120V from both legs

----- Original Message ----- From: "Northstar" Newsgroups: alt.engineering.electrical Sent: Saturday, January 22, 2005 2:08 PM Subject: Re: motor models

independent

--------------- Oh, my, oh my,

You still have not told me the method you used to measure phase. You go on about Lissajous figures- fine- done that- How fat was the ellipse? I am also familiar with the instruments that you mention. What you haven't mentioned is what you actually did.

Now, if you are correct, then it appears that you should throw away your copy of Beranek as you have proven him wrong -because your results do not jibe with his theory and it is a given fact that YOU can't be wrong.

According to his Eq.7.1 to 7.3 and circuit models, IGNORING INDUCTANCE, U =0.0574 @ -59.3 degrees Check it out using your parameters (Rms, Bl, Re,Rmr, Xmd, Cms, E). Eb must be in phase with U so Eb =0.632 @59.3 degrees ( Bl modifies magnitude, not phase - well covered by many sources) Now E=ReI =Eb is a phasor equation which can be split into two equations Real part: 1.41 =7.09Ir +0.632cos (-59.3) OR Ir=(1.41-0.323)/7.09 =0.153 Reactive part: 0 =7.09Ix +0.632sin(-59.3) OR Ix =0.543/7.09 =0.077 where I=Ir+jIx This gives magnitude of I=root(0.153^2 +0.077^2) =0.171 and the phase of I is arctan(0.077/0.153) =26.6 degrees

The above is hardly a barrage

Now these magnitudes of U=0.0574 and I = 0.171 agree with the measured values of 0.0574 and 0.172 (well within data errors). Since on the basis of results that satisfy the theory, I has a phase angle of 26.6 degrees, it follows that Ze has a phase angle of -26.6 degrees. This is basic math.

If, on the other hand, Ze is real, and I is real, YOU have obtained from the real part of E=ReI +Eb

1.41 =7.09*0.172 +Ebcos(angle) Assume that the angle is -72.4 degrees so Ebcos(72.4) =0.190 giving Eb =0.630 (@-72.4) close enough in magnitude.

However, the reactive part then gives:

0 =0 +Ebsin(-72.4) which implies that -0.600 =0

a) Ze and I being real implies that -0.6 =0 ???? b) angle of Eb =72.4 which is not according to Beranek as applied to this speaker. c) The effect of Xmot on Ze has been ignored. No reason given. The only way that this can be ignored is due to cancellation due to the inductance but you have claimed inductance is negligable and correct calculations from your other data confirm this.

Hence you have produced a result which is not in accordance with Beranek or any of his models, nor with Kinsler, etc.

Either you are wrong or they are.

Secondly, with the values of magnitude of Ze=1.41/0.172 =8.2 ohms, Re =7.09, |Zmec|calculated as (11.0)(0.172)/0.0574 =33.0 , corresponding to a |Zmot | =3.67 ohms, a solution, making NO PRIOR ASSUMPTIONS as to phase was given (and you have not given the courtesy of even trying to understand it) , leads to the phase angles that I have. So - using your magnitudes of E, Bl, I, U, Re, which lead to magnitudes of Ze, Re, and Zmec, I get a solution which agrees with the solution using Berenak's models. Your results differ so again Berenak, etc must be wrong. (You get the correct Eb only because you started with the correct I and U - I can assume a phase angle for Ze of, say, 10 degrees and still end up with the correct magnitude of Eb ).

In addition, you still haven't explained away the fact that your power expression leads to a power, transferred to the mechanical side ,of 0.0323 watts This is equal to U^2(Rms+Rmr) +0.0244 watts. The latter corresponds to an added mechanical resistance Rbs = 0.0244/0.0574^2) =7.4 mechanical ohms. This rather large resistance value has been completely overlooked by Beranek, Small, Kinsler, etc., so, again, they must be wrong. All that effort to get parameters Rms, Rmr, etc is wasted as these values obviously do not lead to your results!.

It is also interesting to note that on your premise, Qin=0 and no reactive loss exists in Re so Q transferred to the mechanical side is then 0. However, the reactive power on the mechanical side is also given by XmecU^2 =0.108 vars. Obviously Berenak's Eq. 3.53 through 3.58 are also wrong and it is possible to get a net reactive "power" without having any reactive supplied by the source. Conservation of energy, as well as Berenaks text must be re-written as well.

Just think, you accused me of not agreeing with Berenak while you blithely have thrown his work out the window because you are afraid to learn how to handle phasors.

Now do you wonder why I have doubts as to whether you actually measured phase by any valid (and as yet unmentioned) method? Your numbers simply do not make sense. If you did your analysis properly, they would.

As far as I am concerned, this is the end of waltzing around in circles. You are apparently good at measurements ( I am still assuming that you did measure the parameters Mmd, Rms, etc yourself -did you? ) but hopeless at the math and ability to question yourself.

Not my concern any longer.

Thank you, I have learned something- not from you but from Berenak (not particularly his handling of circuit models which is correct but unnecessarily clumsy- but an interest in exploring the non-speaker or major part of his book.).

