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#2680 by Rodal on 18 Feb, 2017 20:07
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Dr. Rodal -
Yes, ω is the "undamped angular frequency."
I'll have to read your comments more closely when I'm not watching 'The Dark Night Rises' and the worse for half a bottle of red wine. One thing is simple enough though...
The period I referred to as the 'free oscillation period' is the period the pendulum would have if the damping was set to zero - ie not the configuration in real life. Just glance at the equation I quoted.
I'll probably have time to take a good look at your comments on Monday.
Let's also note that you wrote:QuoteThe equation fitted is d²x/dt²+2a(dx/dt)+ω²x=0, where x is the horizontal displacement from the neutral point of the torsion balance. ω is the natural frequency of the undamped pendulum, and a is a constant representing the degree of damping.
The three sections give ω=0.191±0.003 and a=2.55±0.08.
Hence, I understand from this that ω=0.191±0.003 and a=2.55±0.08 are the values you obtained from fitting the equation d²x/dt²+2a(dx/dt)+ω²x=0 to the damped pendulum data (not to a pendulum free of damping).
What damped pendulum data did you fit? I am not sure. I presume that you fit the equation to this data http://forum.nasaspaceflight.com/index.php?topic=41732.msg1642681#msg1642681 ?
Could you let us know what data did you fit ?
The value you obtained based on the damped pendulum data, namely
ω=0.191=2 π f
gives f = 0.191/(2 π) = 0.030 Hertz
and hence gives T = 1/f = 2 π/0.191 = 32.90 seconds ~33 seconds
Hence the period 33 seconds you quoted corresponds to the "undamped natural frequency" ω obtained from the fit of your equation to a way overdamped pendulum data. (So, we have to take this as an estimate, I presume that's why you wrote, that it was plausible, and I do agree with you that is a plausible estimate, since it is indeed a smaller period than the period in the EM Drive data of Monomorphic).
Also, the value you obtained
a=2.55
where 2a = 2 ζ ω
Since really your equation d²x/dt²+2a(dx/dt)+ω²x=0
is a valid model for the single degree of freedom torsional pendulum if, and only if:
x= angle of rotation of the torsional pendulum (radians)
2a = 2 ζ ω
ω = √(k/I) "undamped angular frequency"
k = torsional stiffness of pendulum
I = moment of Inertia
hence the damping ratio ζ is
ζ = a/ω = 2.55/0.191 = 13.35
Therefore you calculated a hugely overdamped pendulum. The critical damping you calculated ζ = 13. 35 is so huge that it is beyond anything shown in this graph for a unit step, also notice that the initial overdamped ζ >1 response to a unit step is supposed to be slowly asymptotic instead of going straigth up like a rocket:
QUESTIONS:
Is Monomorphic's pendulum so hugely, overdamped ?
Is this huge amount of overdamping really due to the oil? or is it due to something else?
Recall that Meberbs pointed out that there seems to be two processes here:
1) The initial response to the step is (comparatively) very fast, it goes up like a rocket, and is oscillatory, and there is a very fast decay of the oscillations
and
2) an extremely slow (by comparison) decay
the damping you calculated is related to the extremely slow decay, way after the oscillations have died out.
Another way to look at this is that the damping may be very different in counterclockwise rotation and in clockwise rotation: the damping in the direction of the step force (straight up) seems to be much smaller than the damping for the recoil motion (coming down)
The response reminds me of the asymmetric seismic response of stacked structures like chimneys following the seismic response code:
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According to the value you calculate ζ = 13. 35 it is not even close to being critically damped (ζ = 1). It is well, well beyond being critically damped. Over 13 times higher damping ratio than required for critical damping. Wow !
Recall that
where for the torsional pendulum m is the moment of Inertia I, therefore your fit states that the damping constant c is more than 13 times larger than 2 √( I k). That is a huge amount of damping according to your fit.
So, it is important to know what data did you fit that gives such a huge value of overdamping for Monomorphic's pendulum.
