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Why can switched reluctance motors acheive high efficiency when coilguns cannot?

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Shrad

Fri Jul 19 2013, 07:31AM

Registered Member #3215 Joined: Sun Sept 19 2010, 08:42PM
Location:
Posts: 780

what if you create a ring coilgun accelerating a steel ball in a circular motion and create a super fast "Y" direction changer at one point of the ring (a bit like a "q" form) so the ball can be directed to a cannon tube and its trajectory be made right?

OR

create a spiral tube accelerator which emulates a way longer cannon, for which the spiral ends in a straight tube

if people want to try this I have two 5V 90A ASTECH supplies which are awaiting a good home ;)

Yandersen

Fri Jul 19 2013, 02:25PM

Registered Member #6944 Joined: Fri Sept 28 2012, 04:54PM
Location: Canada
Posts: 340

Sorry, but I can not stand a way of explaining efficiency through induced voltage. Let me try another way.

Let us assume a coil of constant dimensions as each of the coilgun stage. Let us also assume a constant amount of energy pushed into each coil by a cap. My FEMM experiments solidly state an equal power dissipation and equal pull force as an unavoidable result of those constants. It means that no matter at which initial speed the projectile will enter any of the coils, it will always experience the same increase in kinetic energy. It directly means that the faster the projectile will pass the coil, the shorter the pulse should be. Taking into account the contant power dissipation for each coil we come to the simple conclusion: the faster the projectile moves, the less energy will be dissipated by a coil in order to push the same amount of kinetic energy into the projectile. That is why efficiency is low at low speed - each coil has to hold energy for too long, resulting in high heat dissipation.
I would also remind that my recoup coilgun which was operating around a saturation level at some high stage achieved almost 30% of efficiency while the first stages were at 10% level only.
From my exp I would also add that efficiencies over 10-20% are achievable only if unused energy is recuperated, because only around 10% of energy stored in magnetic field can possibly convert into kinetic energy of projectile - this number depends only on geometry of the coil and projectile and amount of energy stored in a coil (talking about most optimal case - saturation point).

BigBad

Sun Jul 28 2013, 09:35PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
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Posts: 600

Yandersen wrote ...

Sorry, but I can not stand a way of explaining efficiency through induced voltage.

Agreed, it's easier to look in terms of currents; if you do that you can ignore back EMF to a fair extent.

By far the main loss in electric motors are resistive. Resistive losses go as a square law of current.

The force is also generated by the current; for permanent magnet motors or saturated rotors, it's directly proportional.

If we consider a fixed force/effects of a fixed current acting on a rotor/projectile then the force is proportional to the current, but the useful work done is proportional to the distance times the force (or equivalently, the integral of force times speed over the movement.)

So the further the rotor moves in any given time, proportionately more work has been done by the same force and current.

Whereas for the same fixed force the power loss (provided you activate only a fixed region around the projectile) is just constant resistive losses over that region, operating for the time the motor is on for.

So the power loss is constant, whereas the power output increases with speed, so efficiency increases with speed.

To bring the back-emf back in- that helps explain how a constant current can generate more useful work at higher speed- you need to apply a higher voltage to generate the same current at higher speeds due to the back-emf, so you're putting more power in to achieve the acceleration (in strict agreement with conservation of energy).

That's the primary reason why electric motors nearly always get more efficient at high speed.

wrote ...
From my exp I would also add that efficiencies over 10-20% are achievable only if unused energy is recuperated

No, you can also make the motor long enough so that the losses are small relative to the useful work (many more stages or go around a loop).

At low speeds recouperating doesn't help nearly as much, the energy is eaten by the resistive losses. At high speeds, it's a much bigger help.

Yandersen

Mon Jul 29 2013, 02:31AM

Registered Member #6944 Joined: Fri Sept 28 2012, 04:54PM
Location: Canada
Posts: 340

"At low speeds recouperating doesn't help nearly as much ... At high speeds, it's a much bigger help."

