No point in addressing your further dialogue below, since you still don't understand the velocity equation, and in fact still blame the inability on me. Instead, I'll post prove again.
You stated " U= (BlE/Re)/(Zm +(Bl^2)/Re) "
Beranek gives velocity in his eq.7.1 as
. Bl E U = -------------------- (Rg+Re) (Rm+jXm)
which in your form above is
BLE/(Rg+Re) U = ------------------ (Rm+jXm)
where U=velocity, BLE/(Rg+Re)=force, (Rm+jXm)=mech impedance Zm
you have ignored Rg, which is OK as modern-day amplifiers have negligible source resistance Rg. However, Beranek defines resistance Rm in the next eq.7.2 as
Rm = (Bl)^2/(Rg+Re) + Rms + 2 Rmr
This means (Bl)^2/(Rg+Re) is already *included* in mechanical impedance Zm, so you cannot add it to Zm again. Hooting about phasors as you did doesn't cut it. Phase enters the picture in adding Rm and jXm, not in the addition of resistances.
As Beranek shows, (Bl)^2/(Rg+Re), or (Bl^2)/Re with source impedance = zero, must be included *in* Rm to obtain the correct mechanical impedance.
-------------------- I wish that you were able to read and comprehend what you read. For your benefit I have stripped out the stuff in between leaving the responses I made to your comments.
*******
*************************************** Please note the word "same"
**********
-I have rolled them in together
+2Xms-1/wCms] (this is in line with B's Eq3.60
+j[(wMmd+2Xms-1/wCms]
*****************
I fail to see why you keep repeating accusations which are false. True , I did not use Beranek's notation and show the differences between my notation and Beraneks. The total equation for velocity that I obtain is exactly that of Beranek's. Others use a different notation- so what.
It is obvious that you either did not read what I said or did not understand it. That is not my problem. It also appears that you are regurgitating formulae without thinking of their meaning so something as trivial as this appears to throw you for a loop.
So far you have not presented any real challenge (just conceptual and mathematical errors) to what I have said. I doubt whether there is any point continuing.
So what does impoliteness and disparagement get you? Read on to find out. I gave you ample time to find your error, but instead of finding and correcting it you really believe the error is mine. Therefore it is obvious you don't even know you made an error, and that you are the one whose understanding is weak. Plus... you arse off too much. Too bad.
Now to your error, and it is fundamental, not trivial. Starting by recapping what I tried to help you with (to no avail):
You stated " U= (BlE/Re)/(Zm +(Bl^2)/Re) "
Beranek gives velocity U in his eq.7.1 as
. Bl E U = -------------------- (Rg+Re) (Rm+jXm) rearranging in the form you used above gives
BLE/(Rg+Re) U = ------------------ (Rm+jXm)
where U=velocity, BLE/(Rg+Re)=force, (Rm+jXm)=mech impedance Zm
you have ignored Rg, which is OK as modern-day amplifiers have negligible source resistance Rg. However, Beranek defines resistance Rm in his next eq.7.2 as
Rm = (Bl)^2/(Rg+Re) + Rms + 2 Rmr
This means (Bl)^2/(Rg+Re) is already *included* in mechanical impedance Zm, so you cannot add it to Zm again.
End of recap, now simplifying for your benefit:
-----
At mechanical resonance the reactance Xm is effectively zero, so the Xm term drops out of the equation, leaving Zm to be just the resistance (Rm+jXm)= Rm. Now, you stated, with reference to Beraneks equation
" His Rm does include (Bl^2)/Re. My Rm doesn't "
Fine, you are adding resistances and your equation is valid at mechanical resonance, where your equation gives the same velocity as Beraneks eq. 7.1 *at resonance*. Clear enough?
Now above resonance the load is partly reactive and reactance Xm does
*not* drop out of the impedance term (Rm+jXm). So above resonance and restating *your* equation above
U= (BlE/Re)/(Zm +(Bl^2)/Re)
noting Zm *with reactance present* must be (Rm+jXm), staying with *your* equation, and substituting (Rm+jXm) for your Zm
U= (BlE/Re)/(Rm+jXm)+(Bl^2)/Re)
Now impedance (Rm+jXm) has an angle as well as a magnitude, and therefore it is a vector, while (Bl^2)/Re) is resistive per Beraneks equations, as well as per Small, and also as you used it, and you cannot add the two arithmetically. This gives the wrong velocity at
*other than resonance*, whereas Beraneks eq. 7.1 is valid at *any frequency*. This is not a trivial error, it is a major error in fundamental principle. Pity, did you say?
BTW, I did a rather thorough search, and nowhere did you say your velocity equation applied only at resonance, so there is no wiggle room there.
Finally, you stated " some knowledge of phasors would be useful "... True, and we both have some of that knowledge, but knowing how to apply that knowledge in the area we discussed is also useful. Perhaps even more important is to have a non-arsing off approach, but I suppose that may be a built-in trait. Too bad.
