RU2671932C1 - Method of adjusting parameters of law of mechanical oscillations of power factors in centrifugal vibration exciter - Google Patents

Abstract

FIELD: machine building.SUBSTANCE: invention relates to vibration equipment, particularly to agroindustrial complex, and can be used for grain processing enterprises in the process and transport equipment, and also in other industries related to the processing of bulk materials. According to the invention, in a four-balanced vibration exciter, which excites oscillations of force factors according to an asymmetric law to ensure a symmetric law of oscillations, meaning the equality of the greatest absolute values of the force factor in the positive and negative directions, change the initial position of the slow-moving imbalances.EFFECT: technical result is a variation in the speed of transportation and higher efficiency 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 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 unbalance inertia forces add up to form a resultant force whose dependence 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 equal to 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, 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).

.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 located symmetrically with respect 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

view

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 quickly 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) obeying 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. 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 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 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.

Therefore, in the transport equipment, in order 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 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 the passage component is small, and the bulk body thickness is many times greater than the particle size, only particles located in the lower layer, into which they fall as a result of self-sorting, are sifted through the 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 setting of the vibration exciter, to provide excitation of oscillations of force factors according to an asymmetric or symmetric law.

The ability to configure the vibration exciter to excite either asymmetric vibrations or symmetric vibrations of force factors in combination with the inclination of the working surface to the horizontal and the communication of the surface of inclined vibrations 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 fluctuations 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 unbalancing in phase rotation of the 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, meaning the largest positive value of the force factor is equal to the modulus of its largest negative value, the initial position of the slowly rotating unbalances is changed by their rotation in any direction by an angle equal to the product of the quotient of dividing 90 ° by gear ratio, synchronizing and matching the phase of the unbalance rotation, by a fractional number from the interval of values from zero point five to four times the value of gear ratio minus point zero point five, provided that the ratio is a fractional number, multiplying by two we get an odd 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. При таких значениях передаточного отношения кинематический цикл механизма вибровозбудителя, то есть время, по истечении которого дебалансы возвращаются в начальное положение, соответствует двум оборотам медленновращающихся дебалансов. При этом число оборотов быстровращающихся дебалансов равно удвоенному значению передаточного отношения.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 a fractional number of the form n = i + 0.5, where i is any positive integer. Such fractional numbers can be characterized as follows: a fractional number, when multiplied by two, we get an odd number 2n = 2i + 1. Note that 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. With such values of the gear ratio, 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 of slowly rotating unbalances. Moreover, the number of revolutions of rapidly rotating unbalances is equal to twice the value of the gear ratio.

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 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 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, 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 the maximum power factors of the same direction in magnitude. We take this direction as positive. Such conditions for the initial position of the 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 therefore 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 ƒ(δ). 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 discussions, the dependence of the excited force factor will be denoted in the general form as ƒ (δ). 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.

; соотношение максимальных силовых факторов, создаваемых силами инерции медленно и быстровращающихся дебалансов.We define the conditions for the initial phasing of slowly 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 slowly rotating unbalances, it is necessary to keep the vibration exciter settings unchanged, which affect the characteristics of the law of oscillations. These parameters are: initial phasing of rapidly 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 i+0,5, где i - любое натуральное число. 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 быстровращающихся 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 slowly 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 i + 0.5, where i is any natural number. The initial initial position of the unbalances is their position in which the inertia forces of the rapidly and slowly rotating unbalances create force factors that are maximum in magnitude in the same direction (Fig. 5) and (Fig. 6). Consequently, the invariable initial position of rapidly 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 slowly rotating unbalances by turning them from the initial initial position by some arbitrary angle y. 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 slowly 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 slowly 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 slowly 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 is a fractional number of the form 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 of slowly rotating 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, since the trigonometric function cosine, which determines the position of slowly rotating unbalances, is a periodic function with a period equal to 360 °, the angle y can take values in the range from 0 ° to 360 °.

The vibration exciter excites fluctuations in 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 y at which the system of equations (8) has a solution.

The solution to the first equation of system (8) is the following values of the angle of rotation of rapidly rotating unbalances from the initial position

where k = 0.1, ... 4n-1;

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

In this case, slowly rotating unbalances will occupy positions corresponding to the following values of the angle δ of their rotation from the initial initial position, that is, the position in which their inertia forces create the maximum force factor in the positive direction

Since the angle y can take values from 0 ° to 360 ° and slowly rotating unbalances for the kinematic cycle of the vibration exciter mechanism make two turns, the sum of the angles δ and γ cannot take values greater than 1080 °, that is, the condition 0 ° <δ must be satisfied + γ <1080 °. Therefore, the solution of the second equation of system (8) has the form

where k ₁ , = 0, 1, 2, 3, 4, 5.

