CN218494081U - Cantilever Beam Dynamic Absorber for Residual Vibration Elimination in Vibration Isolation System - Google Patents

Abstract

The utility model discloses a cantilever beam type dynamic vibration absorber used for eliminating the residual vibration of a vibration isolation system under the condition of excitation frequency deviation, which is characterized in that it comprises: a column (10); a pair of symmetrical Cantilever beam (20); and the mass block (30) that is arranged on a pair of cantilever beams (20), wherein, by adjusting the mass block (30) on the cantilever beam to the distance l of column (10), can make the cantilever beam The natural frequency ω _n of the type dynamic vibration absorber is equal to the vibration frequency after the excitation frequency of the vibration source is shifted.

Description

Cantilever Beam Dynamic Absorber for Residual Vibration Elimination in Vibration Isolation System

technical field

The utility model relates to the technical field of vibration control, in particular to a cantilever beam dynamic vibration absorber for eliminating the residual vibration of a vibration isolation system under the condition of excitation frequency deviation.

Background technique

If there is a rigid connection between the machine (vibration source) and the foundation, the periodic disturbance force generated when the machine is running will be directly transmitted to the foundation in equal magnitude, and then propagated from the foundation to the surroundings, causing vibration noise within a certain range near the machine pollute. If the rigid connection between the machine and the foundation is changed to a suitable elastic connection, it can reduce vibration and noise.

Figure 1 is a theoretical model of a traditional vibration isolation system. A machine of mass M is connected to a rigid foundation through vibration isolators. The vibration isolator can be simplified as a parallel structure of an elastic element with a stiffness coefficient of K and a damping element with a damping coefficient of C. When the machine is running, it is acted by a periodic external force F(t) in the vertical direction.

F(t)＝F ₀ sin(ωt) (1)

In the formula: F ₀ is the amplitude of the external force, ω is the working frequency of the machine, and t is the time.

Take the position of the center of mass of the machine at rest as the origin o, and take upward as the positive direction to establish the x-coordinate axis. Analyze the vertical forces received by the machine at a certain moment in the process of motion, and obtain the differential equation of motion of the machine according to Newton's second law

Solving equation (2), the vibration transmissibility η can be obtained:

r为频率比

That is, the vibration transmissibility η is the ratio of the response force amplitude N ₀ transmitted to the foundation to the periodic external force amplitude F ₀ . When F ₀ is constant, the smaller η, the smaller N ₀ , the better the vibration isolation effect; the larger η, the larger N ₀ , the worse the vibration isolation effect. In addition, in the above equation (3), ζ is the damping ratio

r is the frequency ratio

时，η>1，N₀>F₀，系统处于振动放大区域；当

时，η<1，N₀<F₀，系统处于隔振区域。基于方程(3)，在隔振区域，得到：Fig. 2 is based on the equation (3), under the condition that the damping ratio ζ is equal to 0.05, 0.25, 1 respectively, the relationship curve of the vibration transmissibility η and the frequency ratio r is made. when

When η>1, N ₀ >F ₀ , the system is in the region of vibration amplification; when

When η<1, N ₀ <F ₀ , the system is in the vibration isolation region. Based on equation (3), in the vibration isolation region, we get:

The vibration transmissibility η is infinitely close to the abscissa (η=0) as the frequency ratio r increases. This shows that the protected object (foundation) will always be affected by the periodic external force F(t), and the response force amplitude N ₀ transmitted to the foundation is always greater than 0, which is the inherent defect of the above-mentioned vibration isolation theory. Here _N0 is called the residual vibration of the vibration isolation system. When the frequency ratio r is constant, N ₀ increases with the increase of the damping ratio ζ; when the damping ratio ζ is constant, N ₀ increases with the decrease of the frequency ratio r. In engineering practice, the damping ratio ζ cannot be zero, and the frequency ratio r cannot be very large. Therefore, for some machines, although the vibration isolator isolates most of the vibration transmission, the residual vibration is still very obvious, and these residual vibrations will affect the life of the machine and pollute the surrounding environment.

In addition, in engineering practice, after the machine (vibration source) has been running for a period of time, its operating frequency will not remain unchanged, but will always have some offset (excitation offset) more or less, so the residual vibration will also change with time. changes, which makes it more difficult to eliminate residual vibration.

Therefore, new technical methods are needed to at least partially solve the deficiencies in the prior art.

Utility model content

In order to solve the above-mentioned technical problems, the utility model provides a method for eliminating the residual vibration of the vibration isolation system under the condition of excitation frequency deviation, designs and manufactures a cantilever beam dynamic vibration absorber, and adjusts the position of the mass block on the cantilever beam through threaded wires , to realize the continuous change of the natural frequency of the vibration absorber, which can better adapt to the deviation of the working frequency of the machine.