---------- Neither of us have been. However, I regret that statement and apologise for it.
-----------
This was based on some statements that you have made which indicated a lack of understanding as well as others which attribute statements to authors which, on inspection, they did not make.
-------------
------------------- Fact- several with respect to handling of vectors or phasors and the models.
--------------------
----------------- This is not intended as an insult- it is a statement of fact based on some of your comments and reasoning. This does not imply that you are less capable than I of building good speaker systems- in fact the opposite is true. However your understanding of the models used by Beranek, Kinsler, etc appears to be based on final cookbook equations which are likely all that are needed. However, with respect to circuit models phasors, the analysis thereof, and basic physical concepts, we are in an area where I have been involved for 50 years.
----------
The pity is that you are not stupid- far from it.
-------------------
--------------- Yes, I have been somewhat frustrated. Sorry for that. As to the "error"-It is not there- sorry, you are wrong. I checked carefully. .
-------------
---------- In your recap - you have again simply ignored what I said. I used Zm to represent the actual mechanical and acoustic impedance in the same way that Beranek did in Eq.3.60 but simplified it by using Zm to represent both elements lumped together. In Eq.7.1 I know that Beranek lumps (Bl^2)/Re in his Zm and I said so. I did not "lump" it in but kept it separate and explained this. However, what I got is exactly equivalent to Beranek's 7.1 even though my notation is not exactly the same as his. I showed the difference. I definitely did not add (Bl^2)/Re twice. This is patently clear.
There is nothing in what I said to imply this so I am again puzzled by your contention.
-------.
---------------- My equation is valid at all frequencies of concern. What is the problem that you have in adding (Bl^2)/Re to an impedance as long as the proper rules of phasor or vector arithmetic are followed -as I have done?
----------------
------------ agreed
----------------
------- Better U=(BlE/Re)/[(Rm+jXm) +((Bl^2)/Re)] (nit picking:)) but so far so good
----------------
--------------- Good try- I suspected this was your problem. True, you can't add the "vectors" arithmetically but you can add components (in the same direction) arithmetically. This is what I have done and it is absolutely valid. Kinsler has an appendix showing phasor arithmetic and Siskind should have. If not, any elementary circuits text will cover it.
I did nothing wrong in adding the impedance Rm and the resistive element Rm. I treated Re as Re+j0 which is absolutely valid. So, I am adding vectors or phasors and doing it correctly.
This is how you add them mathematically : Take two phasors A=ax +jay and B=bx +jby then: A+B =(ax+bx) +j(ay +by) this works for any A, B So if A=2 @ 0 = 2+j0 and B=2.83 @45 degrees = is 2+j2 then A+B =(2+2) +j(0+2) =4+j2= 4.47 @ 26.6 degrees
For a graphical check: Draw a horizontal line of length 2. Put an arrowhead on the right end From the end draw a line of length 2.83 at an angle of 45 degrees upwards and to the right. Put an arrowhead on the end. You have now two vectors. Now draw third vector from the beginning of the first one to the far end of the second vector . This is the vector sum. Measure its length and the angle. . Compare with the numbers above. Please try it.
SO: Ze =Re +Rg +jwLe and, in the situation where Rg and wLe can be ignored (0) then Ze =Re +j0 Now (Bl^2)/Ze then becomes (Bl^2)/Re -j0 as a phasor Adding this to Zm=Rm +jXm leads to (Bl^2)/Ze +Zm = [(Bl^2)/Re -j0] +[Rm+jXm]= [(Bl^2)/Re +Rm] +j[0+JXm] which is [(Bl^2)/Re +Rm] +jXm as I said.
I am saying exactly what Beranek has said. I also repeatedly stated where my Zm differs from his. You are free, and more than welcome to attack what I have said above but please be able to present a strong and valid reasoning. There is no point in just saying that I am wrong- point out where and why you think I am wrong - as you just have- thank you. I will always look again and either show where I disagree with you or admit error.
------------ I certainly don't want to wiggle as it is correct at any frequency.
-----------
----------- NO. You have a very rudimentary knowledge of phasors. I have a knowledge of phasors and circuit analysis that has been established, first through multiple circuits courses at undergraduate and graduate levels and also through almost daily use over the past 50 years. This is not boasting but a statement of fact. Practical knowledge of speakers and their construction is your forte- I only built one- a bass reflex enclosure - about 1955 and used a cookbook design at that. However, what we have been talking about so far has been nothing more than a circuit model of a speaker and that is where I have an edge. My first questioning of you was due to statements that you made which did not fit either the model or the physics involved. The rest has followed- some arsing off shared by both of us. Frustration over what could be settled in half an hour or so over a beer.
It has not been my intent to insult, and I apologize as well if I came across to you in such manner.
This is an accusation of lying. Quote text as prove, otherwise you are the liar. Don't he-haw around, just quote the statements you refer to.
