CN103264317A - Evaluation method for operation reliability of milling cutter - Google Patents

Abstract

The invention discloses a method for evaluating the running reliability of a milling tool. The invention firstly collects the three-phase current signals of the main shaft and the feed shaft of the processing machine tool through the Hall sensor, and then extracts the time-domain average value feature and the tooth frequency energy feature through wavelet analysis. For these eigenvectors, by Mean algorithm, obtain the observation vector output function: mixed Gaussian distribution density function. Then the Baum-Welch algorithm is used to train the continuous "hidden-semi-Markov" model, and the parameter estimation results are obtained, and the Chapman-Kolmogorov differential equation is used to calculate the milling tool level of operational reliability. The invention provides decision support for preventive maintenance of milling tools.

Description

A Method for Evaluating the Running Reliability of Milling Tool

technical field

The invention relates to a method for evaluating the running reliability of a milling tool.

technical background

In modern manufacturing, the condition of the tool is very important to ensure the quality of processing and improve productivity. However, tool wear is unavoidable in machining. It will directly affect the machining accuracy and surface roughness of the workpiece, which not only reduces the machining quality, but also affects the safety and normal operation of the machining system in severe cases. Therefore, good tool condition has become a necessary condition in modern machinery manufacturing and automatic processing, and it is also a key technology to ensure the quality of processed workpieces. However, manual judgment of tool status has become an important bottleneck restricting the development of the manufacturing industry. Therefore, it is urgent to design and develop a new method for intelligent monitoring and automatic evaluation of tool operating status. It does not need to wait for the milling tool to run for a long time. If a fault occurs, it can accurately analyze and evaluate the reliability changes of the milling tool, so as to guide the user to take reasonable preventive measures in advance to prevent the quality of the workpiece and the safe operation of the processing system from being affected by tool problems.

Contents of the invention

In order to solve the above-mentioned technical problems existing in the prior art, the present invention provides a method for analyzing the operational reliability of a milling tool that can provide decision support for preventive maintenance.

The technical scheme for solving the above-mentioned technical problems comprises the following steps:

1) According to the design data and use history of milling tools, determine the total number of operating states M; the operating state set of milling tools is expressed as S={S ₁ ,S ₂ ,…,S _m ,…,S _M },s _M Complete tool failure for milling.

2) According to the machining conditions of milling tools, record the cutting parameters, use the Hall sensor to collect the three-phase current signals of the machine tool spindle and the feed axis, and extract the average value in the time domain and the energy value of the tooth frequency signal as feature quantities; specifically include: ①Frequency analysis, wavelet decomposition of the current signal of the machine tool motor, extracting the signal of the tooth frequency component for reconstruction, obtaining the tooth frequency curve, and extracting the energy characteristic value; ②Time domain analysis: taking the mean square of the three-phase current of the feed current signal The wavelet analysis is performed on the root value to extract the characteristic quantity of the signal in the time domain.

为t时刻观测向量，k_m为状态s_m对应高斯分量的数目，

为高斯分布均值参数，Σ_mk为高斯分布协方差矩阵，c_mk是状态s_m对应每个高斯分量的权重；重复步骤3），得到铣削加工刀具所有运行状态的连续混合高斯概率密度函数。3) According to the total number of milling tool operating states M, determine the number of Gaussian distribution functions k _m corresponding to each milling tool operating state; for a certain operating state of the milling tool, the above-mentioned collected characteristic signals are averaged and segmented, and The parameters belonging to a segment in the characteristic signal are composed into a large matrix, and the K-means clustering is performed on the vectors of each segment to obtain the continuous mixed Gaussian probability density function corresponding to a certain state of the milling tool $b_m=\left({\stackrel{\mathrm{\ρ}}{o}}_t\right)={\mathrm{\Σ}}_{k=1}^{k_m}{c}_{\mathrm{mk}}{b}_{\mathrm{mk}}\left({\stackrel{\mathrm{\ρ}}{o}}_t\right)={\mathrm{\Σ}}_{k=1}^{k_m}{c}_{\mathrm{mk}}N({\stackrel{\mathrm{\ρ}}{o}}_t,{\stackrel{\mathrm{\ρ}}{\mathrm{\μ}}}_{\mathrm{mk}},{\mathrm{\Σ}}_{\mathrm{mk}}),$ in:

is the observation vector at time t, k _m is the number of Gaussian components corresponding to the state s _m ,

is the mean parameter of the Gaussian distribution, Σ _mk is the covariance matrix of the Gaussian distribution, and c _mk is the weight of each Gaussian component corresponding to the state s _m ; repeat step 3) to obtain the continuous mixed Gaussian probability density function of all operating states of the milling tool.

