Robotic milling chatter early warning method and system considering in-wave modulation effects

Abstract

The present disclosure provides a robot milling chatter early monitoring method and system considering in-wave modulation effect, relates to the technical field of robot milling processing, and comprises the following steps: acquiring an acceleration non-stationary signal in a robot milling process; decomposing the acceleration non-stationary signal into a plurality of in-wave modulation intrinsic modal components by using variational modal decomposition; estimating the multi-sinusoidal instantaneous frequency of each in-wave modulation intrinsic modal component; determining the in-wave modulation frequency and the robot milling processing state corresponding relationship according to the power spectrum diagram of the multi-sinusoidal instantaneous frequency and the milling processing surface; training a robot milling chatter early monitoring model based on a fractional order wavelet scattering transform network and a support vector machine by using the power spectrum diagram data of the multi-sinusoidal instantaneous frequency; inputting the power spectrum diagram of the multi-sinusoidal instantaneous frequency into the trained robot milling chatter early monitoring model to determine the robot milling chatter state, and obtaining a monitoring success rate. The present application can improve the precision of robot milling chatter early monitoring.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of robot milling, in particular to a robot milling chatter early monitoring method and system considering in-wave modulation effect. BACKGROUND

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute the prior art.

[0003] In recent years, robot milling technology, taking industrial robots as the main motion body, end-mounted electric spindles and milling cutters, has developed rapidly in the manufacturing field. Robot milling technology breaks through the limitations of traditional numerical control machining methods, and has many advantages such as large workspace, high flexibility and low cost. Facing the needs of major manufacturing fields such as aviation and aerospace, robot milling technology is showing a broad application prospect and great commercial value. However, the development of robot milling technology is currently facing many challenges, of which the chatter problem is one of the most classic difficulties in robot milling.

[0004] Due to the weak overall structural stiffness of the serial milling robot (only 2%-5% of that of a numerical control milling machine), the milling cutter at the end of the robot is extremely prone to chatter under the excitation of cutting force, which seriously threatens the machining precision and quality, and even causes serious harm to the robot. During the machining process, in order to minimize the damage caused by chatter to the robot and the workpiece, monitoring and suppression should be completed as early as possible before chatter occurs, but the early chatter in robot milling is extremely weak and difficult to capture and identify.

[0005] At present, one method is to monitor the early chatter of robot milling through milling dynamics modeling, but the current milling dynamics modeling is still incomplete, and there are unpredictable errors between the stable machining theory model and the actual milling system, which makes it difficult to provide accurate stability domain boundaries for robot milling stability prediction, and after optimizing the machining parameters and process, chatter state still occurs. Another method is to collect sensor signals during milling, extract signal features, and use a chatter monitoring model to establish the relationship between the milling state and the signal features. First, force, acceleration, sound and other sensors are used to collect robot milling sensor signals, then the time domain, frequency domain and time-frequency domain features of the robot milling sensor signals are extracted, and finally the extracted features are input into machine learning to complete the monitoring. However, the current chatter monitoring method still has the shortcomings of weak extracted chatter features, difficulty in early chatter monitoring, and the need for a large number of samples for learning and training. SUMMARY

[0006] The robot milling chatter early monitoring method and system considering the wave modulation effect are proposed to solve the above problems, the robot milling processing response presents typical non-stationary characteristics, the instantaneous frequency of which oscillates rapidly according to a multi-sinusoidal wave, which is called a wave modulation signal, different wave modulation frequencies correspond to different states of robot milling processing, and it is found that the transition of the wave modulation frequency is earlier than the appearance of the visible vibration marks on the workpiece surface, which can be used for monitoring the occurrence of early chatter.

[0007] According to some embodiments, the present disclosure adopts the technical scheme as follows:

[0008] The robot milling chatter early monitoring method considering the wave modulation effect comprises:

[0009] An acceleration non-stationary signal in the robot milling processing process is acquired;

[0010] The acceleration non-stationary signal is variational mode decomposed into a plurality of wave modulation intrinsic mode components;

[0011] The moving least square parameterized time-frequency analysis is performed on each wave modulation intrinsic mode component to acquire a multi-sinusoidal wave instantaneous frequency of each wave modulation intrinsic mode component;

[0012] The wave modulation frequency is obtained based on the peak value of the power spectrum diagram of the multi-sinusoidal wave instantaneous frequency, and the corresponding relationship between the wave modulation frequency and the robot milling processing state is determined in combination with the robot milling processing surface;

[0013] Based on the corresponding relationship between the wave modulation frequency and the robot milling processing state, a multi-sinusoidal wave instantaneous frequency power spectrum diagram-robot milling processing state database is constructed, a multi-scale multi-direction sparse feature is extracted by using a fractional wavelet scattering transform network, a robot milling processing state is classified by using a support vector machine, a robot milling chatter early monitoring model is constructed, and effective identification of various robot milling processing states such as stable processing, early chatter and severe chatter is realized.

