RU2621175C1 - Method of regulation of parameters of the law of mechanical vibrations of force factors in the centrifugal vibrator - Google Patents

Abstract

FIELD: machine engineering.

SUBSTANCE: proposed method for regulating the parameters of the law of mechanical oscillations of force factors in a centrifugal exciter that contains four unbalances, pairwise having the same imbalances, rotating at the same angular velocities that have the same initial position, when their centrifugal forces of inertia create the maximum power factors, is achieved by the change in the initial position of rapidly rotating unbalances by rotating them in any direction by an angle equal to 90°, provided that the transmission ratio of the synchronizing and phase-matching rotation of the unbalances is an even number. Perfection of equipment for transportation and separation of grain mixtures is achieved by communicating to the working bodies of traffic machines with parameters that ensure efficient flow of the process carried out in the equipment.

EFFECT: variation of the speed of transportation and increasing the efficiency of the processes of separation of grain mixtures.

17 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.

The purpose of the invention is the expansion of the functionality of a centrifugal vibration exciter when used in vibrating equipment for separating and transporting grain and other bulk materials by communicating to the working bodies of vibration machines with parameters that ensure the most efficient flow of the process carried out in the equipment.

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 straight line 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 дебалансом первой пары;

- центробежная сила инерции, развиваемая дебалансом 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 unbalance 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 inertia forces of the unbalances, folding, form the resulting force, the dependence of which on the angle of rotation of the unbalances has the form

Thus, a force is created that varies according to the inharmonious law, directed along a straight line, which is the axis of symmetry of the location of the unbalanced rotation axes.

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.

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. 3). 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. 4) shows an 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. 4), 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

As you can see, the dependence of the resulting moment obeys the inharmonious law. The dependence of the resulting moment, described by equation (2), 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.

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

. 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. 5) 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. 6) shows a vibration exciter containing four unbalances, designed to excite non-harmonic 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 (4) and (6) 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 symmetrical law. The vibration exciter excites asymmetric fluctuations in force factors (force or moment) if the following conditions are simultaneously met. In the initial position, 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. If the gear ratio is an integer, then the sum of the total numbers of revolutions of the unbalances when they are simultaneously returned to their initial position is an odd number, provided that the gear ratio is an even number. 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.

The implementation of this method of excitation of mechanical vibrations 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 ensure symmetric and asymmetric laws of oscillations of the working body, it is necessary either to create two different vibration drives, or to provide the vibration drive design with the ability to adjust the vibration parameters by changing the initial position of slowly and rapidly rotating unbalances. However, such adjustment of the parameters (asymmetry or symmetry) of the law of oscillations greatly complicates the design of the vibrodrive and its maintenance.

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 law 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 the slowly rotating unbalances, either a symmetric or asymmetric law of oscillations of the working body can be 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 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 reduces the duration of the separation process and the thickness of the layer. Reducing the time of the separation process reduces its effectiveness. Reducing the thickness of the layer 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.

Therefore, in transport equipment, to increase its productivity, the transporting working body must be informed of the asymmetric law of oscillations.

In the separation processes, the effect of vibrations on a granular body is manifested in loosening and self-sorting of this body, on the one hand, and in a feed that 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 a small amount of passage component, and the bulk body thickness is many times greater than the particle size, and only particles located in the lower layer, into which they fall as a result of self-sorting, are sifted through a sieve. 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.

It should be noted that the proposed method allows, depending on the settings of the vibration exciter, to provide excitation of oscillations of force factors according to an asymmetric or symmetrical law.

The ability to configure the vibration exciter to excite either asymmetric oscillations or symmetric oscillations of force factors, in combination with the inclination of the working surface to the horizontal and the message of the surface of inclined oscillations, can significantly expand the range of variation of the vibration displacement velocity. This allows us to conclude that it is possible to use such a vibration drive, depending on its setting, both in transport and in technological equipment.

The objective of the invention is the improvement of equipment for transportation and separation of grain mixtures by communicating to the working bodies of traffic machines according to the laws, the parameters of which correspond to the process carried out in the equipment.