Stop arsing off and quote text, otherwise this is BS.
So... you should not have added a vector and scalar arithmatically, and then blamed me for being the one in error.
All your checking and such below won't help you, until you correct your error.
It is valid at resonance only. See below.
You just exposed your problem, otherwise you are the one giving a "good try". Impedance *above resonance* is not Rm, it contains reactance, and is given as Rm+jXm, *not* Rm as you state directly above. Impedance has both magnitude and angle, and therefore is a *vector*, and you cannot add it arithmatically to Rm, which is a scalor. It gives the wrong magnitude for velocity, as in
***wrong***. What more can I say? If fact, no point in responding to your further ramblings below, where you go through much wasted effort to support you erroneous velocity equation. Time to be a gentleman and a scollar and fess up. Note you should be both :)
I am not accusing you of lying. I note that you referred to Beranek using pf where he didn't. I also referred to situations where you have incorrectly interpreted what has been said- as you have done below in your reply. I do not keep a list of your errors but here is an example "Siskind even notes rotor power input (RPI) at start-up simply as (E^2/R^2)*R, which is of course E^2/R. "
He does not say that - it is your interpretation and distortion of what he did say which you later quoted correctly
"Sorry, you are wrong, it is true for an AC machine. Siskind is referring to an *AC motor* in his book "Electrical Machines" vol. 2, (eq. 80), where he states:
RPI = (Ebr^2 / Rr^2 * Xbr^2) * Rr
RPI = rotor power input Ebr = voltage applied to blocked rotor Xbr = reactance with blocked rotor Rr = Rotor resistance"
This is NOT what you originally quoted. Nor does it mean the same. I explained why. There are other things as well but it is not worth while searching them out
-------------
------------ ">> For net force, phase must be considered at other than mechanical
I said
----------- To which you responded:
"YES. You gave no phasor info. My correction was appropriate"
Even though you claim I'm the one in error, I would not continue this, except for your false accusation that most people would construe as calling someone a liar. Therefore you are not going to bluff your way through with a smokescreen, such that your mistake is buried in the ensuing cascade of non-pertinent equations and espousing. You gave the velocity equation as U= (BlE/Re)/(Zm +(Bl^2)/Re). Mechanical impedance is given as Zm=Rm+jXm. This is not debatable, see Beranek eq. 7.36 and Kinsler eq. 1.28. Zm is a vector, (Bl^2)/Re) is resistance, again not debatable. You cannot add the two arithmetically, which you clearly do.
There is a method called try it and see, that will prove who is correct without further argument. I shall now assign typical magnitudes to the terms in Beraneks eq.7.1
E = 2.0 Bl = 8.0 Rg = 0 Re = 6.0 Rms = 1.5
2Rmr = 1.2 Xm = 35.0
Solve for velocity U using Beraneks eq. 7.1, then do the same using your equation U= (BlE/Re)/(Zm +(Bl^2)/Re). If you claim the same result, then prove it by posting your math work showing such. That's it. Either your equation gives the same result or not. If you cannot do this in a straightforward manner, you have proved your own self wrong.
No proof, just implications I lied. One is tempted to namecall, but I'll just say - there you go again... Too bad.
Jesus Christ man, are you daffy, grasping at straws, or what? This refers to the electrical side and we were ignoring coil reactance, giving Siskinds equation #80 as you note above
RPI = (Ebr^2 / Rr^2) * Rr
RPI = Ebr^2 / Rr
Equating Siskinds and our terms:
Ebr = E, and is constant blocked coil or not Rr = Re, and is constant RPI = power in
giving
Power in = E^2/Re
Which is what I originally said, and as given in your quote of what I said above.
Enough of this crap, just do the math at the top of the post. TIA.
--------------------- As for Beranek's Eq.7.36 which is a transient equation developed basically from the differential equations, he uses Eq.7.2 and 7.3 to define Rm and Xm. So what does 7.36 add to the discussion- nothing that I haven't noted before. No problem with that as it simply reflects the sum of the actual mechanical and acoustic impedances as well as the electrical resistance reflected into the mechanical side where (Bl^2)/Re appears as an equivalent mechanical resistance and can be treated as such.. I am quite happy with that. this is obviously how Berenak and Kinsler thought of it. Look at the development starting wih Fig 7.2 and continuing on to Fig. 7.4 and also note that B differentiates the electrical impedance as seen from the mechanical side from the mechanical and acoustic impedances. For calculation of velocity, it is necessary to take into account the total effect. Further going back to a more fundamental chapter, Eq.3.59 and 3.60 are the basis for Eq 7.1 as well as for my expression. Please note that, at this stage, (as with Kinsler) the Ze appears in the electrical equation and Zm+Zl appears in the mechanical equation and in this case Zm does not include Ze. In q.7.2 and 7.3 Berenak uses a common procedure- As several equations use these terms it is easier to define them once for the chapter and save typing. That does not mean that (Bl^2/Re) is an actual mechanical resistance.
