A method for predicting the remaining life of CNC machine tool components

Abstract

This invention relates to a method for predicting the remaining life of CNC machine tool components, comprising: 1. determining the data type and monitoring location of component status monitoring, building a component status monitoring platform, and collecting CNC machine tool component operating status information in real time; 2. performing trend term elimination, noise reduction, feature extraction, and PCA dimensionality reduction processing on the monitoring signals; 3. based on the CNC machine tool component status monitoring information, considering the machine tool operating conditions, using the new features obtained after dimensionality reduction by principal component analysis as internal covariates, and the operating load and speed as external covariates, establishing a Weibull regression model that fully considers the machine tool operating status information; 4. based on the Weibull regression model, conducting the prediction of the remaining life of the machine tool components. This invention comprehensively considers the external operating conditions and internal vibration characteristics of components during machine tool processing, improving the accuracy of remaining life prediction and accurately predicting the remaining life, which is of significant importance for reducing downtime losses, improving production efficiency, and increasing economic benefits.

Description

Technical Field

[0001] This invention belongs to the field of CNC machine tool technology and relates to a method for predicting the remaining life of CNC machine tool components. Specifically, it involves acquiring monitoring data of the operating status of CNC machine tool components, processing the status monitoring signals of CNC machine tool components, constructing a Weibull regression model for CNC machine tool components, and predicting the remaining life of CNC machine tool components based on the Weibull regression model. Background Technology

[0002] In today's era of rapid technological advancement, remaining life prediction technology has become an important component of intelligent manufacturing. Conducting efficient and accurate remaining life prediction can provide guidance for the formulation of preventive maintenance strategies for manufacturing equipment, which is of great significance for reducing equipment downtime losses and improving equipment safety and reliability.

[0003] As the "mother machines" of intelligent manufacturing, CNC machine tools are highly susceptible to damage if malfunctions are not addressed promptly. This can disrupt the entire production schedule, leading to minor issues like scrapped parts, delayed delivery, and contract termination, or even threatening the safety of operators. Therefore, conducting research on the remaining lifespan prediction of machine tool components, accurately identifying their operating status before failure, and performing appropriate maintenance can significantly reduce maintenance costs and improve machine tool utilization.

[0004] Currently, research on the remaining life prediction of CNC machine tools mainly focuses on components such as bearings, gears, and cutting tools, while research on the remaining life prediction of the entire machine tool and other components is relatively limited. Furthermore, research on the remaining life prediction of CNC machine tools requires a large amount of long-term data, but with the increasing complexity of machine tool structures and functions, coupled with changing and multi-condition operating situations, data collection is limited, making the prediction of machine tool remaining life increasingly difficult. Traditional CNC machine tool remaining life prediction models are mostly based on the single operating conditions of machine tool components. When operating conditions change, the prediction model cannot be updated in a timely manner, resulting in poor model applicability. Alternatively, remaining life prediction may be based solely on the signal characteristics of machine tool components without considering the real-time machining conditions, or it may consider the operating conditions of machine tool components but fail to integrate the two effectively. This inevitably leads to high errors in the remaining life prediction results of machine tool components. Summary of the Invention

[0005] Traditional CNC machine tool remaining life prediction models are mostly based on the operation of machine tool components under a single working condition. This requires separate modeling for each working condition, which is tedious and time-consuming. Alternatively, they may only rely on the signal characteristics of machine tool components for remaining life prediction, without considering the real-time machining conditions of the machine tool, or they may consider the machine tool's operating conditions but fail to integrate the two. This inevitably leads to high errors in the remaining life prediction results of machine tool components. Therefore, this invention takes CNC machine tool components as the research object, and conducts research on the monitoring of component operating status information and remaining life prediction, aiming to explore a more reasonable and accurate remaining life prediction method, and to provide some reference and guidance for manufacturing enterprises to formulate predictive maintenance strategies and manage the health of machine tool components in actual production processes.

[0006] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution, which is described below in conjunction with the accompanying drawings:

[0007] A method for predicting the remaining life of CNC machine tool components includes the following steps:

[0008] Step 1: Based on the basic structure and working principle of the machine tool components, determine the data types and monitoring locations for the machine tool component status monitoring, and collect the operating status information of the CNC machine tool components in real time by building a component status monitoring platform;

[0009] Step 2: Perform trend term elimination, noise reduction, feature extraction, and principal component analysis (PCA) dimensionality reduction on the obtained component status monitoring signals to obtain signal features with better trend characteristics;

[0010] Step 3: Based on the CNC machine tool component status monitoring information and considering the machine tool's operating conditions, a Weibull regression model that considers the machine tool's operating status information is established, using the signal characteristics obtained after PCA dimensionality reduction as the internal covariate and the operating load and speed as the external covariates.

[0011] Step 4: Prediction of remaining life of CNC machine tool components based on Weibull regression model;

[0012] The specific method for collecting the operating status information of CNC machine tool components in step one is as follows:

[0013] (1) Select the data type for machine tool component status monitoring;

[0014] Select signals that can comprehensively reflect changes in the status of machine tool components for monitoring;

[0015] (2) Select the machine tool component status monitoring location;

[0016] The selection of monitoring locations should not affect the normal production and processing of the machine tool, and should facilitate the installation of sensors;

[0017] (3) Select the sensor;

[0018] For high-speed rotating components, non-contact displacement sensors are used to monitor rotational accuracy errors, while for components such as guide rails and cutting tools, accelerometers are used to collect vibration signals.