Don Kelly snipped-for-privacy@peeshaw.ca remove the urine to answer

not necessarily, both , rather all sides of the model equations are affected by different quantities and unlike elements... they can not be cancelled out, or you'd end up with a dead motor moving nothing.

This effect is used in small orbiting satelites but only works proportionaly at zero gravity, the ionic effect i'm looking for has to work on Earth Gravity to do anything at all..... no thrusters, no fanblades. no one teachs this....that i know of they are too busy trying to teach what is common & already known, that, and fiber optics .

Good point... similiar to the top of the armature might be heavier than the bottom. Have you checked this with the calculus yet?

Yes.. the fiber optics are in vogue.. they teach them at the sophomoric level. However I believe the ionic effect may be developed best with the phasor angles. Perhaps measure the gravity angle and align the ions in inverse (largest ones first, of course). Hope this helps.

Northwest

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You again avoid addressing what would prove who is right, and settle the argument. Wonder why?

Also.., you cannot later blame your wrong analysis and misapplication of phasors on ignoring coil inductance, as you were given the opportunity to account for this over two weeks ago, and did not respond (see below). Wonder why? You knew that would pave the way to proving you wrong, that's why.

Again:

YOU HAVE LOST THE ARGUMENT BY YOUR OWN STATEMENT that if Ze is Real, then Rmot =1.109 ohms.

You said: " It appears that, (and you were not clear on what you actually did) you started with the assumption that Ze was real - this gave Rmot =1.109 ohms which is fine if the assumption was correct. "

Now since I measured the phase angle between voltage and current to be zero at 203.4 Hz, we agree that Ze *is* real and Rmot = 1.108 ohms. Then Ze = Re + Rmot = 7.09 + 1.108 = 8.198 ohms Power in is Pin = E^2 / Ze = 1.41^2 / 8.198 = 0.2425 watt Not " Pin=0.2162 watts " as you have consistently claimed.

Now we know you would nit-pick any method I use of measuring phase, so I ask in my last post: "Do you want me to send the speaker to a reputable lab and have phase measured at your expense (or mine, if you're strapped) or what? "

S "I can well understand your curiosity (your word) such as "Why do you treat Ze as real?" and "Why do you ignore Xmot? " However before further details are discussed (at my option, after considering your response here), you need to note your long-standing error and recast your power input expression and entire analysis to include the appropriate use of (Bl)^2/Re. And if you do so, I suggest we start from scratch and I measure coil inductance next time around before anything is started."

You avoided the issue by responding:

"First of all- do check Beranek's 7.2 and determine the phase angle of U with respect to E."

Followed by another profusion of irrelevant equations. You KNOW full well that using coil inductance gives phase between voltage and current as zero somewhere between ~150 and 300 Hz, and you also know that validation of this being 203.4 Hz loses the argument for you by proving both your theory and phase angles to be wrong. You also know your last hope is to nit pick the method of measuring phase. Well... as Arnold Schwarzenegger said "I'll be back", so your reliance on bluster will be short-lived.

Northstar

That sounds just right, aligning the phasor angles with the harmonics from equation subset 1=(horizontal values) with that of subset

2=(vertical values) could produce an interesting grid plate effect at 30-50kVdc .. got to try it some time.

no i have not used calculus for this, but probably will ~>

I have read your comments below. a)You are a fine one to talk about phasors as you have repeatedly shown a lack of understanding of the math and also a weak understanding of the physics and circuit models involved .

b)You have avoided any critical analysis of what i have said (possibly because it does involve phasors and circuit theory which is beyond what you actually understand.) You have not proven me wrong in any respect. c) you blithely ignore the discrepancies that your analysis produces, without even trying to address these points.

d)You recognise that inductance has an effect on resonance but you yourself treat it as negligable. If Ze is real, then you must use Re +jwl in place of Re which still makes your scalar analysis invalid

e)You still don't seem to realise what the Bl^2/Re term and castigate me for not including it in my power expression (a sign of lack of understanding of the circuit model used) but ignore the fact that it doesn't appear in your value of mechanical power (which doesn't include a power U^2(Bl^2)/Re=0.0563 but some ficticious resistance value Rbs). I have been through this several times- obviously you didn't read or didn't understand what you read. (note that circuit 7.2d is just as valid as circuit 7.4 and 7.2d leads to correct power results).

f) Oh yes, you will let me know the inductance if I renounce my errors (even if you don't know what they may be and have failed to point them out). Such generosity. Based on the information that you have provided so far, there is nothing to renounce.

There are other things but what is the point.

bye.

Have a good time,

It might be a good idea to check Re. Could it possibly be 7.90 rather than

7.09 ohms (transposition in recording it)?. Including the effect of inductance sufficient to make Ze real, the major differences that we have would reduce to normal data errors. (Berenak's 7.1 would have to be modified as it ignores L-not a problem) I would suggest not using an ohmmeter for DC resistance measurements but using a reasonable current and voltage. It would also be interesting to check the blocked rotor impedance by the 3 voltmeter method, using a known series resistor of the order of 1 to 3 ohms.

