120V from both legs

(Re+Rmot)^2

------------------ OK, lets suppose that Re is very small -say 0.000001 and the other parameters are the same. E =Eb so U =0.128 This leads to I =0..3814 at 85.81 degrees as Zmec =32.87 @ 85.81 degrees =Beranek's Zm Pin =1.41*0.3814 *cos(85.81) =0.0393 I^2Re=0 so Pmech +Pa =0.0393 But Pmec =(U^2)(2.4) =0.393 which agrees Now lets find (Bl^2)/Re and treat it as a mechanical resistance for power calculations (U^2)(11.01^2)/0 = infinite power!!! Does this make sense. If I follow your reasoning it does. BlE/Re -U(Bl^2)/Re is simply Bl/Re(E-Eb) =BlI You have to take the two terms together. I have gone through this before, several times. I don't intend to do so again. One can solve, as I did, the circuit of Fig 7.2 which has a term Re/Bl^2 for which the power is F^2(Re/(Bl^2)) corresponding to I^2Re and gives the same results for I,Eb, U , powers in and out that is obtained from Eq7.1 etc. but doesn't involve the Norton equivalent that is used in determining Eq7.1 I have done this before - didn't you try to follow it. You show no evidence of having done so. This is an artefact of the model being used which gives correct external power but not correct internal power.

Also you have a power which corresponds to a total mechanical resistance of

9.95 ohms. (0.574^2)(9.95)=0.0328 watts. However, this bears no relationship to (Bl^2)^2 =17.1 or to Rm from Eq.7.2 =19.5 or to any other resistance made up of combinations of (Bl^2)/Re , Rms and 2Rmr. That is why I say that you haven't used or determined the power loss in (Bl^2)/Re. Your value of 9.95 is the result of your error. I would say that you are the one doing the hooting

----------

Now as to what you have done or not done>

------------------- OK. You are hung up on the "power to overcome the back emf. Beranek , Kinsler etc do handle the power correctly - just as I have done. No bluster there. First of all the back emf is a voltage due to motion. If the coil is moving at 0.0574 m/s in a field Bl =11.01, then the voltage produced will have a value of 0.632 volts, regardless of the source of the force to cause motion. Take the equation E-ReI +Eb The power input =EI (cos angle between E and I) =ReI^2 +EbI (cos angle between Eb and I) That is the power input = power lost in Re + power "to overcome Eb" (to use your words) look at that second term. What determines the power? the back emf and the current. Neither alone is power but the product leads to power. Now look again at this power EbI =FU so EbI cos (angle) =FU cos (angle) =the power delivered to the mechanical side. As F=ZmecU where Zmec =2.4+j32.78 , the power EbI cos (angle between Eb and I) =(Rms+2Rmr)U^2 The "power to overcome Eb" is the ACTUAL mechanical power delivered to the ACTUAL mechanical and acoustic resistances. Beranek states as much. So does Kinsler.

I see what you have done; It is wrong. You start with the magnitudes of |Ze|=8.198, Re =7.09 and |Zmot|= 3.674 (from your 32.99 or my 32.87 -both stretched beyond the accuracy of the data but let that be) You do not know, from these magnitudes, the phases of Ze and Zmot although you do know that Re is real. Somehow you get a phase angle for Zmot. 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. You then use 1.109/3.674 to get a phase angle for Zmot. Again OK if the assumption was correct. You then ignored Xmot you still are as you are still saying that Ze =Re

+Rmot which returns to your assumption that Ze is real. If you include the effect of Xmot in you will get Ze =root(8.198^2 +3.503^2) =8.92 ohms as Xmot IS part of Ze. Are you mixing up "real" as measurable with "real" in the mathematical sense?.

The problem is that YOUR BASIC ASSUMPTION HAS NO VALIDITY

You cannot handle this by scalar arithmetic. You don't know the phase of Ze or that of Zmot as your data doesn't give it so simply. You have to realise that Zmot =root(Rmot^2 +Xmot^2) and that Ze =[(Re+Rmot)^2 +Xmot^2) where both Rmot and Xmot are not known, because that is all the data you have to work with.

