CN218494081U - Cantilever beam type dynamic vibration absorber for eliminating residual vibration of vibration isolation system - Google Patents
Cantilever beam type dynamic vibration absorber for eliminating residual vibration of vibration isolation system Download PDFInfo
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- CN218494081U CN218494081U CN202220696267.9U CN202220696267U CN218494081U CN 218494081 U CN218494081 U CN 218494081U CN 202220696267 U CN202220696267 U CN 202220696267U CN 218494081 U CN218494081 U CN 218494081U
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Abstract
The utility model discloses a cantilever beam formula dynamic vibration absorber that is used for residual vibration of vibration isolation system to eliminate under excitation frequency excursion condition, a serial communication port, include: a column (10); a pair of symmetrical cantilever beams (20) fixed on the upright post; and a mass block (30) provided on the pair of cantilever beams (20), wherein the natural frequency ω of the cantilever beam type dynamic vibration absorber can be made by adjusting the distance l from the mass block (30) on the cantilever beam to the column (10) n Equal to the vibration frequency after the vibration excitation frequency of the vibration source is shifted.
Description
Technical Field
The utility model relates to a vibration control technical field, concretely relates to cantilever beam type dynamic vibration absorber that residual vibration of vibration isolation system was eliminated under excitation frequency skew condition.
Background
If the machine (vibration source) is rigidly connected with the foundation, periodic interference force generated during the operation of the machine can be directly transmitted to the foundation in equal magnitude and then spread to the periphery from the foundation, so that vibration noise pollution in a certain range near the machine is caused. If the rigid connection between the machine and the foundation is changed into proper elastic connection, the vibration and noise reduction effect can be achieved.
Fig. 1 is a theoretical model of a conventional vibration isolation system. The machine with mass M is connected to a rigid foundation via vibration isolators. The vibration isolator can be simplified into a parallel structure of an elastic element with a stiffness coefficient K and a damping element with a damping coefficient C. The machine is subjected to a periodic external force F (t) in the vertical direction during operation.
F(t)＝F 0 sin(ωt) (1)
In the formula: f 0 Is the amplitude of the external force, omega is the working frequency of the machine, and t is the time.
And establishing an x coordinate axis by taking the centroid position of the machine when the machine is static as an origin o and taking the upward direction as a positive direction. Analyzing each vertical force applied to the machine at a certain moment in the motion process, and obtaining a motion differential equation of the machine according to Newton's second law
Solving equation (2), the vibration transmissibility η can be obtained:
that is, the vibration transmissibility η is the magnitude N of the response force transmitted to the base 0 And periodic external force amplitude F 0 It is provided with and (4) the ratio. When F is 0 At a certain time, the smaller η, the smaller N 0 The smaller the vibration isolation effect, the better the vibration isolation effect; the greater η, N 0 The larger the vibration isolating effect, the worse. In equation (3), ζ is the damping ratio
r is the frequency ratio
Fig. 2 is a graph of the variation of the vibration transmission rate η with respect to the frequency ratio r in accordance with equation (3) in the case where the damping ratio ζ is equal to 0.05, 0.25, 1, respectively. When in use
Time, eta>1，N 0 >F 0 The system is in a vibration amplification area; when in use
Time, eta<1，N 0 <F 0 The system is in a vibration isolation area. Based on equation (3), in the vibration isolation region, we obtain:
the vibration transmissivity η infinitely approaches the abscissa (η = 0) as the frequency ratio r increases. This indicates that: the protected object (foundation) is always influenced by the periodic external force F (t), and the amplitude N of the response force transmitted to the foundation 0 Always greater than 0, which is an inherent drawback of the vibration isolation theory described above. Where N is introduced into 0 Referred to as residual vibration of the vibration isolation system. When the frequency ratio r is constant, N 0 Increases with increasing damping ratio ζ; when the damping ratio ζ is constant, N 0 Increasing with decreasing frequency ratio r. In engineering practice, the damping ratio ζ cannot be zero, nor can the frequency ratio r be very large. Therefore, for some machines, although the vibration isolators isolate most of the vibration transmission, residual vibrations remain significant, which can affect machine life and contaminate the surrounding environment.
