RU2697520C1 - Method of excitation of mechanical oscillations of power factors with controlled parameters - Google Patents

Abstract

FIELD: vibration equipment.SUBSTANCE: invention relates to industry, in particular, to vibration equipment. Method of excitation of mechanical oscillations of power factors with controlled parameters by centrifugal vibration exciter, exciting oscillations by asymmetric law, consisting of four unbalances, which rotational axes are located on a common base, having identical unbalances in pairs, and have initial position, in which their centrifugal forces of inertia create maximum power factors, and rotating with angular velocities identical at value, that is ensured by transmission, synchronizing and phase-coordinating rotation of unbalances with gear ratio n, which is equal to ratio of angular velocity of fast rotating unbalances to angular speed of slow-moving ones. To obtain a power factor with the highest absolute value directed against the direction of the force factor created by the slow-rotating unbalances, initial position of fast rotating eccentric masses is changed by turning in any direction through an angle equal to 90°, provided that gear ratio n is a fractional number, multiplication of which by two obtains an odd number.EFFECT: technical result is variation of speed of transportation and high efficiency of processes of separation of grain mixtures.1 cl, 15 dwg

Description

The invention relates to vibration technology, in particular to the technique of agriculture, and can be used at grain processing enterprises in technological and transport equipment. In addition, the invention can be used in other industries related to the processing of bulk materials.

Known methods of exciting mechanical vibrations of force factors (force and / or moment) using centrifugal vibration exciters. In this case, the vibration exciter may contain one or more unbalances. Imbalance is a rotating unbalanced link. An unbalance imbalance is the product of an unbalanced mass m and its eccentricity r with respect to the axis of rotation.

A known method of excitation of non-harmonic (obeying an asymmetric law) force fluctuations [1] by a centrifugal vibration exciter containing four unbalances uniformly rotating around parallel axes (Fig. 1). The axis of rotation of the unbalances is located on a common basis. Unbalances in pairs have the same angular velocity in the opposite direction. Moreover, the magnitude of the angular velocity of the first pair of unbalances is half the magnitude of the angular velocity of the second pair of unbalances, that is, the first pair of unbalances rotates with the angular velocity ω ₁ = ω, and the second with the angular velocity - ω ₂ = 2ω. Imbalances rotating with equal angular velocities have the same imbalances, that is, the same products of unbalanced mass m with its eccentricity r with respect to the axis of rotation. Moreover, the imbalances of unbalances rotating with a frequency of 2ω are four times less than the imbalances of unbalances rotating with a frequency of ω. To simplify further considerations, we agree to call unbalances of the same name rotating at equal angular velocities, and the segment connecting the rotation axes of such unbalances to the center distance of the unbalances of the same name. The rotation axes of the unbalance of the same name are located symmetrically with respect to a straight line perpendicular to their center distance. In this case, the axis of rotation of the first pair of unbalances and the axis of rotation of the second pair of unbalances are symmetrically relative to one straight line.

- центробежная сила инерции, развиваемая небалансом первой пары;

- центробежная сила инерции, развиваемая небалансом второй пары. На рисунке (фиг. 2) показано некоторое произвольное положение дебалансов после поворота из начального положения первой пары дебалансов на угол δ₁=δ, второй пары - на угол δ₂=2δ. Как видно из рисунка, горизонтальные составляющие сил инерции одноименных дебалансов взаимно уравновешивают друг друга. Вертикальные составляющие сил инерции дебалансов складываясь, образуют результирующую силу, зависимость которой от угла поворота дебалансов имеет видLet us explain the principle of action of such a centrifugal vibration exciter. With a uniform rotation of the unbalances, centrifugal inertia forces develop:

- centrifugal inertia force developed by the imbalance of the first pair;

- centrifugal inertia force developed by the unbalance of the second pair. The figure (Fig. 2) shows some arbitrary position of the unbalances after turning from the initial position of the first pair of unbalances by an angle δ ₁ = δ, the second pair - by an angle δ ₂ = 2δ. As can be seen from the figure, the horizontal components of the inertia forces of the same unbalance balance each other. The vertical components of the unbalance inertia forces add up to form a resultant force whose dependence on the angle of rotation of the unbalances has the form

directed along a straight line representing the axis of symmetry of the location of the axis of rotation of the unbalances.

The dependence of the resulting force on the angle of rotation of the unbalances described by equation (1) is obtained provided that the position of the unbalances is taken to be such that the centrifugal inertia forces of the first and second pairs of unbalances simultaneously create maximum resultant forces of the same direction. The resultant centrifugal inertia forces of the first and second pairs of unbalances in the initial position are respectively P _P1 = 2m ₁ r ₁ ω ² and P _P2 = 8m ₂ r ₂ ω ² . It is obvious that in this case, in the initial position of the unbalances, the vibration exciter excites the maximum possible force.

As noted above, the imbalance of rapidly rotating unbalances is four times smaller than the imbalance of slowly rotating unbalances, that is, if the imbalance of the slowly rotating unbalance is m ₁ r ₁ = mr, then the imbalance of the rapidly rotating unbalance is m ₂ r ₂ = 0.25mr. Then the resulting force excited by the vibration exciter has the form

The dependence of the resulting force excited by the vibration exciter in dimensionless expression can be represented as

The figure (Fig. 3) shows a graph of the dependence of the resulting force in a dimensionless expression on the angle of rotation of the unbalances for the cycle of operation of the vibration exciter mechanism. Note that the cycle of the vibration exciter mechanism is the time after which the unbalances return to their initial (initial) position. In the case under consideration, during a kinematic cycle, slowly rotating unbalances make one revolution, and fast rotating unbalances - two.

As can be seen from the graph (Fig. 3), the function of the resulting force on the angle of rotation of the unbalance has the largest value equal to two, and the smallest minus one point one hundred twenty five thousandths. This means that the highest values of the force excited by the vibration exciter in opposite directions are not equal to each other. Given the positive and negative directions of the force, the absolute value of the highest value of the resulting force in the positive direction is greater than the absolute value of the highest value of the force in the negative direction, i.e., there is an asymmetry of the law of fluctuations of the force excited by the vibration exciter.

It should be noted that the force developed by such a vibration exciter is capable of informing the base and associated working body of straightforward non-harmonic oscillations if the force passes through the center of mass of the oscillating system. Inharmonicity of the law of oscillations in this case means the inequality of the largest positive value of the acceleration of the working body to the absolute value of the largest negative value of acceleration.