4) Use the continuous hidden semi-Markov model to estimate the reliability level of the tool running state; first, give the initial value to the continuous hidden semi-Markov model CHSMM, and then use the Baum-Welch algorithm to train the model to complete the parameter estimation , to calculate the operational reliability level of the milling tool;

v_m,w_m>0，v_m为尺度参数，w_m为形状参数；观测值模型采用混合高斯分布，即 $b_m=\left({\stackrel{\mathrm{\ρ}}{o}}_t\right)={\mathrm{\Σ}}_{k=1}^{k_m}{c}_{\mathrm{mk}}{b}_{\mathrm{mk}}\left({\stackrel{\mathrm{\ρ}}{o}}_t\right)={\mathrm{\Σ}}_{k=1}^{k_m}{c}_{\mathrm{mk}}N({\stackrel{\mathrm{\ρ}}{o}}_t,{\stackrel{\mathrm{\ρ}}{\mathrm{\μ}}}_{\mathrm{mk}},{\mathrm{\Σ}}_{\mathrm{mk}}),$

为t时刻观测向量，k_m为状态s_m对应高斯分量的数目，

为高斯分布均值参数，Σ_mk为高斯分布协方差矩阵，c_mk是状态s_m对应每个高斯分量的权重。Among them, the state duration model adopts Gamma distribution, namely

v _m ,w _m >0, v _m is a scale parameter, w _m is a shape parameter; the observation model adopts a mixed Gaussian distribution, namely $b_m=\left({\stackrel{\mathrm{\ρ}}{o}}_t\right)={\mathrm{\Σ}}_{k=1}^{k_m}{c}_{\mathrm{mk}}{b}_{\mathrm{mk}}\left({\stackrel{\mathrm{\ρ}}{o}}_t\right)={\mathrm{\Σ}}_{k=1}^{k_m}{c}_{\mathrm{mk}}N({\stackrel{\mathrm{\ρ}}{o}}_t,{\stackrel{\mathrm{\ρ}}{\mathrm{\μ}}}_{\mathrm{mk}},{\mathrm{\Σ}}_{\mathrm{mk}}),$

is the observation vector at time t, k _m is the number of Gaussian components corresponding to the state s _m ,

is the mean parameter of the Gaussian distribution, Σ _mk is the covariance matrix of the Gaussian distribution, and c _mk is the weight of each Gaussian component corresponding to the state s _m .

The specific process of the above step 3) is as follows:

① Model definition: the continuous hidden-semi-Markov model is expressed as $\mathrm{CHSMM}\left(\mathrm{\λ}\right)=({\mathrm{\π}}_m,a_{\mathrm{mn}},c_{\mathrm{mk}},{\stackrel{\mathrm{\ρ}}{\mathrm{\μ}}}_{\mathrm{mk}},{\mathrm{\Σ}}_{\mathrm{mk}},v_m,w_m),$ Among them, M is the total number of tool running states, _m is the running state of the milling tool, the initial state distribution π _m = (π ₁ ,..., π _m ), the state transition probability matrix a _mn indicates that the tool jumps from the first motion state s _m to The probability of motion state s _n .

的估计值

依次对刀具的所有运行状态进行训练，得到每种运行状态的隐-半马尔可夫模型。② Model training: Baum-Welch (Baum-Welch) algorithm is used to train the model, that is, to solve the parameter estimation problem of the model and obtain the model parameters

estimated value of

All the operating states of the tool are trained in sequence to obtain a hidden-semi-Markov model for each operating state.

③Evaluation of operational reliability: After the model training is completed, according to the results of model parameter estimation, the Chapman-Kolmogorov differential equation is used to calculate the operational reliability level of milling tools.