[0019] (4) Establish a machine tool component status monitoring platform;

[0020] The CNC machine tool component status monitoring platform is built, which mainly includes the monitored components, sensors, data acquisition instruments and signal analysis platforms, connecting cables and PC terminals;

[0021] (5) Obtain machine tool component status monitoring information;

[0022] A component condition monitoring test plan was developed. Based on the established machine tool component condition monitoring platform, signals under different working conditions of the components were obtained. The signals collected by the signal test and analysis system were then transmitted to the signal analysis platform to obtain component monitoring information.

[0023] The specific method for signal processing in step two is as follows:

[0024] (1) Elimination of trend terms in component status monitoring signals;

[0025] When the original feature signal shifts up and down near the baseline and the degree of shift changes over time, it is necessary to select the appropriate trend term elimination method based on the characteristics of the acquired signal to obtain the signal after trend term elimination.

[0026] (2) Noise reduction processing of component status monitoring signals;

[0027] Wavelet threshold denoising method is applied to denoise the signal after trend term elimination;

[0028] For any segment of the output signal ω(t) of the CNC machine tool component acquired by the sensor, and given that this signal contains noise, then:

[0029] ω(t)=s(t)+σ(t)…………………………………………(1)

[0030] In the formula, t is time, s(t) is the target signal, or a useful signal that can reflect the operating status of CNC machine tool components; σ(t) is the noise signal.

[0031] For any signal ω(t), its continuous wavelet transform W can be obtained using equation (2). f (ξ,δ);

[0032]

[0033] In the formula, ψ ξ,δ (t) is the wavelet basis function; For ψ ξ,δ The conjugate of (t) is obtained using equation (3) to get ψ. ξ,δ The value of (t);

[0034]

[0035] In the formula, ξ represents the scaling parameter, δ represents the translation parameter, and ξ,δ∈R,ξ≠0;

[0036] Wavelet transform discretization is performed on equations (2) and (3), and the discrete value ξ = 2 is taken. m ,δ=2 m n; m and n are natural numbers; the discrete wavelet transform formula for any signal is obtained using equation (4);

[0037]

[0038] In the formula, W′ f (m,n) is the discrete wavelet transform of ω(t);

[0039] Based on the signal characteristics of machine tool components, a corresponding wavelet basis is selected to perform wavelet decomposition and noise reduction on the original signal of the components, thereby obtaining the noise-reduced signal;

[0040] (3) Feature extraction of component status monitoring signals;

[0041] The component status monitoring signals collected under different operating conditions were analyzed, and the time domain and frequency domain features of the component status monitoring signals were extracted based on their characteristics.

[0042] 1) Extraction of time-domain features from component status monitoring signals;

[0043] The time-domain analysis of the status monitoring signals of CNC machine tool components is based on the expansion of the time-domain amplitude waveform. During the machining operation of the machine tool, the time-domain characteristics of the component signals differ under different working conditions, and the response of each time-domain characteristic to different working conditions is different. The time-domain characteristics are extracted using equations (5)-(8): effective value X rms Peak-to-peak value X v Skewness X α and kurtosis X K ;

[0044]

[0045] X v =max(x i )-min(x i(6)

[0046]

[0047]

[0048] In the formula, N is the number of sampling points (1≤i≤N), x i It is a discrete signal;

[0049] 2) Frequency domain feature extraction of component status monitoring signals;

[0050] The monitored component time-domain signal is converted into a frequency-domain signal using Fourier transform, thereby realizing the extraction of frequency-domain features of the component monitoring signal. The frequency-domain features are extracted using equations (9)-(11): centroid frequency X FC , frequency root mean square X RMSF Frequency standard deviation X RVF ;

[0051]

[0052]

[0053]

[0054] In the formula, A(k) is the signal amplitude, and f k Where K is the frequency, and K represents the number of spectral lines (1≤k≤K);

[0055] 3) Dimensionality reduction of component status monitoring signal features;

[0056] Considering that different features respond differently to machine tool component degradation or failure, principal component analysis (PCA) is applied to reduce the dimensionality of the signal features and remove features with low correlation. First, Equation (12) is used to analyze the g feature samples Z = [z1, z2, ..., z g The signal features are then decentralized to obtain the decentralized signal feature sample C.

[0057]

[0058] In the formula, Let c be the mean of the g-th sample. g This is the g-th decentralized signal feature sample;

[0059] Then, using equation (13), the covariance matrix S of the feature sample set is obtained;

[0060]

[0061] In the formula, c i c represents the element in the i-th row. jRepresents the element in column j, (c i ) T For c i Transpose of;

[0062] Suppose there exists an equation (14), that is, a linear transformation u such that uc i The variance is the largest;

[0063]

[0064] According to equation (14), in order to obtain the maximum covariance, the Lagrange conditional extremum shown in equation (15) is constructed;

[0065]

[0066] Then we have equation (16):

[0067]

[0068] In the formula, λ is the eigenvalue of the covariance matrix S, and u is the eigenvector;

[0069] Based on this, all eigenvalues ​​λ are obtained, where λ1≥λ2≥…≥λ g and the corresponding eigenvectors u1, u2, ..., u g At this point, a new feature Y is obtained:

[0070] Y = U T ×C……………………………………(17)

[0071] In the formula, U=(u1,u2,…,u g ).

