CN113885436A - Single-measuring-point online identification method for principal vibration mode of numerical control machine tool in cutting state - Google Patents
Single-measuring-point online identification method for principal vibration mode of numerical control machine tool in cutting state Download PDFInfo
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Abstract
The invention belongs to the field of structural modal parameter analysis of numerical control equipment, and particularly discloses a single-measuring-point online identification method of a principal vibration mode of a numerical control machine tool in a cutting state, which comprises the following steps: s1, obtaining modal parameters of the numerical control machine tool, further constructing a state space model of the numerical control machine tool, and expanding the state space model; s2, carrying out cutting experiments on the numerical control machine tool, and collecting single-point vibration response signals during cutting; s3, taking the single-point vibration response signal as a system observation sequence, estimating the state variable in the expanded state space model to obtain a state variable estimation value; s4, calculating the mode participation factor of each order mode according to the state variable estimated value, and further identifying the main vibration mode. The method can finish the online identification of the master vibration mode only by a single measuring point, solves the problem of difficult arrangement of the measuring points of the whole machine in the prior method, and provides an effective mode for the online identification of the master vibration mode under the condition of variable cutting parameters of the variable positions in the machining process of the numerical control machine.
Description
Technical Field
The invention belongs to the field of structural modal parameter analysis of numerical control equipment, and particularly relates to a single-measuring-point online identification method for a principal vibration mode of a numerical control machine tool in a cutting state.
Background
With the rapid development of modern manufacturing technology, the requirements of many industries on numerical control machine tools are higher and higher, in order to improve the machining performances such as high speed, high precision and high reliability of the machine tools, the influence of vibration in the machining process of the machine tools on the machining precision and efficiency becomes a non-negligible problem, and the research on the dynamic characteristics of the machine tool structure has important significance on the development of the machine tool industry.
The mode is the natural vibration characteristic of the structure, and for a linear structure, the vibration can be regarded as linear superposition of mode vibration of various orders, and each mode has specific mode parameters including a natural frequency omega, a damping ratio xi and a mode shape psi, and the mode parameters can represent the dynamic characteristic of the machine tool structure. In the cutting state, different modal orders have different participation degrees in vibration, the modal order with the largest vibration participation degree is called the main vibration mode of vibration, and the analysis and characterization of the vibration under different cutting parameters can be realized by analyzing the change of the modal participation degrees under different excitations.
At present, the existing modal participation and principal vibration mode identification method is a modal participation analysis method based on a working deformation mode, and the method requires that measuring points are arranged on the whole machine structure of a machine tool and are consistent with the measuring points of the modal mode, so the method is not suitable for the online identification occasion of the principal vibration mode of the machine tool and the identification occasion of the principal vibration mode of a variable structure.
Disclosure of Invention
Aiming at the defects or improvement requirements in the prior art, the invention provides a single-measuring-point online identification method of the principal vibration mode of a numerical control machine tool in a cutting state, and aims to complete online identification of the principal vibration mode of the machine tool in the cutting state through a single measuring point and solve the problem of difficult arrangement of measuring points of the whole machine tool in the existing principal vibration mode analysis method.
In order to achieve the aim, the invention provides a single-measuring-point online identification method of a principal vibration mode of a numerical control machine tool in a cutting state, which comprises the following steps:
s1, obtaining modal parameters of the numerical control machine tool, constructing a state space model of the numerical control machine tool based on the modal parameters, expanding the state space model, and containing the excitation force in a state variable;
s2, carrying out a cutting experiment on the numerical control machine tool, and collecting a single-point vibration response signal during cutting;
s3, taking the single-point vibration response signal as a system observation sequence, and estimating a state variable in the expanded state space model to obtain a state variable estimation value;
and S4, calculating the mode participation factor of each order of modes according to the state variable estimated value, and further taking the mode with the maximum mode participation factor as the main vibration mode of the numerical control machine.