I showed you how to do it by two methods and also sent you a phasor diagram which would give you a graphical solution. Look them over- see what is done. Note that the results that I got fit your data and also fit the results from other approaches. That doesn't mean we are both right- it means that you have not used the correct mathematical approach. DON'T TRY TO HANDLE VECTORS AS IF THEY ARE SCALARS- IT DOESN'T WORK. Doing half and half also doesn't work.

I have no disagreement with Beranek, et al. I do disagree with your interpretations, some of your physical concepts and particularly with your inability to handle vector or phasor math. This is not intended as a diatribe but is based on observation. The chances are that your errors will not have any real effect- you have Small's reference PAE, etc and the correctness of the input power doesn't affect these. -- Don Kelly snipped-for-privacy@peeshaw.ca remove the urine to answer

Please quote both Beranek and Kinslers statement and reference the page number where they state this. TIA

Northstar

Also please give the magnitude of the net force. TIA

Northstar

The part prior to this is: "EbI =FU so EbI cos (angle) =FU cos (angle) =the power delivered to the mechanical side. As F=ZmecU where Zmec =2.4+j32.78 , the power EbI cos (angle between Eb and I) =(Rms+2Rmr)U^2"

I was not quoting Beranek or Kinsler. If so I would have indicated that. However

Berenak Eq. 3.49 Wave =Re|I|^2 +rm|f3|^2 +ra|p|^2 which corresponds to Re|I|^2 + (Rms +2Rmr)|U|^2

{mechanical responsiveness rm and resistance Rm are discussed by Beranek on page 84. Note that he restricts this to viscous resistance where there is a linear relationship between force and velocity. Rm here doesn't include (Bl^2)/Re. That comes in later, Ch7, when he develops his model. }

The actual and total power transferred to the mechanical side where there are only mechanical elements is (Rms +2Rmr)|U|^2 which is the same as EbIcos (angle) as indicated above.

I emphasised the "actual" mechanical power as this is the "actual and total" power transferred to the mechanical side where there are only the "actual" mechanical and acoustic resistances (i.e. Bl^2)/Re is not one of these actual mechanical side elements and its origin is not on the mechanical side. It is an artefact of the particular model used. I do not, at present, have a reference from Kinsler as I am going from memory of what he said.

The magnitude of the total force =BlI =11.01*0.1714 =1.89N (phase angle

26.56 degrees) or =1.41*11.01/7.09 -17.1(0.0574 @ -59.26) = 1.69+j0.844=1.89 @26.56 degrees Note that BlI =(BlE/Re -[(Bl^2)/Re]U). This is not a coincidence.

I am not sure what you mean by "net" force. Do you mean the part of the total force which is in phase with the velocity?

That would be 1.89 cos (26.56+59.26)=0.138 N (and 0.0574* 0.138 =0.008 watts).

Dividing by zero. Not impressive.

BTW, please leave all the text in this post unclipped for your reply, since proof you are wrong per Beranek is contained herein. Note also included at the top of the post are your four attemps to avoid addressing Beraneks definition of total mechanical resistance Rm, which proves you wrong.

You say in your last post " I was not quoting Beranek or Kinsler. If so I would have indicated that." So it is YOUR INTERPRETATION of Beranek and Kinsler, making your implicication that they state such to be deceitful.

No, see below.

Not true, and what doesn't work is your bluster. The above text shows you disagree with Beranek on the definition of total mechanical resistance. Beranek defines total mechanical resistance as

Rm = (Bl)^2/Re + Rms + 2Rmr.

You say his Rm expression is "total effective mechanical resistance" and then toss out (Bl)^2/Re to calculate mechanical and acoustic power, then go on to base your input power on this disagreement with Beranek, where you give input power as I^Re +(U^2)(Rms +2Rmr. NOTHING ELSE IS REQUIRED TO SHOW THAT YOUR ANALYSIS IS ABSOLUTELY IN ERROR ACCORDING TO BERANEK. YOU ARE HUNG OUT TO DRY AND TWISTING IN THE BREEZE.