The problem is solved by the proposed method of excitation of non-harmonic oscillations of force factors (force or moment) according to an asymmetric law by a centrifugal vibration exciter, 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 power factors, and rotating with the same angular velocity, which is ensured by the transmission, synchronizing 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 of slowly rotating, in which according to the invention, to ensure the symmetry of the law of oscillations, which means that the largest positive value of the force factor is equal to the modulus of its largest negative value, the initial position of rapidly rotating unbalances is changed by turning them in any direction by an angle equal to 90 °, provided that the gear ratio is an even number.

The technical result is to vary the speed of transportation 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 the same pair should 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 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 any real number. For definiteness of further considerations, we assume that n> 1, i.e., 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. We will consider such an initial phasing of unbalances, in which the vibration exciter excites oscillations of 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 an even number. As noted above, with this phasing of the unbalances, the inertia forces of slowly and rapidly rotating unbalances in the initial position should create the maximum force factors. It is obvious that in this initial position, the inertia forces of 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 maximum force factors of the same direction in magnitude. We take this direction as positive. Such conditions for the initial position of unbalances are accepted because these conditions are most easily realized in practice, since the direction of the centrifugal inertia forces coincides with the direction of the eccentricity of the unbalance. The inertia forces of the unbalance of the same name create the maximum force factor if they (inertia forces), and hence the eccentricities, are perpendicular to the straight line connecting the axes of their rotation.

, 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 (4) и (6) коэффициенты а и b равны друг другу, то есть а=b. Поэтому в дальнейших рассуждениях зависимость возбуждаемого силового фактора будем обозначать в общем виде как

. 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 (4) and (6), 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 general terms as

. Obviously, the conclusions obtained in the study of the considered dependencies characterize the parameters of the laws of oscillations of both force and moment.

; соотношение максимальных силовых факторов, создаваемых силами инерции медленно- и быстровращающихся дебалансов.Let us determine the conditions for the initial phasing of rapidly rotating unbalances under which the nature of the law of oscillations of force factors changes from asymmetric to symmetric. Obviously, for such an assessment of the effect of the initial phasing of rapidly rotating unbalances, it is necessary to maintain the vibration exciter settings that affect the characteristics of the law of oscillations. These parameters are: 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 четным числом. 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. 5) и (фиг. 6). 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 an even number. The initial initial position of the unbalances is their position in which the inertia forces of the fast and slow-moving unbalances create force factors that are maximum in magnitude in the same direction (Fig. 5) and (Fig. 6). Therefore, 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. 7) 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 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 nature of the law of oscillations of the force factor from asymmetric to symmetric.

It should be noted that if the gear ratio n of the gear synchronizing and coordinating in phase the rotation of the unbalances is an integer, then the kinematic cycle of the vibration exciter mechanism, that is, the time after which the unbalances return to their initial position, corresponds to one revolution of slowly rotating unbalances. In this case, the number of revolutions of rapidly rotating unbalances is equal to the gear ratio n.

When determining the values of the angle γ, it should be borne in mind that, since the trigonometric function of the cosine is periodic with a period equal to 360 °, the angle γ can take values ranging from 0 ° to 360 °.

The vibration exciter excites fluctuations of force factors according to a symmetric law, if during the kinematic cycle the unbalances can occupy a position in which the inertia forces of rapidly and slowly rotating unbalances simultaneously create force factors equal to zero. In this case, the following system of equations must have a solution:

We determine the values of the angle γ at which the system of equations (8) has a solution.

The roots of the first equation of system (8) are the following values of the angle:

and

The solution to the second equation of system (8) has the form

where k = 0,1, ..., 2n-1;

n is the gear ratio of the transmission, synchronizing and matching phase rotation of the unbalance.

