TF-IGLSTM Thermal Error Prediction Model and Intelligent Machining and Error Control System

Abstract

The present invention discloses a TF-IGLSTM thermal error prediction model, which includes a data input layer, a transformer encoder block, an IGLSTM module, a linear layer, and a data output layer arranged in sequence; the transformer encoder block includes a multi-head attention layer, a connection layer, an Add&Norm layer I, an FFN layer, and an Add&Norm layer II, and a linear module for performing a linear transformation on the input data is provided between the multi-head attention layer and the data input layer; the IGLSTM module includes a plurality of IGLSTM units connected in series. The present invention also discloses an intelligent machining and error control system, which includes a process flow / equipment group, an intelligent machining subsystem, and an error control subsystem. The TF-IGLSTM thermal error prediction model can extract and enhance long-term trends and short-term features to improve the prediction accuracy; the intelligent machining and error control system can perform machining performance evaluation and parameter optimization and perform error control, which can effectively improve the machining efficiency and accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent manufacturing technology, and specifically relates to a TF-IGLSTM thermal error prediction model and an intelligent processing and error control system. Background Art

[0002] Intelligent manufacturing has innovated the scientific basis of traditional manufacturing. Product design and manufacturing have gradually shifted from local quantitative, empirical and qualitative to comprehensive intelligent and quantitative. Therefore, intelligent manufacturing is an open research field with a wide range of research. Intelligent manufacturing aims to solve the intelligent representation, perception, modeling and reasoning in the entire life cycle of product development; in addition, intelligent manufacturing also analyzes common problems such as the behavioral complexity of manufacturing systems, product manufacturability, assemblability and maintainability, and proposes theories and methods for intelligent modeling, studies multi-domain and multi-scale simulation of product development, establishes a multi-objective and comprehensive integrated model, studies the intelligent collaborative product development process, and establishes a dynamic model of the product development process in terms of function, time, cost, quality, etc. In addition, intelligent manufacturing also studies networked control systems and intelligent numerical control systems.

[0003] Nonlinear factors such as friction, vibration, impact, deformation and structural clearance will directly affect the dynamic behavior of manufacturing equipment (ME) under unconventional working conditions such as high speed, high acceleration, large load and large displacement, resulting in changes in the performance of ME, which poses a huge challenge to existing control theories and methods. The dynamic behavior modeling of ME adopts modeling and simulation methods, and provides a theoretical and technical basis for the design of ME by studying the dynamic behavior and performance evolution of ME under complex working conditions and operating states.

[0004] The manufacturing process is an interactive process between ME, tools and workpieces. In the process of intelligent processing, the evolution of material structure and the shape generation of processed parts are inevitable, and the physical fields of force, heat and fluid become the main factors affecting manufacturing accuracy, efficiency and performance. Multi-scale simulation of the manufacturing process reveals the essential properties of the processing process. Optimizing and controlling the manufacturing process is the key to ensuring efficient, high-precision and high-quality manufacturing of parts. The physical field effect in the manufacturing process is characterized by nonlinear coupling, multi-scale effects and strong spatiotemporal changes. Its action mechanism is extremely complex. The core scientific issues that need to be studied are the representation and processing of manufacturing information such as geometric quantities (displacement, multi-coordinate linkage displacement, product size, surface quality, etc.) and physical quantities (force, heat, sound, vibration, speed, etc.), as well as the quantitative prediction of manufacturing physical mechanisms in the manufacturing process and part performance.

[0005] Manufacturing systems concentrate information on MEs, parts, manufacturing processes, and execution processes. Improving the information acquisition, processing, and fusion capabilities of manufacturing systems, especially improving the availability of manufacturing information through the fusion of complex manufacturing information and uncertain information processing, has become the key to ensuring the high efficiency, high reliability, and high-precision product manufacturing of manufacturing systems at the system level. On the one hand, it is crucial to study the acquisition, expression, transmission, fusion, evolution, and utilization of multi-source and multi-process processing quality and process information; on the other hand, it is important to reveal the basic properties (quantification, measurement, value, classification, and evaluation, etc.) and functional rules of manufacturing information. In addition, establishing a processing and utilization mechanism for complex manufacturing system information, especially unconventional information, is of great significance for realizing the active prediction of product processing quality, the online control of manufacturing errors, and the optimization of manufacturing processes.

