CN109884985A - The measurement method of numerically-controlled machine tool complete machine machining state dynamic characteristic - Google Patents
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Abstract
The present invention relates to a kind of measurement methods of numerically-controlled machine tool complete machine machining state dynamic characteristic, the specific steps are as follows: step 1: being respectively mounted vibration acceleration flowmeter sensor on each main component of numerically-controlled machine tool；Step 2: under machining state, the vibration generated using lathe foundation vibration and operation acquires the three-phase vibratory response of each component of numerically-controlled machine tool by multi-channel data acquisition board as excitation；Step 3: using Bayes's operational modal method and Fast Fourier Transform (FFT), obtains numerically-controlled machine tool each channel frequency response function curve under off working state environment, establishes Modal Parameter Identification function；Step 4: the dynamic characteristic parameters such as each rank intrinsic frequency of numerically-controlled machine tool, damping ratio and Mode Shape are obtained by analyzing each channel frequency response function.The present invention solves the problems, such as machining state complete machine tool dynamic characteristic measuring.The characteristics of this method is to be not necessarily to artificial excitation, and can get the dynamic characterization measurement result of complete machine tool machining state.
Description
Technical Field
The invention relates to a method for testing a numerical control machine tool and evaluating the dynamic characteristics of a machine tool structure, in particular to a method for measuring the dynamic characteristics of the complete machine processing state of the numerical control machine tool.
Background
The dynamic characteristics of the machine tool refer to the characteristics of a machine tool system in a vibration state, namely the characteristics that the amplitude and the phase of the machine tool change along with the vibration frequency under a certain vibration exciting force, and main indexes of the dynamic characteristics of the machine tool comprise natural frequency, damping ratio, modal shape, dynamic stiffness and the like. The dynamic characteristics of the machine tool determine the cutting characteristics of the machine tool and directly determine performance indexes such as processing stability, cutting capability and precision of the numerical control machine tool. Therefore, the measurement and evaluation of the dynamic characteristics of the machine tool have important significance for the design and the use of the numerical control machine tool. For measuring the dynamic characteristics of the machine tool, a hammering method is generally adopted, as shown in fig. 1(a) and (B), a pulse excitation signal is given to the machine tool by hammering a certain part a of the machine tool, then a plurality of vibration sensors B are arranged at different positions to measure the response signals of the pulse excitation signal, and the dynamic characteristics of the machine tool are obtained through a signal processing theory. However, the traditional experimental mode method based on the hammering method has the disadvantages that the single hammering of a complex system such as a machine tool is difficult to excite the output response, and the dynamic characteristic test and analysis of the complete machine machining state of the machine tool cannot be realized.
In the machining process of the numerical control machine tool, different cutting technological parameters can generate different vibration frequencies of the numerical control machine tool, and all parts of the numerical control machine tool have different vibration inherent frequencies. In the actual machining process, vibration excited by cutting technological parameters often occurs to cause resonance of key functional parts of the machine tool, so that the machining precision of the machine tool is greatly influenced. Therefore, the natural frequency of each order of the numerical control machine tool can be mastered by measuring the dynamic characteristics of the numerical control machine tool, and the vibration phenomenon of the numerical control machine tool in the machining process is avoided. On the other hand, in the machining state, the dynamic characteristics of the whole machine tool in the machining state are obtained, the dynamic design defects of the machine tool are positioned and evaluated, and the design improvement of the numerical control machine tool plays an important role. The method is also a precondition for evaluating structural design optimization of each main part of the machine tool and monitoring the performance of the machine tool.
Disclosure of Invention
The invention provides a method for measuring the dynamic characteristics of the complete machine processing state of a numerical control machine tool, which solves the problem of measuring the dynamic characteristics of the complete machine of the machine tool in the processing state by using the vibration of a machine tool foundation and the vibration generated by operation as excitation according to a modal parameter identification technology combining a Bayesian theory and operation modal analysis. The method is characterized in that manual excitation is not needed, and the dynamic characteristic test result of the complete machine processing state of the machine tool can be obtained, wherein the dynamic characteristic test result comprises main parameters such as natural frequency, damping ratio, vibration mode, signal-to-noise ratio and the like.
