Oh sure... Snip out the part about who was dishonest.
Snip out your incorrect efficiency magnitudes.
Snip out my analysis where Eb = 0.1905
Snip out my references.
Snip out my Pmec analysis.
Snip out my Zmec data as related to Beraneks eq.7.1
Snip out my data as related to Smalls Eq.31.
Etc, etc etc.
In short, snip out all my proof you are wrong, then fret with your math for a few days and start another attempt to rationalize your errors, along with a fresh group of imprompt remarks (I call them insults).
Regarding the angle of 72.44 degrees, I tried to tell you early on that an effective mechanical resistance Rmec was needed, and you responded positively, but could not refrain from tossing in more insults as usual.
Suffice it to say I was consultant for both Harman International and their subsidiary group for 19 years, as well as manufacturing (a small company) on my own. Dr. Small is also employed at Harman, and I have worked with him before. We found the subject we have discussed difficult to analyze in terms of back emf, however I pursued this aspect on my own off and on over the years. I came here hoping to get insight into an aspect or two that was not quite clear to me (Daestrom was helpful) if you recall. My mistake was in not dropping the dialogue with you early on.
Now... I have solved the dillema you face to my satisfaction, and you have yet to do so, not even being able to derive the correct magnitude to use regarding Rmec as a start. Also your comment regarding conservation of energy below gives little hope for any analysis you come up regarding what we have discussed ever being correct. To your credit, you did suggest private email for the discussion, however having found out your ad hominem oriented character, I'm glad I chose not to go that more "personal" route.
Finally... If you want to go back and reinstate ALL the pertinent data you clipped by using my last reply UNEDITED, and fitting in your UNEDITED comments below, and apologize for your imprompt remarks (if not insults) below, I shall consider responding to your future technical remarks.
--------- They are fine once corrected for the Pa from one side.
------------------
------- 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. This has been pointed out to you before- That is - your analysis has already been shown to be crap. You are trying to use "DC" analysis for an AC situation. It doesn't work If any of your references indicate this - burn them.
--------
----------- I looked at the references I had available- including the one on the net. They don't support you.
----------
----------- Again, you don't satisfy conservation of energy and the initial basis is incorrect. I pointed this out previously. Pa +Pmec should be the same coming from the Pin-I^2Re as from (Rms
+2Rmr)U^2. I get this but you don't.
-----------------
-------------- Sorry, This was also considered.
---------
---------- Right- have you found the approximation in that equation? Or have you even tried to do so?
-------------
You have presented no proof. You have presented incorrect math along with incorrect understanding of basic circuits (and remember that this is what we have been dealing with). Blatent errors, often repeated, are not proof.
----------------
All I ask is that you show where you got this particular angle - you have blustered but not produced. If you have a sound basis for this - show me. If (Bl^2)/Re =17.1 and Rms +2Rmr = 1.57 + 0.83 according to your data, the sum is 19.5. You also give wMmd =35.91 and Cms =0.00025 so wMmd -1/wCms =32.78 This gives an angle of arccos 32.78/19.5 =59.26 degrees. Ignoring Cms gives an angleof 61.5 degrees Ignoring Rms +2Rmr as well as Cms gives 64.5 degrees Ignoring (Bl^2)/Re and Cms give 86 degrees Ignoring (Bl^2)/Re gives 85.8degrees
SO: WHERE THE HELL DO YOU GET 72.44 degrees?????
--------------------
---------
Did you ever try to run your analysis by Dr Small? And get agreement? Surely he didn't have a problem with back emf. From what I can gather he understands phasor analysis but you don't.
How is it that when I do the math , including phase correctly, and showing the steps., I get consistent results while you don't.? The problem is not mine.
----------- I came here hoping to get insight into an aspect or two that was
-------------- Oh dear, you are still thinking along the line that was discredited before. It appears that you still think that (Bl^2)/Re is an actual rather than an equivalent mechanical resistance. I really doubt whether Small would agree with you.
----------- Also your comment regarding
--------- Why? It is fundamental.
------------- To your credit,
------------- I did that for two reasons: a) it is easier to discuss when proper diagrams and non-ascii equations can be used. b) To save you some public humiliation as, whether or not you believe it, I have no desire to "score points" from you. You can still do so if you wan't to unlearn some serious misconceptions.
-----------
Since, all that was said before has become repetitous - there is no point going over it. It is on record. I simply summarised my points. I doubt that my repeating it again will produce a response which will have some meat. For example, you have avoided the consideration of obvious mathematical errors that you have made and also have avoided detailing how you got the magical angle of 72.4 degrees. You have also not attempted to find the approximation in Small's Eq.31 nor have you explained how Pin =E^2/Ze is true if Ze is not purely resistive. You have also avoided the problem of using scalar aritmetic for vector quantities.
You can think, try it- it doesn't hurt.
As for apologies- I apologise for some comments and for those mistakes that I have previously acknowledged. I am not going to apologise for disagreeing with your more blatent errors in math or physics.
I won't be bothering you any more so you can enjoy your Christmas.
No need, since you made the blantent errors, as we shall see below.
Nah... You offer hogwash and crap, not me. Been saving this in case you lose your shitte, which you now have:
First, to reinstate my specs, which you clipped:
Bl = 11.01 Re = 7.09 Rms = 1.57 2Rmr = 0.83 w = 1,278 f = 203.4 v - 0.0574 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 I = 0.172 during steady state motion Sd = 0.0216 area of cone Ze = 8.198 Zmec = 32.99 includes Zr n = 0.0055 = 0.55 % electrical to acoustic efficiency angle between force and velocity = 72.44 deg. angle = 72.44 = phase angle between force and velocity cos angle = cos 72.44 = 0.3017 Eb = 0.1905 Dynamic Pin = 0.244 Pmec+Pa = 0.0328 Pa = 0.001367 n = 0.0056 Pmec + Pa = 0.0328 Cl = 0.2098 copper loss, i.e. I^2R power lost as heat in coil
Now the equivalent circuit per Kinsler 14.10a and Beranek 3.44b, and note we add cos angle, as the frequency is not at mech. resonance:
--------------Re------------------------ + : 1.41 v RMS input : : --------Rl=[(Bl)^2/Zmec+Zr] cos angle---
Re = 7.09 Rl = Zmot = (11.01^2 / 32.99) * 0.3017 = 1.109 Ze = Re + Zmot = 7.09 + 1.109 = 8.199 as measured
Reference on Zmot, Kinsler 14.48b and Beranek right-hand side of 3.62. Note Zr, the air load impedance, was included in Zmec in the specs. Reference on Ze, Kinsler 14.48a and Beranek 3.62.
Now also, Daestrom on Nov. 17 2003 (per Google) noted for a similiar circuit, and although for a DC source, the principle holds for AC (figure as instantaneous with the source positive as shown) "If we draw a 'flowpath' around the circuit from battery, through armature resistance, through CEMF source and back to battery," we see that the voltage drop across Rl may be viewed as CEMF or back emf, which is also depicted as such in the analysis of AC motors by many authorities.
Voltage drop across Re = I Re = 0.172 * 7.09 = -1.219 Voltage drop across Rl = I Rl = 0.172 * 1.109 = -0.1907 Then by Kirchhoffs voltage law: 1.41 + (I Re) + (I Rl) = zero
Just as I said, back emf Eb = 0.1905.
Now you stated two posts back: "oh, yes the real part of Eb is 0.323 Volts". You are off by around 70%, a blantent error.
Now for the fun part :)
Power generating heat in the coil is Pheat = I^2 Re = 0.172^2 * 7.09 = 0.2098 watt Pmec+Pa = I^2 Rl = 0.172^2 * 1.109 = 0.0328 watt Total dynamic power out at steady state is Pout = Pheat + (Pmec+Pa) = 0.2098 + 0.328 = 0.2426 watt Dynamic Pin = E^2/Ze = 0.2425 watt
So (contrary to your criticism) conservation of energy is conserved.
But... the main point here is that mechanical power + acoustic power must be 0.0328, and you said two posts back:
Small clearly states his assumptions that would cause any approximation, and considering them he is right on the money.
he he ...
Right.
Now don't get excited.. I told you where and how to get 72.44 degrees. It is not my fault that your phase angles are off-target. Also (Pmec+Pa) is just as important in deriving 72.44 degrees, and you are off by a factor of 4+. This has been a problem for you, and I have pointed it out in many ways, but to no avail.
You are consistently wrong? I am constant as the northstar :)
It appears it may take years of work for you to figure out the role of (Bl^2)/Re.
If you are truthful on b, I'm sorry for *your* humiliation.