[0006] Precision manufacturing equipment is essential for achieving high-precision machining of key components, but a significant reduction in machining accuracy is inevitable. Thermal error is the main component of the total error, and the existence of thermal error makes it difficult to improve machining accuracy. Therefore, thermal error needs to be precisely controlled, but thermal error often exhibits strong nonlinearity, time-varying, and non-stationary properties, which also means that accurate prediction and effective control are difficult to achieve. Summary of the invention

[0007] In view of this, the purpose of the present invention is to provide a TF-IGLSTM thermal error prediction model and an intelligent processing and error control system, wherein the TF-IGLSTM thermal error prediction model can extract and enhance long-term trends and short-term features to improve prediction accuracy; the intelligent processing and error control system can perform processing performance evaluation and parameter optimization and error control, which can effectively improve processing efficiency and accuracy.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] The present invention firstly proposes a TF-IGLSTM thermal error prediction model, which includes a data input layer, a Transformer encoder block, an IGLSTM module, a linear layer and a data output layer which are arranged in sequence;

[0010] The Transformer encoder block includes a multi-head attention layer, a connection layer, an Add&Norm layer I, an FFN layer, and an Add&Norm layer II. A Linear module for linearly projecting input data is provided between the multi-head attention layer and the data input layer.

[0011] The IGLSTM module includes a plurality of IGLSTM units connected in series, and the principle of the IGLSTM unit is:

[0012]

[0013] i t =σ(W i [h t-1 ,x t ]+b i )

[0014]

[0015] m t =σ(W m [h t-1 ,x t ]+b m )

[0016]

[0017] Among them, x t , h t-1 、c t-1 , c t and h t Respectively represent the input at time t, the weighted input at time t, the output at time t-1, the unit state at time t-1, the unit state to be updated at time t, the unit state at time t, and the output at time t; i t and m t Respectively represent the input gate and output gate; W, W i , W c and W m Represents the weight matrices of input variables, input gate variables, unit states, and output variables respectively; b i 、b c and b m denote the bias matrices of input variables, unit states, and output variables, respectively; σ and tanh denote the sigmoid function and tanh function, respectively; · denotes the product operator.

[0018] The present invention also proposes an intelligent processing and error control system, including a process flow / equipment group, an intelligent processing subsystem and an error control subsystem;

[0019] The process / equipment group includes a collection node for collecting data, an edge node for processing data, and a cloud center for storing data, and a data transmission system is provided between the collection node and the edge node, and between the edge node and the cloud center;

[0020] The intelligent processing subsystem includes an input layer I, a modeling layer I, a decision layer I and a control layer I; the intelligent processing subsystem creates a finite element model and finite element equation of the machine tool system and a finite element model and finite element equation of the workpiece system in the modeling layer I to perform finite element analysis on the machine tool processing process, and predicts the frequency response function at the tool tip according to the finite element analysis results and the real-time processing data of the machine tool in the decision layer I, and evaluates the processing performance at the same time, and according to the evaluation results, the control layer I enables the machine tool to process according to the set cutting parameters;

[0021] The error control subsystem includes an input layer II, a modeling layer II, a decision layer II and a control layer II; the error control subsystem creates the TF-IGLSTM thermal error prediction model as described above in the modeling layer II, and trains the TF-IGLSTM thermal error prediction model using historical thermal error data in the modeling layer II, and transmits the trained TF-IGLSTM thermal error prediction model to the control layer II to update the parameters of the TF-IGLSTM thermal error prediction model in the control layer II, and predicts the thermal error of the machine tool in real time in the control layer II according to the real-time thermal error data input by the input layer, and after obtaining the thermal error prediction data, controls the machine tool through the control layer II to compensate for the thermal error; the decision layer II compares the real-time thermal error data input by the input layer with the set threshold, and if the reason why the real-time thermal error exceeds the set threshold is a machine tool failure, the machine tool is shut down; if the reason why the real-time thermal error exceeds the set threshold is that the prediction accuracy of the TF-IGLSTM thermal error prediction model decreases, the TF-IGLSTM thermal error prediction model is retrained through the modeling layer II.