DC may not work best, note. Maybe use AC, with super-conductive frozen wire, and tune to the resonance. Also use only even-order harmonics - smoother and less friction than the odd-order.

The subsets are nice, but don't add with the scalors, and neglect the reaction. Use the phasors and an angle that gives the desired results. Hope this helps.

Northwest

Anyone wanting to have input, please see below. TIA

Clipped, but for the main issue.

For the third time, you did not address my question. Again:

YOU HAVE LOST THE ARGUMENT BY YOUR OWN STATEMENT that if Ze is Real, then Rmot =1.109 ohms. You said: " It appears that, (and you were not clear on what you actually did) you started with the assumption that Ze was real - this gave Rmot =1.109 ohms which is fine if the assumption was correct. "

Now since I measured the phase angle between voltage and current to be zero at 203.4 Hz, we agree that Ze *is* real and Rmot = 1.108 ohms. Then Ze = Re + Rmot = 7.09 + 1.108 = 8.198 ohms Power in is Pin = E^2 / Ze = 1.41^2 / 8.198 = 0.2425 watt Not " Pin=0.2162 watts " as you have consistently claimed.

Since you appear to question the validity of my measurement, I ask "Do you want me to send the speaker to a reputable lab and have phase measured"

Regardless: Proof that E^2/Ze is the power in, is given by Kinsler on page 366, where he describes the electrical resonance fr where the positive (inductive) reactance of the voice coil cancels the negative motional reactance, resulting in a frequency at which the input reactance is zero. This occurs at 203.4 Hz, making Ze real and power in = E^2/Ze = 0.2425 watt or Pin = I^2 Ze = 0.2425 watt.

Mr. Kelly, with due respect to your math ability and prowess with rotary motor, electrical theory, etc the problem is simply misapplication of your abilities in an area where you lack practical experience. You are at a point here that I traveled by long ago, and was stuck in the very same rut. However it is ironic that the problem is that which you attribute to me, i.e using scalors when phasors are needed.

You say power in = I^2 Re + v^2 Rms + v^2 2Rmr = 0.2177 watt, and then observe that v^2 [(Bl)^2/Re] = 0.0563 watt gives a total of 0.2740 watt which is more power out than in. That is indeed a dilemma, however..

Overall power magnitude cannot be derived as mechanical resistance only times velocity squared, we must consider mechanical resistance plus mechanical reactance, i.e. mechanical impedance. Then mechanical power is the real part of mechanical impedance times velocity squared

Pmec = v^2 (Zmec cos angle) = 0.0574^2 (32.99 * 0.3017) = 0.0328 watt

Note (Zmec PFmec) = Rmec = 9.953, and Pmec = v^2 Rmec = 0.0328 watt

Then noting power generating heat = I^2 Re = 0.172^2 * 7.09 = 0.2097 the power in = power out equation becomes simply

Pin = E^2/Ze = (I^2 Re) + (v^2 Rmec) = 0.2097 + 0.0328 = 0.2425 watt

Exactly matching Pin = E^2 / Ze = 1.41^2 / 8.198 = 0.2425 watt

Now we *know* from Kinsler that E^2/Ze is the power in at 203.4 Hz, velocity was *measured*, we *know* power into heat is I^2 Re, and we *agree* that mechanical impedance Zmec is 32.99, so cos angle can be only 0.3017, i.e cos 72.44 = 0.3017 to satisfy the equation. Note this agrees with Rmot/Zmot = 1.108 / 3.674 = 0.3016, otherwise as Rmec/Zmec = 9.953 / 32.99 = 0.3017.

We cannot just pull out Rms+2Rmr or (Bl)^2/Re and multiply by velocity squared and get meaningful results.

Now to your last questions and comments, and may we please just drop the animosity after this? :)

I told you more than once I came here to learn. Please do likewise.

Uh... Sorry but Kinsler assisted me.

See above.

These factors have their appropriate effect during actual operation and the phase between voltage and current at 203.4 Hz is either zero or it is not.

Sorry, but I did give you the inductance about three weeks ago, and I believe you said it would not help in the facet we were into at the time.

Thank you. I re-checked and 7.09 is correct.

Finally, note that Small calls (Bl)^2/Re electromagnetic damping, Olson says (Bl)^2/Re must be included in damping, and Lahnakowski notes it as equivilant mechanical resistance. Morse calls it mechanical impedance. Beranek doesn't elaborate, but does add (Bl)^2/Re arithmetically to Rms and 2Rmr to get total mechanical resistance.

Now... We are back to square one, which is what I came here for in another life and in the first place :) inquiring about the nature of back emf and its relation to power. There were several respondents to my post, and things looked hopeful, but they appeared to defer to you and things took a downhill turn, so to speak, as it were... time wasted but hopefully we can learn. Also, anyone wanting to have input is welcome to do so, and hopefully will do so.

