forced vibration as it relates to firearme accuracy

[murf]

bart b.,

harral has already been disproven, so just one to go. someone will debunk kolbe sooner or later ... or not.

you asked why the faster bullet leaves at a lower angle, not that it does. i gave you my answer. take it or leave it.

murf

 

[denton]

There are several people on the board with good technical backgrounds and an understanding of the physics of vibration.

Some of the best experimental work was done by Harold Vaughn. He commented that he had searched, and had not found prior research that covered what he did.

The whole schtick of using Finite Element Modeling to try to see what the barrel does traces back to his book.

Here is what he found about the vibration modes cantilever beams, an example of which is a rifle barrel:



A couple of pages later, he notes that Mode 3 was the dominant mode on his barrel, based on about 800 observed oscilloscope traces. His rifle was the style that has a recoil lug under the barrel, a convention not always followed in modern rifles. But in that case, the fact that there is one lug, off center, causes a moment (force x distance) that causes the tip of the barrel to rise.

His experimental results agreed well with the Finite Element Model that he made.

He found that the motion of the barrel imparted about 3.08"/sec transverse velocity to the bullet, and that the effect of the barrel pointing in another direction caused about 1.1" of POI error. Both errors need to be taken into account. Both errors have minimum effect near the end of the arc.

So, yes, there is experimental support of the Finite Element Model and for the model JohnKSa showed earlier.

 

[Bart B.]

Sorry, murf, buy nobody's disproved Kolbe's nor Harral's finite element calculations as to what goes on in the barrel when a bullet's fired through it.

Several have expressed disbelief and other things contrary to calculation's findings. But I've seen nothing to disprove it.

Quote the disproving statements herein and I'll review them. I may have missed something.

 

[JohnKSa]

…does the shot impulse also damp the barrel vibration…

The shot impulse is what causes the vibration—at least a big part of what causes vibration. The barrel whip effect happens quite rapidly and for practical purposes (when talking about the BOSS tuning system) it can be considered part of the shot impulse.

Think of it like this. You can make a tuning fork ring by striking it, or, you can make it ring by “whipping” it if you can generate sufficient force. The specific means you use to get it ringing doesn’t really matter that much. All you’re trying to do is pick a point in the muzzle movement where the muzzle is moving slowly. It doesn’t matter much how the muzzle came to be moving as long as it moves fairly consistently from shot to shot.

The vibration damps out because energy is lost to the system through various means. Just like a bell won't ring forever when hit it with a hammer--eventually the energy losses will damp the vibration/ringing.

…they all show a sharp rise to peak pressure and a gradual fall off to a minimum pressure as the bullet leaves the barrel…

Gradual is a relative term. I suppose you could look at what happens to the metal surface of a bell when a hammer hits it and call some of the effects “gradual” in the context of extremely fine time resolution.

i also don't believe the barrel vibration is generally in the vertical plane. if it were so, groups on target would all be strung out vertically rather than in the normal circular pattern. comment?

The figure I showed does not imply any particular orientation to the vibration pattern. It is merely an amplitude vs. time plot. The amplitude could be vertical, horizontal or perhaps at some angle.

In fact, as you mentioned in a previous post, the barrel likely has a more complicated vibration pattern than the figure shows—it’s probably vibrating in more than one plane at once. It doesn’t matter. As long as the motion is fairly consistent from shot to shot and there are points in the vibration cycle where the muzzle is moving relatively slowly compared to other points in the vibration cycle, the system will still work.

 

[Arizona_Mike]

replied to wrong post

 

[Bart B.]

John,

The barrel's lowest frequency is its resonant one; typically from 50 to 120 cycles per second (Hz). Harmonic multiples are higher frequencies and there are several of them. The ones shown in Varmint Al and Geoffery Kolbe sites at bullet exit are sometimes up in the 800 to 1000 Hz range. That's easily seen as the peak to peak time is the reciprocal of the frequency it's vibrating at. If it's 1.111 millisecond between peaks or valleys, the frequency's 900 Hz. Only the last few inches of the barrel's vibrating that fast.

 

[JohnKSa]

Correct. For this type of application, the fundamental frequency will be the lowest frequency and the harmonics will be multiples of the fundamental. It's always true, in the real world, that harmonics will be present.

The amplitudes of harmonic frequencies drop off significantly and rapidly as they depart from the fundamental frequency which means that for most practical purposes one can neglect higher harmonics, and in many applications one can ignore everything but the fundamental frequency.