According to one aspect of the present invention, there is provided a cantilever beam dynamic vibration absorber for eliminating the residual vibration of the vibration isolation system under the condition of excitation frequency deviation, including:

Column (10);

a symmetrical pair of cantilever beams (20) secured to the uprights; and

a mass (30) mounted on a pair of cantilever beams (20),

Wherein, by adjusting the distance l between the mass block (30) on the cantilever beam and the column (10), the natural frequency of the cantilever beam dynamic vibration absorber can be equal to the vibration frequency ω after the vibration source excitation frequency is shifted.

According to an embodiment of the present utility model, wherein the cantilever beam type dynamic vibration absorber for eliminating the residual vibration of the vibration isolation system under the condition of excitation frequency deviation further includes a foot plate (40), which is fixed on the bottom end of the column (10), The column is thus fixed on the vibration source by the foot plate (40).

According to the embodiment of the present utility model, wherein the cantilever beam type dynamic vibration absorber for eliminating the residual vibration of the vibration isolation system under the condition of excitation frequency deviation further includes a protective cover (50) fixed on the top of the column (10).

According to an embodiment of the present utility model, wherein the cantilever beam (20) is formed with a threaded wire, and the mass block (30) is formed with an internal threaded thread, thus the two are socketed together by threaded connection, thus the mass block (30) ) can be adjusted to the distance to the column (10) by turning.

According to the embodiment of the present utility model, mass block (30) comprises the first sub-mass block (31) and the second sub-mass block (32) of two equal masses, the first sub-mass block (31) and the second sub-mass block (31) and the second sub-mass block (31) The two pieces (32) are tightly attached together.

According to an embodiment of the present utility model, wherein the natural frequency ω _n of the cantilever beam dynamic vibration absorber is:

Among them, E is the elastic modulus of the cantilever beam material, d is the cross-sectional diameter of the cantilever beam, l ₀ is the total length of the cantilever beam, m is the mass of a mass block on a cantilever beam, and l is the mass block on a cantilever beam to The distance from the column, m' is the equivalent mass at the end of the beam that has the same effect as the beam's own weight.

According to the embodiment of the utility model, wherein m is 1%-3% of the mass of the vibration source.

Description of drawings

Figure 1 is a schematic diagram of a theoretical model based on a traditional vibration isolation system;

Fig. 2 is when according to the damping ratio ζ=0.05,0.25,1 of prior art, the change relation curve diagram of vibration transmissibility η and frequency ratio r;

Fig. 3 is a schematic diagram of a two-degree-of-freedom vibration model according to an embodiment of the present invention; and

Fig. 4 is a schematic structural view of a cantilever beam dynamic vibration absorber used for eliminating residual vibration of a vibration isolation system under the condition of excitation frequency deviation according to an embodiment of the utility model.

Detailed ways

The utility model will be further described in detail through specific embodiments below in conjunction with the accompanying drawings. The content shown is used to fully explain the content of the utility model, and is not used to limit the utility model.

Based on the two-degree-of-freedom vibration model, the utility model has carried out theoretical and experimental research on the elimination of residual vibration of the vibration isolation system under the condition of excitation frequency offset. Referring to the two-degree-of-freedom vibration model in Figure 3, the two-degree-of-freedom vibration model is to add a spring-mass system (vibration absorber) to a damped single-degree-of-freedom system (main system). When both m ₁ and m ₂ are in a static state, take the position of the centroid of m ₁ and m ₂ as the origin O ₁ and O ₂ , and upward as the positive direction to establish the x ₁ and x ₂ coordinate axes. When m ₁ is subjected to the periodic external force F ₀ cos(ωt) and m ₁ and m ₂ are in a stable state of motion, take m ₁ and m ₂ as the research objects respectively, and analyze their respective vertical force situations at any instant , based on Newton's second law to establish its vertical motion differential equations

Among them: m ₁ is the mass of the main system; k ₁ is the stiffness of the main system; c ₁ is the damping coefficient of the main system; F ₀ cos(ωt) is the periodic external force applied to m ₁ , F ₀ is the amplitude of the external force, and ω is the frequency of the external force , t is the time; m ₂ is the mass of the shock absorber; k ₂ is the stiffness of the shock absorber.