This method of exciting force fluctuations is implemented in the design of machines with the aim of informing the working body of non-harmonic (asymmetric) rectilinear oscillations.

A known method of exciting non-harmonic oscillations of the moment [2] by a centrifugal vibration exciter containing four unbalance, rotating around parallel axes (Fig. 4). The axis of rotation of the unbalances is located on a common basis. The imbalances rotate evenly, in pairs they have the same angular velocities in magnitude and direction and the same imbalances. The rotation of the unbalances is synchronized and coordinated in phase so that the unbalances of the same name simultaneously occupy positions in which the centrifugal inertia forces developed by them are parallel to each other and directed in opposite directions. Consequently, the centrifugal inertia forces of the same unbalance create a pair of forces, the moment of which is variable in magnitude and direction, and its magnitude and direction depend on the position of the unbalances.

Момент пары, создаваемой силами инерции быстровращающихся дебалансов, равен

Результирующий момент, возбуждаемый вибровозбудителем, равен алгебраической сумме моментов, создаваемых центробежными силами инерции первой и второй пар дебалансов. Зависимость результирующего момента от угла поворота дебалансов имеет видThe figure (Fig. 5) shows the arbitrary position of the unbalances: the unbalances of the first pair, rotating with an angular velocity ω ₁ = ω, are shown when they are rotated from the initial position by an angle δ ₁ = δ; the unbalances of the second pair, rotating with an angular velocity ω ₂ = 2ω, are shown when they are rotated from the initial position by an angle δ ₂ = 2δ. We consider the moment counterclockwise to be positive. As can be seen from the figure (Fig. 5), in the considered position, the inertia forces of the first and second pairs of unbalances form pairs of forces whose moments are positive. The moment of a pair created by the inertia forces of slowly rotating unbalances is

The moment of a pair created by the inertia forces of rapidly rotating unbalances is

The resulting moment excited by the vibration exciter is equal to the algebraic sum of the moments created by the centrifugal inertia forces of the first and second pairs of unbalances. The dependence of the resulting moment on the angle of rotation of the unbalance is

From the analysis of equation (4), we can draw the following conclusions. The dependence of the resulting moment obeys the inharmonious law. The dependence of the resulting moment, described by equation (4), takes place under the condition: in the initial position of the unbalances, the centrifugal inertia forces of the same unbalances create the maximum moments of the same (positive) direction. This initial position of the unbalances can be characterized as follows: the centrifugal inertia forces of the same unbalances are directed perpendicular to the straight lines connecting the axes of their rotation in opposite directions.

The resulting moment excited by such a vibration exciter can inform the base, and, consequently, the working body of the machine associated with it, of either non-harmonic rotational vibrations or rotational-vibrational motion (rotation with rotational vibrations superimposed on it).

то зависимость возбуждаемого вибровозбудителем момента будет иметь видIf the imbalance of the rapidly rotating unbalance is four times less than the imbalance of the slowly rotating unbalance and the distance between the rotation axes of the first and second pairs of unbalances is equal to each other

then the dependence of the moment excited by the vibration exciter will have the form

The dependence of the moment excited by the vibration exciter in dimensionless expression can be represented as

) вибровозбудителя, при которых отношение максимальных значений силовых факторов, возбуждаемых силами инерции медленно и быстровращающихся дебалансов, равно единице, то есть при

При этом за начальное положение дебалансов принято положение, в котором силы инерции одноименных дебалансов создают максимальные по величине силовые факторы (силы или моменты) одинакового направления. Легко убедиться, что при одинаковых соотношениях максимальных значений силовых факторов, возбуждаемых силами инерции медленно и быстровращающихся дебалансов, и при одинаковых условиях начальной фазировки дебалансов, законы колебаний силы и момента в безразмерном выражении будут иметь как одинаковый характер, так и одинаковые параметры колебаний.As can be seen, the right-hand sides of equations (3) and (6) have the same form. Consequently, fluctuations in force and moment obey one law. Note that the dependences of the resulting force and moment, described by equations (3) and (6), respectively, correspond to such installation parameters (masses m ₁ and m ₂ , eccentricities r ₁ and r ₂ , distances between rotation axes of the same unbalances

) vibration exciter, in which the ratio of the maximum values of force factors excited by the inertia forces of slowly and rapidly rotating unbalances is equal to unity, i.e., when

Moreover, the position in which the inertia forces of the same name unbalances create the maximum magnitude force factors (forces or moments) in the same direction is taken as the initial position of the unbalances. It is easy to make sure that for the same ratios of the maximum values of the force factors excited by the inertia forces of slowly and rapidly rotating unbalances, and under the same conditions for the initial phasing of the unbalances, the laws of fluctuations of force and moment in dimensionless expression will have both the same character and the same vibration parameters.

Therefore, depending on the phasing conditions of the unbalances of the same name and the directions of their rotation relative to each other (in one direction or in the opposite direction), a four-unbalanced vibration exciter can excite oscillations of either force or moment obeying the non-harmonic law. Moreover, the laws have the same characteristics (symmetric, asymmetric law, degree of asymmetry of the law of oscillations) with the same ratios of the maximum value of the force factor (force or moment), excited by the inertia forces of slowly rotating unbalances to the maximum value of the force factor, excited by the inertia forces of rapidly rotating unbalances, and under the same conditions initial phasing unbalances.

Дебалансы, вращающиеся с равными по величине угловыми скоростями, имеют одинаковые массы m и эксцентриситеты r относительно оси вращения. Оси вращения одноименных дебалансов, вращающихся с одинаковыми по величине угловыми скоростями, расположены симметрично относительно прямой, перпендикулярной их межосевому расстоянию. При этом оси вращения первой пары дебалансов и оси вращения второй пары дебалансов расположены симметрично относительно одной и той же прямой.The closest in technical essence and the achieved result is a method of excitation of mechanical vibrations of force factors with predicted parameters [3] by a centrifugal vibration exciter containing four unbalances rotating around parallel axes. The axis of rotation of the unbalances is located on a common basis. The imbalances rotate uniformly and in pairs have the same angular velocity. In this case, the angular velocity of the first pair of unbalances is less than the angular velocity of the second pair of unbalances. The first pair of unbalances rotates with an angular velocity ω ₁ = ω, and the second with an angular velocity ω ₂ = nω, where n is the gear ratio of the gear synchronizing and matching in phase the rotation of the unbalances equal to the ratio of the angular velocity of rapidly rotating unbalances to the angular velocity of slowly rotating

Unbalances rotating with equal angular velocities have the same masses m and eccentricities r relative to the axis of rotation. The axis of rotation of the unbalance of the same name, rotating at the same angular velocity, are located symmetrically with respect to a straight line perpendicular to their center distance. In this case, the axis of rotation of the first pair of unbalances and the axis of rotation of the second pair of unbalances are symmetrically relative to the same straight line.