Agree on that - true in simulations and proved in practice as well - first stage is so inefficient due to the large pulse duration that recuperated energy hardly reaching quarter of what was pushed into coil. But high stages may return up to 50-70% of initial energy which can be reused by another stage or saved for the next shot.

Relation of induced back EMF to the cap voltage is somewhat corresponds to the relation of the energy bullet will achieve to the energy in the cap. This is around 10-20% in best case, so EMF does not need to be taken into consideration. All it does is slowing the speed of the current rise, thus reducing the magnetic field and pull force as well. By the backEMF/capV ratio the magnetic coupling between coil and moving bullet can be roughly estimated.
BTW it is a common mistake to think that back EMF is larger at each subsequent stage of a gauss gun. Each subsequent stage has to be wound with less turns of thicker wire to adjust the pulse length to the bullet speed. If all stages have the same shape, the same amount of energy supplied and all are tuned properly, than back EMF will be almost equal for each stage as well as increase in kinetic energy bullet will experience from passing any of the coils. Still, it is impossible to directly check that voltage if coil is connected to the cap - back EMF just slows the rate of current rise being "invisible" by itself.

Saz43

Mon Jul 29 2013, 04:19PM

Registered Member #1525 Joined: Mon Jun 09 2008, 12:16AM
Location: America
Posts: 294

I think I have to take back what I said about induced voltage being the primary effect, Yandersen is right about that. If every coil is the same size with the same power, they will each do approximately the same work on the projectile as it passes through. It makes sense that as the bullet speeds up, the coil is on for shorter periods of time consuming less energy to do the same work, hence better efficiency. This is supported by my 8-stage coilgun, each identical stage adds rougly the same energy even as the projectile speeds up from 0 to 42m/s.

But its still true that induced voltage lowers coil current which improves efficiency (see this oscilliscope reading of coil current in a multistaged gun). However, the effect is pretty small (only 3-5 volts) since even in a fast hobby coilgun the projectile is still too slow for this to make a big difference.

Yandersen

Wed Jul 31 2013, 09:12PM

Registered Member #6944 Joined: Fri Sept 28 2012, 04:54PM
Location: Canada
Posts: 340

"If every coil is the same size with the same power"

Sorry, Saz, but DC and cap-driven coilguns are hard to compare - I will stuck with cap-driven designs for my explanations.
If the same ENERGY pushed by a cap into each coil to circulate in it in a form of a magnetic field, then the power dissipation (R*I*I) in this case is the same for any coil of the same dimensions, so the amount of dissipated energy depends on a pulse duration ONLY - the longer the pulse, the more energy will convert into heat. Don't think of current through the wire - think about cross sectional area of the coil which determines the current density through it - it will differ only due to the amount of energy stored in magnetic field. Heat will be squarely proportional to the current density - so the bigger the coil, the less dense the current will be for the same energy of a magnetic field - less heat dissipation then. If all coils have the same shape and the same energy - all have the same current density. As all of them have the same conductor density, then power of heat dissipation is the same for all those coils too.

Newbies can visualize the problem assuming the coil is an open V-shape bucket, wire is a hose with pump and capacitor is bottle with water: the thinner the hose, the longer it will take to transfer the water from bottle to the bucket or vice-versa, but the speed of water dry-up will depend on the amount of water in a bucket only - the higher the level, the bigger the vaporization area of the water in a V-bucket.

So in order to increase efficiency we need to minimize the pulse time. From one side, it can be done by increasing the current up to the point were force is still proportional to the square of the current - this will increase acceleration and lower the time bullet will spend inside the coil. Assuming no saturation, when we increase the current we increase heat dissipation (R*I*I) and force (F=k*I*I) equally. So doubling the current means 4 time higher heat dissipation and 4 times more force. It also means 4 times more kinetic addition to the bullet and 4 times more input energy required for that. So before saturation kinetic boost is directly proportional to input energy. Heat dissipation is also directly proportional to the input energy (Emagnetic=L*I*I, Pheat=R*I*I). But the higher the force, the shorter the pulse required. The shorter the pulse, the less time for heat dissipation. This results in increase in efficiency with increase of input energy - up to the saturation point, but not any further, where force becomes proportional to the square root of input energy.