Regardless, the overall vibration will be the sum of the fundamental and the harmonics. The sum won't be a clean/pure sine wave, but it will still be true that there will be time intervals during the vibration motion where the muzzle will be moving significantly less than at other identical intervals during the vibration pattern. In fact, depending on what harmonics are present and their relative amplitudes, the overall waveform may have larger intervals where muzzle motion is minimized.

Focusing on the harmonics to the exclusion of the fundamental frequency won't provide a useful understanding of the situation, and treating the harmonics as if they are similar in amplitude to the fundamental will result in an inaccurate picture of what's going on.

 

[JohnKSa]

Ok, here's a plot showing the fundamental and first 4 harmonics plotted on the same axes. The harmonics in this case reduce in amplitude by half as they depart from the fundamental. That's probably an extreme case--you'd expect a FASTER reduction in amplitude than that in most situations and that would result in less deformation to the fundamental when the harmonics are summed in.

The reddish/orange (orangeish/red?) trace is the sum of the fundamental and the first 4 harmonics--that's how the muzzle would actually move if these plots were representative of the physics of the barrel.

Note that while the red/orange trace no longer looks like a sine wave, there are still obviously intervals over which the muzzle would be moving a lot less than at other identical intervals. In fact, at the bottom of the trace you can see that the peaks have widened and flattened. If you tuned the BOSS to select one of those sections, you would actually get less muzzle motion over a longer interval than if you were dealing with the original sine wave.

 

[denton]

To John's point, the vibration of a barrel is not so much like a single note, but rather more like a chord. His analysis agrees with the science that I know.

 

[Bart B.]

A rifle barrel's harmonic frequencies are not even multiples of its resonant one. A barrel's a cantilever beam and vibrates the same way. That's easily seen in Varmint Al's tables showing a barrel's fundamental (resonant) frequency and the harmonics thereof. None of the harmonic frequencies at mode 2 and higher are exact multiples of lower ones.

Search "cantilever beam vibration frequencies" then see why.

Too many folks compare rifle barrel vibration frequencies to audible frequencies from musical instruments (voices?) that "harmonize" when they are exact multiples of each other. That's different than the physics of mechanical things; rifle barrels and cantilever beams fixed at one end.

 

[murf]

johnksa,

another question: the shot impulse also applies 50kpsi to the breach face and the base of the bullet. would the resultant vibrations of these two impulses damp the overall vibration of the barrel? the two pulses occur simultaneous to the impulse delivered to the chamber walls, but at different locations on the barrel.

murf

 

[murf]

all this talk, whether computer model or old man with a piece of chalk on a blackboard, is just theory, hypothesis, or conjecture. does anyone have solid real data to back any of this up? have any barrel vibration measurements been taken? i'm not being facetious here, the only real data i see from anyone is bullet holes in a target, that is why we all know the boss system and load development work. if anyone knows of a website with real data i'd like to know about it.

thanks,

murf

 

[Bart B.]

does anyone have solid real data to back any of this up?

Yes, I gave a link in post 48.

 

[murf]

i'm going to take a shot at disproving kolbe.

ref: bart b. feb. 9 post in the muzzle brake on accuracy thread

kolbe assumes in his study that the barrel vibrations are caused by the impulsive movement applied to the back of the barrel as the rifle recoils and rotates about its center of gravity. here i'm assuming he means that the vibration imparted to the breach face (the back of the barrel) causes the rifle to recoil.

movement of the bullet down the barrel causes the rifle to recoil (newton's third law of motion), not a vibration caused by a 50kpsi impulse.

murf

 

[murf]

thanks for that reminder, bart b. that will give me something to do today.

murf

 

[Arizona_Mike]

johnksa,

another question: the shot impulse also applies 50kpsi to the breach face and the base of the bullet. would the resultant vibrations of these two impulses damp the overall vibration of the barrel? the two pulses occur simultaneous to the impulse delivered to the chamber walls, but at different locations on the barrel.

murf

Keep in mind the speed of sound in steel is over 19,000 fps. The entire barrel will be ringing while the bullet is still getting going.

 

[Bart B.]

Speed of sound in steel varies from about 16,000 to 1900 Hz. Varies with the steel properties. Harrel's and Kolbe's calculations were based on the barrel's bore axis which, for all practical purposes, the recoil axis.

Amplitudes metal moves caused by those sound waves is small compared to that caused by the barreled action being whipped like a bait casting rod flinging a lure way out there where the bass are. In fact, casting rods behave exactly like free floated rifle barrels; they're fixed at one end for the most part.