As shown above, it is YOUR errors that disagree with Beranek, Morse, Lahnakowski, and others.

Northstar

parameters.

---------- OVERKILL -TRUE. No problem - assume all parameters the same except that Re =1 ohm. Then you will get U=0.124 @-15.1 degrees; I=0.370 @70.7 Pin =1.41*0.37*cos 70.7 =0.173 watts (U^2)(Bl^2)/Re=1.87 watts or 10 times the total input power. WOW! Note that Pin-I^2Re =0.0367 =(2.4)U^2 which is what I would expect. My point still holds

------------------------------

I calculated the power transferred to the mechanical side and showed that EbIcos(angle between Eb and I "EbI =FU so EbI cos (angle) =FU cos (angle) =the power delivered to the mechanical side. As F=ZmecU where Zmec =2.4+j32.78 , the power EbI cos (angle between Eb and I) =(Rms+2Rmr)U^2" I gave you Beranek's Eq.3.49 and I will add Fig 3.43 which is the same as Beranek's 7.2b In this equation, the mechanical loss becomes, as I said, (Rms+2Rmr)U^2 as rm(f3^2) corresponds to RmsU^2 , etc. My interpretation of this is correct. No (Bl^2)/Re factor appears here. Also Beranek states(p81) "logically the total power supplied by the generator e to the circuit must be equal to the sums of the powers dissipated in the resistive elements because the circuit is passive" No fuss about the nature of Eb as the induced voltage is replaced by a voltage drop across an impedance. What I have said is in line with this so I am not misconstruing or misinterpreting anything here.

The only error that I made is that I expected you to think well enough to make the connections yourself.

--------------

-------- See below.

Beranek Section 3.11 p84 paragraph starting with "Let us determine.." dealing with the figure of Fig3.44. In that circuit Ze is the electrical impedance measured with the mechanical elements "blocked", that is, u=0; zm is the mechanical mobility of the mechanical elements with the electrical circuit "open circuited" ; and zl is the mechanical mobility of the acoustic load on the diaphragm." Note that he also states after Eq3.60 that "Zm =1/zm" and "Zl =1/zl " Note also that he says "mechanical mobility of the mechanical elements" MECHANICAL ELEMENTS! Note also that "open circuit" conditions" imply no current and effective electrical impedance =infinity. Thus there is no effect on the mechanical side due to the electrical elements and , in particular (Bl^2)/Re =0 This is what I have been calling Zmec =(Rms+2Rmr) +j(Xmd-1/wCms) =2.4+j32.78 =32.9 magnitude and 85.8 degrees phase. Kinsler also refers to open circuit and blocked coil impedances and is a bit easier to follow than Beranek.

Further the circuits of Fig 3.44 a and b are replicated with more detail in Fig. 7.2 b and d. Berenak's Eq.7.1 is based on these circuits and the change from a velocity source to a force source as in Fig 7.3 This is the Norton equivalent that I have been talking about. It gives the correct velocity and the correct actual force applied to the actual mechanical elements (hence the correct loss in the actual mechanical elements) but as (Bl^2)/Re is internal to the Norton Equivalent - it gives no valid information with regard to this element. Hence it is not included in the power equations.

Now go back to Eq.3.59 and 3.60 Ignoring inductance and combining Zm +Zl as Zmec=(Rms +2Rmr)+j(Xmd-1/wCms) corresponding to the definition of Zm =1/ zm as quoted above these become

E=ReI +BlU (3.59) BlI =ZmecU (3.60) (3.59) gives I=(E-BlU)/Re (3.60 then gives Bl (E-BlU)/Re =ZmecU or BlE/Re =[(Bl^2)/Re +Zm]U which leads to Berenak's Eq. 7.1

What I have said, repeatedly, is in full agreement with Berenak et al. The effect of Re as seen from the mechanical side is included as a damping term but it is NOT of mechanical origin AND losses in (Bl^2)/Re have no meaning.

