CN107609249A - The discrimination method of machine joint parameter based on frequency response function method - Google Patents
The discrimination method of machine joint parameter based on frequency response function method Download PDFInfo
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- CN107609249A CN107609249A CN201710793306.0A CN201710793306A CN107609249A CN 107609249 A CN107609249 A CN 107609249A CN 201710793306 A CN201710793306 A CN 201710793306A CN 107609249 A CN107609249 A CN 107609249A
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Abstract
The present invention relates to a kind of discrimination method of the machine joint parameter based on frequency response function method, this method establishes the mathematical modeling of overall structure joint portion by frequency response function method, optimization object function is established with the frequency response function error minimum of the frequency response function of mathematical model prediction and experiment test, jointing parameters are obtained by genetic algorithm optimizing and are used as initial value, the size for only changing wherein a certain parameter carries out model analysis to overall structure, determine sensitivity of the parameter at every first-order modal, the parameter is recognized at most sensitive mode, all jointing parameters are picked out by that analogy.Emulation with test result indicates that, the uniformity for the frequency response function curve of integrally-built frequency response function curve and experiment test that the jointing parameters recognized using this method are predicted is preferable, and jointing parameters identification result has higher precision.
Description
Technical field
The present invention relates to a kind of method for recognizing mechanical jointing parameters pair and determining integrally-built dynamic characteristic, specifically relate to
And a kind of machine joint parameter identification method based on frequency response function method, belong to mechanical dynamics property technical field.
Background technology
There is being largely fixedly connected in mechanical structure, such as bolt, rivet, welding, bonding, fixing combination portion is deposited
Integrally-built damping is being added, is reducing integrally-built rigidity, integrally-built dynamic characteristic is deteriorated.Therefore it is accurate
Ground identification jointing parameters pair determine that integrally-built dynamic characteristic is significant.
In terms of the research of jointing parameters identification, frequency response function method principle is simple, experiment is convenient, is that jointing parameters are distinguished
The important method of knowledge.The basic thought of frequency response function method is each according to the annexation between minor structure in mechanical structure, coupling
The frequency response function of minor structure determines integrally-built frequency response function, then jointing parameters are recognized.
Mainly there are two problems during frequency response function method recognizes jointing parameters at this stage：(1) identification equation includes
The integrally-built frequency response function of experiment test is needed, the measurement noise for being difficult to eliminate can be introduced, cause parameter identification result to go out
Existing ill-posed problem；(2) all parameter items of joint portion are recognized in same frequency range, causes the precision of parameter identification not
It is high.
The content of the invention
For the deficiency in terms of jointing parameters identification in prior art, the present invention proposes a kind of to respectively joining in joint portion
The independent sensitivity analysis of number, the discrimination method of the machine joint parameter based on frequency response function method individually recognized, for solving
Frequency response function method when recognizing jointing parameters because measurement noise causes the ill-posed problem that identification result occurs, it is and all
Parameter and improves the accurate identification of jointing parameters the identification of same frequency range causes identification result inaccurate the problem of.