[0014] According to some embodiments, the present disclosure adopts the technical scheme as follows:

[0015] The robot milling chatter early monitoring system considering the wave modulation effect comprises:

[0016] The signal acquisition module is configured to acquire an acceleration non-stationary signal in the robot milling processing process;

[0017] The signal decomposition module is configured to variational mode decompose the acceleration non-stationary signal into a plurality of wave modulation intrinsic mode components;

[0018] The signal analysis module is configured to perform a moving least square parameterized time-frequency analysis on each wave modulation inherent modal component to obtain a multi-sine instantaneous frequency of each wave modulation inherent modal component; and obtain a wave modulation frequency based on a power spectrum peak of the multi-sine instantaneous frequency, and determine a corresponding relationship between the wave modulation frequency and a robot milling processing state in combination with a milling surface.

[0019] The state monitoring module is configured to input a power spectrum graph of the multi-sine instantaneous frequency into a robot milling chatter early monitoring model, extract multi-scale and multi-directional sparse features through a fractional order wavelet scattering transform network in the robot milling chatter early monitoring model, classify the multi-scale and multi-directional sparse features based on the corresponding relationship between the wave modulation frequency and the robot milling processing state by using a support vector machine, and complete identification of three robot milling processing states, i.e., a stable state, an early chatter state and a severe chatter state.

[0020] According to some embodiments, the present disclosure adopts the technical solutions as follows:

[0021] A computer program product comprises a computer program, which, when executed by a processor, implements the robot milling chatter early monitoring method considering the wave modulation effect.

[0022] According to some embodiments, the present disclosure adopts the technical solutions as follows:

[0023] A non-transitory computer-readable storage medium is configured to store computer instructions, which, when executed by a processor, implement the robot milling chatter early monitoring method considering the wave modulation effect.

[0024] According to some embodiments, the present disclosure adopts the technical solutions as follows:

[0025] An electronic device comprises a processor, a memory and a computer program; the processor is connected with the memory, and the computer program is stored in the memory; when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device implements the robot milling chatter early monitoring method considering the wave modulation effect.

[0026] Compared with the prior art, the present disclosure has the following beneficial effects:

[0027] The robot milling chatter early monitoring method and system of the present disclosure consider the wave modulation effect. After obtaining the acceleration non-stationary signal of robot milling, the multi-component acceleration non-stationary signal is decomposed into a plurality of wave modulation intrinsic modal components by using the variational modal decomposition, and then the moving least square parameterized time-frequency analysis method is used to estimate the multi-sine instantaneous frequency of all wave modulation intrinsic modal components. The moving least square time-frequency analysis method has the advantage of local fitting capability, and can accurately fit the multi-sine instantaneous frequency; and does not require any prior information of the acceleration non-stationary signal. The power spectrum diagram is obtained by performing Fourier transform on the obtained multi-sine instantaneous frequency, and the power spectrum peak value is the wave modulation frequency. The corresponding relationship between the wave modulation frequency and the milling processing state is determined in combination with the milling surface, the change of the wave modulation frequency is earlier than the appearance of the visible vibration lines on the workpiece surface, the sensitivity of the robot milling chatter feature is improved, and the early monitoring of the robot milling chatter can be realized.

[0028] The robot milling chatter early monitoring database is constructed, and the robot milling chatter early monitoring model using the fractional wavelet scattering transform network and the support vector machine is used to realize the effective identification of the robot milling processing state. The fractional wavelet scattering transform network has the advantages of sufficient theoretical support, stability and invariance to the translation, rotation and scale change of the input signal; the pre-defined wavelet and scale filter is used, and the small sample can also work effectively; the sparse representation is provided, the energy is mainly concentrated in a small number of wavelet scattering coefficients, which helps to reduce the calculation complexity and improve the data processing efficiency, and the sparse features in different scales and directions can be automatically extracted; the multi-scale and multi-direction sparse features can be extracted under the condition of small sample data set, and the problem of requiring a large number of samples for learning and training is solved. BRIEF DESCRIPTION OF DRAWINGS

[0029] The drawings accompanying the specification of the present disclosure serve to provide a further understanding of the present disclosure, and the illustrative embodiments of the present disclosure and the description thereof are used to explain the present disclosure, and do not constitute an improper limitation on the present disclosure.