The beneficial effects of the present invention are as follows: the present invention extracts the time-domain and frequency-domain characteristic information of the above-mentioned signals by using the wavelet analysis method by collecting the main shaft current and the feed axis current signal of the processing machine tool, and then uses the continuous hidden semi-Markov model and cutting Pullman-Kolmogorov differential equation to calculate the operational reliability level of milling tools. This provides important reference information for the maintenance decision analysis of milling machining center tools.

Description of drawings

Figure 1 is a flow chart of the present invention.

Fig. 2 is the time-domain mean value time-domain waveform of the machine tool spindle current signal in the present invention.

Fig. 3 is the frequency domain waveform of the machine tool spindle current signal in the present invention.

Fig. 4 is the running reliability curve of the milling tool of the present invention.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings and embodiments. The method of the invention first collects the current signals of the main shaft and the feed shaft of the processing machine tool through the Hall sensor, then uses the wavelet analysis method to perform feature extraction, and then performs parameter estimation through the continuous hidden semi-Markov model, and uses the Chepman-Kolmo Gorlov's differential equation calculates the operational reliability level of milling tools to provide decision support for preventive maintenance.

As shown in Figure 1, the present invention comprises the following steps:

The first step is to determine the running state of the milling tool.

According to the design data and use history of the milling tool, determine the total number M of its operating status. The running state set of the milling tool is expressed as S={S ₁ ,S ₂ ,…,S _m ,…,S _M }, and s _M is the complete failure of the milling tool.

The second step is to extract the feature quantity of the running state of the milling tool.

The hall sensor is used to collect the three-phase current signals of the main shaft and feed shaft of the processing machine tool. The sampling interval and the number of groups of signals collected each time can be determined according to the actual situation of the enterprise. Then the mean value in the time domain and the energy value of the tooth frequency signal are extracted as feature quantities. The specific process is as follows: (1) Frequency analysis, wavelet decomposition is performed on the current signal of the machine tool motor, and the signal of the tooth frequency component is extracted for reconstruction to obtain the tooth frequency curve and extract the energy characteristic value. (2) Time-domain analysis: take the root mean square value of the three-phase current of the feed current signal for wavelet analysis, and extract the characteristic quantities of the signal in the time domain.

The third step is to extract the probability density function of the observation sample sequence.

和Σ_mk，得到铣削加工刀具某个状态所对应的连续混合高斯概率密度函数 $b_m=\left({\stackrel{\mathrm{\ρ}}{o}}_t\right)={\mathrm{\Σ}}_{k=1}^{k_m}{c}_{\mathrm{mk}}{b}_{\mathrm{mk}}\left({\stackrel{\mathrm{\ρ}}{o}}_t\right)={\mathrm{\Σ}}_{k=1}^{k_m}{c}_{\mathrm{mk}}N({\stackrel{\mathrm{\ρ}}{o}}_t,{\stackrel{\mathrm{\ρ}}{\mathrm{\μ}}}_{\mathrm{mk}},{\mathrm{\Σ}}_{\mathrm{mk}}).$ 依次类推，得到铣削加工刀具所有运行状态的连续混合高斯概率密度函数。According to the total number M of milling tool running states, the number k _m of Gaussian distribution functions corresponding to each milling tool running state is determined. For a certain operating state of the milling tool, the above-mentioned collected feature signals are averaged into segments, and the parameters belonging to a segment in the feature signal are formed into a large matrix, and K-means clustering is performed on the vectors of each segment, and three The key parameter c _mk ,

and Σ _mk , to obtain the continuous mixed Gaussian probability density function corresponding to a certain state of the milling tool $b_m=\left({\stackrel{\mathrm{\ρ}}{o}}_t\right)={\mathrm{\Σ}}_{k=1}^{k_m}{c}_{\mathrm{mk}}{b}_{\mathrm{mk}}\left({\stackrel{\mathrm{\ρ}}{o}}_t\right)={\mathrm{\Σ}}_{k=1}^{k_m}{c}_{\mathrm{mk}}N({\stackrel{\mathrm{\ρ}}{o}}_t,{\stackrel{\mathrm{\ρ}}{\mathrm{\μ}}}_{\mathrm{mk}},{\mathrm{\Σ}}_{\mathrm{mk}}).$ By analogy, the continuous mixed Gaussian probability density function of all operating states of the milling tool is obtained.

The fourth step is to evaluate the operational reliability of milling tools.