*** Oh, my, Take my results and go at each supposed error- I have no problem with that. I do have a problem with you saying "WRONG" but not presenting any valid basis for the comment. At least, when I disagree with you, I present the reasoning. If you prove any basic math or physics errors, I will happily admit them. So far, except for a few typos and the use of the acoustic power from both sides of the diaphram (which I admitted- please cut out Beraneks' PAE as he too does that), you haven't come up with anything.
---------------- Stop here: the above quantities are specs or base data from measurements. The following are calculated from these and are not specifications.
**OK but Magnitude only- no phase information.
** Again magnitude but no phase information.
*** Based on an approximation using Small's expression and based on an incorrect Pin using Beranek.
***No basis for this angle is given. I asked for your basis for this- you haven't yet given it.
******This is incorrect. The relationship between Eb and U is given by Eb=BlU If you go back to the basics, Faraday's Law gives eb(t)=d(turns*flux)/dt and this reduces, for the geometry of a speaker, to eb(t)=(Bl)u(t) as is given in countless texts. (eb(t) and u(t) are the instantaneous magnitudes of the back emf and the velocity) This is a scalar equation- valid for DC or any frequency or waveform. For a sinusoidal velocity u(t) =Umax* cos (wt + a) where a is a phase shift with respect to a reference. Then eb(t) =BlUmax* cos(wt+a) when u is maximum, so is e, when u is 0, so is e - they are in phase and the magnitudes are related by Bl For steady state, U may be replaced by a vector or phasor giving both the magnitude and phase. The magnitude is generally given in rms values (Umax/root(2)) So we have a vector U @ a and a corresponding vector Eb @ a The two are in phase and the magnitude of Eb =(Bl)* magnitude of U That is back emf in a nutshell- there is really no more to it. Assuming a power factor does not give you Eb but gives the real component of it - IF - you have the angle correct. You haven't.
*This assumes that I is in phase with E - on that basis EI =1.41*0.172 =0.2425 is the maximum possible Pin. The 0.244 value appears to be in error (minor quibble). Pin , if the input power factor is less than 1, will be less than 0.2425
** this is incorrect and is based on a value for Pin that is greater than what is possible You can check on this as Pmec+Pa is also given by (Rms +2Rmr)U^2 If your value is right the check should agree-- it doesn't.
***This is right.
****Small's approach includes an approximation which is good at higher frequencies and the efficiency appears to be related to the reference efficiency given by Beranek in 7.18 and 7.19. This is done for convenience to save calculation effort. Do you not see where the approximation comes in? Your value from Beranek is based on an input power which is, as I said above, is too high. In addition, efficiency is found from Pa and Pin so using n and Pa to check Pin is going around in circles.
*NO.
******This value, at least, is correct.
------------- First of all, the angle of 72.44 degrees - again, I ask where it comes from.
----------
*****On the basis of your current of 0.172A and E=1.41, you find Zin
8.198 - fair enough. However, the problem is that you have assumed, again , that E and I are in phase. There is no basis for this assumption. The magnitude of Zmec that you get is essentially the same as what I get for Zm' but it appears that you calculated it on the basis of (11.01^2)/1.109 =32.99 and now you reverse th e calculation and offer it as proof. I did give you the results of assuming a current with a phase angle of about
26.6 degrees That is I=0.172 @ 26.6 degrees. This leads to Zin =8.198 @ angle -26.6 degrees =7.33 -j3.67 ohms accounting for Re leads to Zmot =0.24-j3.67 =3.68 @-86.25 degrees and the corresponding Zmech =(11.01^2)/3.68 =32.96 @ 86.25 degrees =2.16 +j 32.89 Compare this to 2.4 +j 32.78 calculated from (Rms +2Rmr)+j (wMmd =1/wCms) . The angle chosen for I is an approximation but note that |Ze| =8.198, |I|=0.172 and |Zmech| =32.96 are all very close to the values that I obtained using your data. .>
-----------
****And I included it. I used your specs.
****True for DC or instantaneous values, but for AC steady state rms vector quantities. , you must use the vector quantity Zmot. You are not doing calculations using instantaneous values but with the rms phasor values. The effect of the load does appear as an impedance which is not necessarily real. You haven't accounted for this fact. As for back emf as given by various texts- I have likely run through and have owned more such texts than you have seen. I still have several machines texts written at a far higher level than Fitzgerald or Siskind. In fact, there is one such (old) within arm's length: "Electromechanical Energy Conversion" by V. Gourishankar and D. H. Kelly which was used at the university level. So what?- There is no need to explain back emf or Kirchoff's Laws to me- I knew these things solidly 50 years ago and have done related work since then (as well as having faced grilling on my knowledge by many better than either of us.
***** WRONG. You have done all calculations on the basis of real numbers instead of complex numbers. This is a common error for students in their first AC circuits course. This is what I have been trying to tell you. For AC, none of your texts will tell you to do what you are saying. You have assumed that I is real and that Zmot (not Rl) is real. They are real only at resonance but will have associated phase angles otherwise. I am saying that Zmot =3.7@ an angle of -85 degrees (capacitive and note Kinsler's electrical model) and that the current is 0.172 @ an angle near
25.5 degrees. Kirchoff's Law still works. but it becomes 1.41 -7.09(0.172 @25.5) -(3.7 @ -85)(0.172 @ 26.5) =0 (NB: You have a sign problem in your statement of KVL if you are using conventional current ) That is, use vector quantities or use two equations for real and reactive components. The circuit consists of an impedance and a resistance in series- your circuits text references should show you how to handle this.
**** and also it is 0.632 volts from (11.01)* 0.0576
*****Sorry, it is not my error. It is your use of "DC methods" for AC conditions. Note that the equation :
1.41 -7.09I =Eb =BlU can be broken into two equations on the basis that I=0.172 @ angle i and Eb =11.01(0.0574) @ angle u =0.632 @ angle u Then:
1.41-(7.09)(0.172)cos (i) =0.632 cos(u) Real part
0-(7.09)(0.172)sin (i) =0.632 sin (u) Reactive part. Both have to be satisfied. You have used the first one only and have assumed i =0 and u =72.44 so you get
1.41 -1.2195 =0.1905 which corresponds to 0.632 cos 72.44 Now the second equation becomes -1.2195*0 =0.632sin -72.44) =0.6025 or 0.6025 =0 OOPS! Suppose that I is not at angle 0 then sin (i) = 0.6025/1.2195 =0.494 and angle i =29.6 degrees now 1.41 =1.2195 cos (29.6) =0.35 but it should be 06025 Maybe u is wrong so try cos(u) =0.350.632 =0.554 and u is -56.4 degrees, not -72.4 degrees. We can repeat this until the results converge, satisfying both equations. This will be close to i=26.57 degrees and u =-59.65 degrees Now Pin =EI cos 26.57 =0.2169 watts I^2 =0.2098 watts Pmec +Pa =0.2169-0.2098 =0.0071 which should be 0.0079 so more refinement on the angles is needed. (note that calculating Pa +Pmec from Pin-I^2Re is subject to larger errors than using (Rms +2Rmr)U^2- from basic error analysis) correspondingly 1.41-ReI =1.41 -1.2195(cos 26.57+j sin 26.57) =(1.41-1.091)-j0.544 =0.3200 -j 0.544 with a magnitude of 0.632 and a phase of 59.65 degrees. Note that Beranek's Zm has an angle of arctan (32.78/19.5) =59.26 degrees
Now I don't expect you to follow the above, based on past experience, but the upshot of it is that a)The angle between force and velocity, which is not the angle between back emf and velocity (which is 0) nor is it the angle between E and U (59 degrees) is definitely NOT 72.44 degrees as that leads to nonsense values. b) The current has a phase angle and this must be taken into account when calculating voltages or when calculating power or the phase of Zin.
I stand by my original calculations as attached below.
**OK
****Based on an incorrect Zmot. Try (0.172^2)* 3.7 cos 85.3 degrees =0.0095 as a rough approximation. compare to (0.0574^2)(Rms +2Rmr) =0.0079 Now take a look at the values that I calculated based on data you provided. There is a check between the values as calculated from U as found by Berenak's 7.1, as well as the current from BlI=Zmec U and the calculation of both Eb and the powers from E and I. Your calculations fail that check because you have made inappropriate assumptions and calculations for vector quantities. ------
--------- Certainly you got these values as you have done what is effectively DC calculations. you still ignore the fact that I^Re +(U^2)(Rms +2Rmr) should give you the input power. (0.172^2)(7.09) +(0.0574^2)(1.57 +0.83) =0.2098 +0.0079 =0.2177 watts which is not 0.2426 watts. There is an problem as if your calculations were right, there shouod not be this difference. You also use Dynamic Pin =E^2/Ze As I have said before, this is true only if Zin is real. Otherwise it is not true E^2/Ze =Pin +jQin where Qin is the reactive vars input.