The figure (Fig. 6) shows a vibration exciter containing four unbalances, designed to excite non-harmonic fluctuations of force, provided that the centrifugal inertia forces of the first and second pairs of unbalances in the initial position develop the maximum forces of the same direction.

The dependence of the force excited by such a vibration exciter has the form

The dependence of the excited force in dimensionless expression can be represented as

- коэффициент, равный отношению максимального значения силы, создаваемой силами инерции медленновращающихся дебалансов, к максимальному значению силы, создаваемой силами инерции быстровращающихся дебалансов.Where

- a coefficient equal to the ratio of the maximum value of the force created by the inertia forces of slowly rotating unbalances to the maximum value of the force created by the inertia forces of rapidly rotating unbalances.

The figure (Fig. 7) shows a vibration exciter containing four unbalances, designed to excite nonharmonic oscillations of the moment, provided that the centrifugal inertia forces of the first and second pairs of unbalances in the initial position develop maximum magnitudes of the same direction.

The dependence of the moment excited by this vibration exciter has the form

The dependence of the excited moment in dimensionless expression can be represented as

- коэффициент, равный отношению максимального значения момента, создаваемого силами инерции медленновращающихся дебалансов, к максимальному значению момента, создаваемого силами инерции быстровращающихся дебалансов.Where

- a coefficient equal to the ratio of the maximum value of the moment created by the inertia forces of slowly rotating unbalances to the maximum value of the moment created by the inertia forces of rapidly rotating unbalances.

As can be seen, the right-hand sides of equations (8) and (10) completely coincide when the coefficients a = b are equal. Consequently, the laws of oscillations of force and moment, excited by a four-balance vibration exciter, have the same characteristics with the same ratio of the maximum values of force factors created by the inertia forces of slowly and rapidly rotating unbalances.

Such a four-unbalance vibration exciter, depending on the initial phasing of the unbalances and the gear ratio, which synchronizes and matches the phase of the unbalance rotation, can create fluctuations in force factors (force or moment) that obey either an asymmetric or symmetric law. The vibration exciter excites asymmetric fluctuations in force factors (force or moment) if the following conditions are simultaneously met. In the initial position, the centrifugal inertia forces of slowly and rapidly rotating unbalances create maximum force factors. The sum of the total numbers of revolutions of the unbalances of the first and second pairs when they simultaneously return to their initial position, that is, for the kinematic cycle of the vibration exciter mechanism, is an odd number. Obviously, the second condition is satisfied for certain values of the gear ratio of the transmission, synchronizing and matching the phase of the rotation of the unbalances. The second condition is fulfilled if the gear ratio n of the gear synchronizing and coordinating in phase the rotation of the unbalances is a fractional number consisting of an integer part expressed by any natural number and a fractional part equal to five tenths. That is, the gear ratio n is a fractional number of the form n = i + 0.5, where i is any positive integer. Such a fractional number can be characterized as follows: a fractional number, when multiplied by two, an odd number is obtained - 2n = 2i + 1. With this value of the gear ratio, synchronizing and phase-matching the rotation of the unbalances, in the four-balance centrifugal vibration exciter during the kinematic cycle of the vibration exciter mechanism, the slowly rotating unbalances make two turns, and the number of full turns of the rapidly rotating unbalances is an odd number equal to twice the gear ratio n. Therefore, for such values of the gear ratio n, the sum of the total numbers of revolutions of the unbalances when they are simultaneously returned to their initial position is an odd number - 2i + 1 + 2 = 2 (i + 1) +1. The vibration exciter excites symmetric fluctuations in force factors when one of the following conditions is met. In the initial position, the centrifugal inertia forces of slowly and rapidly rotating unbalances create force factors equal to zero. The sum of the total numbers of revolutions of the unbalances of the first and second pairs per kinematic cycle is an even number. Note that in this initial position of the unbalances, the centrifugal inertia forces of the same unbalances are directed along the straight line connecting the axes of their rotation in opposite directions and balance each other.

The implementation of this method of excitation, mechanical fluctuations of power factors with predicted parameters in the drives of vibration technological and transport equipment for processing grain and other bulk materials allows you to inform the working bodies of machines of vibrations with various parameters of the law of motion. That is, to create a drive that allows you to provide the parameters of the law of oscillations of the working body in accordance with the process carried out in the equipment. However, such a drive has one significant drawback: a limited range of variation of the parameters of the law of oscillations of force factors.

So, to reverse the direction of the force factor with the highest absolute value, that is, to change the direction of the asymmetry of the law of oscillations of the force factor, the position of the vibration exciter must be changed. The vibration exciter must be rotated 180 ° from its original position. If such a change in the position of the vibration exciter is necessary, you must first dismantle the vibration exciter, and then carry out its installation and adjustment in a new position. In this case, such a permutation of the vibration exciter should be provided for by the design of the machine.

Therefore, the use of known methods of communicating to the working bodies of traffic machines according to laws whose parameters correspond to the type of process carried out in the equipment is accompanied by a complication of the drive design, as well as the creation of various designs of drive mechanisms.

Implementation of the proposed method for regulating the parameters of the laws of fluctuations of force factors in the design of equipment for processing grain and other bulk materials will create a unified drive in which by changing the initial position of rapidly rotating unbalances, a change in the opposite direction of the force factor with the highest modulus value is provided.

It is known that the reason for the average directional movement of particles of a loose body along a horizontal uniformly rough surface that performs horizontal vibrations is the asymmetry of the surface vibration law, which is expressed in the fact that the largest value of the acceleration of the supporting surface in one of the directions differs in absolute value from the largest value of acceleration in the opposite direction. The average speed of transportation of particles of a loose body relative to an oscillating surface, all other conditions being the same (vibration frequency of the supporting surface, shear resistance coefficients of the particles relative to the surface) depends on how much the largest positive value of the surface acceleration differs in magnitude from the largest negative acceleration. The direction of the average transportation speed depends on the modulus of which of the two largest values of the plane acceleration is greater - positive or negative.