[0030] Figure 1 The experimental equipment for the robot milling chatter early monitoring of the embodiment of the present disclosure;

[0031] Figure 2 The robot milling chatter early monitoring method flowchart of the embodiment of the present disclosure;

[0032] Figure 3 The moving least square parameterized time-frequency analysis method schematic diagram of the embodiment of the present disclosure;

[0033] Figure 4A short-time Fourier transform time-frequency diagram of a robot milling acceleration non-stationary signal, a power spectrum diagram of the robot milling acceleration non-stationary signal, and a corresponding workpiece surface of robot milling processing of an embodiment of the present disclosure;

[0034] Figure 5 A correspondence diagram of an in-wave modulation frequency of a robot milling acceleration non-stationary signal and a milling processing state of an embodiment of the present disclosure;

[0035] Figure 6 A fractional order wavelet scattering transform network model schematic diagram of an embodiment of the present disclosure.

[0036] Figure 7 A classification result of a training set and a test set of an embodiment of the present disclosure. DETAILED DESCRIPTION

[0037] The present disclosure will be further described below in conjunction with the accompanying drawings and embodiments.

[0038] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present disclosure. Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present disclosure belongs.

[0039] It should be noted that the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit exemplary embodiments according to the present disclosure. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should also be understood that when the terms "comprise" and / or "include" are used in the specification, there is a presence of a feature, step, operation, device, component, and / or combinations thereof.

[0040] Embodiment 1

[0041] In an embodiment of the present disclosure, a robot milling chatter early monitoring method and system considering in-wave modulation effect are provided, which can be manifested as rapid oscillation of the instantaneous frequency of the robot milling processing response in the form of a multi-sinusoidal wave, wherein the frequency of the multi-sinusoidal wave is referred to as the in-wave modulation frequency. Therefore, the signal model is established as,

[0042]

[0043] wherein z k (t) represents an in-wave modulation inherent modal component, K is the total number of modes, a k (t) and F k (t) are the instantaneous amplitude and the instantaneous frequency of the kth in-wave modulation inherent modal component, respectively.

[0044] The multi-sinusoidal wave instantaneous frequency is further written as,

[0045]

[0046] Among them, f base,k , f h,k ε h,k , f h,k and θ h,k They are center frequency, intra-wave modulation amplitude, intra-wave modulation frequency and intra-wave modulation initial phase respectively.

[0047] The intra-wave modulation effect of the robot milling processing response can be expressed as the multi-sinusoidal instantaneous frequency F of the signal k (t) with f base，k As the center frequency, f h，k In order to further determine the relationship between the wave modulation effect and the robot milling processing state, it is necessary to accurately estimate the multi-sine wave instantaneous frequency F k (t).

[0048] like Figure 1 It is a robotic milling equipment and early vibration monitoring system. The robot model is KUKA KR210R2700-2, the electric spindle model is ABGO311A1S, the milling cutter is a three-tooth tungsten steel milling cutter, the workpiece material is Al6061, the acceleration sensor is Dytran 3263A2, the signal collector is DH5922D, and the acquisition software is DHDAS dynamic signal acquisition and analysis system.

[0049] like Figure 2 The present disclosure provides a method for early detection of chatter in robot milling considering the intra-wave modulation effect. The implementation framework is as follows:

[0050] Step 101: Acquire a non-stationary acceleration signal during robot milling processing;

[0051] Step 102: Decompose the acceleration non-stationary signal into multiple intra-wave modulated intrinsic modal components using variational mode decomposition.

[0052] Step 103: Estimate the instantaneous frequency of the multi-sine wave modulated natural mode component within each wave using a moving least squares parameterized time-frequency analysis method.

[0053] Step 104: Determine the correspondence between the modulation frequency within the wave and the milling processing state of the robot according to the power spectrum of the instantaneous frequency of the multi-sine wave and the milling processing surface.

[0054] Step 105: Use the power spectrum dataset of the instantaneous frequencies of multiple sine waves to train a robot milling chatter early monitoring model based on a fractional-order wavelet scattering transform network and a support vector machine.

[0055] Step 106: input the power spectrum diagram test set of the multi-sinusoidal instantaneous frequency into the trained robot milling chatter early monitoring model to determine the robot milling stable, early chatter and severe chatter states, and obtain the monitoring success rate.

[0056] The specific implementation process is as follows:

[0057] Further, in step 102, the variational mode decomposition assumes that all components are narrowband signals concentrated around the respective center frequency, so the variational mode decomposition establishes a constrained optimization problem according to the component narrowband condition to estimate the center frequency of the signal component and reconstruct the corresponding component. As shown in Figure 4 The frequencies of the milling signals are all concentrated around the tooth passing frequency, and the number of tooth passing frequencies and their multiples is equal to the number of layers of the variational mode decomposition. The variational mode decomposition establishes a constrained optimization problem according to the component narrowband condition to estimate the center frequency of the signal component and reconstruct the corresponding component. The specific constrained optimization problem is as follows,

[0058]

[0059] where ω k is the center frequency.