So the first point we get solid: to maximize the efficiency, each coil must not oversaturate the projectile. If all coils are the same in shape, then equal energy input means almost equal saturation picture for any of the coils. Determine energy a coil need to be pumped with to get the tip of the iron projectile at 2.2T field and you will know the energy of the cap for each stage.

From the other side, pulse duration can be lowered by reducing the length of the projectile - shorter projectile will pass coil faster. This topic is not that simple, unfortunately - it is a trade-off. The shorter the projectile, the less it's mass, so even if it accelerates faster and passes shortly, it will grab less kinetic energy from passing the coil. But shorter pulse means less heat dissipated, though. I think, this problem can not be answered in general. But definitely, there is a shape of the coil and a projectile exist which will show the highest efficiency possible. And for DC applications, half bridges, cap-driven or recuperational designs there will be a slightly different "ideal" shape. The barrel will introduce another distortion also. I would recommend iterational simulation way: having a simulator (FEMM) calculating the shot we can start from long projectile (4 length to 1 diameter f.e.) and gradually cut the projectile little by little each new simulation and see the difference in numbers. There will be one peak of efficiency at some projectile length (I expect it to be somewhere at 1.5:1...2:1 length to diameter ratios). Once it found, start cutting the length of the coil (initially it was the same as length of the bullet) and find the efficiency peak for it (usually coil is little longer than the bullet). Then cut projectile again, and then coil. Ensure each step saturation checked and energy adjusted (shrinked) to prevent oversaturation (especially on coil-cut cycles). Finally you will get the best length of the coil and projectile and energy input for your design. Will mention also that ideal outer diameter for the coil is 3 times bigger than it's inner diameter - for all lengthes, so keep it so always.
One thing I can say for sure: coils and bullets long like Saz shown are a way too far from that ideal shape. At least for the cap driven recuperational designs it will be (which is not true for Saz anyway, but still, TOO LONG!).

Cutting the projectile length keeping all other parameters the same will always result in decrease in force. Howhether, for a long projectiles the shrink in mass is much more dramatic than slight decrease in force, so acceleration (a=F/m) rises uncomparably higher than work weakens (A=F*s). The pull force can be roughly estimated by the difference in field density between the tip of the projectile (must be 2.2T for iron) and it's back end (as low as possible). If coil is caged in iron and operating at saturation point, then part of the projectile outside the hole is a dead weight, so the shorter it is, the better - acceleration-wise (read pulse_length-wise).

Another hint for efficiency-squeezers is a particular area in a coil, passing which projectile experience the highest force - ideally coil must run at full current only when projectile passing this part of the coil - wasting the same energy as heat while generating little force is non-sense. For bare coils this area is just 1/3 of the coil length - from the point where bullet is 1/3 inside and up to the point where bullet's tip passes 2/3 of the coil. For iron-caged coils the area of highest pull force is longer - almost the whole coil length. Area of the highest force starts from the point where bullet' tip passes the iron washer and reaching the actual wired part. Area ends at the point where bullet tip reaching the line between wire and exit iron washer. So for the coils with external iron and iron washers at the ends the ideal projectile length will be equal to the total coil length minus one thickness of the iron washer.

Hope this material will help you guys reach better efficiencies. :)

Steve Conner

Tue Aug 06 2013, 10:51AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

The way I see it, the low efficiency is because the airgap is much bigger than in a motor, and the magnetic circuit is made of unfavourable materials.

You can solve the "low efficiency at low speeds" and saturation issues at least in theory by using a larger number of stages, each better matched to the projectile speed at that point, and each transferring a smaller amount of energy to avoid saturation.

