Motor torque and back emf

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typo Re/Ze = 0.201 at fc
Bill W.
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----- Original Message -----
Newsgroups: alt.engineering.electrical Sent: Tuesday, December 23, 2003 4:23 PM Subject: Re: motor torque and back emf

----------- Derivations for the phase angles ?? I used standard comlex number representation as I indicated. If I say v=A+jB then the phasor (not actually a vector) has sides A, B and hypotenuse sqrt(A^2 +B^2) which is the "magnitude" and the angle is inverse tan (B/A) No deriviations other than this general one are needed. I let my calculator do the conversion work as it has the capability to do this directly. As for missing magnitudes -where?. - I gave the magnitudes wherever necessary and in some cases where it wasn't necessary. I did not and will not give magnitudes to equations but only to numerical calculations using those equations. -----------------------

----------- E-IRe =BLv is the fundamental circuit equation that must be satisfied. BLv and E-(IRe) must be the same. If not there is something wrong. You had concerns here. That is why I pointed out that use of phase as well as magnitude information is necessary -and, in that case, the relationship is correct as shown in my calculations. ---------

----------
----------- I read what you said. I don't think that I am mixed up. With no motion the force is indeed EBL/Re as this corresponds to the electrical equivalent of a short circuit (Eb =Blv=0) The force causing motion -i.e. the actual force is simply (Bl)I or the Lorentz force. The E(Bl)/Re combined with the (Bl)^2/Re is a current source equivalent. I showed how this comes about. It has nothing to do with power factor. There appears to be a terminology problem here. By net force, do you mean that component of (Bl)E/Re that is in phase with the velocity (and contributing to average power) ? That is true. Is it a real force acting on the mechanical system? No. The real force is the Lorentz force and the component of this which is in phase with the velocity is the force producing mechanical power. The Lorentz force is given by (Bl)E/Re -(Bl)^2/Re ( and I showed this)

------------- Small is correct- and power is indeed expended. What is happening in what he describes is that the motion of the cone will induce a voltage in the short circuited coil and this voltage produces a current in the shorted coil (try it). The current will produce a Lorentz force which will oppose the motion. You sense this as an increased mechanical resistance.Nothing new about this - just plain ordinary regenerative braking. The mechanical energy that you put in is being dissipated in the coil resistance - i.e. electrically. It appears as a mechanical resistance because of the force/current and voltage/velocity relationships, and can be treated as such. However, its origin and the energy involved is in the electrical resistance and not part of the actual(as opposed to the manifested) mechanical resistance. That is why I have separated this resistance from the actual mechanical resistance for the purpose of calculating actual mechanical power. To look at it from another viewpoint, Small (J.Audio Eng. Soc. Vol20, p383-95 June 72) and Berenak give models in which all elements are refered to the acoustic side. That doesn't make the electrical and mechanical elements into actual as opposed to equivalent acoustic elements any more than referring them all to the electrical side makes the mechanical and acoustic elements actual R,L and C components. >

---------- your equation is correct for the "average" velocity as calculated from the displacement. However, the average and rms values are different. If rms values are used in one place then rms values must ve used throughout. The difference between the average and rms is a factor of 1.11 for a sinusoid.
Given a sinusoid x= (Xm)sin (wt) where Xm is the peak magnitude and w is 2*pi*frequency What you give for the velocity is 4f*Xm OK The actual velocity is dx/dt =wXm cos(wt) with a maximum velocity 2*pi*f*Xm rms value =(Root(2))*pi*f*Xm =4.44*f*Xm This is the bugger factor. It will be different for a different wave shape.

cannot
---------- If the maximum deflection of a sinusoid of frequency f is Xm, its rms magnitude is Xrms =Xm/root(2) and the rms magnitude of the velocity is Vrms =2*pi*Xrms (phase shift of 90 degrees with respect to displacement). Similarly the rms acceleration will be 2*pi*Vrms (180 degrees out of phase with the displacement). Isn't this an easier way to go ad ensuring all values are rms.