In addition, in engineering practice, after a machine (vibration source) has been operated for a while, its operating frequency is not constant, but always somewhat shifted (excitation shift), and therefore the residual vibration is changed, which makes the removal of the residual vibration more difficult.
Therefore, there is a need for new technical solutions that at least partially address the deficiencies of the prior art.
SUMMERY OF THE UTILITY MODEL
In order to solve the technical problem, the utility model provides a residual vibration elimination method of vibration isolation system under excitation frequency excursion condition designs and makes cantilever beam formula dynamic vibration absorber, adjusts the position of quality piece on the cantilever beam through the screw thread, realizes the continuous variation of bump leveller natural frequency, can adapt to the condition of machine operating frequency excursion betterly.
According to the utility model discloses an aspect provides a cantilever beam formula dynamic vibration absorber that is used for residual vibration of vibration isolation system to eliminate under the excitation frequency skew condition, include:
a column (10);
a pair of symmetrical cantilever beams (20) fixed on the upright post; and
a mass (30) disposed on the pair of cantilever beams (20),
the natural frequency of the cantilever beam type dynamic vibration absorber can be equal to the vibration frequency omega after the vibration source excitation frequency is shifted by adjusting the distance l between the mass block (30) on the cantilever beam and the upright post (10).
According to the utility model discloses an embodiment, wherein the cantilever beam formula dynamic vibration absorber that is used for vibration isolation system residual vibration to eliminate under the excitation frequency skew condition still includes sole (40), fixes in the bottom of stand (10), and the stand passes through sole (40) from this and fixes on the vibration source.
According to the utility model discloses an embodiment, wherein the cantilever beam formula dynamic vibration absorber that is used for vibration isolation system residual vibration to eliminate under the excitation frequency excursion condition still includes and fixes protection casing (50) on stand (10) top.
According to an embodiment of the invention, wherein the cantilever beam (20) is formed with a thread and the mass (30) is formed with an internal thread, whereby the two are sleeved together by a threaded connection, whereby the mass (30) can be adjusted to the distance of the column (10) by rotation.
According to an embodiment of the invention, the mass (30) comprises two first (31) and second (32) sub-masses of equal mass, the two sub-masses (31, 32) being fitted together.
According to an embodiment of the present invention, wherein the natural frequency ω of the cantilever beam type dynamic vibration absorber 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.
According to an embodiment of the invention, wherein m is 1% -3% of the mass of the vibration source.
Drawings
FIG. 1 is a schematic diagram of a theoretical model according to a conventional vibration isolation system;
fig. 2 is a graph of the variation of the vibration transmissivity η with the frequency ratio r according to the prior art at damping ratios ζ =0.05, 0.25, 1;
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 diagram of the cantilever beam type dynamic vibration absorber for eliminating residual vibration of the vibration isolation system under the condition of exciting frequency deviation according to the embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the following detailed description of the preferred embodiments, which is provided for fully explaining the present invention and is not intended to limit the present invention.
The utility model discloses the people is based on two degrees of freedom vibration models, and the research of theory and experiment has been carried out to the remaining vibration elimination of vibration isolation system under the excitation frequency skew condition. Referring to the two-degree-of-freedom vibration model of fig. 3, a two-degree-of-freedom vibration model is obtained by attaching a spring-mass system (vibration absorber) to a damped one-degree-of-freedom system (main system). m 1 、m 2 All are in a static state, in m 1 、m 2 The centroid position of 1 、O 2 Upward is the positive direction, and x is established 1 、x 2 Coordinate axes. When m is 1 Subjected to a periodic external force F 0 cos (. Omega.t) and m 1 、m 2 When all are in stable motion state, respectively in m 1 、m 2 Analyzing the vertical stress condition of each instant at any moment for the research object, and establishing a vertical motion differential equation set thereof based on Newton's second law
Wherein: m is 1 The primary system mass; k is a radical of 1 Primary system stiffness; c. C 1 The damping coefficient of the main system; f 0 cos (ω t) is applied to m 1 Periodic external force of (F) 0 Is the external force amplitude, omega is the external force frequency, t is the time; m is 2 The mass of the vibration absorber; k is a radical of 2 Is the absorber stiffness.
