RU2441714C1 - Mode of excitation of resonant mechanical oscillations - Google Patents

Abstract

FIELD: vibration equipment.

SUBSTANCE: invention refers to vibration equipment and can be used to excite mechanic oscillations at the resonant frequencies. It is proposed to ensure elastic mounting of masses in two orthogonally related directions along ox, oy axis, to adjust oscillating system setting effective own frequencies of, correspondingly, rolling bodies and masses and effective resonant angular spin rate of rotors (calculation formula provided). The invention also considers the cases of progressive oscillation masses excitement along the elliptic trajectory and along circular lines.

EFFECT: power consumption reduction and operation enhancement.

3 cl, 2 dwg

Description

The invention relates to vibration technology and can be used in all industries for the excitation of mechanical vibrations at resonant frequencies.

One of the most promising ways to create high-performance energy-saving vibrating machines is based on the phenomenon of resonance. In the resonant state, the vibrational system of the machine makes a movement close to its own, in which the elastic and inertial forces are mutually balanced, and the energy of the pathogen is used only to overcome dissipative forces. However, due to the shortcomings of the resonant circuits of existing vibration machines with the usual resonance of forced oscillations - low stability, complexity of adjustment, they are not widely used in industry (Goncharevich I.F. -8. Vibrations in technology: a Handbook in 6 volumes. T 4. Vibration processes. M: Mechanical Engineering, 1981, p.139-141, p.351).

In many vibration machines and installations, not one, but several vibration exciters installed on the same working body (carrier body) are used. A necessary condition for the normal functioning of such machines is the coordinated synchronous operation of vibration exciters.

A known method of excitation of mechanical vibrations, based on the use of the phenomenon of self-synchronization of two or more kinematically and electrically unrelated inertial (unbalanced) vibration exciters (unbalanced rotors) mounted on a common working body (carrier body), which can oscillate on an elastic suspension. The rotors of the vibration exciters receive rotation from independent asynchronous electric motors or DC motors (Blekhman I.I. What can vibration be? M .: Nauka. 1988. P.132, Fig. 1, a).

The phenomenon of self-synchronization is that the rotors of two or more unbalanced vibration exciters rotate with the same or multiple angular velocities ω and with certain mutual phases, while the same rotors on a fixed base have different rotation speeds ω _i , i = 1, 2, ..., s, s≥2. Velocities ω _i are called partial and are assumed to be fairly close.

At present, the most widespread are vibration machines and installations with two self-synchronizing vibration exciters, since with an increase in their number, the synchronization areas are greatly narrowed.

This solution has the following disadvantages:

- Resonant modes of vibration of machines and plants with self-synchronizing unbalanced vibration exciters, which are the most energetically effective, are practically unrealizable due to their low stability under the usual resonance of forced vibrations. For this reason, these machines operate in a far-resonant mode of oscillation.

- In the case of resonance tuning, in order to overcome the region of intense resonant oscillations, it is necessary to have an engine whose power is 5-6 times higher than the power required to operate in the resonance mode.

- The large centrifugal forces created during the rotation of the unbalances load the bearings, which reduces their life and entails a large unproductive energy consumption for overcoming the resistance to rotation of the shaft. There are other drawbacks, among which we note that in the resonant mode of operation, the driving force must have an additional component acting against the forces of inertia.

As a prototype adopted parametric vibration exciter and the method of its operation according to the patent of the Russian Federation No. 2072660 (application No. 94008295, B06B 1/16, publ. 01.27.1997).

The parametric vibration exciter contains a housing, a drive shaft, elastic elements and rolling elements; at least one inertial element is rigidly fixed on the drive shaft in the form of a balanced flywheel (rotor) equipped with a pair of open treadmills that are symmetrically relative to two mutually perpendicular diameters, and their centers are offset from the axis of rotation of the flywheel in diametrically opposite directions, and circular running the tracks of one pair are rotated around the axis of the flywheel by an angle of 90 ° relative to the other, rolling bodies with the possibility of rolling in the form of four odds are placed on circular racetracks different balanced runners.

