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Stopping machines from vibrating themselves apart · Mechanical Engineering Made Simple

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  Welcome back to mechanical engineering made simple.
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  Imagine designing a massive, like, incredibly expensive
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  machine, right? Yeah.
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  Something that's perfectly balanced.
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  Exactly. It's precision engineered,
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  bolted securely to a thick concrete floor, and the moment
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  you turn it on, it spontaneously decides to tear itself to
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  pieces. Which is absolutely terrifying
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  to watch, by the way, right? There are no external
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  earthquakes, no bumpy roads, no broken parts.
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  The machine literally destroys itself using its own momentum.
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  And this is well, this is the invisible battle happening all
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  around you every single day. It really is.
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  I mean, it's happening in the laundry room right now.
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  It's happening under the hood of your car, and it's even
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  happening deep inside the hulls of massive cruise ships out on
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  the ocean. Absolutely.
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  It's everywhere. So today, the mission for this
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  deep dive is to explore this hidden, you know, often
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  destructive world of mechanical vibrations.
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  We're going to look at 2 specific things today.
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  Right, the core problem and then the solution.
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  Yeah, first, this terrifying phenomenon called self excited
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  vibrations where a machine basically becomes its own worst
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  enemy, and 2nd, the absolute genius engineering tricks like
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  dynamic absorbers and dampers that engineers used to save
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  them. It's a really fascinating area
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  of physics. It is so if you've ever wondered
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  why your washing machine doesn't just walk out the front door,
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  you are in the right. Place It really is a battle, and
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  to understand how we fight it, we first have to distinguish
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  between the two main types of vibration that engineers worry
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  about. Right, because they aren't all
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  the same. Exactly.
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  Most people are very familiar with forced vibration.
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  Think of driving your car over a bumpy, unpaved Rd.
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  Or, you know, having an unbalanced wheel on your car
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  that shakes your steering wheel at a certain speed.
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  Sure, that's a perfect example. In a forced vibration, the
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  alternating force that is shaking the system exists
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  entirely independently of the motion.
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  Meaning if you magically grab the car and hold it perfectly
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  still, that bumpy Rd. is still there, right?
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  The external force hasn't gone away at all.
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  Precisely. But self excited vibration is a
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  completely different beast. In a self excited vibration, the
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  alternating force that sustains the motion is actually created
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  by the motion itself. Oh wow.
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  Yeah, if you stop the motion, the force entirely disappears.
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  OK, let's unpack this, because that sounds almost like magic.
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  I mean, how does a vibration feed itself without an external
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  force? Well, to understand it we really
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  need to look at the physics of what we call negative damping.
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  Negative damping. OK, Yeah.
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  If we look at the characteristic equation of a damp free
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  vibration. Oh, here comes the.
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  I'll keep it simple, I promise. It's just MX double dot plus CX
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  dot plus KX equals 0. Right, the classic mass spring
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  damper set up. Exactly.
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  So in a normal system, that damping coefficient the C is
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  positive. Which means the vibrations
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  naturally die out over time, right?
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  Yes, but if a physical mechanism causes that C to become less
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  than 0, the exponential factor becomes positive.
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  Wait, so the machine starting from almost nothing just
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  oscillates with an ever increasing amplitude?
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  Exactly. It just builds and builds until
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  something physically breaks or some extreme restraint limits it
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  so. It's kind of like pushing a
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  child on a swing. That's a great analogy, yeah.
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  But imagine the swing itself is somehow generating the pushes
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  from its own momentum. Yes.
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  The motion literally creates the push.
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  But wait, how does a lifeless piece of metal just decide to
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  create negative damping? I mean, a spitting shaft doesn't
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  have a little motor deciding to push it.
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  No it doesn't. So where is the energy coming
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  from? It hides in tangential forces,
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  and a classic example from the sources we're looking at is
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  called hysteretic whirl. Hysteretic like hysteresis, the
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  internal friction inside the material itself.
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  Spot on. When a solid metal shaft bends
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  and rotates at high speeds, the metal fibers on the outside of
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  the bend are constantly stretching.
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  And the ones on the inside are compressing.
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  Right, because of internal friction, the metal doesn't
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  perfectly and instantly bounce back.
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  There's a slight phase shift, well, a delay between the
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  strain, which is the physical bending, and the stress.
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  The stress being the internal force trying to snap it back
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  straight. Exactly.
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  So the resulting elastic restoring force isn't perfectly
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  parallel to the deflection. So it's essentially getting
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  tired and lagging behind its own rotation.
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  Yes, and that sideways angle creates A tangential component
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  that pushes the shaft forward. Causing a forward whirl.
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  Right, a forward world that just builds and builds.
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  Wow, so the machine is basically cannibalizing its own rotational
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  energy to push itself sideways? That is a dangerous loop.
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  It's. Extremely dangerous.
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  But so far, we're just talking about tired solid metal.
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  What if the machine isn't solid? Like what if we're dealing with
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  a hollow rotor? That introduces a whole new
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  variable. Fluids.
