CN114273974B - Vibration signal-based cutter runout parameter online estimation method in high-speed milling - Google Patents
Vibration signal-based cutter runout parameter online estimation method in high-speed milling Download PDFInfo
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Abstract
The invention discloses a cutter run-out parameter on-line estimation method based on vibration signals in high-speed milling, which comprises the steps of firstly preprocessing an original vibration signal obtained by acquisition to obtain a time domain vibration signal; then, frequency domain displacement signals are obtained through secondary integration aiming at the time domain vibration signals, and then the frequency domain displacement signals are converted into time domain displacement signals through inverse discrete Fourier transform; and finally, estimating and obtaining the average runout amount of the cutter according to the time domain displacement signals, and taking the average runout amount of the cutter as the runout length of the cutter to realize the on-line estimation of the runout parameters of the cutter based on vibration signals in high-speed milling. According to the invention, on-line estimation is quickly performed on the jump distance of the cutter based on the real-time vibration signal in the high-speed milling process, so that the cutter parameter identification efficiency is greatly improved, the cutter abrasion characteristic in the high-speed milling process is accurately analyzed, the cutter abrasion prediction efficiency is improved, the service life of the cutter is prolonged, and the processing quality of a workpiece is improved.
Description
Technical Field
The invention relates to an on-line estimation method for a tool jump parameter in high-speed milling, in particular to an on-line estimation method for a tool jump parameter in high-speed milling based on a vibration signal.
Background
The high-speed milling processing takes high cutting speed, high feeding speed and high processing precision as main characteristics, has the capabilities of high comprehensive benefit, high market response speed and the like, and is widely applied to the industries of automobiles, household appliances, aerospace production, electronics, optics, biomedicine and the like. Currently, based on methods such as high-speed cutting theory, many students have conducted extensive research and in-depth analysis on modeling of milling processes and wear of tool features in high-speed milling.
During high speed machining, the tool inevitably jumps. Tool runout is one of the key parameters for modeling the milling process and tool wear profile analysis. The cutter jump can cause the inconsistent wear of different cutter teeth of the cutter, and further the service life of the cutter and the processing quality of a workpiece are affected. The current estimation methods can be classified into a physical theory method and a data driving method according to data and information types required for tool runout estimation. The physical theory method estimates the specific cutter abrasion loss through established mechanisms and empirical formulas, wherein physical parameters need to be determined through an experimental method. The data driven method is another, more common method that predicts the future state of wear on a numerical basis from the current state of tool wear. Specifically, the data driving method is further divided into an Artificial Intelligence (AI) method (e.g., support vector machine, artificial neural network, fuzzy theory, long-short term memory, etc.) and a statistical method (e.g., multiple linear regression, gaussian mixture regression, hidden markov model, etc.). In recent years, a number of hybrid artificial intelligence methods have been proposed by many students to predict tool wear. However, the above method requires training using a large amount of multi-layer data and redundant time, affecting the tool wear prediction efficiency.
Disclosure of Invention
The invention provides an on-line estimation method for cutter run-out parameters based on vibration signals in high-speed milling, which is used for carrying out cutter wear estimation based on time sequence analysis according to real-time vibration signals, so that cutter wear characteristics in the high-speed milling process are analyzed more accurately, cutter wear prediction efficiency is improved, the service life of a cutter is prolonged, and the processing quality of a workpiece is improved.
The invention adopts the following technical scheme for realizing the purpose:
the invention relates to a cutter runout parameter on-line estimation method based on vibration signals in high-speed milling processing, which is characterized in that:
first, for the original vibration signal A obtained by acquisition R Preprocessing to obtain a time domain vibration signal A P ；
Then for the time domain vibration signal A P Obtaining the frequency domain displacement signal D by integration λ Converting the frequency domain displacement signal into a time domain displacement signal d through inverse discrete Fourier transform i ；
And finally, estimating and obtaining the average jump quantity of the cutter according to the time domain displacement signal, and taking the average jump quantity of the cutter as the jump length of the cutter to realize the on-line estimation of the jump parameters of the cutter based on the vibration signal in high-speed milling.
The tool runout parameter on-line estimation method based on the vibration signal in the high-speed milling process is also characterized in that:
the preprocessing of the original vibration signals obtained by acquisition means: obtaining an original vibration signal A by monitoring with an accelerometer R For the original vibration signal A R Smoothing is carried out in the time domain, so that high-frequency random interference signals are weakened, and irregular trend items are eliminated.