The average speed of vibration displacement is the main parameter that determines the performance of transport equipment, and in the separating equipment - the productivity and efficiency of the process carried out in this equipment. The average speed of vibration displacement affects the efficiency of the separation process through the thickness of the layer of granular material and its residence time on the working body. With a constant length of the working surface (for example, the length of the sieve), an increase in the average speed of the free-flowing body decreases the duration of the separation process and the layer thickness. Reducing the time of the separation process reduces its effectiveness. Reducing the thickness of the granular body to a certain limit, as a rule, increases the efficiency of the separation process. A further decrease in the layer thickness below a certain value leads to a decrease in the efficiency of the process.

Consequently, in transport equipment, in order to increase its productivity, the transporting working body must be informed of the asymmetric law of oscillations with the greatest difference in the values of the maximum positive and negative acceleration.

In the separation processes, the effect of vibrations on a loose body is manifested in loosening and self-sorting of this body on the one hand, and in the feed, which ensures the continuity of the process on the other. Sometimes the effectiveness of the separation process is determined primarily by self-sorting. Examples of such processes include: cleaning grain from equal mineral impurities in stone separation machines; sieve separation process, in which there is little passage component and the bulk body thickness is many times greater than the particle size, while only particles in the lower layer are sieved through the sieve, into which they fall due to self-sorting. If the concentration of the feed-through component in the initial mixture is high, as, for example, when cleaning grain from large impurities in a separator or during screening separation of a grain mixture with a high concentration of a fine fraction, self-sorting does not have a large effect on the results of the process as a whole and screening is crucial.

According to the above, in separating machines, the parameters of the law of oscillations of the working body must correspond to the type of process carried out in the machine. If necessary, the law of oscillations of the working body should ensure effective self-sorting of the grain mixture. The effectiveness of self-sorting is directly dependent on the duration of exposure to vibrations on the granular body. In the implementation of the separation process, the effectiveness of which is determined by the efficiency of the sieving process, the law of oscillations of the working body should provide the optimum speed for sifting particles of the granular body relative to the sieve surface. The direction of asymmetry of the law of oscillations in combination with the inclination of the working surface to the horizontal and the communication of the surface of inclined oscillations opens up wide possibilities for varying the speed of vibration displacement.

It should be noted that the proposed method allows you to change in the opposite direction the largest absolute value of the force factor excited by the exciter. This means that the vibration exciter setting allows you to change to the opposite direction of transportation of the processed material on a vibrating working surface. This effect of adjusting the parameters of the laws of fluctuations of force factors can be used in drives of transport equipment, equipment for the implementation of the processes of separation, dosing and mixing of bulk materials.

The technical problem of the invention is the expansion of the arsenal of technical means to increase the efficiency of separation processes of grain mixtures.

This technical problem is solved by the proposed method of excitation of mechanical oscillations of force factors (force or moment) with adjustable parameters by a centrifugal vibration exciter, exciting oscillations according to an asymmetric law, consisting of four unbalances, the rotation axes of which are located on a common base, pairwise having the same imbalances and have an initial position, in which their centrifugal inertia forces create maximum force factors, and rotating with the same angular according to the invention, to obtain a force factor with the highest absolute value, directed against the direction of the force factor created by slow-revolving unbalanced shafts, which is provided by a gear synchronizing and matching in phase the rotation of the unbalances with a gear ratio n equal to the ratio of the angular velocity of the rapidly rotating unbalances to the angular velocity of the slowly rotating , change the initial position of rapidly rotating unbalances by turning them in any direction by an angle equal to 9 0 °, provided that the gear ratio n is a fractional number, when multiplied by two, an odd number is obtained.

The technical result is to vary the magnitude and direction of the transportation speed and increase the technological efficiency of the separation of grain mixtures.

To communicate to the working bodies of machines of vibrations with parameters corresponding to the process being carried out, we apply a centrifugal vibration exciter with four unbalances.

является передаточным отношением передачи, синхронизирующей и согласовывающей по фазе вращение первой и второй пар дебалансов.The imbalances, that is, the products of the unbalanced mass m and its eccentricity r relative to the axis of rotation, of the two unbalances of one pair must be equal to each other. These unbalances should have the same speed ω. The imbalances of the second pair of unbalances must also be equal to each other and may differ in magnitude from the imbalances of the first pair of unbalances. The imbalances of the second pair must have the same speed, but different from the speed of the first pair of unbalances. We keep the previously adopted numbering of unbalances. We will consider the first pair of unbalances to be unbalances that rotate with frequency ω ₁ = ω, and the second pair - with frequency ω ₂ = nω, n is a fractional number of the form i + 0.5, where i is any natural number. Obviously, n> 1, that is, the second pair of unbalances rotates with a higher frequency. The rotation of the unbalances must be appropriately synchronized and coordinated in phase. This can be achieved through either a gear (gear) transmission, or a gear belt drive, that is, a gear that excludes slipping of the driving and driven links. Note that the relation

is the gear ratio of the transmission, synchronizing and phase matching the rotation of the first and second pairs of unbalances.

Such a vibration exciter makes it possible to obtain various laws of oscillations of force factors (force or moment). These force factors, depending on the design (location) of the vibration exciter, are either transmitted directly to the working body of the machine, or to the output link of the actuator associated with the working body.

As noted above, the asymmetry of the law of fluctuations of power factors means that the largest positive value of the force factor is not equal to the absolute value of its largest negative value. For definiteness of further considerations, we introduce the concept of the direction of asymmetry of the law of oscillations of the excited force factor. The asymmetry of the law of oscillations is considered positive if the largest positive value of the force factor is greater than the absolute value of the largest negative value of the force factor. The asymmetry of the law of oscillations is negative if the absolute value of the largest negative value of the force factor is greater than the largest positive value of the force factor. We will consider such an initial phasing of unbalances, in which the vibration exciter excites fluctuations in the force factor according to an asymmetric law and the gear ratio of the gear synchronizing and matching the phase of the unbalance rotation is a fractional number of the form n = i + 0.5, where i is any natural number. As noted above, with such phasing of unbalances, the inertia forces of slowly and rapidly rotating unbalances in the initial position should create the maximum force factors. Obviously, in this initial position, inertial forces, slowly and rapidly rotating unbalances, can create force factors of the same or opposite direction. For definiteness of further reasoning, we assume that in the initial position the inertia forces of slowly and rapidly rotating unbalances create the maximum power factors of the same direction in magnitude. We take this direction as positive.

