CN110470380B - Vibration isolator mechanical impedance testing method considering base influence - Google Patents

Vibration isolator mechanical impedance testing method considering base influence Download PDF

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CN110470380B
CN110470380B CN201910296412.7A CN201910296412A CN110470380B CN 110470380 B CN110470380 B CN 110470380B CN 201910296412 A CN201910296412 A CN 201910296412A CN 110470380 B CN110470380 B CN 110470380B
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vibration isolator
vibration
mechanical impedance
force
signal
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王敏庆
王骁
盛美萍
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Northwestern Polytechnical University
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    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
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Abstract

The invention provides a vibration isolator mechanical impedance testing method considering base influence, which can use a flexible base with limited mass and limited rigidity in the testing process, also can consider the influence of the base characteristic on the vibration isolator mechanical impedance and make up for the defect of a blocking method, so that the obtained mechanical impedance is more in line with the mechanical impedance characteristic of a vibration isolator in an actual vibration isolation system. The invention does not need to use a special impedance table for testing, thereby reducing the testing condition and the testing cost; and the problem of test error caused by the fact that the impedance table does not meet the blocking requirement does not need to be considered.

Description

Vibration isolator mechanical impedance testing method considering base influence
Technical Field
The invention relates to the technical field of vibration isolator tests, in particular to a vibration isolator mechanical impedance testing method considering base influence.
Background
The mechanical impedance of the vibration isolator is used as a representation of the dynamic characteristic of the vibration isolator, is a main index for designing and optimizing the performance of the vibration isolator and an important parameter for evaluating the effect of a vibration isolation system, and the accurate acquisition of the mechanical impedance becomes an indispensable ring in the design and application process of the vibration isolator. Because most vibration isolators have complex structures and different material characteristics, and are easily influenced by environmental factors such as load working conditions, temperature and the like, it is difficult to establish an accurate mathematical model to obtain an analytic solution of the mechanical impedance of the vibration isolators, and therefore, a special test device is usually adopted to obtain the mechanical impedance of the vibration isolators and the mechanical impedance is obtained by depending on test.
At present, the mechanical impedance of the vibration isolator is obtained by adopting a blocking method basically at home and abroad. In the testing principle of the blocking method, a base connected with the vibration isolator is assumed to be fixed, the base has infinite effective mass and rigidity, the end part of the vibration isolator is blocked on a special blocking table in the testing process, the speed of the blocking end of the vibration isolator is zero, and the testing conditions conform to the principle assumption of the method. However, in an actual vibration isolation system, any base does not have infinite effective mass and stiffness at any frequency, and for a base with finite mass or high flexibility, the higher the frequency is, the richer the structural mode of the base is, the more the structural resonance points are, and the base does not meet the assumption of infinite effective mass and stiffness. Because the blocking method does not consider the influence of the base on the mechanical impedance of the vibration isolator, the mechanical impedance obtained by adopting the blocking method is often different from the mechanical impedance of the vibration isolator in an actual vibration isolation system to a certain extent, namely the blocking method has obvious system errors.
Disclosure of Invention
In order to solve the problems, the invention provides a vibration isolator mechanical impedance testing method considering the influence of the base, which can consider the influence of the base characteristics on the mechanical impedance of the vibration isolator in the process of obtaining the mechanical impedance of the vibration isolator, so that the obtained mechanical impedance is more consistent with the mechanical impedance of the vibration isolator in an actual vibration isolation system.
The technical scheme adopted by the invention is as follows:
the vibration isolator mechanical impedance testing method considering the influence of the base is characterized by comprising the following steps of: the method comprises the following steps:
step 1: building a test system, wherein the test system comprises a vibration exciter, a tested vibration isolator, a base, an acceleration sensor and a force sensor; two ends of the vibration isolator to be tested are respectively connected with the vibration exciter and the base through force sensors, and the acceleration sensor is arranged on the vibration isolator to be tested; the base structure in the test system is the same as the base structure connected with the vibration isolator to be tested in the actual vibration isolation system;
step 2: starting the vibration exciter to obtain a force signal F at the input end of the vibration isolator1①Force signal F at the output2①Acceleration signal a at the input of the vibration isolator1①Acceleration signal a of output terminal2①；
And step 3: adjusting the length or width or thickness of the base structure in the test system within 10%, keeping other conditions unchanged, starting the vibration exciter again, and acquiring a force signal F at the input end of the vibration isolator1②Force signal F at the output2②Acceleration signal a at the input of the vibration isolator1②Acceleration signal a of output terminal2②；