The tool runout parameter on-line estimation method based on the vibration signal in the high-speed milling process is also characterized in that: the method comprises the following steps:
step 1: original vibration signal acquisition and pretreatment:
acquisition of the original vibration signal A R For the original vibration signal A R Preprocessing by adopting a five-point three-time smoothing method to obtain a preprocessed time domain vibration signal A P ；
Step 2: obtaining a time domain displacement signal through signal processing:
for the time domain vibration signal A P Firstly, performing discrete Fourier transform to obtain a frequency domain vibration signal X λ Then to the frequency domain vibration signal X λ Integrating to obtain frequency domain displacement signal D λ The method comprises the steps of carrying out a first treatment on the surface of the For the frequency domain displacement signal D λ Obtaining a time domain displacement signal d through inverse discrete Fourier transform i ；
Step 3: estimating a tool runout parameter from the time domain displacement signal:
according to the time domain displacement signal d i Obtaining a displacement track fitting curve through a nonlinear least square method;
the tool jump position is recorded as (O) x ,O y ) Refers to the center point seat (O) x ,O y )；
The sampling frequency of the sample is omega, the duration of one period of rotation of the milling cutter is T, and the sampling number in one period is omega T;
will be within each periodThe displacement signal sequence is marked as theta q ；
For the displacement signal sequence theta q And carrying out nonlinear least square method solution: constructed with tool-jumping position (O) x ,O y ) And the tool jump length r is a multi-element nonlinear target function set of multiple target variables, and the optimal solution of each target variable is obtained as the tool jump parameter by adopting a least square method aiming at the target function set, so that the tool jump parameter estimation based on the vibration signal in the high-speed milling process is realized.
The tool runout parameter on-line estimation method based on the vibration signal in the high-speed milling process is also characterized in that:
will be the original vibration signal A R Each element is sequentially recorded as a discrete number sequence { a } Ri }；
By applying time domain vibration signal A P Each element is sequentially recorded as a discrete number sequence { a } Pi }；
Wherein i=0, 1, …, (U-1); u is the number of samples to be sampled;
obtaining a time domain vibration signal A according to (1) P ；
In the formula (1): u=2, 3, …, (U-3);
for sequence { a } Pi Performing discrete Fourier transform to obtain frequency domain vibration signal X represented by formula (2) λ ：
In formula (2), λ=0, 1, …, (U-1); j is the imaginary number of the unit
For frequency domain vibration signal X λ Integrating to obtain a frequency domain displacement signal D represented by the formula (3) λ ：
In the formula (3), ω λ =2ΣΔf; Δf is the frequency resolution, Δf=1/T s ，T s The total duration of the sample data;
obtaining a time domain displacement signal d represented by the formula (4) through inverse discrete Fourier transform i ：
In the formula (4), L λ Is the frequency characteristic of the band-pass filter characterized by equation (5):
in the formula (5), f u For a lower cut-off frequency f d Is the upper cut-off frequency;
then, the shift signal sequence θ in each period q As characterized by formula (6):
in the formula (6), the amino acid sequence of the compound,
for displacement signal sequence theta q Solving a nonlinear least square method, and decomposing each group of displacement signal sequences into components theta of an x axis xq And a component θ of the y-axis yq Characterized by formula (7):
constructing a multi-element nonlinear target function set f (O x ,O y R) is as formula (8):
first, each target variable in the formula (8) is assigned an initial value, and then the solution is carried out by using a nonlinear least square method, so that an optimal solution of each target variable is obtained.
Compared with the prior art, the invention has the beneficial effects that:
the invention rapidly makes on-line estimation on the jump distance of the cutter based on the real-time vibration signal in the high-speed milling process, greatly improves the identification efficiency of cutter parameters, thereby accurately analyzing the abrasion characteristics of the cutter in the high-speed milling process, improving the prediction efficiency of cutter abrasion, prolonging the service life of the cutter and improving the processing quality of workpieces
Drawings
FIG. 1 is a flow chart of a method for estimating tool runout parameters according to the present invention;
fig. 2 (a) is a schematic diagram of an experimental three-blade ball nose milling cutter;
FIG. 2 (b) is a schematic diagram showing the operation of the three-edged ball nose milling cutter shown in FIG. 2 (a);
FIG. 3 is a schematic diagram of the result of preprocessing the original vibration signal by using a five-point three-time smoothing method;
FIG. 4 is a graph showing the acquisition of displacement signals in the time and frequency domains from the preprocessed vibration signal;
fig. 5 is a schematic diagram of a result of obtaining a tool run-out length estimation by performing a nonlinear least square solution on a displacement signal.
