Latest / Mechanical Engineering Made Simple / (#78) Shaft Deflection Gearing Belts and Chains

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(#78) Shaft Deflection Gearing Belts and Chains · Mechanical Engineering Made Simple

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  Welcome back, design junkies, to mechanical engineering made
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  simple. Glad to be here.
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  OK, let's fire U the machine. We are jumping into a deep dive
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  today on the literal components that make our industrialized
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  world spin machine element design and mechanisms.
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  That's right. And we've compiled sources that,
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  you know, they really skip the abstract theory.
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  Yeah, this is all practical stuff.
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  It's pure, practical, tested design data, the kind of
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  knowledge that comes straight from major manufacturers.
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  So our mission for this deep dive is to extract that high
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  leverage knowledge. We're talking about the
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  procedures, the safety margins, all the non negotiable physical
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  laws for designing complex systems.
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  And we're going to focus on power transmission shafts and of
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  course, everyone's favorite gearing.
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  It's funny because no matter how complex the final machine is, it
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  always comes back to the basics, doesn't it it?
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  Always does. The foundation is still the
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  simple machines. I mean the lever the inclined
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  plane which gives you the wedge and the screw and the wheel and
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  axle the. Pulley, the gear wheel, all
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  that. Exactly.
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  And you know, there are some modern editions people talk
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  about, like the hydraulic press. And what was that other one, the
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  Rolomite device? The rolomite?
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  Yeah, it was. I think the US Patent Office
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  actually declared it a new simple machine some years back.
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  It's fascinating. But for us today are sticking to
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  the industrial workhorses. Absolutely.
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  We're talking about the precise standards and constraints for
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  components that have to run reliably for decades.
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  You need to know it will perform exactly as you calculated.
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  OK, let's unpack this power transmission fundamentals.
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  Let's start with belts. A lot of people mix up sheave
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  and pulley. They do, and it's a critical
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  distinction really, as sheave is the grooved wheel.
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  It's specifically for V belts. And a pulley.
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  A pulley is well, traditionally it's the wheel for a flat belt.
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  It's a simple thing, but mixing them up sort of signals you
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  don't grasp the underlying physics.
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  Speaking of V belts, we have the classic sizes A through E and
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  then the narrow V belts, the 3V5V8V.
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  Right. Why do designers go for the
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  narrow V belts when they need high power?
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  It's all about power, more density.
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  The narrow V belts are just engineered better for the job.
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  The load from the belts tension cords gets transferred much more
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  directly to the sides of the sheaf grooves.
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  So it's a more efficient transfer of force.
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  A much more efficient transfer. So for the same width, A narrow
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  V belt gives you a significantly higher power rating.
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  You just get more work done in less space.
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  And the actual work, the horsepower comes from the pole,
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  right? The difference in tension
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  between the tight and slack side.
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  That's the core of it and you can't just design for that.
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  You have to check your geometry. The designer has to calculate
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  the arc of contact correction factor, we call it.
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  G OK, what happens if you don't? Well if your belt doesn't wrap
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  far enough around the smaller sheave, your arc of contact is
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  too small, you lose load carrying.
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  Capacity and it starts to slip. It just slips.
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  You have to account for that reduction in your design.
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  And I'm guessing speed is a hard limit here.
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  Oh absolutely. Friction is heat, and
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  centrifugal force is trying to pull the belt right off the
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  sheave, so designers have to keep narrow V belts below 6500
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  feet per minute. And classic V belts.
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  A little lower, below 6000. If you go past those limits,
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  you're just guaranteeing failure, and a dangerous failure
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  at that. OK, let's shift from belts to
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  chains. Roller chain.
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  It's super reliable, comes in riveted and detachable types,
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  but the real decision seems to be the sprocket.
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  That's where the budget meets the road, so to speak.
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  You have to choose a commercial sprocket or a precision
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  sprocket. So when do you have to spend the
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  extra money for precision? Anytime you have high speed,
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  high loads, fixed centers or the big one, any application that
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  needs accurate timing. Like for registration marks on a
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  printing press or something. Exactly.
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  If your machine needs that chain to be in a very specific place
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  at a specific time, you need the manufacturing tolerance of a
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  precision sprocket. Commercial sprockets are fine
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  for, say, a farm implement, but not for that.
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  This is where the source material got really interesting.
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  You gave a pretty serious warning about quality control.
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  It did, yeah. The sources stress that while US
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  made roller chain is generally up to spec, you know ANSI and
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  ASTM standards. Imported chain means very
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  careful inspection. They actually compared it to
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  counterfeit hardware. Yes, like bolts and screws that
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  say they're a certain grade but fail way below their advertised
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  strength. That is terrifying.
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  You could design a whole system based on the strength of a
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  component and if the part you bought isn't what it claims to
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  be. The whole thing fails
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  catastrophically. It's a huge liability.
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  It just means you have to be so diligent about where your parts
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  are coming from. Your design is only as good as
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  its weakest link. Literally.