Further preferably, the state space model of the numerical control machine is as follows:
wherein q isnDisplacement vector representing nth order mode, diagonal element diag (- Γ)1,-Γ2,...,-Γn)＝diag(2ξ1ω1,2ξ2ω2,...,2ξnωn)，ξnAs damping ratio, ωnIs the natural frequency; phi is an,nF is the excitation force for the mode shape normalized by mass.
As a further preferred, the state space model is simplified and expanded, so that the excitation force F is included in the state variables to be estimated, specifically including:
simplifying state space model correspondence to
Wherein the variable X corresponds to
A correspondingly contains natural frequency omeganAnd a composite parameter ΓnB corresponds to the (n +1) × (n +1) dimensional coefficient matrix containing the mode shape Φ;
expanding the simplified state space model to obtain an expanded state space model of
Wherein A iskIs unfolded as
The expansion of G is
XkIs unfolded as
XkNamely the state variable to be estimated containing the exciting force F; w represents white noise.
Preferably, the state variable in the expanded state space model is estimated by a Kalman filtering algorithm to obtain a state variable estimation value.
Preferably, when estimating the state variable by using a Kalman filter algorithm, the state estimate is reversely corrected by using the error filter value, which specifically comprises:
wherein the content of the first and second substances,
representing the state variable X at time kkThe optimal estimate of (2), i.e. the state variable estimate;
is XkIs estimated to be the state of (a),
is the error filter correction value, KkFor filtering the gain matrix, HkTo observe the matrix, ZkThe sequence was observed for the system.
Preferably, after the state variable estimated value is obtained, the modal displacement is converted into a frequency domain expression, and the frequency domain expression is substituted into a kinetic equation to perform modal decoupling, so that each order of vibration response amplitude of the vibration structure, namely the modal participation factor of each order of modal is obtained.
Preferably, in step S1, a tapping experiment is performed on the numerical control machine tool in a non-cutting state, an excitation signal of an excitation point and a vibration response signal of a measurement point are collected, a frequency response function matrix of the numerical control machine tool is further obtained through calculation, and then the frequency response function matrix is identified through a modal parameter identification algorithm, so as to obtain a modal parameter of the numerical control machine tool.
Generally, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
1. the method constructs a state space model based on modal parameters, expands the state space model, and includes excitation force in state variables, so that only cutting vibration response with single degree of freedom is input, namely, only a single measuring point is needed to complete master vibration mode identification, and measuring point arrangement is not needed for the whole machine of the numerical control machine tool.
2. The method can realize the online identification of the main vibration mode, effectively improve the modal analysis efficiency, save human errors in the modal analysis and greatly reduce the subsequent time cost; meanwhile, the method has high identification precision, can accurately estimate the main vibration mode, and provides powerful basis for vibration suppression control, damage detection and other work of the mechanical structure.
3. The method selects the Kalman filtering algorithm based on the system observable signal to estimate the system state information so as to finish the identification of the master vibration mode in the cutting state, and the algorithm is reliable and effective, has high identification precision, can accurately estimate the master vibration mode, and is particularly suitable for the online identification of the machine tool master vibration mode.
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FIG. 1 is a flow chart of a single-measuring-point online identification method of a principal vibration mode of a numerical control machine tool in a cutting state according to an embodiment of the invention;
FIG. 2 is a flow chart of state variable recursive updating in a Kalman filtering algorithm according to an embodiment of the present invention;
fig. 3 (a) to (e) are frequency domain diagrams of first-order to fifth-order modes after the vibration signal decomposition of the cutting experiment according to the embodiment of the invention;
fig. 4 is a comparison graph of the reconstructed vibration signal and the measured vibration signal of each order mode according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The single-measuring-point online identification method for the principal vibration mode of the numerical control machine tool in the cutting state, as shown in fig. 1, comprises the following steps:
(1) the method comprises the following steps of carrying out a knocking experiment on a numerical control machine tool serving as an identification object, identifying modal parameters of the numerical control machine tool, wherein the modal parameters comprise natural frequency, modal vibration mode and damping ratio, and specifically comprising the following substeps:
(1-1) selecting a numerical control machine tool, arranging a measuring point and an excitation point, and carrying out a knocking experiment. In knock experiments, generally speaking, when the machine tool vibrates very severely, the signal-to-noise ratio of the acquired signal is also very high, so that excitation points and measuring points need to be preferably arranged at positions where the vibration is relatively strong to ensure the quality of the acquired signal. In addition, in the experiment, an excitation signal of an excitation point and a vibration response signal of a measuring point need to be collected, so that preparation for subsequent parameter identification is made.