To achieve the above object, the technical solution adopted by the present invention is：A kind of machine joint based on frequency response function method
The discrimination method of parameter, comprises the following steps：
Step 1：Jointing parameters are established based on frequency response function method and pass through identification model
Overall structure W is split as minor structure A, B with being connected the joint portion J of minor structure, wherein e1, e2 is on joint portion
Point, a, b are joint portions with the point on outer portion, are analyzed to obtain integrally-built origin frequency response function and express according to frequency response function method
Formula：
H represents frequency response function in formula, and subscript a, b, e1, e2 represent excitation point and response point respectively, and subscript J represents to combine
Portion, it is integrally-built frequency response function that upper target *, which represents this frequency response function, and target frequency response function represents the frequency of minor structure on no *
Ring function；
By the expression formula of overall structure origin frequency response function change form jointing parameters basic identification formula：
Z in formulaJRepresent joint portion impedance；
Step 2：Jointing parameters model is established, it is determined that finally recognizing equation
Using the other parts of the joint portion, then mechanical structure of the impedance matrix analog mechanical structure of 2 node 4DOFs
Consider translation and rotate two frees degree, then identification formula substantially can be rewritten as：
K in formulattRepresent translation rigidity, krrRepresent rotational stiffness, cttWith crrCorresponding damping parameter is represented, i represents plural number
Unit, w represent angular frequency, and tt represents that translation frequency response function, rr represent to rotate frequency response function, tr (rt) expression translations with rotating coupling
Frequency response function is closed, such asRepresent the translation frequency response function of overall structure b points excitation a point responses；
Step 3：The frequency response function of finite element solving minor structure
The FEM model of minor structure is established according to the physical parameter of minor structure, step 2 is calculated according to finite element theory
Identification formula in minor structure A and minor structure B all frequency response functions, including translation frequency response function, rotate frequency response function and coupling
Close frequency response function；
Step 4：Finite difference calculus seeks integrally-built origin frequency response function
Using finite difference calculus, by testing the translation frequency response function of two neighbor points in overall structure, wherein one is calculated
All frequency response functions of point；
Step 5：Identification of Genetic Algorithm jointing parameters
Using the minor structure that step 3, step 4 calculate and integrally-built frequency response function, pass through overall structure translation frequency
Ring functionTheoretical value and the error minimum of experiment value establish optimization object function, use genetic algorithm optimizing to determine to combine
Initial value Z of portion's parameter as sensitivity analysisAt the beginning of j-：
Step 6：Jointing parameters kttSensitivity analysis
Only change k in jointing parametersttSize, and simulate joint portion to overall structure carry out model analysis, by right
Than the natural frequency value obtained during different parameters, sensitivity of the parameter at every first-order modal is determined；
With 2 times of kttBuild jointing parameters Zj_2ktt：
With 0.5 times of kttBuild jointing parameters Zj_05ktt：
Use ZAt the beginning of j_、Zj_2kttWith Zj_05kttThis three groups of parameter simulation joint portions carry out model analysis to overall structure, can obtain
Corresponding 3 groups of integrally-built frequency response function curves and natural frequency value；
Seek kttFrom 0.5 times of kttIt is changed to 2 times of ktt, cause it is integrally-built per single order natural frequency value variable quantity, with relative
Error represents that specific method for solving can be formulated as：
Wherein ω2ktt-n、ωktt-nWith ω05ktt-nZ is represented successivelyj_2ktt、Zj_kttWith Zj_05kttWhat simulation joint portion obtained consolidates
There are frequency values, n represents integrally-built n-th order intrinsic frequency.δktt-nRepresent the relative error of n-th order；
Find out intrinsic frequency relative error δktt-nMaximum corresponding to order n, the rank mode is exactly kttCorresponding entirety
The most sensitive mode of structure；
Step 7：krrSensitivity analysis
The method of repeat step 6 is to krrSensitivity analysis is carried out, finds out krrThe corresponding sensitive mode of overall structure；
Step 8：Analytic method recognizes the final result of jointing parameters
Step 3 and step 4 are obtained to the identification equation that the frequency response function come substitutes into step 2, obtained in step 6 most sensitive
K is recognized at modettWith ctt, k is recognized at the most sensitive mode that step 7 is gone outrrWith crr, composition matrix form is as final
As a result.
The beneficial effects of the invention are as follows：
The discrimination method of the machine joint parameter based on frequency response function method of the present invention, is established whole by frequency response function method
The mathematical modeling of body structure joint portion, built with the frequency response function error minimum of the frequency response function of mathematical model prediction and experiment test
Vertical optimization object function, obtains jointing parameters by genetic algorithm optimizing and is used as initial value, only change the big of wherein a certain parameter
It is small that model analysis is carried out to overall structure, determine sensitivity of the parameter at every first-order modal.Distinguished at most sensitive mode
Know the parameter, pick out all jointing parameters by that analogy.Emulation with test result indicates that, using this method recognize combination
The uniformity of the frequency response function curve of integrally-built frequency response function curve and experiment test that portion's parameter is predicted is preferable, with reference to
Portion's parameter identification result has higher precision.
Brief description of the drawings
Fig. 1 is frequency response function method modeling schematic diagram；
Fig. 2 is jointing parameters identification block diagram；
Fig. 3 is girder construction model schematic；
Fig. 4 is that finite difference calculus seeks overall structure frequency response function schematic diagram；
Fig. 5 is to kttSensitivity analysis；
Fig. 6 is to krrSensitivity analysis；
Fig. 7 is result verification figure.