Solving equations (5), the amplitudes X ₁ and X ₂ of m ₁ and m ₂ can be obtained

if

等于外力频率ω，则m₁处于静止状态，残余振动得以消除，方程(7)即为无阻尼动力吸振器的设计依据。将方程(7)代入方程(6)中的X₂式，可得X₂＝F₀/K₂。这种特殊的运动现象可解释为：吸振器的弹性元件对m₁的弹性作用力与m₁受到的周期外力是一对时刻方向相反、大小相等、且作用于同一直线上的平衡力，从而抑制了m₁的振动。Then, in equation (6), there is X ₁ =0. This shows that: as long as the natural frequency of the vibration absorber

is equal to the external force frequency ω, then m ₁ is in a static state, and the residual vibration is eliminated. Equation (7) is the design basis for the undamped dynamic vibration absorber. Substituting Equation (7) into X ₂ in Equation (6), X ₂ =F ₀ /K ₂ can be obtained. This special motion phenomenon can be explained as: the elastic force of the elastic element of the shock absorber on m ₁ and the periodic external force on m ₁ are a pair of balance forces with opposite directions and equal magnitudes acting on the same straight line at all times, so The vibration of _m1 is suppressed.

Based on the above research, the implementation of the utility model designs a cantilever beam dynamic vibration absorber, which is used to eliminate the residual vibration of the vibration isolation system under the condition of excitation frequency deviation.

The vibration system formed by a continuous uniform cantilever beam under the action of its own weight, its first-order natural frequency is

Among them, l ₀ is the total length of the cantilever beam, ρ _l is the linear density of the beam, E is the elastic modulus of the beam material, and I is the moment of inertia of the beam cross section.

Arranging equation (8) into the following form

Among them, m' is the equivalent mass at the end of the beam that has the same effect as the beam's own weight, that is,

The natural frequency of the vibration system composed of mass m and weightless cantilever beam is:

Among them, l is the distance from the center of mass of the mass block to the side of the column.

Considering the joint action of the equivalent mass m' and mass m on a circular cross-section cantilever beam with diameter d, the natural frequency ω _n of the vibration absorber is

When the natural frequency ω _n of the dynamic vibration absorber in equation (12) is equal to the excitation frequency ω of the vibration isolation system, the mass vibration of the vibration source can be eliminated.

The above equation (12) is the application theory of the cantilever beam dynamic vibration absorber.

Fig. 4 is a schematic structural view of a cantilever beam dynamic vibration absorber used for eliminating residual vibration of a vibration isolation system under the condition of excitation frequency deviation according to an embodiment of the utility model.

With reference to Fig. 4, the cantilever beam type dynamic vibration absorber can comprise a column (10), a pair of symmetrical cantilever beams (20) fixed on the column, a mass block (30) arranged on a pair of cantilever beams (20), a fixed At the bottom foot plate (40) of column (10) and the protective cover (50) that is fixed on the top of column (10). The column is fixed on the vibration source (50) (such as the machine of the main system) through the foot plate (40).

More specifically, a pair of cantilever beam dynamic vibration absorbers are designed symmetrically in terms of structure, considering the force balance and smooth operation of the main system after the additional vibration absorber is added. Thread wires can be symmetrically driven from both ends of a circular section steel rod with a diameter of d. Drill a circular through hole equal to the diameter of the steel rod at the middle position of the steel column (10) top with a square cross section. Put the steel rod (that is, the cantilever beam 20) with threaded wires at both ends into the through hole of the column. The edge of contact with the steel rod is welded with spot welding. Under the condition that the column is perpendicular to the foot plate (40), weld the foot plate to the lower end of the column. The foot plate is symmetrically provided with bolt through holes, and the foot plate can be fixed on the mass block of the main system by bolts and nuts, or the foot plate is directly welded on the mass block (vibration source 60) of the main system.

Two identical cantilever beams 20 distributed symmetrically are respectively equipped with mass blocks 30 of the same mass. A mass with a mass of m can be composed of two nut-like first sub-mass blocks 31 and second sub-mass blocks 32 of the same mass with internal threads, and their mass is equal to half of the mass m of the mass block . The internal threads of mass block 1 and mass block 2 are matched with the external thread threads of the cantilever beam. By rotating the first sub-mass block 31 and the second sub-mass block 32, they can move left and right on the cantilever beam through the thread thread . After positioning, the first sub-mass 31 and the second sub-mass 32 that are close together are reversely tightened, and the small elastic deformation generated by the engaged thread wires is used to obtain additional friction, thereby locking the mass on the cantilever beam A certain specified position, the loosening and offset of the quality block will not occur in the subsequent work.

Protective cover 50 is welded into the cuboid shape that does not have lower cover with thin steel plate. After passing the bolt through the through hole at the center of the upper cover of the protective cover, screw it into the screw hole at the top of the pillar to fix the protective cover on the top of the pillar. The protective cover wraps the cantilever beam and the mass block. When the vibration isolation system is indoors, it can avoid being affected by human or animal contact, dust accumulation, etc.; when the vibration isolation system is outdoors, it can also avoid being affected by wind. Erosion or disturbance by , rain, snow or birds etc.