EDIT: Rert, actually if you could fit the equation also to the EM Drive OFF data, after 7:57:21, for the time duration starting at 7:57:34 and ending at 7:58:10:
then it would be very interesting to compare. What ζ = a/ω would you calculate for the EM Drive OFF data ? (here it looks like ζ < 1 ). Would the undamped natural frequency ω calculated for the EM Drive OFF data of Monomorphic agree with the undamped natural frequency ω=0.191 giving T=33 seconds ? -
#2681 by Rodal on 19 Feb, 2017 00:10
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Is the damping oil being used responding with a lower viscosity (hence motion goes up straight up like a rocket) to the sudden application of the unit step force, and responding with a higher viscosity (hence extremely long decay) to the slow decay when there is no force ?
Is the oil being used by Monomorphic Rheopectic ? (a very unusual word, also referred to as "inverse thixotropy")
https://en.wikipedia.org/wiki/Rheopecty
Is the damping fluid being used a printing ink? Is it a grease ? (made so that it has lower viscosity during high rates: during pumping so that it can easily flow through restricted passages in the pump, and behave with higher viscosity at low rates after that)
http://www.emeraldinsight.com/doi/pdfplus/10.1108/eb052357 -
#2682 by rfmwguy on 19 Feb, 2017 00:36
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Sigh...several pages/days later, reduction of dampening is finally acknowledged.
You and your compatriot are quite mistaken. Perhaps you should defer to those who have actually done EmDrive experimentation. I encourage Jamie to reduce, not increase dampening. But this of course is up to him. He should avoid needless speculation by those with only a keyboard and not hands on experience working with this device.
Damping makes no sense as the cause of the delay. To start with, damping is zero when velocity is zero, so it can't have a stiction-like effect (also stiction doesn't make sense for this setup.)
Congrats on a bonifide emdrive run! Axial insertion is probably the way to go. Glad Q was so high with foil! Good experimental find. I'd agree swing mass dampening is your culprit on persistence and startup delay. A smaller paddle should work or lift it partially out of bath. You will notice Y axis LDS was showing no signs of thermal lift. At your lower power, heating of the frustum should be minimal. May not register on IR.Do have a concern why it takes more than 10 sec for the force to appear and it lingers for around the same time after power was removed.
Thanks Phil.
Perhaps this is because I am still very over damped. I am going to reduce the size of the dampening paddle. I may even need to switch to a lighter weight oil. I'm using gear oil right now and it is VERY viscous. This was all necessary when testing with the heavy and noisy magnetron, but now that is gone, a little more finesse is required...
Also, the system is clearly underdamped, not overdamped based on the oscillations after power off. A tap test would demonstrate this clearly. Reducing damping still would make for interesting additional data, but the current damping looks good.
More data is obviously needed, but my hypothesis would be a thermal effect where heating takes some time to diffuse to wherever the portion is that causes the motion (or it takes time for a convection current to get set up.) Similar effects explain the delay at the end as well.
The oscillations after power off appear to be around a decaying point, supporting the hypothesis that this may be purely thermal.
p.s. I've learned to be just as bold and arrogant sounding as others here on the sidelines. -
#2683 by rfmwguy on 19 Feb, 2017 01:10
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Not sure who made top graph but whomever picked up on the fact that the EmDrive effect has an anomalous reversal about 75% of the way towards peak displacement is spot on. That's how you know it's an emdrive effect and not some sort of thermal anomaly. Of the dozens of data sets and 10s of thousands of data points I collected on both teeter totter and torsion beam, I noticed this in almost every run. My chart below the other shows a typical run. This was one of my last with the 750W magnetron on a torsion beam. With only 1 watt on a nice torsion stand, mono has the same basic anomaly. This is how I know he has a real emdrive in the works. Congrats. -
#2684 by meberbs on 19 Feb, 2017 01:37
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See the statement from my previous post that I bolded. Contrary to your incorrect reading of my post, I did not suggest increasing damping.
Sigh...several pages/days later, reduction of dampening is finally acknowledged.Damping makes no sense as the cause of the delay. To start with, damping is zero when velocity is zero, so it can't have a stiction-like effect (also stiction doesn't make sense for this setup.)