[0060] Solving the above constrained optimization problem, the Lagrange multiplier λ and the second-order penalty factor α are introduced, and the above equality constrained optimization problem is equivalent to an unconstrained optimization problem by means of the augmented Lagrange function, as follows,

[0061]

[0062] where <> is the inner product operation.

[0063] Each z k and ω k is updated by the alternating direction multiplier method,

[0064]

[0065] Finally, a plurality of wave-intrinsic mode modulation components are obtained.

[0066] Further, in step 103, the specific moving least squares parameterized time-frequency analysis method is used to estimate the multi-sinusoidal instantaneous frequency of the wave-intrinsic mode modulation component, which is

[0067] The variational mode decomposition method is used to decompose the acceleration non-stationary signal into a plurality of wave-intrinsic mode modulation components, denoted as z1, z2, …, z k , which can be written as,

[0068]

[0069] where A(t) and F(t) are the instantaneous amplitude and instantaneous frequency, respectively, assuming that the instantaneous amplitude variation rate is much smaller than the instantaneous frequency.

[0070] The parametric time-frequency analysis method is,

[0071]

[0072] where g() and σ are the Gaussian window function and its parameters; u and t are the time and the middle time node of the Gaussian window, respectively; f is the angular frequency; is the parametric demodulator kernel.

[0073] Substituting equation (6) into equation (7) gives,

[0074]

[0075] Based on equation (9), the estimation procedure of the parametric time-frequency analysis method is shown in Figure 3 (a), which includes the following three steps:

[0076] 1) Instantaneous frequency rotation

[0077] 2) Instantaneous frequency shift

[0078] 3) Perform short-time Fourier transform.

[0079] Ideally, i.e. Equation (9) can be simplified as,

[0080]

[0081] The maximum spectral energy of the parametric time-frequency analysis is,

[0082] max||PTFA(t,f)|| 2 =||PTFA(t,F(t))|| 2 =||A(t)| 2 (11)

[0083] It can be seen that when the kernel of the parametric demodulator is equivalent to the instantaneous frequency, the parametric time-frequency analysis can provide an ideal time-frequency distribution. The existing parametric time-frequency analysis kernels include polynomials, splines, and Fourier functions. For rapidly varying instantaneous frequencies, these kernels require more kernel parameters to avoid overfitting problems. Therefore, the currently proposed kernels are not suitable for estimating rapidly varying instantaneous frequencies.

[0084] In order to accurately estimate the multi-sinusoidal instantaneous frequency of the non-stationary signal of the robot milling acceleration, the moving least squares local fitting method is used as the kernel To fit the instantaneous frequency of multiple sine waves.

[0085] The moving least squares method is a method for performing local fitting within the support domain. The local fitting diagram is as follows: Figure 3 (b), function x h (t) at t l The approximate fitting of the moment can be expressed as,

[0086]

[0087] α(t)=[α0(t),α1(t),...,α V (t)] T (14)

[0088] Among them, t l Time data points in the support domain; λ T (t l ) and α(t) are the basis function vector and parameter vector respectively, and V is the degree of the basis function.

[0089] The fitting error of the moving least squares is,

[0090]

[0091] Where L is the number of data points; w(s l ) and b are the Gaussian weight function and its parameters, respectively; r is the radius of the support region. It can be seen that the weight of data points outside the support region is 0, so each data point outside the support region does not participate in the data fitting.

[0092] Formula (15) is written in matrix form as follows:

[0093] J(α(t))=[Qα(t)-x h ] T W[Qα(t)-x h ] (17)

[0094] x h =[x h (t1),...,x h (t L )] T (18)

[0095]

[0096] Taking the derivative of formula (17) and making it equal to 0, we have,

[0097]

[0098] At this time, α(t) can be expressed as,

[0099] a(t) = [Q T WQ] -1 Q T Wx h (22)

[0100] The moving least squares can be finally obtained from equation (12) and equation (22) as,

[0101] [x(t1),...,x(t L )] T = Ωx h (23)

[0102] Ω = λ Τ (t)[Q T WQ] -1 Q T W (24)