I gave you the step by step development of my equation starting from E=ReI +BlU F= BlI =ZmU Berenak did the same except for using Zm+Zl as the basis for Eq7.1
Now as to adding a scalar and a vector: Your contention is wrong. I don't ask you to believe me but I do ask that you at least try to apply the rules for vector addition. Note that I did not add a scalar and a vector- I added real to real and reactive to reactive which is valid even if one of the reactive components is 0. Instead of bluffing, why don't you simply learn how to add vectors? That is all I have done. -----------
------------- OK but I will use Zmb for Beranek's "Zm" and Zmk for my "Zm" in the hope that the difference will be plain to you.
Beranek: Bl^2/Re+Rg =64/ 6 =10.67 Rm from Eq.7.2 =10.67 +1.5+1.2=13.37 Zmb =13.37 +j 35= 37.47 @ angle 69.1 degrees (Zmb is Beranek's Zm including the Bl^2/Re term) From 7.1
*Please note that any scalar can be represented as a vector but the reverse is not true. Vector or phasor arithmetic includes scalar arithmetic as a subset so it is perfectly valid to use phasor arithmetic with scalars (but it is inconvenient and to do so). Normally I wouldn't carry the j0 term along but did so for emphasis.
I gave you an example to try for yourself - evidently you haven't, nor have you even gone to another reference to see how to add vectors or phasors. Why? Don't trust me (as if you did) but look at how it is done. Is that too much to ask? You want to learn but this desire seems to break down when you run into something contrary to pre-conceived notions -so much so that you don't check out the possibility that the pre-conceived notions might possibly be in error. Why?
--------------
What you interpreted Siskind as saying and what HE actually said are still two different things. What he said is not what you implied that he said. That is my point. Do you get it?
You said that "Siskind even notes rotor power input (RPI) at start-up simply as
This is definitely NOT what he said. You did NOT indicate that, in the case of reactance being negligable, this is what it would be (which is definitely not the case for an induction motor which is the subject of Siskind's equation) but left it as "Siskind says ....."
This is not the only time that you have indicated "xxx says..." when what you are saying is an "interpreted" version hiding as an original quote. That IS crap.
If you wish to quote an author - do it exactly - THEN do your interpretation. Otherwise it is intellectual dishonesty. I don't think it is deliberate lying on your part but has the same effect.
(In this case, your interpretation is about as much use as Siskind's RPI which, out of context, is meaningless (I don't even know why he bothers as doesn't appear to be useful as is) and, given the differences between an induction motor and a speaker, cannot be logically extended to a speaker - an induction motor is more complex electrically and magnetically)
In any case, where Re is the ONLY circuit element involved Pin =E^2/Re is quite correct. No problem there and no need to distort what Siskind actually said. If Re is in series with another resistance or a reactance- then Pin =E^2/Re is incorrect unless E is the voltage across Re alone. Hence in a speaker E^2/Re is the power in, ONLY if there is no coil inductance and there there is no mechanical load (that is blocked coil). In other situations, it is not true and only provides an upper limit to the input power. This has been discussed before so a misquote of Siskind is really not providing any new information.
If you want to think objectively- fine. If not- that's your prerogative and not worth further discussion.
This is absolutely UNTRUE. See Google, where I noted on 12 Nov, 2004, that coil inductance was assumed negligible:
formatting link
" IOW the inductance of the coil is neglected for low frequencies per the above, and since that is what is almost universally done, it is what I have done, and shall continue to do. Siskind even notes rotor power input (RPI) at start-up simply as (E^2/R^2)*R, which is of course E^2/R. "
You have a problem dealing with the truth, otherwise are ignorant in relating inductance to reactance. Which is it?
----------
You said" " I note that you referred to Beranek using pf where he didn't."
When ask for proof, you could not do so. You have a problem backing up what you say.
-----------
You said: " I did nothing wrong in adding the impedance Rm and the resistive element Rm. "
Impedance is NOT Rm. You have a problem with the most elementary basics of electronics.
-----------
You said:
You added so: " Zm +(Bl^2)/Re) "
Zm IS a vector, (Bl^2)/Re) IS a scalor. You have a problem with vectors.
-----------
You said"
" why don't you simply learn how to add vectors? "
You have a problem with projection.
---------
You said: " I have no intention of being polite "
You have a problem with the most basic courtesy.
-----------
-----------
Your equation is a jumble. Likely deliberate, otherwise you have a problem with the stating of a simple equation. Your equation does NOT equal 0.0712 as written. Otherwise UNJUMBLE it and prove it does, or you are wrong. And it is NOT that difficult to make the equations readable here.
So again, would you please just unjumble your equation and stop wasting our time? TIA
Northstar email snipped-for-privacy@hotmail.com remove the high card to reply
When I open the post in a separate window and apply a 'fixed' text size to view it, it (Don's equation) is quite readable. Perhaps you need to try a different news reader.