No. If conservation of energy was conserved then I^2Re +U^2(rms +2Rmr) should be equal to the power in. Since your calculations are wrong-
***** Sorry, the error is on your part. You have proven that you do not understand the basics of simple AC analysis. You haven't even tried to make any valid checks on to your results. You have Eb =0.1905 by your "DC type" calculations where Eb =0.632 by BlU You have applied a power factor to this to make up the difference but the basic equation is not BlU*pf and you have not given any reason for applying this particular pf to the back emf which is not determined by the phase angle between force and velocity. You have calculated power on the premise that E and I are in phase and give no justification for assuming that they are so. You then simply ignore the fact that calculation of the powers can be done using U and I magnitudes as well as the parameters Rms, Rmr and Re. and that the results of these calculations disagree with what you claim.
Please note that I laid all steps of my calculations out step by step and also ran checks to detect errors in calculations. This is something that you haven't done.
-***- In fact you have done no such thing. You have waved your hands but not given the basis. Show me. If you are right then it will be obvious, if not, and all indications are that it is not right, then I can see where it is wrong. You still haven't said how to get this angle. There is no relationship between this angle and that of Zm, Zm' I, or anything else that I can see. Otherwise I wouldn't have asked. My phase angles are correct. You have given no evidence to the contrary or pointed out just how they may be in error. Sorry to disappoint you.
------
** I definitely know the role of that term. No problem on my part. I also did, more than once, show just how it appears. In fact, it appears that I have a better grasp on it than you do.
**** Oh, I was being truthful and I am not humiliated. All your calculations are based on incorrect math and to some extent, a lack of understanding of the various physical relationships behind the math. Might I suggest again, that you do try to learn basic AC circuit analysis. You have references and Beranek, Kinsler, and, I hope, Small, do it correctly. Sorry to disappoint you.
Bl = 11.01 measured Re = 7.09 measured Rms = 1.57 2Rmr = 0.83 w = 1,278 f = 203.4 measured v - 0.0574 Mmd = 0.0281 (includes mass of the air load, such that *total* mass reactance wMmd+2Xms = wMmd = 35.91 measured Cms = 0.000250 E = 1.41 measured Rg = 0 I = 0.172 during steady state motion measured Sd = 0.0216 area of cone measured Ze = 8.198 measured Zmec = 32.99 includes Zr n = 0.0055 = 0.55 % electrical to acoustic efficiency angle between force and velocity = 72.44 deg. angle = 72.44 = phase angle between force and velocity cos angle = cos 72.44 = 0.3017 Eb = 0.1905 Dynamic Pin = 0.244 Pmec+Pa = 0.0328 Pa = 0.001367 n = 0.0056 Pmec + Pa = 0.0328 Cl = 0.2098 copper loss, i.e. I^2R power lost as heat in coil
Cut into my analysis before numbers are even given, with distraction and false statements. To use your words, you are twisting in the wind.
Ze was measured, not calculated. Phase is accounted for in Ze itself, as I used it. Your ignorance as the the method used is not my fault. Also my usage gives correct results, yours does not.
I gave the correct phase angle, as we shall see twice again below. Your inability to derive it is not my fault, and proves your incompetence. My angle gives correct results, and yours does not.
Unbelievable incompetence, otherwise bluster. Hard to say which, as even my specs above show 0.0056. You get very little correct.
Nor will you get it, as my analysis re power in = power out proves the phase angle of 72.44 degrees is correct, as will my analysis below regarding Ze. Reason: Facts mean nothing to you in your desperate effort to cover up your erronrous analysis, and I will not supply you what I have learned the hard way for you to throw up a smoke screen around. Again, my angle of
72.44 deg. gives correct power in = power out and correct electrical impedance Ze. If that's not good enough for you, keep worrying about the derivation. Maybe you'll luck up. In fact, IMO the fact that you cannot find the derivation for the angle, accounts for much of your bluster. It is deravable in a number of ways and you are incapable of doing this. Bugs you doesn't it...
The following is for the record, so please do not separate the next
11 lines of my Ze analysis, and leave your comments below them. TIA
Yes, I agree that assuming (using) a power factor does not give you Eb but gives the real component of it, and using my angle of 72.44 gives: power factor = cos angle = cos 72.44 = 0.3017 Motional impedance then is (Beranek and Kinsler references given earlier) Zmot = [(Bl)^2/Zmec+Zr] cos angle = (11.01^2 / 32.99) * 0.3017 = 1.109 Ze = Re + Zmot note Zmot is real, and is added to Re which is real = 7.09 + 1.109 = 8.199 Matching *measured* impedance exact. and agreeing with E/I, as it must for AC. Ze = 1.41 / 0.172 = 8.198
This proves irrefutably that my phase angle of 72.44 is correct. Do you now agree? Yes or no?
No, this was proven correct earlier. A simpler example for you, where mechanical power equals power in minus power lost as heat:
And again, you ask in vain, at least until you understand the basics, and stop arsing off.
No. with E and I in phase, P = I^2 Re = 0.2098 as with blocked coil with E and I not in phase, P = I^2 Ze = 0.2425 as at steady state, otherwise P = E^2/Ze = 1.41^2/8.198 = 0.2425.
You apparently are *all* mixed up.
OK, then you know I am correct where I used Kirchhoffs law.
Jeeeezzzzzzzz........ Can you not see the terms are all resistive??? And they are *properly* resistive??? You are serious, aren't you? I am about to think something is amiss re your stated history. Or is this a game for you? Surely not if your name is real...
And they are proven wrong above. Eb = 0.1905 and Pmec+Pa = 0.0328 watt.
And on you go, even with your analysis proven wrong.
Pin = Pout E^2/Ze = I^2 Re + I^2 Rl
0.2425 = 0.2098 + 0.0328 = 0.2426
I suppose you consider 0.04% wrong.
BS
No. Eb is given as Blv cos angle = 11.01*0.0574*0.3017=0.1907 With due respects, you need a break, IMO.
Projection at its finest.
Really bugs you doesn't it. Since the phase angle of 72.44 degrees is proven correct twice above, the fact that you cannot derive it, proves you cannot understand some of the basics, and why your analysis is in error, as well as that you are less than competent here.
I am dissapointed only due to time wasted.
Then prove it. Show me how (Bl)^2/Re relates to back emf, other that what I gave you regarding this, or something just as valid in how it relates to the mechanical side. That is your challenge.
I don't think you can do it. We shall see.
You are out of your field too far to dissapoint me. Dream on.
I don't think you should mess with Smalls efforts too much, Pal.
You shot yourself in the foot here.. Again.
And again, this is for the record, please leave intact and reply below the ***** TIA
Efficiency per Beranek is:
Beranek Pin = E^2/Ze = 0.2425 His eq. 3.53 Beranek Pout = v^2 Rmr = 0.001367 His eq. 7.5 n = 0.001367 / 0.2425 = 0.0056 = 0.56%
You see the references, use them.
Now Smalls efficiency: His eq.31
n = (po/2 pi c) * [(Bl)^2/Re] * (Sd^2/M^2)
n = 0.000544 * 17.097 * 0.5909 = 0.0056 = 0.56%
You see the reference, use it.
*****
That is exact correlation of a lot of terms, as well as tying Beranek to Small exactly, along with showing the accuracy of my data. To disagree with power in, efficiency, etc as you do above does not speak well at all for you.
-------- And how did you measure Ze ? If you used an impedance meter, there is a problem. If you used E/I then it is calculated and you have given only the magnitude. If you have any phase information, you haven't shown it. Your subsequent work implies that you have assumed that it is resistive. Sorry, that doesn't wash.>
Your angle gives garbage and you know it but refuse to admit it. I note that you still haven't given the basis, with numbers, for your angle calculation. Give it or shut up.
-----------
_-------- Your specs include the incorrect values that you have calculated. Sorry.
You have the Pout correctly. The Pin is incorrect as E^2/Ze is not the real power in. It does give the magnitude of the complex power Pin +jQin but not the real power Pin which is what is of importance in calculating efficiency. I have tried to get this point across to you before. Example: a 2 ohm resistor is in series with a 2 ohm reactance E=2V Zin =root(2^2 +2^2) =root(8) =2.83 vaE^2/Zin = 4/2.83 =1.41 watts I=2/2.83 =0.707A and I^2R =(0.707^2)*2 =1 watt Pin =EI (pf) = 2*0.707*(2/2.83) =1 watt Neither of these correct values for power input is the same as E^2/Zin The facts of the case is that your calculation of Pout/Pin is based on a value of Pin that is incorrect. No amount of BS on your part will get around this fact of life. .