Bottom line as I see it is that (Bl)^2 /Re represents the motor resistance manifested in the *electromagnetic* field of the motor, is the created by back emf opposing the applied voltage, and further that power from the source is required to be dissipated into this resistance to overcome the back emf.

Northstar

you probably don't know how much sense that makes };-)

how can i get a clean (waveform) ac supply from a battery pack of, lets say +-20VDC ?

It won't work well with a sawtooth, though a square wave can be used at a 1st & 2nd stage amplifier + useing some high speed digtal counters to ignite the grids, but the repetitive use of plain ol multivibrators was recomended instead.

------------ If you are at resonance, I have no problem with that. However, it brings into question the other parameters. As I have indicated, with the parameters as given, there are problems. That is why I wondered if, somewhere, somehow, there was a digit exchange in the value for Re. The problem is that Zmec is easily calculable from the parameters given - the open circuit mechanical impedance Zmec= 2.4+j32.78 =32.87 @ 85.81 degrees. The magnitude compares with your value of 32.99 within reasonable error (data is good) but the phase angle differs from yours.

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In fact it can be so derived. --and you have actually done it both ways below -in contradiction of what you say above-so what is the fuss?. Complex mechanical power =P+jQ =U^2(Rmec +jXmec) and the real part of this is U^2(Rmec) The difference between what you get and what I get is that I have used Rmec =Rms +2Rmr and based my mechanical power on that (i.e. real part of U^2(2.4+j32.78) =U^2(2.4) =0.008.

You have based it on an Rmec =9.95 which =2.4+7.55 and the 7.55 portion is the anomaly. If it exists, then Berenak's circuit models (as well as Kinsler's) are wrong. The machanical parameters that you measured do not account for all the mechanical loss terms and would then be useless. Do you see the dilemma.?

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It should match exactly as you originally used Pin and I^2Re to get the

0.0328 watt value and divided this by U^2 to get 9.953 which you have now multiplied by U^2 to get 0.0328 and added I^2 to get Pin -in a circle. You haven't calculated the mechanical power from the parameters that you gave -i.e. Rms, Rmr and if Berenak's models are correct, this should give the correct value.

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-------- I am happy with the magnitude of 32.99 but the angle is at odds with the angle found from the mechanical parameters that you provided as stated above. We have been through this before. Hence, either you were not at resonance or some of the data you provided is incorrect because if the data you provided is correct, then the assumption that Ze is real is false, and vice versa. That is what i have been trying to say. Your phase angle assumption leads to a apparent mechanical resistance of about 9.5 which is not accounted for by any of the data or by any of the theory. There is a contradiction-to be resolved.

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-------- Why not?- Using U^2(Rms+2Rmr) is quite valid and follows directly out of Eq3.49 (as noted before) - you haven't given a reason for it not to be. This is simply the real part of U^2(Zmec) as indicated above.

In fact it is generally a more accurate way to find the mechanical power than subtracting I^2Re from the input power.

------- From what I recall, Kinsler dealt quite correctly with this. Certainly at resonance, Ze becomes real and in that case the real power in is E^2/Ze =I^2(Ze) only because the reactive part of Ze becomes 0. There is no problem there.

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The above doesn't deal with the discrepancies that were pointed out.

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Agreed. Inductance does have an effect- it is not negligable so you have Ze =Re +jwL +Rmot +jXmot where Xmot is negative and for Ze real Ze =Re

+Rmot I am happy with that. I am not happy with your value of Rmot. Certainly if I use my value of Rmot based on Zmec as calculated, then the magnitude of Ze becomes, at resonance, about 7.35 ohms, not 8.2 ohms. On this basis, we are back to a problem of either not being at or near resonance or some of the data you have provided is wrong- That is why I asked about Re.

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Sorry, I don't recall getting it. That may have been my fault.

-------- Is this a re-measurement or a check of data previously written down? Is this DC cold or warm?. Do you have AC locked coil impedance data? If this is so, and you are at resonance, then Berenak's models appear to be wrong. In addition there is a non-negligable resistance term that is unaccounted for in his models or your data.

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--------- True it is an equivalent mechanical resistance- no problem there. but it is a result of the model manipulation that is used. BlE/Re -(Bl^2)/Re =BlI =ZmecU It is unfortunate that the model of Fig. 7.4 was the one he used - as the model of Fig 7.2d on which 7.4 is based, is actually more straightforward.

----------- In the speaker, there is a back emf Eb=BlU which is due to the motion of the coil. No more no less. It doesn't matter how the coil is moved. In other words, an emf will be generated if the circuit is open and the coil is moved mechanically. The force, BlI, produces motion and F=ZmecU.

Electromagnetically, the electrical side only sees the mechanical side through Eb=BlU and the mechanical side only sees the electrical side through the force BlI. These are the only terms coupling the two sides.

In the case of a linear impedance load as in the speaker, the electrical side sees an impedance Eb/I =BlU/(Zmec/Bl) =Bl^2(U/F) =Zmot and the power into this electrical impedance impedance is the power dissipated in Zmot. which is virtual electrical impedance. The source of this impedance is due to the mechanical force and motion.