From equation (11) it follows that the roots of the second equation of system (8) are the following six values of the sum of the angles δ and γ: 1) δ + γ = 90 °; 2) δ + γ = 270 °; 3) δ + γ = 450 °; 4) δ + γ = 630 °; 5) δ + γ = 810 ° and 6) δ + γ = 990 °.

It should be noted that when determining the values of the angle y, the following conditions must be taken into account: if δ + γ = 90 °, then the condition 0 ° <γ <90 ° must be fulfilled, that is, in this case the angle y cannot take values greater than 90 °; if δ + γ = 270 °, then 0 ° <γ <270 °; if δ + γ = 450 °, then the values of the angle γ lie in the interval from 0 ° to 360 °, that is, 0 ° <γ <360 °; if δ + γ = 630 °, then 0 ° <γ <360 °; if δ + γ = 810 °, then 90 ° <γ <360 °; if δ + γ = 990 °, then 270 ° ≤γ <360 °.

To determine the values of the angle γ, the system of equations (8) was solved by sequentially considering each of the six values of the sum of the angles δ and γ. In this case, we took into account what values the angle γ can take for the considered value of the sum of the angles δ + γ. Analysis of the solution allowed us to propose a method for calculating the values of the angle γ.

We will not dwell on the solution of the system of equations (8). As an example, consider the solution to this system of equations for the first value of the sum of angles.

Let us determine what values the angle γ can take in the case when the root of the second equation of the system is

From equation (12) it follows that

After substituting the expression for the angle δ from equation (10) into equation (12) and transformations, we obtain

In this case, when determining the angle y, the following condition must be taken into account: if γ + δ = 90 °, then the condition 0 ° <γ <90 ° must be fulfilled, that is, in this case the angle γ cannot take values greater than 90 °. Since 0 ° <γ <90 °, the following inequality

Consider the fulfillment of the first condition of inequality (15), i.e.

After substituting the expression for the gear ratio n = i + 0.5 and transformations, we have

The right-hand side of inequality (17) represents a series of odd numbers, since the coefficient k takes values from a number of natural numbers, including zero. The left side of the inequality is a fractional number, which has the integer part i and the fractional part equal to zero point five. Therefore, the maximum value of the coefficient k is determined from the condition

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

It follows from the equation that

If the integer part i of the fractional number n is an odd number, then the maximum value of the coefficient k is determined by the formula

Consider the fulfillment of the second condition of inequality (15), i.e., the conditions

After transformations of inequality (22), we have

Obviously, inequality (23) holds for any value of the coefficient k. Therefore, the variable coefficient k has a minimum value of zero, i.e.

To simplify further considerations, we rewrite equation (14) for determining the values of the angle γ in the form

Where

From equation (25) it follows that the angle γ is obtained by multiplying two factors. The first factor is the quotient of dividing 90 ° by the gear ratio n of the gear, synchronizing and matching the phase of the unbalance rotation. This factor is a constant value, since it depends only on the value of the gear ratio n of the transmission used in the vibration exciter to synchronize and coordinate the phase of rotation of the unbalances. The second factor C ₁ represented by equation (26) is a variable due to the variability of the number k.

We determine the minimum and maximum values of the variable factor C ₁ .

If the integer part i of the fractional number n is an even number, then to determine the minimum and maximum values of the variable factor C ₁ , we substitute into equation (26) the values of k _max and k _min from equations (20) and (24), respectively. After the transformations we get

and

If the integer part i of the fractional number n is an odd number, then to determine the minimum and maximum values of the factor C ₁ , we substitute the values of k _max and k _min into equations (26) from equations (21) and (24), respectively. After the transformations we get

The maximum value of the factor C ₁ , in this case (δ + γ = 90 ° and 0 <γ <90 °), does not depend on whether the integer part i of the fractional number n is even or odd. In both cases, the maximum value of the variable factor C is determined by the formula (28)

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

Since the coefficient k can take values from a number of natural numbers, including zero, then, as can be seen from formula (26), each subsequent value of the factor С ₁ differs from the previous one by two units. Therefore, the values of the factor C ₁ are fractional numbers of the same type as the gear ratio n. That is, the factor C ₁ is a fractional number, the fractional part of which is equal to zero point five. Knowing the minimum and maximum values of the factor C ₁ , it is easy to determine its values, which it takes on the interval of values from C _1min to C _1max .

The results of determining the values of the angle γ for the other five values of the roots of the second equation of system (8) allow us to draw the following conclusion.

The system of equations (8) has a solution if the angle γ is determined, firstly, as the product of two factors: the first factor is the quotient of dividing 90 ° by the gear ratio n of the gear, synchronizing and matching the phase of the unbalance rotation; the second factor sequentially takes values equal to fractional numbers from the interval of values from zero point five tenths to four times the gear ratio n minus point zero point five, secondly, provided that the gear ratio n is a fractional number, multiplying it by two, we get odd number.

