Thread: Eric P. Dollard
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Old 07-02-2012, 07:14 PM
garrettm4 garrettm4 is offline
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Synthesis of Electrical Energy Via Parameter Variation Pt3

Effective Hysteretic Resistance h:

The solution for finding the time variant resistance or artificial resistance can be found by reverse solving the expression for oscillatory frequency.



Since we are dealing with a compound wave, we need to reverse solve this equation twice for both natural oscillatory frequencies.



Two solutions exist for h_1:





Two solutions exist for h_2:



Mathematically considered, negative quantities are an actual possibility, thus the reason values for -h were listed. I would be thrilled if Mr. Dollard had something to say about this, but I doubt he will give a response to this post. I have some thoughts on this result, but will keep them to my self for now, as I am not confident enough on the accuracy of my conclusions.

Thus the total effective resistance of the circuit:



For the circuit in question, total effective resistance R = 9.305 ohms

The effective resonant frequency is:



For the circuit in question, effective resonant frequency f_osc0 = 232 cps

It should be pointed out that there are an unlimited number of resonant points in this type of system, due to the arbitrary value of the static storage element, in my case it was a parallel bank of 2 30uF capacitors. However, there will only be a limited number of static storage element values that derive a LARGE resonant oscillation, this is the ultimate problem of this type of circuit, I substituted many different values to get the largest oscillation which is seen in the oscillogram given earlier. I have some books coming on non-linear oscillations, maybe after a few weeks of reading, I'm pretty dense when it comes to absorbing new information, I will be able to give a solution to this very important problem.

Furthermore, the only way to avoid the compounded two-period wave, is to have a time variant capacitance (spring) to go with the time variant inductance (mass). That or a switched capacitor would solve the problem of a compounded two-period wave. Which may be desirable for certain applications and may very well lead to a larger resonant oscillation in the circuit, but, will remain un-experimented with for now. This reasoning is derived from the fact that we are operating outside of both resonant conditions calculated for the circuit. If only one mode of resonant exchange existed, and the circuit was operated inside of that mode, it would seem that the oscillations incurred would be greater than having two modes present and operating outside of both of them.

Tech Note 1, there are multiple modes of excitation for parametric systems, the mode used in this experiment was natural excitation. This requires a conjugate energy storage medium, in this case a capacitor, and whereby no power is already flowing through the system and all power provided was due solely to parameter variation. Mr. Murray, however, shows that an alternate mode exists when used in conjunction with a system that has a circulation or transfer of energy already taking place, by varying the parameter within the limits set by the "host" systems natural oscillatory rate. Curiously, in this condition NO conjugate storage medium is needed. Over excited synchronous motors already do this with AC power systems.

Tech Note 2, the magnitude of the current and voltage vectors of the oscillatory system given in this series of posts could have been assisted with a vacuum tube or transistor circuit adding gain into the system. This would be seen as a negative resistance used to cancel the natural and artificial losses of the oscillatory system. This is useful to find the maximum amplitude of oscillation possible, this idea is brought up in the book "Theory of Oscillations" by A Andronow & C Chaikin, 1949.

*The Curious Case of Confusion

I originally thought that I used the invert function on my oscilloscope to adjust the waveform to proper representation, however, this has now been found to not be the case. The waveform as seen in the first oscillogram in Pt1 was actually drawn correctly. I tested the circuit with a direct current to check that the current and voltage traces moved in the same direction on the scope and after playing around for 30 minutes or so, I concluded that they were in proper polarity.

Below, are two more oscillograms. They have different values from the one shown in Pt1 because the watt-meter was disconnected and the current waveform was cleaned up by placing an electrostatic shield around the current clamp and an rC snubber on the DC motor:

*This is the correct and triple checked oscillogram of the circuit in operation. As can be seen it is the same as the one given in Pt1, but with higher peek values due to the watt-meter not being hooked up.



*This is the incorrect oscillogram. Due to the oddity of the waveform generated, I thought I had hooked up a probe backwards, so I captured this oscillogram as a correction, but this was NOT the case.



Conclusion

While the experiment didn't provide all that much electrical output, I am confident enough to say that this is a potentially viable solution to the worlds "energy crisis", or more aptly the worlds "intelligence crisis".

The amount of mechanical energy needed to turn the shaft is almost entirely INDEPENDENT to the electrical output. This was determined by applying a direct current of 10 amperes, well above the operating current of the coil, and using the same DC motor to drive the rotor. The results were found to have negligible effect on power draw of the DC motor. Next an alternating current of 4 amperes RMS (max I was able to provide) was administered in the same manner, the effect being even less than that of the DC, when the DC was lowered to the same effective value of the alternating current.

Concluding, it isn't mechanical energy that is being converted, but merely the rate of change in inductance or any other storage parameter. Thus you can assume that if you derived a method to change a storage parameter's value with minimal effort or exerted force, you would certainly have a system develop a COP well above unity.

The mechanical circuit equivalent is a changing mass for a mass-spring oscillator. If you were to increase the mass on the fall and lower the mass on the rise of the mechanical oscillatory period, you would exhibit negative resistance (due to gravity) and self sustained oscillations. The only energy required is that of changing the mass, which would take quite some ingenuity to resolve. If the energy exerted to change the mass is less than the energy imparted by gravity to the mass, you would have a COP greater than unity for a mechanical system.

The underlying principle of parameter variation is universal to all fields of science involving energy movement through storage elements and is not limited to electrical circuits.

Next up, when I get around to it, will be how to calculate for any arbitrary amount of electrical power to be generated by a parametric system with losses and other problems included, this however, will not be any time soon.

Food for thought,
Garrett M
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Last edited by garrettm4; 07-04-2012 at 04:09 AM.