And 4, step 4: establishing a mechanical impedance matrix equation of the vibration isolator:
Figure GDA0002654047690000021
wherein
Figure GDA0002654047690000022
Representing an impedance matrix of the vibration isolator; f1Indicating the force signal at the input of the vibration isolator, F2Indicating vibration isolator output endForce signal of V1Indicating the speed signal, V, of the input of the vibration isolator2A speed signal indicative of an output of the vibration isolator;
for mechanical impedance Z21And Z22And the force and acceleration signals obtained in step 2, establishing the following formula
Figure GDA0002654047690000023
Wherein alpha isijRepresenting mechanical impedance ZijReal part of, betaijRepresenting mechanical impedance ZijImaginary part of, F'iRepresenting a force signal FiReal part of (F) "iRepresenting a force signal FiImaginary part of a'jRepresenting an acceleration signal ajReal part of (a) "jRepresenting an acceleration signal ajThe subscript (r) in the lower right-hand corner of the symbol indicates the force and acceleration signals corresponding to step 2; substituting the formula into a mechanical impedance matrix equation of the vibration isolator, and converting the speed quantity into an acceleration quantity by using j omega V ═ a to obtain the acceleration quantity
Figure GDA0002654047690000031
For the force and acceleration signals obtained in step 3, the following formula is established
Figure GDA0002654047690000032
Subscript II represents the vibration data obtained in the step 3, and the formula is substituted into a mechanical impedance matrix equation of the vibration isolator to obtain the vibration data
Figure GDA0002654047690000033
Can obtain matrix form
Figure GDA0002654047690000034
For machineMechanical impedance Z11And Z12The following formula is established
Figure GDA0002654047690000035
By using the vibration data obtained in step 2 and step 3, a matrix form can be obtained
Figure GDA0002654047690000036
And 5: substituting the two groups of vibration data obtained in the step 2 and the step 3 into the two matrix equations to solve each alphaijAnd betaijAnd according to the following formula:
Figure GDA0002654047690000041
and calculating the value of each mechanical impedance of the vibration isolator.
Advantageous effects
The invention has the following advantages:
1. the method for testing the mechanical impedance of the vibration isolator can use the flexible base with limited mass and limited rigidity in the testing process, so that the influence of the characteristic of the base on the mechanical impedance of the vibration isolator can be considered, the defect of a blocking method is made up, and the obtained mechanical impedance is more consistent with the mechanical impedance characteristic of the vibration isolator in an actual vibration isolation system;
2. a special impedance table is not needed for testing, so that the testing condition is reduced, and the testing cost is reduced;
3. the problem of test errors due to the impedance table failing to meet the "blocking" requirement does not need to be considered.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic view of an exemplary vibration isolation system;
FIG. 2 is a schematic diagram of input and output signals of the unidirectional single-input single-output vibration isolator;
FIG. 3 is a schematic diagram of a test system for a method of testing mechanical impedance of an isolator taking into account pedestal effects;
FIG. 4 is a schematic diagram of the connection between the sensor and an external instrument;
FIG. 5 is a vibration isolator mechanical impedance Z obtained by the blocking method and the vibration isolator mechanical impedance testing method taking into account the pedestal effect11Comparing the images;
FIG. 6 is a graph of the mechanical impedance Z of the isolator using the blocking method and the method described in this patent12Comparing the images;
FIG. 7 is a graph of the mechanical impedance Z of the isolator using the blocking method and the method described in this patent21Comparing the images;
FIG. 8 is a graph of the mechanical impedance Z of the isolator using the blocking method and the method described in this patent22Comparing the images;
the respective reference numerals in fig. 3: 1-vibration exciter, 2-upper force sensor, 3-vibration isolator, 4-lower force sensor, 5-base, 6-lower acceleration sensor, 7-upper acceleration sensor, 8-bracket and elastic rope.
Detailed Description
The following detailed description of embodiments of the invention is intended to be illustrative, and not to be construed as limiting the invention.
As shown in fig. 3, in this embodiment, a small single-input single-output steel spring vibration isolator under no load condition is used as the vibration isolator to be tested, and only the mechanical impedance in the Z direction is considered. If the tested vibration isolator is large, a rigid transition piece is generally required to be additionally arranged between the force sensor and the tested vibration isolator, so that the force sensor is stressed uniformly, and the test is accurate. The tested vibration isolator of the embodiment is small, so that a transition piece does not need to be additionally arranged.
The method comprises the following steps:
step 1: a test system is set up as shown in fig. 3, and comprises an exciter 1, a vibration isolator 3, a base 5, an acceleration sensor and a force sensor. Vibration exciter 1 adopts support and elastic cord 8 to hang, install top force transducer 2 between vibration exciter 1 and the input of isolator 3, the structure of base 5 is the same with the base structure that isolator 3 is connected in actual vibration isolation system, install below force transducer 4 between the output of isolator 3 and base 5, install top acceleration sensor 7 at the input of isolator 3, below acceleration sensor 6 is installed to the output of isolator 3, and as shown in fig. 4, be connected each acceleration sensor and each force transducer with external instrument.