------------- I did all calculations on the basis of rms values. I never use average values for calculating power in an AC situation -it doesn't work except for square waves or DC. -That is part of the reason why the rms concept was established. The only reason that I can think of for the agreement in numerical values is that this average velocity or some other average value was used in determining Bl . To calculate power due to a current in a resistor, The use of I^2R for DC where I is the average current, is correct. In the case of AC, it was recognised (about 100 +years ago) that the use of average power didn't work. One could (correctly) integrate the instantaneous power over a cycle and take the average. This led to an average of [R(Imax)^2]/2 Out of this the rms concept was developed. Irms =Imax/root(2) so that the average power was given by (Irms^2)R. That is the rms value is the current which produces the same heat as a DC current of the same magnitude. It is applicable to all waveforms (different bugger factors) The power factor concept came about when it was recognised that only the component of current which is in phase with the voltage produced average power. The remainder was called volt amps reactive (var) Because of the nature of the in-phase/out of phase components of currents and voltages, an existing mathematical technique was adapted for calulations - that is a double barrelled or complex number arithmetic - and further on into Laplace transforms signal processing methods. Just tools but useful tools. -------------

----------- Understood. My contention is that the difference between the actual mechanical impedance and the equivalent mechanical impedance must be clear even if they are combined for some calculations .>

--------- Go to a general engineering dynamics text. One of these should cover it - likely using free body diagrams rather than the equivalent circuit approach which Small and Berenak apparently used. It is pretty straight forward- as you have indicated, the mass becomes a dominant factor.
By the way Bullock, T.S. gives an analysis which parallels work by Olson and Locanthi(sp?) AES 1986 preprint 2841 (H-2) It is shown on www.hal-pc.org/~bwhitejr/ There is an error where Sd rather than Sd^2 is used in the Re term referred to the acoustic side. As the U of A library was closed over the holiday period, I was unable to get at some references that I wanted. In addition, all copies of Kinsler were out until the 15th of Jan. Where I live is too far from a library with the desired journals, etc. I'll check with a friend in town who taught mech eng'g. and he may have a reference. >