Don starts with a numerator term of '8*2/6' and a denominator term that is the sum of two vectors. The first vector is (10.67 + j0) and the second vector is (2.7 + j35). Adding these two vectors yields [(10.67+2.7) + j(0+35)]. Taking the '/6' term from the numerator to the denominator, he then has just 16 (the results of 8*2) in the numerator term and (6)(13.37+j35) in the denominator.
The 'scalar' 10.67 is a purely resistive element? So to convert this to an impedance vector is trivial, just add j0 as Don did (purely resistive elements have zero reactance). Then adding the vector (10.67+j0) to the vector (13.37+j35) is accomplished by adding the two real terms and adding the two imaginary terms. Don shows this as [(10.67+2.7) + j(0+35)] = (13.37+j35).
This *does* work out to magnitude 0.0171174 @ -69.1 degrees, just exactly as he said and like the first form.
Neither: I have simply pointed out that Siskind did NOT say " rotor power input (RPI) at start-up simply as (E^2/R^2)*R, which is of course E^2/R. "
I know that, in the case of the speaker motor under blocked coil conditions, the input power is E^2/Re is valid- I said that before. I also know that it is not valid except under that particular condition. This is trivial. I also pointed out some discrepancies that you had with regard to input impedance, power and what you erroneously called a power factor. However, you have given what "Siskind says" as something other than what he actually says and this implies that he gives an expression with inductance ignored. This he didn't do.
If you had simply given what he actually said, then went on about ignoring the coil inductance, that would be a different matter And I would have no fundamental conflict with that (other that the situation that Siskind is considering doesn't actually apply). Give a quote then extrapolate- don't extrapolate then modify what "Siskind says" .
You are straining to present a trivial point from an expression which applies to another type of motor where the inductance cannot be ignored. (In addition the Siskind expression is as far as I can tell, of little or no use even in analysis of an induction motor).
-------------
--------- As I did not find it and am not going to look any more - I withdraw that comment with apologies.
---------------- -----------
--------\ This is not electronics but simple circuit theory. It is quite valid to treat a resistance as a vector impedance Rm+j0. You still haven't tried to check out how to add vectors. Did you think that I was adding the magnitude of the resistance to the magnitude of Zm? I have no intention of doing so as that is wrong. -----------
Not my problem You have the tools to learn if you weren't so upset about my not taking your statements as always being correct. .
-------------
-------------- Yes, I don't project nearly as well as you do.
--------
-------------- Only when I get none .
------------
= --------------
j(0+35)] (6)(13.37+ j35)
------------------ I note that Daestrom had no problem with the equations or the results Berenak:
Bl^2/Re+Rg =64/ 6 =10.67 Rm from Eq.7.2 =10.67 +1.5+1.2=13.37 Zmb =13.37 +j 35= 37.47 @ angle 69.1 degrees (Zmb is Beranek's Zm) including the Bl^2/Re term) From 7.1 U =(BlE)/[(Re)(Rmb+jXmb) =(8*2)/[(6)(13.37+j35)=(16)/[(6)(13.37+j35) =16/[(6)(37.47 @ 69.1)] =0.0712 @ -69.1 degrees
Kelly: Zmk =1.5+1.2+j 35= 2.7 + j35 =35.1 @85.6 (NOTE: NOT the Zm of Beranek as it doesn't include the Bl^2/Re term)
+j(0+35)=(16)/[(6)(13.37+j35)] =16/[(6)(37.47 @69.1)] =0.0712 @ -69.1 degrees Identical as I said
In the above, I used (Bl^2)/Re +j0 =10.67+j0 to emphasise the addition is that of phasors. However, the j0 term doesn't have to be carried along explicitly. Note that the addition is ( resistive + resistive) and (reactive + reactive) .
. Is it so hard to look at the summary in Kinsler's appendix and see how it is done?.
Thank you for clarifying the jumble, and I assume 0.0171174 is a typo, and you meant velocity magnitude as 0.0712 rounded.
First, the original objection I expressed to Dons velocity equation, which he *originally* gave on Nov. 13, 04 as
U= (BlE/Re)/(Zm +(Bl^2)/Re)
Zm as we had used it and as Beranek gives it is Zm=Rm+jXm, where Beranek defines the total mechanical resistance term Rm as
Rm = (Bl)^2/(Re+Rg)+Rms+2Rmr.
Now when Don originally gave the equation and when I originally objected, he had not stated that he had omitted (Bl)^2/Re from Rm and thereby from Zm. Note he has now renamed his impedance term as Zmk. The Zm term in his equation then was the actual total impedance including (Bl)^2/(Re+Rg), and he cannot then add (Bl)^2/(Re+Rg) back to impedance Zm, as it is already included in Zm.
