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(#125) Why Your Solenoid Actuator Is Weak · Mechanical Engineering Made Simple

• 0:00
  Welcome back to mechanical engineering made simple.
• 0:02
  It is. It's really fantastic to be
• 0:05
  back. Today we are going to dive into
• 0:06
  a story about a device that I think every single engineer or
• 0:13
  tinkerer has underestimated at least once in their life.
• 0:16
  Oh, definitely. Because it looks deceptively
• 0:18
  simple, right? It's essentially just a spool of
• 0:20
  copper wire and a chunk of steel.
• 0:22
  You are talking about the solenoid actuator I.
• 0:25
  AM And honestly, it's a classic trap.
• 0:27
  You look at the diagram and it's just a coil and a plunger.
• 0:30
  You think, how hard can this be? I run current, the magnet turns
• 0:33
  on, the thing clicks right. But then you actually build 1.
• 0:36
  Or, you know, you try to troubleshoot one in a piece of
• 0:38
  industrial machinery, and you realize that getting that
• 0:41
  satisfying snap involves some seriously nuanced physics.
• 0:45
  It really does. I mean, on paper it is the
• 0:48
  simplest machine in existence, but the gap between making a
• 0:52
  magnet and making a useful actuator that actually does work
• 0:55
  is huge. That gap is filled with concepts
• 0:58
  like inductance, reluctance, and the principle of virtual work.
• 1:02
  And to navigate that gap for this deep dive, we're going to
• 1:05
  follow the very real struggles of a protagonist we'll call
• 1:09
  Alex. OK.
• 1:10
  Now Alex is a mechanical engineer working on a pretty
• 1:13
  high stakes project. He's designing a safety locking
• 1:16
  latch for a pressurized industrial door.
• 1:19
  Oh wow. OK, so this isn't just a toaster
• 1:21
  lever. If this latch fails, the door
• 1:24
  could blow open or the safety interlocks could fail.
• 1:27
  The stakes are real. Exactly.
• 1:30
  The requirements are super clear.
• 1:32
  When the control system sends a signal, a Skeel bolt, which is
• 1:35
  our plunger, needs to shoot forward, compress a heavy spring
• 1:39
  and lock that door solid. Which is a very standard linear
• 1:42
  actuator application. Right, so Alex does what any of
• 1:46
  us might do. He grabs a plastic spool, winds
• 1:49
  a few hundred turns of magnet wire around it, sticks a steel
• 1:52
  bolt about halfway into the hole and hooks it up to his 24 Volt
• 1:55
  power supply. Sounds reasonable so far.
• 1:57
  He's ready for the big moment. He flips the switch, expecting a
• 2:00
  loud industrial clunk. But I can already see where this
• 2:03
  is going. Yeah, instead of a clunk, you
• 2:04
  get to a twitch. A twitch.
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  The bolt kind of lazily slides forward maybe 1/4 of an inch,
• 2:10
  vibrates a little bit, and it just stops.
• 2:13
  It doesn't even come close to compressing the locking spring.
• 2:16
  It's weak. It's weak, it's sad, and Alex is
• 2:19
  standing there scratching his head thinking I have current
• 2:21
  flowing. I have a magnet.
• 2:23
  Why do I have 0 force? That is the classic twitch of
• 2:27
  failure, and I bet I know what his first instinct is to fix it.
• 2:30
  Oh, absolutely. He looks at the power supply
• 2:33
  dial and thinks I just need more juice.
• 2:35
  Right. He's about to crank the voltage
• 2:37
  from 24 up to 48. Which is the engineering
• 2:40
  equivalent of just yelling louder at someone who doesn't
• 2:42
  speak your language. It really is.
• 2:44
  Yeah. And before Alex melts his coil
• 2:46
  into a puddle of copper and plastic, let's freeze time.
• 2:49
  Yeah, We need to help him understand why his latch is
• 2:52
  failing. Yes.