[0072] Define the i-th principal component y i The formula for calculating the "variance contribution rate" is:

[0073]

[0074] Then there are the first h principal components y1, y2, ..., y h The "cumulative variance contribution rate" is:

[0075]

[0076] When the cumulative variance contribution rate of the current h principal components is greater than 95%, the first h principal components are taken as new features. At this time, we have:

[0077]

[0078] The remaining (gh) new features were discarded;

[0079] Based on the obtained machine tool component status monitoring information, signal processing was completed, and the principal components (PC) after dimensionality reduction were obtained.

[0080] This invention uses the principal components after PCA dimensionality reduction as internal covariates of the remaining life prediction model, and the load and speed of the machine tool components as external covariates to establish a remaining life prediction model for the machine tool components.

[0081] The specific method for constructing the Weibull regression model in step three is as follows:

[0082] The fault data of the machine tool components follow a Weibull distribution. The cumulative fault probability function F(t) of the Weibull distribution model is shown in Equation (21):

[0083]

[0084] In the formula, t is the time variable, t≥0; θ is the scale parameter, θ>0; γ is the shape parameter, γ>0;

[0085] The scaling parameters of the model are described by internal and external covariates during the operation of machine tool components. The Weibull model is then extended to the Weibull regression model (WRM). The failure probability function of the WRM model is shown in equation (22).

[0086]

[0087] In the formula, R(t) represents the reliability function; a0 represents the intercept; I is the internal covariate, q (1≤l≤q) represents the number of internal covariates; E is the external covariate, p (1≤j≤p) represents the number of external covariates; a is the regression coefficient of the internal covariate, a l (1≤l≤q) represents the regression coefficient of the l-th internal slope variable, and b is the regression coefficient of the external covariate. j (1≤j≤p) represents the regression coefficient of the j-th external covariate;

[0088] Generalizing equation (22), we obtain the fault probability function F(t,I,E) of the WRM model as follows:

[0089]

[0090] Thus, the failure rate function λ(t,I,E) of the WRM model is obtained, as shown in formula (24):

[0091]

[0092] Based on formulas (23) and (24), the probability density function f(t,I,E) of the WRM model is derived as follows:

[0093]

[0094] This completes the establishment of the Weibull regression model for CNC machine tool components;

[0095] The specific steps of the CNC machine tool component remaining life prediction method based on the Weibull regression model in step four are as follows:

[0096] (1) Clarify the reliability function of machine tool components;

[0097] Based on the construction principle of the Weibull regression model in step three, the reliability function of the machine tool component at time t is obtained as follows:

[0098]

[0099] In the formula, a0 is the intercept, γ is the shape parameter of the distribution, and a1, a2, ..., a q The internal covariates are PC1, PC2, ..., PC. q The regression coefficients are b1 and b2, which are the regression coefficients of the external covariates load L and velocity S, respectively.

[0100] (2) Estimation of parameters for the WRM model of machine tool components;

[0101] The parameters of the WRM model are estimated by applying the maximum likelihood estimation method. According to formula (22), the log-likelihood function L(γ,θ′) is as follows:

[0102]

[0103] In the formula, θ′=exp(a0+a1×PC1+a2×PC2+…+a q ×PC q +b1×L+b2×S);

[0104] For the parameters a0, a1, a2, ..., a in equation (27), respectively q The partial derivatives of b1 and b2 are calculated and set to zero to obtain the optimal values ​​of each parameter. The parameters are then solved using the fminsearch function in MATLAB programming software to obtain the WRM model of the machine tool components under different working conditions.

[0105] (3) Prediction of remaining life of machine tool components;

[0106] The remaining life prediction of CNC machine tool components refers to the time difference between the current time t0 and the user-required reliability threshold or failure time t of a key machine tool component, which is the remaining life of the component. Let the remaining life function be RUL(t,Z(t)), and the reliability function be R. The geometric meaning of the remaining life at time t0 is the area under the reliability function curve on the operating interval [t0,t]. Then:

[0107]

[0108] In the formula, Z(t) represents the operating condition information of the machine tool components;

[0109] Therefore, the reliability of the machine tool component is obtained according to equations (26) and (27), and combined with equation (28), the remaining life of the machine tool component at time t0 is predicted. The WRM remaining life prediction model is demonstrated by leave-one-out cross-validation. One set of data from the collected data is used as test data, and all the remaining data is used for parameter estimation of the WRM model, thereby verifying the accuracy of the machine tool component remaining life prediction method.

[0110] This completes the prediction of the remaining life of CNC machine tool components based on the Weibull regression model.

[0111] Compared with the prior art, the beneficial effects of the present invention are:

[0112] The machine tool component remaining life prediction method of this invention takes the condition monitoring information of the component under different operating conditions as input, comprehensively considers the operating conditions and signal characteristics of the component during the machine tool processing, applies the principal components after PCA dimensionality reduction as internal covariates, and takes the load and speed of the component as external covariates to establish a Weibull regression model. The optimal parameter values ​​of the model are obtained through parameter estimation, thereby realizing the prediction of the remaining life of the machine tool component. Considering the operating conditions of the machine tool component, the accuracy of the remaining life prediction is improved. The accurate and reasonable remaining life prediction results are of great significance for reducing downtime losses of manufacturing enterprises, improving enterprise production efficiency, and increasing economic benefits. Attached Figure Description

[0113] Figure 1 This is a flowchart of the method for predicting the remaining life of CNC machine tool components according to the present invention;

[0114] Figure 2 This is the monitoring point for the CNC machine tool spindle of the present invention;

[0115] Figure 3 This is a schematic diagram of the CNC machine tool component status monitoring platform of the present invention;

[0116] Figure 4a This is the original waveform diagram of the CNC machine tool spindle acceleration signal of the present invention;

[0117] Figure 4b This is a waveform diagram of the CNC machine tool spindle acceleration signal after the trend term is eliminated, according to the present invention.