In the following, a rotating electric machine is taken as an example for illustration.

A machine with a mass of 100kg and a rotational speed of 1000r/min is placed on a rubber pad with a damping coefficient of 2100N·s/m and a stiffness coefficient of 4×10 ⁵ N/m. According to equation (3), the damping ratio ζ is calculated as 0.166, the frequency ratio r is 1.65, and the vibration transmissibility η is 0.63, indicating that: N ₀ =0.63F ₀ , that is, the magnitude of the response force on the foundation is 63% of the magnitude of the periodic external force, and the residual vibration is obvious.

In order to design a lightweight vibration absorber, the mass m of the mass block is generally selected to be 1% to 3% of the mass of the main system (eg vibration source). Here, if m is 2% of the machine mass, then m=2kg, and both the first sub-mass and the second sub-mass are 1kg. The cantilever beam is made of A3 steel with the widest application and good comprehensive performance in machining, strength and welding. The density of the steel cantilever beam is ρ=7810kg/m ³ , and the diameter d=12mm. The calculated linear density of the beam is ρ _l =0.8833kg/m . The total length of the designed beam is l ₀ =400mm, based on equation (10), the equivalent mass m'=0.08586kg is calculated. The modulus of elasticity of the beam is E=210GPa, and the mass block m=2kg.

Substituting relevant parameters into Equation (12), which is equal to the excitation frequency of the vibration isolation system 1000r/min, is calculated: the distance from the center of mass of the mass to the side of the column is l = 298.1mm.

Due to one or a combination of reasons such as voltage drop, excessive load, excessive bearing wear, cage-type rotor bar breakage or desoldering, the motor speed of the machine deviates from 1000r/min to 990r/min . According to equation (12), it can be calculated that l=300.3mm from the center of mass of the mass block to the side of the cantilever beam. During operation, it is only necessary to move the mass block outward by 2.2mm and make fine adjustments. This operation is flexible, simple and convenient. The cantilever beam dynamic vibration absorber proposed in this application can be used to eliminate the residual vibration of the vibration isolation system under the condition of excitation frequency shift, which is more in line with the actual engineering application.

The above description of the implementation examples is for those of ordinary skill in the technical field to understand and apply the utility model. It is obvious that those skilled in the art can easily make various modifications to these embodiments, and apply the general principles described here to other embodiments without creative effort. Therefore, the utility model is not limited to the embodiments here, and improvements and modifications made by those skilled in the art according to the disclosure of the utility model without departing from the scope of the utility model should be within the protection scope of the utility model.

Claims (6)

1. A cantilever beam type dynamic vibration absorber for eliminating residual vibration of a vibration isolation system is characterized by comprising:

a column (10);

a pair of symmetrical cantilever beams (20) fixed on the upright column; and

a mass (30) disposed on the pair of cantilever beams (20),

wherein, the distance between the mass (30) on the cantilever beam and the upright post (10) is adjustedFrom l, the natural frequency omega of the cantilever beam type dynamic vibration absorber can be enabled _n Equal to the vibration frequency after the vibration excitation frequency of the vibration source is shifted.

2. The vibration isolation system residual vibration canceling cantilever beam type dynamic vibration absorber according to claim 1, further comprising a foot plate (40) fixed to a bottom end of the pillar (10), whereby the pillar is fixed to the vibration source through the foot plate (40).

3. The vibration isolation system residual vibration canceling cantilever beam type dynamic vibration absorber according to claim 1, wherein the cantilever beam (20) is formed with a threaded wire and the mass (30) is formed with an internally threaded wire, whereby the two are nested together by a threaded connection, whereby the mass (30) can be adjusted to the distance to the column (10) by turning.

4. The vibration isolation system residual vibration canceling cantilever beam type dynamic vibration absorber according to claim 1, wherein the mass (30) comprises two first (31) and second (32) sub-masses of equal mass, both the first (31) and second (32) sub-masses being fitted closely together.

5. The vibration isolation system residual vibration canceling cantilever-beam type dynamic vibration absorber of claim 1, wherein said cantilever-beam type dynamic vibration absorber has a natural frequency ω _n Comprises the following steps:

wherein E is the elastic modulus of the cantilever beam material, d is the cross section diameter of the cantilever beam, l ₀ The length of the cantilever beam is m, the mass of a mass block on the cantilever beam, l is the distance from the mass block on the cantilever beam to the upright post, and m' is the equivalent mass which is positioned at the tail end of the beam and has the same effect with the self weight of the beam.

6. The vibration isolation system residual vibration canceling cantilever beam type dynamic vibration absorber according to claim 1, wherein m is 1% to 3% of the mass of the vibration source.

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