(1-2) acquiring a frequency response function of the machine tool based on the excitation signal and the vibration response signal acquired in the step, and identifying the mode parameters,
in the formula, X (j ω) represents the Fourier transform of the output signal, i.e. the vibration response signal of the measuring point at a certain position of the machine tool, F (ω) represents the Fourier transform of the input signal, i.e. the excitation signal, and H (j ω), i.e. the frequency response function of the measuring point, can be obtained by dividing the output signal X (j ω) by the input signal F (ω). And integrating the frequency response functions of the measuring points to obtain a frequency response function matrix H (omega). And identifying the frequency response function matrix H (omega) by using various modal parameter identification algorithms to obtain the modal parameters of the numerical control machine tool. At present, modal parameter identification algorithms are developed more maturely, and the method can select corresponding algorithms according to different practical situations.
(2) Constructing a state space model under a modal coordinate based on the modal parameters;
in a physical coordinate system, the dynamic expression of an n-order linear free vibration system is as follows:
substituting X into φ q and multiplying φ on both sides of the expression simultaneouslyTTherefore, decoupling operation is realized on the dynamic expression, and a motion equation under an independent modal coordinate system can be obtained:
in the formula, phiTIndicates the mode shape after the inversion, Mr、Cr、KrRespectively representing a structural mass matrix and a structural damping matrix under a modal coordinate systemAnd a structural stiffness matrix, all of which are diagonal matrices, q represents a modal displacement vector,
denotes the differential of q and f denotes the excitation force vector. The equation of motion can be converted into:
wherein, I is a quality matrix after normalization processing under modal coordinates, and gamma and omega2All diagonal matrices under the modal coordinates are specifically: Γ ═ diag (Γ)1,…,Γj,…,Γn)＝diag(2ξ1ω1,…,2ξjωj,…,2ξnωn)，
Xi in the formulanRepresenting the damping ratio, ωnRepresenting the natural frequency and n the order of freedom of the system vibration. Constructing a state space model based on the kinetic equation to obtain:
the simplified expression of the state space model can obtain:
wherein the variable X corresponds to
qnA displacement vector representing an nth order mode; a correspondingly contains natural frequency omeganAnd a composite parameter ΓnB corresponds to the (n +1) × n dimensional coefficient matrix containing the mode shape Φ. Also, X is a sequence consisting of modal decomposition factorsThe method is used for representing the specific participation degree of each order of mode in the machine tool structure vibration, and then estimating the specific participation degree, so that the identification of the main vibration mode is realized.
In addition, the system output displacement matrix Y under the state space model expression is CxX, wherein
The output velocity matrix V of the system can be derived from the displacement matrix Y and can be expressed as
The output acceleration matrix of the system can be obtained by the same method, and finally, the output acceleration matrix S of the system is expressed as S ═ Cv(A·x+B·F)＝CaX+DaF, the dynamic characteristics of the system can be expressed by the state variable X.
(3) The method comprises the steps of carrying out cutting experiments on a numerical control machine tool serving as an identification object, and collecting single-point vibration response signals in the cutting process of the numerical control machine tool on line, namely observation sequences at all times in the whole cutting process.