[0103] Further, Figure 4 are the short-time Fourier transform time-frequency diagram, power spectrum diagram and corresponding robot milling machining surface of the robot milling acceleration non-stationary signal. It can be seen that the power spectrum diagrams of the robot milling machining stability and early chatter are similar and difficult to distinguish. Figure 5 The left and middle graphs are the time-frequency diagram and instantaneous frequency obtained by using the moving least squares parameterized time-frequency analysis method for the acceleration non-stationary signal collected under three machining states of robot milling. Figure 4 The short-time Fourier transform time-frequency diagram of the left graph is dispersed and fuzzy and cannot reveal the wave modulation effect, while the time-frequency diagram obtained by the proposed method is Figure 5 The left graph time-frequency diagram is energy concentrated, and the multi-sinusoidal instantaneous frequency represented by the wave modulation effect is accurately estimated, that is, the instantaneous frequency is centered on the tooth passing frequency as the center frequency, and oscillates rapidly with the wave modulation frequency as the modulation frequency. Therefore, the multi-sinusoidal instantaneous frequency of the acceleration signals of the robot milling machining stability, early chatter and severe chatter is obviously different and easy to distinguish.

[0104] Further, in step 104, the multi-sinusoidal instantaneous frequency is Fourier transformed to obtain its power spectrum, such as Figure 5 The right graph in the middle graph is the power spectrum diagram obtained by Fourier transforming the multi-sinusoidal instantaneous frequency, and the wave modulation frequency is obtained from the power spectrum peak value. According to the robot milling machining surface and the corresponding wave modulation frequency of the robot milling machining stability, early chatter and severe chatter, the corresponding relationship between the wave modulation frequency and the robot milling machining is determined as:

[0105] The robot milling machining stability corresponds to the multi-sinusoidal instantaneous frequency centered on the tooth passing frequency and its multiple frequency as the center frequency, and oscillates with the rotation frequency as the wave modulation frequency;

[0106] The early chatter state of the robot milling process corresponds to a multi-sine instantaneous frequency centered on the tool tooth passing frequency and its multiple frequencies, and oscillates with multiple mixed wave modulation frequencies;

[0107] The severe chatter state of the robot milling process corresponds to a multi-sine instantaneous frequency centered on the tool tooth passing frequency and its multiple frequencies, and oscillates with a certain intra-wave modulation frequency less than the rotation frequency.

[0108] Further, in step 105, a small sample training set of the multi-sine instantaneous frequency power spectrum is established, a predetermined kernel of the fractional wavelet scattering transform network is determined, multi-scale and multi-directional sparse features are extracted using the fractional wavelet scattering transform network, the multi-scale and multi-directional sparse features are classified using a support vector machine, the training of the robot milling chatter early monitoring model is completed, and a training success rate is obtained.

[0109] The robot milling chatter early monitoring model based on the fractional wavelet scattering transform network feature extraction and the support vector machine classification is specifically,

[0110] For an input signal f(t)∈L 2 (R d ), the d-dimensional fractional wavelet transform is expressed as,

[0111]

[0112] where the fractional wavelet kernel is expressed as,

[0113]

[0114] where λ and t represent the scale and time translation parameters, respectively. Note that when α=π / 2, the fractional wavelet transform degenerates into a wavelet transform.

[0115] When d>1, directionality is introduced into the fractional wavelet transform to represent changes in different directions, and a set of finite rotation factors is set as r k , k∈{1,2,…,K}, the fractional wavelet transform rotates a single fractional wavelet kernel ψ(t) through the rotation factor r k , and then obtains it through the scale stretching of the scale factor 2 p (p∈Z). In short, the fractional wavelet transform with directionality can discretize the scale factor λ in the fractional wavelet kernel into 2 p and r k direction, that is, the scale factor λ can be written as λ p,k =2 p r k and |λ p,k |=2 p , at this time the fractional wavelet ψ α,λ,t(τ) can be written as

[0116] From the multi-resolution analysis of the fractional wavelet transform, it can be known that the fractional wavelet transform can decompose the input signal into the high frequency details and the low frequency profile of different fractional frequency bands, and the fractional wavelet transform of the input signal is equivalent to the input signal passing through the fractional filter composed of the wavelet functions and the scaling functions of different scales, so as to obtain the low frequency profile and the high frequency details of the input signal of different fractional frequency bands.

[0117] For a given fractional scaling function, the low frequency profile of the input signal can be expressed as,

[0118]

[0119] wherein,

[0120]

[0121] The function with low-pass characteristics The low frequency part of the input signal is extracted by the scaling of the scaling function φ(t), and for the scaling 2 p The input signal high frequency details satisfying 2 p ≤2 J can be calculated by the fractional wavelet transform,

[0122]

[0123] It can be found that the fractional wavelet transform is essentially a linear operator,

[0124]

[0125] The low frequency profile reflects the large scale characteristics of the input signal, and has good invariance to local changes such as translation, rotation and scaling, while the high frequency details reflect the small scale geometric characteristics of the image, and for the scaling 2 p ≤2 J , the input signal high frequency details W f α (λ p,k ,τ) calculated by the fractional wavelet transform are covariant to the translation and time shift of the input signal, and cannot be directly used for signal recognition, but the high frequency details are indispensable part of the input signal classification, and need to be processed to meet the invariance.