-------- It doesn't bug me. I do not have your practical experience in the area of loudspeakers and acoustics. I bow to you in this respect and can learn from you in this regard -not so much the theory but the application of the parameters per se in practical enclosure design. I do know circuit analysis and electro-mechanical energy conversion (which this is) and, in these areas and I have reason to believe that I have a better understanding of such analysis and modelling than you do.
Some of what we have been at loggerheads about is terminology but some is fairly fundamental.
Take care
Don Kelly snipped-for-privacy@peeshaw.ca remove the urine to answer
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Thank you for the references, and we shall see what we shall see. :)
We will have only hassles until we settle the role of (Bl)^2/Re = 8.89. You stated in effect that no power is required to accelerate the mass, and your mechanical power equation says so, where you give mechanical power at 227.4 Hz as Pmec = 1.664 * 0.066 * 0.0492 = 0.0054 watt
or (as equated to my notation of power dissipated into the suspension resistance)
Pmec = v^2 * Rms = 0.0493^2 * 2.23 = 0.0054 watt
Note Rms = mechanical resistance of the suspensions, so your equation shows the power dissipated into this resistance, with no power shown as dissipated into the (Bl)^2/RE = 8.89 resistance. Note Small's term for (Bl)^2/RE is Rme. My view is that (Bl)^2/RE *must* be added to Rms to calculate the mechanical power, i.e Pmec = v^2 * [ Rms + (Bl)^2/RE ] = 0.0493^2 * (2.23 + 8.89) = 0.027 watt
agreeing with Halliday and convention
P = F v cos angle = 1.75 * 0.0493 * 0.313 = 0.027 watt
where angle = arc sin Xmec/Zmec = 71.78 then cos angle or PF mec = 0.313
Now hang on here please, as 0.313 may not agree with your current magnitude (as I recall it was your original magnitude however), but *bear with me* without getting into this aspect at the moment, i.e. "wait for it" :)
First, try looking at the physical driver so: The neck of the coil former equates to the usual motor's shaft. In other words, in the usual motor, the driven armature is attached to the shaft, and the shaft drives the load. Here the driven coil/armature is attached to the coil former and it drives the load, i.e. the cone and air mass. The point being, the cone and air mass ***is*** the load, it is not a part of the motor. As such then, at 227.4 Hz the mass load will require power to be accellerated, since the mass gets a free ride ***only*** at resonance, not at 227.4 Hz.
Now the net force magnitude in your above equation is
Fnet = 1.664 * 0.066 = 0.11 or v *Rms = 0.11
I maintain net force is v * [Rms + (Bl)^2/RE] = 0.548
giving Pmec = Fnet * v = 0.548 * 0.0493 = 0.027 watt
and not (as you note) 0.11 * 0.0492 = 0.0054 watt.
--------
Noting respect for Halliday, I shall now stay with him, and show that net force is indeed 0.548 and not 0.11. Starting, with scalar (energy-based) magnitudes:
Halliday:
Work = delta KE
Where kinetic energy KE is
KE = 1/2 m v^2 = 0.5 * 0.0253 * 0.0493^2 = 0.0000307
i.e
Work = delta KE = 1/2 m v^2=0.5*0.0253*0.0493^2 = 0.0000307
with mass and velocity measured, and starting from zero velocity.
Halliday:
Fnet = work/distance = w/d = 0.0000307/0.0000543 = 0.566
for distance traveled during 1/4 cycle, note.
This is close enough to convention, and to that which I have given earlier as
F net = F cos angle = 1.75 * 0.313 = 0.548 ************
Note carefully between *********** here, please
*** The net force expression *includes* (Bl)^2/Re so ***
F net=(v Rms)+(v (Bl)^2/Re)=(0.0493*2.23)+(0.0493*8.89)=0.548
This can be written as
Fnet = v * (Rms + (Bl)^2/Re) = 0.0493 * 11.12 = 0.548
Showing the damping coefficient or damping constant is based on Rms ***plus*** (Bl)^2/Re at 227.4 Hz, so that again, at 227.4 Hz
Pmec = v^2 * [Rms + (Bl)^2/Re] = 0.027 watt
again agreeing with Halliday and convention
P = F v cos angle = 1.75 * 0.0493 * 0.313 = 0.027 watt
and not your mechanical power of
Pmec = 1.664 * 0.066 * 0.0492 = 0.0054 watt
**************
Now to Halliday again:
Halliday (and Serway) state ***regarding forced oscillations***
F max x max = --------------------------------------------- sqrt [ m^2 (w^2-wo^2)^2 + (b^2*w^2) ]
solving for b (damping coefficient)
| F max^2 | | ----------- - [ m^2 (w^2-wo^2)^2 ] | | x max^2 | b = sqrt| -----------------------------------| = 11.05 | w^2 | agreeing with, Rms + (Bl)^2/Re = 11.12
We see the damping term is not just Rms, but instead must include (Bl)^2/Re, as I have noted all along.
Then, yet again, giving mechanical power at 227.4 Hz of
P mec = v^2*[Rms+(Bl)^2/Re] = 0.0493^2*11.12 = 0.027 watt
and not your
Pmec = 1.664 * 0.066 * 0.0492 = 0.0054 watt
----------
Since you appear to respect Small as well as Halliday, note that he gives
(Bl)^2/Re Rat = Ras + ------------ Sd^2
These are acoustic magnitudes. Converting to mechanical by multiplying by Sd^2 gives
Rmec = Rms + [ (Bl)^2/Re ]
Again the damping term must include (Bl)^2/Re and again mechanical power is
Pmec = v^2 * [ Rms + (Bl)^2/RE ] = 0.0493^2 * (2.23 + 8.89) = 0.027 watt
If this doesn't convince you, I can show you the same thing with Serway, Kinsler, and Beranek as I have previously done.
Another term is used to make a power equation workable at resonance. Also the resistive term (Bl)^2/Re can be related to the the retarding force of the load and back emf. We may consider these later if this is settled, as this has likely been a bit frustrating for both of us. Oh yes, one more thing, as Columbo used to say... Could you please be explicit and give magnitudes in your response? Or as Jack Webb on Dragnet said.. "Just the facts Mam, just the facts".
Bill W.
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says...