Seen from the electrical side the circuit impedance is Re +Zmot. No Bl^2/Re term involved. The power into Eb is EbI(cos phase angle of I with respect to Eb). Since The electrical and mechanical sides are connected through an ideal transformer so this term represents the power transferred to the mechanical side. This model from the source side is shown in Fig 7.2c.where all values are referred to the electrical side. Basically the mechanical load appears as the impedance Zmot =Eb/I. This is where the back emf appears- it doesn't exist on the mechanical side. Also, in referring everything to the electrical side, the back emf as an induced voltage is replaced by the voltage drop across the equivalent impedance Zmot appearing just as if the load was not electromechanical but a passive impedance. It is true that Eb is a voltage opposing the source but this voltage has nothing to do with Re but only depends on the velocity. It will affect the current and in that way affect the power transfer.

In fig 7.2d, Beranek makes a change to the mechanical side, bringing both the source and the Re terms to the mechanical side of the circuit to eliminate the transformer. Then E is replaced by E/Bl which is a velocity source, in series with Re/(Bl^2) which is a mechanical admittance (Berenak treats it as mobility ohms) and the model gives E/Bl =Re/(Bl^2)F +ZmecU Note that Eb is not involved and never is involved on the mechanical side. Re/(Bl^2) simply represents Re as seen from the mechanical side. The real power in this model is given by Pin=(E/Bl)F cos (angle between E/Bl and F) which is the same as EI cos angle between E and I loss: (Re/Bl^2)F^2 =ReI^2 is the coil loss remaining power is RmecU^2 =U^2(real part of Zmec) =FU cos angle between F and U Note that the effect of Re is present and is a damping term but the power involved corresponds to I^2Re. Eb has nothing to do with it other than the fact that EbI =FU

In Fig. 7.3, Berenak makes a source change so that all values are in mechanical impedances and the circuit becomes a bit simpler. Olsen probably did this as well- an electrical engineer might have bothered but wouldn't have bothered with the next step usijg duallity to get fig 7.4. In fig. 7.3 the velocity source Eb/Bl behind Re/(Bl^2) is converted to a force source BlE/Re behind (Bl^2)/Re .This model is correct only to the right of the terminals- which is sufficient for calculation of the actual force and velocity as well as the actual power in the mechanical elements. It does not properly represent the losses in Re. Fig. 7.2d does represent the losses correctly as does the model of Fig 7.2c.

You need a high-speed divider to switch between + amd - , then round off the edges with with a pulse-tumbler.

Recommended by who? Use of multivibrators could be an old wifes tail. Perhaps your best bet is to mix the cosmeratic rays out of phase with the gravity ions and adjust their amplitude to nearly zero with the phasor angles, leaving enough gravity power E = mc^2 to do the job.

Northwest

So... for the fourth time, you do not answer the above question, but you have finally conceded that if 203.4 Hz is the frequency of electrical resonance, then Ze is real at 203.4 Hz and power input is E^2/Ze = 0.2425 watt, and not your power magnitude of "Pin=0.2162 watts" as you have claimed, which would also make your phase angles and analysis in error as well. This leaves only the frequency of electrical resonance to be verified, so again, do you want me to send the speaker to an independent and reputable lab to have phase measured, or do you want to accept my measured frequency of 203.4 Hz?

Regarding your latest comments below, I will not continue to respond to your offensive queries based on your erroneous magnitudes of phase, resistance, power, etc such as (from below) where you say " You have based it on an Rmec = 9.95 which =2.4+7.55 and the 7.55 portion is the anomaly. " 2.4 is *your* erroneous mechanical resistance magnitude. Don't subtract it from *my* Rmec and then ask me to justify the result. Either:

1. You are conniving and try to pull off this kind of trickery
2. You are stonewalling to avoid coming out and admitting your errors.
3. Your understanding of the overall theory is weak, and you refuse to be open to learning.

Sorry, but I think it is a combination of the 3.

Northstar

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------------------------------- I was looking at the other data as being correct. If Rmot =1.109, then other data that you gave me is wrong. You were the one who indicated that L was negligable so that on this basis I questioned the resonance. It was only after I did question it that you indicated that it was of importance. At the time, you had not given any indication that you had measured the phase - indicating that it was an assumption. Unfortunately, the model with L ignored and with no assumptions as to the phase of Ze, fit the data, given, very well.

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see below- I still have problems with this Rmot as I have explained before. If it is right, and resonance exists, then other data is wrong. The problem is which data is wrong

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And you really didn't read what I said- I just pointed out inconsistencies between the results using the data given (and used in Berenak's models) and your Rmot. If, for example, Re =7.93, the theory and the measured values agree very well. This leads to a larger I^2R loss.

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with your Rmot (not with your calculation of it but with some of the data involved)

-------- I will accept the resonant frequency as 203.4Hz and the input power as indicated. However, I still disagree with your conclusions as indicated below. If you had said, when I first asked, how you knew Ze was real, much acrimony ( but not questioning) could have been eliminated.