[0118] Figure 5a This is a waveform diagram of the spindle vibration signal before wavelet denoising according to the present invention;

[0119] Figure 5bThis is a waveform diagram of the spindle vibration signal after wavelet denoising according to the present invention;

[0120] Figure 6a This is a comparison chart of the effective value variation trend of the CNC machine tool spindle under different working conditions according to the present invention;

[0121] Figure 6b This is a comparison chart of the peak-to-peak value variation trends of the CNC machine tool spindle under different working conditions according to the present invention;

[0122] Figure 6c This is a comparison chart of the deviation trends of the CNC machine tool spindle under different working conditions according to the present invention;

[0123] Figure 6d This is a comparison chart of the kurtosis variation trend of the CNC machine tool spindle under different working conditions according to the present invention;

[0124] Figure 7a This is a comparison chart of the frequency domain characteristics of the CNC machine tool spindle under operating condition 1 according to the present invention;

[0125] Figure 7b This is a comparison chart of the frequency domain characteristics of the CNC machine tool spindle under working condition 2 according to the present invention;

[0126] Figure 7c This is a comparison chart of the frequency domain characteristics of CNC machine tool spindle working condition 3 according to the present invention;

[0127] Figure 7d This is a comparison chart of the frequency domain characteristics of CNC machine tool spindle working condition 4 according to the present invention;

[0128] Figure 8 The present invention relates to the variance contribution rate and cumulative variance contribution rate of each characteristic component of the CNC machine tool spindle;

[0129] Figure 9 This is the predicted result of the remaining life of the machine tool spindle under the operating condition 1 of the present invention;

[0130] Figure 10a This is the predicted result of the remaining life of the machine tool spindle under the operating condition 2 of the present invention;

[0131] Figure 10b This is the predicted result of the remaining life of the machine tool spindle under operating condition 3 of the present invention;

[0132] Figure 10c This is the prediction result of the remaining life of the machine tool spindle under operating condition 4 of the present invention. Detailed Implementation

[0133] The present invention will now be described in detail with reference to the accompanying drawings:

[0134] See Figure 1The remaining life prediction method for CNC machine tool components of the present invention includes the following steps: determining the data type and monitoring location of component status monitoring based on the basic structure and working principle of the machine tool component; building a component status monitoring platform; collecting the operating status information of the CNC machine tool component; performing trend term elimination, noise reduction, feature extraction, and dimensionality reduction processing on the collected signals; constructing a Weibull regression model; and predicting the remaining life of the machine tool component based on the Weibull regression model.

[0135] I. Machine Tool Component Operating Status Information Collection

[0136] 1. Determine the data types and monitoring locations for machine tool component status monitoring;

[0137] Signals that can comprehensively reflect changes in the status of machine tool components should be selected for monitoring; the selection of monitoring locations should not affect the normal production and processing of the machine tool, and should facilitate the installation of sensors;

[0138] 2. Sensor selection;

[0139] For high-speed rotating components, non-contact displacement sensors are used to monitor rotational accuracy errors, while for components such as guide rails and cutting tools, accelerometers are used to collect vibration signals.

[0140] 3. Establish a machine tool component status monitoring platform;

[0141] The CNC machine tool component status monitoring platform is built, which mainly includes the monitored components, sensors, data acquisition instruments and signal analysis platforms, connecting cables and PC terminals;

[0142] 4. Obtain machine tool component status monitoring information;

[0143] A component condition monitoring test plan was developed. Based on the established machine tool component condition monitoring platform, signals under different operating conditions of the components were obtained. The signals collected by the signal test and analysis system were then transmitted to the signal analysis platform to obtain component monitoring information.

[0144] II. Machine Tool Component Status Monitoring Signal Processing

[0145] 1. Elimination of trend items in component status monitoring signals;

[0146] When the original feature signal shifts up and down near the baseline and the degree of shift changes over time, it is necessary to select the appropriate trend term elimination method based on the characteristics of the acquired signal to obtain the signal after trend term elimination.

[0147] 2. Noise reduction processing for component status monitoring signals;

[0148] Wavelet threshold denoising method is applied to denoise the signal after trend term elimination;

[0149] For any segment of the output signal ω(t) of a CNC machine tool component acquired by a sensor, and this signal contains noise, then ω(t) = s(t) + σ(t), where t is time, s(t) is the target signal, and σ(t) is the noise signal. For any signal ω(t), its continuous wavelet transform expression is: Where ψ ξ,δ (t) is the wavelet basis function; For ψ ξ,δ The conjugate of (t), Where ξ represents the scaling parameter and δ represents the translation parameter, and ξ,δ∈R,ξ≠0. Since the acquired machine tool component signals are discrete signals, wavelet transform discretization processing is required, and the discrete value ξ=2 is taken. m ,δ=2 m n (where m and n are natural numbers), using the formula The discrete wavelet transform of any signal is obtained, where W′ f (m,n) is the discrete wavelet transform of ω(t); then, according to the signal characteristics of the machine tool components, the corresponding wavelet basis is selected to perform wavelet decomposition and noise reduction on the original signal of the components, and thus the noise-reduced signal is obtained.