---------->
----------- Why should Zmot be real? Zmec has a phase angle which is arctan (Xmd-1/wCms)/(Rms +2 RMr) =arctan (32.78/2.4)= 85.81 degrees and its magnitude is root (2.4^2
+32.78^2)=32.87 This is based on your data. (32.99 as calculated from the current is very close in magnitude- a good check)
1/Zm =(1/32.87) with a phase angle of -85.81 degrees So Zmot =(11.01^2)/32.87 =3.69 at an angle of -85.81 degrees. IT IS NOT REAL (i.e Resistive) (See Beranek -top paragraph p.85, just before Eq.3.63, as I have pointed out before, or see any text regarding inversion of phasor quantities- Kinsler has an appendix.) IT HAS A REACTIVE COMPONENT. Note that I am using real in the mathematical sense as must be done for vectors or phasors. Using your value of 32.99 for the magnitude of Zmot, then (11.01^2)/32.99 =3.67 which is close to my magnitude using your values. ?
You have added the phase angle which is arbitary and unproven.
1/Zmo
------------- EMPHATICALLY NO. You have given a phase angle of 72.44 degrees with nothing to indicate how you get it. Your proof means nothing. You have still not given a basis for a proof. You have a Zmot =(11.01^2)/32.99 =3.67 ohms and have then applied a pf of cos 72.44 and ignored the reactive part of Zmot You can't simply ignore the reactive part. It makes life easier but is incorrect. You have a value of Zmec +Zr =32.99 calculated from I and U. No phase given. You then get 3.67 ohms. However, this is not 1.109 ohms so you then assume that you need a factor of cos 72.4 degrees to correct it. You have assumed Zmot =1.109 +j0 that it is real. You have no evidence for this but it is convenient. Actually what you have is 8.198^2 =(7.09 +3.67 cos (a))^2 + (3.67 sin(a))^2 What is the angle a for which this is true? This equation can be solved for the cos(a) and the result is -86.2 degrees This leads to Zin =8.197 @ 26.53 degrees From Zmec+Zr = 2.4 +j32.78 =32.87 @ 85.81 degrees, as I calculated it from your data. Zin =7.09 +(11.01^2)/32.87@ 85.81 =7.09 +3.69 @-85.81 =7.09 +0.269 -j3.68 =8.22 @ 26.6 degrees Your E/I n is damned close in magnitude considering all data errors (in fact is due to the difference between I=0.1714 and I =0.172 -within instrumentation and data errors).
However, you will not believe this so why do I bother.
------------- To use your argument I will assume Pin =E^2/Re which is no more incorrect than your usage of Pin= E^2/Ze Then Pin =0.2808 and I^2Re =0.2098 so Pmec +Pa =0.0707 Same reasoning but with a different incorrect value for Pin. If you had calculated the actual Pin based on the current and voltage and the actual electrical pf then you would have the correct Pin. Use of incorrect math as you have done doesn't prove your point. This is particularly so when you have an easy way to check your value for Pmec +Pa.
convenience
------ And again, you have avoided the issue.
--------------- With E and I not in phase then P =(I^2 Ze)* cos (angle between E and I) So it is 0.2425 cos (angle bertween E and I) which is definitely less than
0.2425 = hence my value (based on the angle between E and I of 26.6+ degrees ) of 0.2168(-) As for E^2/Ze -- this is EI =I^2Ze and again, you have not considered the phase angle between E and I. You have calculated values as if they were in phase. Remember power factor- you used it incorrectly where it shouldn''t be used but, where you should use it- you haven't. Who is mixed up?
resistance,
---------- No problem except when you do your calculations, you simply ignore phase and calculate as if it were DC. That basic mathematical error is what I am bitching about- not the equations per se- but your calculations.
-----------------
-------- Not a game- I am serious- It is an exercise in futility. And the history is as stated.
You have said that E and I are not in phase so how do calculations using only the real components give the whole story?. You can calculate: Real part of E = Re* Real part of I +Real part of Eb but you must also calculate: reactive part of E =Re* reactive part of I + reactive part of Eb This you haven't done Instead you have chosen to work with magnitudes only and this is incorrect.
You say that the terms are all resistive. But if E and I are not in phase, then Ze =E/I will have an associated phase angle- it won't be resistive. Can't have it both ways. Also ReI will not be in phase with E.
---------
You have proven nothing except an inability to use your math correctly.
calculation
--------- Please note "Rough approximation" which is more accurate than your "exact" values.>
--------------- Lets see: you calculated Pin -I^2Re =0.2425 - 0.2098 = 0.0328 and then added 0.2098 to both sides to get 0.2425 = 0.2098 +0.0328
3 -2 =1 so 2+1 =3 is the sort of thing that you have done above. Do you think this is meaningful?
----------- Eb = BlU - pure and simple. No pf involved If you are talking about the real part of Eb then as Eb is in phase with U and has the same pf as U. This depends on Zm as given by Beranek - which in this case with your data- is 59.25 degrees.
wMmd -1/wCms
-------- In fact you have given no proof. You have made some incorrect assumptions and thus arrived at this angle. Sorry, what you call a "proof" is invalid. You still have not shown how you calculate this. It appears that you have calculated the correct magnitude of Zmot and as it didn't agree with the value you had measured assuming Ze as real, you put in a bugger factor. which appeared to be cos 72.44 degrees. This you then apply to the Eb calculation where it simply doesn't apply or make sense.
------- Actually it doesn't relate to back emf except in that it does affect the equivalent mechanical impedance. I have done this before, more than once and you simply didn't get it. Basic equations : E=ReI +Eb =ReI +BlU F=BlI =ZmecU where E is the applied voltage, I is the current , F is the force, U is the velocity - all as rms phasor quantities (could be done in instantaneous values given E=Emax cos(wt) but this is the mess that phasors overcome) Zmec =(Rms+2Rmr)+j(wMmd-1/wCms) I =(Zmec U)/Bl E =Re(ZmecU/Bl) +BlU or BlE/Re ={Zmec +(Bl^2)/Re }U giving U =(BlE/Re)/[(Bl^2)/(Re) +Zmec] Note that this is Beranek's Eq.7.1
and Eb =BlU = E/[1 +ZmecRe/(Bl^2)] =EZmot/(Re +Zmot) Also note that F=BlI which is not BlE/Re except under blocked coil conditions.
all properly taking into account the phase as well as magnitude. I have done all the calculations using your data. The measured magnitude of I that you later gave me is a good confirmation of the accuracy of the data and the calculations. The agreement between Eb =E-RI using phasors and BlU is another check. The calculation of Pmec +Pa from Pin-I^2Re gives the same result as cacluation of Pmec +Pa from (Rms+2Rmr)U^2 . Yours doesn't and that in itself should ring a bell- something wrong in the cacluated values.
Since I got his results independently, all I am doing is confirming for myself, how he got there.
----------- Have I? Show that Zin is real and why? . Show that your angle of 72.44 degrees has a basis in fact ( I have shown the contradictions that this does produce)? Tell me how E^2/Ze is Pin when the voltage and current are not in phase (and Zin is not real)?
---------- Beranek's Eq. 3.53 gives E^2/Ze =Pin +j Qin.= Real power in + reactive "power" in
If current and voltage are not in phase then Pin is NOT E^2/Zin as Zin will not be real. You will have to use (E^2/Ze)* cos [angle between E and I (which is the same as the angle of Ze)] You haven't so your pin is incorrect.
----------- Again, you have an incorrect Pin. The equation is correct- your math is wrong
----- I did- correctly.
------------ I did correctly - this is based on a reference power of E^2/Re so it is an approximation to PAE
--------------
I disagree with your power input. That is the main difference. Beranek gives actual efficiency while Small doesn't. You have two separate results. They shouldn't correlate as PAE is not the actual efficiency. If your Pin was correct, then you would not get an efficiency which matches the PAE.. I used a PAE with Beranek using (U^2)Rmr /E^2/Re to get a PAE of 0.49%.You should also get the same result. I used Small as written to get 0.56% I also used Small corrected to w^2Sd^2/Zm in place of Sd^2/M^2 ( as would be found by use of Rmr as above) and got 0.49% Small's value is a PAE which includes an approximation Note that it doesn't use Pin at all.
I used (U^2)Rmr/Pin with the correct Pin and got 0.7% You used an incorrect Pin to get 0.55%
Your value is supposed to be an actual efficiency which should always be higher than the PAE. Correlation between the two is a a fiction as they are two different things. The value should be different than Small's PAE.
Go back to Small and others and read the text. Do the same with circuits texts and learn how to handle vectors correctly. That is all I ask. I am tired of correcting the same errors over and over again. I 'm sorry that you don't appear to have the experience to analyse a very simple circuit model or to run proper checks on your values, preferring to bugger factor the results to fit.