при одинаковых условиях начальной фазировки дебалансов и при одинаковых соотношениях максимального значения силового фактора, создаваемого силами инерции медленновращающихся дебалансов к максимальному значению силового фактора, создаваемого силами инерции быстровращающихся дебалансов. Выполнение последнего условия означает, что в уравнениях (8) и (10) коэффициенты a и b равны друг другу, то есть a=b. Поэтому в дальнейших рассуждениях зависимость возбуждаемого силового фактора будем обозначать в общем виде как ƒ(s). Очевидно, что выводы, полученные при исследовании рассматриваемых зависимостей, характеризуют параметры законов колебаний, как силы, так и момента.It should be noted that, as noted above, such a vibration exciter containing four unbalances, depending on the phasing conditions of the unbalances, can excite either force fluctuations or moment fluctuations. Moreover, the characteristics of the laws of fluctuations in a dimensionless expression coincide for the same values of the gear ratio

under the same conditions for the initial phasing of unbalances and with the same ratios of the maximum value of the force factor created by the inertia forces of slowly rotating unbalances to the maximum value of the force factor created by the inertia forces of rapidly rotating unbalances. The fulfillment of the last condition means that in equations (8) and (10), the coefficients a and b are equal to each other, that is, a = b. Therefore, in further considerations, the dependence of the excited force factor will be denoted in the general form as ƒ (s). It is obvious that the conclusions obtained in the study of the considered dependencies characterize the parameters of the laws of oscillation, both force and moment.

As noted above, the dependence of the force factor is asymmetric if, in the initial position, slowly and rapidly rotating unbalances create the maximum power factors of the same direction and if the gear ratio of the gear synchronizing and matching the phase of the unbalance rotation is a fractional number of the form n = i + 0.5 where i is any positive integer. Moreover, the dependence of the force factor is generally described by the equation уравн (s) = a cosδ + cosnδ, and the largest force factor in absolute value has a positive direction that coincides with the direction of the force factors created by the inertia forces of slowly and rapidly rotating unbalances in the initial position.

соотношение максимальных силовых факторов, создаваемых силами инерции медленно и быстровращающихся дебалансов.Let us evaluate the effect of the initial phasing of rapidly rotating unbalances on the direction of the maximum absolute value of the force factor excited by the vibration exciter. Obviously, in order to assess the effect of the initial phasing of rapidly rotating unbalances, it is necessary to keep the vibration exciter settings unchanged, which affect the characteristics of the law of oscillations. These parameters include: initial phasing of slowly rotating unbalances; gear ratio

the ratio of the maximum force factors created by the inertia forces of slowly and rapidly rotating unbalances.

является дробным числом вида n=i+0,5, где i - любое натуральное число. В этом случае исходным начальным положением дебалансов является такое их положение, при котором силы инерции быстро и медленновращающихся дебалансов создают силовые факторы, максимальные по величине одинакового направления (фиг. 6) и (фиг. 7). Следовательно, неизменным начальным положением медленновращающихся дебалансов является положение, в котором их центробежные силы инерции создают максимальный по величине силовой фактор в положительном направлении.As agreed above, we will study the effect of the initial phasing of rapidly rotating unbalances in a vibration exciter designed to excite asymmetric oscillations of force factors, provided that the gear ratio

is a fractional number of the form n = i + 0.5, where i is any natural number. In this case, the initial initial position of the unbalances is their position in which the inertia forces of the fast and slowly rotating unbalances create force factors that are maximum in magnitude in the same direction (Fig. 6) and (Fig. 7). Consequently, the invariable initial position of the slowly rotating unbalances is the position in which their centrifugal inertia forces create the maximum force factor in the positive direction.

We change the conditions for the initial phasing of rapidly rotating unbalances by turning them from the initial initial position by some arbitrary angle γ. The figure (Fig. 8) shows the new initial position of the unbalances in the exciter designed to excite oscillations of force. The new initial position of the unbalances differs from the initial initial position in that the rapidly rotating unbalances are rotated relative to the initial position by an arbitrary angle γ in the direction of their rotation.

Then, the dependence of the excited force factor in dimensionless expression for a new initial position of unbalances can be represented as

where γ is the detuning angle of rapidly rotating unbalances from the initial position, in which their inertia forces create the maximum force factor.

Let us determine the values of the angle γ at which such a change in the initial position of rapidly rotating unbalances is accompanied by a change in the opposite direction of the largest absolute factor of the force factor excited by the vibration exciter.

It should be noted that if the gear ratio n is a fractional number of the form n = i + 0.5, where i is any natural number, then the kinematic cycle of the vibration exciter mechanism, that is, the time after which the unbalances return to their initial position, corresponds to two revolutions slow-moving unbalances. Moreover, the number of revolutions of rapidly rotating unbalances is equal to twice the value of the gear ratio.

When determining the values of the angle γ, it should be borne in mind that the angle γ can take values in the range from 0 ° to 360 °, since the periodic function cosδ has a period equal to 360 °.

The direction of the largest force factor in absolute value will be reversed, that is, from the positive direction to the negative one, if, with a new initial phasing of the unbalances, they can occupy a position in which the inertia forces of the rapidly and slowly rotating unbalances simultaneously create maximum force factors in the negative direction.

If fast and slowly rotating unbalances occupy a position in which their centrifugal inertia forces simultaneously create maximum force factors in the negative direction, then the following system of equations has a solution

The first equation of system (12) has the following two roots δ = 180 ° and δ = 540 °, since slowly rotating unbalances for the kinematic cycle of the vibration exciter mechanism make two turns.

The second equation of system (12) has the following root values

where k = 0, 1, 2, ... - the maximum value of the coefficient k depends on the value of the gear ratio n of the transmission, synchronizing and coordinating in phase the rotation of the unbalances.