The working body (the plate to which, for example, the vibratory conveyor tray is attached), vibration exciter (balanced flywheel (rotor) with rolling bodies) and elastic bonds form an oscillatory system. The flywheel is a monolithic part with treadmills on both its planes.

Resonant mechanical vibrations in the direction of the axis oX are excited due to periodic forced changes in the inertial parameters of the oscillatory system.

The physical essence of the known method of excitation of oscillations consists in the fact that flywheel imbalance is automatically formed in the zone of parametric resonance, which leads to the appearance of a disturbing force. However, the flywheel plays the role of a kinetic energy accumulator. In the non-resonant zone, the flywheel is completely balanced.

The disadvantages of the prototype are as follows:

- Until now, the question remains open about the possibility of coordinated synchronous operation of two or more parametric vibration exciters without special additional synchronizing means.

- Designed to excite unidirectional (along the axis ox) rectilinear mechanical vibrations, which significantly limits the scope of its application.

- The inability to excite circular and elliptical vibrations of the working body.

These shortcomings are eliminated by the proposed solution.

The problem is being solved of creating a fundamentally new energy-saving method for exciting resonant mechanical vibrations of multivibrator machines and plants with the expansion of operational capabilities and productivity.

The technical result is the excitation of resonant mechanical vibrations by coordinated synchronous operation of two or more parametric vibration exciters installed on a common working body (carrier body) connected to the base by elastic bonds, with the achievement of the effect of self-synchronization without external interference. In this case, a previously unknown generalized principle of self-synchronization is implemented, combining the well-known principles of self-synchronization of oscillating bodies such as pendulums and rotating bodies such as unbalanced rotors.

This technical result is achieved by the fact that resonant vibrations are excited by periodically forcibly changing the inertial parameters of the oscillatory system formed by the masses M ₁ and M ₂ on an elastic suspension and two or more identical parametric vibration exciters, including rotors with treadmills and rolling bodies in them and driven into rotation from independent electric motors, carry out elastic suspension of the masses M ₁ and M ₂ in two mutually perpendicular directions along the axes oh, oh, make settings the oscillatory system, setting the average value of the partial angular rotational speeds of the rotors of the vibration exciters ω, the effective eigenfrequencies λ ₁ , λ ₂ respectively of the rolling elements and masses M ₁ , M ₂ that satisfy the resonance relation

ω = λ ₁ + λ ₂ ,

where λ ₁ = νω, λ ₂ = (λ _2x + λ _2y ) / 2, λ _2x , λ _2y are the eigenfrequencies corresponding to the translational antiphase modes of oscillations of the masses M ₁ and M ₂ in the direction of the axes ox, oy, and the oscillation is self-synchronized system, as a result of which, between the masses M ₁ and M ₂ , a synchronous resonant antiphase oscillation mode with a frequency of Ω ₂ ≅λ _{2 is established} , and between the rolling bodies a synchronous resonant coherent oscillation mode with a frequency of Ω ₁ ≅νω, with the center of mass (gravity) the system of rolling bodies of each of the rotors rotates around their axes with about otherness angular velocity Ω = Ω ₂ in the direction of rotor rotation, while the angular velocities of the rotors themselves may be different;

to excite translational oscillations of masses M ₁ and M ₂ along elliptical trajectories, the natural frequencies λ _2x , λ _2y are chosen different, but so that these frequencies are close and located in the resonance zone, and the frequency λ ₂ is determined by the formula

λ ₂ = (λ _2x + λ _2y ) / 2.

Figure 1 shows a diagram of one of the possible devices that implements the proposed method, and figure 2 is an inertial element of a parametric vibration exciter.

The vibration device consists of two identical bodies (steel plates) 1 and 2. The plates are connected to each other and the base plate 3 by coil springs 4. The springs are clamped between the cups and sockets in the plates using studs 5 and nuts with locknuts 6. The base plate 3 is installed on the base 7. This elastic system has wide possibilities for regulating the lateral stiffness of compressed springs by changing their length.

Two identical parametric vibration exciters 8 are symmetrically mounted on the plate 1 and are driven in rotation from independent asynchronous motors 9 or DC motors. The axis of the drive shafts 10 of the vibration exciters 8 are parallel and removed from the center of mass O of the plate 1 at the same distance. Adjusting weights 11 are fixed on plates 1, 2.

