CN108229055B - Optimized design method of three-way equal-rigidity air-floating vibration isolation system with overlapped mass and rigidity - Google Patents
Optimized design method of three-way equal-rigidity air-floating vibration isolation system with overlapped mass and rigidity Download PDFInfo
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Abstract
The invention provides an optimal design method of a three-dimensional equal-rigidity air-floating vibration isolation system with rigid superposition, which comprises the following steps: (1) determining design parameters of a vibration control system; (2) determining a preliminary scheme of an air-floating vibration control system; (3) establishing a finite element variable model with variable design parameters according to the design parameters, and dividing the grids with proper precision to realize full-parametric modeling of the whole finite element; (4) calculating a mode; (5) determining an ideal design parameter model: judging whether the parameters related to the mode of the air floating type vibration control system obtained through mode calculation meet a certain relation, if so, recording the design parameters of the air floating system at the moment, and if not, returning to the step (2) to modify the preliminary scheme of the air floating type vibration control system; (6) and (3) correcting an ideal model: and according to the value range of the design parameters in the actual engineering and the economic target meeting the minimum consumption, the design parameters are corrected after selection so as to determine the final scheme of the vibration control system.
Description
Technical Field
The invention relates to a design method of a vibration isolation system, in particular to an optimal design method of an air-floating vibration isolation system.
Background
According to the principle of vibration control, active control and passive control can be divided. The active vibration control means that in the vibration control process, a certain control strategy is applied according to the vibration of the structure or the system detected by the sensor, and the actuator is driven to apply a certain force or moment to the structure or the system through real-time calculation so as to control the vibration of the structure or the system. The passive control device has simple structure and easy realization, and currently, air springs are generally adopted at home and abroad as passive vibration isolation elements. For passive vibration isolation systems, the natural frequency should be as low as possible in order to obtain good vibration isolation for various disturbances. However, in a practical sense, it is difficult to reduce the natural frequency to 1Hz or lower. Therefore, the passive vibration isolation system has a limited control effect on micro-vibration, and has basically no capability of acting on direct interference on the platform, so that under the condition that the initial conditions are limited, how to quickly realize the overall high-efficiency design in the prior art is not disclosed in the case of large-scale special-shaped air floating platform passive vibration isolation projects such as asymmetric arrangement of precise equipment, non-uniform grouping of large-scale air springs, high specific gravity of special-shaped branch modal vibration participation and the like, and technical personnel in the field tend to abandon a passive control device and turn the passive control device to an active control device.
At present, when the traditional technical method aims at the vibration control of precision equipment, only the reduction of the fundamental frequency of an air-floating vibration control system is generally considered, and when the frequency meets the design requirement, the damping ratio of the system is adjusted to meet the vibration reduction requirement, so that the mode of the system is possibly disordered, and meanwhile, the stability of the system is poor. The conventional method thus has the following disadvantages:
(1) when the traditional technical method is used for controlling the vibration of the precision equipment, the three-directional rigidity of the system is usually not considered to be equal, only the fundamental frequency is considered to be reduced, the fundamental frequency of the system is blindly reduced, and the difference of the first three-order modal fundamental frequencies of the system is large in practical use, so that the system mode is disordered, the vibration reduction efficiency is low, and even high-order modal resonance can occur to cause a high-order resonance phenomenon.
(2) The traditional technical method generally adopts a method of controlling the system fundamental frequency and adjusting damping ratio to damp vibration. When the damping is large, the system rigidity is large, so that the system fundamental frequency is increased, and the requirement that the fundamental frequency of the precision equipment is less than 1Hz is difficult to meet; when the damping is smaller, the system stability is poor and the vibration reduction efficiency is low.
Disclosure of Invention
In order to overcome the defects in the prior art, the design concept of the invention is that an air-floating type micro-vibration control design method is adopted for the precision equipment according to the requirements of the operating environment, based on the vibration isolation theory, the dual quantitative discrimination technology of the relationship between the modal vibration type mass accumulation participation coefficient and the mutual ratio of the first three basic frequencies is established by utilizing the power characteristics of a passive air-floating system when masses are just overlapped, an infinite freedom degree power system is designed into a similar single-mass point single-freedom degree system, finally, the equal or similar rigidity of the air-floating type vibration isolation system in three directions, namely two horizontal directions and one vertical direction is realized, and the high-efficiency control is easy to be carried out on the micro-vibration environment of the precision equipment.