[0150] 3. Feature extraction of component status monitoring signals;

[0151] The component status monitoring signals collected under different operating conditions were analyzed, and the time domain features and frequency domain features of the component status monitoring signals were extracted based on their characteristics.

[0152] (1) Extraction of temporal features from component status monitoring signals;

[0153] Time-domain analysis of CNC machine tool component condition monitoring signals is based on time-domain amplitude waveform expansion. During machine tool processing and operation, the time-domain characteristics of component signals differ under different working conditions, and each time-domain characteristic responds differently to different working conditions. This analysis utilizes the formula... Extracting effective value X rms Using formula X v =max(x i )-min(x i Extracting peak-to-peak value X v Utilization Extracting skewness X α Utilization Extracting kurtosis X K Where N is the number of sampling points (1≤i≤N), x i It is a discrete signal;

[0154] (2) Extraction of frequency domain features of component status monitoring signals;

[0155] The monitored component time-domain signal is converted into a frequency-domain signal using Fourier transform, thereby enabling frequency-domain feature extraction of the component monitoring signal. This is achieved using the formula... Extracting the centroid frequency X of the frequency domain features FC Utilization Extraction frequency root mean square X RMSF Utilization Extracting frequency standard deviation X RVF ;

[0156] (3) Dimensionality reduction of component status monitoring signal features;

[0157] Considering that different features respond differently to machine tool component degradation or failure, PCA is applied to reduce the dimensionality of signal features, removing features with low correlation. Firstly, the formula is used... For g feature samples Z = [z1, z2, ..., z g The signal features are decentralized to obtain decentralized signal feature samples C; then, the formula is used... Obtain the covariance matrix S of the feature sample set; assume that an equality exists. That is, a linear transformation u makes uc i The variance is maximized; construct the Lagrange conditional extrema:

[0158] L(u,s,λ)=u T Su+λ(1-|u| 2 )

[0159] st(|u| 2 =1)

[0160] Then we have the equation:

[0161]

[0162] Where λ is the eigenvalue of the covariance matrix S, and u is the eigenvector;

[0163] Based on this, all eigenvalues ​​λ are obtained, where λ1≥λ2≥…≥λ g and the corresponding eigenvectors u1, u2, ..., u g At this point, a new feature Y is obtained: Y = U T ×X, where U=(u1,u2,…,u g Define the i-th principal component y. i The formula for calculating the "variance contribution rate" Then there are h principal components y1, y2, ..., y h The "cumulative variance contribution rate" is When the cumulative variance contribution rate of the current h principal components is greater than 95%, the first h principal components are taken as new features. At this time, we have:

[0164]

[0165] The remaining (gh) new features are discarded, and the signal processing is completed to obtain the dimensionality-reduced principal components PC.

[0166] III. Establishment of the Weibull Regression Model

[0167] The fault data of machine tool components follow a Weibull distribution. The cumulative fault probability function F(t) of the Weibull distribution model is as follows:

[0168]

[0169] Where t is the time variable, t≥0; θ is the scale parameter, θ>0; γ is the shape parameter, γ>0;

[0170] Using the speed and load during machine tool operation as external covariates and the dimensionality-reduced principal components (PCs) as internal covariates, the Weibull model is generalized to the Weibull regression model (WRM). In this case, the failure probability function of the WRM model is:

[0171]

[0172] In the formula, R(t) represents the reliability function; a0 represents the intercept; I is the internal covariate, q (1≤l≤q) represents the number of internal covariates; E is the external covariate, p (1≤j≤p) represents the number of external covariates; a is the regression coefficient of the internal covariate, a l (1≤l≤q) represents the regression coefficient of the l-th internal slope variable, and b is the regression coefficient of the external covariate. j (1≤j≤p) represents the regression coefficient of the j-th external covariate;

[0173] Therefore, the failure rate function λ(t,I,E) of the WRM model is obtained:

[0174]

[0175] Furthermore, the probability density function f(t,I,E) of the WRM model is derived as follows:

[0176]

[0177] IV. Prediction of Remaining Life of CNC Machine Tool Components Based on Weibull Regression Model

[0178] 1. Reliability function of machine tool components;

[0179] Based on the constructed Weibull regression model, the reliability function R(t,PC,L,S) of the machine tool component at time t is obtained as follows:

[0180]

[0181] In the formula, a0 is the intercept, γ is the shape parameter of the distribution, and a1, a2, ..., a q The internal covariates are PC1, PC2, ..., PC. q The regression coefficients are b1 and b2, which are the regression coefficients of the external covariates load L and velocity S, respectively.

[0182] 2. Estimation of parameters for the WRM model of machine tool components;

[0183] The maximum likelihood estimation method is applied to estimate the parameters of the WRM model. Based on the failure rate function of the WRM model, the log-likelihood function is obtained as follows:

[0184]

[0185] In the formula, θ′=exp(a0+a1×PC1+a2×PC2+…+a q ×PC q +b1×L+b2×S);

[0186] For the parameters a0, a1, a2, ..., a in the above formula respectively q The partial derivatives of b1 and b2 are calculated and set to zero to obtain the optimal values ​​of each parameter. The parameters are then solved using the fminsearch function in MATLAB programming software to obtain the WRM model of the machine tool components under different working conditions.

[0187] 3. Prediction of remaining life of machine tool components;

[0188] The remaining life prediction of a CNC machine tool component refers to the time difference between the current time t0 and the user-required reliability threshold or the time t of failure, which is the remaining life of the component. Let the remaining life function be RUL(t,Z(t)), and the reliability function be R. The geometric meaning of the remaining life at time t0 is the area under the reliability function curve on the operating interval [t0,t]. Then we have... Z(t) represents the operating condition information of the machine tool component; thus, the remaining life of the machine tool component at time t0 can be predicted.