The presented conclusions correspond to the case when, in order to change the nature of the law of oscillations of the force factor from asymmetric to symmetric, the initial position of the slowly rotating unbalances is changed by turning them by an angle γ in the direction of rotation.

It should be noted that when determining the values of the angle γ, the direction coinciding with the direction of rotation of the unbalances was taken as the positive direction of reading the angle. Thus, the conclusions presented above correspond to the case of determining the positive values of the angle γ.

Similar conclusions were obtained for the case of a change in the initial position of slowly rotating unbalances by turning them in the opposite direction to the direction of rotation of the unbalances, that is, when rotating slowly rotating unbalances by an angle of γ. Note that in this case the dependence of the force factor in a dimensionless expression has the form

. При этом, всякому положительному значению угла γ₊ соответствует такое отрицательное значение угла γ_, что сумма абсолютных значений этих углов равна 360°. Из представленных выше рассуждений следует, что для любого положительного значения угла у₊ существует отрицательное значение угла γ_, при котором зависимость ƒ(δ)=cosnδ+acos(δ-γ_) совпадает с зависимостью ƒ(δ)=cosnδ+acos(δ+у₊). Такое совпадение зависимостей можно объяснить следующим образом. Дебалансы занимают одно и то же начальное положение при повороте медленновращающихся дебалансов из исходного начального положения в положительном направлении на угол у₊ или в отрицательном направлении на угол равный по абсолютной величине

=360° - у₊. Аналогично, дебалансы занимают одинаковое начальное положение при повороте медленновращающихся дебалансов в отрицательном направлении на угол γ_ или при их повороте в положительном направлении на угол у₊=360° -

It has been established that the nature of the law of oscillations of the force factor changes from asymmetric to symmetric if the negative values of the angle γ in absolute value are equal to the positive values of the angle, that is, each positive value of the angle γ corresponds to the negative value of the angle equal to it in absolute value

. Moreover, to any positive value of the angle γ _{+ there} corresponds such a negative value of the angle γ_ that the sum of the absolute values of these angles is 360 °. From the above reasoning, it follows that for any positive value of the angle y ₊ there is a negative value of the angle γ_ at which the dependence ƒ (δ) = cosnδ + a cos (δ-γ_) coincides with the dependence ƒ (δ) = cosnδ + a cos ( δ + y ₊ ). Such a coincidence of dependencies can be explained as follows. Unbalances occupy the same initial position when you turn slowly rotating unbalances from the initial initial position in the positive direction by the angle y ₊ or in the negative direction by an angle equal in absolute value

= 360 ° - y ₊ . Similarly, the unbalances occupy the same initial position when the slowly rotating unbalances are turned in the negative direction by the angle γ_ or when they are turned in the positive direction by the angle y ₊ = 360 ° -

To confirm the methodology for determining the values of the angle y proposed above, the dependences ƒ (δ) = cosnδ + a cos (δ + γ) and ƒ (δ) = cosnδ + a cos (δ-γ) of force factors were studied for the gear ratio n of the transmission, synchronizing and phase-matching rotation of unbalances equal to 1.5; 2.5; 3.5; 4.5 and 5.5. In the study of the dependences at the selected gear ratio n, the angle γ was calculated. For the calculated values of the angle γ, graphs of the dependences of force factors were constructed and these dependences were studied for extrema.

. На рисунках (фиг. 9), (фиг. 10), (фиг. 11), (фиг. 12), (фиг. 13) и (фиг. 14) представлены зависимости силовых факторов для начальных положений медленновращающихся дебалансов при положительных значениях угла γ, определенных по предложенной выше методике. В рассматриваемом случае (n=1,5) угол у принимает следующие значения: 30°; 90°; 150°; 210°; 270° и 330°. Следует заметить, что такое начальное положение дебалансов представлено на рисунке (фиг. 7) для некоторого произвольного положительного значения угла у. Как видно из рисунков (фиг. 9), (фиг. 10), (фиг. 11), (фиг. 12), (фиг. 13) и (фиг. 14) законы колебаний силовых факторов симметричные. Максимальное положительное значение силового фактора равно максимальному по абсолютной величине значению силового фактора в отрицательном направлении.In the figures (Fig. 8), (Fig. 9), (Fig. 10), (Fig. 11), (Fig. 12), (Fig. 13) and (Fig. 14) as an example, the dependences of the power factor for the case: the gear ratio n of the gear synchronizing and matching the phase of the rotation of the unbalance is equal to one point five tenths (n = 1.5); 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 is -1. In the figure (Fig. 8), the dependence corresponds to the initial position of the unbalances, in which the inertia forces of 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 maximum in absolute value of the force factor in the negative direction. In the case under consideration

