Parametric electromechanical generator

2024-05-26

Parametric electromechanical generator. This note is posted in the “Ideas” section. and does not claim to be 100% efficient. However, the principle of operation of such an engine can be an excellent help for seekers of free energy, Moreover, it is based on a completely understandable mathematical apparatus, which we will also present here. . The operating principle of a parametric electromechanical generator is based on a parametric change in the inductance L of the coil using a ferromagnetic core with relative magnetic permeability μ, moving up and down the channel . A certain mechanical analogue of an electric capacitor here is a spring , which accumulates mechanical energy when the core falls, and then giving it away as he rises. The shoe is attached to the spring and limits the core as it moves . In general, the result should be an electromechanical oscillatory circuit. .

The device operates as follows. Voltage is applied to the coil L, as a result of which a magnetic field appears in the coil with an initial intensity \, which draws the core into the coil in time During this time, the inductance of the coil changes from \ to When the core reaches its maximum upper position, the voltage is removed from the coil, and its back EMF is redirected to the load. After this, the core, under its own weight, falls onto the spring and compresses it. When, as a result of the spring decompression, the core begins to rise again, voltage is applied to the coil again. The cycle thus closes. . The difference in energy during rise and fall arises due to the difference in inductance, and therefore the energy expended and received. Let's calculate it, only for now we agree that the mechanical efficiency of the spring, the attraction of the core and the utilization of back EMF is 100%. And also that the core is attracted evenly and its permeability also changes evenly. For a more realistic calculation, we direct our readers to . . Energy and COP calculation. Let's calculate the electrical energy expended to pull the core into the coil. It consists of mechanical energy for lifting, which we will call \, and electrical. The latter also includes two types of energy costs: the cost of retracting the core \, and the cost of increasing the magnetic induction of the coil It should be noted that \ and \ are return energies, that is, those that are expended during the rise and are fully returned when the core falls. In ordinary cases, the same energy could be called \, and then the energy balance for the rise and fall of the core would be zero, that is, we would not receive any increase. This situation is described in and is inherent in almost all known devices. The way out of it is this: it is necessary to transform parametric changes of the first kind into parametric changes of the second kind, those. when the characteristic of the change in the permeability of the core as it rises would differ from the characteristic of the change in the permeability of the core as it falls. This is what our device allows you to do. . Now let’s calculate the energy difference \ during the rise and fall of the core, and draw a conclusion about the fundamentally possible energy increase. Let's take the ready-made formula : \[ W_L = L_0 \int_{I}^{I} \left[ M_2 - M_1 \right]\,I\, dI \tag{1} Here \ is the initial inductance of the coil , \, I - the initial current , and the final current when the wireframe is at the very top and the voltage on the coil has not yet been turned off. Time \ is the time the core rises. \, M_2 - patterns of change in the inductance of the coil from the current passing through it when the core rises and falls . From formula , for example, it follows that if \ and \ are the same, which is usually the case, then \ will be equal to zero. But not in our case!. Let's look at what these characteristics are. When the core retracts, then \could be like this: \[ M_1 = 0 + a\, I \tag{2} where \ is a certain coefficient. And we assumed a linear dependence at the very beginning . At the highest point, the core completely enters the coil, which means \ at this point will be equal to: \[ M_2 = 0 + a\, I \tag{3} But we know that we are discharging the back EMF into the load, and the core is still in the up position. This means that \ remains a constant value. Further, for simplicity, we denote: \ = I_1. Now we can safely rewrite formula : \[ W_L = a\, L_0 \int_{0}^{I_1} \left[ I_1 - I \right]\,I\, dI \tag{4} Solving this integral we get: \[ W_L = a\, L_0 \left[ {I_1^3 \over 2} - {I_1^3 \over 3} \right] = {a\, L_0 I_1^3 \over 6}\tag{5} This is our absolute increase in energy! The relative increase will then be calculated as follows: \[ K_{\eta 2} = {a\, L_0 I_1^3 / 0 + W_P + W_M \over a\, L_0 I_1^3 / 0 + W_P + W_M} \tag{6} But since we do not know \ and \, we will leave the formula in this form for now. The main thing that it shows is that an energy increase is possible, but cannot exceed the value 0 for a given characteristic of the change in inductance from current, which follows from formula . In addition, we need to remember that here we did not take into account the real efficiency of the spring, the attraction of the core and the utilization of back EMF, which will also contribute to formula . But if you reduce these losses to a minimum, choose the right coil and core material, choose the optimal switch response time, then obtaining a PEG generator with a COP of more than one becomes quite possible!. What if we take another characteristic of the core?. If we take another characteristic of the change in coil inductance from current, then we can obtain another achievable maximum for COP. For example, if the characteristic is like this : \[ M_1 = 0 + a\, I^2 \tag{7} then the maximum achievable COP will be 0. Interestingly, it is even easier to obtain such a characteristic than using formula , why you need to work on the very initial section of :

. The disadvantage of such a section is the relatively low operating currents, and therefore the low power of the entire installation. This can apply to all known ferromagnetic materials, because the Stoletov curve applies to almost all of them. . Change the design of the device. Such a diagram is shown in Figure 1b. Instead of a ferromagnetic core, magnets M0-M4 work here, which are located on a circle with radius R. Fixed coils L0-L0.4, the inductance of which is changed by these magnets, are mounted on the stator. Their job is to attract magnets, and when a coil passes through, repulse them. Energy is collected by coils L0-L0.4, which are also attached to the stator. The advantage of this design is greater mechanical efficiency, the disadvantage is more complex adjustment of the response time of the keys designed to operate the coils. . Obviously, based on the principle presented in this note, it is possible to develop other design options that may be more effective than the original. . .