Go and do your homework. I have better things to do
If anyone wants to have input here, or come to Kellys aid :) , they are welcome to do so.
Mr. Kelly I came here in peace, for help with a facet or two concerning back emf, but you chose to make our exchange an effort on your part to show your superiority. I repeatedly suggested you drop the condescending remarks, but to no avail. You repeatedly used your self-proclaimed expertise with phase angles (vector analysis if you prefer) to try to put me down . Well... you are caught in your own web, as phase itself was your primary undoing, and you have apparently tried to dodge all the bullets you care to, and said Bye. So be it. Therefore I shall now summarize my position which shows your errors, but first I'll deal with the errors in your last post, the first one being a real beauty.
BTW, you didn't even have the courtsey to leave the short 11 lines of my Ze analysis intact as I requested (with a TIA). Same for the
9 lines of my efficiency analysis, with the same polite request. This speaks to your intent better than anything I can say. Again, so be it.
This is an example of your lack of insight into the basics here, and a common mistake made by non-thinking neophytes. In this case the real power is not just the I^2 R power going into heat, but is the total of the power creating heat and that moving the mechanical load. You have neglected the mechanical load in your example above, making it another of your errors. Your above analysis does not apply where there is mechanical motion involved. I believe Fitzgerald makes this clear, with transformers vs motors as example.
Let's look at your example as it applies to a loudspeaker motor:
E = 2 = voltage applied R = 2 = resistance X = 2 = reactance Z in = sqrt 2^2 + 2^2 = 2.828 I = E/Zin = 2 / 2.828 = 0.707 Pin = E^2 / Zin = 2^2 / 2.828 = 1.414 watt I^2 R = 0.707^2 * 2 = 1 = power creating heat PF = R / Zin = 2 / 2.828 = 0.707 Pmec = Pin - (I^2 R) = 0.414 watt agreeing with Pmec = E^2/R*PF*(1-PF) = (2^2/2)*0.707*(1-0.707) = 0.414 and Pmec = E^2/Zin * (1-PF) = 2^2/2.828 * (1 - 0.707) = 0.414 and Pmec = (EI) - (EI * PF) = (2*0.707) - (2*0.707) * 0.707 = 0.414
Now Pin = E^2/Zin = 1.414 watt just as I said, and so as to conserve energy (hate to be wasteful) :) Pin = Pout, i.e. electrical power in = power generating heat + mec power E^2/Zin = (I^2 R) + [(EI) - (EI * PF)]
See the EI*PF in there, it is your power generating heat, but we must also move the mechanical load. The difference in my power in of E^2/Ze=2.828 and the heating power I^2 R = is that power.
Also, we see this mechanical power also agrees with I^2*Rel, which was where you made your fatal mistake by using I^2*R, where
Rel = Zin - R = 2.828 - 2 = 0.828
then mechanical power is
Pmec = I^2*Rel = 0.707^2 * 0.828 = 0.414 watt
So... your example without velocity, force, etc need not uhhh... phase us. I don't know if you will comprehend the above, but I've done my best to enlighten you here.
-----------------------------
Now since you have said "bye", I'll assume no more arsing off from you, and give the derivation for the phase angle of 72.44. Note that this is primarily for the benefit of others who may be interested, that likely would be more polite. For instance you said in your last post:
" Your angle gives garbage and you know it but refuse to admit it. I note that you still haven't given the basis, with numbers, for your angle calculation. Give it or shut up. "
OK, but let this be a lesson to you in handling vectors..
cos angle = arc cos (Wl / pi w A^2 Zmec) = arc cos 0.3017 = 72.44 degrees
where Wl = work done on the mec. load per cycle = real work applied - work done to create heat = (I^2 Ze T) - (I^2 Re T) = (0.172^2*8.198*0.004916) - (0.172^2*7.09**0.004916) = 0.0001611 Pi = 3.1416 w = 1278 A = amplitude = v avg T /4 = 0.9 * 0.0574 * 0.004916 / 4 = 0.00006349 Zmec = BlI/v = (11.01 * 0.172) / 0.0574 = 32.99
Giving PFmec = cos angle = cos 72.44 = 0.3017
Just as I said, phase angle is 72.44 degrees, and cos angle = 0.3017.
Note there are several much simpler derivations.
Now back to my Ze derivation, and I shall make it simpler for you this time around:
Effective elecrtical resistance due to mechanical load Rel is Rel = [(Bl)^2 / Zmec+Zr] cos angle = (11.01^2 / 32.99) * 0.3017 = 1.109 Ze = Re + Rel = 7.09 + 1.109 = 8.199
agreeing with E/I, as it must for AC.
Ze = 1.41 / 0.172 = 8.198
Thus proving that PFmec = cos angle = cos 72.44 = 0.3017 is correct, and that your angle of 59.26 is wrong.
Your error is steeped in not allowing for mechanical power as noted above, for example you calculate Pmec+Pa as
" Pmec +Pa =0.2169-0.2098 =0.0071 which should be 0.0079 "
Your magnitude of 0.0079 is wrong, the reason being that your mechanical resistance Rmec is wrong, and this is the crux of your problems. You cannot express Rmec as Rms + 2 Rmr, you must include (Bl)^2/Re. Ring a bell :) (Bl)^2/Re is the motor impedance itself, and is resistive, *however* ... different types of resistances when added arithmetically do not always give reliable results (check the physics books under columb damping or friction), and the *real* Rmec is not as you have uses it where
The above is explainable and derivable in *much* simpler ways, but I chose the above due to your continuing requests re phase angle. The derivation is very clear using Beraneks eq. 7.1.
The bottom line is that your phase angle of 59.26 is wrong. With the correct Rmec you would gave gotten
Phase angle = arc cos 9.955 / 32.99 = 72.44.
Sorry, but as I said, you got caught in your own web of vectors and phase angles, plus your obnoxious attitude helped prevent you from being open-minded.
You replied: " Your specs include the incorrect values that you have calculated. "
The above takes care of your "incorrect values" bit. However I need to make a point re your confusion on power input. Note that Small defines his Pin = E^2/Re as *nominal* power, he does not call it real power. I call E^2/Re applied power. Anyway, nominal is defined as quasi or acknowledged as apart from real. His *reference* efficiency equation is eq. 31, which as I noted is
n = (po/2 pi c) * [(Bl)^2/Re] * (Sd^2/M^2)
n = 0.000544 * 17.097 * 0.5909 = 0.0056 = 0.56%
agreeing with Beranek efficiency as (eq. 3.53 and 7.5)
Pin = E^2/Ze = 0.2425 Pout = v^2 Rmr = 0.001367 n = Pout / Pin = 0.001367 / 0.2425 = 0.0056 = 0.56%
This is *exact* agreement between two of the main authorities, if not the two main ones, and the fact that you question efficiency needs no further comment from me.
BTW, the agreement says volumes about the accuracy of my data, since so many different parameters are involved in the two equations.
----------------------------------------
The following type of error from your last post has been a problem many times:
I said: Zmot = (11.01^2 / 32.99) * 0.3017 = 1.109
Zmot is not my term, it is Kinslers, (I prefer Rel). Nonetheless, you see 0.3017 there? It is the cosine of the angle, i.e. PFmec and it is being used to derive the effective or real part of the mechanical impedance as converted to the electrical side, which is (Bl)^2/Zmec cos angle. Yet you claim
"You have a Zmot =(11.01^2)/32.99 =3.67 ohms and have then applied a pf of cos 72.44 and ignored the reactive part of Zmot "
Cos angle takes care of the reactive part, not ignores it. This is typical of your lack of care in discerning terms, yet you base your following tirade of equations and criticism on your misinterpretation:
" "You can't simply ignore the reactive part. It makes life easier but is incorrect. You have a value of Zmec +Zr =32.99 calculated from I and U. No phase given. You then get 3.67 ohms. However, this is not 1.109 ohms so you then assume that you need a factor of cos 72.4 degrees to correct it. You have assumed Zmot =1.109 +j0 that it is real. You have no evidence for this but it is convenient. Actually what you have is 8.198^2 =(7.09 +3.67 cos (a))^2 + (3.67 sin(a))^2 What is the angle a for which this is true? This equation can be solved for the cos(a) and the result is -86.2 degrees This leads to Zin =8.197 @ 26.53 degrees From Zmec+Zr = 2.4 +j32.78 =32.87 @ 85.81 degrees, as I calculated it from your data. Zin =7.09 +(11.01^2)/32.87@ 85.81 =7.09 +3.69 @-85.81 =7.09 +0.269 -j3.68 =8.22 @ 26.6 degrees "
Then you take it up again a few lines later with your erroneous phase angle:
" Why should Zmot be real? Zmec has a phase angle which is arctan
This type of thing from you has been a problem I tolerated many times without comment, rather than get into a hassle with you about it, all the while with you asking if I bother to read your what you said regarding whatever.