Detailed Description
The on-line estimation method for the tool runout parameters based on vibration signals in the high-speed milling process in the embodiment is as follows:
first, for the original vibration signal A obtained by acquisition R Preprocessing to obtain a time domain vibration signal A P ；
Then for the time domain vibration signal A P Obtaining the frequency domain displacement signal D by integration λ Converting the frequency domain displacement signal into a time domain displacement signal d through inverse discrete Fourier transform i ；
And finally, estimating and obtaining the average jump quantity of the cutter according to the time domain displacement signal, and taking the average jump quantity of the cutter as the jump length of the cutter to realize the on-line estimation of the jump parameters of the cutter based on the vibration signal in high-speed milling.
The on-line estimation method for the tool runout parameters based on vibration signals in the high-speed milling process in the embodiment comprises the following steps:
step 1: original vibration signal acquisition and pretreatment:
obtaining an original vibration signal A by monitoring with an accelerometer R For the original vibration signal A R Smoothing in time domain by adopting five-point three-time smoothing method to obtain time domain vibration signal A subjected to smoothing in time domain P Thereby weakening the high-frequency random interference signal and eliminating irregular trend items;
step 2: obtaining a time domain displacement signal through signal processing:
for time domain vibration signal A P Firstly, performing discrete Fourier transform to obtain a frequency domain vibration signal X λ Then to frequency domain vibration signal X λ Integrating to obtain frequency domain velocity signal V λ Obtaining a frequency domain displacement signal D through secondary integration λ The method comprises the steps of carrying out a first treatment on the surface of the For frequency domain velocity signal V λ And frequency domain displacement signal D λ After inverse discrete Fourier transform, the time domain velocity signal v can be obtained i And a time domain displacement signal d i ；
Step 3: estimating an average tool runout from the time domain displacement signal:
according to the time domain displacement signal d i Obtaining a displacement track fitting curve through a nonlinear least square method;
the tool jump position is recorded as (O) x ,O y ) Refers to the center point seat (O) x ,O y ) The method comprises the steps of carrying out a first treatment on the surface of the Aiming at a vertical machine tool, taking the center point of the tool nose of a milling cutter before machining as a coordinate origin, wherein an x-axis is parallel to the feeding direction of a workpiece, and a y-axis is perpendicular to the feeding direction of the workpiece, and establishing a plane coordinate system XOY; the central point of the cutter tip of the milling cutter is marked as (O) due to the jumping of the cutter during the processing x ,O y ) I.e. the tool jump position (O x ,O y )；O x For the x-axis coordinate, O, of the center point of the tip of the milling cutter in a coordinate system XOY y The Y-axis coordinate of the center point of the tool nose of the milling tool in a coordinate system XOY;
the sampling frequency of the sample is omega, the duration of one period of rotation of the milling cutter is T, and the sampling number in one period is omega T;
the displacement signal sequence in each period is recorded as theta q ；
For the displacement signal sequence theta q And carrying out nonlinear least square method solution: constructed with tool-jumping position (O) x ,O y ) And the tool jump length r is a multi-element nonlinear target function set of multiple target variables, and the optimal solution of each target variable is obtained as the tool jump parameter by adopting a least square method aiming at the target function set, so that the tool jump parameter estimation based on the vibration signal in the high-speed milling process is realized.