Suppose that I avoid (Bl^2)/Re altogether and solve the circuit by referring all to the electrical side. (Bl^2)/Re does not appear then but Zmot appears which doesn't include an Re related term (see Berenak Eq 3.62 along with the definitions that he uses for Zm as noted above). I did this 2 ways. a) solving E=(Re +Zmot)I 1.41 ={7.09+[(11.01^2)/32.87 @85.8]I or I = (1.41/8.23) =0.171 magnitude and a phase angle with respect to E of

26.6 degrees BlU =E(Zmot)/Ze =1.41(3.69/8.23) =0.632 (at a phase angle of -59.3 degrees) giving U= .0.0574 Pin, Ploss, Pmec +Pa are all as I found before and Pmec +Pa corresponds to U^2(Rms+2Rmr) as it should.

b) Using the magnitudes of Ze, Zmot and Re to find Rmot and Xmot and proceeding from there. Same result.

This is what you tried to do but you started from an invalid assumption and used invalid math as I have pointed out and you have not yet defended in a rational manner. You have used one approach and have made blatent errors. You then blithely ignore these or pull out erroneous justifications which are not based on fact - using circular reasoning etc including coming up with some ficticious mechanical resistance which, if true, means that Berenak's Rm and Zm of chapter 7 (which are not the ones defined in Ch3 upon which the work of Ch7 rests) and that there is really no point at alll in trying to determine Rms, Xmd, etc as they really don't mean anything. I can't swallow that.

MY ANALYSIS IS CORRECT ACCORDING TO BERANEK - I FEEL NO BREEZE Come on, man, Think! Try to learn the appropriate math and use it. I'm not trying to put you down but I won't agree with blatent contradictions and incorrect math or physical concepts.

SEE BELOW

So you don't respond above to my proof you are wrong according to Beranek, and instead say "See below". Then you jump down a page or so and do another dissertation. You can jump around, but you cannot prove 2+2=4 is wrong just because your math gives 0.963.

Summarizing that which you did not respond to above, along with your earlier evasionary tactics and your disagreement with Beranek.

You first asserted: " Please note that nowhere does Beranek call (Bl^2)/Re an "actual" mechanical resistance. " Your second assertion (after my rebuttal): " Note that nowhere does he state that Rm is "the" mechanical resistance. " Your third assertion (after my rebuttal): " I should have noted that he does not call it that in Chapter 7. Thanks for the correction. I noticed that in Ch.3. it is not the Rm used in Chapter 7. " Your fourth assertion (after my rebuttal): " Thank you - I missed that. It is the total effective mechanical resistance, which includes the effect of the electrical resistance as seen from the mechanical side. "

You then stated: " I have no disagreement with Beranek, et al. "

You redefine Beraneks "total mechanical resistance" expression Rm to be "total effective mechanical resistance" then toss out (Bl)^2/Re in his Rm = (Bl)^2/Re + Rms + 2Rmr, and use (Rms + 2Rmr) as mechanical resistance in your input power equation of I^2 Re + (U^2)(Rms + 2Rmr). Then you say " I have no disagreement with Beranek, et al. " HOW BRAZEN CAN YOU BE? NOTHING ELSE IS REQUIRED TO SHOW THAT YOUR ANALYSIS IS ABSOLUTELY IN ERROR ACCORDING TO BERANEK. WAKE UP MAN, A COLD BREEZE IS BLOWING FROM THE NORTH.

Northstar

I fail to see what Beranek has to do with it };-) Beranek's Law below~>

Is this the right Beranek ?

Just that ones own model is always better then the rest simply because it's yours, and has nothing to do with any theory behind it i guess }:)

Mr. Kelly: Will you please resubmit your last post in your usual format. Both my newsreaders fail to read it properly. TIA

Northstar

I don't know the problem- I didn't change any format. It did arrive on the newsgroup as sent. What appeared to be the problem? Was it all, or only part, garbled? Basically - I am still disagreeing with you :)

However, this might help overall- If you wish, I can send you a detailed analysis on the basis of Beranek's circuit of Fig. 7.2 (which he later modifies by the Norton Equivalent of Fig. 7.3 (see text) and taking of a dual to get Fig 7.4a which is the basis of Eq.7.1). The circuits of fig

7.2 are valid models and, in fact, the use of the Norton and the dual is really not necessary. I do think that this introduces more problems than it solves. The advantage of Fig. 7.2 is that the identifacation of the power dissipating terms is clearer than in 7.4.