Solving equation set (5) to obtain m 1 、m 2 Amplitude X of 1 ，X 2
If it is used
Then, in equation (6), there is X 1 And =0. This indicates that: as long as the natural frequency of the vibration absorber
Equal to the frequency of the external force omega, then m 1 And (3) in a static state, eliminating residual vibration, wherein equation (7) is the design basis of the undamped dynamic vibration absorber. Substituting equation (7) into X in equation (6) 2 Formula (I) can obtainX 2 ＝F 0 /K 2 . This particular motion phenomenon can be explained as: elastic element pair m of vibration absorber 1 Elastic force of (2) and (m) 1 The applied periodic external force is a pair of balanced forces which are opposite in time direction and equal in magnitude and act on the same straight line, thereby inhibiting m 1 The vibration of (2).
Based on the research, the utility model discloses an embodiment has designed cantilever beam formula dynamic vibration absorber for eliminate the residual vibration of vibration isolation system under the excitation frequency excursion condition.
The vibration system formed by the continuous uniform cantilever beam under the action of self-weight has the first-order natural frequency of
Wherein l 0 Total length of cantilever beam, p l And E is the beam linear density, E is the beam material elastic modulus, and I is the beam cross section moment of inertia.
The equation (8) is arranged in the form
Where m 'is the equivalent mass at the end of the beam, the same as the effect of the beam's own weight, i.e.
The natural frequency of the vibration system consisting of the mass m and the weightless cantilever beam is as follows:
wherein l is the distance from the mass center of the mass block to the side surface of the upright post.
When the combined consideration is given to the combined action of the equivalent mass m' and the mass block m on the cantilever beam with the circular section and the diameter d,vibration absorber natural frequency omega n Is composed of
When the natural frequency ω of the dynamic vibration absorber in equation (12) n When the vibration frequency is equal to the vibration exciting frequency omega of the vibration isolating system, the mass vibration of the vibration source is eliminated.
The above equation (12) is an application theory of the cantilever beam type dynamic vibration absorber.
Fig. 4 is a schematic structural diagram of the cantilever beam type dynamic vibration absorber for eliminating residual vibration of the vibration isolation system under the condition of exciting frequency deviation according to the embodiment of the invention.
Referring to fig. 4, the cantilever beam type dynamic vibration absorber may include an upright (10), a pair of symmetrical cantilever beams (20) fixed to the upright, a mass (30) provided on the pair of cantilever beams (20), a bottom end foot plate (40) fixed to the upright (10), and a protection cover (50) fixed to the top end of the upright (10). The uprights are fixed to a vibration source (50) (e.g. a machine of the master system) by means of foot plates (40).
More specifically, a pair of cantilever beam type dynamic vibration absorbers are symmetrically designed in structure in consideration of the stress balance and the running stability of the main system after the vibration absorbers are added. The thread can be symmetrically turned from both ends of a round section steel bar with the diameter d. A round through hole with the diameter equal to that of a steel rod is drilled in the middle of the upper part of a steel upright post (10) with a square cross section. The steel rod (namely, the cantilever beam 20) with the threaded wires at the two ends penetrates into the through hole of the upright post, the through hole is positioned in the middle of the steel rod, and the steel rod and the upright post are welded by spot welding at the contact edge of the through hole on the left side surface and the right side surface of the upright post and the steel rod when the steel rod is vertical to the upright post. And under the condition that the upright post is vertical to the foot plate (40), the foot plate is welded at the lower end of the upright post. 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 through bolts and nuts or directly welded on the mass block (vibration source 60) of the main system.