In particular, the original vibration signal A R Each element is sequentially recorded as a discrete number sequence { a } Ri -a }; by applying time domain vibration signal A P Each element is sequentially recorded as a discrete number sequence { a } Pi -a }; wherein i=0, 1, …, (U-1); u is the number of samples to be sampled;
obtaining a time domain vibration signal A according to (1) P ；
In the formula (1): u=2, 3, …, (U-3), and each element a Pu Corresponding coefficients are the same and are all 1/70 x < -6 24 34 24 > -6]；
For sequence { a } Pi Performing discrete Fourier transform to obtain frequency domain vibration signal X represented by formula (2) λ ：
In formula (2), λ=0, 1, …, (U-1); j is the imaginary number of the unit
For frequency domain vibration signal X λ Integrating to obtain a frequency domain displacement signal D represented by the formula (3) λ ：
In the formula (3), ω λ =2ΣΔf; Δf is the frequency resolution, Δf=1/T s ，T s The total duration of the sample data;
obtaining a time domain displacement signal d represented by the formula (4) through inverse discrete Fourier transform i ：
In the formula (4), L λ Is the frequency characteristic of the band-pass filter characterized by equation (5):
in the formula (5), f u For a lower cut-off frequency f d Is the upper cut-off frequency;
lower cut-off frequency f u And an upper cut-off frequency f d Selecting according to the milling natural frequency nN/60 of the cutter; selecting a minimum closed neighborhood with natural frequency as the center, wherein the minimum closed neighborhood can contain a complete frequency domain waveform, and the left endpoint value of the minimum closed neighborhood is taken as a lower limit cut-off frequency f u The right endpoint value of the minimum closed neighborhood is taken as the upper limit cut-off frequency f d 。
Then, the shift signal sequence θ in each period q As characterized by formula (6):
in (6)，
For displacement signal sequence theta q And carrying out nonlinear least square method solution: setting the initial angle and the x-axis clamping angle of the displacement signals to be 0, decomposing each group of displacement signal sequences into components theta of the x-axis xq And a component θ of the y-axis yq Characterized by formula (7):
constructing a multi-element nonlinear target function set f (O x ,O y R) is as formula (8):
firstly, assigning initial values to all target variables in the formula (8), and solving by using a nonlinear least square method to obtain an optimal solution of each target variable;
variable O x Initial value O of x_guess Variable O y Initial value O of y_guess And the initial value r of the variable r guess Characterized by formula (9):
and (3) experimental verification:
and a three-edge ball-end milling cutter is selected to mill the nickel-based superalloy Inconel 718 continuously, the diameter of the cutter is 0.6mm, and the sampling frequency is 50KHz. The tool and the machining platform are as shown in fig. 2a and 2 b.
The method is used for carrying out on-line estimation on the tool jump parameters in high-speed milling based on vibration signals, and the flow of the method is shown in figure 1.
Fig. 3 (a) shows an x-axis raw vibration signal obtained by acquisition, fig. 3 (b) shows a y-axis raw vibration signal obtained by acquisition, fig. 3 (c) shows an x-axis preprocessed vibration signal, and fig. 3 (d) shows a y-axis preprocessed vibration signal. The original vibration signals in the diagrams (a) and (b) in fig. 3 contain high-frequency random noise mixed in during data acquisition, so that discrete data sequences of the vibration signals show a plurality of burrs and are not smooth; to attenuate the influence of these random disturbance signals, the original vibration signal is smoothed by a five-point three-time smoothing method, and the vibration signal after the pretreatment is shown in fig. 3 (c) and (d). After removing the noise signal in the high frequency component, the amplitude of the curve in the time domain spectrum is reduced.
Fig. 4 (a) shows an x-axis time domain displacement signal, fig. 4 (b) shows a y-axis time domain displacement signal, fig. 4 (c) shows an x-axis frequency domain displacement signal, and fig. 4 (d) shows a y-axis frequency domain displacement signal. As can be seen in fig. 4 (a) and (b), the time domain vibration signal amplitudes of the x-axis and the y-axis are substantially stationary in the sampling interval after the discrete fourier transform. As can be seen from fig. 4 (c) and (d), the spectrum has a distinct peak around the natural frequency.
Finally, the tool jump parameters are obtained by solving the optimization target function set, and as shown in fig. 5, the tool tip center presents an approximate circular track in an x-y plane view because the time domain vibration signal amplitude values of the x axis and the y axis are kept stable in the sampling interval. And adopting a nonlinear least square method to fit the track to obtain a fit circle taking the tool jump length r as a radius. The center of the fitted circle is very close to the origin (0, 0), indicating that the tool has a very small inclination angle during machining.
The method is an effective means for indirectly estimating the tool runout based on vibration signals, and the method can complete on-line real-time estimation of the tool runout by means of the vibration signals, thereby being beneficial to on-line monitoring and characteristic analysis of physical parameters of the process such as tool wear in the high-speed milling process.