You and your compatriot are quite mistaken. Perhaps you should defer to those who have actually done EmDrive experimentation. I encourage Jamie to reduce, not increase dampening. But this of course is up to him. He should avoid needless speculation by those with only a keyboard and not hands on experience working with this device.
Also, the system is clearly underdamped, not overdamped based on the oscillations after power off. A tap test would demonstrate this clearly. Reducing damping still would make for interesting additional data, but the current damping looks good.
More data is obviously needed, but my hypothesis would be a thermal effect where heating takes some time to diffuse to wherever the portion is that causes the motion (or it takes time for a convection current to get set up.) Similar effects explain the delay at the end as well.
The oscillations after power off appear to be around a decaying point, supporting the hypothesis that this may be purely thermal.
p.s. I've learned to be just as bold and arrogant sounding as others here on the sidelines.
I did not bother responding to your post before, because your post was simply rude. -
#2685 by meberbs on 19 Feb, 2017 01:42
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...
TT made the top graph in a futile attempt to use ignorance of how a spring-damper system works to demonstrate Shawyer's nonsensical description of forces.
Not sure who made top graph but whomever picked up on the fact that the EmDrive effect has an anomalous reversal about 75% of the way towards peak displacement is spot on. That's how you know it's an emdrive effect and not some sort of thermal anomaly. Of the dozens of data sets and 10s of thousands of data points I collected on both teeter totter and torsion beam, I noticed this in almost every run. My chart below the other shows a typical run. This was one of my last with the 750W magnetron on a torsion beam. With only 1 watt on a nice torsion stand, mono has the same basic anomaly. This is how I know he has a real emdrive in the works. Congrats.
You left off the chart from your run where the RF was broken and you got roughly the same total displacement, which shows that your other results were probably almost entirely thermal in nature. -
#2686 by Rodal on 19 Feb, 2017 01:51
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See the statement from my previous post that I bolded. Contrary to your incorrect reading of my post, I did not suggest increasing damping.
Sigh...several pages/days later, reduction of dampening is finally acknowledged.Damping makes no sense as the cause of the delay. To start with, damping is zero when velocity is zero, so it can't have a stiction-like effect (also stiction doesn't make sense for this setup.)
You and your compatriot are quite mistaken. Perhaps you should defer to those who have actually done EmDrive experimentation. I encourage Jamie to reduce, not increase dampening. But this of course is up to him. He should avoid needless speculation by those with only a keyboard and not hands on experience working with this device.
Also, the system is clearly underdamped, not overdamped based on the oscillations after power off. A tap test would demonstrate this clearly. Reducing damping still would make for interesting additional data, but the current damping looks good.
More data is obviously needed, but my hypothesis would be a thermal effect where heating takes some time to diffuse to wherever the portion is that causes the motion (or it takes time for a convection current to get set up.) Similar effects explain the delay at the end as well.
The oscillations after power off appear to be around a decaying point, supporting the hypothesis that this may be purely thermal.
p.s. I've learned to be just as bold and arrogant sounding as others here on the sidelines.
I did not bother responding to your post before, because your post was simply rude.
What may be confusing to the audience is that the tap tests (anybody please correct me if my understanding of the tap tests is wrong) appear to have been made with increased damping instead of the original setup used for the EM Drive tests
Sorry if this is wrong, but this is just my present understanding.
And, RERT's analysis shows that the decay response to the above tap test is HUGEly overdamped , at 13 times the damping ratio for critical damping, while the initial response to the step has much lower damping (it goes up like a rocket).
. The damping is very asymmetric. I asked whether this is due to Monomorphic perhaps using a grease for the tap tests that behaves more viscous at low rates and less viscous at high rates.
Yet some people were claiming that the delayed response for the EM Drive test was due to damping (this runs contrary to the tap tests !!! )
So the behavior in the tap test appears quite different than the behavior for the EM Drive test
As toQuoteSigh...several pages/days later, reduction of dampening is finally acknowledged
the acknowledgement is not universal. I certainly would not ignore PotomacNeuron's opinion. Nor it is it "finally," as Meberbs never advocated for higher damping.
Meberbs certainly never advocated for a critically damped or much less advocated for an overdamped pendulum at 13 times the amount of critical damping.