Two masses of the device, one of which is M ₁ (total mass of bodies 1, 8, 9, 11, 13), and the other M ₂ (total mass of bodies 2, 11) form a two-mass oscillatory system.

The elastic system provides the possibility of translational antiphase free oscillations of masses M ₁ and M ₂ in any directions of the oxy plane (rotor plane of rotation 8), defined by the fixed axes ox, oy.

The choice of the two-mass dynamic model is due to the fact that with antiphase resonance vibrations of the masses M ₁ and M _{2, the} vibration effect transmitted to the laboratory bench is largely compensated.

Each of the vibration exciters includes at least one rotor 8 having, on both sides, a pair of open racetracks 12 located symmetrically with respect to its two mutually perpendicular diameters. The centers of the treadmills 12 are offset from the axis of rotation of the rotors by the same distance AB = l towards the treadmill (figure 2). In the treadmills 12 are placed the same balanced rolling elements 13 of mass m each with the possibility of running the tracks 12.

The coordinate system Ax'y'z 'with the beginning in the center of mass of the rotor 8 moves progressively relatively motionless O ₁ x ₁ y ₁ z ₁ , and the axis z' is directed along the axis of the drive shaft (figure 2). In the position of static equilibrium, the axes of these coordinate systems coincide.

The position of the mass M ₁ is determined by the coordinates x, y, and the rolling bodies with angles φ _k , k = 1, 2, ..., N (N = 4) (figure 2). The orientation of the treadmills is determined by the angles ψ _k = ω ₁ t + 2πk / N, where ω ₁ is the angular velocity of the left rotor, k = 1, 2, ..., N. Note that the angles ψ _{k are} counted relative to the coordinate system relatively uniformly rotating with the rotor .

, где ω_i - угловая скорость i-го ротора вибровозбудителя. Вторую подсистему образуют связанные пружинами массы М₁ и М₂.The method is as follows. With a uniform rotation of the rotors of the vibration exciters, the rolling bodies form in the field of centrifugal inertia forces a subsystem of rolling oscillators (pendulums) with suspension points at the centers of curvature of the treadmills with natural frequencies

where ω _i is the angular velocity of the i-th rotor exciter. The second subsystem is formed by the masses M ₁ and M ₂ connected by springs.

For operating vibrations, resonance vibrations at a frequency λ ₂ corresponding to translational antiphase vibrational modes of masses M ₁ and M ₂ in the direction of the axes ox and oy are taken. Moreover, the shape of the resonant oscillations at a frequency of λ ₂ is close to the corresponding form of free vibrations.

The two-mass vibrational subsystem is held by elastic bonds along all twelve possible coordinates in space. In the general case, the solution of free vibrations in the absence of damping consists of j = 12 harmonics that enter each coordinate and add up without affecting each other. In different coordinates, the individual harmonics are either in the same phase or in antiphase. Other phase shifts are not possible. If the amplitude of one harmonic is known for any harmonic, then the amplitudes of this harmonic are also determined for all other coordinates using distribution coefficients χ _ij , where i is the coordinate number, j is the natural frequency number.

The shape of the resonant oscillations at a frequency λ _{j of an} undamped system coincides with the natural form of free vibrations with a frequency λ _j . Obviously, even with a slight damping, the shape of the resonant vibrations will be close to the shape of free vibrations.

The vibration system of the vibration device is tuned by setting the average angular rotation speed ω of the vibration exciter rotors, parameters ν, ε, effective natural frequencies λ ₁ = νω, λ ₂ = (λ _2x + λ _2y ) / 2, respectively, of the rolling bodies and masses M ₁ , M ₂ satisfying the resonance relation

,ω = λ ₁ + λ ₂ for

,

, S≥2, λ_2x, λ_2y - собственные частоты, соответствующие поступательным противофазным формам колебаний масс М₁ и М₂ в направлении осей ox, oy,

, ε=σν²Nmρ_C/(2M₁l) - коэффициент, пропорциональный отношению общей массы тел качения к массе М₁,