(4) Expanding the state space model so as to contain the excitation force F in the state variable to be estimated; then, taking the online collected single-measuring-point vibration response signal as a system observation sequence input, and estimating a state variable in the extended state space model through a Kalman filtering algorithm to obtain a state variable estimation value; the specific process is as follows:
the Kalman filter can estimate and compensate the system state variable based on the output signal of the observable system, and when the algorithm is used, a simplified expression of a state space model is required
And performing extended reconstruction, wherein after extension, the following results are obtained:
in the above formula, AkIs unfolded as
The expansion of G is
XkHas an expansion form of
W represents white noise, and this step includes an excitation force variable F (i.e., cutting force) in a state variable X to be estimatedkAmong them.
After the system state space model is subjected to linear discretization, a state updating equation of the algorithm can be obtained:
wherein, the subscript k represents the kth update of the equation and can be recorded as k time, XkRepresenting the state vector of the system at time k, phik,k-1Representing an n x n-dimensional system state transition matrix, Γk,k-1Representing a noise input matrix of dimension n x p, Wk-1Representing process white noise; zkM-dimensional observation sequence, V, representing a k-time systemkRepresenting an m-dimensional observation noise sequence, Γk,k-1Expressed as an n x p dimensional process noise input matrix, HkIs an observation matrix. Considering Wk-1And VkIs white noise, then E [ W ]k-1]＝E[Vk]0, so the state update equation can be simplified as:
suppose that at time k, the observation sequence [ Z ] has been obtained by actual observation1,…,Zk-1,Zk]In the above formula, however,
represents Xk-1Is estimated based on the estimated time of the measurement,
represents XkIs estimated to be the state of (a),
represents ZkIs estimated. From this, the actual observed value Z can be obtainedkAnd its state estimated value
Have an error therebetween
The specific expansion formula is as follows:
next, the state estimation value is reversely corrected based on the error filtered value in the above equation, so that:
in the above formula, the first and second carbon atoms are,
represents XkOptimal estimation of, KkThis is the filter gain matrix, which is not yet determined at this time. The above formula shows that k is X at timekThe optimal estimate of (2) is composed of two parts, one part being XkState prediction value of
The other part is error filtering correction value
Two are combinedThe optimal estimated value of the state variable can be obtained by partial summation
Filter gain matrix KkThe acquisition method comprises the following steps:
the actual observed value of the state variable X at the moment k is known as XkRecording the estimated value of its state
Has an estimation error of
Optimal estimation of state variable X
Has an estimation error of
To be provided with
Calculating an optimal filter matrix K for the target function by taking the minimum value as a requirementkThe following can be obtained:
from the above equation, the variance matrix P of the state variable prediction errorkComprises the following steps:
in the above formula, RkVariance matrix representing observation noise, taking Pk,k-1A variance matrix for the state variable single step prediction error, whose expansion is:
in summary, when P iskTake the minimum value Pk＝[I-KkHk]Pk,k-1Then, an optimal filter gain matrix K can be obtainedkThe expression of (a) is:
the above equation derivation for the Kalman filter algorithm is shown in FIG. 2, and generally speaking, the modal parameters of the machine tool (i.e., the initial values of the system) are known
) On the premise that the Kalman algorithm only needs to input the observation sequence [ Z ] of the system1,…,Zk-1,Zk]Recursive calculations can be performed, so that a single-point vibration response signal is input as an observation sequence [ Z ] of the system1,…,Zk-1,Zk]Namely, the estimated value of the state variable at the k moment of the system can be obtained
(5) Calculating a modal participation factor of each order of modal according to the state variable estimation value, and then identifying and verifying the master vibration modal according to the modal participation factor, wherein the method specifically comprises the following steps:
state variable estimation
Is unfolded as
Wherein q isnRepresenting the modal displacement corresponding to the nth mode, and q isnConversion to frequency domain expression qr＝QrejωtAnd substituting into a kinetic equation to perform modal decoupling (q)nI.e. qr) The following can be obtained:
modal participation factor Q in the formularOutput amplitude, Q, for the action of the r-th order mode in the vibration of the machine tool structurerThe magnitude of (2) can represent the participation degree of the r-th order mode in the excitation vibration, and the mode participation factor Q of each order moderBy comparison, Q can be recognizedrThe mode with the largest numerical value is the main vibration mode.