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Try to relate your Rmec to the theory- I would like to know how you justify it.

--------

In fact - I have been dealing with the modelling and circuit analysis -including the physics behind it- my area of experience- not yours.

It seems that any questioning of your results is not allowed- too bad.

I just looked at the circuit models and equations given by Berenak. I may not have your practical experience with speakers but I have more experience in handling electromechanical energy conversion devices and far greater experience in handling circuit analysis (more so than Berenak whose background is mechanical and acoustics- not circuit analysis). The modelling is nothing more than circuit analysis and I am quite comfortable with that. With the data that you provided, the actual mechanical impedance is given by Zmec =(Rms+2Rmr) +j(Xmd-1/wCms) =2.4 +j 32.78 =32.87 @85.81 degrees. at

203.4 Hz. This Zmec is the open circuit impedance as shown on the right or mechanical side of the "transformer" of Beranek's Fig 7.2b as well as in 7.2a,c Do you have a problem with Berenak's model? If so, where? This has a magnitude which is within 0.4% of your value of 32.99 as calculated - well within the accumulated error in the data given. It is also the Zm of Eq.3.60. Hence, if it is wrong, the models are wrong or the data is wrong. On the basis of your Ze being correct, and real - the value that you get for Zmec = 32.99 (say 33.0) Now you have a resistance Rmec =9.95 ( differing from the theoretical value by 7.75 ) and as Zmec =32.99 , Xmec = 31.45 - somewhat lower than that calculated from Xmd-1/wCms. This is where the model handled correctly (and I have done that) disagrees with your values.

This disagreement means that either the model is wrong (i.e. Berenak is wrong) or that the data for this model is wrong. Assuming that the model is correct, and that you are correct as to being at resonance, the data that you provided has an error. Using this data gives Zmot =3.69 @ 85.81 so the magnitude is in agreement with your magnitude. However, the data then gives Rmec =0.27 ohms. This is, of course much smaller than your 1.109 ohms. The problem is then -what part of the data is wrong? - Zmot magnitude is OK and Rmot is too small to have much effect, the problem appears to be in the value of Re. That is why I asked about this value.

Taking the inductance into account and Re=7.09 leads to a Ze =7.35 ohms at resonance- based on the data. This is obviously wrong. so there is a data problem. I suggest that it is in the value of Re. Either the value of 7.09 is wrong or the AC resistance is appreciably greater than 7.09 ohms. It is quite common for AC resistance at 60Hz to be 10% larger than at DC (due to skin effect and proximity effects in a coil) so a 10% increase at 200Hz, even with smaller wire, is quite possible. Your measured Ze would include such an increase if it is there. A DC measurement wouldn't. That is worth doing a blocked coil measurement of voltage and current, using the 3 voltmeter method to determine the actual coil impedance at this frequency. Failing that, a re-measurement at DC using, say, a 1 to 2 V source rather than an ohmmeter. This is not an attempt to insult you.

In conclusion there is a choice: a) you are not at resonance b) You are at resonance and Berenak's models are wrong c)You are at resonance and the other data, most likely Re is in error.

I would suggest that c is the problem. I depend on you for the measurements- but I don't depend on you for the analysis.

if you think cosmic rays have anything to do with Ion Generators you'd do well continuing with Mr. Kelly on Your motor, rather than dispense any jiberish here..

thanks & farewell

Bottom line from the last few posts:

Now since I measured the phase angle between voltage and current to be zero at 203.4 Hz, we agree that Ze *is* real and Rmot = 1.108 ohms. Then Ze = Re + Rmot = 7.09 + 1.108 = 8.198 ohms Power in is Pin = E^2 / Ze = 1.41^2 / 8.198 = 0.2425 watt Not " Pin=0.2162 watts " as you have consistently claimed.

THEREFORE YOU HAVE LOST THE ARGUMENT, since proof that E^2/Ze is the power in, is given by Kinsler on page 366, where he describes the electrical resonance fr where the positive (inductive) reactance of the voice coil cancels the negative motional reactance, resulting in a frequency at which the input reactance is zero. This occurs at 203.4 Hz, making Ze real and power in = E^2/Ze = 0.2425 watt or Pin = I^2 Ze = 0.2425 watt.

You have finally conceded that if 203.4 Hz is the frequency of electrical resonance, then Ze is real at 203.4 Hz and power input is E^2/Ze = 0.2425 watt, and not your power magnitude of "Pin=0.2162 watts" as you have claimed, which would also make your phase angles and analysis in error as well. This leaves only the frequency of electrical resonance to be verified, so again, do you want me to send the speaker to an independent and reputable lab to have phase measured, or do you want to accept my measured frequency of 203.4 Hz?

Thank you.