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  Yes, yeah, trapped fluid world is another major culprit.
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  Think about high speed centrifuges with liquid trapped
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  inside hollow spinning rotors. Hold on, that doesn't make sense
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  to me. If I take a bucket of water and
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  swing it in a circle, centrifugal force just pins the
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  water flat against the outside walls.
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  Yeah. So shouldn't the liquid just
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  pool outward radially and balance itself?
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  You would think so if the fluid were perfectly frictionless, but
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  you have to factor in viscosity. Oh right, the fluid is sticky.
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  Exactly. The spinning surface of the
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  inside of that hollow cavity isn't totally smooth to the
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  fluid, it actually drags the viscous fluid along with it.
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  Creating an angle of advance. Yes.
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  So the fluid doesn't just pull straight outward on the heavy
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  side, it gets dragged forward. Oh I see, because the heavy pool
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  of fluid is now physically leading the deflection.
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  Exactly. So its centrifugal force isn't
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  pointing straight out either. It has a tangential component
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  pulling the rotor. Forward pulling the machine off
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  its axis. Right, creating a forward whirl
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  once again. But perhaps the most myelin
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  example isn't from fluids or internal metal fatigue.
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  It's from external contact. Dry friction whip.
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  Dry friction whip. OK, like what happens when an
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  unlubricated shaft rubs against the stationary stator?
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  Yes, like if a massive steam turbine shaft sags just enough
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  to touch the steel housing. What's fascinating here is the
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  direction of the destruction. How do you mean?
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  Well, when the rotating shaft makes contact with the dry
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  stator, Coulomb friction creates a massive tangential force.
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  But think about the geometry of two circles touching.
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  OK, if a shaft is spinning clockwise and it rubs against
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  the inside of a stationary ring, the friction actually causes the
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  shaft to roll along the inside of that ring.
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  Oh, like a gear meshing? Exactly.
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  If you picture a clockwise spinning gear walking around the
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  inside of a larger ring gear, it walks counterclockwise.
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  Exactly like a gear, the friction drives a whirling
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  motion that is backward counter to the direction of shaft
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  rotation. And that is a catastrophic
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  feedback loop. The harder it rubs, the harder
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  it pushes itself backward. Which increases the centrifugal
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  force. Which makes it rub even harder
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  into the casing. Right.
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  Real world turbines have literally ripped themselves off
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  their mouths in seconds because this dry friction whip melts the
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  metal. It just causes the rotor to
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  explode through the casing. That is wild.
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  It really is. So what does this all mean?
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  If machines naturally develop these destructive tangential
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  forces, engineers must have a way to fight back.
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  I mean, we can't always just make the metal thicker.
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  No, Eventually things get too heavy to be practical.
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  Right, so how do we kill the vibration?
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  This brings us to the second-half of our mission,
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  Dynamic absorbers and the first defense is the tuned undamped
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  dynamic absorber. OK, an undamped absorber.
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  Yes, the concept is incredibly elegant.
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  If a system is being forced to vibrate at a constant frequency,
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  you can just attach an auxiliary mass on a spring tuned exactly
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  to that same frequency. A sacrificial mass.
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  We intentionally attach something else to the machine
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  just so it can vibrate instead. That is the goal.
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  This auxiliary mass enforces a node.
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  Enforces a node. What does that look like in
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  practice? It means the small attached mass
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  ends up vibrating violently. It creates a reaction force that
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  perfectly cancels out the excitation.
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  Leaving the primary machine sitting dead still.
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  Precisely. The expensive tool you care
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  about sits dead still while the little mass hidden inside goes
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  crazy. You know, this makes me think of
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  high end electric hair Clippers. Oh, that's a great example.
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  Right, because they operated 120 Hertz from the power supply.
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  The cutter blade is moving back and forth incredibly fast,
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  generating massive unbalanced forces.
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  But if they place a precisely tuned mass spring system inside
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  the handle. The internal mass takes all the
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  punishment, it vibrates wildly and the Clipper handle stays
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  perfectly still in your hand. It's a perfect application
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  because the wall power never changes its frequency.
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  But wait, this only works if the frequency never changes, right?
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  What if the machine speeds up or slows down?
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  I mean, doesn't the absorber become a massive problem then?
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  That is the exact fatal flaw of the undamped absorber, really.
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  Yes, an untuned absorber splits the system into two completely
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  new natural frequencies. Oh no.
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  So instead of having one speed where the machine shakes itself
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  apart, you've just doubled your chances of hitting a resonance
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  point. Exactly.
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  If the machine speed varies, it will hit one of those new
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  resonances and vibrate worse than before.
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  OK. So building on that realization,
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  how do we protect machines that do change speeds?
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  Because washing machines, car engines, they speed up and slow
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  down constantly. That's where we move to systems
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  that dynamically change their tuning.
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  Let's look at the home washing machines.
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  Spin dryer. Oh yeah.