• 2:53
  And to do that, we have to look at how we actually calculate the
• 2:56
  force on that plunger, because it turns out there's a hard way
• 3:00
  to do it in a smart way. And unfortunately, most of us
• 3:04
  learn the hard way in physics class, which is exactly why Alex
• 3:07
  is confused right now. He's probably thinking about the
• 3:09
  Lorentz force. The Lorentz force, yeah, that's
• 3:11
  when we all memorize, right? F equals QE plus QV QV cross B.
• 3:16
  Right. It tells you the force on a
• 3:18
  single charged particle moving through a magnetic field.
• 3:22
  It is strictly, fundamentally true.
• 3:24
  Every single electron spiraling through Alex's wire is
• 3:28
  experiencing this force. So.
• 3:30
  Alex is thinking, OK, I just need to sum up all those forces.
• 3:33
  But think about what that actually entails.
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  You have a spiral coil, so the current direction is constantly
• 3:38
  changing in three dimensions. You have a magnetic field that
• 3:41
  curves and changes intensity depending on where you are in
• 3:44
  the coil. To calculate the net force on
• 3:46
  the plunger using Lorentz, you would need to do a vector cross
• 3:50
  product calculation for every differential element of the wire
• 3:54
  and the core. Which is a vector calculus
• 3:56
  nightmare. It is entirely computationally
• 3:58
  exhausting. It's like trying to predict the
• 4:00
  flow of a river by tracking every single water molecule
• 4:03
  individually. You might get the right answer
• 4:05
  eventually, but it gives you 0 intuition about how to fix the
• 4:09
  physical. Design.
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  So we abandoned the hard way. We need the smart way and the
• 4:13
  sources call this the energy method.
• 4:15
  Or the principle of virtual work.
• 4:17
  This is the exact shift Alex needs to make.
• 4:20
  Instead of asking what is the force on this electron, you ask
• 4:24
  how does the energy in the system change if I move the
• 4:27
  plunger? OK, let's unpack this.
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  We're moving from vectors to energy.
• 4:31
  How does that help us find the force?
• 4:33
  Well, think about a ball sitting at the top of the hill.
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  Why does gravity pull it down? Because the ball wants to lower
• 4:39
  its potential energy, it wants to go from a high energy state
• 4:42
  to a low energy state. Precisely.
• 4:44
  Electromechanical systems have a very similar drive.
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  The magnetic field stores energy, and the system will
• 4:50
  generate a force to rearrange itself into a state where it can
• 4:53
  store that energy most efficiently.
• 4:55
  OK, in the case of a solenoid, the system wants to maximize its
• 4:59
  inductance. Maximize inductance.
• 5:01
  It sounds like a textbook catch phrase, but what does it
• 5:03
  actually mean physically? What is this system trying to
• 5:05
  do? Think of the magnetic field
• 5:07
  lines like a stream of water. They really, really want to flow
• 5:11
  through iron. Iron is like a wide open pipe
• 5:14
  for magnetic flux. But air?
• 5:16
  Air is like a clogged pipe. It's very hard for the field to
• 5:19
  travel through air. OK, so in Alex's broken latch,
• 5:23
  the plunger sitting halfway out, there's a big air gap inside the
• 5:27
  coil. Exactly.
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  The magnetic field is trying to complete its loop, but it has to
• 5:31
  jump across this massive gap of air.
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  It's strained, it's inefficient. The inductance is low because
• 5:37
  the path is so difficult. And the system knows that if the
• 5:40
  plunger were to move inward, that air gap would disappear.
• 5:43
  OK, yes, the system senses that moving the steel plunger into
• 5:48
  the gap will make the path easier.
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  It will increase the inductance. So the force you feel that
• 5:53
  physical pull on the plunger is actually the system trying to
• 5:56
  grab the steel and stuff it into the air gap to make the magnetic
• 6:00
  flow easier. That makes so much more sense
• 6:02
  than calculating electron vectors.
• 6:04
  Yeah, the force is just the system trying to close the gap.
• 6:06
  Correct. And we can actually quantify
• 6:08
  this. The sources give us a specific
• 6:10
  equation that really illuminates Alex's problem.