Yes, your phase angle is incorrect. Allow me to explain with a short analysis using that which we now agree on:

With agreement that power input is E^2/Ze = 0.2425 watt, mechanical power then must be power in minus power into heat Pmec = Pin - Ph = E^2/Ze - I^2^Re = 0.2425 - 0.2097 = 0.0328 watt. Noting we agree that mechanical impedance Zmec = 32.99, mechanical power must also be velocity squared times the real part of impedance Pmec = v^2 (Zmec cos angle) = 0.0574^2 (32.99 * 0.3017) = 0.0328 watt We see that only cos angle = 0.3017 satisfies the equation, giving phase angle to be arc cos 0.3017 = 72.44 degrees. And the real part of mechanical impedance is Rmec = Zmec cos angle = 32.99 * 0.3017 = 9.953 Xmec is sqrt(Zmec^2 - Rmec^2) = 31.453 and mechanical impedance becomes Zmec = Rmec + jXmec = 9.953 + j31.453 = 32.99 @ angle 72.44 degrees The power in - power out equation can then be written then as E^2/Ze = (I^2 Re) + [v^2 (Zmec cos angle)] = (0.172^2 * 7.09) + [0.0574^2 (32.99 * 0.3017)] = 0.2425 watt Matching input E^2/Ze = 1.41^2 / 8.198 = 0.2425 exact Note that impedance was re-measured on Jan 19, 05, and is correct at 8.198 ohms, and can be proven by another lab if you wish. Noting that Zmec cos angle = Rmec, then in the form you use, power in = power out as E^2/Ze = (I^2 Re) + v^2 Rmec = (0.172^2 * 7.09) + (0.0574^2 * 9.953) = 0.2425 watt

Showing your phase angle, power magnitude, and analysis to be wrong, and your statement "My understanding of the theory is, in fact far stronger than yours." to be untrue.

There is no anomaly. You have simply used Rms+2Rmr as the mechanical resistance instead of the real part of mechanical impedance, which is Zmec cos angle.

7.55 does not exist, so there is no dilemma. 9.953 - 2.4 = 7.55 is based on your erroneous mechanical resistance of 2.4.

Sorry, but no contradiction. I had given phase angle as 72.44 way back, and we agreed on Zmec = 32.99, so my data given clearly allows Rmec = Zmec cos angle = 9.953.

My data is correct. Rmot is just the real part of Zmot, given as Rmot = Zmot cos angle = 3.674 * 0.3017 = 1.108, or more complete Rmot = [(Bl)^2 / Zmec] cos angle = (11.01^2 / 32.99) * 0.3017 = 1.108 Then Ze is real as Ze = Re + Rmot = 7.09 + 1.108 = 8.198 electrical ohms, both as calculated and measured.

Both.

One generally needs to question to learn. Acrimony while questioning is not the best policy, if you want to stay on the good side of the guru :)

No justification needed other than that given. Rmec is just the real part of impedance - Rmec = Zmec cos angle. Now the relation to Beraneks 7.1 is another matter, and can be shown, but will not be done here. It remains as an exercise for the student :)

Beranek is correct. I have explained what 7.1 encompasses plus you pulled resistance terms out of a vector and used them in scalor form. This is your problem, and you need to work on it. No offense intended, and in fact you have the math ability to do it, but first you must understand 7.1 includes both the mechanical *and* the electromagnetic effects.

Again, there is no theoretical value of 7.75 - I assume you mean 7.55 - this is based on your erroneous mechanical resistance of 2.4 subtracted from the correct mechanical resistance of 9.953.

Sorry, but the latter was not my loss.

Northstar

If you would have had a teacher, you would have understood is is not jibberish. Your understanding is weak, mine is far superior. The cosmic rays create the eons, at least the small ones - look it up.

Bless you and the horse you rode in on.

Northwest

-------------------------------------------- Rms=1.57 2Rmr =0.83 so the sum is 2.40 Your data. If you want to include (Bl^2)/Re then the sum is 19.5 (which is not Rmec) You have 9.95 which is neither fish nor fowl. The difference, if you cared to read, between 9.95 and 2.4 =7.55 which is unaccounted for in the model. What is the physical reason for this and why does Berenak's model not account for it? What is the resistance of the speaker at 200 Hz as opposed to DC? Do you know?

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----- See below

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------ When first you sent data, I asked about L. You implied that it was negligable. There is a world of difference between it being negligable and wL =-Xmot. However, I should have asked "Why 203.4 Hz rather than 150 or

200Hz. " I also should have twigged that this specific frequency was the resonant frequency as otherwise it would be of no special importance.

------- Not good enough. Are you now saying that Rm of Eq7.2 is (Bl^2)/Re +9.95? and that Rms+ 2Rmr =9.95? Then 7.1 won't give you the correct velocity. Alternatively, are you assuming that Bl^2)/Re +Rms +2Rmr =9.95 requiring negative Rms +2Rmr? as (Bl^2)/Re is larger than 9.95 Curiouser and curioser

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------------- Where did I incorrectly pull resistance terms out of a vector and use them as a scalar? Are you referring to a power calculation? I did nothing wrong there-I explained that. What's your problem with what I did- except that you incorrectly said that I couldn't. Get it straight- I can (and you effectively did so too, without recognising it). Sheesh, this is pretty low level circuit analysis. This is your problem, and you need to work on it.