Don Kelly" wrote in news:w3XFd.78924$Xk.2604@pd7tw3no:

Clipped

You stated " Pin=0.2162 watts "

I measured the phase between voltage and current and the phase angle passes through zero at 203.4 Hz, giving dynamic power input Pin of

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

Showing your power magnitude and analysis to be in error. You are welcome to visit my lab and see the above verified.

BTW: MIME - version 1.0 was in the header of your garbled post, where usually MIMEOLE version 6.0 is found. Anyway I finally got it readable.

Northstar

Also note you gave power input as

" Power input is I^2Re +(Rms+2Rmr)U^2 "

which is Pin = (0.172^2 * 7.09) + [(1.57 + 0.83) * 0.574^2] = 0.2177

Northstar

You say that you measured the phase angle- If it was zero, then there is something else present, as the reactance Xmot is not zero at that frequency. What did you use to measure it? What is the inductance of the coil? You have a Ze =8.198 which corresponds to 1.41/0.172 --I have no problem with that. Also, which side of the "ammeter" did you have the voltmeter- source side or coil side? Please fill in the details. I would love to visit your lab but I doublt whether it is a practical distance to travel.

My analysis is based on your data and errors that may exist are due to errors or omissions in that data. The analysis, per se, has been done, carefully, several different ways and redone carefully for each way. No conflicts between independent approaches and calculations. Since I have given you step by step results- you should be able to follow these steps and search for errors or omissions- if they occur and exactly where.

All results agree, including results based on the magnitudes of Ze,Re and Zmot (where no given phase angle was assumed -i.e. the approach that you used without making your assumptions-this is completely independent of the previous calculation approaches ). You have seen these results- did you try to follow them step by step?

If I use your results and take Ze as real as well as your phase angle (which implies an Xmot, there are inconsistencies which I can't swallow -either your effective resistance is correct and your values for Rms, Xmd, etc are wrong, or these values are correct and your effective resistance is wrong. If both are right, then Berenak's models are wrong (and they are not wrong). That appears to be the choice. I carefully redid the analysis of Berenak's circuit of Fig. 7.2 and came up with the same results as obtained from Fig 7.4 and Eq.7.1.

In your second message you wrote: "Also note you gave power input as

" Power input is I^2Re +(Rms+2Rmr)U^2 "

which is Pin = (0.172^2 * 7.09) + [(1.57 + 0.83) * 0.574^2] = 0.2177"

I used a velocity of 0.0574 m/s magnitude and a current of 0.1714A magnitude. Pin =[Re/(Bl^2)]F^2 + U^2(Rms+2Rmr) taking Rms=1/rms and 2/zmr =2Rmr (as Xmr is included in Xmd) Actually we are both using values to a greater accuracy than warranted. Pin=0.216 by my numbers and 0.218 by your numbers are still optimistic accuracy but assume 3 significant figures which is all that the data really allows at most.

From Fig. 7.2d Pin =[Re/(Bl^2)]F^2 + U^2(Rms+2Rmr) taking Rms=1/rms and 2/zmr =2Rmr (as Xmr is included in Xmd) and [Re/(Bl^2)]F^2 =Re(I^2)

You said earlier: "Your analysis is based on a calcuation which is correct only when E and I are in phase. That isn't true so your results are hogwash."

THEREFORE SINCE WE FIND E AND I ARE IN PHASE, MY ANALYSIS AND CONCEPT IS CORRECT AND YOURS IS WRONG. Simply put, with the phase angle between E and I = zero at 203.4 Hz, Pin = E^2/Ze = 0.2425. You gave Pin = " Pin=0.2162 watts " which is wrong. NO OTHER DETAILS ARE NEEDED.