---------- Since (Bl)^2/Re is directly a result of the coil's electrical resistance, power in this term is not mechanical power. This is a representation of the electrical resistance as seen from the mechanical side. It does have an effect on the behaviour of the system. It is also very clear where it comes from. I have shown this. As to what Halliday actually says- I do not know. What you have quoted, so far, of Halliday and others does not counter my argument.

--------------------- There is no fundamental difference between the speaker as a motor and a conventional motor except that the armature in the speaker moves linearly in and out while that of the conventional motor rotates. (It is also possible drive a DC motor with a low frequency AC source and have oscillatory motion in which mass plays an important part). There are other devices than speakers which use linear motors. Even a doorbell is one such device. The principles of operation are the same.
All I am working with is the defining equations of the device. If these are wrong, you were asked to say where they are wrong.
Mass will be accelerated - definitely- at all frequencies unless the cone is clamped so it wont move. However, the component of the force associated with the acceleration of the mass is 90 degrees out of phase with the
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This is a *non-answer*, just bull and more bull. Your angle of 14.46 is wrong. The correct phase angle between voltage and current is
Phase angle = arc cos Re/Ze = arc cos 5.78/6.21 = 21.44 deg.
It is not 14.46 degrees as you state. I use here ***measured values*** of Re and Ze, and you have altered them to support your argument. This is bull and is not acceptable.
Bill W.
++++++++++++++++++

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Yes, but in essence you get 3. :)
Really, then why do you call b = Rms only at 227.4 Hz?

I assume you mean x max, i.e. displacement from center equilibrium, or amplitude?

Mr. Kelly, I regret you are confrontational and inflexible re your error, but that is your right. I had hoped for better than that which is transpiring and tried to avoid confrontation, but you leave me no other choice than to walk away. I have stuck around in the hopes we may eventually get to another stage where I would appreciate input. However, it appears you feel you operate with a direct line from the Heavens... Why do you not just admit your major error, redo your analysis, and move on? Or is it that you have a problem with BLI at 227.4 Hz? :)
Bill W.
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says...

indicated
can
---------- Sorry, the over-estimation was on my side- I expected more sophisticated mathematical and physical understanding. -----------

----------- As I asked - did you figure out how Halliday got this equation? Apparently not. I don't disagree with it as have checked it and it is absolutely correct. In addition, this equation, proves nothing. It is derived directly from an equation which I gave.
----------------- -

wrong.
------------- True and I have used basic electrical (not electronic) and mechanical theory. CORRECTLY. I worked directly with the starting equations and laid out all steps in the analysis. Did you even try to follow these steps. Can you use comlex numbers? -------------

in
except
calculated
velocity
------------ Did you measure displacement or velocity.? I saw the equation for extrapolation - fair enough, but with the parameters Re,E, Rms, K, M,Bl
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says...

No, it is from Hallidy, Resnick, and Walker Fundamentals of physics, sixth edition, and given re forced oscillations. Serway and others give the same, and proves you wrong. Here it is again, along with your reply, which *** says it all ***.
| F max^2 | | ----------- - [ m^2 (w^2-wo^2)^2 ] | | x max^2 | b = sqrt | -----------------------------------| = 11.05 | w^2 |
agreeing with, Rms + (Bl)^2/Re = 11.12
You replied:

----------------
I said:

You replied:

Really... I said I measured, you reply asking ask if I measured... We can take a break if you wish, Mr. Kelly.
----------------
Regarding accuracy of measurements, you stated:

Mr. Kelly, we have a rather extensive set of lab instruments. This includes 3 Fluke, 2 Simpson, and 2 HP voltmeters, factory calibrated. These were checked against each other to insure accuracy at the start of my measurements. They all read the same, except one Simpson was very slightly off and of course was not used. The data was taken with *two* meters monitoring (a Fluke and a Simpson), and a minimum of five measurements made for *each* magnitude, to insure repeatibility and therefore accuracy. I hope your medical doctor uses this kind of precaution and care. :).
-------------------- --------------------
Mr. Kelly, please consider the following CAREFULLY and with an open mind:
Also if you will, please leave the following between the ++++++'s all together (reply below the second +++++'s) as I have stated my case herein. TIA
++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++
You stated:

Without complex notation, in the most simple form:
Ze = E / I = 1.41 / 0.227 = 6.21
EXACTLY AS MEASURED, not 6.07 as you calculate.
Now you ask if I can do complex numbers. So then, to please me' Lord. :)
Ze = Re + j Xe = sqrt (5.78^2 + 2.27^2) = 6.21
Again agreeing with measured impedance of 6.21.
where Xe = Re (tan angle) = 5.58 * .393 = 2.27
and angle = arc cos Re/Ze = arc cos 5.78/6.21 = 21.44 deg.
Again.. this uses accurately measured magnitudes, and is clearly basic theory re Fitzgerald. Note also that your incorrect phase angle re voltage and current of 14.46 degrees invalidates your analysis.
Now............ if you continue to use your above theory, i.e. "Ze =5.78 +0.1-j1.517 = 5.88+j 1.517 which leads to a magnitude of root (5.88^2 +1.517^2) =6.07 ohms and a phase angle of arctan 1.517/5.88 .46 degrees Or, using arccos (5.88/6.07) .36 degrees." please outline and give ALL magnitudes and ALL equations for EACH and EVERY term, as I have done. In other words, please return the courtesy I have shown you here, as I am getting ***VERY*** weary of seeing your numbers without accompanying substantion beside them. That's as in ***VERY*** weary.
++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++
Again, please leave the following between the ++++++'s all together (reply below the second +++++'s) as I am now stating my case re the mechanical side herein. TIA
+++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++
You stated:

Your Zmec of 33.82 and angle of 86.22 are wrong, again in most simplistic terms:
Zmec = Fapplied / velocity = 1.75 / 0.0493 = 35.50
Then in complex notation, again to please me' Lord :)
Zmec = Rmec + j x mec = sqrt (11.12^2 + 33.75^2) = 35.53
where Xmec = Rmec (tan angle) = 11.12 * 3.03 = 33.74
close enough to our agreed x mec of 33.75
where angle = arc cos Rmec/Zmec = arc cos 11.12/35.53 = 71.76 deg.
And again, if you continue to use your above theory, i.e.

please outline and give ALL magnitudes and ALL equations for EACH and EVERY term, as I have done above. In other words, please return the courtesy I have shown you here, as again I am getting ***VERY*** weary of seeing your numbers without substantion beside them.
++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++
You said:

I assume here you that by Re you mean (Bl)^2/Re. If so, sloppy, but it does not matter *what* you call (Bl)^2/Re, it is part of the resistive damping, i.e.
Rmec = Re + (Bl)^2/Re = 11.12.
Can you not see this, and that including (Bl)^2/Re in your Zme (my Zmec) which you state as
gives the correct Zm or Zmec as noted above of
Zmec = Rmec + j Xmec = sqrt (11.12^2 + 33.75^2) = 35.53
----------------------
I ask:
"DID YOU EVEN PLUG IN THE NUMBERS INTO THE HALLIDAY EQUATION, AND SEE THAT IT WORKS AT ANY FREQUENCY, THEN TRY YOURS WITH Rms ONLY AT 227.4 HZ?"
You replied

Yep, about as clear as mud. Again you are yakking without support of numbers. Here, do this please for 227.4 Hz: Show Halliday's damping equation plugging in the numbers and show what you get. Do it as I have done, i.e. "outline and give ALL magnitudes and for EACH and EVERY term"
-------------
You stated:

I believe you ask earlier about this, and I've been there and done that. At 227.4 Hz:
v max = w A = 2 pi f A = 1428.8 * 0.0000543 = 0.0775 v max = pi/2 * delta x / delta t = 3.14/2 * 0.0000543 /0.001 = 0.0775 v max = F max / Z mec = 2.75 /35.53 = 0.0774 v max = pi/2 * v avg = 3.14/2 * 0.0493 = 0.0774 v max = a t = 70.44 * 0.0011 = 0.0775 v max = a max /w = 110.65 / 1428.8 = 0.0774 v max = pi/2 sqrt (2 KE/m) = 3.14/2 sqrt (2 * 0.0000307/0.0253) = 0.0774
finally, per Mr. Newton, with F = ma = 0.0253 * 70.44 = 1.78
v max = F/m * t = 1.78 / 0.0253 * 0.0011 = 0.0774
Does that suffice?
Note all correlate at 0.0774 to 0.0775. Are you impressd now with my measurements? I am. :)
-----------------
You said:

Sorry, but your Ze of 6.07 is based on your misapplication of my data, as proven above. No one who reads the above would agree with your magnitude of 6.07, rendering it as incorrect. Bull? :)
I suppose you heard on your direct line from the Heavens that if the calculations don't match tha measurements, then you should change the measurements?
Reminds me of the Boyles method of weighing a hog. You place the hog on a see-saw plank, pile rocks on the other end until balanced, then carefully guess the weight of the rocks. :)
----------------
You said with reference to me describing my measured data as tools:

Finally I see what may be your problem here. No, they are where the rubber meets the road. They are reality, that which is indisputable, if measured properly. That which proves an equation valid or not. Apparently to you they are secondary to your calculations. I now see why you have trouble accepting a result you get when plugging numbers into, say Halliday's equation.
-----------
You said:

There you go again...
------------
You said:

You are welcome. Thank you for your time as well.
Bill W.
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------------ That depends on what F is used. For example, If the cone is driven mechanically and the Fmax and Xmax are measured, the damping can be calculated using this expression. If for that situation, the electrical circuit is open- then the damping will be strictly due to the mechanical resistance (i.e. Rms). If the coil is shorted, then the effect of the electrical side will come in and the damping will be Rms +(BL)^2/Re. When energised from the electrical side and current produces the force- then the latter term will apply. I agree with this.
Somehow, I don't see where something that I agree with proves me wrong.
As for the development of this expression for the damping term. Again you are simply quoting equations without consideration of their physical basis- so and so says such and such. They are correct but you can only assume that. Rather than just assume (as you did) that the expression was correct, I derived it. That is what I was getting at. I can simply use F' =(BlE/Re) =[(Bl)^2/Re + Zm]V where Zm= Rms +j(wM-K/w) This is an expression I have shown before - it is useful. Then noting that wo^2=K/M and that, for a sinusoid, Vmax=wxmax where xmax is the maximum excursion. F'max/xmax = F'rms/xrms = w F'/V Now do some algebraic manipulation and the Halliday expression results with (Bl)^/Re +Rms replacing b Halliday , Serwick, etc simply did this very thing. Nothing new or exciting-just a re-arrangement of an equation. You can do that as an exercise. ------------- > You replied:

--------- I stand corrected. --------------------

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You didn't leave my statement intact.. Your original answer to the above was "sweetness and light to you too"
Anyway.. You have NOW finally obtained one of the defining texts on the subject, and found a way to try and sidestep your mistake. OK... do it the hard way.

Really. *NOW* you say that if the cone is driven mechanically at open circuit, the damping is strictly due to Rms, but if energised electrically the damping is Rms+(BL)^2/Re. Since you have rejected the Rms+(BL)^2/Re term, why didn't you tell me long ago that you employed mice (or whatever) to push the cone back and forth. In other words, for three weeks or more, I try to convince you that in normal operation damping is Rms+(BL)^2/Re, not just Rms, so now that you understand better (thanks to Kinsler et all), you agree with me.
So then... you are correct with your analysis when mice push the cone. Feel better now? :)

Sure, you agree NOW.

Darn it, Halliday didn't consider mice pushing the cone.