The invention aims to provide an optimal design method of a three-dimensional equal-rigidity air-floating vibration isolation system with rigid superposition, which comprises the following steps:
(1) design parameter determination: determining design parameters of a vibration control system according to the load, the allowable vibration value of the precision equipment, the building structure form and the foundation;
(2) determining a preliminary scheme of the air floating type vibration control system, including the number, arrangement mode and model of air springs;
(3) parametric modeling: and establishing a finite element variable model with variable design parameters according to the design parameters, and dividing the grids with proper precision to realize full-parametric modeling of the whole finite element.
(4) And (3) modal calculation: calculating to obtain parameters related to the mode of the air floating type vibration control system;
(5) determining an ideal design parameter model: judging whether the parameters related to the mode of the air floating type vibration control system obtained through mode calculation meet a certain relation, if so, recording the design parameters of the air floating system at the moment, and if not, returning to the step (2) to modify the preliminary scheme of the air floating type vibration control system;
(6) and (3) correcting an ideal model: and reasonably correcting the design parameters after comparison and selection according to the value range of the design parameters in the actual engineering and the economic target meeting the minimum consumption, thereby determining the final scheme of the vibration control system.
Preferably, the design parameters of step (1) include: basic thickness h of high-rigidity platform of air floatation system1T-shaped droop thickness h of high-rigidity platform of air floatation system2And the basic side length w, the mass and/or the rigidity of the high-rigidity platform of the air floatation system.
Preferably, the step (2) includes:
(2-1) determining the number of the required air springs according to the mass of the precision equipment;
(2-2) determining an air spring arrangement mode according to a top plate of the system platform;
and (2-3) selecting the type of the air spring according to the implementation experience of similar engineering.
Preferably, the suitable accuracy in the step (3) is that the difference between the basic frequency values in the modal calculation results of adopting two adjacent mesh refinements is not more than 0.1%, and the mesh accuracy of the system is considered to meet the suitable accuracy.
Preferably, the modality-related parameters in the step (4) include: front three-order vibration mode x1、x2、x3And its frequency value f1，f2，f3Vibration mode mass participation coefficient delta1，δ2，δ3。
Preferably, obtaining the modality-related parameters of the step (4) comprises: solving partial differential equation for inherent dynamic characteristics of the air floating platform by adopting a separation variable method to obtain front third-order vibration type x of the air floating type vibration control system1、x2、x3And its frequency value f1，f2，f3Vibration mode mass participation coefficient delta1，δ2，δ3。
Preferably, the certain relationship in step (5) includes: delta1+δ2+δ3> 95% and | f1/f2-1|＜5％、|f1/f3-1|＜5％、|f2/f3-1| < 5%, wherein δ1，δ2，δ3Representing the mass participation coefficient f of the front third-order vibration mode of the air-floating vibration control system1，f2，f3And the first three-order frequency value of the air floating type vibration control system is represented.
Preferably, the step (6) comprises: according to the basic thickness h of the high-rigidity platform of the air floatation system in the actual engineering1T-shaped droop thickness h of high-rigidity platform of air floatation system2And the value range of the basic side length w of the high-rigidity platform of the air floatation system, the economic target of lowest consumption is met, and the basic thickness h of the high-rigidity platform of the air floatation system with the design parameters is reasonably corrected after selection1T-shaped droop thickness h of high-rigidity platform of air floatation system2And the basic side length w of the high-rigidity platform of the air floatation system, thereby determining the final scheme of the vibration control system.
By utilizing the optimization design method, the following technical effects can be achieved:
(1) the center of mass of the vibration isolation system coincides with the center of rigidity. The structure with the character of rigid superposition has good stability and uniform stress and deformation. The design target is applied to an air floatation vibration isolation system, so that the integral translation modal shape of the system can participate in the accumulation coefficient to obtain a higher value, and the vibration participation contributions of the non-translation modal shape of the system, such as torsional deformation, bending mode and the like, can be greatly reduced.
(2) The unidirectional design is easy to realize to obtain the three-direction equal rigidity characteristic. The components of the air floatation vibration isolation system are air springs, and the effects of equal rigidity in three directions can be obtained easily by designing the vertical rigidity of the air springs and utilizing the structural characteristics of air spring membranes through the selection and combined analysis design of single air springs. And because the order of magnitude of the conventional pulsating and stationary environment vibration load in three directions is basically the same, if the three-direction deformation is consistent in the system design, the vibration reduction or energy consumption level is consistent, and the system is favorable for improving the comprehensive vibration reduction capability of the system.