[0189] The leave-one-out cross-validation method was used to demonstrate the remaining useful life prediction model of the machine tool component. One set of data from the collected data was used as test data, and the remaining data was used for parameter estimation of the WRM model, thereby verifying the accuracy of the remaining useful life prediction method of machine tool components.

[0190] Example

[0191] CNC machine tool component remaining life prediction method

[0192] This invention uses the spindle, a key component of a CNC machine tool, as an example to illustrate the implementation. Taking a specific model of CNC machine tool spindle as the research object, based on the basic structure and working principle of the spindle, vibration signals are selected as the spindle's condition monitoring index, and the optimal monitoring point of the spindle is determined. (See reference...) Figure 2 .

[0193] For high-speed rotating components like spindles, non-contact sensors are selected. This invention uses a 5E101 eddy current displacement sensor and a 1A313E accelerometer to monitor the vibration performance of the CNC machine tool spindle. A DH5922D dynamic signal testing and analysis system is used to collect the spindle's status signals, and this system is combined with the DHDAS signal analysis platform. Real-time signal acquisition and analysis are achieved by connecting the sensors. A schematic diagram of the component status monitoring platform is provided. Figure 3 .

[0194] This invention focuses on a single process in the production and processing of parts by a machine tool user company, conducting monitoring experiments. During the processing, a B17R0.8 tool is used for finishing the workpiece surface. A 5E101 eddy current displacement sensor and a 1A313E accelerometer are used to measure the vibration signal of the machine tool spindle during the processing, with a sampling frequency of 2kHz. To obtain the vibration state of the machine tool spindle under different operating conditions during processing, the normal processing condition of the workpiece is used as the standard, and the spindle speed is reasonably changed to obtain the vibration signal of the spindle at different speeds. The specific processing parameter settings are shown in Table 1.

[0195] Table 1. Processing parameter settings under different working conditions

[0196]

[0197] Based on the characteristics of the acquired signals, a low-pass filtering method was applied to eliminate the trend term. A comparison of the spindle acceleration signals before and after trend term elimination was performed. (See attached document.) Figure 4a , Figure 4b Wavelet thresholding denoising was applied to denoise the signal after trend term removal. See the comparison charts of the signal waveforms before and after denoising. Figure 5a , Figure 5b By comparison, it can be found that the signal obtained after wavelet denoising is significantly improved by removing the noise signal while retaining the original vibration signal of the spindle.

[0198] Based on the calculations in steps two (5)-(8), the time-domain characteristics of the spindle vibration signal under different working conditions are compared. (See attached diagram.) Figure 6a , Figure 6b , Figure 6c , Figure 6d ,Depend on Figure 6a , Figure 6b , Figure 6c , Figure 6d It can be seen that during the machining operation of the machine tool, the vibration signal of the spindle exhibits different time-domain characteristics under different working conditions, and the response of each time-domain characteristic to different working conditions is different. Similarly, according to equations (9)-(11) in step two, the trend diagrams of the frequency domain characteristics under different working conditions can be obtained. (See attached diagram.) Figure 7a , Figure 7b , Figure 7c , Figure 7d ,Depend on Figure 7a , Figure 7b , Figure 7c , Figure 7d It can be seen that the frequency domain characteristics of the machine tool spindle vibration signal differ under different working conditions, and the amplitude of the signal frequency domain characteristic frequency will also show a certain trend of change as time goes on and wear intensifies.

[0199] According to equations (12)-(20) in step two, PCA feature dimensionality reduction is performed on the signal. Taking working condition 1 as an example, the feature values ​​of each signal feature vector under this working condition are calculated, as shown in Table 2.

[0200] Table 2. Eigenvalues ​​of vibration signal feature vectors under operating condition 1

[0201]

[0202] Simultaneously, the variance contribution rate and cumulative variance contribution rate of each characteristic component were calculated, revealing that the cumulative variance contribution rate of the first five characteristic components was 95.03%. (See reference...) Figure 8 Therefore, the new feature vector after dimensionality reduction can include most of the information of the original feature vector.

[0203] Based on the Weibull regression model construction method in step three, and combining equations (21)-(25), the principal components after dimensionality reduction of the spindle signal are used as internal covariates, and speed and load are used as external covariates to construct the Weibull regression model of the spindle. Based on equations (26)-(27) in step four, the parameters are solved using the fminsearch function in the MATLAB programming software, and the reliability function of the machine tool spindle WRM model under operating condition 1 is obtained:

[0204]

[0205] θ′=exp(0.054+0.060×PC1+0.036×PC2-10.220×PC3-1.357×PC4-19.420×PC5+2.417×L-0.095×S)

[0206] Similarly, the WRM model of the machine tool component spindle under different working conditions can be obtained, and the corresponding parameter values ​​are shown in Table 3.

[0207] Table 3. WRM model parameter values ​​of machine tool spindles under different operating conditions.

[0208]

[0209] Therefore, according to step four (28), combined with the collected machine tool operating condition information, the reliability values ​​of each component of the machine tool at any time and under any operating condition are obtained, and then the remaining life prediction study of the machine tool components is carried out.