I count otlski, SeeShells and myself advocating for low damping, an underdamped pendulum such that the response is mainly governed by the elastic force, with the damping being low enough so that is does not influence by much the calculation of the frequency.
(Otlski put it well: "When evaluating a new instrument design, I prefer to have no damping until I fully understand the system response without it."). (And, SeeShells gave a very specific suggestion for low viscosity damping: regular water with anti-freeze.) On the other hand PotomacNeuron maintains that Critical Damping (damping so high that there are no oscillations whatsoever, no frequency and no period) is OK with him. -
#2687 by PotomacNeuron on 19 Feb, 2017 02:26
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I count otlski, SeeShells and myself advocating for low damping, an underdamped pendulum such that the response is mainly governed by the elastic force, with the damping being low enough so that is does not influence by much the calculation of the frequency.
(Otlski put it well: "When evaluating a new instrument design, I prefer to have no damping until I fully understand the system response without it."). (And, SeeShells gave a very specific suggestion for low viscosity damping: regular water with anti-freeze.) On the other hand PotomacNeuron maintains that Critical Damping (damping so high that there are no oscillations whatsoever, no frequency and no period) is OK with him.
Your summary about my opinion is accurate. The reason I say it is OK is that underdampling will not give you much faster response you want, for the oscillation itself is slow due to high inertia of momentum and low elastic return force. -
#2688 by Monomorphic on 19 Feb, 2017 02:41
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New dampening system. "Lab Jack" added to more precisely control paddle depth into dampening fluid. I also replaced the heavy weight gear oil with concentrated antifreeze coolant.
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#2689 by masterharper1082 on 19 Feb, 2017 03:05
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In addition to Dr. Rodal's excellent advice here, simply keep your "standard" viscous fluid in a narrow temperature range at time of test. Even water and propylene glycol (RV antifreeze) have a very significant viscosity change with temperature. They just have a lower viscosity at "room" temperature.Ideally, one wants the torsional pendulum to be underdamped enough so that the period of torsional oscillations is pretty insensitive to damping. This may require a fluid with small damping, for example SeeShells used water with anti-freeze.
Someone sent me a private message recommending pure silicone fluids as they have low viscosity change at temperature (low VTC).
http://www.clearcoproducts.com/pure-silicone-low-viscosity.html
https://www.zoro.com/teflon-silicone-15-lb-plastic-jug-ms-tsl/i/G0706800/
Be careful using silicone fluids like this, because it is a polydimethylsiloxane (PDMS). PDMS liquids are unusual liquids because they are viscoelastic, meaning that at long flow times, it acts like a viscous liquid, similar to honey. However, at short flow times, it acts like an elastic solid, similar to rubber. Actually, certain grades of PDMS if rolled into a sphere and thrown onto the same surface (short flow time), will bounce almost like a rubber ball (Mark, J. E.; Allcock, H. R.; West, R. “Inorganic Polymers”)
Because of PDMS's chemical stability, it is often used as a calibration fluid for viscoelasticity measurements in a Rheometer. The elastic shear modulus of PDMS varies with preparation conditions, but is typically in the range of 100 kPa to 3 MPa. The loss tangent is very low (tan δ ≪ 0.001).
So, you would be trading a viscosity that is less dependent on temperature by another characteristic that is difficult to quantify (unless you get a good Rheometer price >~$50,000): viscoelasticity, an elastic modulus that depends on quickness of flow, something that is undesirable for a scientific test to verify force of something as unknown and controversial as the EM Drive.
I am not familiar with the particular grades of PDMS posted above, I have no idea as to what is the elastic shear modulus of the grades you posted, but I would lean towards something simpler that has well-known properties, a fluid that is not viscoelastic (water with anti-freeze, very low viscosity oils, etc.)
mh -
#2690 by Rodal on 19 Feb, 2017 03:14
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New dampening system. "Lab Jack" added to more precisely control paddle depth into dampening fluid. I also replaced the heavy weight gear oil with concentrated antifreeze coolant.