HSMM (Hidden Semi-Markov Model, Hidden-Semi-Markov Model) is an extension of HMM (Hidden Markov Model, Hidden Markov Model). In order to improve the limitation of the exponential distribution of the state residence time in the hidden Markov model, on the basis of the hidden Markov model, the hidden-semi-Markov model allows customizing the residence time distribution according to the actual problem. From the use history of milling tools, the Gamma distribution is used as the probability distribution function of the state dwell time. At the same time, the output function of the observation sequence is fitted with a mixed Gaussian distribution.

的估计值

依次对刀具的所有运行状态进行训练，得到每种运行状态的连续隐-半马尔可夫模型。Step (a1): Model training. First, initialize the parameters of the continuous hidden semi-Markov model, in which the initial state distribution adopts a uniform distribution, and set the number of iterations and convergence error. Then use the Baum-Welch algorithm to train the model to get the model parameters

estimated value of

All operating states of the tool are trained sequentially to obtain a continuous hidden-semi-Markov model for each operating state.

为状态转移矩阵。对微分方程进行拉氏变换，可得： $s\·\left[\begin{array}{c}{P}_0\left(s\right)\\ P_1\left(s\right)\\ M\\ P_k\left(s\right)\\ P_{k+1}\left(s\right)\end{array}\right]-\left[\begin{array}{c}{P}_0\left(0\right)\\ P_1\left(0\right)\\ M\\ P_k\left(0\right)\\ P_{k+1}\left(0\right)\end{array}\right]=\left[\begin{array}{ccccc}{\hat{a}}_{00}& 0& L& 0& 0\\ {\hat{a}}_{01}& {\hat{a}}_{11}& L& 0& 0\\ M& M& & M& M\\ {\hat{a}}_{0k}& {\hat{a}}_{1k}& L& {\hat{a}}_{\mathrm{kk}}& 0\\ {\hat{a}}_{0(k+1)}& {\hat{a}}_{1(k+1)}& L& {\hat{a}}_{k(k+1)}& {\hat{a}}_{(k+1)(k+1)}\end{array}\right]\·\left[\begin{array}{c}{P}_0\left(s\right)\\ P_1\left(s\right)\\ M\\ P_k\left(s\right)\\ P_{(k+1)}\left(s\right)\end{array}\right],$ 其中铣削加工刀具在初始条件时处于正常状态，可得P(0)=(p₀(0),P₁(0),L,P_k(0),P_k+1(0))=(1,0,0,0)。Step (a2): Evaluation of milling tool operational reliability. Let P _j (t)=P(q _t =s _j ) represent the probability that the equipment is in state s _j at time t. According to the Chapman-Kolmogorov differential equation, P'(t)=P(t)·A, where P(t)=(p ₀ (t),P ₁ (t),L,P _k (t), P _k+1 (t)) is the state vector, P'(t) is the first-order differential state vector of P(t),

is the state transition matrix. Laplace transform the differential equation, we can get: $\mathrm{the\; s}\&CenterDot;\left[\begin{array}{c}{P}_0\left(\mathrm{the\; s}\right)\\ P_1\left(\mathrm{the\; s}\right)\\ m\\ P_k\left(\mathrm{the\; s}\right)\\ P_{k+1}\left(\mathrm{the\; s}\right)\end{array}\right]-\left[\begin{array}{c}{P}_0\left(0\right)\\ P_1\left(0\right)\\ m\\ P_k\left(0\right)\\ P_{k+1}\left(0\right)\end{array}\right]=\left[\begin{array}{ccccc}{\hat{a}}_{00}& 0& \mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HDA00003202086500012.png,HDA00003202086500021.png"\; state="\{\{state\}\}">L</figure-callout>}& 0& 0\\ {\hat{a}}_{01}& {\hat{a}}_{11}& \mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HDA00003202086500012.png,HDA00003202086500021.png"\; state="\{\{state\}\}">L</figure-callout>}& 0& 0\\ m& m& & m& m\\ {\hat{a}}_{0k}& {\hat{a}}_{1k}& L& {\hat{a}}_{\mathrm{kk}}& 0\\ {\hat{a}}_{0(k+1)}& {\hat{a}}_{1(k+1)}& L& {\hat{a}}_{k(k+1)}& {\hat{a}}_{(k+1)(k+1)}\end{array}\right]\&Center\; Dot;\left[\begin{array}{c}{P}_0\left(\mathrm{the\; s}\right)\\ P_1\left(\mathrm{the\; s}\right)\\ m\\ P_k\left(\mathrm{the\; s}\right)\\ P_{(k+1)}\left(\mathrm{the\; s}\right)\end{array}\right],$ Among them, the milling tool is in a normal state at the initial condition, and P(0)=(p ₀ (0),P ₁ (0),L,P _k (0),P _k+1 (0))=( 1,0,0,0).