I offer to prove the above 1. "your analysis has already been shown to be crap."

1. "I am saying that you really have very little grasp of the concepts"
2. "It is because you are committing sophomoric errors"
3. "I erroneously gave you too much credit for the ability to think."

These four insolent remarks apply to you pal, not me.

Northstar

"Northstar" wrote in message news: snipped-for-privacy@news.supernews.com...

news:w3XFd.78924$Xk.2604@pd7tw3no:

However, my approach will still give the correct results in the case that E and I are in phase. No assumptions as to phase are made- If, indeed, the measured magnitudes of Ze=8.20 ohms, Re=7.09 ohms E=1.41, I =0.172 and U=0.0574 are correct, and inductance is negligable - then the results do agree with the results using the parameters that you gave me and found using the models that Beranek uses. I have used your data with full acceptance of its validity but without assumptions as to phase- finding that from the data. You have not yet provided any critical analysis of these results which have been given in detail. If, in fact, Ze is real, then it is necessary to consider the inductance of the coil and use Re+jwLe rather than Re for the coil impedance as the only reason that Ze can be real is if there is a resonance taking place (with or without a peak as is noted by both Kinsler and Beranek). Please note that E and I will be in phase only at two frequencies- at the normal resonant point and at the resonant point between the mass reactance (looking electrically as a capacitance) and the coil inductance. This is not particularly simple to calculate but is easy to estimate at about 3 mH. The circuit model used by both of us does NOT include the inductance. Without consideration of the inductance then all that happens is that the impedance will approach Re as the frequency becomes very large- without change of sign of the reactive part as Zmot approaches -j(Bl^2)/wMmd which in turn approaches 0. In real life inductance exists (but doesn't affect the phase angle between velocity and force) so that above the "second resonance" wL becomes dominant, leading to a change of sign of the reactive and an increase in Ze. The question is "are you there?" That is why I would like to factor in the inductance. This is not difficult. That is why I want information on how you measured the phase angle and on the inductance of the coil. Also it would be interesting to see what the coil total locked rotor resistance is at 200+ Hz. You mention checking phase but you haven't said how you checked phase. Is it too much to ask?

-----------------

------ I would- but I am retired and don't have the facilities and do not intend to spend the money to get proper instrumentation and I am not going to spend the money to travel to your place -wherever it is. You know that so the offer is really a non- offer and you are too good a businessman to pay the way- costs unknown. You say "check phase" but is it a hardship to tell how you checked phase and the instrument setup you used.-i.e give a direct answer to what was a direct question?

1)you made an analysis using scalar arithmetic- that is incorrect. 2)You have repeatedly shown that you do not understand phasors or some of the physics involved, reying on canned formulae without looking at the basis of these. These points have been addressed before3)A result of 1 and 2. 4)Where I made this comment- it applied.- I wish it were not so.

5)You are not stupid- You also have given good data. It is like pulling teeth to ask how you made some measurements. I have no faith in your math (basic scalar arithmetic is OK), a lack of faith in your understanding of the physics involved but do have faith in your measurements- which I have used, with correct math- to get my results.

I'm not out to "get you" - that would bring me no satisfaction. However I have been assuming that you would be interested in the application of the theory, done correctly, to your data and that this would be, as Martha says "a good thing". I originally wanted to see how you got the various Theile-Small parameters but this has disappeared into the fog of hurt feelings (not mine- I have been exposed to worse criticism at IEEE meetings and elsewhere -as it should be.). Recognise your strengths- and also your weaknesses. I think you have been largely self taught- which is OK but difficult as your teacher is not able to correct you when you are wrong. All I have been trying to do, is to catch mathematical and conceptual errors. You have been trying, unsuccessfully, is to defend these errors. Why?

If you want to give me the information that I asked for -I would greatly appreciate it.

You're a wiley one alright, about the most so I've seen. You say: "However, my approach will still give the correct results in the case that E and I are in phase." and "If, in fact, Ze is real, then it is necessary to consider the inductance of the coil."

Bullshit. I got the correct result *without* using coil inductance.