Two identical cantilever beams 20, which are symmetrically distributed, are respectively provided with a mass block 30 with the same mass. The mass m may consist of two first 31 and second 32 sub-masses of the same mass, in the form of nuts, with an internal thread, each of which has a mass equal to half the mass m of the mass. The internal thread of the mass 1 and the mass 2 are matched with the external thread of the cantilever beam, and the first sub-mass 31 and the second sub-mass 32 can move left and right on the cantilever beam through the thread by rotating. After positioning, the first sub-mass 31 and the second sub-mass 32, which are close together, are screwed back on each other, and additional friction is obtained by a slight elastic deformation of the engaged thread wires, so that the masses are locked in a certain designated position of the cantilever beams, without loosening and deflection of the masses occurring in the following work.
The shield 50 is welded with a thin steel plate in a rectangular parallelepiped shape without a lower cover. And (4) penetrating a bolt through a through hole in the center of the upper cover of the protective cover, and screwing the bolt into a screw hole in the top end of the pillar to fix the protective cover on the top end of the pillar. The cantilever beam and the mass block are wrapped in the protective cover, so that when the vibration isolation system is indoors, the vibration isolation system can be prevented from being influenced by touch of people or animals, dust accumulation and the like; when the vibration isolation system is outdoors, it can also be protected from erosion or interference by wind, rain, snow, birds, or the like.
The following is an exemplary description of a rotating electric machine.
A machine with a mass of 100kg and a rotation speed of 1000r/min, a damping coefficient of 2100 N.s/m and a rigidity coefficient of 4 x 10 5 On the rubber pad of N/m, the damping ratio zeta is calculated to be 0.166, the frequency ratio r is 1.65 and the vibration transmissibility eta is 0.63 by the equation (3), which shows that: n is a radical of 0 ＝0.63F 0 I.e. the amplitude of the response force received by the foundation is 63% of the amplitude of the periodic external force, the residual vibration is significant.
In order to design a lightweight vibration absorber, the mass m of the mass is typically chosen to be 1% to 3% of the mass of the primary system (e.g., vibration source). If m is 2% of the machine mass, m =2kg, and both the first and second sub-masses are 1kg. The cantilever beam is made of A3 steel with the widest application and good comprehensive performances of machining, strength, welding and the like, and the density rho =7810kg/m of the steel cantilever beam 3 Diameter d of d=12mm, beam linear density ρ is calculated l =0.8833kg/m. Design of the Beam Total Length l 0 =400mm, the equivalent mass m' =0.08586kg is calculated based on equation (10). The beam elastic modulus E =210GPa, and the mass m =2kg.
Substituting the relevant parameters into equation (12), and calculating to obtain the following parameters, wherein the parameters are equal to the vibration exciting frequency of the vibration isolation system of 1000 r/min: the distance l =298.1mm from the mass center of the mass block to the side face of the upright post.
Due to the combination of one or more of the reasons of voltage reduction, overlarge load, overlarge bearing abrasion, cage type rotor conducting bar fracture or desoldering and the like, the rotating speed of a machine motor deviates, and the rotating speed is reduced from 1000r/min to 990r/min. From equation (12), l =300.3mm from the mass center to the cantilever side can be calculated. During operation, the mass block is moved outwards by 2.2mm and is finely adjusted. The operation is flexible, simple and convenient. The cantilever beam type dynamic vibration absorber provided by the application can be used for eliminating residual vibration of a vibration isolation system under the condition of vibration excitation frequency deviation, and more accords with the practical engineering application condition.
The above description of the embodiments is provided to facilitate understanding and application of the present invention by those of ordinary skill in the art. It will be readily apparent to those skilled in the art that various modifications to these embodiments may be made, and the generic principles described herein may be applied to other embodiments without the use of the inventive faculty. Therefore, the present invention is not limited to the embodiments herein, and those skilled in the art should understand that modifications and alterations made without departing from the scope of the present invention are within the protection scope of the present invention.
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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| CN202220696267.9U CN218494081U (en) | 2022-03-28 | 2022-03-28 | Cantilever beam type dynamic vibration absorber for eliminating residual vibration of vibration isolation system |
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