We determine what values the angle γ takes at δ = 180 °. We substitute the value δ = 180 ° into equation (13) and after the transformations we obtain

As can be seen from equation (14), the formula for determining the angle γ contains two factors. The first factor is 180 °. The second factor is the expression in parentheses on the right side of equation (14). The formula for determining the second factor includes the gear ratio n of the gear synchronizing and matching in phase the rotation of the unbalances, as well as the coefficient k, which depends on this gear ratio n.

To simplify further considerations, we denote

Since the angle γ can take values from 0 ° to 360 ° (0 ° <γ <360 °), the condition

Consider the condition

After substituting n = i + 0.5 and transformations, we obtain

The left side of the last inequality is an odd number. If the integer part i of the fractional number n = i + 0.5 is an odd number, then the minimum value of the coefficient k is determined from the condition

Solving equation (19) with respect to k _min , we obtain

Express the minimum value of the coefficient k _min through the gear ratio n of the transmission, synchronizing and matching phase rotation of the unbalance. To do this, substitute in equation (20) i = n-0.5. After the transformations we get

If i is an even number, then the minimum value of the coefficient k is determined from the condition

From equation (22) we obtain

We consider the fulfillment of the second condition of inequality (16), namely, the condition

After substituting into the inequality (24) the expressions of the gear ratio n = i + 0.5 and the transformations, we obtain

If i is an odd number, then the maximum value of the coefficient k is determined from the condition

From equation (26) we obtain

If i is an even number, then the maximum value of the coefficient k is determined from the condition

From equation (28) we obtain

In the case considered (δ = 180 °), the minimum value of the coefficient k is equal to its maximum value, provided that the integer part i of the fractional number n = i + 0.5 is an odd number, and the minimum and maximum values of the coefficient k are equal to each other under the condition that the integer part i of the fractional number n = i + 0.5 is an even number. The values of the coefficient k depend on the value of the gear ratio n of the transmission, synchronizing and matching the phase of the rotation of the unbalances. The minimum and maximum values of the coefficient are expressed by different formulas, depending on whether the integer part i of the fractional number n = i + 0.5 is an odd number or an even number.

To determine the values of the factor С _{1, we} substitute in the formula (15) the corresponding values of the coefficient k from equations (21) and (23) or from equations (27) and (29). After the transformations we get: if i is an odd number

if i is an even number

As can be seen from equalities (30) and (31), the value of the factor C ₁ depends only on what number is odd or even the integer part i of the fractional number n = i + 0.5.

In the case considered, the angle γ takes two values: γ = 90 °, if i is an even number; γ = 270 ° if i is an odd number.

Let us determine what values the angle γ can take for the case when the first equation of system (12) has a root δ = 540 °. After substituting the value δ = 540 ° into equation (13) and transformations, we obtain

We denote

According to the condition 0 <γ <360 °, the inequality

Consider the condition

After substituting n = i + 0.5 and transformations, we write inequality (35) in the form

If i is an odd number, then the minimum value of the coefficient k is determined from the condition

From equation (37) we obtain

If i is an even number, then the minimum value of the coefficient k is determined from the condition

From equation (39) we obtain

Consider the fulfillment of the second condition of inequality (34), namely, the condition

After substituting n = i + 0.5 and transformations, we write inequality (41) in the form

If i is an odd number, then the maximum value of the coefficient k is determined from the condition

From equation (43) we obtain

If i is an even number, then the maximum value of the coefficient k is determined from the condition

From equation (45) we obtain

In the considered case (δ = 540 °), the minimum value of the coefficient k is equal to its maximum value, provided that the integer part i of the fractional number n = i + 0.5 is an odd number, and the minimum and maximum values of the coefficient k are equal to each other under the condition that the integer part i of the fractional number n = i + 0.5 is an even number.

To determine the values of the factor C _{2, we} substitute into the formula (33) the values of the coefficient k from equations (38) and (40) or from equations (44) and (46). After the transformations we get: if i is an odd number

if i is an even number

As can be seen from equalities (47) and (48), the value of the factor C ₂ depends only on how many odd or even numbers the integer part i of the fractional number n = i + 0.5.

In the case considered (δ = 540 °), the angle γ takes two values: γ = 90 ° if i is an odd number; γ = 270 ° if i is an even number.

Summarizing the above reasoning, we can draw the following conclusion. The system of equations (12) has a solution if the angle γ is determined, firstly, as the product of two factors: the first factor is 180 °; the second factor takes two values equal to 0.5 and 1.5, regardless of the magnitude of the gear ratio n of the transmission, synchronizing and coordinating in phase the rotation of the unbalances, secondly, provided that the gear ratio n is a fractional number (n = i + 0.5), when multiplied by two, we get an odd number (2n = 2i + 1). Consequently, in the vibration exciter in question, in order to obtain a force factor with the highest absolute value directed against the direction of the force factor created by slowly rotating unbalances, the initial position of the rapidly rotating unbalances is changed by turning them either by an angle γ = 90 ° or an angle γ = 270 °.

The presented conclusions correspond to the case when, in order to obtain the force factor with the highest absolute value, directed against the direction of the force factor created by slowly rotating unbalances, the initial position of rapidly rotating unbalances is changed by turning them by an angle γ in the direction of their rotation.

Similar conclusions were obtained for the case when the initial position of rapidly rotating unbalances is changed by turning them in the direction opposite to the direction of rotation of the unbalances, that is, when rotating fast-moving unbalances by an angle of γ.

In this case, the dependence of the force factor in dimensionless expression has the form

With such a change in the initial position of rapidly rotating unbalances, the vibration exciter creates a force factor with the highest absolute value, directed the direction of the maximum force factor created by slowly rotating unbalances, provided that the system of equations has a solution

We will not dwell in detail on the solution of the system of equations (50); its solution is similar to the solution of the system of equations (12) considered in detail above. We note some general and distinctive features in determining the positive and negative values of the angle γ.

Note that the first equation of system of equations (50) coincides with the first equation of system (12). The roots of the first equation of system (50) are the following two values of the angle δ: angle δ = 180 °; angle δ = 540 °. The second equation of system (12) has the following root values

where k = 0, 1, 2, ... - the maximum value of the coefficient k depends on the value of the gear ratio n of the transmission, synchronizing and coordinating in phase the rotation of the unbalances.

At δ = 180 °, the angle γ can be determined by the formula

Equation (52) for determining negative values of the angle γ differs from equation (14) for determining positive values of the angle γ only in sign. The minus sign in equation (52) can be attributed either to a constant factor equal to 180 ° or to a variable factor C ₁ = 1 + 2k-n.