[0022] The beneficial effects of the present invention are:

[0023] The TF-IGLSTM thermal error prediction model of the present invention can extract and enhance the long-term trend and short-term characteristics of thermal error data by using the encoder block of the Transformer network by setting the Transformer encoder block. By designing the IGLSTM module, in the IGLSTM unit, the forget gate and the input gate in the LSTM neural network are integrated into a new gate, and the gate no longer learns the information to be forgotten and the new input information separately, thereby reducing the number of parameters to be learned; in addition, the design of the gate is to make the processing of the unit information more intensive and orderly while selecting the unit information to be forgotten and updated; in order to improve the training efficiency, the IGLSTM module converts the input information x at the current moment into the input information x at the current moment. t With h t Combined with the update of c tA similar update mechanism enables the model to focus on the information of the previous moment, thereby further enhancing the short-term memory behavior. It is more suitable for describing the thermal error mechanism than the traditional LSTM and improves the short-term memory capacity without increasing the model learning parameters. In this way, combining the Transformer encoder block with the IGLSTM module can extract and enhance long-term trends and short-term features to improve prediction accuracy.

[0024] The intelligent processing and error control system of the present invention includes a process flow / equipment group, an intelligent processing subsystem and an error control subsystem, wherein the process flow / equipment group includes an acquisition node, an edge node for processing data and a cloud center for storing data, and data transmission between the acquisition node and the edge node and between the edge node and the cloud center is realized through a data transmission system; the intelligent processing subsystem establishes a machine tool model and a cutting model, and integrates them to obtain a frequency response function to evaluate the processing performance and optimize the cutting parameters; the error control subsystem constructs a TF-IGLSTM thermal error prediction model to perform error control; the intelligent processing subsystem and the error control subsystem are not two independent units, the intelligent processing subsystem simulates the processing from the positive direction and optimizes the cutting parameters from a theoretical perspective; the error control subsystem studies the processing from the opposite direction; the output information in the processing process is used to evaluate and control the current processing state, and to check whether the intelligent processing process is executed according to the predetermined state. The two subsystems complement each other and jointly ensure the reliable execution of the intelligent processing process, which can effectively improve the processing efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0026] Figure 1 It is a framework diagram of the intelligent processing and error control system of the present invention;

[0027] Figure 2 This is a schematic diagram of the data collection architecture;

[0028] Figure 3 This is the structural diagram of the intelligent gateway;

[0029] Figure 4 It is a schematic diagram of the framework of the intelligent processing subsystem;

[0030] Figure 5 This is the milling dynamics model diagram;

[0031] Figure 6 It is the framework diagram of the error control subsystem;

[0032] Figure 7 is a schematic diagram of the main shaft thermal model;

[0033] Figure 8 This is the structural diagram of the TF-IGLSTM thermal error prediction model;

[0034] Fig. 9 It is the structural diagram of LSTM unit;

[0035] Fig.10 It is the structural diagram of IGLSTM unit;

[0036] Fig.11 It is the structural diagram of the Transformer encoder block;

[0037] Fig.12 It is a structural schematic diagram of a machined part;

[0038] Fig.13 The appearance and internal structure of the main axis; (a) appearance structure; (b) internal structure;

[0039] Fig.14 is the frequency response function of the tool tip; (a) FRF G in the X direction xx ; (b) FRF G in the Y direction xx ; (c) FRF G xx ;

[0040] Fig.15 Lobe diagram for chatter stability; (a) rough milling; (b) fine milling;

[0041] Fig.16 Figure 1 is an experimental verification diagram; (a) VMC850D milling machine; (b) machined workpiece;

[0042] Fig.17 It is the YK73200 grinder test bench;

[0043] Fig.18 Schematic diagram of measuring thermal errors of 5 displacement sensors;

[0044] Fig.19 To simulate working conditions; (a) working condition 1; (b) working condition 2;

[0045] Fig. 20 Temperature change and deformation change after noise reduction; (a) Temperature change under working condition 1 (b) Temperature change under working condition 2; (c) Thermal deformation under working condition 1 (d) Thermal deformation under working condition 2;

[0046] Fig.21 is the loss function of different optimizers;

[0047] Fig. 22 Model training performance under different batch sizes; (a) Changes in Loss value under different batch sizes; (b) Changes in error under different batch sizes;

[0048] Fig.23 The fitting curve under working condition 1; (a) the change of Loss value during model training; (b) the fitting curves of different models;

[0049] Fig.24 It is the prediction result curve graph;

[0050] Fig.25 Schematic diagram of error mapping; (a) thermal deformation of gear profile grinder; (b) relative position error;

