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ABOUT THE REALITY OF THE INERCIOID
Cand. Tech. Sciences Samonov SA / Samonov SA
Mechanical inertosis is a device driven by a resultant inertial force, which is created by synchronously rotating in opposite directions, loads-deformations. A classification and a brief analysis of the designs of such devices can be found in V. Okolotin's article "Searching for an inertoid" at www.nt.org \ tp \ ts \ pi \ htm . It was also noted there that reliable information about the possibility of a stable unidirectional movement exists only in relation to inertoids, with accelerated cargoes ( IBM ). However, a fairly convincing explanation of the principle of the IBM is not given.
From the course of theoretical mechanics, the solution of the problem of the motion of an elliptic pendulum is known. The mechanical inertia is essentially a double elliptical pendulum, only located in the horizontal plane ( see Fig. 1 )
To study the inertial motion, we use the design scheme of a single ideal pendulum ( see Fig. 2 ), where the following notations are adopted:
M 1 - mass of the pendulum slider (inertial truck);
M 2 - weight of the unbalance load;
L - the length of the lever;
Φ - the angle of rotation of the unbalance;
Φ ' is the angular velocity of the unbalance;
X - displacement of the pendulum;
X ' is the linear velocity.
Equations of motion of such a pendulum, in the absence of friction, looks like this:
Where:
Φ '' is the angular acceleration of the unbalance;
X '' is the acceleration of the pendulum.
We transform this equation to the form:
After integration (m 1 + m 2 ) x '- m 2 l φ' ssin φ = С 1 , where С 1 is an arbitrary constant depending on the initial conditions. If the motion started at the time t = t 0 = 0 , when x '= 0; X = 0; Φ '= ω 0 ; Φ = φ 0 ; Then
It follows from expressions (1) and (2) that when starting from a place, the direction and magnitude of the linear velocity of the pendulum at any time are determined by the condition: the amount of motion of the elements of a given mechanical system in the projection on the x axis must remain constant and equal to the amount of movement of the unbalance in the projection On the x- axis at the initial instant of time.
If, for example, at the beginning of the movement, the imbalance was in the first quadrant, and as the angle of rotation increases, the projection m 2 lφ sinφ increases its negative value, then to compensate for its increase the pendulum must move in the positive direction along the x axis with increasing velocity.
The linear velocity of the pendulum with allowance for the initial conditions:
Pendulum movements taking into account the initial conditions:
From the equation it follows that under ideal conditions the displacement of the pendulum in one revolution of the unbalance does not depend on the law of variation of its angular velocity. Let us consider two characteristic modes of motion of a pendulum:
A) the motion from the longitudinal axis begins at the instant t = t 0 = 0 , at φ 0 = 0, φ '= ω 0 , then
The pendulum must reciprocate from the origin of coordinates at a variable speed;
B) the motion begins at the instant t = t 0 = 0 , for φ 0 = π / 2 , φ '= ω 0 , then
The pendulum must move at a variable speed.
The motion of the pendulum with allowance for friction and the constancy of the angular velocity of the unbalance can be analyzed by the following equation:
Where F тр is the frictional force acting on the pendulum of the pendulum,
Sign x ' is the sign of speed ( sign x' = 1, for x> 0, sign x '= -1, for x <0 ).
Let us determine the law of variation of the speed of a pendulum, for example, for the mode of motion (a) .
After starting, the pendulum must make the first stop at time t 1 , when
Where 
- the value of the centrifugal force.
From the last equation, it is easy to determine the time t 1 and the corresponding angle of rotation of the imbalance to the first stop ω 1 = ω 0 t 1 ( see Figure 1 ).
Since at the moment of stopping, the component of the centrifugal force acting along the X axis considerably exceeds the frictional force, the pendulum should immediately start moving, but under other initial conditions. The next stop should occur at time t 2 with newly changed initial conditions. Since the initial conditions are constantly changing, the pendulum must make erratic movements. The movement can theoretically be ordered and made unidirectional, if we ensure that at the instant t 2 the balance is again in the initial position. A similar picture is retained for the regime of motion (b) .
The experimental verification of the revealed regularities was carried out on the inertial model, which is a three-wheeled truck with an asynchronous single-phase RD-09 motor-reducer with an output shaft speed of n = 30 rpm . ( Ω 0 = 3.14 1 / s ). Lever length l = 0.235 m with unbalanced load m 2 = 0,23 kg directly attached to the output shaft. The trolley was supported by a ground steel plate. With a trolley mass m 1 = 1.74 kg, the design value of the trolley drag resistance, taking into account friction loss in the rolling bearings, was estimated as F tr = 0.04N . The calculated value of the centrifugal force is φ n = 0.53Н . At a ratio of φ n / F тр ≈ 15, the expected value of the angle of the first stop for mode (a) should be in the range from 1600 to 1700 . For mode (b) - in the range from 3100 to 3200 (the angle reading for convenience is indicated from the transverse axis).
The experience of studying the nature of the movement of the trolley for mode (a) was that the stationary trolley was released at the moment of passage by the unbalance of the longitudinal axis of the trolley (turning angle 0 ). For mode (b) , mark the corresponding angle of rotation 0 from the transverse axis. In both cases, the angles of the stops and the ranges of angles in which these or other movements of the trolley occurred were recorded. The actual picture of the change in the speed and displacement of the trolley differed significantly from the calculated one especially for mode (b) and is explained on the pie charts. Thus, the diagram in Fig. 3 shows the changes in the speed of the trolley for the first turn of the unbalance, in Fig. 4 - for the second turn (mode of motion (b) .
In the first and second quadrants ( see Fig. 3 ), the trolley was accelerated in the negative direction along the x axis, in the third quadrant it was intensively slowed down, then it followed the middle quadrant. After that the acceleration and braking in the V quadrant, again with the height, followed and, starting from the VI quadrant, the bogie moved to the reciprocating displacement regime, characteristic for regime (a) without friction. The author finds it difficult to explain the physical nature of the described effect. It seems that we are seeing a kind of self-synchronization of the inertosis, when the stops of the inertoid come in time with the intersection of the unbalance of the longitudinal axis, and friction apparently does not participate in the synchronization. It can be assumed that there is a certain algorithm for changing the angular velocity of the unbalance in which this effect makes it possible to achieve an asymmetry of the forward and backward momentum of the resultant inertial forces. As a result, the IBM demonstrates its ability to move without problems. The author tested the model of the IUG of its own design, which steadily moved in the specified direction during unidirectional reciprocating movements (forward motion with a preliminary pullback).
The author invites interested organizations and individuals to cooperate in organizing profound researches of IBM , which will allow to give a definitive answer to the question about the reality of inertness.
print version
Author: Ph.D.
Samonov Sergey Anatolyevich
PS The material is protected.
Date of publication 15.12.2004гг
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