Short of ideally controlling the temperature of the damping fluid bath, as pointed out by masterharper1082, perhaps you can at least stick a thermometer inside the dampening fluid bath, just to keep a record as a control of what the temperature was during an EM Drive test
Keeping a record of the temperature of the damping fluid bath would enable later to compare different tests, particular if at some later time you have further tests performed during a different season.
See viscosity vs temperature tables in the link pointed out by SeeShells:
http://forum.nasaspaceflight.com/index.php?topic=41732.msg1643881#msg1643881 -
#2691 by masterharper1082 on 19 Feb, 2017 13:33
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That would be fine. I didn't mean to infer that active control of the fluid temperature is needed, for sure not during running of experiments. Just keep your jug of fluid indoors so it "soaks" at a relatively even temperature. You will get some variation of viscosity with whatever temperature changes occur, but it is not a big deal if your damping ratio changes by 10% - as long as you are under damped, with safety margin, to begin with.New dampening system. "Lab Jack" added to more precisely control paddle depth into dampening fluid. I also replaced the heavy weight gear oil with concentrated antifreeze coolant.
Short of ideally controlling the temperature of the damping fluid bath, as pointed out by masterharper1082, perhaps you can at least stick a thermometer inside the dampening fluid bath, just to keep a record as a control of what the temperature was during an EM Drive test
Keeping a record of the temperature of the damping fluid bath would enable later to compare different tests, particular if at some later time you have further tests performed during a different season.
See viscosity vs temperature tables in the link pointed out by SeeShells:
http://forum.nasaspaceflight.com/index.php?topic=41732.msg1643881#msg1643881
Add me to the voices in favor of underdamped response. In my opinion, the main reason for damping is to "settle down" the response for the next experiment, or the next step change within the same test. It is a convenience to make a test sequence go more quickly.
mh -
#2692 by as58 on 19 Feb, 2017 13:58
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And, RERT's analysis shows that the decay response to the above tap test is HUGEly overdamped , at 13 times the damping ratio for critical damping, while the initial response to the step has much lower damping (it goes up like a rocket).
. The damping is very asymmetric. I asked whether this is due to Monomorphic perhaps using a grease for the tap tests that behaves more viscous at low rates and less viscous at high rates.
I don't understand how you come to conclusion that damping is asymmetric (it could be, but I don't see why it should be). Isn't the fast initial response because the tap force is much larger than spring return force?
edit: If you mean the fast initial drop and high-frequency oscillations, I agree with PotomacNeuron that they're probably related to the oscillations in the beam. -
#2693 by Rodal on 19 Feb, 2017 14:16
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Damping variable depending on shear rate was not a conclusion but just one of several things to investigate.And, RERT's analysis shows that the decay response to the above tap test is HUGEly overdamped , at 13 times the damping ratio for critical damping, while the initial response to the step has much lower damping (it goes up like a rocket).
. The damping is very asymmetric. I asked whether this is due to Monomorphic perhaps using a grease for the tap tests that behaves more viscous at low rates and less viscous at high rates.
I don't understand how you come to conclusion that damping is asymmetric (it could be, but I don't see why it should be). Isn't the fast initial response because the tap force is much larger than spring return force?
Another alternative is that there is more than one process involved here: one fast and and one slow (as Meberbs posted).
Concerning << Isn't the fast initial response because the tap force is much larger than spring return force?>>
The equation of motion for a single degree of freedom system (here written in terms of torsional oscillations) is:
d²θ/dt²+2 ζ ω (dθ/dt)+ω²θ=0
with
θ=angular rotation (radians = dimensionless)
ζ = damping ratio (dimensionless)
ω = undamped angular natural frequency (1/sec)
where RERT calculated, for the tap test slow decay after the tap test:
ω=0.191 (1/sec)
ζ = 13.35
2 ζ ω= 2* 2.55 (1/sec) = 5.10 (1/sec)
If you calculate the transient response to a ramp, you will get a large value for the velocity dθ/dt, which when multiplied by the huge value of the damping ratio ζ = 13.35 , by the damping coefficient 2 ζ ω= 2* 2.55 = 5.10 gives you a very large damping force opposing the motion, therefore instead of the response going up straight like a rocket, it should give you a slow asymptotic approach.