Right off, confusion (lack of magnitudes). This can be construed as (using your angle of 86.22, and your Zm of 33.82)
F' = 1.75 = .548
Which of course is wrong. Want to give magnitudes and prove yourself correct?
------------------------
Also, I'm sure you gave this before, but would you be so kind as to do a worked example with my data on these two simple equations - just for the record? TIA
E-RI = BlV
BLI = ZmV
-------------------------

Would you please state the *total* amplitude of power you see being transfered to the mechanical side? Is it 0.0054 watt?
---------------------------

Fluke, Simpson, and HP meters factory calibrated are not accurate? We even measured current through precision resistors and the voltage across them to check agreement with I = E/R. Again, since your calculations don't match measurements, one questions measurements?
---------------------------
As I told you, I am weary of your equations without detail re magnitudes, and you have again failed to provide magnitudes below, so I'll hold up on answering the remainder here, except for an item or two. I gave you my most nifty set of maximum velocity equations as a test. Shucks, there might even be an original. Who knows?
v max = w A = 2 pi f A = 1428.8 * 0.0000543 = 0.0775 (1) v max = pi/2 * delta x / delta t = 3.14/2 * 0.0000543 /0.0011 (2) = 0.0775 v max = F max / Z mec = 2.75 /35.53 = 0.0774 3) v max = pi/2 * v avg = 3.14/2 * 0.0493 = 0.0774 (4) v max = a t = 70.44 * 0.0011 = 0.0775 (5) v max = a max /w = 110.65 / 1428.8 = 0.0774 (6) v max = pi/2 sqrt (2 KE/m) = 3.14/2 sqrt (2 * 0.0000307/0.0253) = 0.0774 (7)
finally, per Mr. Newton, with F = ma = 0.0253 * 70.44 = 1.78 (8) v max = F/m * t = 1.78 / 0.0253 * 0.0011 = 0.0774
I added this comment: "Note all correlate at 0.0774 to 0.0775. Are you impressd now with my measurements? I am. :)
Now I would have been delighted at one time, had someone given me these, but you.... nooooooooooo you nit-pick and complain like an old maid.... You even assigned them numbers, so you can do a more effective job of nit-picking. Your reply:

using 2+3 = 5 to show that 5-2 = 3 does mean something too. It means you got an equation right. :)
----------------

No, as I said earlier, over 1% deviation is suspect. 3% is *very* suspect.
-----------------

Fine if you keep the mice well fed :)
Bill W.
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says...
Sorry, another typo...

0.001 should be 0.0011 for delta t, as it was elsewhere below.

I'm through now... sorry. :)
Bill W.
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says...
Sorry, a typo in my last post:

5.58 should be Re of 5.78 as noted above and below.

Bill W.
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remove the urine to answer
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You might find some useful information here: http://www.selinc.com/techpprs.htm
Art.

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Yes, I did. Thank you.
Bill W.
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----- Original Message -----
Newsgroups: alt.engineering.electrical Sent: Tuesday, December 16, 2003 1:51 PM Subject: Re: motor torque and back emf

---------- I have no problem with this magnitude. All I have done is to include phase as in some cases it is important. -----------------------