[0126] Considering the high frequency details W f α (λ p,k ,τ) and its modulus |W f α (λ p,k|W f α (λ p,k ,τ)|, which describes the envelope of high frequency details and varies slowly. Then, the modulus of |W (λ

[0127]

[0128] However, in fact, only the low frequency part of |W is reserved, and the high frequency details are still lost. The lost high frequency details can be recovered by performing a fractional wavelet transform on |W f α (λ p,k ,τ)|, i.e.,

[0129]

[0130] Then, the inner product procedure in equations (31) and (32) needs to be repeated to form a series of invariant signal representations until the high frequency component |W f α (λ p,k ,τ)| is zero.

[0131] The set of all scales and directions 2 p r k (p≤J,1≤k≤K) in the fractional directional wavelet transform is

[0132] Δ={λ p,k =2 p r k |2 p <2 J ,1≤k≤K} (33)

[0133] Let l (m) be an ordered vector whose elements l n (m) satisfy l n (m) =2 p n r k (p n ≤J,1≤n≤m) denote the scales and directions of the fractional directional wavelet, l (m) can be expressed as

[0134] l (m) =(l1 (m) ​,l2 (m) ,…,l m (m) )∈Δ m (34)

[0135] For a path l of length m n (m) ,have,

[0136]

[0137] Among them U α represents the fractional wavelet scattering transform transmission operator. The function of this operator is to obtain the envelope of the high-frequency information of the input signal f(t). The scattering transmission operator can be further extended to multiple elements of a route, expressed as,

[0138]

[0139] The fractional wavelet scattering transform coefficient of the signal can be defined as the input signal f(t) passing through the path l (m) Fractional wavelet scattering transform transmission operator U α [l n (m) ]f(t) and fractional scaling function The inner product of

[0140]

[0141] Subsequently, in order to construct the fractional-order wavelet scattering transform network, combined with the relationship between inner product and convolution, formula (27) is written in the form of fractional-order convolution:

[0142]

[0143] The function The low-pass feature of corresponds to the low-frequency profile of the signal, which is obtained by scaling the scaling function φ(t), that is,

[0144]

[0145] Accordingly, formula (29) can be written as a fractional convolution form:

[0146]

[0147] The fractional directional wavelet The bandpass characteristics of the multi-scale 2 p ≤2 J The high-frequency details of the corresponding input signal are obtained by scaling the wavelet function ψ(t), that is,

[0148]

[0149] Accordingly, equation (30) can be written in fractional convolution form as,

[0150]

[0151] In summary, the input signal profile at scale 2 J is equivalent to the result of low-pass filtering of the signal f(t) by the filter , while the input signal detail part can be viewed as the result of band-pass filtering of the signal f(t) by the filter at scale 2 p ≤ 2 J .

[0152] For a path of length m, the result of the fractional scattering transmission operator acting on the input signal f(t) through the path is,

[0153]

[0154] The fractional wavelet scattering transform coefficients of a signal can be defined as,

[0155]

[0156] The fractional wavelet scattering transform network model constructed according to the above derivation is shown in Figure 6 . This model gives the principle diagram of a 3-layer fractional wavelet scattering transform network. In this model, the input signal f(t) computes all the fractional wavelet scattering transform coefficients S α (l (m) )f(t) for m = 0, 1, 2, which are the outputs of each layer, while the corresponding fractional wavelet scattering transform transmission operator U α (l n (m) )f(t) is the input of the next layer.

[0157] The set of all paths l (m) corresponds to the Δ m paths of the network model, and L (m) is defined as the set of Δ m paths, i.e.,

[0158] L (m) = {l (m) |l (m) ∈ Δ m , m ∈ N} (45)

[0159] where L (0) is the empty set.

[0160] In particular, the output of the first layer of the network model is,

[0161]

[0162] The fractional-order wavelet scattering transform transmission operator of this layer is:

[0163]

[0164] For the mth layer, all paths l of length m (m) The fractional-order wavelet scattering transform transmission operator is:

[0165]

[0166] For the mth layer, the fractional wavelet scattering transform coefficients of all previous layers are output as,

[0167]

[0168] The power spectrum of the instantaneous frequency of multiple sine waves is input into this fractional-order wavelet scattering transform network to obtain multi-scale and multi-directional fractional-order wavelet scattering transform coefficients, that is, multi-scale and multi-directional sparse features.