(3) The equivalent simple substance point single degree of freedom system is beneficial to system interference identification. Through the quality and rigidity coincidence design, the vibration control system is equivalent to a simple substance point three-freedom-degree system, the three-direction rigidity of the system is equal, the first three-order frequency is close, the vibration participation contribution is consistent, the system is similar to the simple substance point single-freedom-degree system, the smooth single-peak frequency response function characteristic is realized, the vibration control is more convenient, and the system is easy to diagnose and identify when being interfered.
The above and other objects, advantages and features of the present invention will become more apparent to those skilled in the art from the following detailed description of specific embodiments thereof, taken in conjunction with the accompanying drawings.
Drawings
Some specific embodiments of the invention will be described in detail hereinafter, by way of illustration and not limitation, with reference to the accompanying drawings. The same reference numbers in the drawings identify the same or similar elements or components. Those skilled in the art will appreciate that the drawings are not necessarily drawn to scale. The objects and features of the present invention will become more apparent in view of the following description taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a flow chart of an optimization design method of a three-dimensional equal-stiffness air-floating vibration isolation system with coincident mass and stiffness according to an embodiment of the invention;
fig. 2 is a preliminary scheme of an air-floating vibration control system according to an embodiment of the present invention.
Detailed Description
Referring to the attached drawing 1, a flow chart of an optimization design method of a three-way equal-stiffness air-floating vibration isolation system with just-coincident mass is shown, and the method comprises the following steps:
(1) design parameterNumber determination: determining design parameters of a vibration control system according to the load, the allowable vibration value of the precision equipment, the building structure form and the foundation, wherein the design parameters comprise: basic thickness h of high-rigidity platform of air floatation system1T-shaped droop thickness h of high-rigidity platform of air floatation system2The basic side length w, the mass and/or the rigidity of the high-rigidity platform of the air floatation system;
(2) determining a preliminary scheme of the air floating type vibration control system, including the number, arrangement mode and model of air springs as shown in fig. 2, wherein the preliminary scheme comprises the following steps:
(2-1) determining the number of the required air springs according to the mass of the precision equipment;
(2-2) determining an air spring arrangement mode according to a top plate of the system platform;
(2-3) selecting the type of the air spring according to implementation experience of similar engineering;
(3) parametric modeling: establishing a finite element variable model with variable design parameters according to the design parameters, dividing the grids with proper precision, and realizing full-parametric modeling of the whole finite element, wherein in the embodiment, the difference between the basic frequency values in the modal calculation result of refining the grids by adopting two adjacent times is not more than 0.1%, the grid precision of the system is considered to meet the proper precision, and of course, other judgment standards can be adopted according to the design precision requirement, as long as the judgment standards are approved by those skilled in the art.
(4) And (3) modal calculation: calculating to obtain the parameters related to the modes of the air floating type vibration control system, wherein the parameters related to the modes in the embodiment comprise: front three-order vibration mode x1、x2、x3And its frequency value f1，f2，f3Vibration mode mass participation coefficient delta1，δ2，δ3The method for obtaining the modal-related parameters is to solve partial differential equation by adopting a separation variable method according to the inherent dynamic characteristics of the air floating platform to obtain the front three-order vibration type x of the air floating type vibration control system1、x2、x3And its frequency value f1，f2，f3Vibration mode mass participation coefficient delta1，δ2，δ3；
(5) Determining an idealDesigning a parameter model: judging whether parameters related to the air floating type vibration control system mode obtained through mode calculation meet a certain relation: delta1+δ2+δ3> 95% and | f1/f2-1|＜5％、|f1/f3-1|＜5％、|f2/f3-1| < 5%, wherein δ1，δ2，δ3Representing the mass participation coefficient f of the front third-order vibration mode of the air-floating vibration control system1，f2，f3Representing the first three-order frequency value of the air floating type vibration control system, recording the design parameters of the air floating system at the moment if the relation is met, and returning to the step (2) to modify the preliminary scheme of the air floating type vibration control system if the relation is not met;
(6) and (3) correcting an ideal model: according to the basic thickness h of the high-rigidity platform of the air floatation system in the actual engineering1T-shaped droop thickness h of high-rigidity platform of air floatation system2And the value range of the basic side length w of the high-rigidity platform of the air floatation system, the economic target of lowest consumption is met, and the basic thickness h of the high-rigidity platform of the air floatation system with the design parameters is reasonably corrected after selection1T-shaped droop thickness h of high-rigidity platform of air floatation system2And the basic side length w of the high-rigidity platform of the air floatation system, thereby determining the final scheme of the vibration control system.