The following are specific examples:
(1) a milling machine machining center with the model of GMC1600H/2X40 is selected to perform a modal experiment, the experimental sampling frequency is selected to be 2048Hz, the excitation points are selected at the positions of tool tips to increase the structural vibration and improve the signal quality, and the measuring points are uniformly distributed on a main shaft of the machine tool to obtain a vibration response signal generated by the main shaft in an excited mode. A force hammer is used for carrying out a knocking experiment to obtain a knocking excitation signal and a measuring point response signal, then the signals are input into commercial calculation software to obtain a frequency response function, and further modal parameters are identified.
(2) The tapping experiment of the embodiment identifies the natural frequency omega in the X direction of the machine tool coordinate systemnComprises the following steps: omega1＝27Hz、ω3＝93Hz、ω4＝143.2Hz、ω5181.5Hz, damping ratio xinComprises the following steps: xi1＝2.2％、ξ2＝3.5％、ξ3＝4.6％、ξ4＝2.7％、ξ52.42%. And substituting the modal parameters into a kinetic equation and converting the kinetic parameters into a modal coordinate system to establish a state space model so as to prepare for subsequent model expansion.
(3) The conditions of the cutting experiment parameters of the embodiment are as follows: the main shaft rotating speed is 300rpm, the feeding speed is 0.07 mm/tooth, the radial cutting width is 30mm, and the axial cutting depth is 2 mm. In a cutting experiment, cutting excitation is caused by cutting of a cutter, so that excitation points do not need to be arranged, and a unique measuring point is arranged on a main shaft to acquire a cutting vibration response signal with single degree of freedom on line.
(4) Expanding the state space model, including the excitation force F in the state variable X to be estimated, and then combining with the Kalman filtering algorithm to carry outAnd performing recursive estimation. Inputting observation sequence [ Z ] of each time of the system in algorithm1,…,Zk-1,Zk]The algorithm automatically carries out continuous recursion calculation and finally outputs the estimated value of the state variable of the system at the k moment
(5) Variable of state
It contains the state information of the system at the time k, and after the estimated value is obtained in the last step, the modal displacement and the expression q of the excitation force signal are expressedr＝Qrejωt，F＝fejωtSubstituting the obtained signal into the vibration structure and performing modal decoupling to obtain the r-th order vibration response amplitude Q of the vibration structurerI.e. modal decomposition factor. Outputting the frequency domain signal and the time domain signal of each order of mode after decomposition, drawing a time domain graph and a frequency domain graph, judging according to the amplitude of frequency domain response, and regarding the maximum amplitude as a master vibration mode; as shown in fig. 3, the frequency domain response amplitude of the first-order mode is the largest under the parametric excitation in this example, so that the first-order mode can be determined to be the dominant vibration mode.
(6) Finally, the vibration signals of each order of mode are superposed and restored to obtain a reconstructed signal, the reconstructed signal is compared with the original measured signal, and the reconstructed signal and the original measured signal are matched with each other quite, as shown in fig. 4, so that the correctness of the vibration decomposition signals of each order of mode obtained by the method is verified. Therefore, single-measuring-point online identification of the master vibration mode of the numerical control machine tool is completed.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. A single-measuring-point online identification method for a principal vibration mode of a numerical control machine tool in a cutting state is characterized by comprising the following steps:
s1, obtaining modal parameters of the numerical control machine tool, constructing a state space model of the numerical control machine tool based on the modal parameters, expanding the state space model, and containing the excitation force in a state variable;
s2, carrying out a cutting experiment on the numerical control machine tool, and collecting a single-point vibration response signal during cutting;
s3, taking the single-point vibration response signal as a system observation sequence, and estimating a state variable in the expanded state space model to obtain a state variable estimation value;
and S4, calculating the mode participation factor of each order of modes according to the state variable estimated value, and further taking the mode with the maximum mode participation factor as the main vibration mode of the numerical control machine.