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  Let's move to the backbone of all this shafts, the structural
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  spine of rotating machinery, and they're under a whole cocktail
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  of different stresses. That's a good way to put it.
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  You've got your bending and torsional stresses, sure, but
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  the real design constraints are usually the deflections.
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  So angular and linear deflection.
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  Right. Torsional deflection and what we
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  call Delta X and then there's the big one, the operational
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  limit, critical speed, we'll get to that.
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  First, deflection. What's the practical hard limit
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  when a shaft is carrying something that has to be stiff
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  like a gear? OK.
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  So for gearing, stiffness is almost always more important
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  than raw strength. The rule of thumb, The
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  recommended Max is an angular deflection of no more than 0
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  point O 8° per foot of length. Zero point O 8°.
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  That's tiny. It's incredibly small, but if
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  you violate it you guarantee massive misalignment in your
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  gear of teeth. They'll just chew each other up.
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  Your bearings will fail. It's a non negotiable threshold.
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  And you have a great example that shows how geometry can
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  totally overpower material strength.
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  We do so take a standard one and 1/4 inch diameter shaft.
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  It's supporting A4 under pound load.
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  The calculated linear deflection the delta X was 0.0 the 302
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  inches. 30,000 sounds. Still a layman, yeah, but for a
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  gearing application that's completely unacceptable.
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  That run out would destroy the system.
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  So. You can't just use a stronger
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  steel. No, that's the point.
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  The solution isn't a stronger material, it's a stiffer
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  geometry. You have to make the shaft
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  diameter bigger or move the support bearings much closer
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  together. Geometry dictates performance
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  here. Once you have the geometry then
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  you can talk materials. Medium carbon steels like 10:45
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  are common, but they need heat treating.
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  What about those specialized high manganese steels?
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  Things like stress proof and fatigue proof, They're
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  metallurgical magic. They get their incredible
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  strength. We're talking 100,000 even
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  125,000 PSI yield strength from severe cold working.
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  And the big advantage is. No heat treatment.
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  That's a massive win. It saves money, simplifies
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  manufacturing, and crucially, it prevents the distortion and
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  warping that you so often get with long heat treated shafts.
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  A fantastic trade off, but what if your chefs just can't be in
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  line? That's where the hooks coupling
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  comes in, right? The universal joint.
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  The card and universal joint, yeah it's the standard solution,
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  but it has a major inherent flaw which is non uniform angular
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  velocity. Meaning the output shaft speeds
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  up and slows down with every single rotation, even if the
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  input is perfectly. Steady precisely, and it's not a
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  small effect. Let's look at the numbers.
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  Say you have a driver shaft at a constant 250 RPM and the joint
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  angle is 23°. OK, The speed fluctuation on the
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  driven side is 41.5 RPM. Wow, that's huge.
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  It's massive. That variance creates severe
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  vibration and wear on any system trying to maintain smooth
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  motion. So what's the fix?
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  How does the designer get around this?
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  You have to use two of them, two U joints with an intermediate
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  shaft, but the alignment is everything.
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  The main driver and driven shafts have to be parallel and
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  the forks on that intermediate shaft must be aligned in the
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  same plane. The first joint creates the
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  variation and the second one perfectly cancels it out.
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  As long as it's set up correctly.
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  As long as it's perfect, yeah. Let's get into controlling
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  motion clutches and brakes. The sources layout two major
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  categories. Yep.
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  You have your positive clutches, which use interlocking teeth.
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  They're for hard, reliable engagement.
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  And then you have the workhorses, the friction
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  clutches. Disc cone centrifugal.
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  All those, all of those, they just rely on friction surfaces
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  to transmit torque. And for those, the goal is to
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  prevent slipping. What kind of safety margin do
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  the sources recommend? You can't just design for the
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  maximum torque. The coefficient of friction
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  changes with heat wear contaminants, so you need a
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  buffer. Safety factor.
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  Exactly. The slipping torque capacity of
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  the clutch needs to be greater than the drivers Max torque
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  multiplied by a safety factor of say 1.4 E to 1.6 year that
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  guarantees it will hold. That's the engineer's insurance
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  policy. Now, when we're calculating for
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  clutches and brakes, the key variable is inertia.
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  Inertia. Yeah.
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  The fundamental calculation is WR squared.
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  Weight times the radius of gyration square.
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  Right. And it's absolutely critical for
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  one reason above all others, heat dissipation.
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  When you stop a mass, all that kinetic energy has to go
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  somewhere. It becomes heat.
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  The clutch of braid has to be big enough to soak up that
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  thermal load without failing. But in a big machine you have
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  parts spinning at all different speeds.
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  The clutch is only at 1 speed. So how do you account for all
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  that? Energy.
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  That's where you get into the concept of reflected inertia,
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  right? It's like kinetic energy
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  accounting. You mathematically reduce the
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  inertia of every moving part, the fast fan, the slow conveyor
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  down to an equivalent WR squared value at the speed of the clutch
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  shaft. So you can add it all up you.