Embodiment
The specific implementation method of the present invention is described in further detail below in conjunction with the accompanying drawings.
The discrimination method of the machine joint parameter based on frequency response function method of the present invention, comprises the following steps：Step 1：
The general identification model of jointing parameters is established based on frequency response function method
Overall structure W is split as minor structure A, B with being connected the joint portion J of minor structure, as is shown in fig. 1.Wherein e1, e2
It is the point on joint portion, a, b are joint portions with the point on outer portion.
According to the definition of minor structure A, minor structure B and overall structure W frequency response function, the pass of its displacement and external force can be obtained
It is formula：
X represents the displacement vector of structure in formula, and θ represents the angle vector of structure, and F represents the force vector of structure, and M represents knot
The force vector of structure, H represent frequency response function.Minor structure corresponding to subscript A, B expression, W represent overall structure.Subscript a, b, e1, e2
Represent excitation point, response corresponding to frequency response function.It is integrally-built frequency response function that upper target *, which represents this frequency response function, on no *
Target frequency response function represents the frequency response function of minor structure.
Assuming that joint portion not by external force, then the power between joint portion is active force and reaction force：
Fe1=-Fe2 (4)
The frequency response function H of joint portionJWith equiva lent impedance ZJIt is reciprocal, then have：
Ignore the quality of joint portion, the dynamics formula of joint portion can be obtained：
Xe2-Xe1=HJFe1 (6)
Joint preceding formula, integrally-built origin frequency response function expression formula can be obtained：
The expression formula of overall structure origin frequency response function, which is changed form, can try to achieve the general identification formula of jointing parameters：
Step 2：Jointing parameters model is established, it is determined that finally recognizing equation
Using the joint portion of the impedance matrix analog mechanical structure of 2 node 4DOFs, can be expressed as：
Wherein kttRepresent translation rigidity, krrRepresent rotational stiffness, cttWith crrCorresponding damping parameter is represented, i represents plural number
Unit, w represent angular frequency.
The other parts of mechanical structure are also contemplated for translation and rotate two frees degree.Then recognizing can be expressed as in formula：
Wherein tt represents that translation frequency response function, rr represent to rotate frequency response function, tr, rt represent translation and rotate Coupling frequency response
Function.Such asRepresent the translation frequency response function of overall structure b points excitation a point responses.
The jointing parameters identification block diagram identification jointing parameters according to Fig. 2.
Step 3：The frequency response function of finite element solving minor structure
The FEM model of minor structure is established according to the design parameter of minor structure.
All frequency response functions of minor structure A and minor structure B in identification formula, including translation are calculated according to finite element theory
Frequency response function, rotate frequency response function and Coupling frequency response function.
Step 4：Finite difference calculus seeks integrally-built origin frequency response function
E1 and e2 are bolted composition overall structure, as shown in Figure 3.C points are set near a points, such as Fig. 4 institutes
Show, B＆K 4525b type three-way vibration sensors are set in a points and c points respectively, suspend overall structure in midair with elastic string, simulation is freely
State, a points and c points are encouraged respectively with Kistler 9724A2000 types exciting force hammer, passed with LMS test exciting force hammers with vibration
The signal of sensor, and the 4 translation frequency response functions that can obtain the excitation of a points and the response of a points are analyzed, write as matrix form：
The distance between 2 points of a, c is measured, s=30mm is set to, according to formula：
Forward difference formula T can be obtained1f。
Convolution (12), (13) can obtain integrally-built origin frequency response function：
Step 5：Identification of Genetic Algorithm jointing parameters initial value
Pass through the translation frequency response function of integrally-built origin frequency response functionTheoretical value and experiment value error most
It is small to establish optimization object function, jointing parameters are determined using genetic algorithm optimizing, as shown in table 1, as sensitivity analysis
Initial value：
The genetic algorithm optimizing result of table 1
It is expressed as with formula：
Step 6：kttSensitivity analysis
With 2 times of kttBuild jointing parameters Zj_2ktt：
With 0.5 times of kttBuild jointing parameters Zj_05ktt：
Use ZAt the beginning of j_、Zj_2kttWith Zj_05kttThis three groups of new parameter simulation joint portions carry out model analysis to overall structure, can obtain
Integrally-built frequency response function curve, as shown in figure 5, can also obtain integrally-built intrinsic frequency response value simultaneously, seek parameter kttFrom 0.5
Times kttIt is changed to 2 times of kttUnder cause integrally-built per single order natural frequency value variable quantity, be expressed as with relative error：
Wherein ω2ktt-n、ωktt-nWith ω05ktt-nZ is represented successivelyj_2ktt、Zj_kttWith Zj_05kttWhat simulation joint portion obtained consolidates
There are frequency values.N represents integrally-built n-th order intrinsic frequency.δktt-nRepresent the relative error of n-th order.Result is counted in table 1
In.Find out relative error δktt-nMaximum corresponding to n, be exactly kttThe most sensitive mode of corresponding overall structure.kttTo entirety
The rank mode of structure the 4th is most sensitive.