There is P(s)=(p ₀ (s), P ₁ (s), L, P _k (s), P _k+1 (s)), and the inverse Laplace transform is performed on P(s) to obtain the equipment at t The probability of being in different states at any time P(t)=(p ₀ (t), P ₁ (t), L, P _k (t), P _k+1 (t)), so that the milling tool can be calculated at time t The reliability of R (t) = 1-P _{k + 1} (t).

Below in conjunction with the present invention of concrete example, make further elaboration:

1: According to the design data and use history of a milling tool, the total number of operating states is determined to be 4, s ₁ is a normal state, s ₂ is a mildly deteriorated state, s ₃ is a severely deteriorated state, and s ₄ is a complete failure state.

2: When this tool is actually processed, the cutting parameters are spindle speed 130r/min, feed speed 140mm/min, depth of cut 1mm, end mill processing, 6 teeth, sampling frequency 1000Hz. The sampling interval is 48 hours, and the total sampling time T=960 hours. Wavelet analysis is used to extract time domain and frequency domain features. Fig. 2 is the time-domain waveform of the time-domain mean value of the machine tool spindle current signal; Fig. 3 is the frequency-domain waveform of the machine tool spindle current signal;

3: Divide the above characteristic signal into four segments on average, each state corresponds to 4 Gaussian distribution functions, and use the K-means algorithm to obtain the probability density function of the observation vector: a mixed Gaussian density function. In order to save space, here are only the mixed Gaussian distribution function parameters corresponding to the tool being in a normal state at a certain time t: the weight parameter matrix is weight=[0.345 0.287 0.129 0.239], the mean matrix mean=[0.0099 0.0079 0.5568 0.3234], the correlation Variance matrix cov=[3.9448 3.8648 6.3945 7.4736].

4: Evaluation of milling tool operation reliability. First, the initial value is given to the continuous hidden semi-Markov model CHSMM. If the initial state distribution is uniform, the total number of tool operating states M=4. Then, the Baum-Welch algorithm is used to train the model, complete the parameter estimation, and calculate the operational reliability level of the milling tool. Figure 4 is a graph of the operational reliability level of the milling tool.

The present invention is not limited to the above-mentioned specific embodiments, and those skilled in the art can adopt various other specific embodiments to implement the present invention according to the disclosed content of the present invention. Changes or modified designs all fall within the protection scope of the present invention.

Claims (4)

1. the appraisal procedure of a Milling Process cutter operational reliability the steps include:

1) historical according to design data and the use of Milling Process cutter, determine its running status sum M; Milling Process cutter running status set representations is S={S ₁, S ₂..., S _m..., S _M, s _MFor the Milling Process cutter entirely ineffective;

2) at milling cutter processing operating mode, the record cutting parameter utilizes sensor to gather machine tool chief axis and feed shaft three-phase current signal, therefrom extracts the energy value of average on the time domain and tooth frequency signal as characteristic quantity;

3) according to Milling Process cutter running status sum M, determine the corresponding gauss of distribution function number of each Milling Process cutter running status k _m, _mBe Milling Process cutter running status s _mSubscript, be used for representing s _mAt a certain running status of Milling Process cutter, characteristic signal to above-mentioned collection averages segmentation, and big matrix of parameter composition of a section will be belonged in the characteristic signal, vector to each section carries out the K mean cluster, obtains the corresponding continuous mixed Gaussian probability density function of certain state of Milling Process cutter $b_m=\left({\stackrel{\mathrm{\&rho;}}{o}}_t\right)={\mathrm{\&Sigma;}}_{k=1}^{k_m}{c}_{\mathrm{mk}}{b}_{\mathrm{mk}}\left({\stackrel{\mathrm{\&rho;}}{o}}_t\right)={\mathrm{\&Sigma;}}_{k=1}^{k_m}{c}_{\mathrm{mk}}N({\stackrel{\mathrm{\&rho;}}{o}}_t,{\stackrel{\mathrm{\&rho;}}{\mathrm{\&mu;}}}_{\mathrm{mk}},{\mathrm{\&Sigma;}}_{\mathrm{mk}}),$ Wherein:

Be t moment observation vector, t is constantly, k _mBe state s _mCorresponding gauss of distribution function number,

Be Gaussian distribution Mean Parameters, Σ _MkBe Gaussian distribution covariance matrix, c _MkBe state s _mThe weight of corresponding each Gaussian component; Repeating step 3), obtain the continuous mixed Gaussian probability density function of all running statuses of Milling Process cutter;

4) adopting continuously latent half Markov model to come that the cutter running status is carried out reliability level estimates; At first to the continuously latent given initial value of half Markov model CHSMM, then adopt the Baum-Welch algorithm to the model training, finish parameter Estimation, carry out Milling Process cutter operational reliability level calculation;

Wherein, the state duration model adopts Gamma to distribute, namely

v _m, w _m0, v _mBe scale parameter, w _mBe form parameter; The observation model adopts mixed Gaussian to distribute, namely $b_m=\left({\stackrel{\mathrm{\&rho;}}{o}}_t\right)={\mathrm{\&Sigma;}}_{k=1}^{k_m}{c}_{\mathrm{mk}}{b}_{\mathrm{mk}}\left({\stackrel{\mathrm{\&rho;}}{o}}_t\right)={\mathrm{\&Sigma;}}_{k=1}^{k_m}{c}_{\mathrm{mk}}N({\stackrel{\mathrm{\&rho;}}{o}}_t,{\stackrel{\mathrm{\&rho;}}{\mathrm{\&mu;}}}_{\mathrm{mk}},{\mathrm{\&Sigma;}}_{\mathrm{mk}}).$

2. the appraisal procedure of a kind of Milling Process cutter operational reliability as claimed in claim 1 is characterized in that: step 2) comprising:

1) frequency analysis is carried out wavelet decomposition to the machine motor current signal, and the signal that extracts the tooth frequency content is reconstructed, and obtains the tooth frequency curve, carries out the extraction of energy feature value;

2) time-domain analysis: get feeding current signal three-phase current root-mean-square value and carry out wavelet analysis, extract the characteristic quantity on the signal time domain.

3. the appraisal procedure of a kind of Milling Process cutter operational reliability as claimed in claim 1 is characterized in that: step 2) described in sensor be Hall element.

4. as the appraisal procedure of the described a kind of Milling Process cutter operational reliability of arbitrary claim among the claim 1-3, it is characterized in that: the detailed process of step 4) is as follows:

1) model definition: latent-semi-Markov model is expressed as continuously $\mathrm{CHSMM}\left(\mathrm{\&lambda;}\right)=({\mathrm{\&pi;}}_m,a_{\mathrm{mn}},c_{\mathrm{mk}},{\stackrel{\mathrm{\&rho;}}{\mathrm{\&mu;}}}_{\mathrm{mk}},{\mathrm{\&Sigma;}}_{\mathrm{mk}},v_m,w_m),$ Wherein, latent state is that the quantity of cutter running status is M, initial state distribution π _m=(π ₁..., π _m); State transition probability matrix a _MnThe expression cutter is from motion state s _mJump to motion state s _nProbability, c _MkBe state s _mThe weight of corresponding each Gaussian component, Be Gaussian distribution Mean Parameters, Σ _MkBe Gaussian distribution covariance matrix, v _mBe scale parameter, w _mBe form parameter;

2) model training: adopt Bao Mu-Wei Erqi (Baum-Welch) algorithm to the model training, namely solve the parameter Estimation problem of model, obtain model parameter

Estimated value

Successively all running statuses of cutter are trained, obtain the latent-semi-Markov model of every kind of running status;

3) operational reliability assessment: after model training is finished, according to the result of model parameter estimation, adopt Qie Puman-Andrei Kolmogorov differential equation, calculate Milling Process cutter operational reliability level.

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