Claims (2)
1. An on-line estimation method for tool runout parameters based on vibration signals in high-speed milling processing is characterized by comprising the following steps:
first, to adoptCollecting the obtained original vibration signal A R Preprocessing to obtain a time domain vibration signal A P The method comprises the steps of carrying out a first treatment on the surface of the The preprocessing of the original vibration signals obtained by acquisition means: obtaining an original vibration signal A by monitoring with an accelerometer R For the original vibration signal A R Smoothing in the time domain to weaken high-frequency random interference signal and eliminate irregular trend item;
then for the time domain vibration signal A P Obtaining the frequency domain displacement signal D by integration λ Converting the frequency domain displacement signal into a time domain displacement signal d through inverse discrete Fourier transform i ；
Finally, estimating and obtaining the average runout amount of the cutter according to the time domain displacement signal, and taking the average runout amount of the cutter as the runout length of the cutter to realize the on-line estimation of the runout parameters of the cutter based on vibration signals in high-speed milling;
the tool runout parameter on-line estimation method based on vibration signals in high-speed milling processing comprises the following steps:
step 1: original vibration signal acquisition and pretreatment:
acquisition of the original vibration signal A R For the original vibration signal A R Preprocessing by adopting a five-point three-time smoothing method to obtain a preprocessed time domain vibration signal A P ；
Step 2: obtaining a time domain displacement signal through signal processing:
for the time domain vibration signal A P Firstly, performing discrete Fourier transform to obtain a frequency domain vibration signal X λ Then to the frequency domain vibration signal X λ Integrating to obtain frequency domain displacement signal D λ The method comprises the steps of carrying out a first treatment on the surface of the For the frequency domain displacement signal D λ Obtaining a time domain displacement signal d through inverse discrete Fourier transform i ；
Step 3: estimating a tool runout parameter from the time domain displacement signal:
according to the time domain displacement signal d i Obtaining a displacement track fitting curve through a nonlinear least square method;
the tool jump position is recorded as (O) x ,O y ) Refers to the center point seat (O) x ,O y )；
The sampling frequency of the sample is omega, the duration of one period of rotation of the milling cutter is T, and the sampling number in one period is omega T;
the displacement signal sequence in each period is recorded as theta q ；
For the displacement signal sequence theta q And carrying out nonlinear least square method solution: constructed with tool-jumping position (O) x ,O y ) And the tool jump length r is a multi-element nonlinear target function set of multiple target variables, and the optimal solution of each target variable is obtained as the tool jump parameter by adopting a least square method aiming at the target function set, so that the tool jump parameter estimation based on the vibration signal in the high-speed milling process is realized.
2. The on-line estimation method of tool runout parameters based on vibration signals in high-speed milling according to claim 1, wherein the method comprises the following steps:
will be the original vibration signal A R Each element is sequentially recorded as a discrete number sequence { a } Ri }；
By applying time domain vibration signal A P Each element is sequentially recorded as a discrete number sequence { a } Pi }；
Wherein i=0, 1, …, (U-1); u is the number of samples to be sampled;
obtaining a time domain vibration signal A according to (1) P ；
In the formula (1): u=2, 3, …, (U-3);
for sequence { a } Pi Performing discrete Fourier transform to obtain frequency domain vibration signal X represented by formula (2) λ ：
In formula (2), λ=0, 1, …, (U-1); j is the imaginary number of the unit
For frequency domain vibration signal X λ Integrating to obtain a frequency domain displacement signal D represented by the formula (3) λ ：
In the formula (3), ω λ =2ΣΔf; Δf is the frequency resolution, Δf=1/T s ，T s The total duration of the sample data;
obtaining a time domain displacement signal d represented by the formula (4) through inverse discrete Fourier transform i ：
In the formula (4), L λ Is the frequency characteristic of the band-pass filter characterized by equation (5):
in the formula (5), f u For a lower cut-off frequency f d Is the upper cut-off frequency;
then, the shift signal sequence θ in each period q As characterized by formula (6):
θ q ＝{d (q-1)ωT+1 ,d (q-1)ωT+2 ,…,d qωT } (6)
in the formula (6), the amino acid sequence of the compound,
for displacement signal sequence theta q Performing nonlinear least squaresMultiplying the solution, decomposing each group of displacement signal sequences into the component theta of the x-axis xq And a component θ of the y-axis yq Characterized by formula (7):
constructing a multi-element nonlinear target function set f (O x ,O y R) is as formula (8):
first, each target variable in the formula (8) is assigned an initial value, and then the solution is carried out by using a nonlinear least square method, so that an optimal solution of each target variable is obtained.
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