Table 1kttSensitivity analysis table
Step 7：krrSensitivity analysis
The method of repeat step 6 is to krrCarry out sensitivity analysis.Integrally-built frequency response function curve as shown in fig. 6,
Natural frequency value and error statistics are as shown in table 2, krrIt is most sensitive to the rank mode of overall structure the 1st.
Table 2krrSensitivity analysis table
Step 8：Analytic method recognizes the final result of jointing parameters
Step 3 and step 4 are obtained to the identification equation that the frequency response function come substitutes into step 2, obtained in step 6 most sensitive
(900Hz) recognizes k at modettWith ctt.(96Hz) recognizes k at the most sensitive mode that step 7 is gone outrrWith crr, form matrix
Form is as final result, as shown in table 3.
3 final identification result of table
Step 9：The result
By the overall structure frequency response function H of frequency response function, Identification of Genetic Algorithm prediction of result obtained by experiment test* ab_tt, this
The frequency response function that literary method identification result is predicted is drawn in the figure 7, and intrinsic frequency Data-Statistics are in table 4.This paper side is seen from Fig. 7
The result of method identification can more accurately reflect integrally-built dynamic characteristic.The identification result institute of context of methods is seen from table 4
The worst error of the intrinsic frequency of determination is 1.09%, compared to the error of other documents 2% or so, context of methods identification precision compared with
It is high.
The identification result of the genetic algorithm of table 4 and context of methods contrasts
Claims (1)
1. a kind of discrimination method of the machine joint parameter based on frequency response function method, it is characterised in that comprise the following steps：
Step 1：Jointing parameters are established based on frequency response function method and pass through identification model
Overall structure W is split as minor structure A, B with being connected the joint portion J of minor structure, wherein e1, e2 is the point on joint portion,
A, b be joint portion with the point on outer portion, integrally-built origin frequency response function expression formula is analyzed to obtain according to frequency response function method：
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It is integrally-built frequency response function that target *, which represents this frequency response function, and target frequency response function represents the frequency response letter of minor structure on no *
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By the expression formula of overall structure origin frequency response function change form jointing parameters basic identification formula：
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Z in formulaJRepresent joint portion impedance；
Step 2：Jointing parameters model is established, it is determined that finally recognizing equation
Using the joint portion of the impedance matrix analog mechanical structure of 2 node 4DOFs, then the other parts of mechanical structure are also contemplated for
Two frees degree of translation and rotation, then recognizing formula substantially can be rewritten as：
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K in formulattRepresent translation rigidity, krrRepresent rotational stiffness, cttWith crrCorresponding damping parameter is represented, i represents that plural number is single
Position, w represent angular frequency, and tt represents translation frequency response function, and rr represents to rotate frequency response function, and tr, rt represent that translation couples with rotating
Frequency response function, such asRepresent the translation frequency response function of overall structure b points excitation a point responses；
Step 3：The frequency response function of finite element solving minor structure
The FEM model of minor structure is established according to the physical parameter of minor structure, distinguishing for step 2 is calculated according to finite element theory
Know all frequency response functions of minor structure A and minor structure B in formula, including translation frequency response function, rotation frequency response function and coupling frequency
Ring function；
Step 4：Finite difference calculus seeks integrally-built origin frequency response function