. The figures (Fig. 9), (Fig. 10), (Fig. 11), (Fig. 12), (Fig. 13) and (Fig. 14) show the force factors for the initial positions of slowly rotating unbalances with positive values of the angle γ determined according to the method proposed above. In the case under consideration (n = 1.5), the angle y takes the following values: 30 °; 90 °; 150 °; 210 °; 270 ° and 330 °. It should be noted that this initial position of the unbalances is shown in the figure (Fig. 7) for some arbitrary positive value of the angle y. As can be seen from the figures (Fig. 9), (Fig. 10), (Fig. 11), (Fig. 12), (Fig. 13) and (Fig. 14), the laws of oscillation of force factors are symmetrical. The maximum positive value of the force factor is equal to the maximum absolute value of the force factor in the negative direction.

The results of determining the extrema of the dependences of the force factor at negative values of the angle γ confirmed the previously obtained conclusion. With a gear ratio of n = 1.5, the angle y has the following negative values: -30 °; -90 °; -150 °; -210 °; -270 ° and -330 °. In the study of these dependences, it was found that the dependence ƒ (δ) = cos1.5δ + cos (δ + 30 °) coincides with the dependence ƒ (δ) = cos1.5δ + cos (δ-330 °), since in this case, firstly, the unbalances occupy the same initial position, and secondly, cos (δ + 30 °) = cos (δ-330 °). The second position is easily proved using well-known formulas. For the same reasons, the dependences coincide: ƒ (δ) = cos1.5δ + cos (δ + 90 °) and ƒ (δ) = cos1.5δ + cos (δ- 270 °); ƒ (δ) = cos1.5δ + cos (δ + 150 °) and ƒ (δ) = cos1.5δ + cos (δ-210 °);

ƒ (δ) = cos1.5δ + cos (δ + 210 °) and ƒ (δ) = cos 1.5δ + cos (δ-150 °);

ƒ (δ) = cos 1.5δ + cos (δ + 270 °) and ƒ (δ) = cos1.5δ + cos (δ-90 °);

ƒ (δ) = cos1.5δ + cos (δ + 330 °) and ƒ (δ) = cos1.5δ + cos (δ -30 °).

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 change the law of fluctuations of the force factor from asymmetric to symmetric, change the initial position of the slowly rotating unbalances by turning them in any direction by an angle equal to the product of the quotient of dividing 90 ° by the gear ratio, synchronizing and matching the phase of the unbalance rotation by a fractional number from the range of values from zero point five to four times the gear ratio minus point zero point five provided that the gear the ratio is a fractional number, when multiplied by two we get an odd 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. 15), rigidly connected with the working surface of the conveying device. In the figure (Fig. 15), the dotted line shows the initial position of the slowly rotating unbalances corresponding 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 of the same positive direction. This initial position of the unbalances based on the vibration exciter (Fig. 15) 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 maximum in absolute value of its negative value. In the figure (Fig. 15), for the case when the gear ratio n of the gear synchronizing and matching the phase of the unbalance rotation is one point five tenths (n = 1.5) based on the vibration exciter with signs 01, 02, 03, 04, 05 and 06 marked six different initial positions of slowly rotating unbalances, in which the vibration exciter excites oscillations of the force factor (force) according to the symmetric law. Moreover, the symmetry of the law of oscillations means that the maximum positive value of the force factor is equal to the maximum negative value in absolute value. In the figure (Fig. 15), slowly rotating unbalances are shown in one of six possible initial positions of the unbalances, in which the law of oscillations of the force factor excited by the vibration exciter is symmetric.

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 suffices to use one of the six possible initial positions of the slowly 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. At the same time, depending on the initial phasing of the unbalances, the resulting force oscillates either according to an asymmetric or symmetric law. Consequently, the vibrator, depending on its setting, allows the working surface to be informed of 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 communication of the working surface of asymmetric oscillations, ceteris paribus, is accompanied by an increase in the transportation speed, 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.

Bibliography.

1. Patentschrift No. 955 756 (DFR), Cl. 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)

A method for controlling the parameters of the law of mechanical vibrations of force factors in a centrifugal vibration exciter, which excites vibrations according to an asymmetric law, 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 magnitude force factors, and rotating with the same magnitude angular velocities, which is ensured by the transmission, synchronizing and matching in phase, the rotation of unbalances, with a gear ratio n 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, they change the initial position of the slowly rotating unbalances by rotation in any direction by an angle equal to the product of the quotient of dividing 90 ° by the gear ratio n of a transmission synchronizing and coordinating in phase the rotation of the unbalances by a fractional number from the interval of values from 0.5 to 4n-0.5 with a step equal to unity, provided that the gear ratio n is a fractional number, when multiplied by two it turns out an odd number.

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