We determine the values of the angle γ for the value of the angle δ = 90 °, which is the first root of the first equation of system (8). For this, we substitute the value δ = 90 ° from equation (9) into equation (11). After the transformations we get

As can be seen from formula (12), the angle γ can be defined as the product of two factors: the first factor is 90 ° and is a constant; the second factor - the expression in parentheses is the value of the variable, due to the variability of the coefficient k.

To simplify further considerations, we introduce the notation

In accordance with the accepted designation, equation (12) can be represented as

It should be noted that the angle γ is considered positive if the new initial position of the rapidly rotating unbalances is obtained by rotating this pair of unbalances in the direction coinciding with the direction of their rotation. The angle γ is negative if the rapidly rotating unbalances turn into a new initial position against the direction of their rotation.

Since the angle γ takes positive values in the case under consideration, the inequality

Since the gear ratio n is an even number, it can be represented as

.where i is a natural number equal to

.

We substitute the expression for the gear ratio n from equation (16) into inequality (15) and after the transformations we obtain

Since i and k are integers, the expression in parentheses of inequality (17) cannot take positive values, i.e., the condition

or

From inequality (19) it follows that the minimum value of the coefficient k is

To determine the minimum value of the variable factor C, we substitute the value k _min from equation (20) into equation (13). After the transformations we get

We obtain the maximum value of the variable factor C _{1 by} substituting in equation (13) the maximum value of the coefficient k equal to k _max = 2n-1

Let us determine what values the variable factor C ₁ can take in the range of values from C _1min to C _1max .

We substitute the expression for the gear ratio n from equation (16) into equation (13) and after the transformations we obtain

From equation (23) it can be seen that the variable factor C ₁ is an odd number. Therefore, the variable factor C ₁ in equation (14) takes values from a series of odd numbers lying in the range from one to three times the gear ratio n of the gear, synchronizing and matching the phase of unbalance rotation, minus one.

We determine at what values of the angle γ the system of equations (8) has a solution if the root of the first equation of the system is δ = 270 °.

We substitute δ = 270 ° into equation (11) and after the transformations we obtain

In the case under consideration, the angle γ can be defined as the product of a constant factor equal to 90 ° and a variable factor, which we denote

In accordance with the accepted notation, we write equation (24) in the form

Since the angle γ is positive, the inequality

We substitute the expression for the gear ratio n from equation (16) into inequality (27). After the transformations we get

Since i and k are integers, to satisfy inequality (28), the condition

From inequality (29) it follows that

Therefore, the minimum value of the coefficient k at which inequality (28) holds is equal to k _min = 1.5n. As stated above, the maximum value of the coefficient k is k _max = 2n-1.

Then the minimum and maximum values of the variable factor C _{2 are} respectively equal

and

It is easy to see that the variable factor C ₂ is an odd number. Therefore, in this case, the variable factor C ₂ takes values from a number of odd numbers lying in the range from unity to the gear ratio n minus one.

The following conclusion can be drawn from the presented reasoning. The range of values of the variable factor C ₁ contains the range of values of the variable factor C ₂ . Therefore, the system of equations (8) has a solution for the values of the angle γ, which can be defined as the product of two factors: a constant factor equal to 90 °; a variable factor that takes values from a series of odd numbers lying in the range from one to three times the gear ratio n of the gear, synchronizing and matching in phase the rotation of the unbalances, minus one.

It should be noted that the arguments presented above relate to the case when a new initial position of rapidly rotating unbalances is obtained by turning them from the initial initial position by an angle γ in the direction of their rotation. In this case, the angle γ takes positive values.

The angle γ takes negative values if, in order to obtain a new initial position of the rapidly rotating unbalances, they are rotated from the initial initial position against the direction of rotation. Then, to determine the negative values of the angle γ, it is necessary to consider the solution of the system of equations

We will not dwell on the solution of the system of equations (33). Consider some features of its solution.

The solution of the second equation of system (33) has the form

where k = 0,1,2, ..., 2n-1.