[0169] The multi-scale and multi-directional sparse features are input into the support vector machine to complete the classification of three robot milling processing states: smooth, early vibration, and severe vibration.

[0170] like Figure 7 As shown, the training success rate is 99.3827% and the test success rate is 98.1481%.

[0171] According to steps 101-106 above, the present invention uses a moving least squares parameterized time-frequency analysis method to estimate the instantaneous frequencies of all multi-sine wave intramodulation intrinsic modal components. This method reveals the intramodulation phenomenon and obtains the intramodulation frequency without requiring any prior information about the non-stationary acceleration signal. It also determines the correspondence between the intramodulation frequency and the stable, early chatter, and severe chatter states of robotic milling, thereby resolving the issue of weak chatter characteristics and enabling early monitoring of robotic milling chatter. A robotic milling chatter early monitoring model combining a fractional-order wavelet scattering transform network and a support vector machine effectively identifies robotic milling processing states. The advantage of this model is that it can rapidly extract and classify multi-scale and multi-directional sparse features from a small sample data set, resolving the issue of requiring a large number of samples for training.

[0172] Example 2

[0173] In one embodiment of the present disclosure, a system for early monitoring chatter in robot milling considering intra-wave modulation effect is provided, comprising:

[0174] The signal acquisition module is configured to acquire an acceleration non-stationary signal in a robot milling process.

[0175] The signal decomposition module is configured to perform variational modal decomposition on the acceleration non-stationary signal to obtain a plurality of wave modulation intrinsic modal components.

[0176] The signal analysis module is configured to perform moving least squares parameterized time-frequency analysis on each wave modulation intrinsic modal component to obtain a multi-sine instantaneous frequency of each wave modulation intrinsic modal component, obtain a wave modulation frequency based on a power spectrum peak of the multi-sine instantaneous frequency, and determine a corresponding relationship between the wave modulation frequency and a robot milling state in combination with a milling surface.

[0177] The state monitoring module is configured to input a power spectrum of the multi-sine instantaneous frequency into a robot milling chatter early monitoring model, extract multi-scale and multi-directional sparse features through a fractional order wavelet scattering transform network in the robot milling chatter early monitoring model, classify the multi-scale and multi-directional sparse features based on the corresponding relationship between the wave modulation frequency and the robot milling state by using a support vector machine, and complete identification of three robot milling states, i.e., a stationary state, an early chatter state, and a severe chatter state.

[0178] Embodiment 3

[0179] The present disclosure provides a computer program product comprising a computer program, which, when executed by a processor, implements the robot milling chatter early monitoring method considering the wave modulation effect.

[0180] Embodiment 4

[0181] The present disclosure provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the robot milling chatter early monitoring method considering the wave modulation effect.

[0182] Embodiment 5

[0183] The present disclosure provides an electronic device comprising a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory; when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device implements the robot milling chatter early monitoring method considering the wave modulation effect.

[0184] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 one or more flow or blocks

[0185] These computer program instructions can also be loaded into a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 one or more flow or blocks

[0186] The above description is only a specific implementation of the present disclosure, and is not intended to limit the protection scope of the present disclosure. It should be understood by those skilled in the art that various modifications or changes can be made to the technical solutions of the present disclosure without departing from the spirit and scope of the present disclosure, and these modifications or changes should also be considered as falling within the protection scope of the present disclosure.

Claims

1. An early detection method for chatter in robot milling considering the intra-wave modulation effect is characterized by: include: Obtaining the non-stationary acceleration signal during robot milling processing; Decomposing the non-stationary acceleration signal variational mode into a plurality of intra-wave modulation intrinsic mode components; Performing moving least squares parameterized time-frequency analysis on each wave-internal modulation natural mode component to obtain the multi-sinusoidal instantaneous frequency of each wave-internal modulation natural mode component; The intra-wave modulation frequency is obtained based on the peak value of the power spectrum of the instantaneous frequency of multiple sine waves. Combined with the milling surface, the corresponding relationship between the intra-wave modulation frequency and the robot milling processing state is determined. The power spectrum of the instantaneous frequency of multiple sine waves is input into the early monitoring model of robot milling chatter. The multi-scale and multi-directional sparse features are extracted through the fractional-order wavelet scattering transform network in the early monitoring model of robot milling chatter. Based on the correspondence between the intra-wave modulation frequency and the robot milling processing state, the multi-scale and multi-directional sparse features are classified using a support vector machine to complete the identification of three robot milling processing states: smooth, early chatter and severe chatter.