At δ = 540 °, we obtain the following formula for determining negative values of the angle γ

Equation (53) for determining negative values of the angle γ differs from equation (32) for determining positive values of the angle γ only in sign. In equation (53) as well as in equation (52), the minus sign can be attributed either to a constant factor equal to 180 ° or to a variable factor C ₁ = 1 + 2k-3n.

For definiteness, we will consider further considerations. That in equations (52) and (53) to determine the negative values of the angle γ, the minus sign refers to the constant factor.

We note some general and distinctive features in determining the positive and negative values of the angle γ. In both cases, the angles γ are determined as the product of two factors. The first factor in both cases has the same absolute value equal to 180 °. The second factor in both cases takes two values equal to 0.5 and 1.5, regardless of the value of the gear ratio n of the transmission, synchronizing and matching in phase the rotation of the unbalances. Thus, the difference in determining the positive and negative values of the angle γ lies only in the sign of the first constant factor in the formulas for determining the values of the angle γ.

The considered methodology for determining the positive and negative values of the angle γ allows us to draw the following conclusions. The angle γ takes two positive values, which are respectively equal to γ ₁₊ = 90 ° and γ ₂₊ = 270 °, and two negative values - γ _1- = -90 ° and γ _2- = -270 °. The positive and negative values of the angle γ are pairwise equal to each other in absolute value. The sum of the minimum and maximum absolute values of the angle γ is 360 °, that is, γ ₁₊ + | γ _2- | = 360 ° and γ ₂₊ + | γ _1- | = 360 °. This indicates that the unbalances occupy the same initial position when you turn the rapidly rotating unbalances from the initial initial position in the positive direction by the angle γ ₁₊ or in the negative direction by the angle γ _2- . Similarly, unbalances occupy the same initial position when rotating fast-moving unbalances in a negative direction by an angle γ _{1 -} _ or when they turn in a positive direction by an angle γ ₂₊ . Obviously, this explains the coincidence of the dependences: ƒ (δ) = cos (nδ + 90 °) + a cosδ coincides with ƒ (δ) = cos (nδ-270 °) + a cosδ; ƒ (s) = cos (nδ-90 °) + a cosδ coincides with ƒ (δ) = cos (nδ + 270 °) + a cosδ.

To confirm the proposed method for determining the values of the angle γ, the dependences ƒ (δ) = cos (nδ + 90 °) + cosδ and ƒ (δ) = cos (nδ-90 °) + cosδ force factors were studied for the gear ratio n of the gear synchronizing and phase matching rotation of unbalances equal to 1.5; 2.5; 3.5; 4.5 and 5.5. In the study of dependencies at a selected gear ratio n, dependency graphs were constructed and these dependencies were examined for extrema.

In the figures (Fig. 9), (Fig. 10), (Fig. 11), (Fig. 12), (Fig. 13) and (Fig. 14) as an example, the dependences of the power factor for two values of the gear ratio n transmission synchronizing and phase matching the rotation of unbalances. The figures (Fig. 9), (Fig. 10) and (Fig. 11) show the dependences at a gear ratio n equal to n = 1.5. In the figures (Fig. 12), (Fig. 13) and (Fig. 14) - with n equal to n = 2.5. The dependences of the force factor presented in the above figures correspond to the case when the ratio of the maximum force factors created by the inertia forces of slowly and rapidly rotating unbalances is equal to unity, that is, provided that the coefficient a = 1. In the figure (Fig. 9), the dependence corresponds to the initial position of unbalances, in which the inertia forces of slowly and rapidly rotating unbalances create maximum force factors in a positive direction. It should be noted that such an initial position of unbalances is shown in the figures (Fig. 6) and (Fig. 7) in vibration exciters: to excite oscillations of force (Fig. 6); to excite oscillations of the moment (Fig. 7). As can be seen from the figure (Fig. 9), the maximum positive value of the force factor is greater than the maximum in absolute value of the force factor in the negative direction. In this case, 2.0> | -1.634 |. The figures (Fig. 10) and (Fig. 11) show the dependences of force factors for two new initial positions of rapidly rotating unbalances. The dependence in the figure (Fig. 10) corresponds to the new initial position of the rapidly rotating unbalances obtained by turning them from the initial starting position by an angle of γ + 90 °, that is, by turning in the direction of their rotation. The dependence in the figure (Fig. 11) corresponds to the new initial position of the rapidly rotating unbalances obtained by turning them through an angle γ = -90 °, that is, against the direction of their rotation. As can be seen from the figures (Fig. 10) and (Fig. 11), the dependences have the same direction of the maximum force factor in absolute value. In this case, the maximum positive value of the force factor is less than the maximum in absolute value of the force factor in the negative direction (| -2.0 |> 1.634). It should be noted that at such initial positions of rapidly rotating unbalances corresponding to the values of the angle γ equal to γ = + 90 ° and γ = -90 °, the direction of the maximum in absolute value of the force factor excited by the vibration exciter is opposite to the direction of the maximum force factor created by the inertia forces of the slowly rotating unbalance in the starting position. In the figure (Fig. 12), the dependence corresponds to the initial initial position of the unbalances, that is, the position in which the inertia forces of the slowly and rapidly rotating unbalances create maximum force factors in the positive direction and the gear ratio n of the gear synchronizing and matching the unbalance rotation in phase is n = 2.5. As can be seen from the figure (Fig. 12), the maximum positive value of the force factor is greater than the maximum in absolute value of the force factor in the negative direction. In this case, 2.0> | -1.834 |. The figures (Fig. 13) and (Fig. 14) show the dependences of force factors for two new initial positions of unbalances. The new initial positions were obtained by turning the rapidly rotating unbalances by the angles γ = + 90 ° and γ = -90 °, respectively. As can be seen from the figures (Fig. 13) and (Fig. 14), the dependences have the same direction of the maximum force factor in absolute value. The maximum positive value of the force factor is less than the maximum in absolute value of the force factor in the negative direction | -2.0 |> 1.834. Moreover, the direction of the maximum in absolute value of the force factor excited by the vibration exciter is opposite to the direction of the maximum force factor created by the inertia forces of slowly rotating unbalances in the initial position.

Thus, the above reasoning allows us to draw the following conclusion.