,

- относительные коэффициенты линейного демпфирования тел качения и массы М_1. Здесь I_B - момент инерции тел качения относительно оси обкатки, n₀=b₀/2I_B, n=b/2M₁ - приведенные коэффициенты линейного демпфирования в направлении координат φ_k и x, y, b=(b_x+b_y)/2; b₀, b_x, b_y - обобщенные коэффициенты линейного сопротивления в направлении координат φ_k и x, y, ρ_C=ВС; σ - число роторов вибровозбудителей.Where

, S≥2, λ _2x , λ _2y - eigenfrequencies corresponding to the translational antiphase vibrational modes of masses M ₁ and M ₂ in the direction of the axes ox, oy,

, ε = σν ² Nmρ _C / (2M ₁ l) is a coefficient proportional to the ratio of the total mass of the rolling bodies to the mass M ₁ ,

,

are the relative coefficients of linear damping of the rolling elements and masses M _1. Here I _B is the moment of inertia of the rolling bodies relative to the running axis, n ₀ = b ₀ / 2I _B , n = b / 2M ₁ are the linear damping coefficients in the coordinate direction φ _k and x, y, b = (b _x + b _y ) / 2; b ₀ , b _x , b _y - generalized linear resistance coefficients in the direction of coordinates φ _k and x, y, ρ _C = BC; σ is the number of rotors of vibration exciters.

To excite translational antiphase oscillations of masses M ₁ and M ₂ along elliptical trajectories in the plane of rotation of the rotors of the vibration exciters defined by the axes ox, oy, the natural frequencies λ _2х , λ _2у are chosen different, but so that they are close and located in the resonance zone, and λ ₂ = (λ _2x + λ _2y ) / 2.

To excite translational antiphase oscillations of masses M ₁ and M ₂ along circular paths, the natural frequencies are chosen equal to λ _2x = λ _2y = λ ₂ for b _x при b _y .

When two (or any even number) rotors of vibration exciters rotate in opposite directions, resonant translational rectilinear oscillations of masses M ₁ and M _{2 are} excited in the direction of the oy axis.

The device operates as follows. Energy is supplied to the vibrating system of the vibrating device by means of rotating rotors of vibration exciters.

First, we consider the separate operation of vibration exciters, for example, the left.

, которые выполняют функции инерционного элемента вибрационного устройства. Колеблющиеся массы М₁, М₂ могут выполнять роль рабочих органов. Если за рабочий орган взята масса М₂, то масса М₁ выполняет роль реактивной массы.When the rotor 8 is rotated uniformly with an angular velocity of ω ₁ , the rolling bodies of this rotor form a subsystem of N identical rolling oscillators (pendulums) with running axes at the centers of curvature of the treadmills with the same natural frequencies

that perform the functions of the inertial element of the vibrating device. The oscillating masses of M ₁ , M ₂ can serve as working bodies. If the mass M _{2 is} taken as the working body, then the mass M ₁ acts as a reactive mass.

и выполнении порогового условия

в системе возбуждается многократный комбинационный параметрический резонанс с возникновением коллективного взаимодействия указанных выше подсистем. При этом колебательная система виброустановки синхронизируется на частотах

, где

,

- некратные частоты генерации.The uniform rotation of the rotor 8 generates a periodic change in the inertial parameters (inert properties) of the oscillatory system with a period of 2π / ω ₁ . When setting up

and the fulfillment of the threshold condition

multiple Raman resonance resonance is excited in the system with the occurrence of collective interaction of the above subsystems. In this case, the vibration system of the vibration installation is synchronized at frequencies

where

,

- multiple generation frequencies.

. Поскольку

, то неуравновешенная центробежная сила инерции будет возбуждать резонансные колебания масс М₁, М₂, которые в свою очередь вызывают резонансные колебания осцилляторов качения.Due to the synchronization of the phases of the rolling oscillators according to the type of oscillating pendulums (Huygens phenomenon), the center of mass of the system of rolling bodies describes, as a first approximation, a circle with respect to the coordinate system Ax'y'z '(Fig. 2), which moves progressively relative to the stationary Oxyz. The angular velocity of the center of mass along this circle is

. Insofar as

, then the unbalanced centrifugal inertia force will excite the resonant oscillations of the masses M ₁ , M ₂ , which in turn cause resonant oscillations of the rolling oscillators.