[0210] Taking operating condition 1 as an example, this invention uses the first 172 of the 173 collected data sets for parameter estimation of the WRM model, and the remaining data set as test data to predict the remaining lifespan under operating conditions 1. The WRM model is then applied to predict the remaining lifespan of the machine tool spindle. The prediction results are available in the reference section. Figure 9 Similarly, the predicted remaining life of the machine tool spindle under different operating conditions can be obtained. (See [reference needed]). Figure 10a , Figure 10b , Figure 10c A 20% margin of error in remaining lifetime prediction is generally acceptable. Figure 10a , Figure 10b , Figure 10c It can be observed that the remaining life of machine tool components predicted by the WRM model is very close to the actual remaining life of the components, with most falling within the 20% error range.

[0211] This invention selects data types for monitoring the operational status of CNC machine tool components based on their structural characteristics, determines the monitoring locations, and establishes a CNC machine tool component operational status monitoring platform to acquire component status monitoring data. The acquired monitoring signals undergo signal processing including trend term elimination, noise reduction, and feature extraction. Considering the different responses of different features to machine tool component degradation or failure, PCA is applied to reduce the dimensionality of the signal features. Using the reduced principal components as internal covariates and the component load and speed as external covariates, a Weibull regression model is established. Optimal parameter values ​​are obtained through parameter estimation, thereby enabling the prediction of the remaining life of key machine tool components. Accurate and reasonable remaining life prediction results are significant for reducing downtime losses in manufacturing enterprises, improving production efficiency, and increasing economic benefits.

Claims

1. A method for predicting the remaining life of CNC machine tool components, comprising the following steps: Step 1: Determine the data types and monitoring locations for machine tool component status monitoring, and collect real-time operating status information of CNC machine tool components by building a component status monitoring platform; Step 2: Perform trend term elimination, noise reduction, feature extraction, and principal component analysis on the obtained component status monitoring signals to obtain signal features; Step 3: Based on the status monitoring information of CNC machine tool components and considering the operating conditions of the machine tool, a Weibull regression model of machine tool components that considers the operating status information of the machine tool is established, using the signal characteristics obtained after dimensionality reduction by principal component analysis as internal covariates and the operating load and speed as external covariates. Step 4: Prediction of remaining life of CNC machine tool components based on Weibull regression model; The specific method for establishing the Weibull regression model for the machine tool components in step three is as follows: The fault data of machine tool components follow a Weibull distribution, and the cumulative fault probability function of the Weibull distribution model is... As shown in formula (21): ……………………………（21） In the formula, It is a time variable. ; It is a scale parameter. ; These are shape parameters. ; Using the speed and load during machine tool operation as external covariates, and the principal components after dimensionality reduction... As an internal covariate, the Weibull model is extended to the Weibull regression model (WRM). In this case, the failure probability function of the WRM model is shown in equation (22): ………………（22） In the formula, Represents the reliability function; Indicates the intercept; For internal covariates, Indicates the number of internal covariates; As an external covariate, Indicates the number of external covariates; These are the regression coefficients of the internal covariates. Indicates the first The regression coefficients of the internal slope variables These are the regression coefficients of external covariates. Indicates the first The regression coefficients of the external covariates; Generalizing equation (22), we obtain the fault probability function of the WRM model. for: ………………………（23） Therefore, the failure rate function of the WRM model is obtained. As shown in formula (24): ………………（24） Based on formulas (23) and (24), the probability density function of the WRM model is derived. for: …（25） This completes the establishment of the Weibull regression model for CNC machine tool components.

2. The method for predicting the remaining life of CNC machine tool components according to claim 1, characterized in that: The real-time acquisition of CNC machine tool component operating status information in step one is carried out using the following method: (1) Select the data type for machine tool component status monitoring; Select signals that can comprehensively reflect changes in the status of machine tool components for monitoring; (2) Select the machine tool component status monitoring location; The selection of monitoring locations should not affect the normal production and processing of the machine tool, and should facilitate the installation of sensors; (3) Select a sensor; For high-speed rotating components, non-contact displacement sensors are used to monitor rotational accuracy errors, while for components such as guide rails and cutting tools, accelerometers are used to collect vibration signals. (4) Establish a machine tool component status monitoring platform; The CNC machine tool component status monitoring platform is built, which mainly includes the monitored components, sensors, data acquisition instruments and signal analysis platforms, connecting cables and PC terminals; (5) Obtain machine tool component status monitoring information; A component condition monitoring test plan was developed. Based on the established machine tool component condition monitoring platform, signals under different operating conditions of the components were obtained. The signals collected by the signal test and analysis system were then transmitted to the signal analysis platform to obtain component monitoring information.

3. The method for predicting the remaining life of CNC machine tool components according to claim 1, characterized in that: The process of eliminating trend terms in the component status monitoring signal specifically refers to: When the original feature signal shifts up and down near the baseline and the degree of shift changes over time, it is necessary to select the appropriate trend term elimination method based on the characteristics of the acquired signal to obtain the signal after trend term elimination. The noise reduction processing of the component status monitoring signal specifically refers to: Wavelet threshold denoising method is applied to denoise the signal after trend term elimination; For any segment of the output signal of the CNC machine tool component collected by the sensor And if the signal contains noise, then: ……………………………………（1） In the formula, For time, The target signal, or a useful signal that can reflect the operating status of CNC machine tool components; This is a noise signal; For any signal Using equation (2), its continuous wavelet transform is obtained. ; …………………………………（2） In the formula, These are wavelet basis functions; for The conjugate of is obtained using equation (3). The possible values ​​of ; ……………………………………（3） In the formula, Indicates the scaling parameter. Represents the translation scale parameter, and has ; Wavelet transform discretization is performed on equations (2) and (3), and discrete values ​​are obtained. ; and Let be a natural number; use equation (4) to obtain the discrete wavelet transform formula for any signal; …………………………（4） In the formula, That is Discrete wavelet transform; Based on the signal characteristics of machine tool components, a corresponding wavelet basis is selected to perform wavelet decomposition and noise reduction on the original signal of the components, thereby obtaining the noise-reduced signal; The feature extraction of the component status monitoring signal specifically refers to: The component status monitoring signals collected under different operating conditions were analyzed, and the time domain and frequency domain features of the component status monitoring signals were extracted based on their characteristics.