Then if you redo your math above with Dons original equation as stated, i.e. with a single vector term of impedance Zm=Rm+jXm, and where (Bl)^2/(Re+Rg) is included in Rm, plus the resistive term (Bl)^2/(Re+Rg) in the denominator you will get an erroneous result giving velocity as too high in magnitude.
As to adding a vector and scalor per se, note again that Don originally gave mechanical impedance as (Zm +(Bl^2)/Re), which if Zm contains (Bl)^2/(Re+Rg), and noting Don did not say (Bl)^2/(Re+Rg) was excluded, then Zm is a true impedance and a vector, whereas (Bl)^2/(Re+Rg) is resistive and therefore a scalor, and his equation does not include j.
Again, from Google: " IOW the inductance of the coil is neglected for low frequencies per the above, and since that is what is almost universally done, it is what I have done, and shall continue to do. Siskind even notes rotor power input (RPI) at start-up simply as (E^2/R^2)*R, which is of course E^2/R. "
I did NOT modify Siskinds equation 80. That is not my style. I do not play around with equations trying to "win" or "trap" someone as you appear to do. His equation is EXACTLY as I gave it originally with the stipulation that inductance is ignored, WHICH I NOTED IN THE SAME POST AS I GAVE THE EQUATION, as quoted above. And... this DOES apply to what we discussed, just as Thiele and Small ignore inductance in the TS reference work. If you would be less sloppy on your "know-all equation speils", and admit your errors, you would have no need to grasp at straws.
Upset? You assume that I'm upset? Impressive. Call it upset if you like, but I call it intolerance, of which I have little or none for someone implying I lied, when I damn well did not.
Respect? After you, Pal.
Thank you for clarification. I'll just say regarding Zm and Zmk, you can't change the rules in the middle of the game. Please see my reply to Daestrom in this thread re your equation.
------------- . Somehow you have developed a fixation such that you misinterpreted what I said on Nov. 13
"The equations that you refer to are initially established from phasor relationships. Note that he establishes the fundamental equations for the model in ch3 and these are in phasor terms. These are the same equations that I am using. " This was followed by
"To say that E=ReI +BlU gives I =(E-BlU)/Re and then note that I =F/(Bl) =ZmU/(Bl) to get ZmU/(Bl) =E/Re -BlU/Re and from this get U= (BlE/Re)/(Zm +(Bl^2)/Re) will be correct for phasor quantities E,I, Zm and U. It will not be correct if only magnitudes are used."
The implication there is that the Zm that I was using is the Zm +Zl of Eq.3.60 - It is the actual mechanical impedance plus the acoustic impedance referred to the mechanical side. It is NOT, and never was the Zm that Beranek used in Eq.7.1. Later, I repeatedly explained to you that the Zm that I used was different than that used by Beranek.. This apparently did not get through.
----------------------
-------------- No- Again, you misinterpret: Please note that I said: "OK but I will use Zmb for Beranek's "Zm" and Zmk for my "Zm" in the hope that the difference will be plain to you." I did this as you, even after many repeated explanations, simply ignored what I had said and ranted away on the basis of your (deliberate) misconceptions. I had hoped that the different subscript would make it clear. You are twisting in the wind.
----------------
---------- Hwever, when you do the math with the Zm that I used, (now Zmk) or with the Zm that Beranek used (or Zmb) the result is the same.
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No I did not give mechanical impedance as Zm +(Bl^2)/Re and you bloody well know it.
Note also that (Bl)^2/(Re+Rg) =(Bl)^2/(Re+Rg)+j0 There is no difference as j0 =0+j0=0-j0 =0 and adding zero doesn't change anything. ----------------- As for Siskind: You wrote: "I did NOT modify Siskinds equation 80. That is not my style. I do not play around with equations trying to "win" or "trap" someone as you appear to do. His equation is EXACTLY as I gave it originally with the stipulation that inductance is ignored, WHICH I NOTED IN THE SAME POST AS I GAVE THE EQUATION, as quoted above"
You wrote:Siskind even notes rotor power input (RPI) at start-up simply as (E^2/R^2)*R, which is of course E^2/R. "
This is NOT what he said as indicated by your later quote of what he actually said. You said that the inductance could be ignored and THEN brought in Siskind as "support." As I said before, bring in your reference and then give the result in the case of inductance being negligable. Sorry, the implication that Siskind "notes" that RPI is E^2/R is there but in the actual context of Eq. 80, it is simply not true. Siskind never considers the case of negligable reactance as it simply doesn't occur in the induction motor. To imply that he did is wrong. This is what you have done. It is along the lines of what you claim that I said- what is actually said is made into what you want to be said. Is this deliberate? I don't know but at this stage, I don't give a damn. Also please note that I have given the steps in any derivations of equations and have tried to be sure that all quantities are specified as I have used them. It appears that this is "playing around" to you. I erroneously gave you too much credit for the ability to think.
You definition was EXACTLY THE SAME as Beranek equations 7.1 and 7.36, proving you change history rather than admit an error. Too bad.