----------------------------------
You said:
" Eb = BlU - pure and simple. No pf involved.
This is emphatically wrong, except at mechanical resonance where force is in phase with velocity. Typical of your lack of understanding some of the basics of what we discussed.
Eb equals BLv times the cos angle between force and velocity. At resonance force and velocity are in phase, and cos angle = PF = 1 and EB = BLv, but above resonance force and velocity are *not* in phase. Eb at 203.4 Hz is
Check Kinsler and Morse on this, especially Morse. They make this clear.
-------------------------------------------
You said:
" Go back to Small and others and read the text. Do the same with circuits texts and learn how to handle vectors correctly. That is all I ask. I am tired of correcting the same errors over and over again. I 'm sorry that you don't appear to have the experience to analyse a very simple circuit model or to run proper checks on your values, preferring to bugger factor the results to fit. "
So who buggers who or what? he he... Just kidd " Go and do your homework. I have better things to do "
You certainly do have better things to do *now*. Let me know if you need extra pencils.. :)
Northstar email snipped-for-privacy@hotmail.com remove the high card to reply
** Let's see, I questioned your interpretation and math.? I also got snide remarks. I repeatedly suggested you drop the condescending
** You were no more polite than I was. I recognised your abilities but also recognised lack of abilities. Should I have said, "Oh, that's fine, thank you", when you made blatent errors, and didn't even try to check them out?
You repeatedly used your self-proclaimed
I snipped nothing. I interjected comments at points and marked these. This doesn't detract from your errors but simply points them out.
---------
**Why?- the example was that of a series R and X. However, it makes no difference. I am interjecting here with ** to point out what I agree with and disagree with.
**so far so good
**incorrect. There is no net power in the reactance. This is fundamental in all texts. Instantaneous power is in during part of the cycle and returned in another part of the cycle. In this case EI* =E^2/Zin = Pin +jQin because you must account for the phase angle. The real power is due to the component of current that is in phase with the voltage--Hence the concept of power factor. That is EI cos 45 =2(0.707)*(0.707) =1 watt The reactive volt-amps in is, in this case, 1va and is a measure of the energy that is being shuttled into and out from the reactance.
.
**the above two lines are OK
**Pin =EI*pf =2*(0.707)*(0.707) =1 watt Pin-I^2 =Pmec =0
Your misunderstanding of the example shows your error. That is basic power calculations for an R-X series circuit. This is the root of the problem. Real power and apparent power are two different things. As for a motor or speaker, sure there is power transferred to the mechanical side- I never denied that. I simply have pointed out the error that you repeated in the example above. Note also that there is reactive input to the speaker and this also gets transferred to the mechanical side but does no work. If you had tried to follow my calculations based on your data, I gave the power and the reactive transferred as well as gave check sums working from U^2(Rmec +jXmec) and these agreed. You don't have this agreement. Why? Because of your erroneous assumptions. Sorry- go back to all your references and READ THEM! Try to understand them. The first is Siskind as it is AC analysis which is the main problem (as shown by your incorrect answer to the example.
Please note that the magnitude of EI =E^2/Ze =I^2(Ze) is the magnitude of the input volt amps- what is sometimes called "apparent power" and the real power is EI(cos angle between E and I). The reactive "power" EI(sin angle between E and I ) does no real work whether in an R-L circuit or in a motor.
Your understanding of this is seriously flawed.
-----------
** even here you are making the mistake of dealing with things as if they were DC. Zin and R are not in phase. Arithmetic subtraction is incorrect. you use Z= root(R^2 +X^2) to get root (4+4) =2.828 because R and X are at right angles Then you simply do arithmetic subtraction and cal the result a resistance. I terms of directions substitue East for R and North for X
2 units east and 2 units north gives 2.828 units NE No problem there but now you want to say 2.828 units NE -2 units E = 0.828 units E That is exactly what you have done. Does it make sense? NO.
------------------- As I said, you won't find what you say in any references. You have given your own interpretation to such references based on what appears to be a desire to use DC analysis for AC situations. If you wish, we can start from the time varying quantities and develop from there- however, surely Siskind does this.
Crude: If Vrms = 0.0574 then A should be 0.0574(root(2))/1278 =0.0000635 (Vrms*1.414/w) In addition, you are assuming that the energy input in a cycle is 4 times that in a 1/4 cycle. Sorry- that isn't true- nor is your analysis. You have also tried to use a simplified and incorrect approach to the power by only considering 1/4 cycle when, it is obvious, as I once pointed out to you, that that is not correct as things are different in the next half cycle as could be seen by drawing the waveforms of e and i with different phase angles, and plotting the product and eyeballing the average.
If e =Emax cos(wt) and i=Imax sin(wt+a) the product ei =(Emax*Imax) cos(wt)cos(wt+a)=(2Erms*Irms)*cos(wt)*[(cos(wt)*cos(a)) -(sin(wt)*sin(a))] =(Erms*Irms)*[cos(a)*cos^2(wt) + cos(wt)*sin(wt)*sin(a)] Over a period or more, Pave =Erms*Irms*cos(a) This is covered in your Siskind (or should be) and he does explain power factor. The reactive component neither deilvers or draws an average power.
-------------
** OK
.
------
** This is, as I suspect, based on your erroneous concept of the real power input
***
E/I
****** You have again gone around in circles. Main problem is that you have assumed Zin is real (and how that can be so when E and I are not in phase, is a quandary) and you have calculated from your Zmech value, an equivalent VA which , in briefer terms is U^2(32.99) =0.1087. Now you use your incorrect E^2/Ze -I^2Re =0.0328 (and that is what you have done above -just thrown in a factor T and worked over 1/4 cycle) So you get 0.0328/0.1087 =0.3017 and call this a pf and carried out your calculations. You have conveniently ignored the fact that if E and I are in phase, Zin will not be real. Also you have ignored the fact that if Zmech is not real, then Zmot is not real and Zin cannot be real. You have calculated Pin on the basis that Zin is real (E and I in phase). You have then decided that the real part of Zin must be 8.198 -7.09 =1.108 ( accuracy not warranted) but (11.01^2/32.99 =3.674 so you have come up with a phase angle of 72.44 degrees to make it fit. The problem is that Zin is not real and the phase angle of Zmot is not 72.44 degrees. I have shown you calculations based on your own data, that give Zmec, Zmot, Ze as well as calculated I that is in agreement with your I.
This mechanical impedance includes the value of Rms as an "equivalent mech resistance as seen by the mechanical system" No problem there. It is used to determine U. However, it is clearly not the mechanical resistance (i.e. the open circuit resistance) which is Rms +2Rmr. Are you saying that your Rms is in error?
** Nonsense. You are still going around in circles based on an incorrect Pin and assumptions which are not warranted.
------
**But the phase angle given for U, using Beranek is arctan (32.78/19.5)=59.26 degrees which isn't 72.44 degrees. Better tell Beranek that he was wrong. Oh, yes, this isn't the value to use as Beranek's Zm is not Zmec for which the values using your data becomes 32.87 at a phase angle of 85+ degrees. This gives Zmot =3.69 @ -85.81 and Zin =8.23 @ -26.56 degrees. You have 8.198 @ angle 0 based on 1.41/0.172 and this magnitude agrees well considering all measurement and parameter errors. Note that I calculated from U is 0.1714 @ 26.56 degrees which agrees well with 0.172 for magnitude.
----------
--------------
**Oh yes, you have calculated an R based on a phase angle of 72.44 degrees and then used this R to calculate the phase angle. try again.
** I have no problem at all with that.
** Again, look at 3.53 E^2/Ze =Wave +jQave The real power is Wave. and you have failed to read beyond that point. Qave is the reactive power which is neither loss nor useful power but is simply a measure of energy shuffled into and out from storage. This is why the concept of power factor arose- to differentiate between the apparent power and the real power. See Siskind. You have been using the wrong real input power all along. Even if you were using the correct input power, the result would differ from Small's reference power as a)Small doesn't use the actual power input but a "nominal power" (which is a better term than "applied power" as power isn't "applied". b) Berenak's 7.5 =U^2Rmr (one side) leads to an actual efficiency of U^2Rmr/Pin where Pin is the actual input power divided. Hence exact agreement should not be expected as the "Power reference" is different. c)In addition, Small does use an approximation as I pointed out. This will also make a difference Change the Pin in Beranek to E^2/Re and change Zm to wM and you will get Small's equation. Try it.
This approximation along with your erroneous input power produces agreement by coincidence so "exact "agreement between your value and another which SHOULD NOT agree is nonsense.