The technical scheme of the invention is as follows:
a method for measuring the dynamic characteristics of the complete machine processing state of a numerical control machine tool comprises the following specific steps:
the method comprises the following steps: a vibration accelerometer sensor is arranged on each main part of the numerical control machine tool;
step two: in a machining state, the vibration of a machine tool foundation and the vibration generated by operation are used as excitation, and the three-phase vibration response of each part of the numerical control machine tool is acquired through a multi-channel data acquisition card;
step three: obtaining frequency response function curves of all channels of the numerical control machine tool in a non-working state environment by using a Bayesian operation modal method and fast Fourier transform, and establishing a modal parameter identification function;
step four: and obtaining dynamic characteristic parameters of the numerical control machine tool, such as inherent frequency, damping ratio, modal shape and the like of each order by analyzing frequency response functions of each channel.
The principle and the method for acquiring the three-phase vibration response of each part of the numerical control machine tool through the multi-channel data acquisition card in the machining state are as follows:
the linear vibration system of the numerical control machine tool with n degrees of freedom meets the equation of motion:
wherein M is equal to Rn×n、C∈Rn×n、K∈Rn×nRespectively a mass matrix, a damping ratio matrix and a rigidity matrix of the system; the structural response of the multi-degree-of-freedom structure satisfying linear classical damping is assumed to be:
wherein,is a global mode shape vector of the j order;the mode response is the j order mode response, the mode order is m, and the mode response satisfies the decoupling mode power equation:
wherein, ω isj，ζjAnd Wj(t) are scalar quantities representing the natural frequency, damping ratio and modal force of the j-th order mode of the machine tool, respectively. The main parameters of the mode identification are natural frequency, damping ratio and vibration mode;
the numerical control machine tool generates weak vibration under the condition of random working condition excitationN is the sampling number in each acquisition channel for the vibration acceleration response data obtained by testing; the acceleration response obtained by the hypothesis test is composed of the structural environment vibration test signal and the prediction error of the model, i.e.
Wherein, { εj∈RnThe "prediction error" is the error between the model response and the test response due to the test noise and the model error. Carrying out Fast Fourier transform (Fast Fourier transform, FFT) on the acquired machine tool acceleration signal D, namely
In the formula i2＝-1；FkAnd GkRespectively representThe real and imaginary parts of (c); Δ t is the sampling step, corresponding to k being 2,3, …, Nq，fkGiven (k-1)/(N Δ t), the augmentation matrix is assumedAn amplification matrix { Z obtained by FFT of acceleration signals acquired from a machining statekStarting from the parameter, identifying the dynamic characteristic modal parameter theta of the machine tool, wherein the parameter is f, zeta, Se(ii) a Φ, where f ═ fj:j＝1,…,m}，ζ＝{ζjJ-1, …, m-and Φ - Φ1,…,Φm]∈Rn×mRespectively representing the natural frequency and the damping ratio in the m-order natural mode and the corresponding integral vibration mode of the machine tool; s is belonged to Cm×mAnd SeRespectively representing the spectral density matrix of the state excitation and the prediction error spectral density;
the method can be obtained by the Bayesian theory principle:
p(θ|D)∝p(D|θ) (6)
p (θ | D) represents the posterior probability of θA density function; p (D | theta) is a likelihood function. From the stochastic process analysis we can see that when high sampling rate and sufficient data length are met, the FFT results are approximately independent and satisfy a gaussian distribution, so ZkSubject to a zero mean Gaussian combined distribution to obtain a likelihood function of
In the formula, det (-) represents determinant; ckIs ZkFor the purpose of analysis and calculation, the theoretical covariance matrix of (a) is a negative log-likelihood function, expressed as L (θ), and p (D | θ) ═ exp [ -L (θ) for analysis]Wherein
Thus, the optimized value of the modal parameter θ can be obtained by maximizing the posterior probability density function, i.e., minimizing the negative log likelihood function L (θ).
Compared with the prior art, the invention has the following beneficial effects:
the dynamic characteristics of the machine tool are generally measured by adopting a hammering method, a pulse excitation signal is given to the machine tool by hammering a certain part of the machine tool, then a plurality of vibration sensors are arranged at different positions to measure response signals of the pulse excitation signal, and the dynamic characteristics of the machine tool are obtained by a signal processing theory. However, the traditional experimental mode method based on the hammering method has the disadvantages that the single hammering of a complex system such as a machine tool is difficult to excite the output response, and the dynamic characteristic test and analysis of the complete machine machining state of the machine tool cannot be realized.
The invention can obtain the dynamic test data of the machine tool in the real machining state, and ensures the accuracy of the dynamic parameters of the machine tool.