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 we find the phase angle between voltage and current is 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 and 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. YOU HAVE LOST THE ARGUMENT BY YOUR OWN STATEMENT, and your best bet is to just face-up and admit your errors.

You said above "It is like pulling teeth to ask how you made some measurements." There is a reason for this, which is that I do not care to go through another tirade of equations from you based on INCORRECT phase angles. Sorry, but you can shove them. As to how I measured phase angle, I did it correctly. Stereophile Magazine, edited by John Atkinson who also does the technical reviews on equipment, publishes the most comprehensive and accurate specs on loudspeakers available. He gives the phase angle on speakers in each speaker review, and you will find the phase is zero at the resonant frequency of a closed box woofer, and that the phase angle also passes through zero between around 150 Hz and 300 Hz. This is undisputable fact, and I offered to prove it to you as well. You need to admit your analysis is wrong or shut up.

BTW, your reply above reeks with egotism, a "put someone down" attitude, and insults. Very unprofessional and suckful.

Northstar

swallow -either

-------------- If L is negligable- then the phase will not pass through 0 except at the main resonant point.

You have claimed that the phase did pass through 0 at 203Hz but have not said how you know that.

HOW DO YOU KNOW THAT THE PHASE ANGLE IS 0 AT THIS FREQUENCY.

I asked how you measured that- you haven't answered that question. Why? Did you actually measure phase or did you assume it. So far you have given nothing to indicate that it wasn't the latter.

Now, as to the results that I obtained. I note that the phase angle of U according to Beranek's 7.1 is -59.3 degrees The phase angle of Zmec based on arctan (Xmd-1/WCms)/(Rms +2Rmr) is 85.8 degrees - this is the "open circuit impedance corresponding to Zm in Eq3.60. This leads to a phase angle for Zmot of -85.8 degrees This is NOT 72.4 degrees as it would be if your values were correct. . Considering that the calculated magnitude of I =0.171+ A as compared to

0.172 as measured, and velocity mangnitude of 0.0574 m/s - both in agreement with your values within data accuracy, I would suggest that the calculated values are quite good. Also noting that given Ze=8.20(vs my 8.23 due to the minor difference between the calculated and measured current) and that Zmec =32.99 vs 32.87 (again due to the difference in the current values) as well as Re =7.09 ohms the results using these magnitudes, without assuming Ze as real lead to phase angles which, as I have shown (and the math hasn't been refuted by you) are in full agreement with what I had previously calculated by using 3 other approaches. If Ze were, in fact real, this apprach would lead to that result. It doesn't- not because the approach is wrong but because it appears that Ze is, in fact, not real.

You say that Ze is real but, ignoring inductance, that is not possible as Xmot does exist. (Eq 7.16 can be used for an approximation (or use wL=-Xmot or L =0.0029mH) If wL is not negligable, the effect is a reduction of Ze to the order of

7.3- 7.4 ohms at a minimum( and as Rmot is frequency dependent - the 0 phase and minimum Ze points are different)

In other words, using your values for the magnitudes of Ze, Re and Zmot, the results are in agreement with the previous results which puts your phase angle passing through 0 in question.

You are basing your values on incorrect calculations based on an incorrect assumption. Your own data leads to the conclusions that I get - whichever way the problem is approached- as long as the correct mathematical tools are used.

Now, as to power: Pin = I^2Re +(Rms+2Rmr)U^2 assuming that Berenak is right. This is obvious on examination of his circuit model of Fig 7.2. (and Eq.3.49) Do you think these are invalid? If so- why? You have a Pin=0.2425 and I^2Re =0.2098 Then the remaining "power" =0.0327 of which (Rms+2Rmr)U^2 =0.0079 leaving a power of 0.0248 unaccounted for. Where did it go? You have claimed an additional mechanical resistance of 7.5 mechanical ohms to account for this loss. This is not (Bl^2)/Re nor is it attributable to anything other than your incorrect handling of the vector relationships. In fact, it doesn't exist.

With correct handling of the relationships and with your correct magnitudes and other data that you have given, the power transferred to the mechanical side is in agreement with my calculated results and other anomalies that you have will also disappear.