Yes, you said that - 15 DAYS LATER, on Nov 28, 04 per Google, in another attempt to change history.
Deliberate misconceptions? Per the above, this is proof of your projection.
You wish.
Now here is the crux of the matter. Although per yourself, you are a whiz at phasors, as is Captain Kirk :) , sorry but you are a miserable failure at putting them in practica in the area we discussed. You gave mechanical impedance as Zm +(Bl^2)/Re, and apparently don't even know it, otherwise you are purposely being disingenuous. Your equation again:
" U= (BlE/Re)/(Zm +(Bl^2)/Re) "
Since velocity = applied force / mechanical impedance, you DID give mechanical impedance as Zm +(Bl^2)/Re. Enough said, except you really should be more prudent in equating my math to sophomoric level. Remarks like that can come back to bite you on the arse.
Unless you cannot comprehend the sequence of my statements in that post, this is a deliberate attempt to imply that I lied, because I said in the SAME post ***PRIOR*** to giving Siskinds equation
" the inductance of the coil is neglected for low frequencies per the above, and since that is what is almost universally done, it is what I have done, and shall continue to do. (in fact Small states input power as E^2/Re, with the coil inductance neglected). "
This was clearly with reference to a speaker motor, not an induction motor. There was NO implication that Siskind considers the case of negligable reactance in an induction motor. Having bobbled your velocity equation, then instead of admitting your mistake, you resorted to personal insult. Too bad.
--------------------- The problem is that you assumed that I used Zm =Rm +jXm and YOU assumed that I used Beraneks definition of Zm, Rm and Xm. Please note that when you brought this up, I explained (repeatedly- from the 21th (in response to your first challenging this in the 17th) the difference between my notation and Beranek's. To quote: "The difference, which I explained before, is that I used Zm as the actual mechanical impedance ( Berenak in Eq 7.1 to 7.3 does not name it as mechanical impedance or anything else- his Rm and Xm are simply shorthand notation which is common practice to keep equations easier to follow. Nothing more.) His Rm does include (Bl^2)/Re. My Rm doesn't, as I explained more than once, and on the basis of the development from scratch. As a result [(Bl^2)/Re +Rm] is the same as Beraneks Rm. I could have used Beraneks notation but I started with E=ZeI +BlU F=BLI =ZmU where Ze =Re +j0 ignoring inductance and source resistance Zm the mechanical and acoustic impedance=(Rms+2Rmr) +j[(wMmd +2Xms-1/wCms] Thus I have my (Bl^2)/Re + Zm =[ (Bl^2)/Re +Rms +2Rmr ] +j[(wMmd
+2Xms-1/wCms] which agrees with Beranek's Zm . There is no difference. The addition is done correctly. (Think: Ze =Re=Re +j0) I kept the (Bl^2)/Re term separate only to emphasise that it is electrical in origin, not mechanical. Beranek's Fig. 7.4 emphasises this. There is no difference between what I say and what Beranek or Kinsler say. We are working by the same rules of analysis and get the same results even if somewhat different terminology is used along the way."
What part of this do you not understand?
Also note that I have consistently used the Zm as the actual mechanical/acoustic impedance as can be seen from what I wrote at earlier dates. I deliberately used a different notation on the 28th as you didn't seem to understand the above. >
projection.
------------- YOU have assumed that I gave. mechanical impedance as Zm +(Bl^2)/Re. I didn't and neither did Beranek. If you cared to read what he said, there is nowhere in Ch. 7 that he refers to this as "Mechanical impedance" In fact, if you look at how he gets Eq.7.1 he writes "The voice coil velocity u0, neglecting w^2L^2 compared with (Rg+Re)^2, is found from Fig.7.4a" In other words he solved the circuit of 7.4a, ignoring L to get Eq.7.1 Now look at Fig 7.4a and note that Beranek clearly distinguishes between the electrical, mechanical and acoustic elements of this equivalent circuit. Note, in particular that he includes (Bl^2)/Re in the electrical part of the circuit model. You seem to have a problem in that I also did the same. His use of Rm and Xm in Eq 7.1 could just as easily been expressed as G and H or any other pair of otherwise unused symbols. YOU have assumed that his Zm is the actual mechanical impedance. It is not and no amount of bluster will make it so.
-------- EXACTLY. There is no problem with your saying this. What I objected to and you don't seem to understand is that Siskind did not "note" any such thing. To say that he did is false. There are no two ways about this. You have presented an interpretation which is based on what YOU said and when you say that "Siskind notes...." you are explicitly saying that he actually did refer to this. This is in line with YOUR interpretation of what I said and of what Beranek said. You are marching to your own drummer and facts simply get in the way of your interpretation.
----------- So why did you even refer to Siskind ? You are dealing with a speaker motor- he wasn't- I'm glad that you recognise this.
Come, on, use your brain - THINK- don't just take formulae and put interpretations in that were not intended by the authors. How can I have any faith in what claim that Small or others have said when you have put in obvious distortions.?