Through the steps, a three-dimensional equal-rigidity design process of the air floating type vibration isolation system based on mass-rigid coincidence can be established comprehensively, the complex infinite freedom engineering problem is efficiently converted into an effective and controllable single-particle single-freedom system, and the system is prevented from generating torsional response. The process can efficiently guide the design of the air-floating passive vibration isolation system, is easy to improve the vibration isolation performance of the system, and is beneficial to discrimination and analysis of stable interference signals in the system maintenance process.
While the present invention has been described with reference to the particular illustrative embodiments, it is not to be restricted by the embodiments but only by the appended claims. It will be understood by those skilled in the art that variations and modifications of the embodiments of the present invention can be made without departing from the scope and spirit of the invention.
Claims (4)
1. An optimal design method of a three-way equal-rigidity air-floating vibration isolation system with coincident mass and rigidity is characterized by comprising the following steps:
(1) design parameter determination: determining design parameters of a vibration control system according to the load, the allowable vibration value of the precision equipment, the building structure form and the foundation;
(2) determining a preliminary scheme of the air floating type vibration control system, including the number, arrangement mode and model of air springs;
(3) parametric modeling: establishing a finite element variable model with variable design parameters according to the design parameters, and dividing the grids with proper precision to realize full-parametric modeling of the whole finite element;
(4) and (3) modal calculation: calculating to obtain parameters related to the mode of the air floating type vibration control system;
(5) determining an ideal design parameter model: judging whether the parameters related to the mode of the air floating type vibration control system obtained through mode calculation meet a certain relation, if so, recording the design parameters of the air floating system at the moment, and if not, returning to the step (2) to modify the preliminary scheme of the air floating type vibration control system;
(6) and (3) correcting an ideal model: reasonably correcting the design parameters after comparison and selection according to the value range of the design parameters in the actual engineering and the economic target meeting the minimum consumption, thereby determining the final scheme of the vibration control system;
wherein the modality-related parameters in the step (4) include: front third-order vibration type x of air-floating vibration control system1、x2、x3And its frequency value f1，f2，f3And the mode mass participation coefficient delta1，δ2，δ3；
Wherein the certain relationship in step (5) comprises: delta1+δ2+δ3>95% and | f1/f2-1|<5％、|f1/f3-1|<5％、|f2/f3-1|<5％；
Wherein the step (6) comprises: according to the basic thickness h of the high-rigidity platform of the air floatation system in the actual engineering1T-shaped droop thickness h of high-rigidity platform of air floatation system2And the value range of the basic side length w of the high-rigidity platform of the air floatation system, the economic target of lowest consumption is met, and the basic thickness h of the high-rigidity platform of the air floatation system with the design parameters is reasonably corrected after selection1T-shaped droop thickness h of high-rigidity platform of air floatation system2And the basic side length w of the high-rigidity platform of the air floatation system, thereby determining the final scheme of the vibration control system;
and (3) the proper precision in the step is that the difference of basic frequency values in the modal calculation result of adopting two adjacent grid refinements is not more than 0.1%, and the grid precision of the system is considered to meet the proper precision.
2. The optimized design method of the three-dimensional equal-stiffness air-floating vibration isolation system with rigid superposition according to claim 1, wherein the design parameters of the step (1) comprise: basic thickness h of high-rigidity platform of air floatation system1T-shaped droop thickness h of high-rigidity platform of air floatation system2And the basic side length w, the mass and/or the rigidity of the high-rigidity platform of the air floatation system.
3. The optimized design method of the three-dimensional equal-rigidity air-floating vibration isolation system with rigid superposition according to claim 1, wherein the step (2) comprises the following steps:
(2-1) determining the number of the required air springs according to the mass of the precision equipment;
(2-2) determining an air spring arrangement mode according to a top plate of the system platform;
and (2-3) selecting the type of the air spring according to the implementation experience of similar engineering.
4. The optimized design method for air floating vibration isolation system with three equal stiffness and stiffness according to claim 1, wherein obtaining the parameters related to the modes in the step (4) comprises: for the inherent dynamic characteristics of the air-floating platform, adoptSolving partial differential equation by using separation variable method to obtain front third-order vibration mode x of air-floating vibration control system1、x2、x3And its frequency value f1，f2，f3Vibration mode mass participation coefficient delta1，δ2，δ3。
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