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  Let's hear it. The force is equal to 1/2 times
• 6:15
  is the current squared multiplied by and this is the
• 6:18
  key term here. The change in inductance with
• 6:20
  respect to position, OK. Let's visualize that equation
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  force equals one half I ^2 * d LDX.
• 6:27
  Exactly DLDX. That is the derivative.
• 6:31
  It represents the slope of the inductance.
• 6:33
  It basically asks the question, if I move the plunger 1mm, how
• 6:38
  much does the inductance improve?
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  So it's a bang for your butt calculation.
• 6:41
  That's exactly what it is. If moving the plunger gives a
• 6:44
  huge increase, recent inductance, a huge improvement
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  in the magnetic path, then DLDX is big and the force is huge.
• 6:51
  Yeah, but if moving the plunger barely changes anything.
• 6:54
  Then the force is tiny and I think we just diagnosed Alex's
• 6:58
  problem. We did.
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  Alex has his plunger starting way out in the air.
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  The air gap is huge. When the plunger moves a tiny
• 7:04
  bit from that position, the magnetic path doesn't get that
• 7:06
  much better. It's still mostly air.
• 7:08
  So DLDX is small. It's very small, yeah.
• 7:11
  The system effectively shrugs and says, well, moving the
• 7:13
  plunger doesn't really help me much right now, so I'm not going
• 7:15
  to pull very hard. But as the plunger gets closer.
• 7:17
  As it gets closer, it starts to bridge the gap.
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  Suddenly every millimeter of movement drastically improves
• 7:23
  the magnetic path. The inductance sty rockets so
• 7:26
  DLDX becomes massive and the force spikes.
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  This is a huge realization for anyone designing these.
• 7:34
  A solenoid isn't like a hydraulic piston that pushes
• 7:36
  with constant force. It's highly non linear.
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  It's weak at the start and incredibly strong at the end.
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  Which is terrible for Alex because he needs to compress a
• 7:46
  heavy spring right from the beginning of the stroke.
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  He is trying to start his movement in the dead zone.
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  So cranking the voltage isn't the answer.
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  He needs to fix the geometry. And this leads us to another
• 7:58
  concept from the notes that helps visualize the fix, which
• 8:01
  is the magnetic circuit. Yes, this is the bread and
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  butter of magnetic design. Electrical engineers love
• 8:06
  circuits, so we just map magnetism onto circuit rules.
• 8:10
  Makes things so much easier to see.
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  So let's run the comparison. In an electric circuit you have
• 8:15
  voltage pushing current against resistance.
• 8:17
  Right. And in a magnetic circuit you
• 8:19
  have magnetomotive force which is your number of turns times
• 8:23
  your current or N times I pushing magnetic flux against
• 8:26
  reluctance. Reluctance.
• 8:28
  I love that word. It just sounds like the material
• 8:30
  is stubbornly refusing to cooperate.
• 8:33
  That is exactly what it is doing.
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  Reluctance is a measure of how much material resists magnetic
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  flux. Iron has very little reluctance.
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  Air has massive, huge reluctance.
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  So looking at Alex's latch through this lens, he has a
• 8:47
  circuit. The coil provides the push, but
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  his circuit has a giant resistor in the middle of it, which is
• 8:53
  the air gap. He's trying to drive current
• 8:55
  through a brick wall. The force we talked about
• 8:57
  earlier, another way to define it is that the system is trying
• 9:00
  to minimize reluctance. It wants to delete that air gap
• 9:04
  resistor and replace it with a short circuit of steel.
• 9:07
  So knowing all this, the energy method, inductance, reluctance,
• 9:11
  how does Alex actually fix the latch?
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  He's sitting there with this twitching bolt.
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  What does he do? He needs a three-step plan.
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  First geometry. He has to redesign the mechanism
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  so the plunger starts deeper inside the coil.
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  He needs to eliminate that initial dead zone so that DLDX
• 9:26
  is high right from the very start.