, тогда как ротор инерционного элемента вращается с угловой скоростью ω₁. При ν=0.25 угловая скорость

приблизительно на 25% ниже угловой скорости ω₁.Thus, an invisible unbalance is automatically formed, which rotates at an angular speed.

, while the rotor of the inertial element rotates with an angular velocity ω ₁ . At ν = 0.25, the angular velocity

approximately 25% below the angular velocity ω ₁ .

.Turning off the left vibration exciter and considering the uniform rotation of the rotor 8 of the right vibration exciter with an angular velocity ω ₂ sufficiently close to ω ₁ , we arrive at the formation of a second invisible unbalance that rotates at an angular velocity

.

When the vibration exciters work together, the invisible unbalances are self-synchronized as unbalanced rotors. In this case, the invisible unbalances rotate with the same angular velocity Ω, while the angular velocities of the rotors of inertial elements can be different.

Here, self-synchronization of oscillating bodies such as pendulums and rotating bodies such as unbalanced rotors is simultaneously realized. The coordinated work of vibration exciters is achieved by the system itself without external interference and manifests itself as a result of its self-organization.

In contrast to the self-synchronization of several conventional unbalanced vibration exciters mounted on one carrier body, the self-synchronization region of several parametric vibration exciters does not depend on their number and is determined by the width of the resonance zone (region of instability of the equilibrium position). This area can be arbitrarily wide.

An example implementation of the method.

To test the feasibility of the practical implementation of the method, the current model was made according to Fig.1.

A four-pendulum inertial element of mass m _IE = 1.72 kg (rotor 8 with rolling bodies 13) of each of the vibration exciters was fixed on the cantilever end of the drive shaft of the DC motor. The model used the same electric motors with a power of 77 W with an adjustable speed (0-3000 rpm). Rotors and rolling bodies with a mass of m = 0.105 kg each are made of steel.

The oscillatory system of the model setup is constructed so that M ₁ = 27.7 kg, M ₂ = 20 kg, λ _2x = 150.7 s ^-1 , λ _2y = 155.4 s ^-1 , ν = 0.25, ε = 0.007. Here, λ _2x , λ _2y are the experimentally determined (by the method of forced oscillations) eigenfrequencies of translational antiphase rectilinear oscillations of masses M ₁ , M ₂ in the direction of the axes ox, oy. Note that in the direction of the ox axis, lateral vibrations of the compressed coil springs are used. The detuning of their own translational antiphase modes of oscillation of the masses of M ₁ and M _{2 was} carried out using the adjusting weights 11 and changing the stiffness of the springs.

,

.At the first stage of testing, the separate operation of vibration exciters was investigated. They were alternately introduced into the mode of Raman parametric resonance with angular velocities ω ₁ = 193 s ^-1 , ω ₂ = 198 s ^-1 . In this case, the following values of the frequencies of generation of antiphase oscillations of masses M ₁ , M ₂ were recorded:

,

.

The angular velocity of rotation of the rotors and the frequency of oscillations of the masses M ₁ , M ₂ were measured using a strobotachometer, and the amplitude of the oscillations was measured using a BP-1 hand-held vibrograph.

Under stroboscopic illumination and a slight mismatch in the frequency of lamp flashes, out-of-phase oscillations of the masses M ₁ and M ₂ along elliptical trajectories (almost according to the harmonic law) were observed. We note the absence of beats of two fairly close eigenfrequencies λ _2x , λ _2y , which indicates the synchronization of the generation frequencies according to Huygens.

When the vibration exciters worked together, the following results were obtained: ω ₁ = 189.4 s ^-1 , ω ₂ = 197.8 s ^-1 , Ω ₂ = 149 s ^-1 . In this case, translational antiphase oscillations of the masses M ₁ , M ₂ along elliptical trajectories were observed.

Resonant oscillations of the masses M ₁ , M ₂ along circular paths are obtained as a special case for λ _2x = λ _2y and b _x ≅ b _y .

With the opposite direction of rotation of the rotors, translational rectilinear antiphase oscillations of masses M ₁ , M ₂ in the direction of the oy axis were observed.