In a centrifugal vibration exciter containing four unbalances rotating around parallel axes located on a common base and having angular velocities and imbalances pairwise identical in magnitude, occupying the initial position in which their centrifugal inertia forces create maximum magnitude force factors, which is ensured by a synchronizing transmission and phase-coordinated rotation of unbalances with a gear ratio equal to the ratio of the angular velocity of rapidly rotating unbalances to the angular velocity is slow rotating, to obtain the power factor with the highest absolute value, directed against the direction of the force factor created by slowly rotating unbalances, change the initial position of the rapidly rotating unbalances by turning them in any direction by an angle equal to 90 °, provided that the gear ratio n of the gear synchronizing and the phase-coordinated rotation of the unbalances is a fractional number, when multiplied by two, an odd number is obtained.

The proposed method of excitation of mechanical vibrations of power factors with an adjustable direction of the maximum absolute value of the power factor excited by the vibration exciter can be used to improve transport and technological equipment of grain processing enterprises.

In the case of using the proposed method in transport equipment, the device operates as follows.

The axis of rotation of the unbalances is placed on a common base (Fig. 15), rigidly connected with the working surface of the conveying device. The axis of rotation of the unbalances of the same name, that is, unbalances having the same imbalances and rotating with the same angular velocity, are located symmetrically relative to the perpendicular to the straight line connecting the axis of rotation of these unbalances. In this case, the axis of rotation of the first pair of unbalances and the axis of rotation of the second pair of unbalances are symmetrically relative to one straight line. Note that with this arrangement of the axis of rotation of the unbalances, the straight lines connecting the axis of rotation of the same unbalance must be parallel to each other. On the basis of (Fig. 15), the “+” sign marks the initial position of the unbalances, in which the inertia forces of fast and slowly rotating unbalances create maximum force factors (forces) in one (positive) direction. In this case, the direction of the maximum force factor excited by the vibration exciter coincides with the direction of the maximum force factor created by slowly rotating unbalances in the initial position. In the figure (Fig. 15), signs 1 - and 2 - denote two different initial positions of rapidly rotating unbalances, in which the maximum force factor (force) excited by the vibration exciter has a direction opposite to the direction of the force factor created by the inertia forces of slowly rotating unbalances in the initial position. In the figure (Fig. 15), rapidly rotating unbalances are shown in one of two possible initial positions, in which the direction of the maximum absolute value of the force factor excited by the vibration exciter is opposite to the direction of the maximum force factor created by the inertia forces of slowly rotating unbalances in the initial position. The dotted line shows the initial position of rapidly rotating unbalances, when their inertia forces create the maximum force factor, and the maximum force factor excited by the vibration exciter coincides in direction with the direction of the maximum force factor created by the inertia forces of slowly rotating unbalances in the initial position.

It should be noted that with the design of the drive using the proposed method for regulating the parameters of fluctuations of power factors, it is sufficient to use one of two possible new initial positions of rapidly rotating unbalances, which allow changing the maximum power factor excited by the vibration exciter in the opposite direction. This position should be selected position, which is the most simple in design in this particular equipment.

When the unbalances rotate, their centrifugal inertia forces create the resulting force, which is linearly oscillating according to the asymmetric law. Under the action of such a resulting force, the working surface performs linear oscillations according to an asymmetric law, that is, the largest positive value of the surface acceleration is not equal to the modulus of the largest negative acceleration value.

The grain mixture enters the working surface and, under the influence of vibrations, is transported along it. Transportation speed determines the performance of the transport equipment. The direction of the largest absolute acceleration of the working surface in combination with its inclination to the horizontal and the communication surface of inclined vibrations opens up wide possibilities for varying the speed of transportation.

In the case of application of the proposed method for regulating the direction of asymmetry of rectilinear fluctuations in force in technological equipment for the implementation of separation processes, the device operates as follows.

Consider the operation of the device on the example of cleaning the grain mixture from large impurities.

The initial grain mixture in a continuous stream enters the sieve surface, performing rectilinear vibrations. Oscillations of the surface provide transportation of the grain mixture and its self-sorting. In the process of self-sorting, large impurities float into the upper layer of the grain stream. When moving, the particles of the grain mixture pass over the openings of the sieve surface and are sifted when favorable conditions occur. Since when cleaning grain from large impurities, the initial grain mixture consists mainly of passage (grain) particles, self-sorting does not have a big impact on the results. process as a whole and sieving is crucial. The proposed method of reversing the direction of the maximum absolute value of the force together with the use of the inclination of the working surface to the horizontal and the inclination of the direction of oscillation create the conditions for the grain mixture to communicate speed relative to the working surface, which provides the most efficient flow of the sifting process, that is, allows the working body to inform oscillations with parameters corresponding to the most efficient sieving process.

Similarly, conditions can be created for the most efficient implementation of the separation process, in which the self-sorting process is of decisive importance.

Thus, the use of the proposed method for regulating the direction of asymmetry of the law of oscillations can improve the efficiency of the sieve separation process.

In addition, the implementation of the proposed method for the excitation of mechanical vibrations of power factors with adjustable parameters opens up the prospect of creating a unified drive for transport and technological equipment of grain processing enterprises.

Bibliography:

1. Patentschrift No. 955 756 (DFR), K1. 81 e, Gr. 53, Internat. K1. B 65 g, Jan 10, 1957.

2. RU 2528271 C2 10.30.2012.

3. RU 2528550 C2 12/21/2012.

Claims (1)

The method of excitation of mechanical vibrations of force factors with adjustable parameters by a centrifugal vibration exciter, exciting vibrations according to an asymmetric law, consisting of four unbalances, the rotation axes of which are located on a common base, pairwise having the same imbalances, and have an initial position in which their centrifugal inertia forces create the maximum the magnitude of the force factors, and rotating with the same largest angular velocities, which is ensured by the transmission, synchronizing and coordinating phase rotation of the unbalances with a gear ratio n equal to the ratio of the angular velocity of the rapidly rotating unbalances to the angular velocity of the slowly rotating ones, characterized in that to obtain the force factor with the highest absolute value, directed against the direction of the force factor created by the slowly rotating unbalances, change the initial position of the rapidly rotating unbalances by their rotation in any direction by an angle equal to 90 °, provided that the gear ratio n is a fractional number, with hardening which two get an odd number.

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