-----------
**The agreement between your magnitudes of I as measured, U as measured, Zmec magnitude as measured and magnitude of Ze as measured, with my calculated values from your data, is better than one could normally expect. That is good. The agreement between your two efficiency figures says volumes- but not in the way that you mean.
Much of your argument and "proof" is based on circular calculations based on incorrect premises. I have pointed out the inconsistencies which you want to ignore (and in the long run, the main thing that happens is that the efficiency is somewhat different than what you think it is). . I have also pointed out the error in assuming Pin =E^2/Ze if E and I are not in phase. You have a phase angle for Zmec which you can't justify and applied it where it shouldn't apply. You have tried to explain it away by coming up with some ficticious R = about 10 ohms by hand waving based on the wrong angle that you have obtained. The facts are that E and I are not in phase, Zin is not real and your phase angle doesn't apply to E=BlU. In addition, your phase angle along with your calculation of Zin as real, leads to serious contradictions.
The truth is that you do not know how to handle vector quantities, or even simple circuit analysis. The model is basically a simple transformer with resistance on one side and a RLC circuit on the other side. It is not difficult. You quote equations but have no real idea of what they mean or how they are obtained. Outside of that , you are good with your meters.
No answer is needed, I've had my say and if you don't even try to think, there is no point going on.
" we have a vector U @ a and a corresponding vector Eb @ a The two are in phase and the magnitude of Eb =(Bl)* magnitude of U That is back emf in a nutshell- there is really no more to it. Assuming a power factor does not give you Eb but gives the real component of it - IF - you have the angle correct. "
My calculation for real back emf is Eb = Blv PF = 11.01 * 0.0574 * 0.3017 = 0.191 where PF = cos angle = cos 72.44 = 0.3017
Please give your magnitude, power factor, and angle for real back emf, as I don't recall seeing your magnitude, at least. TIA
I'll get back to you on your last post after Santa leaves.
------- Actual back emf magnitude is 0.632 volts. If you could measure it, that is what you get. You could measure it by mechanically moving the coil at the given velocity and measuring the open circuit voltage. Not that easy to do. Real component of Eb as opposed to the magnitude of Eb is as you say-- IF you have the correct phase angle.
- which you don't. Eb will be in phase with the velocity. The actual force will be in phase with the current. Neither will be in phase with the reference applied voltage except at resonance. In addition to satisfying the real part of E-IRe =Eb , it is necessary to satisfy the reactive or imaginary part (bad name - but we are stuck with it) as well. I do have a correction to make:
I said: "If e =Emax cos(wt) and i=Imax sin(wt+a) the product ei =(Emax*Imax) cos(wt)cos(wt+a)=(2Erms*Irms)*cos(wt)*[(cos(wt)*cos(a)) -(sin(wt)*sin(a))] =(Erms*Irms)*[cos(a)*cos^2(wt) + cos(wt)*sin(wt)*sin(a)] Over a period or more, Pave =Erms*Irms*cos(a)"
Correction: If e =Emax cos(wt) and i=Imax sin(wt+a) the product ei =(Emax*Imax)cos(wt)cos(wt+a)=(2Erms*Irms)*cos(wt)*[(cos(wt)*cos(a)) -(sin(wt )*sin(a))] =2Erms*Irms*[cos(a)*cos^2(wt) + cos(wt)*sin(wt)*sin(a)]
This reduces to Erms*Irms*[(1-cos(2wt))cos(a) -(sin(2wt)sin(a)] Taking the average over a period give Pave =Erms*Irms* cos(a) as the cos(2wt) and the sin(2wt) terms have a zero average over a half cycle of the fundamental. In the first 1/4 cycle the term {cos(2wt)cos(a) -sin(2wt)sin(a) may be positive and add to the cos(a) term In the next 1/4 cycle they wil reverse sign and subtract from the cos(a) term. Result is that over a half cycle or longer, the effect of these on the average power input is zilch. This is the basis of consideration of the concept of power factor. Also, Use of average values of E and I for power calculations simply don't cut it. That is why rms is used.
I have given these before. The information is there Eb =0.632 @ 59.26 degrees power factor of Eb is meaningless. Power factor of EbI does have meaning. Note that EbI =FU as Eb and U are in phase and F and I are in phase. Neither are in phase with the applied voltage E. I have told you that U is at angle -59.26 with respect to the reference (E=1.41 @angle 0) and that I=0.1714 @26.56 degrees with respect to the reference. This indicates that the PF of EbI is cos(59.26+26.56) =0.0729 On this basis IRe +Eb = (0.1714 @ 26.56)(7.09) +0.632 @ -59.26 =1.41 @ 0 =E applied as it should do.
You have been given all this information.
All that I can add, is that the magnitudes and phase angles should be rounded off to no more than 3 significant digits as the base data doesn't warrant a greater "precision"
Fair enough. All the best to you and yours in this season. Right now, all the above is really unimportant.
You were the instigator of the snide remarks. I suggested several times
early on * that you refrain. You did not, so you got what you gave. As to abilities and errors, the record speaks for itself, and your lack of understanding of fundamentals is clear.
You should be as sharp in applying your math as you are at coniving. I didn't say you snipped. I requested: " The following is for the record, so please do not separate the next 11 lines of my Ze analysis, and leave your comments below them. TIA " Then after you interjected comments (as you call it), I said: " BTW, you didn't even have the courtsey to leave the short 11 lines of my Ze analysis intact as I requested (with a TIA). Same for the 9 lines of my efficiency analysis, with the same polite request." Then you imply I mispoke if not lied with your "I snipped nothing" remark. Your interjection was inconsiderate and rude. Your "I snipped nothing" remark was deviousness.
Bullshit. It's in plain english above. You offered the analogy as example (your word, see above) of my input power magnitude to a loudspeaker being wrong (see above). You made an absolute error in giving an analogy.
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For the record, here is my rebuttal to your analysis intact, where I noted:
"Let's look at your example as it applies to a loudspeaker motor:"
E = 2 = voltage applied R = 2 = resistance X = 2 = reactance Z in = sqrt 2^2 + 2^2 = 2.828 I = E/Zin = 2 / 2.828 = 0.707 Pin = E^2 / Zin = 2^2 / 2.828 = 1.414 watt I^2 R = 0.707^2 * 2 = 1 = power creating heat PF = R / Zin = 2 / 2.828 = 0.707 Pmec = Pin - (I^2 R) = 0.414 watt agreeing with Pmec = E^2/R*PF*(1-PF) = (2^2/2)*0.707*(1-0.707) = 0.414 and Pmec = E^2/Zin * (1-PF) = 2^2/2.828 * (1 - 0.707) = 0.414 and Pmec = (EI) - (EI * PF) = (2*0.707) - (2*0.707) * 0.707 = 0.414 Now Pin = E^2/Zin = 1.414 watt just as I said, and so as to conserve energy (hate to be wasteful) :) Pin = Pout, i.e. electrical power in = power generating heat + mec power E^2/Zin = (I^2 R) + [(EI) - (EI * PF)]
1.414 = (0.707^2*2) + [(2*0.707) - [(2*0.707 * 0.707)] = 1.414 See the EI*PF in there, it is your power generating heat, but we must also move the mechanical load. The difference in my power in of E^2 / Zin= 1.414 and the heating power I^2 R = 1 is that power. Pmec = (E^2/Zin) - (I^2 R) = (2^2 / 2.828) - (0.707^2 * 2) = 0.414 watt Also, we see this mechanical power also agrees with I^2*Rel, which was where you made your fatal mistake by using I^2*R, where Rel = Zin - R = 2.828 - 2 = 0.828 then mechanical power is Pmec = I^2*Rel = 0.707^2 * 0.828 = 0.414 watt
End of rebuttal.
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I shall ignore your non-pertinent interjections in my rebuttal analysis that follow, where you refer to a resistor in series with an inductor rather than a speaker circuit, which must contain provision for power to drive the mechanical and air load. You are scraping the bottom of the barrel here.
My next comments are at *****
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Instantaneous power is in during part of the cycle and returned
*****
End of ignoring your non-pertinent comments.
??? I offered no references to to a resistor in series with an inductor. You are mixed up here.
You need to learn to use analogies that apply.
This is a an example of how you rely on math, at the expense of common sense, which is at the root of your errors. My equation is written to portray what actually happens. Follow through here and learn. I gave amplitude, i.e. distance the mass travels from equilibrium to an end point of motion as:
A = amplitude = v avg T /4 = 0.9 * 0.0574 * 0.004916 / 4 = 0.00006349
First, noting that average velocity is RMS velocity times 0.9, and that T is the time taken for the mass to travel one full cycle, which is
4 quarter cycles, then amplitude (distance traveled by the mass) in a quarter cycle of straight line motion in one direction must be average velocity v avg times time taken to travel that quarter cycle = v avg T/4. Like traveling at an average of 50 mph for 2 hours, then distance traveled is 100 miles. Not that don't know such, but rather that your reliance on math obscures how to apply it in usable fashion. Your equation is correct, but non-intuitive, and IMO more prone to cause error in application.