Drawings
FIG. 1 is a schematic view of a conventional method for measuring dynamic characteristics of a numerically controlled machine tool;
wherein, (a) a schematic diagram and (b) an example diagram;
FIG. 2 is a schematic view of the method for measuring dynamic characteristics of a numerically controlled machine tool according to the present invention;
wherein, (a) a schematic diagram and (b) an example diagram;
FIG. 3 is a right view of the measurement point arrangement of a certain type of machine tool;
FIG. 4 is a left side view of a measuring point arrangement of a certain type of machine tool;
FIG. 5 shows a first-order vibration mode of a machine tool of a certain type;
FIG. 6 is a second-order vibration mode of a machine tool of a certain type;
FIG. 7 shows a third vibration mode of a machine tool of a certain type.
Detailed Description
The invention is further described with reference to the following figures and examples.
As shown in fig. 2(a) and (b), a method for measuring the dynamic characteristics of the complete machine processing state of a numerical control machine tool specifically comprises the following steps:
the method comprises the following steps: a vibration accelerometer sensor B is arranged on each main part of the numerical control machine tool;
step two: in a machining state, the three-phase vibration response of each part of the numerical control machine tool is acquired through a multi-channel data acquisition card by using the machine tool foundation vibration C and the vibration D generated by operation as excitation;
step three: obtaining frequency response function curves of all channels of the numerical control machine tool in a non-working state environment by using a Bayesian operation modal method and fast Fourier transform, and establishing a modal parameter identification function;
step four: and obtaining dynamic characteristic parameters of the numerical control machine tool, such as inherent frequency, damping ratio, modal shape and the like of each order by analyzing frequency response functions of each channel.
The measurement principle of the invention is as follows:
the linear vibration system of the numerical control machine tool with n degrees of freedom meets the equation of motion:
wherein M is equal to Rn×n、C∈Rn×n、K∈Rn×nRespectively a mass matrix, a damping ratio matrix and a rigidity matrix of the system. The structural response of the multi-degree-of-freedom structure satisfying linear classical damping is assumed to be:
wherein,is a global mode shape vector of the j order;the mode response is the j order mode response, the mode order is m, and the mode response satisfies the decoupling mode power equation:
wherein, ω isj，ζjAnd Wj(t) are scalar quantities representing the natural frequency, damping ratio and modal force of the j-th order mode of the machine tool, respectively. The main parameters of the mode identification are the natural frequency, the damping ratio and the mode shape.
Numerical control machine toolCan generate weak vibration under the excitation condition of random working conditionsAnd N is the sampling number in each acquisition channel for testing the obtained vibration acceleration response data. The acceleration response obtained by the hypothesis test is composed of the structural environment vibration test signal and the prediction error of the model, i.e.
Wherein, { εj∈RnThe "prediction error" is the error between the model response and the test response due to the test noise and the model error. Performing Fast Fourier Transform (FFT) on the acquired machine tool acceleration signal D, namely
In the formula i2＝-1；FkAnd GkRespectively representThe real and imaginary parts of (c); Δ t is the sampling step. Corresponding to k 2,3, …, Nq，fk(k-1)/(N Δ t). Hypothesis augmenting matrixThe content of the study is an augmentation matrix { Z ] obtained by FFT of acceleration signals acquired from a processing statekStarting from the parameter, identifying the dynamic characteristic modal parameter theta of the machine tool, wherein the parameter is f, zeta, Se(ii) a Φ, where f ═ fj:j＝1,…,m}，ζ＝{ζjJ-1, …, m-and Φ - Φ1,…,Φm]∈Rn×mRespectively representing the natural frequency and the damping ratio in the m-order natural mode and the corresponding integral vibration mode of the machine tool; s is belonged to Cm×mAnd SeRespectively representing the spectral density matrix of the state excitation and the prediction error spectral density.
The method can be obtained by the Bayesian theory principle:
p(θ|D)∝p(D|θ) (6)
p (θ | D) represents the posterior probability density function of θ; p (D | theta) is a likelihood function. From the stochastic process analysis we can see that when high sampling rate and sufficient data length are met, the FFT results are approximately independent and satisfy a gaussian distribution, so ZkSubject to a zero mean Gaussian combined distribution to obtain a likelihood function of
In the formula, det (-) represents determinant; ckIs ZkThe theoretical covariance matrix of (1). Further for the convenience of analysis and calculation, a negative log-likelihood function is extracted for analysis, and expressed as L (theta), then p (D | theta) ═ exp [ -L (theta) ]]Wherein
Thus, the optimized value of the modal parameter θ can be obtained by maximizing the posterior probability density function, i.e., minimizing the negative log likelihood function L (θ).