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Please excuse the top posting here, but the muddle in this thread has become impossible to wade through.
Also.. please excuse the duplicate posts yesterday. Got "editor memory error" upon clicking on post, then Supernews or whoever didn't show the post for over a half hour. Excuses, excuses, but blame *must* be laid.. :-)
I'll likely move on shortly. My email is at the end of the post here, if anyone wants to contact me.
------
Mr. Kelly
Thank you for your data, etc below.
Now... One thing I've learned is to appreciate simplicity. Einstein said things should be as simple as possible, but no simpler... Since you've taken my joking as serious, this may prove good advice here... Anyway along this line, and I don't want be derisive, and you won't like what I'm about to say, but I believe answers and points made can usually be made simple. You get into so many side issues with your dissertations, that frankly it's hardly worth the effort to wade through and try to ferret out the needed info. In fact I have wondered if you were intent on causing confusion, but have gone along so far, assuming you are well intended. I'll try below to ferret out the points of contention and address them as concisely as possible.
-------
You stated "Small and others are based on the math - the same math that I am using."
No. As example Kinsler, Beranek, and others state:
Zmec = F/v = 1.75/0.0493 = 35.5
This is just v = F/Zmec rearranged. Simple and intuitive. More force - go faster, more impedance - go slower. Basic. Requires no decoration. Yet you give the result as 33.82. The same math as Beranek and Kinsler would give 35.5.
-------
You stated: "You have not given reasoning for your contention. You have made quotes but the one you have given re (BL)^2/Re supports my contention- not yours. I have stated that it is the electrical resistance term referred to the mechanical side - as such, even though it is an "equivalent mechanical resistance" it is not an actual mechanical resistance." I really shouldn't waste my reasonong here... My derivation and logic behind
(Bl)^2/Re = 7.17^2/5.78 = 8.89
If we call the quantity R or Z the impeding quantity Iq, than taking the logical equation for velocity above
v = F/Zmec
Then from the force applied Fapp side
v = Fapp/Iq
transposing
Iq = Fapp/v
sub in for Fapp
E (Bl)/Re 1.41*7.17/5.78 Iq = ------------ = ---------------- = 35.48 v 0.0493
Then from the load or retarding side, logically we use back emf Blv instead of driving emf E
Blv (Bl)/Re (Bl) v (Bl) Iq = -------------- = ------------ = (Bl)^2/Re = 8.89 v v Re Just as I said (which you scoffed at), (Bl)^2/Re is the resistance the motor encounters in overcoming the back emf BLv, or as Small and Kloss said, it is the ***mechanical*** resistance of the driver motor.
Three pages of aside or unrelated equations coming up? :-)
----------
You stated "If it is the blocked coil force (and it is) then it cannot be used as the actual mechanical force when motion exists."
How many more times do I have to tell you I am ***not*** doing this. In how many more ways can I state that net force equals applied force*cos angle.
Fnet = Fapp cos angle = E (Bl)/Re * Rmec/Zmec
= 1.41*7.17/5.78 * 11.12/35.5 = 0.548
Sorry but I think you don't understand mechanical that well. Think of it this way. Push a sliding door direct in its line of motion, i.e. from zero angle. cos angle or power factor = cos zero = 1 .
Fnet = F*PF = 1.75*1 = 1.75
All your apploed force is useful in moving the door. Now push from an angle of 45 degrees.
Fnet = F*PF = 1.75*cos 45 = 1.75*0.707 = 1.237
0.707 of your applied force is useful in moving the door.
Now push (you do it) :-) from an angle of 90 degrees
Fnet = F*PF = 1.75*cos 90 = 1.75*0 = 0
None of your applied force is used to move the door. (you may stop pushing now..) :-)
Bottom line, net force is Fnet = Fapp cos angle = E (Bl)/Re * Rmec/Zmec
= 1.41*7.17/5.78 * 11.12/35.5 = 0.548
You claim 1.664. Quote "That is why I calculated the net mechanical force acting on the mechanical impedance (1.664 N)"
Maybe two pages here? :-)
-------
You stated "Then Pmec =1.664*0.0492*0.066 =0.0054 W" Halliday and Morse: P = F * v * cos angle = 1.75*0.0493*0.313 = 0.027 Beranek and Villchur: P = v^2 * Rmec = 0.0493^2*11.12 = 0.027 Colloms: P = F^2/Zmec^2 * Rmec = 1.75^2/35.5^2*11.12 = 0.027 Kinsler: P = F^2/Zmec cos angle = 1.75^2/35.5*0.313 = 0.027
or
Restating my net mechanical power equation:
Using my *measured* amplitude A or d (distance the mass travels from equilibrium position to the end point of motion) at 227.4 Hz of 0.0000543, and the power equation P = work/time, then for 1/4 cycle Pmec net = Fnet*d/t = 0.548*0.0000543/0.0011 = 0.027 Now, if you don't agree that 0.027 is net mechanical power, instead of your magnitude of 0.0054, then WHICH OF THESE DO YOU DISPUTE?
a. F net = F cos angle = 1.75*0.313 = 0.548
b. d or A is *measured* amplitude, i.e distance the mass travels during 1/4 cycle at 227.4 Hz = 0.0000543.
c. Time for a quarter cycle is T/4 = 1/f divided by 4,
1/227.4 t = ----------- = 0.0011 4
And another question.. why do you get a different result than Halliday, Morse, Beranek, Villchur, Colloms, and Kinsler?
--------
We need to get on the same page or wrap this up. We'll never get to acoustic power, etc this way.
--------
My email is snipped-for-privacy@mounet.com (divide 8 by 2)
Bill W.
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