From equation (34) at δ = 90 ° it follows that

To simplify further considerations, we denote the variable factor of equation (35)

In the case under consideration, the inequality

Inequality (37) is satisfied provided

or

Inequality (39) is satisfied if the minimum value of the coefficient k is

Note that the maximum value of the coefficient k is

The maximum and minimum values of the variable factor C _{3 are} respectively equal

and

The variable factor C ₃ can be written as

The last equation confirms that the absolute values of the variable factor C ₃ are odd numbers from the interval from one to three times the gear ratio n of the gear, synchronizing and matching the phase of the unbalance rotation, minus one.

If by solving the first equation of system (33) we take the phase angle δ = 270 °, then the values of the angle γ at which the system has a solution can be determined by the formula

It is easy to prove that the variable factor C ₄ = 3n-1-2k in absolute value represents a series of odd numbers in the range from unity to gear ratio minus one, that is, from 1 to n-1.

Since the range of values of the factor C ₃ contains the range of values of the factor C ₄ , the angle γ can be defined as the product of 90 ° by odd numbers from the range of values from 1 to 3n-1, taken with a minus sign.

Thus, the positive and negative values of the angle γ are pairwise equal to each other in absolute value.

It should be noted that the total number of values of the angle γ (positive and negative) determined according to the considered method is equal to the tripled gear ratio n of the gear synchronizing and matching the phase of the unbalance rotation. Moreover, half of the values of the angle γ are positive and half negative values. In this case, the minimum value of the angle γ in absolute value is 90 °, regardless of the value of the gear ratio n. The absolute value of each subsequent value of the angle γ differs from the previous one by 180 °. Therefore: the first value of the angle γ differs from the third by 360 °; the second-order value of the angle γ differs from the fourth by 360 °. That is, each previous value of the angle γ differs from the subsequent one through one angle value by 360 °. For example, if the gear ratio is n = 2, then the angle γ takes the following positive and negative values. Positive: γ ₁₊ = 90 °; γ ₂₊ = 270 ° and γ ₃₊ = 450 °. Negative: γ _1- = -90 °; γ _2- = -270 ° and γ _3- = -450 °. It should be noted that the angle γ has these values for any value of the gear ratio n of the gear, synchronizing and matching the phase of the unbalance rotation. With an increase in the gear ratio, the number of calculated values of the angle γ increases, while maintaining the ratio of the angles. Each subsequent value of the angle γ differs from the previous value by 360 ° if these values have odd serial numbers in the series of calculated values of the angle γ. The values of angle γ under even serial numbers in the series of calculated values of angle γ have the same ratio of values. So, for example, if the gear ratio is n = 4, then the angle γ takes the following positive and negative values. Positive: γ ₁₊ = 90 °; γ ₂₊ = 270 °; γ ₃₊ = 450 °; γ ₄₊ = 630 °; γ ₅₊ = 810 ° and γ ₆₊ = 990 °. Negative: γ _1- = -90 °; γ _2- = -270 °; γ _3- = -450 °; γ _4- = -630 °; and γ _5- = -810 ° and γ _6- = -990 °.

From the point of view of the practical implementation of the results of calculating the values of the angle γ, the first two positive and the first two negative values are of interest. This statement has the following explanation. A turn of unbalances by an angle that is a multiple of 360 ° is not accompanied by a change in their initial position. Consequently, rapidly rotating unbalances occupy new initial positions when they are rotated from the initial initial position either by an angle of γ ₁₊ = 90 °, or by an angle of γ ₂₊ = 270 °. The rotation of rapidly rotating unbalances from the initial starting position by an angle of γ ₃₊ = 450 ° is equivalent to their rotation by an angle of γ ₁₊ = 90 °. The rotation of the unbalances by the angle γ ₄₊ = 630 ° is equivalent to their rotation by the angle γ ₂₊ = 270 °. That is, the rotation of the rapidly rotating unbalances from the initial starting position to any angle γ, the value of which corresponds to an odd serial number in the series of calculated values of the angle γ, is equivalent to the rotation of the unbalances by the angle γ ₁₊ = 90 °. A turn of unbalances by any angle γ, the value of which corresponds to an even serial number in the series of calculated values of the angle γ, is equivalent to a turn of unbalances by an angle γ ₂₊ = 270 °.