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  Don't ask the solenoid to pull from across the room.
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  Got it. 2nd is the return path. This is a super common rookie
• 9:34
  mistake. The flux go through the center
• 9:36
  of the coil, but how does it get back to the other end?
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  Usually just through the air around the outside of the coil,
• 9:40
  right? Right, and that is a huge source
• 9:42
  of reluctance. The air outside the coil is just
• 9:45
  as bad as the air inside. Alex needs to wrap the coil in a
• 9:49
  steel shell or AC bracket. He needs to build a magnetic
• 9:52
  highway for the flux to loop back.
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  So he's encasing the coil in iron to keep the reluctance low
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  for the whole entire loop. Exactly and 3rd materials.
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  He needs to make sure his plunger is made of a high
• 10:05
  permeability steel. If he's using standard stainless
• 10:08
  steel for example, some grades of that are non magnetic.
• 10:12
  That would be like using plastic.
• 10:14
  He needs a material that loves magnetic flux.
• 10:16
  OK, so let's Fast forward. Alex takes this advice.
• 10:19
  He adds a steel bracket around the coil.
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  He adjusts the mounting so the plunger starts closer to the
• 10:24
  center. He flips the switch.
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  Again, and this time, snap. It hits hard.
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  It compresses the spring. The door locks.
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  He didn't just add power, he removed the resistance, or
• 10:34
  rather the reluctance that was choking the system.
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  He worked with the energy field instead of fighting it.
• 10:39
  Now that's a massive win for Alex, but I want to complicate
• 10:42
  his life a little bit. Let's say theoretically, Alex
• 10:46
  gets bored with safety latches. He sees this solenoid and
• 10:50
  things. You know, if I don't put a
• 10:52
  stopper on this, I could shoot this bolt right across the room.
• 10:56
  The coil gun pivot. Every engineer tries this
• 10:59
  eventually. Can I make a projectile
• 11:01
  launcher? But the notes mention a specific
• 11:03
  trap here. It's a dynamic problem called
• 11:06
  the suck back effect. This is a great cautionary tale
• 11:09
  about the energy method. Remember the golden rule?
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  The system wants to maximize inductance.
• 11:14
  Right, and inductance is maximized when the iron core is
• 11:16
  perfectly centered inside the coil.
• 11:18
  Correct. So as the bolt is flying towards
• 11:21
  the center, the force is pulling it forward.
• 11:23
  It's accelerating. Life is good, but what happens
• 11:26
  the instant the bolt passes that center point?
• 11:28
  Well, now it's leaving the region of maximum inductance.
• 11:30
  Exactly. It's moving into a state of
• 11:32
  lower inductance, and since the system hates that DLEDX flips
• 11:37
  its sign, it becomes negative. The force reverses direction
• 11:40
  instantly. So the coil stops pulling it
• 11:42
  forward and starts yanking it backward.
• 11:43
  It tries to suck it back into the center.
• 11:46
  If Alex just leaves, the power on, the bolt will shoot forward,
• 11:49
  get yanked back, oscillate a few times, and just settle in the
• 11:52
  middle. It won't launch at all, it'll
• 11:53
  just get trapped. To make a coil gun you really
• 11:56
  had to be faster than the physics.
• 11:58
  You have to cut the current. You need to kill the magnetic
• 12:01
  field at the exact microsecond the projectile reaches the
• 12:04
  center. You pull it in and then bam,
• 12:06
  turn off the magnet so it can coast out on its own momentum.
• 12:09
  But that timing seems impossible to just guess the bolt is moving
• 12:13
  fast. How do you know when it's there?
• 12:15
  This brings us to another fascinating concept from the
• 12:18
  source material, which is back EMF.
• 12:20
  Back EMF, we usually talk about that with motors.
• 12:23
  Well, solenoid is just a linear motor.
• 12:26
  As that steel plunger races through the magnetic field, it
• 12:29
  disrupts the flux lines. Faraday's law of induction kicks
• 12:33
  in. The physical movement itself
• 12:35
  induces a voltage in the wire that opposes the current you're
• 12:38
  putting in. So the faster the bolt moves,
• 12:40
  the more pushback voltage you get.