So, the oscillatory system of the vibrating device self-synchronizes at the frequency of rotation of invisible unbalances (at the frequency of oscillations of masses M ₁ , M ₂ ), while the angular velocities of the rotors of the vibration exciters themselves are different. A synchronous mode is established between the rotors, in which a total disturbing force arises.

When parametric vibration exciters work together, a previously unknown generalized principle of self-synchronization is implemented, combining two well-known principles - self-synchronization of oscillating bodies such as pendulums (Huygens phenomenon) and self-synchronization of rotating bodies such as unbalanced rotors.

The proposed method of excitation has the following advantages:

1. Resonant oscillations are excited under any initial conditions. The self-excitation effect provides almost absolute stability of the resonant mode of oscillations (within the resonance zone) at high quality factor of the oscillatory system.

2. The installed power of the vibrodrive can be significantly (twice) reduced in comparison with the inertial (unbalanced) self-synchronizing vibration exciters used in industry with the resonance setting, i.e. The method is among the new energy-saving technologies.

3. The increase in the amplitude of parametric oscillations according to the exponential law makes it advantageous to use the proposed method of excitation in vibration machines that work with frequent shutdowns and ons (for example, in dispensers). It is not necessary to stop the engine. It is enough to remove the vibrator from the resonance zone.

4. A vibrator with self-synchronizing parametric vibration exciters is a self-organizing "technical team" in which individual objects are tuned to the rhythm of the collective as a whole.

5. The effect of the expansion of the resonance zone is realized with a significant increase in the linear damping of the working body relative to the level of damping of the rolling elements. In all other cases, an increase in damping narrows the resonance zone.

6.With an increase in the number of self-synchronizing conventional inertial (unbalanced) vibration exciters installed on one carrier body, the synchronization region narrows significantly, while the synchronization region of parametric vibration exciters does not depend on the number of vibration exciters and is determined by the width of the resonance zone, and the resonance zone can be arbitrarily wide.

Claims (3)

1. The method of excitation of resonant mechanical vibrations, which consists in the fact that resonant vibrations are excited by periodically forcing the inertial parameters of the oscillatory system formed by masses M ₁ and M ₂ on an elastic suspension and two or more identical parametric vibration exciters, including rotors with treadmills and bodies rolling in them and driven into rotation from independent electric motors, characterized in that they carry out elastic suspension of the masses M ₁ and M ₂ in two mutually perpendicular In the axial directions along the axes ox, oy, the vibrational system is tuned, setting the average value of the partial angular rotational speeds of the vibration exciters rotors ω, the effective natural frequencies λ ₁ , λ ₂ , respectively, of the rolling elements and masses M ₁ and M ₂ , which satisfy the resonance relation
ω = λ ₁ + λ ₂ ,
where λ ₁ = νω, λ ₂ = (λ _2x + λ _2y ) / 2, λ _2x , λ _2y are the eigenfrequencies corresponding to the translational antiphase modes of oscillations of the masses M ₁ and M ₂ in the direction of the axes ox, oy, and the oscillation is self-synchronized system, as a result of which between the masses M ₁ and M ₂ a synchronous resonant antiphase oscillation mode with a frequency of Ω ₂ ≅λ _{2 is established} , and between the rolling bodies - a synchronous resonant coherent oscillation mode with a frequency of Ω ₁ междуνω, while the center of mass (gravity) the system of rolling bodies of each of the rotors rotates around their axes with one Nakova angular velocity Ω = Ω ₂ in the direction of rotor rotation, while the angular velocities of the rotors themselves may be different. 2. The method according to claim 1, characterized in that in order to excite translational oscillations of masses M ₁ and M ₂ along elliptical trajectories, the natural frequencies λ _2x , λ _2y are chosen different, but so that these frequencies are close and located in the resonance zone, and the frequency λ _{2 is} determined by the formula λ ₂ = (λ _2x + λ _2y ) / 2. 3. The method according to claim 1, characterized in that for the excitation of translational circular oscillations of masses M ₁ and M _{2 the} natural frequencies λ _2x , λ _2y are chosen equal, and λ ₂ = λ _2x = λ _y .

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