4. The method for predicting the remaining life of CNC machine tool components according to claim 3, characterized in that: The extraction of the time-domain features of the component status monitoring signal specifically includes: The time-domain analysis of the status monitoring signals of CNC machine tool components is based on the expansion of the time-domain amplitude waveform. During the machining operation of the machine tool, the time-domain characteristics of the component signals differ under different working conditions, and the response of each time-domain characteristic to different working conditions is different. The time-domain characteristics are extracted using equations (5)-(8): effective value Peak-to-peak value skewness and kurtosis ; ……………………………………（5） ……………………………（6） ………………………………………（7） ………………………………………（8） In the formula, Number of sampling points ( ), It is a discrete signal.

5. The method for predicting the remaining life of CNC machine tool components according to claim 3, characterized in that: The extracted frequency domain features of the component status monitoring signal specifically include: The monitored component time-domain signal is converted into a frequency-domain signal using Fourier transform, thereby realizing the extraction of frequency-domain features of the component monitoring signal. The frequency-domain features are extracted using equations (9)-(11): centroid frequency. Root mean square frequency Frequency standard deviation ; ………………………………………（9） ……………………………………（10） …………………………………（11） In the formula, The signal amplitude, For frequency, Indicates the number of spectral lines ( ).

6. The method for predicting the remaining life of CNC machine tool components according to claim 1, characterized in that: The component status monitoring signals undergo principal component analysis for dimensionality reduction, specifically including: Considering that different features respond differently to machine tool component degradation or failure, principal component analysis (PCA) is applied to reduce the dimensionality of the signal features and remove features with low correlation. First, equation (12) is used to... Feature samples The signal features are decentralized to obtain decentralized signal feature samples. ; …………………（12） In the formula, For the first Sample mean, For the first A decentralized signal feature sample; Then, using equation (13), the covariance matrix of the feature sample set is obtained. ; ………………………………（13） In the formula, Indicates the first row element, Indicates the first Column elements, for Transpose of; Suppose there exists an equation (14), that is, a linear transformation Make The variance is the largest; …………………………（14） According to equation (14), in order to obtain the maximum covariance, the Lagrange conditional extremum shown in equation (15) is constructed; ……………………（15） Then we have equation (16): ……………………………（16） In the formula, Covariance matrix eigenvalues, For feature vectors; Based on this, all eigenvalues ​​are obtained. ,in and the corresponding feature vectors At this point, new features are obtained. : ……………………………………（17） In the formula, ; Definition of the first Principal components The formula for calculating the "variance contribution rate" is: ……………………………………（18） Then there is a previous Principal components The "cumulative variance contribution rate" is: ……………………………………（19） current When the cumulative variance contribution rate of each principal component is greater than 95%, the first one is taken. Each principal component is used as a new feature, at which point: …………………………（20） the remaining The new features were then discarded; Based on the obtained machine tool component status monitoring information, signal processing was completed, and the dimensionality-reduced principal components were obtained. .

7. The method for predicting the remaining life of CNC machine tool components according to claim 1, characterized in that: The specific method for predicting the remaining life of CNC machine tool components based on the Weibull regression model in step four is as follows: (1) Clarify the reliability function of machine tool components; Based on the construction principle of the Weibull regression model in step three, the machine tool components are obtained in... Reliability function at time t for: …（26） In the formula, The intercept is... The shape parameter of the distribution, Internal covariates The regression coefficients, and These are the external covariate loads. and speed The regression coefficients; (2) Estimation of parameters for the WRM model of machine tool components; The maximum likelihood estimation method is used to estimate the parameters of the WRM model. According to formula (22), the log-likelihood function is obtained. as follows: ………………（27） In the formula, ; For the parameters in equation (27) respectively Calculate the partial derivatives and set them to zero to obtain the optimal values ​​of each parameter. Use the fminsearch function in MATLAB programming software to solve for the parameters and obtain the WRM model of the machine tool components under different working conditions. (3) Prediction of remaining life of machine tool components; The remaining life prediction of CNC machine tool components refers to the prediction of the remaining life of key machine tool components from the current moment. Run until the user-required reliability threshold or failure time. The time difference is the remaining lifetime of the component. Let the remaining lifetime function be... The reliability function is , The geometric meaning of remaining lifetime at a given moment is that the reliability function curve is within the operating range. Given the area on top, we have: ………………………………（28） In the formula, This represents the operating status information of machine tool components; Therefore, the reliability of the machine tool assembly is obtained according to equations (26) and (27), and combined with equation (28), the reliability of the machine tool assembly in time is realized. The remaining useful life prediction method for machine tool components was tested using leave-one-out cross-validation. A set of data from the collected data was used as test data, and the remaining data were used for parameter estimation of the WRM model to verify the accuracy of the remaining useful life prediction method for machine tool components.

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