• 12:42
  Exactly. And if Alex is clever, he can
• 12:45
  use this. If he hooks up an oscilloscope
• 12:48
  like they do in the lab modules, he can watch the voltage across
• 12:51
  the coil. He'll see a spike or a that
• 12:54
  perfectly corresponds to the speed of the plunger.
• 12:56
  The coil is basically acting as its own speedometer.
• 12:58
  It is. He can use that signal to
• 13:01
  trigger the shut off. He's using the interaction
• 13:03
  between the mechanics and the electronics to time the shot
• 13:06
  perfectly. That is incredibly cool.
• 13:08
  It's using the problem, the back EMF as the actual solution.
• 13:13
  That is the essence of good mechatronics design right there.
• 13:16
  OK, so we fixed the latch and we built a theoretical coil gun.
• 13:20
  I want to pivot now to the post mortem.
• 13:22
  Let's look at the frequently asked questions.
• 13:24
  These are the things that Alex and you listening might run into
• 13:27
  after you build the thing. The why is it doing that phase?
• 13:30
  Exactly. So scenario 1, Alex's latch is
• 13:33
  working. It's snap shut but he leaves in
• 13:35
  lock for an hour. He comes back, touches the coil
• 13:38
  and burns his finger. It's incredibly.
• 13:40
  Hot This is the most common complaint with solenoids and it
• 13:43
  goes straight back to energy conservation.
• 13:44
  We're putting electrical energy in.
• 13:46
  Right. And we want mechanical workout
• 13:48
  which is force times distance. But think about but once the
• 13:51
  latch is closed, is it moving? No distance is 0.
• 13:54
  If distance is 0, mechanical work is 0.
• 13:57
  So you are pumping 24 volts and maybe 2 amps into this coil.
• 14:02
  That's 48 watts of power. Where is it going?
• 14:05
  It's not moving the bolt, so it has to be heat. 100% of it
• 14:08
  becomes heat. It's just I squared our losses.
• 14:12
  You are essentially turning your latch into a very expensive,
• 14:16
  very inefficient heater. Solenoids are notoriously bad at
• 14:20
  holding in my position. So did Alex design it wrong?
• 14:22
  Not necessarily, but he needs a control strategy.
• 14:25
  Real industrial controllers often use a hit and hold
• 14:28
  circuit. They hit it with high current to
• 14:30
  get that big DLDX snap, and then once it's closed they drop the
• 14:34
  voltage down to just a trickle. Just enough current to keep it
• 14:38
  there without melting the insulation.
• 14:39
  That makes a lot of sense. Yeah, OK.
• 14:41
  Scenario 2. Alex thinks I learned about
• 14:44
  magnetomotive force. It's number of turns times
• 14:46
  current or north times I. So if I want more force, I'll
• 14:50
  just double the number of turns on my coil.
• 14:52
  Ah yes, the more turns equals more power fallacy.
• 14:55
  Why is it a fallacy though? The math says n * I more N
• 15:00
  should mean more force. It does if you can keep the
• 15:02
  current the exact same. But here's the catch.
• 15:06
  Copper wire has resistance. If you double the number of
• 15:09
  turns, you're doubling the physical length of the wire.
• 15:11
  So you're doubling the resistance.
• 15:13
  Right, and Ohm's law is stubborn.
• 15:16
  If resistance double S and your voltage is fixed like from a
• 15:19
  power supply or battery, your current gets cut in half.
• 15:22
  So you doubled N, but you halved I.
• 15:24
  And you end up with the exact same magnetic force, but now
• 15:28
  your coil is twice as big and twice as expensive.
• 15:31
  It's a 0 sum game unless you change the wire gauge or bump up
• 15:34
  the voltage. You have to optimize, you can't
• 15:36
  just add more. It's never as simple as just add
• 15:38
  more wire. OK, last question.