Using finite difference calculus, by testing the translation frequency response function of two neighbor points in overall structure, calculate wherein
All frequency response functions；
Step 5：Identification of Genetic Algorithm jointing parameters
Using the minor structure that step 3, step 4 calculate and integrally-built frequency response function, pass through overall structure translation frequency response letter
NumberTheoretical value and the error minimum of experiment value establish optimization object function, determine joint portion using genetic algorithm optimizing
Initial value Z of the parameter as sensitivity analysisAt the beginning of j-：
Step 6：Jointing parameters kttSensitivity analysis
Only change k in jointing parametersttSize, and simulate joint portion to overall structure carry out model analysis, by contrast not
The natural frequency value obtained during same parameter, determine sensitivity of the parameter at every first-order modal；
With 2 times of kttBuild jointing parameters Zj_2ktt：
With 0.5 times of kttBuild jointing parameters Zj_05ktt：
Use ZAt the beginning of j_、Zj_2kttWith Zj_05kttThis three groups of parameter simulation joint portions carry out model analysis to overall structure, can obtain correspondingly
3 groups of integrally-built frequency response function curves and natural frequency value；
Seek kttFrom 0.5 times of kttIt is changed to 2 times of ktt, cause integrally-built every single order natural frequency value variable quantity, use relative error
Represent, specific method for solving can be formulated as：
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Wherein ω2ktt-n、ωktt-nWith ω05ktt-nZ is represented successivelyj_2ktt、Zj_kttWith Zj_05kttThe intrinsic frequency that simulation joint portion obtains
Rate value, n represent integrally-built n-th order intrinsic frequency, δktt-nRepresent the relative error of n-th order；
Find out intrinsic frequency relative error δktt-nMaximum corresponding to order n, the rank mode is exactly kttCorresponding overall structure
Most sensitive mode；
Step 7：krrSensitivity analysis
The method of repeat step 6 is to krrSensitivity analysis is carried out, finds out krrThe corresponding sensitive mode of overall structure；
Step 8：Analytic method recognizes the final result of jointing parameters
Step 3 and step 4 are obtained to the identification equation that the frequency response function come substitutes into step 2, in the most sensitive mode that step 6 obtains
Place's identification kttWith ctt, k is recognized at the most sensitive mode that step 7 is gone outrrWith crr, composition matrix form is as final result.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108572072A (en) * | 2018-04-09 | 2018-09-25 | 上海理工大学 | Ball-screw Drive Systems Identifying Dynamical Parameters method based on frequency response function method |
| CN111044240A (en) * | 2019-12-18 | 2020-04-21 | 沈阳鼓风机集团股份有限公司 | System and method for determining basic support stiffness of compressor |
| CN112345642A (en) * | 2020-10-28 | 2021-02-09 | 扬州大学 | Harvester health monitoring method considering primary and secondary structure decomposition equivalence |
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| CN104850713A (en) * | 2015-05-28 | 2015-08-19 | 西北工业大学 | High-precision calculating method of random vibration dynamic stress of mechanical structure |
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| CN104850713A (en) * | 2015-05-28 | 2015-08-19 | 西北工业大学 | High-precision calculating method of random vibration dynamic stress of mechanical structure |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108572072A (en) * | 2018-04-09 | 2018-09-25 | 上海理工大学 | Ball-screw Drive Systems Identifying Dynamical Parameters method based on frequency response function method |
| CN111044240A (en) * | 2019-12-18 | 2020-04-21 | 沈阳鼓风机集团股份有限公司 | System and method for determining basic support stiffness of compressor |
| CN111044240B (en) * | 2019-12-18 | 2021-06-22 | 沈阳鼓风机集团股份有限公司 | System and method for determining basic support stiffness of compressor |
| CN112345642A (en) * | 2020-10-28 | 2021-02-09 | 扬州大学 | Harvester health monitoring method considering primary and secondary structure decomposition equivalence |
| CN112345642B (en) * | 2020-10-28 | 2023-03-24 | 扬州大学 | Harvester health monitoring method considering primary and secondary structure decomposition equivalence |
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