The specific embodiment is as follows:
a. a model number machine tool complete machine is selected as a structure to be tested, a high-precision three-axis acceleration sensor with the measuring range of +/-2 g and the sensitivity of 2000 mu mv is adopted in an experiment, and a modal test system is formed by a multi-channel data acquisition card and a computer to record data. The distribution of the relevant measuring points E is shown in FIG. 3 and FIG. 4;
b. and (3) obtaining the first ten-order natural frequency of the complete machine tool and the corresponding complete machine tool vibration mode by using a modal parameter identification technology combining Bayes theory and operation modal analysis, as shown in table 1. 5-7 show three-dimensional mode diagrams corresponding to the first three-order frequency of the machine tool respectively; finally, a complete machine tool complete machine dynamic characteristic test report is formed.
TABLE 1
Claims (2)
1. A method for measuring the dynamic characteristics of the complete machine processing state of a numerical control machine tool is characterized by comprising the following specific steps:
the method comprises the following steps: a vibration accelerometer sensor is arranged on each main part of the numerical control machine tool;
step two: in a machining state, the vibration of a machine tool foundation and the vibration generated by operation are used as excitation, and the three-phase vibration response of each part of the numerical control machine tool is acquired through a multi-channel data acquisition card;
step three: obtaining frequency response function curves of all channels of the numerical control machine tool in a non-working state environment by using a Bayesian operation modal method and fast Fourier transform, and establishing a modal parameter identification function;
step four: and obtaining dynamic characteristic parameters of the numerical control machine tool, such as inherent frequency, damping ratio, modal shape and the like of each order by analyzing frequency response functions of each channel.
2. The method for measuring the dynamic characteristics of the complete machine processing state of the numerical control machine according to claim 1, wherein: the principle and the method for acquiring the three-phase vibration response of each part of the numerical control machine tool through the multi-channel data acquisition card in the machining state are as follows:
the linear vibration system of the numerical control machine tool with n degrees of freedom meets the equation of motion:
wherein M is equal to Rn×n、C∈Rn×n、K∈Rn×nRespectively a mass matrix, a damping ratio matrix and a rigidity matrix of the system; the structural response of the multi-degree-of-freedom structure satisfying linear classical damping is assumed to be:
wherein,is a global mode shape vector of the j order;the mode response is the j order mode response, the mode order is m, and the mode response satisfies the decoupling mode power equation:
wherein, ω isj，ζjAnd Wj(t) are tables, respectivelyA scalar showing the natural frequency, damping ratio and modal force of the j-th order mode of the machine. The main parameters of the mode identification are natural frequency, damping ratio and vibration mode;
the numerical control machine tool generates weak vibration under the condition of random working condition excitationN is the sampling number in each acquisition channel for the vibration acceleration response data obtained by testing; the acceleration response obtained by the hypothesis test is composed of the structural environment vibration test signal and the prediction error of the model, i.e.
Wherein, { εj∈RnThe "prediction error" is the error between the model response and the test response due to the test noise and the model error. Carrying out Fast Fourier transform (Fast Fourier transform, FFT) on the acquired machine tool acceleration signal D, namely
In the formula i2＝-1；FkAnd GkRespectively representThe real and imaginary parts of (c); Δ t is the sampling step, corresponding to k being 2,3, …, Nq，fkGiven (k-1)/(N Δ t), the augmentation matrix is assumedAn amplification matrix { Z obtained by FFT of acceleration signals acquired from a machining statekStarting from the parameter, identifying the dynamic characteristic modal parameter theta of the machine tool, wherein the parameter is f, zeta, Se(ii) a Φ, where f ═ fj:j＝1,…,m}，ζ＝{ζjJ-1, …, m-and Φ - Φ1,…,Φm]∈Rn×mRespectively representing the natural frequency and the damping ratio in the m-order natural mode and the corresponding integral vibration mode of the machine tool; s is belonged to Cm×mAnd SeRespectively representing the spectral density matrix of the state excitation and the prediction error spectral density;
the method can be obtained by the Bayesian theory principle:
p(θ|D)∝p(D|θ) (6)
p (θ | D) represents the posterior probability density function of θ; p (D | theta) is a likelihood function. From the stochastic process analysis we can see that when high sampling rate and sufficient data length are met, the FFT results are approximately independent and satisfy a gaussian distribution, so ZkSubject to a zero mean Gaussian combined distribution to obtain a likelihood function of
In the formula, det (-) represents determinant; ckIs ZkFor the purpose of analysis and calculation, the theoretical covariance matrix of (a) is a negative log-likelihood function, expressed as L (θ), and p (D | θ) ═ exp [ -L (θ) for analysis]Wherein
Thus, the optimized value of the modal parameter θ can be obtained by maximizing the posterior probability density function, i.e., minimizing the negative log likelihood function L (θ).
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