• 15:41
  We see this in speakers and some fancy actuators.
• 15:43
  They put a permanent magnet inside the coil assembly.
• 15:47
  Why isn't the coil supposed to be the magnet?
• 15:49
  This is a phenomenal efficiency hack.
• 15:51
  We just talked about how much heat Alex created just to hold
• 15:53
  the latch. He's essentially renting the
• 15:55
  magnetic field using electricity and he pays for that rent and
• 15:58
  heat. And a permanent magnet owns the
• 16:00
  field. Exactly.
• 16:02
  A permanent magnet provides a strong bias field for free.
• 16:05
  It's there forever with 0 energy cost.
• 16:09
  So in a speaker or a specialized motor, you use the permanent
• 16:12
  magnet to do the heavy lifting of creating the baseline field.
• 16:16
  OK, then you use your coil current only to modulate that
• 16:19
  field to push or pull against the bias.
• 16:22
  So you get way more force for way less.
• 16:24
  Current exactly. You are using the electricity
• 16:27
  for fine control, not just for the brute force creation of the
• 16:30
  field. It's much smarter design.
• 16:32
  So bringing it all back to Alex, he started with a plastic spool
• 16:36
  and a dream, and he ended up navigating vector calculus,
• 16:40
  energy methods, magnetic circuits, and thermal
• 16:42
  management. And hopefully you realize that a
• 16:44
  solenoid isn't just a magnet, it's an energy conversion
• 16:47
  machine. It's a device that is constantly
• 16:49
  trying to minimize its reluctance and maximize its
• 16:52
  inductance and. Once you understand what the
• 16:54
  machine wants to close that air gap to store energy, you can
• 16:58
  design around it. You stop fighting the physics
• 17:00
  and start using it. Before we wrap up, is there one
• 17:03
  final image or concept you want to leave everyone with?
• 17:07
  Something for you listening to visualize when you're staring at
• 17:10
  a coil of wire. Yes, we talked extensively about
• 17:13
  the energy method, but sometimes it helps to think in terms of
• 17:16
  magnetic pressure. Magnetic pressure like a gas.
• 17:20
  Sort of, yes. Imagine the magnetic field lines
• 17:23
  in that air gap aren't just abstract lines.
• 17:25
  Imagine they are rubber bands that are packed tightly
• 17:27
  together. OK, rubber bands.
• 17:29
  These rubber bands have two properties.
• 17:31
  One, they want to be as short as possible.
• 17:33
  They are under tension, that is the physical force pulling the
• 17:37
  plunger in the lines trying to shorten themselves.
• 17:40
  But 2, they push sideways against each other.
• 17:42
  They hate being crowded. This is the magnetic pressure.
• 17:45
  So they are pulling lengthwise and pushing sideways.
• 17:48
  Right. And that tension, that deep
• 17:49
  desire to shorten, is what snapped Alex's latch shut.
• 17:53
  He simply provided a path, the iron core, that allowed those
• 17:56
  rubber bands to relax and get short.
• 17:59
  If you can visualize the field as a bundle of tension looking
• 18:02
  for release, you can intuitively troubleshoot almost any magnetic
• 18:06
  actuator. The rubber band theory of
• 18:08
  magnetism. I like it.
• 18:10
  It takes the invisible and makes it completely tactile.
• 18:13
  It works surprisingly well in the.
• 18:14
  Field Well Alex, wherever you are, I hope your door is locked
• 18:18
  tight and your coil isn't overheating.
• 18:20
  And watch out for that suck back effect if you try to build the
• 18:23
  launcher. Absolutely.
• 18:25
  Thanks for joining us for this deep dive into the deceptively
• 18:28
  complex world of solenoids. And if you haven't already, get
• 18:31
  over to our YouTube channel Mechanical Engineering Made
• 18:34
  Simple, where we post hands on how to videos, visual
• 18:37
  breakdowns, and practical engineering walkthroughs.
• 18:39
  You can actually use a family that solves together, stays
• 18:43
  together.