That is a monumental penalty for a small
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  increase in load. It's huge, and the second rule
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  is just as important. Doubling the speed reduces
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  bearing life to 1/2. So controlling load and speed
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  isn't just about performance. It's about controlling the
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  maintenance schedule, the downtime, the entire life cycle,
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  cost of the machine itself. The sensitivity brings us to
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  maybe the ultimate constraint in all of mechanical design.
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  The precision fit, the fit of a bearing into its housing, is
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  often the last and most critical step.
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  It really is. EU customary classes of fit
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  range from RC1 which are close sliding fits just for accurate
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  location. All the way U to FN 5.
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  Which are the heavy force fits use for parts that are designed
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  to be highly stressed and never ever move again.
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  Let's use an example, an RC3 precision running fit on a 1 1/2
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  inch nominal shaft. The tolerance window required is
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  just incredibly narrow. The shaft and the hole have to
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  be machined to clearances that are often less than two
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  thousandths of an inch across the entire diameter.
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  That's tighter than a human hair.
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  Tighter than a human hair across the whole part.
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  If you miss that tolerance by even a fraction, the shaft will
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  either seize up from heat expansion or it will vibrate
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  itself to pieces. Immediate fatigue failure.
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  And for the tightest connections the interference or force fits
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  you have to calculate the stresses.
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  You have to. Designers must treat the parts
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  as thick walled cylinders to calculate the internal stresses.
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  This determines how much torque can be transmitted and the axial
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  force you need to physically press them together.
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  And the stress analysis is absolutely critical here.
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  Because the maximum tangential and radial stresses happen right
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  in the contact surfaces, designers have to use stress
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  concentration factors, maybe 1.5 to 2 point O, especially for
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  thick hubs pressed onto a shaft if you neglect those factors.
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  You risk a sudden brittle fracture or a catastrophic
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  fatigue failure somewhere down the line.
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  Absolutely. So our deep dive today has moved
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  us all the way from the generalized motion of gears,
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  through the controlled linear action of cams and linkages and
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  finally into the critical support systems defined by
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  bearings, these hyper precise fits.
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  The complexity forces designers to master combined disciplines.
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  You can't just be a mechanical engineer anymore.
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  You can't. You have to understand
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  mechanical, electrical and electronic systems.
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  And that really is the ultimate insight when you look at modern
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  electromechanical products, whether it's an industrial
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  switch assembly or a high precision titanium camera
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  shutter, It demands that engineers become general
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  practitioners. Yeah, you have to grasp all
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  three disciplines rather than sticking to a narrow specialty.
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  Precision in one area requires mastery in all the others.
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  And this complexity brings us right back to the limitations of
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  pure analysis. You know, we discussed how
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  incredibly difficult it is to mathematically solve the precise
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  motion of something like a four bar linkage.
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  And that difficulty often forces modern engineers to rely on
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  computer aided design and, critically, physical dynamic
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  analysis. So here's the final thought.
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  When you look at any complex machine operating smoothly
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  today, an engine, a robotic arm, a printing press, anything, ask
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  yourself this. Are the specific movements you
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  are watching the result of elegant mathematics that
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  perfectly modeled the entire system from the start?
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  Or were they finely tuned by watching a prototype's slow
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  motion video captured at 12,000 frames per second, with
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  engineers correcting the geometry based on observed
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  physical reality?