You've displayed this misunderstanding of application before. Take I^2 R power for example. Even though the voltage and current change sign each half cycle, the square of the current tines resistance (power) is always positive.
Which college did you eyeball at? :)
Wrong. The reactive component (such as an inductor) draws power from the source, then delivers it back. You need to learn the basics. On the other hand in a sense, this has become entertaining.
No, and this is the most important and critical to our differences. You have failed to consider that the motor resistance itself requires power from the source to overcome. Most all our differences hinge on this fact.
First I muct acknowledge an error in stating my Rl equation, where I mis-noted Zmot as real. Zmot is real only at mechanical resonance.
Kinsler and most others show Zmot = (Bl)^2/Zmec, which is an impedance, except at resonance. If away from resonance, phase must be considered, such that Zmot = (Bl)^2/Zmec PFmec = (11.01^2 /32.99) * 0.3017 = 1.109. Then the impedance Ze seen by the source is Ze = Re + Zmot = 7.09 + 1.109 = 8.199, just as I said before.
You can now have fun with your angles, but it won't change this.
Bullshit. Phase angle is arc cos Rmec/Zmec, where the equivilant resistance Rmec is given in physics books as the ratio of energy expended on the mechanical load per cycle (work done per cycle) to pi w A^2, such that Rmec = Wl / pi w A^2 = 0.0001612 / (3.1416 * 1,278 * 0.00006349^2 = 9.955
otherwise effective Rmec is just Fnet/v = 0.5714/0.0574= 9.96
It is NOT Rme+2Rmr = 2.4 as you claim. When you realize your error on this, it will clear up 98% of the problems.
Then phase angle = arc cos 9.955/32.99 = 72.44 andwhere Wl = pi Fnet max A = 3.1416 * (sqrt 2 * 0.5714) * 0.00006349 = 0.0001612 and net force Fnet was given before.
Concerning effective resistance, how about referring to Halliday, Serway, Hartog, Morse, Villchur, Thompson, Shebana, and others before doing another phase angle speil. You will be in error until you clear this up.
I addressed your "going around in circles" remarks previously, but you did not consider that I might be correct.
A final attempt to solve the problem regarding (Bl)^2/Re. However it will not help, unless you think the following through as you go, and without getting caught up in the phase bit.
First, sorry for the caps, but:
THERE WILL BE NO AGREEMENT UNTIL YOU ADD A TERM TO YOUR INPUT POWER TO PROVIDE POWER TO OVERCOME THE MOTOR IMPEDANCE (Bl)^2/Re. BACK EMF CREATES AN IMPEDANCE THAT REQUIRES POWER FROM THE SOURCE TO OVERCOME.
Here is where the confusion lies (trying to be polite here... :) You cannot just toss (Bl)^2/Re out of Beraneks eq.7.1 as you have to derive power input. It is an impedance caused by back emf that must be overcome. Consider this closely this time, please:
impedance = force/velocity, force due to back emf = Bl Eb/Re, then impedance = Bl Eb/Re / v, but Eb = Blv so impedance = Bl Bl v / v Re = (Bl^2)/Re = impedance due to back emf
Sorry, but again, this is an impedance requiring power from the source to overcome. You cannot just toss it out. Consider the following, at steady state:
Looking at the denominator in 7.1, which i call electromechanical impedance Zemec, and noting it the electrical effect as well as the mechanical, we can factor out the electrical part (Bl^2)/Re with the electrical power factor Re/Ze = 7.09 / 8.198 = 0.8648 leaving the *mechanical* impedance as
Now... this is an impedance and we find the real part Rmec with the cosine angle between force and velocity = cos 72.44 = 0.3017 = electrical power factor PFe
This is to correct 2 mis-wordings at *** in my analysis, where at one point I wrote electrical power factor PFe (should heve been mechanical power factor PFmec), and at the other point I wrote PFe (should have been PFmec). The magnitudes are correct, just mis-labeled. Sorry.
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Looking at the denominator in Beranels eq. 7.1, which i call electromechanical impedance Zemec, and noting it the electrical effect as well as the >mechanical, we can factor out the electrical part (Bl^2)/Re with the electrical power factor Re/Ze = 7.09 / 8.198 = 0.8648 leaving the *mechanical* impedance as
---------------- Actually the analogy is apt. You have a basic misconception. \ The only average power input is equal to the power dissipated in the resistance, the mechanical resistance and in the air load - that is in Re, Rms, and Rmr. There is no average power into the mass or the spring. These are energy storage elements as are inductance and capacitance of an electrical circuit.
Morse and Lahnakoski explain how there is an additional resistance, due to electrical parameters. Morse wrote 7.1 in 1936, 18 years before Berenak, and his book would be valuable to anyone as enlightment into
7.1. Morse helped make MIT into an acoustics research center early on. Beranek was there also and he integrated the electrical and mechanical in his equation. It's not immediately apparent, but it's there.
I sense a measure of respect between us and let's not say you are in error per se, but rather that the problem is your power input magnitude is low to match your output power magnitude. This is because you are working with the mechanical, and most all your data is correct, so far as the mechanical goes. I see this as a loss to both of us, as well as to anyone who has been following our exchange, and there is little point in us continuing to claim the other is wrong. We simply are working two different theories, without integration.
I'll summarize very briefly here. You give input power as 0.217, but per Beraneks eq. 3.53 dynamic power is
Pin = E^2/Ze = 1.41^2 * 8.198 = 0.2425 watt
Then noting we agree that acoustic power out is
Power out Pa = v^2 * Rmr = 0.0574^2 * 0.415 = 0.001367
Then per Small as power in = power out / efficiency where his eq.31 gives efficiency n = 0.00564 (and this efficienct magnitude agrees with Beranek)
Pin = Pa/n = 0.001367 / 0.00564 = 0.02424 watt
These two magnitudes of power input are not equal by coincidence.
I'm sorry we are at impasse, and perhaps you may want to look into the works of Morse, Lanakowski, and the Thiele/Small works.
You are welcome to get back to me at any time, and again, best to you and yours in the Holliday season.
----------- There is a resistance which is the equivalent resistance of the electrical parameters and this is taken in in Beranek's 7.1. I have never denied this. Similarly, as seen from the electrical side, there is an equivalent resistance due to the mechanical parameters. This is Zmot =(Bl^2)/Zmech However, the parameters that you have measured -that is Re, Rms and (2)Rmr represent all the dissipative elements. There are no others. Equation 7.1 is not rocket science and is readily determined, as I have done, from Berenak's 3.59 and 3.60 which describe the basic electrical and mechanical equations in steady state and are simultaneous equations- that is- they are interdependent. How the (Bl^2)/Re term appears, and why, is very apparent.
I see you don't intend to agree with Small, Beranek, or even me :)
OK... Perhaps this will help... and I shall reply at minimum, since as noted before, it is pointless to proceed in detail until this is cleared up.
(Bl)^2/Re is a mechanical impedance due to electrical origin. The back emf Eb creates a mechanical force and a MECHANICAL impedance. (I capitolized for emphasis, Morse italicizes). It requires power from the electrical source to overcome and only E^2/Re contains enough power to overcome (Bl)^2/Re plus the resistances Re, Rms, and 2Rmr. E^2/Ze cannot do so, and there is very good reasoning and math for this. Note the power overcoming (Bl)^2/Re never reaches the mechanical stage, it does not get past the *electromagnetic* stage. Again, only E^2/Re can supply this power, along with the other needed. Beyond this I am getting into propritary data.
If you want me to get you a copy of Morse's book, send me your address, and also while acquiring a copy I'll send you his partinent equations.
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You say below:
Yes, you noted Eb previously as 0.632, then stated " the real part of Eb is 0.323 " which I assume you derived as 0.632 cos 59.26 = 0.323.
Then by the motor rule, where mechanical power = I * Eb , where of course Eb is real:
Pmec + Pa = I Eb = 0.172 * 0.323 = 0.0556
This is not 0.0079 as you have stated.
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Also you say below: " U=0.632/11.01 =0.0574 (@ 59.65 degrees) "
Yes, U = BlU / Bl = U
I am inclined to agree. :)
Northstar email snipped-for-privacy@hotmail.com remove the high card to reply
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Per Siskind cos angle = R/Z plain and simple, nothing more or less to it.
EI * Re / Ze = 1.41 * 0.172 * (7.09 / 8.2) = 0.2097
But this is power into heat I^2 Re = 0.2097
and you have no power left to overcome mechanical resistances.
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