I originally did not intend to answer but I couldn't resist reacting to your distortions of what I and others have said. Unless you have something meaningful to say (and recently you haven't), I will not respond further. -- Don Kelly snipped-for-privacy@peeshaw.ca remove the urine to answer
Now you say above " Thus I have my (Bl^2)/Re + Zm =[ (Bl^2)/Re +Rms +2Rmr ] +j[(wMmd+2Xms-1/wCms] which agrees with Beranek's Zm . There is no difference. "
Lets solve for your (Bl^2)/Re + Zm' where Zm' is Beraneks equation with (Bl^2)/Re left out of Rm, as you say you did
Your method does not work. You are wrong. In error. Mistaken, even. You should be ashamed of having made gratuitous remarks about sophomore level, and such. Too bad.
Now, considering below where you say " Come, on, use your brain - THINK- " Per my math above, you should not have to think (thank heavens) :) Perhaps this will help: Per Google, you said: " I have further thoughts (in place of sleeping) re Theile - etc etc " Maybe you need to get a little sleep so *you* can think, and stop wasting out time.
PS If you respond, please ***do not clip*** from this post. TIA
Also if you do not respond, please note:
I'm a lover of peace, protector of the downtrodden, (always for the underdog, unless he's losin'... :) I'm true-blue Odie Colodie.. Descended from Royalty. Constant as the north star, and there when you need me. With words that serve to inspire and enlighten... Peace unto you Brother, and the horse you rode in on. So to speak.
Northstar email snipped-for-privacy@hotmail.com remove the high card to reply
PS Lest you become elated :), note all in the equation after [(Bl^2)/Re] is one parameter, i.e. the impedance as you defined it without (Bl^2)/Re. As such, perhaps better stated enclosed as { ---- }
----------- Since you did not bother to give the frequency, I had to reconstruct. It appears that with the magnitudes that you gave for Beranek's Zm , then Xm=38.71 This agrees with the magnitude of 38.78 that you give for Zm'
I get, from Berenak's expression Zm =19.5+j38.71=42.34 @ angle 63.27 degrees
Now Zm' =2.4+j38.71 =38.78 @ angle 86.45 degrees
Adding (Bl^2)/Re to Zm' gives 17.1 +(2.4+j38.71) =19.5 +j38.71 =38.78 @ angle 86.45 degrees So (Bl^2)/Re +Zm' = Berenak's Zm in both magnitude and phase.
You set the trap but caught yourself.
It appears that you took root[(17.1^2)+38.78^2)] =42.38 and called it vector addition
This is NOT how you add vectors. Where did you get the idea that it was?
Please do as I suggested, and go back and learn how to do it. Add the real components: add the reactive components- then you can use Pythagorus' theorem to find the magnitude. I once asked you to do an example graphically and check it.
I have taken the liberty to clip all but the technical part you respomded to, and we can discuss the Siskind bit or whatever later if you wish. I used a non-updated set of specs, and the specs should not have included 2Xms. Since the driver was not measured in a vacuum during the mass measurement, the mass of the air load Ma was included in Mmd, and thereby the mass reactance 2Xms (Beraneks Xmr). As the cone moves back and forth, it brings the air load along with it, the air load being stuck to the cone, as it were. Adding 2Xms=5.92 to (w Mmd) throws Zm way off. My apology. Same for leaving out the frequency, but it is simply f=1278/2 pi = 203.4 Hz. The driver is an 8 inch woofer, operating in a 1 cubic foot sealed box, no stuffing.
So... Shall we start over? I shall solve each equation exactly as before, but with correct total mass reactance, and my comments (as left unclipped above) are unchanged. All your criticism should be unaffected, but the magnitudes will be accurate and valid as a true representation of the driver. So please re-state your criticism, using the correct specs, which I shall now list. Again, my apology and TIA.
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Bl = 11.01 Re = 7.09 Rms = 1.57
2Rmr = 0.83 w = 1,278 f = 203.4 Mmd = 0.0281 (includes mass of the air load, such that *total* mass reactance wMmd+2Xms = wMmd = 35.91 Cms = 0.000250 E = 1.41 Rg = 0
Directly above you give this equation, saying it agrees with Beraneks Zm:
" =[ (Bl^2)/Re +Rms +2Rmr ] +j[(wMmd+2Xms-1/wCms] which agrees with Beranek's Zm. "
Then with Beraneks Zm, (which you give correctly, BTW), the correct Zm is
Now you say above " Thus I have my (Bl^2)/Re + Zm =[ (Bl^2)/Re +Rms +2Rmr ] +j[(wMmd+2Xms-1/wCms] which agrees with Beranek's Zm . There is no difference. "
Lets solve for your (Bl^2)/Re + Zm' where Zm' is Beraneks equation with (Bl^2)/Re left out of Rm, as you say you did
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