For an impulse the initial velocity dθ/dt is boundless, hence the response instead of going up like a rocket should be a slow asymptotic approach for such a huge damping ratio ζ = 13.35.
Only for negligible damping ratio ζ ~ 0 you will get an intiial response going up like a rocket.
Take a gander at the figure below for the response to an impulse:
Take a look at the response for ζ =4 and please appreciate how slow it is compared with lower values of ζ , like ζ=0.1, and then take into account what it would look like for ζ =13.35
So . the initial fast initial response is incompatible with the damping ratio value of ζ =13.35 obtained for the very slow decay after that , and like Meberbs stated, there appears to be two processes involved here, one fast and one slow, or another alternative is that the damping is shear-rate dependent.
On the contrary, the initial response to the tap test, instead of acting like ζ =13.35 huge damping ratio, it acts like
ζ <<1, because
1) it displays oscillations. An overdamped system ζ =13.35 should display NO oscillations, and no frequency and no period (that is elementary)
2) it displays a dynamic overshoot (a dynamic magnification factor). An overdamped system ζ =13.35 should display NO overshoot, on the contrary, an overdamped system should display undershoot (that is elementary)
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Concerning << I agree with PotomacNeuron that they're probably related to the oscillations in the beam.>> It is an elementary fact that overdamped systems display no oscillations, no frequency, no overshoot and display undershoot. Hence the slow decay after the tap test with ζ =13.35 is completely incompatible with the initial response. -
#2694 by as58 on 19 Feb, 2017 14:37
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For an impulse the initial velocity dθ/dt is boundless, hence the response instead of going up like a rocket should be a slow asymptotic approach for such a huge damping ratio ζ = 13.35.
I don't think this discussion is particularly useful, but I don't think modelling the initial tap as an impulse that only sets the initial velocity is accurate. I would rather say that it is a (large, short time) driving force that stops when the pendulum has reached its initial displacement (and possibly tapers off so the the initial velocity is close to zero). -
#2695 by Rodal on 19 Feb, 2017 14:43
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I don't think that it is useful for me to further answer you after having taken the time to answer with equations and figures to your opinion and you replying rudely <<I don't think this discussion is particularly useful>>. I may change my opinion if you show us a useful analytical model of the response rather than further re-posting of your opinions.For an impulse the initial velocity dθ/dt is boundless, hence the response instead of going up like a rocket should be a slow asymptotic approach for such a huge damping ratio ζ = 13.35.
I don't think this discussion is particularly useful, but I don't think modelling the initial tap as an impulse that only sets the initial velocity is accurate. I would rather say that it is a (large, short time) driving force that stops when the pendulum has reached its initial displacement (and possibly tapers off so the the initial velocity is close to zero). -
#2696 by Monomorphic on 19 Feb, 2017 14:49
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Magnetic tap tests using antifreeze and the largest paddle I have completely submerged. It looks a little too under damped, but promising. It may be possible to increase the size of the paddle by adding to it.
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#2697 by Rodal on 19 Feb, 2017 14:52
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Magnetic tap tests using antifreeze and the largest paddle I have completely submerged. It looks a little too over damped, but promising. It may be possible to increase the size of the paddle by adding to it.
1) It looks underdamped (ζ < 1) which is perfectly fine, and what we were looking for.
2) It looks like it was supposed to look
The intiial response is now compatible with the decay
3) Thanks to SeeShells for suggesting water+antifreeze.
4) Based on the fact that this looks like an underdamped viscous system is supposed to look like, I strongly suspect the gear oil to have had inverse thixotropy: lower viscosity at high shear rate and higher viscosity at low shear rate (a useful characteristic for pumping high viscosity oils and grease, but bad for using as a damper) -
#2698 by Monomorphic on 19 Feb, 2017 14:52
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Magnetic tap tests using antifreeze and the largest paddle I have completely submerged. It looks a little too over damped, but promising. It may be possible to increase the size of the paddle by adding to it.
1) It does not look overdamped at all (by overdamped meaning ζ > 1). It looks underdamped (ζ < 1) which is perfectly fine, and what we were looking for.