2. The method for early detection of chatter in robot milling considering the intra-wave modulation effect according to claim 1, characterized in that: The non-stationary acceleration signal variational mode is decomposed into a plurality of intra-wave modulation intrinsic mode components, including: According to the tooth passing frequency and the number of its multiples of the acceleration non-stationary signal, the parameters of variational modal decomposition are determined. The acceleration non-stationary signal is decomposed into multiple intra-wave modulation natural modal components using the variational modal decomposition method.

3. The method for early detection of chatter in robot milling considering the intra-wave modulation effect as claimed in claim 1, characterized in that: A moving least squares parameterized time-frequency analysis is performed on each intra-wave modulated natural mode component. The moving least squares method performs local fitting of the instantaneous frequency of multiple sine waves in the support domain. Without requiring any prior information of the acceleration non-stationary signal, the instantaneous frequency of multiple sine waves of each intra-wave modulated natural mode component is obtained.

4. The method for early detection of chatter in robot milling considering the intra-wave modulation effect as claimed in claim 1, characterized in that: The power spectrum of the multi-sine wave instantaneous frequency is obtained by Fourier transforming the multi-sine wave instantaneous frequency. The peak of the power spectrum of the multi-sine wave instantaneous frequency is the wave modulation frequency. The robot milling processing state includes stable, early chatter and severe chatter state. The corresponding relationship between the wave modulation frequency and the robot milling processing state is determined as follows: The stable state of robot milling processing corresponds to the instantaneous frequency of multiple sine waves with the tooth passing frequency and its multiples as the center frequency, and the rotation frequency as the modulation frequency within the wave oscillation; The chatter state in the early stage of robot milling corresponds to the instantaneous frequency of multiple sine waves with the cutter tooth passing frequency and its multiples as the center frequency, and oscillates with multiple mixed wave internal modulation frequencies; The severe chatter state of robot milling corresponds to the instantaneous frequency of multiple sine waves with the tooth passing frequency and its multiples as the center frequency, and oscillates at a certain wave modulation frequency that is less than the rotation frequency.

5. The method for early detection of chatter in robot milling considering the intra-wave modulation effect as claimed in claim 1, characterized in that: In the early monitoring model for chatter in robot milling, the fractional-order wavelet scattering transform network uses predefined wavelets and scaling filters, and can work effectively even with small samples. It has sufficient theoretical support and is stable and invariant to translation, rotation, and scaling changes of the input signal. Providing sparse representation, the energy is mainly concentrated in a small number of wavelet scattering coefficients, which helps to reduce computational complexity and improve data processing efficiency.

6. Robot milling chatter early detection system considering the wave intramodulation effect, characterized by: include: A signal acquisition module is used to obtain the non-stationary acceleration signal during the robot milling process; A signal decomposition module, configured to decompose the non-stationary acceleration signal variational mode into a plurality of intra-wave modulation intrinsic modal components; The signal analysis module is used to perform moving least squares parameterized time-frequency analysis on each intra-wave modulated natural modal component to obtain the multi-sine wave instantaneous frequency of each intra-wave modulated natural modal component; the intra-wave modulation frequency is obtained based on the peak value of the power spectrum of the multi-sine wave instantaneous frequency, and the corresponding relationship between the intra-wave modulation frequency and the robot milling processing state is determined in combination with the milling processing surface; The state monitoring module is used to input the power spectrum of the instantaneous frequency of multiple sine waves into the early monitoring model of robot milling vibration. The multi-scale and multi-directional sparse features are extracted through the fractional-order wavelet scattering transform network in the early monitoring model of robot milling vibration. Based on the correspondence between the intra-wave modulation frequency and the robot milling processing state, the multi-scale and multi-directional sparse features are classified using a support vector machine to complete the identification of three robot milling processing states: stable, early chatter and severe chatter.

7. The robot milling chatter early detection system considering the intra-wave modulation effect as claimed in claim 6, characterized in that: The non-stationary acceleration signal variational mode is decomposed into a plurality of intra-wave modulation intrinsic mode components, including: According to the tooth passing frequency and the number of its multiples of the acceleration non-stationary signal, the parameters of variational modal decomposition are determined. The acceleration non-stationary signal is decomposed into multiple intra-wave modulation natural modal components using the variational modal decomposition method.

8. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for early monitoring of chatter in robot milling considering the intra-wave modulation effect as described in any one of claims 1 to 5 is implemented.

9. A non-transitory computer-readable storage medium, characterized in that The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, the method for early monitoring of robot milling chatter considering the intra-wave modulation effect as described in any one of claims 1 to 5 is implemented.

10. An electronic device, characterized in that: include: A processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the robot milling chatter early monitoring method considering the wave intra-modulation effect as described in any one of claims 1-5.

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