This can be proved as follows. All values of the angle γ having odd serial numbers in the series of calculated values of the angle γ, in the general case, can be represented as

where j = 0,1,2, ... is a series of integers, including zero, the maximum value of the number of the series depends on the gear ratio n.

All values of the angle γ having even serial numbers in the series of their calculated values, in the general case, can be represented as

Since the trigonometric cosine function is periodic, the period of which is 360 °, then the conditions

and

That is, the rotation of fast-moving unbalances from the initial starting position to any angle whose value corresponds to an odd ordinal number in the series of calculated values of the angle γ is equivalent to the rotation of the unbalances by the angle γ ₁₊ = 90 °. A turn of unbalances by any angle, the value of which corresponds to an even serial number in the series of calculated values of the angle γ, is equivalent to a turn of unbalances by an angle of γ ₂₊ = 270 °.

Thus, it is proved that all calculated positive values of the angle γ determine two new initial positions of rapidly rotating unbalances. One new initial position of the unbalances is obtained by turning them through an angle of γ ₁₊ = 90 °. The second new starting position is at an angle of γ ₂₊ = 270 °.

Similar conclusions were obtained for the case of negative values of the angle γ. All calculated negative values of the angle γ determine two new initial positions of rapidly rotating unbalances. The first position is obtained when rotating fast-moving unbalances from the initial position by an angle γ _1- = -90 °. The second - at an angle of γ ₂ -270 °.

It should be noted that the new initial position of the rapidly rotating unbalances obtained when they are rotated through the angle γ ₁₊ = 90 ° coincides with the new initial position of the unbalances obtained when they are rotated through the angle γ _2- = -270 °. Also, the position of the unbalances coincides if they are rotated from the initial starting position in one case by an angle γ _1- = -90 °, in another - by an angle γ ₂₊ = 270 °.

совпадает с зависимостью

; зависимость

совпадает с зависимостью

. Совпадение этих зависимостей можно доказать следующим образом. Косинус суммы двух углов равен косинусу разности двух углов, если первое слагаемое в сумме углов равно уменьшаемому в разности углов, а сумма абсолютных значений второго слагаемого в сумме углов и вычитаемого в разности углов равна 360°. То естьThis coincidence of the initial positions of the unbalances indicates the coincidence of the dependences of force factors: dependence

coincides with addiction

; dependence

coincides with addiction

. The coincidence of these dependencies can be proved as follows. The cosine of the sum of the two angles is equal to the cosine of the difference of the two angles, if the first term in the sum of the angles is equal to the decrease in the angle difference, and the sum of the absolute values of the second term in the sum of the angles and subtracted in the angle difference is 360 °. I.e

since 90 ° + ⎪-270 ° ⎪ = 360 °.

For the same reason, there is equality

From the above reasoning it follows that it is possible to change the nature of the law of oscillations of the force factor from asymmetric to symmetrical by changing the initial position of rapidly rotating unbalances by turning them from the initial initial position either by an angle γ = 90 ° or an angle γ = -90 °.

и

силовых факторов при значениях передаточного отношения n передачи, синхронизирующей и согласовывающей по фазе вращение дебалансов, равных 2, 4, 6, 8 и 10. При исследовании для выбранного значения передаточного отношения n строили графики зависимостей силовых факторов и исследовали эти зависимости на экстремумы. Следует заметить, что для каждого значения передаточного отношения такие исследования проводили при двух значениях угла γ: γ=90° и γ=-90°To confirm the above conclusion, the dependences were studied

and

force factors with the values of the gear ratio n of the gear synchronizing and matching in phase the rotation of the unbalances equal to 2, 4, 6, 8, and 10. In the study for the selected value of the gear ratio n, we constructed the dependences of the force factors and examined these dependences for extrema. It should be noted that for each value of the gear ratio, such studies were carried out at two values of the angle γ: γ = 90 ° and γ = -90 °

силового фактора коэффициент а=1.We give as an example the graphs of the dependences of power factors for three values of the gear ratio n: n = 2; n = 4 and n = 6. Note that in all the presented examples of dependencies, 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, depending on

force factor coefficient a = 1.