Most centerfire rifle cartridges put somewhere between a 60,000 and 65,000 psi force against the bolt face. Actual force is about equal to the area in square inches inside the case against its head multiplied by psi number. The inside of a .308 Win case at its head is about .4 inches; that's about 1/8th square inch. At 64,000 psi, pressure against the bolt face caused by that area is about 8,000 pounds. If you want to use the whole case head area at .1735 square inch, the force will be about 11,100 pounds. Lasts for only a few microseconds.

There's recoil formulas to calculate the forces backwards a rifle has. More force backwards means greater angles a given barrel wiggles through. More the recoil axis is away from center of mass holding the rifle, the greater those whip angles will be. Keep in mind that while the pressure in the barrel builds up to maximum, it pushes the bullet forward and the rest of the rifle backwards. A good way to see the effects is to chronograph loads with the rifle held against your shoulder. Holding it as tight as possible will produce higher average fps numbers than holding it with only a little pressure against your shoulder. That, too impacts how much and what direction the barrel whips. But the frequencies it does so at will be the same across all holding pressures.

 

[JohnKSa]

A rifle barrel's harmonic frequencies are not even multiples of its resonant one.

Then they aren't harmonics. The definition of harmonics:
http://dictionary.reference.com/browse/harmonic

Physics. of, relating to, or noting a series of oscillations in which each oscillation has a frequency that is an integral multiple of the same basic frequency.​

But even if they aren't harmonics, it doesn't really matter. The basic principles still apply. If you add a number of sine waves together you will always get a resulting signal which will have maxima and minima.

Search "cantilever beam vibration frequencies" then see why.

Too many folks compare rifle barrel vibration frequencies to audible frequencies from musical instruments (voices?) that "harmonize" when they are exact multiples of each other. That's different than the physics of mechanical things; rifle barrels and cantilever beams fixed at one end.

The basic principles still apply. The amplitudes of the various modes will fall off as frequency increases past the main resonant frequency and will therefore have less effect on the overall movement of the muzzle than the main resonant frequency.

another question: the shot impulse also applies 50kpsi to the breach face and the base of the bullet. would the resultant vibrations of these two impulses damp the overall vibration of the barrel? the two pulses occur simultaneous to the impulse delivered to the chamber walls, but at different locations on the barrel.

Do you have some reason to believe that they would or are you just grasping at straws? Remember a hypothesis, the first step in proving a theory or in a proper experiment, is an educated guess, not just wild speculation.

https://www.vocabulary.com/dictionary/hypothesis

A hypothesis is something more than a wild guess but less than a well-established theory.​

To get an impulse to cancel would be very difficult--you could get cancellation if you input two impulses at exactly the same point and at exactly the same amplitudes and in exactly opposite directions. Theoretically you could get some cancellation effect if you could very precisely control the timing/amplitude/position of an impulse input, but for two impulses to have any significant cancellation effect on each other by chance would be very unlikely.

Otherwise, making the common assumptions, the overall response will be the sum of the two impulse responses taking the input times into consideration.

...have any barrel vibration measurements been taken?

...movement of the bullet down the barrel causes the rifle to recoil (newton's third law of motion), not a vibration caused by a 50kpsi impulse.

Regardless of how the vibration is induced or what the vibration measurements show, it can be accurately represented as the sum of sine waves of differing frequencies and that the amplitudes of the various frequencies will reduce as frequency increases beyond the main resonant frequency.

We know the first part is true because of Fourier's theorem and we know the last part is true due to the physics of vibration of real-world objects.

In other words, regardless of what starts the barrel vibrating, the basic principles that make the BOSS work will still apply.

 

[denton]

The term "barrel harmonics" is probably just a corruption of the proper term, "harmonic motion". Harmonic motion is simply motion that repeats over and over. All math functions that repeat forever are somehow based on sines and cosines, and pretty much any waveform that you want can be synthesized from various combinations of those two functions.

When we use the improper term "barrel harmonics" it conveys a wrong impression that we are talking about integer multiples of a fundamental frequency.

In any event, if a barrel oscillates at 2, 3, and 4X a fundamental, it is technically an overtone, which is just a little off frequency from the true harmonic.

Take the output of a crystal controlled oscillator, and run it through a doubler circuit, and you get a true harmonic. Excite the crystal at about 3X its fundamental, and you get the third overtone, not an exact harmonic, but close.

 

[Bart B.]

Another question: the shot impulse also applies 50kpsi to the breach face and the base of the bullet. would the resultant vibrations of these two impulses damp the overall vibration of the barrel?