Step 2: starting the vibration exciter 1, and acquiring a first group of force signals F at the input end of the vibration isolator 3 by using the upper force sensor 21①Acquiring a first set of force signals F at the output of vibration isolator 3 using lower force sensor 42①The upper acceleration sensor 7 is used to obtain a first set of acceleration signals a at the input of the vibration isolator 31①A first set of acceleration signals a at the output of vibration isolator 3 is obtained using lower acceleration sensor 62①。
And step 3: increasing or reducing the length (width and thickness) of the base structure in the test system by 5 percent, keeping other conditions unchanged, starting the vibration exciter 1 again, and acquiring a second group of force signals F at the input end of the vibration isolator 3 by using the upper force sensor 21②Acquiring a second set of force signals F at the output of vibration isolator 3 using lower force sensor 42②Acquiring a second set of acceleration signals a at the input end of vibration isolator 3 by using upper acceleration sensor 71②Acquiring a second group of acceleration signals a at the output end of the vibration isolator 3 by using the lower acceleration sensor 62②。
And 4, step 4: from fig. 2, the mechanical impedance matrix equation for vibration isolator 3 is given:
Figure GDA0002654047690000061
in the formula (1), the reaction mixture is,
Figure GDA0002654047690000062
represents the impedance matrix of vibration isolator 3; f1Indicating the force signal at the input of vibration isolator 3, F2Indicating the force signal, V, at the output of vibration isolator 31Indicating the speed signal, V, of the input of vibration isolator 32Representing the speed signal at the output of vibration isolator 3.
For mechanical impedance Z21And Z22And the first set of force and acceleration signals obtained in step 2, establishing the following formula
Figure GDA0002654047690000063
In the formula (2) < alpha >, (B)ijRepresenting mechanical impedance ZijReal part of, betaijRepresenting mechanical impedance ZijImaginary part of, F'iRepresenting a vibration force signal FiReal part of (F) "iRepresenting a vibration force signal FiImaginary part of a'jRepresenting a vibration acceleration signal ajReal part of (a) "jRepresenting a vibration acceleration signal ajThe subscript (r) in the lower right-hand corner of the symbol denotes the first set of force and acceleration signals in step 2. If it is desired to obtain the mechanical impedance of vibration isolator 3, each α needs to be solvedijAnd betaijThe value of (c).
According to formula (1):
F2＝Z21V1+Z22V2(3)
the velocity signal V and the acceleration signal a in the frequency domain have the following relationships:
jωV＝a (4)
in the formula (4), ω represents the vibration circular frequency. The formula (2) is substituted for the formula (3), and the velocity signal V is converted into the acceleration signal a by the formula (4), so that:
Figure GDA0002654047690000064
formula (5) is simplified to obtain:
Figure GDA0002654047690000071
the real part and the imaginary part of equation (6) are written separately:
Figure GDA0002654047690000072
similarly, for the second set of force and acceleration data acquired there are:
Figure GDA0002654047690000073
in equation (8), subscript @ represents the second set of vibration data, equation (8) is simplified by substituting equation (3), and the real part and the imaginary part in the equation are separated to obtain:
Figure GDA0002654047690000074
combining formula (7) with formula (9) yields:
Figure GDA0002654047690000075
writing equation (10) in the form of a matrix equation:
Figure GDA0002654047690000076
for mechanical impedance Z11And Z12It is also possible to establish:
Figure GDA0002654047690000081
and obtained via a similar derivation process:
Figure GDA0002654047690000082
writing equation (13) in the form of a matrix equation:
Figure GDA0002654047690000083
and 5: substituting the first and second sets of vibration data obtained in step 2 and step 3 into the two matrix equations (11) and (14) to solve each αijAnd betaijAnd according to the following formula:
Figure GDA0002654047690000084
and calculating the value of each mechanical impedance of the vibration isolator.
The method for testing the mechanical impedance of the vibration isolator can use the flexible base with limited mass and limited rigidity in the testing process, so that the influence of the characteristic of the base on the mechanical impedance of the vibration isolator can be considered, the defect of a blocking method is overcome, and the obtained mechanical impedance is more consistent with the mechanical impedance characteristic of the vibration isolator in an actual vibration isolation system.
In step 3, when the second set of vibration response data is obtained, the size of the base 5 is slightly adjusted, and an additional vibration response data set is obtained and used in the calculation of the mechanical impedance of the vibration isolator, so that the linear correlation degree between the sets of vibration data is reduced, the condition number of the coefficient matrix in the formulas (11) and (14) is prevented from being too large in the calculation process, the ill condition of the coefficient matrix is prevented, and the accuracy of the final mechanical impedance result is improved.
As shown in fig. 5 to 8, which are comparative graphs of the mechanical impedances of the vibration isolator obtained by the blocking method and the method disclosed in the present patent, since the method disclosed in the present patent takes the influence of the pedestal on the mechanical impedance of the vibration isolator into consideration, the mechanical impedance obtained by the method disclosed in the present patent has a difference from the mechanical impedance obtained by the blocking method, and the difference is mainly reflected in a higher frequency.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.