The figures (Fig. 8), (Fig. 9) and (Fig. 10) show the dependences of the power factor for the case when the gear ratio n of the gear synchronizing and matching the phase of the unbalance rotation is two (n = 2). In the figure (Fig. 8), the dependence corresponds to the initial position of the unbalances, in which the inertia forces of the slowly and rapidly rotating unbalances create maximum force factors in the positive direction. Note that this initial position of the unbalances is shown in the figures (Fig. 5) and (Fig. 6) in vibration exciters: for excitation of force oscillations (Fig. 5); to excite oscillations of the moment (Fig. 6). As can be seen from the figure (Fig. 8), the maximum positive value of the force factor is greater than the absolute value of the maximum force factor in the negative direction. In the case under consideration, 2.0> | -1.125 |. The figures (Fig. 9) and (Fig. 10) show the dependencies for the new initial positions of rapidly rotating unbalances: in the figure (Fig. 9), the dependence corresponds to the rotation of rapidly rotating unbalances from the initial initial position to a new initial position by an angle γ = 90 °; in the figure (Fig. 10), the dependence corresponds to the rotation of rapidly rotating unbalances to a new initial position by an angle γ = -90 °. As can be seen from the figures (Fig. 9) and (Fig. 10), the laws of oscillations of force factors are symmetrical. The maximum positive value of the force factor is equal to the absolute value of the maximum value of the force factor in the negative direction.

The figures (Fig. 11), (Fig. 12) and (Fig. 13) show the dependences of the force factor for the case when the gear ratio n = 4. In the figure (Fig. 11), 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. As can be seen from the figure (Fig. 11), the maximum positive value of the force factor is greater than the absolute value of the maximum force factor in the negative direction. In the case under consideration, 2.0> | -1.722 |. In the figures (Fig. 12) and (Fig. 13), the dependences correspond to the new initial positions of the unbalances: in the figure (Fig. 12) the dependence corresponds to the rotation of the rapidly rotating unbalances from the initial initial position by an angle γ = 90 °; in the figure (Fig. 13) - at an angle γ = -90 °. As can be seen from the figures (Fig. 12) and (Fig. 13), the laws of oscillations of force factors are symmetrical.

The figures (Fig. 14), (Fig. 15) and (Fig. 16) show the dependences of the force factor with a gear ratio n equal to six (n = 6). In the figure (Fig. 14), the dependence corresponds to the initial initial position of the unbalances. As can be seen from the figure (Fig. 14), the dependence of the force factor is asymmetric. The maximum positive value of the force factor is greater than the absolute value of the maximum force factor in the negative direction (2.0> | -1.87 |). In the figures (Fig. 15) and (Fig. 16), the dependences correspond to the new initial positions of rapidly rotating unbalances. The dependence of the force factor in the figure (Fig. 15) corresponds to the case when the detuning angle γ of the rapidly rotating unbalances from the initial initial position is γ = 90 °. In the figure (Fig. 16), the dependence corresponds to the case when the detuning angle γ = -90 °. As can be seen from the figures (Fig. 15) and (Fig. 16), the laws of oscillations of force factors are symmetrical.

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 the largest magnitude force factors, which is ensured by the transmission, synchronizing and phase matching rotation of the unbalances, with a gear ratio equal to the ratio of the angular velocity of rapidly rotating unbalances to the angular velocity slower novraschayuschihsya to change the law of the power factor of oscillations with asymmetrical to symmetrical change the initial position of rapidly rotating eccentric weight by means of their rotation in either direction at an angle of 90 °, provided that the gear transmission ratio, synchronization and agreed in phase unbalance rotation, is an even number.