2) It looks like it was supposed to look The intiial response is now compatible with the decay
SORRY! I meant under damped. Will edit post.. -
#2699 by PotomacNeuron on 19 Feb, 2017 14:58
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Damping variable depending on shear rate was not a conclusion but just one of several things to investigate.And, RERT's analysis shows that the decay response to the above tap test is HUGEly overdamped , at 13 times the damping ratio for critical damping, while the initial response to the step has much lower damping (it goes up like a rocket).
. The damping is very asymmetric. I asked whether this is due to Monomorphic perhaps using a grease for the tap tests that behaves more viscous at low rates and less viscous at high rates.
I don't understand how you come to conclusion that damping is asymmetric (it could be, but I don't see why it should be). Isn't the fast initial response because the tap force is much larger than spring return force?
Another alternative is that there is more than one process involved here: one fast and and one slow (as Meberbs posted).
Concerning << Isn't the fast initial response because the tap force is much larger than spring return force?>>
The equation of motion for a single degree of freedom system (here written in terms of torsional oscillations) is:
d²θ/dt²+2 ζ ω (dθ/dt)+ω²θ=0
with
θ=angular rotation (radians = dimensionless)
ζ = damping ratio (dimensionless)
ω = undamped angular natural frequency (1/sec)
where RERT calculated, for the tap test slow decay after the tap test:
ω=0.191 (1/sec)
ζ = 13.35
2 ζ ω= 2* 2.55 (1/sec) = 5.10 (1/sec)
If you calculate the transient response to a ramp, you will get a large value for the velocity dθ/dt, which when multiplied by the huge value of the damping ratio ζ = 13.35 , by the damping coefficient 2 ζ ω= 2* 2.55 = 5.10 gives you a very large damping force opposing the motion, therefore instead of the response going up straight like a rocket, it should give you a slow asymptotic approach.
For an impulse the initial velocity dθ/dt is boundless, hence the response instead of going up like a rocket should be a slow asymptotic approach for such a huge damping ratio ζ = 13.35.
This conclusion is incorrect.To reach your conclusion “hence the response instead of going up like a rocket should be a slow asymptotic approach for such a huge damping ratio ζ = 13.35.”，You need at least the following assumptions: 1. The beam-damper system is rigid; 2. The pivot is fixed; 3. The beam-damper system's rotation axis is always vertical to the earth (no tilting). None of them is true. Especially assumption 2 and 3. Even SeeShells‘ double captured wire is not immune from swinging (breaks assumption 2 and 3).Quote
Only for negligible damping ratio ζ ~ 0 you will get an intiial response going up like a rocket.
Take a gander at the figure below for the response to an impulse:
Take a look at the response for ζ =4 and please appreciate how slow it is compared with lower values of ζ , like ζ=0.1, and then take into account what it would look like for ζ =13.35
So . the initial fast initial response is incompatible with the damping ratio value of ζ =13.35 obtained for the very slow decay after that , and like Meberbs stated, there appears to be two processes involved here, one fast and one slow, or another alternative is that the damping is shear-rate dependent.
On the contrary, the initial response to the tap test, instead of acting like ζ =13.35 huge damping ratio, it acts like ζ <<1, because
1) it displays oscillations. An overdamped system ζ =13.35 should display NO oscillations, and no frequency and no period (that is elementary)
2) it displays a dynamic overshoot (a dynamic magnification factor). An overdamped system ζ =13.35 should display NO overshoot, on the contrary, an overdamped system should display undershoot (that is elementary)
------------------
Concerning << I agree with PotomacNeuron that they're probably related to the oscillations in the beam.>> It is an elementary fact that overdamped systems display no oscillations, no frequency, no overshoot and display undershoot. Hence the slow decay after the tap test with ζ =13.35 is completely incompatible with the initial response.
Perhaps this is because I am still very over damped. I am going to reduce the size of the dampening paddle. I may even need to switch to a lighter weight oil. I'm using gear oil right now and it is VERY viscous. This was all necessary when testing with the heavy and noisy magnetron, but now that is gone, a little more finesse is required...
The intiial response is now compatible with the decay