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  Add it all up. It gives you the total energy
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  the clutch has to manage. If you miss that step, your heat
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  calculations are wrong and your component will cook itself.
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  It's the only way to size your heat sink properly.
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  OK, let's pivot to power screws. Jack screws.
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  Used for lifting, clamping. They use square Acme V threads
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  and the number one calculation priority is estimating the
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  surface bearing pressure on those threads.
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  To make sure they don't shear off.
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  Exactly. And just like with clutches, the
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  simple first pass equation isn't quite good enough.
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  It needs a safety factor. It does.
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  The simple formula tends to give you an underestimate of the real
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  pressure. So you have to apply a safety
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  factor, maybe 1.25 to 1.35. Get the final safe pressure you
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  designed for. OK, let's dive into the final
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  and maybe most complex topic, the world of gearing, starting
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  with the most common the spur gear.
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  The spur gear and the magic behind it is a very specific
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  tooth shape called the envelope profile.
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  And that's essential for what? For uniform angular velocity,
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  it's a mathematical curve that ensures speed transfer stays
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  perfectly constant and smooth even if there are slight errors
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  in the center distance between the gears.
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  The big choice designer has to make here is the pressure angle
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  or PA, usually 14.5° versus 20°. What's the trade off?
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  It's a classic strength versus smoothness debate.
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  The 14.5° gears are smoother, quieter, and a bit more
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  forgiving of alignment errors. For precision.
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  Great for precision, but the 20° PA gears are just stronger.
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  They have a higher load carrying capacity hands down.
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  But there's a catch, isn't there, if you use too few teeth.
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  There is. It's called undercutting.
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  If you design a 20° PA gear with, say, fewer than 18 teeth,
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  the manufacturing process actually starts to remove
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  material from the base of the tooth.
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  Weakening it. Right at the point of highest
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  stress. So you gain strength from the
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  angle, but lose it all back by trying to make the gear too
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  small. And all of this is based on the
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  Lewis equation. The Barth revision.
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  Yeah, It treats the tooth like a simple canti liver beam.
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  It's still the foundation. OK, what about helical gears?
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  Helical gears are for parallel shafts and you have to pair them
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  right. A left hand pinion needs a right
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  hand gear. And the big advantage over a
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  spur gear? They're much quieter because the
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  teeth engage gradually. They also have better tooth
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  strength and a much greater load capacity for the same size.
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  But there's a downside. A big one.
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  The angle ankle teeth create an axial load, a thrust load, and
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  that force has to be absorbed by thrust bearings.
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  If you don't spec the right bearing system, the whole
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  assembly will tear itself apart. Got it.
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  Let's talk worm gearing. These are for really specialized
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  jobs. They are.
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  They're perfect for three things.
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  Huge speed reduction in a tiny space, transmitting high torque
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  at a right angle and resisting back driving.
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  Meaning the output can't easily turn the input.
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  Exactly. And that extreme ratio comes
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  from? It's the number of teeth on the
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  worm wheel divided by the number of leads on the worm itself,
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  which is usually just one to four.
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  But there's a catch with the torque output.
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  Right, a crucial 1. The output torque isn't just
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  input torque times a ratio. You also have to multiply by the
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  efficiency. There's a lot of sliding
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  friction, so you lose a significant amount of energy as
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  heat. The sources mentioned a bunch of
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  other specialty gears. Yeah, 0 bevel hypoid spiroid.
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  The spiroid gears are worth remembering.
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  They're known for combining a very high ratio with a compact
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  design that's cheap to mass produce.
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  OK, let's end the design talk with the most practical tool of
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  all. You're in a shop, You've got an
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  old gear, no documentation. How do you figure out what it
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  is? You need a gear tooth gauge.
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  Simple as that. It's a simple tool.
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  It's like a set of templates. You use it to physically
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  identify the dynamical pitch, how fine the teeth are, and the
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  pressure angle 14.5 or 20°. You just match the profile.
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  It's the designers decoder ring. This has been fantastic.
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  It really shows how every single component from AV belt to a gear
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  is governed by these incredibly detailed design constraints and
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  safety margins. Absolutely.
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  We've talked about systems limited by heat, by stiffness,
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  by material stress, but if we tie it all back to the
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  foundation, the shaft, there's one constraint that can override
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  everything else. And it's a powerful final
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  thought for you, the designer. And that would be the dynamic
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  limit. That would be the importance of
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  critical speed. OK, for any given shaft with its
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  diameter and length, there is a specific RPM, the first critical
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  speed, where it becomes dynamically unstable.
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  It starts to whip like a jump rope.
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  Regardless of how strong the material is.
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  It doesn't matter how strong the steel is, the calculation shows
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  that the ultimate performance of a rotating system isn't limited
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  by its static strength, but by its structural dynamics.
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  So. Structure beats strength.
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  In high performance design structure almost always beats
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  strength. It's a critical trade off you
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  face every single day. Dynamic stability over static
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  strength. A perfect note to end on.
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  Thank you for tuning into this deep dive.
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  Until next time.