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  When a load of wet clothes is unbalanced, the basket wants to
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  tear itself apart as it speeds up through its critical speed.
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  To stop that, engineers use a fluid or ball balancer.
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  Like a hollow ring at the top filled with viscous fluid or
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  metal balls. Yes, now below the critical
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  speed, the fluid pools on the heavy side.
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  Wait, on the heavy side, doesn't that just make the unbalanced
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  significantly worse? It absolutely does.
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  Below critical speed it increases the vibration.
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  Then why use it? Because as any rotating system
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  passes through its critical speed, it undergoes a massive
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  180° phase shift. The phase shift, Yes, it stops a
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  rotating around its geometric physical center and starts
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  rotating around its center of gravity.
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  Oh, so the heavy wet towel is suddenly pulling the physical
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  center of the drum toward the center of gravity.
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  Exactly, and because the axis of rotation shifts, it causes the
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  fluid or balls to move to the completely opposite side, which.
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  Perfectly neutralizes the unbalance, right?
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  That is brilliant because it's completely self regulating.
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  Exactly, The physics just automatically fling the
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  counterweight to the correct side.
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  But what about torsional vibration like in car engines?
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  Engines constantly change RPM, so a fixed spring is useless.
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  How do we tune an absorber to a moving target?
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  Well, if we connect this to the bigger picture, we find the
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  pendulum absorber. Pendulum inside a spinning
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  engine block. Yes, you attach a pendulum to a
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  spinning crank hub and because centrifugal force increases with
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  the square of the rotational speed.
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  Wait, so the invisible spring holding the pendulum magically
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  gets stiffer as the engine Revs higher?
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  Exactly. Its natural frequency increases
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  perfectly In Sync with the engine speed.
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  Wow, so it's completely self tuning.
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  Right, it neutralizes specific orders of integration, like the
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  4.5 order in an engine. Rather than a fixed frequency,
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  the pendulum just wiggles back and forth, absorbing all the
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  energy. Saving the crankshaft from
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  snapping in half. Precisely.
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  OK, here's where it gets really interesting.
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  So I want to scale things up. We've talked about hair Clippers
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  and washing machines. What's the biggest vibration
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  problem we can solve? What about a massive ship
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  rolling in the ocean? For ships we use anti roll
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  tanks. They act as giant auxiliary mass
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  dampers. So like giant wing tanks on
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  opposite sides of the hull? Yes, connected by massive pipes
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  and water sloshing between them acts as a tuned mass.
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  I assume the flow is restricted by valves, yes?
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  To provide precise damping By tuning that sloshing delay, you
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  create a massive counterforce. So the water arrives late.
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  When the ocean tries to push the ship back, the thousands of tons
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  of water is still trapped on the other side, dragging the ship
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  heavily back upright. Exactly.
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  On the German luxury liners Bremen and Europa, these exact
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  tanks reduce the maximum roll from 15° down to just 5°.
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  That is incredible. But that's a completely passive
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  system, right? Just relies on gravity.
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  Can we do better than just waiting for water to slosh back
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  and forth? We can we move to activated
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  vibration absorbers. Massive gyroscopes can be
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  precessed by motors. Precessed, meaning physically
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  twisted on their axis. Yes, an activated system uses a
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  servo mechanism. When a sensor detects even a
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  fraction of a degree of roll, a servo motor actively twists the
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  gyroscope. Oh, and when you twist a
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  spinning gyro, it fights back at a 90° angle.
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  Exactly, it exerts maximum stabilizing torque instantly.
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  So it totally overrides the oceans, attempts to vibrate the
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  hull. You're using an intelligent
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  machine to combat the RAW forces of nature in real time.
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  It's engineering at its finest. It really is.
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  So we've gone from a lifeless piece of metal vibrating itself
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  to death all the way to massive servo motors actively twisting
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  tons of spinning steel to calm the ocean.
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  Let's tie it all together for you.
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  Listening. Yeah, let's.
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  Do that. Whether you're trying to figure
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  out why a piece of machinery on your workbench is humming
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  uncontrollably, designing a new power tool, or just appreciating
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  the invisible physics keeping your washing machine from
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  destroying your laundry room, understanding how to balance
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  these forces is literally like having a superpower.
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  It changes how you see the world.
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  It does. You realize you don't always
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  have to fight the energy directly.
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  With thicker walls, you can redirect that destructive energy
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  into a harmless sacrificial mass.
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  You can tune the system to effectively fight itself.
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  And you know that concept goes far beyond mechanical
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  engineering. How do you mean?
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  Think about your own life and workflows.
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  Where do you have self excited and negative feedback loops that
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  feed on their own momentum? Oh wow, and what kind of
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  auxiliary mass or mental dampener could you creatively
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  introduce to absorb that destructive energy before it
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  shakes your foundation? Master the critical few or the
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  trivial many will master you. If this episode gave you a solid
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  take away, drop a comment. Takes you a few seconds, but it
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  tells me this workbench is worth keeping alive.