------- Eq.7.1 actually doesn't. It relates to the circuits of Fig.7.4 which is are simple passive electrical circuit models. The earlier development does (7.2b does -in the ideal transformer ) but by the time you get to 7.2c and beyond, the model has become a passive electrical circuit. The electromagnetic effects are contained in the basic equations 3.59, 3.60 and these are merely F=BlI and Eb=BlU. The model works because the mechanical and electrical behaviour is mathematically linear so equlvalent impedances can be used. I do recognise electromagnetic effects- that was my bread and butter for 50 years. A speaker is a very simple electromagnetic device (In most such devices, BlU and BlI are not applicable as the geometry is much more complex. ).

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-------- That is right- there is no theoretical value of 7.75. There is also no theoretical value of 9.95. Theoretical values should all be represented in the model. What element in any of Beranek's models does it relate to?

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--------------- a)At resonance using the data I=0.172, U=0.0574, Bl=11.01, Re= 7.09 and E=1.41 the result that you get is Zmec=33.0 (not 32.99 as the data isn't that good) at a phase angle of about 72.4 degrees. You have a pmec +Pa =0.03= 0.0328 and your calculations are correct on the basis of this data

b) Using Beraneks model, and recognising that it shows the mechanical impedance terms Mmd, Cms, Rms, and zmr/2 which is 2(Rmr+jXmr) and using your values for these, I got Zmec =32.9 at a phase angle of 85.8 degrees. (Rms

+2Rmr =2.4 , )(Xmd-1/wCms=32.8 ) The power that I get is 0.008 watts The simple calculations have also been done correctly on the basis of the data that you first gave me and if the values that I get are wrong, then please calculate Zmec from this data (If you prefer, find Rm and Xm of Eq. 7.1 which is short circuit mechanical impedance not the open circuit impedance which is the actual Zmec. )

Magnitudes agree but phase doesn't. This leads to quite a difference in Zin, power input, and power output. Berenak's model has passed the test of time and both of us have done the calculations correctly. If the model and data are good and all calculations are correct, there should be agreement within the accuracy of the data. Otherwise either the model or the data is wrong.

******************** Conclusion, There is a data error-like it or not- either in Re or in the parameters Rms, Rmr, Xmd, Cms. *********************** . Did you check the 200Hz resistance of the blocked coil or did you just stick an ohmmeter on the terminals? It could be quite different. If you don't know how, I can show you a simple method.

Where it the error? - the model should fit the results and it doesn't. That is, calculation from the parameters that you have given, including rather than ignoring inductance will not give the results you get. Including inductance, it will not give the values that one gets without L, either. It will lead to a Ze of about 7.36 ohms which is obviously incorrect on the basis that your Ze =8.20 ohms. If Rm is about 7.9 rather than 7.09 ohms, or Ze=7.36 ohms, the model works. It will also work for Rms+2Rmr=9.95 So which will you have?

By the way, I really would like to see how you relate your value of 9.95 ohms to any of the terms in Berenak's 7.1. It is not Rms+2Rmr nor is it (Bl^2)/Re +Rms +2Rmr. Have you discovered something that Berenak, Kinsler etc missed?

Also, I still do not have the inductance that you were going to send. You may have done so but I didn't see it- and estimating it as about 2.7 to 2.9 mH depending on yours or mine Xmot .This will not be negligable and requires a modification of Eq.7.1 (or simply ignoring Eq.7.1 and solving the circuit of Fig 7.2.

Sincerely,

You are proven wrong above on your phase angle, mechanical resistance, and power magnitudes. Therefore in view of your condescending attitude of the past, perhaps you should just admit your lack of understanding of the theory involved, and stop trying (as you do below) to pull out of the fire, what is already charred beyoud recognition, i.e. your analysis. Math ability is admirable, but doesn't help unless applied properly.

As to your two questions: 1. Skin effect can affect resistance at high frequencies, but is certainly not a consideration here. 2. Regarding your dilemma about why Beranek does not account for your magnitude of 7.55, be assured he does. I explained the rational on this repeatedly, but you were blinded by your dismissive mindset.

Now here's the kicker - after being proven wrong on the main issues, your attitude still hasn't changed and you say below concerning math, power, or whatever "This is your problem, and you need to work on it." Your attitude does not deserve consideration in rehashing over again that which you bring up below, and was discussed before, with you still denouncing my understanding all the while. In short, you are in no position to continue your dismissive attitude. Clear enough?

Concerning your attempt to blame me for your errors, you say below "There is a data error-like it or not- either in Re or in the parameters Rms, Rmr, Xmd, Cms." I have taken the time to remeasure, and my data as given stands. There is no data error, and the speaker remains open to measurement of any parameters by a reputable independent labratory as proof my data is correct.

It is said that when a poor carpenter makes a mistake, he often blames it on the tools, but in this case the tools (my data) are good and true, and and open to inspection. You were wrong and that is that.

Northstar email snipped-for-privacy@hotmail.com remove the high card to reply

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