But you can't do anything about the airgap and still have a thing that looks like a gun, firing a projectile that looks like a bullet. Your efficient coilgun will end up looking like a linear switched reluctance motor, launching a slab of laminated iron from a track made of transformer E cores.

Energy recovery helps. With a large airgap, you are mostly pumping inductive energy into the airborne part of the magnetic field, rather than doing real work against the back EMF induced by the projectile. With energy recovery you could potentially get most of the inductive energy back.

In a motor, the current associated with this inductive energy is called magnetizing current, and the ratio of inductive current to work-doing current is called power factor. A coilgun is a motor with a lousy power factor, because the design prioritised phallic symbolism over efficiency.

A designer of switched reluctance motors might prefer to say that it had a lousy "inductance gradient" but it is basically the same thing.

BigBad

Wed Aug 07 2013, 08:58PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600

AFAIK the theory behind the airgap and it's relationship with efficiency is due to Eric Laithwaite, who was well regarded for this work, unlike his gyroscope stuff(!)

Goodness factor

The second result listed there is only strictly true in induction motors but IRC the general relations hold up pretty well in switched reluctance motors including coilguns.

So a large gap by no means implies low efficiency, although at sufficiently low excitation frequencies/linear speed that is certainly what you will get.

I don't think long/fast coilguns are inherently inefficient, but short/slow coil guns certainly are pretty damn inefficient.

[quote]
BTW it is a common mistake to think that back EMF is larger at each subsequent stage of a gauss gun. Each subsequent stage has to be wound with less turns of thicker wire to adjust the pulse length to the bullet speed. If all stages have the same shape, the same amount of energy supplied and all are tuned properly, than back EMF will be almost equal for each stage as well as increase in kinetic energy bullet will experience from passing any of the coils. Still, it is impossible to directly check that voltage if coil is connected to the cap - back EMF just slows the rate of current rise being "invisible" by itself.
[/quote1375909558]

I'm not convinced by this argument. By breaking a section of coil up into smaller sections (presumably connected in parallel or similar) you've certainly reduced the required voltage, but at the expense of requiring proportionately more current; it's much the same effect as if you've added a lossless transformer inline; the energy or power due to the back EMF is the same.

It will depend a bit on whether you're trying to get constant acceleration or constant power though; if you're going for constant acceleration, then the current/active wiring seen by the projectile is constant along the bore, if you're going for constant power, then the acceleration and current/wiring is reducing along the bore and will give a slightly different effect; it will give you reduced back EMF.

johnf

Thu Aug 08 2013, 09:20AM

Registered Member #230 Joined: Tue Feb 21 2006, 08:01PM
Location: Gracefield lower Hutt
Posts: 284

At last
Steve is on the right track
Magnetic coupling
the better the coupling the better the efficiency
motors good very little air gap and closed magnetic circuit
coil gun bad bigger air gap and open magnetic circuit
fix those two and the coil gun will be more powerful for the same power input

BigBad

Thu Aug 08 2013, 01:28PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600

No, no.

Large air gaps aren't lossy in themselves, otherwise air cored inductors wouldn't be useful, and Tesla coils would be much less interesting.

All they mean is you need a bigger electromagnet to produce a bigger field to give the same force on the projectile, and that in turn raises the resistive losses proportionately.

But as the speed goes up the resistive loss power becomes lower than the useful power the projectile is getting:

w = f x s (work is force times distance)

differentiating wrt time, with f constant

dw/dt = f x ds/dt

P = f x v (power is force times speed)

so useful power is proportional to speed, so at high enough speed you will get very good efficiency for the same current/force/losses in/on the coils.

At the end of the day, a coil gun is just another electric motor, it's a family characteristic of electric motors to be inefficient, at high torque, low speed which is where almost everyone is running their coilguns.

The fix is to run multistages, and low currents for the first few stages and then increase the currents for the later stages.

But you do need to recirculate the energy at high speeds, that big airgap stores a lot of magnetic energy, you need to suck that back out and put it into the next stage along.

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