No, it doesn't dampen barrel vibrations. It's amplitude isn't big enough and that's proved by Kolbe's calculator that shows no barrel vibration at all if the center of mass behind the rifle is in line with the recoil axis. Barrel stays straight and only the shock waves bouncing back and forth in equal amounts all around the barrel are moving. Same reason nais don't bend when you smack their head squarely with a hammer and all the force axis on the nail head is well aligned with its long axis. Hit that head at an angle and the nail bends.

That impulse is the powder (exploding?) at a point about an inch or so in front of the breech face. Therefore, there's two shock waves generated. One goes forward to the muzzle then reflects back. The other goes to the back end of the barrel then reflects back forward; it'll be a short distance behind the one that started forward. They both go back and forth in the barrel until they eventually die out.

At the muzzle end, they'll enlarge the bore about .0001" (depending on pressure around 10,000 psi and diameters) and that's the key part of OCW load development theory. Bullets should exit when those shock waves are somewhere else; according to OCW theory. The claims are that the muzzle enlarged that much causes accuracy problems. I never saw any accuracy problems in the four 7.62 NATO chambered Garand barrels I wore out whose muzzle belled out over .0010" from cleaning rod wear over 2000 rounds of barrel life and cleaned every 50 or so shots. Still shot sub MOA test groups at 600 yards just like a new barrel. No copper wash at all the last half inch of the bore and bore gauges showed that's how much it wore away.

Nothing I've read disproves Harral nor Kolbe.

And the BOSS does tune barrels for bests accuracy but not as they claim. Close, but not perfect to effect all fired bullets.

 

[murf]

johnksa,

pressure pushes out in all directions. we have talked about the pressure pushing out on the chamber walls when the shot goes off, but have not talked about the pressure pushing back on the breach face, or the pressure pushing forward on the bullet. if the shot impulse imparts a transverse vibration to the barrel due to the expansion of the chamber walls, i would think the same impulse would impart another vibration to the barrel due to compression of the breach face (bolt face) and/or the base of the bullet.

bart b.,

as far as i know, the net movement of a vibrating mass is zero (it will always remain in the same spot from when it started vibrating to when the vibration stops). the only thing that is going to move that rifle is the reaction to the bullet moving down and out of the barrel.

murf

 

[JohnKSa]

pressure pushes out in all directions. we have talked about the pressure pushing out on the chamber walls when the shot goes off, but have not talked about the pressure pushing back on the breach face, or the pressure pushing forward on the bullet. if the shot impulse imparts a transverse vibration to the barrel due to the expansion of the chamber walls, i would think the same impulse would impart another vibration to the barrel due to compression of the breach face (bolt face) and/or the base of the bullet.

None of that provides the least bit of rationale for why one might suspect cancellation/damping might occur.

What I'm asking is why you would think those impulses and vibrations would cancel rather than add. Having summed effects makes a lot of sense. Cancellation is quite a specific case and it wouldn't make sense to assume that cancellation could happen unless there was compelling evidence or a strong scientific explanation/rationale for why it might.

So let's say we're talking about a way to prevent car accidents, and you propose that we come up with a system that uses the flashes from meteors to help prevent car accidents at night by providing illumination during the critical moments before a crash occurs. It would be reasonable for a person you press for information as to why that's not a good solution, to ask you why you think it is, rather than spending any time on an analysis.

In the same manner, I was asking you if you had some rationale/explanation for why the effects of the discharge would cancel/damp the vibrations, given the unlikely nature that something like that would happen, before I went off and spent time doing analysis related to your question.

 

[denton]

As long as the steel is within its elastic limit, the vibrations simply add together linearly without interacting.

If the steel is not within its elastic limit, you'll have something more interesting than barrel vibrations to pay attention to.

 

[murf]

johnksa,

i appreciate the time you and everyone else is taking to answer my questions. i was looking for you input as to whether the breach face/bullet base pressure is significant. you answered that with your first statement.

i've been trying to answer your question about impulse/vibration cancellation. there is not a whole lot of info out there. most studies are about viscous/non-viscous damping on cantilever systems. conclusions are that there is damping but no one seems to be able to quantify it. i kind of figured this out since a barrel stops vibrating rather quickly all on its own.

murf

 

[murf]

bart b.,

that is interesting about the shot impulse sending a wave forward toward the muzzle and at the same time sending an identical wave back toward the breech. if one could time these two opposing waves, one could reduce, or cancel out the amplitude of the wave.

the muzzle bore diameter enlarging .00001" @ 10,000 psi sounds reasonable since the chamber diameter enlarges about .001" @ 60,000 psi, so i've heard.

thanks for the info. what works in the field from someone that has been there is always welcome.

the boss works. how it works, pretty obvious from various posts on this thread and others, is still up in the air.

murf