Claims (1)

1. A vibration isolator mechanical impedance testing method considering base influence is characterized in that: the method comprises the following steps:
step 1: building a test system, wherein the test system comprises a vibration exciter, a tested vibration isolator, a base, an acceleration sensor and a force sensor; two ends of the vibration isolator to be tested are respectively connected with the vibration exciter and the base through force sensors, and the acceleration sensor is arranged on the vibration isolator to be tested; the base structure in the test system is the same as the base structure connected with the vibration isolator to be tested in the actual vibration isolation system;
step 2: starting the vibration exciter to obtain a force signal F at the input end of the vibration isolator1①Force signal F at the output2①Acceleration signal a at the input of the vibration isolator1①Acceleration signal a of output terminal2①；
And step 3: adjusting the length or width or thickness of the base structure in the test system within 10%, keeping other conditions unchanged, starting the vibration exciter again, and acquiring a force signal F at the input end of the vibration isolator1②Force signal F at the output2②Acceleration signal a at the input of the vibration isolator1②Acceleration signal a of output terminal2②；
And 4, step 4: establishing a mechanical impedance matrix equation of the vibration isolator:
wherein
Figure FDA0002654047680000012
Representing an impedance matrix of the vibration isolator; f1Indicating the force signal at the input of the vibration isolator, F2Indicating the force signal, V, at the output of the vibration isolator1Indicating the speed signal, V, of the input of the vibration isolator2A speed signal indicative of an output of the vibration isolator;
for mechanical impedance Z21And Z22And the force and acceleration signals obtained in step 2, establishing the following formula
Figure FDA0002654047680000013
Wherein alpha isijRepresenting mechanical impedance ZijReal part of, betaijRepresenting mechanical impedance ZijImaginary part of, Fi' representing the force signal FiReal part of (F)i"indicates the force signal FiImaginary part of a'jRepresenting an acceleration signal ajReal part of (a) "jRepresenting an acceleration signal ajThe subscripts i and j are respectively 1 or 2, and the subscript (r) at the lower right corner of the symbol represents the corresponding force and acceleration signals in the step 2; substituting the formula into a mechanical impedance matrix equation of the vibration isolator, converting the speed quantity into an acceleration quantity by j omega V-a, wherein omega represents the frequency of a vibration circle to obtain
Figure FDA0002654047680000021
For the force and acceleration signals obtained in step 3, the following formula is established
Figure FDA0002654047680000022
Subscript II represents the vibration data obtained in the step 3, and the formula is substituted into a mechanical impedance matrix equation of the vibration isolator to obtain the vibration data
Figure FDA0002654047680000023
Can obtain matrix form
Figure FDA0002654047680000024
For mechanical impedance Z11And Z12The following formula is established
Figure FDA0002654047680000025
By using the vibration data obtained in step 2 and step 3, a matrix form can be obtained
Figure FDA0002654047680000026
And 5: substituting the two groups of vibration data obtained in the step 2 and the step 3 into the two matrix equations to solve each alphaijAnd betaijAnd according to the following formula:
Figure FDA0002654047680000031
and calculating the value of each mechanical impedance of the vibration isolator.
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