Thank you - It is obvious that inductance is not involved in the value of Ze =8.2 ohms. Since this magnitude is in accordance with the magnitude found from the circuit model as calculated from your data, it is apparent that your data is good and the circuit models that Berenak presents are valid.

The only reason that a second resonance occurs is because of the coil inductance/mass reactance resonance. No inductance, no resonance. No resonance, then Ze is not real. That's the nature of the beast.

Now, if Ze is real then the actual coil impedance becomes about 7.09 +j3.68 ohms for Zmot =0.27 -j3.68 leading to Ze =7.36 ohms. Obviously you are not at resonance. It is also obvious that you did NOT get the correct answer as has been pointed out. Incorrect math is known to produce this problem. Do the math correctly and it will disappear.

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As to power -see above. not my error. You are blustering again. Try thinking and questioning yourself as well as me. it works better.

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------- More Bluster. I agree that it passes through 0 between 150 and 300 Hz. This depends on the inductance. If the inductance is 0, then the phase angle will not pass through 0. This is discussed by Kinsler and also by Beranek (p192) and is readily apparent in Fig.7.2 and 7.4 So what else is new? Oh yes, is an infinite baffle now the same as a closed box? Berenak modifies the model in Ch. 8 for the latter. Your data and Berenaks work in Ch. 7 is for an infinite baffle.

A claim that you measured phase angles correctly is one thing, backing it up with how, is another. You haven't provided this back up and are still avoiding it. why?

As to the phase angles that I have used- see above. If you question the value given - then show why it is wrong. If you question the phasor diagram that I sent you- what is wrong with it. It fits the magnitude data given as do the results from Berenak's models (all of them).

I have plugged various values of inductance into the model to calculate Ze. With a large enough L, the phase angle will pass through 0 at 203 Hz. The problem is that, at that point, the value of Ze is about 7.3 ohms, not 8.2 ohms which will only be so, at that frequency, if L is negligable. The above reference does not say that it is 0 at 203.4 Hz. For L=2mH the second resonance is about 240-250 Hz and at 203.4 Hz, Ze =7.46 ohms For L=3mH the second resonance is about 190-200 Hz and at 203.4 Hz, Ze =7.36 ohms For L =0, the second resonance does not exist and at 203.4 Hz Ze =8.23 ohms (based on data that you gave me) .

Oh Dear, It appears that I have offended you. That is not the intention. Is it professional for you to cling to incorrect analysis, even though it presents dilemmas and inconsistencies, as you have done, in the face of evidence that, just possibly you might be wrong? This is what you are doing and it appears that you are blustering to cover up. Why?.

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Both the bluster and stonewalling is coming from you, and your questions are impertinent until you address the following:

As noted: YOU PROVE YOURSELF WRONG WITH YOUR OWN WORDS ASSUMING PHASE BETWEEN VOLTAGE AND CURRENT IS ZERO AT 203.4 HZ, AND IT IS.

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 as 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.

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

Now I told you I measure correctly (which you should know already), and I offered to prove the phase angle to you in person and you declined, so 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? Or how about the method suggested by Agilent Technologies or Hewlett- Packard with Lissajous figures using a Tektronix oscilloscope, HP oscillator. and Fluke frequency counter? What would suit you?

Sorry, but another barrage of equations using your incorrect theory and phase angles will not be considered as an answer here.

Northstar

yeah ! what gives man ?

you still pondering that motor that doesn't excist ? chances are it'll never excist until you agree somehow on something...

Build a cheap/quick Ion Drive Motor.

I had developed a " NO HAY " theory years ago but i lost all the equations I had derived towards it... all i remember is:

I started something like this:

Plus Gravity and Thrust integrated into it:

[ the (=>) symbol up & down from the center of (~) ]

1st) coupling being: Friction Velocity

Can anyone here derive a Quadratic equation from this so far?

I can't draw it all here so just forget it :) maybe when i get my pc online..

Later Gents: It's comin down heavy out there ! Bbbbrrrrrrrrr