2. The method for single-point online identification of the principal vibration mode of the numerically-controlled machine tool under the cutting state according to claim 1, wherein the state space model of the numerically-controlled machine tool is as follows:
wherein q isnDisplacement vector representing nth order mode, diagonal element diag (- Γ)1，-Γ2，...，-Γn)＝diag(2ξ1ω1，2ξ2ω2，...，2ξnωn)，ξnAs damping ratio, ωnIs the natural frequency; phi is an，nF is the excitation force for the mode shape normalized by mass.
3. The method for single-point online identification of the dominant vibration mode of the numerical control machine tool in the cutting state as claimed in claim 2, wherein the simplification and expansion of the state space model are performed, so as to include the excitation force F in the state variable to be estimated, and specifically comprises:
simplifying state space model correspondence to
Wherein the variable X corresponds to
A correspondingly contains natural frequency omeganAnd a composite parameter ΓnB corresponds to the (n +1) × (n +1) dimensional coefficient matrix containing the mode shape Φ;
expanding the simplified state space model to obtain an expanded state space model of
Wherein A iskIs unfolded as
The expansion of G is
XkIs unfolded as
XkNamely the state variable to be estimated containing the exciting force F; w represents white noise.
4. The method for single-point online identification of the dominant vibration mode of a numerically-controlled machine tool in a cutting state as claimed in claim 1, wherein the state variable in the expanded state space model is estimated by a Kalman filter algorithm to obtain a state variable estimation value.
5. The method for single-point online identification of the dominant vibration mode of a numerically-controlled machine tool in a cutting state as claimed in claim 4, wherein when the state variable estimation is performed by Kalman filtering algorithm, the state estimation value is reversely corrected by an error filtering value, specifically:
wherein the content of the first and second substances,
representing the state variable X at time kkThe optimal estimate of (2), i.e. the state variable estimate;
is XkIs estimated to be the state of (a),
is the error filter correction value, KkFor filtering the gain matrix, HkTo observe the matrix, ZkThe sequence was observed for the system.
6. The method for single-point online identification of the dominant vibration mode of the numerically-controlled machine tool under the cutting state as claimed in claim 1, wherein after the state variable estimation value is obtained, the modal displacement is converted into a frequency domain expression, and the frequency domain expression is substituted into a kinetic equation to perform modal decoupling, so that the vibration response amplitude of each order of the vibration structure, namely the modal participation factor of each order of the modal is obtained.
7. The method for single-point online identification of the dominant vibration mode of a numerically-controlled machine tool under the cutting state according to any one of claims 1 to 6, wherein in step S1, a tapping experiment is performed on the numerically-controlled machine tool under the non-cutting state, an excitation signal of an excitation point and a vibration response signal of a measuring point are collected, a frequency response function matrix of the numerically-controlled machine tool is further calculated, and then the frequency response function matrix is identified through a modal parameter identification algorithm to obtain modal parameters of the numerically-controlled machine tool.
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| CN102507119A (en) * | 2011-11-14 | 2012-06-20 | 华中科技大学 | Analytical method for cutting and excitation experimental mode of numerically-controlled equipment |
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| CN113157012A (en) * | 2021-03-01 | 2021-07-23 | 北京理工大学 | Method and system for controlling mechanical vibration |
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| CN112935865A (en) * | 2021-01-29 | 2021-06-11 | 华中科技大学 | Method for improving thin-wall part processing stability and supporting device |
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