The proposed method for regulating the parameters of the law of mechanical fluctuations of power factors 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 located on a common base (Fig. 17), rigidly connected with the working surface of the conveying device. In the figure (Fig. 17), the dotted line shows the initial position of the fast-moving unbalances corresponding to the initial initial position of the unbalances, that is, the position in which the inertia forces of the slow and fast-moving unbalances create the maximum force factors of the same positive direction. This initial position of the unbalances based on the vibration exciter (Fig. 17) is marked with a “+” sign. As noted above, with such an initial position of unbalances, the vibration exciter excites oscillations of the force factor according to an asymmetric law. In this case, the asymmetry of the law of oscillations is expressed in the fact that the maximum positive value of the force factor is greater than the absolute value of its maximum value in the negative direction. In the figure (Fig. 17), based on the vibration exciter, signs 01 and 02 mark two different initial positions of rapidly rotating unbalances, in which the vibration exciter excites vibrations of the force factor (force) according to a symmetric law. Moreover, the symmetry of the law of oscillations means that the maximum positive value of the force factor is equal to the absolute value of its maximum value in the negative direction. In the figure (Fig. 17), rapidly rotating unbalances are shown in one of two possible initial positions of the unbalances, in which the law of oscillations of the force factor excited by the vibration exciter is symmetrical.

It should be noted that with the design of the drive using the proposed method for regulating the parameters of the law of mechanical vibrations of force factors, it is sufficient to use one of the two possible initial positions of rapidly rotating unbalances, which allows to obtain a symmetric law of oscillations of the force factor. 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 a rectilinearly oscillating resulting force. Moreover, depending on the initial phasing of the unbalances, the resulting force oscillates either according to the asymmetric or symmetric law. Therefore, the vibrator, depending on its setting, allows you to inform the working surface of the oscillations according to asymmetric or symmetric laws. The asymmetry of the law of oscillations of the working surface means that the largest positive value of the surface acceleration is not equal to the modulus of the largest negative acceleration. If the law is symmetric, then the largest positive value of the surface acceleration is equal to the absolute value of the largest negative value of acceleration.

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. It should be noted that the message of the working surface of asymmetric vibrations, all other conditions being the same, is accompanied by an increase in the speed of transportation, and hence the productivity of the transport equipment. In addition, the ability of the drive to report asymmetric or symmetric vibrations to the working surface in combination with tilting the surface to the horizontal and communicating inclined vibrations to it allows to significantly expand the range of variation of the transport speed.

In the case of applying the proposed method 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 with rectilinear vibrations of the sieve surface.

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, and the grains of the main culture are immersed in the lower layer of the grain flow. When moving, the grains pass over the openings of the screen 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 of the process as a whole and screening is crucial. The proposed method for communicating the working surface with either asymmetric or symmetric vibrations in combination with tilting the working surface to the horizontal and communicating oblique vibrations to it ensures that the speed of the grain mixture relative to the sieve surface creates the most favorable conditions for screening.

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 parameters of the law of mechanical vibrations of force factors allows to increase the efficiency of screen separation.

In addition, the implementation of the proposed method for regulating the parameters of the law of mechanical fluctuations in force factors opens the prospect of creating a unified drive for transport and technological equipment of grain processing enterprises.

Information sources

1. Patentschrift No. 955756 (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 (force or moment) according to an asymmetric law by a centrifugal vibration exciter, consisting of four unbalances, the rotation axes of which are located on a common base, having the same imbalances in pairs, and having an initial position in which their centrifugal inertia forces create the maximum in magnitude force factors, and angular speeds rotating with the same magnitude, which is ensured by the transmission, synchronizing and matching the phase of the unbalance rotation, with gear ratio equal to the ratio of the angular velocity of rapidly rotating unbalances to the angular velocity of slowly rotating, characterized in that to ensure the symmetry of the law of oscillations, which means that the largest positive value of the force factor is equal to the modulus of its largest negative value, the initial position of the rapidly rotating unbalances is changed by turning them in any direction by an angle equal to 90 °, provided that the gear ratio of the gear synchronizing and phase matching rotation unbalance is an even number.

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