[0051] Fig.26 This is a physical picture of gear grinding;

[0052] Fig. 27 is the measurement error; (a) ECS is not implemented; (b) ECS is implemented. DETAILED DESCRIPTION

[0053] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0054] like Figure 1 As shown, the intelligent processing and error control system of this embodiment includes a process flow / equipment group, an intelligent processing subsystem and an error control subsystem. The process flow / equipment group includes a collection node for collecting data, an edge node for processing data and a cloud center for storing data. A data transmission system is provided between the collection node and the edge node, and between the edge node and the cloud center;

[0055] The intelligent processing subsystem includes an input layer I, a modeling layer I, a decision layer I and a control layer I; the intelligent processing subsystem creates a finite element model and finite element equation of a machine tool system and a finite element model and finite element equation of a workpiece system in the modeling layer I to perform finite element analysis on the machine tool processing process, and predicts the frequency response function at the tool tip according to the finite element analysis results and the real-time processing data of the machine tool in the decision layer I, and evaluates the processing performance at the same time, and according to the evaluation results, the control layer I enables the machine tool to process according to the set cutting parameters;

[0056] The error control subsystem includes an input layer II, a modeling layer II, a decision layer II and a control layer II; the error control subsystem creates the TF-IGLSTM thermal error prediction model as described above in the modeling layer II, and trains the TF-IGLSTM thermal error prediction model using historical thermal error data in the modeling layer II, and transmits the parameters of the trained TF-IGLSTM thermal error prediction model to the control layer II to update the parameters of the TF-IGLSTM thermal error prediction model in the control layer II, and predicts the thermal error of the machine tool in real time according to the real-time thermal error data input by the input layer in the control layer II, and after obtaining the thermal error prediction data, controls the machine tool through the control layer II to compensate for the thermal error; the decision layer II compares the real-time thermal error data input by the input layer with the set threshold, and if the reason why the real-time thermal error exceeds the set threshold is a machine tool failure, the machine tool is shut down; if the reason why the real-time thermal error exceeds the set threshold is that the prediction accuracy of the TF-IGLSTM thermal error prediction model decreases, the TF-IGLSTM thermal error prediction model is retrained through the modeling layer II.

[0057] Specifically, the intelligent processing and error control system of this embodiment is described in detail as follows.

[0058] 1. Intelligent processing and error control system

[0059] 1.1 System Architecture

[0060] The intelligent processing and error control system consists of three parts, namely, process flow / equipment group (PF / EG), intelligent processing subsystem (IMS) and error control subsystem (ECS), such as Figure 1 As shown. These three parts are interconnected. PF / EG is the data source and application object of IMS and ECS. IMS and ECS are not two independent units. IMS simulates the machining process from the positive direction and optimizes the cutting parameters from a theoretical perspective. ECS studies the machining process from the opposite direction. That is, the output information in the machining process is used to evaluate and control the current machining status and check whether the intelligent machining process is executed according to the predetermined status. These two subsystems complement each other and jointly ensure the reliable execution of the intelligent machining process.

[0061] 1.2 Process flow / equipment group

[0062] Multiple processing equipment on the production line form an equipment group to realize multi-process processing of complex parts. Each processing equipment or process is a control node in the manufacturing process of complex parts. Cutting parameters should be optimized and thermal errors should be controlled in real time. PF / EG is at the bottom of the entire intelligent processing and error control system, providing geometric and physical parameters for the intelligent processing subsystem. In addition, the sensor network obtains a large amount of manufacturing information and provides data support for the error control subsystem.

[0063] 1.2.1 Data Transmission

[0064] Data collection architecture such as Figure 2 As shown. Multiple gateway nodes are distributed in a distributed manner to collaboratively complete the collection work. Network connection settings are required to achieve wireless connection of the edge computing smart gateway. When the system is running, the big data platform starts the server for transmission control protocol (TCP) communication. When the smart gateway is turned on, it treats the server's network as a client and sets each edge computer through the host management platform. The number of ZigBee collection nodes is managed by the smart gateway. When the networking mode of the collection node is enabled, the smart gateway sends a beacon. When the collection node captures the beacon under the corresponding channel, it will reply with a relational address packet to realize a self-organizing network. The host computer sets the collection parameters and sends it to the smart gateway in the form of a command packet; after parsing, the command packet is encapsulated into the format of the control command packet of the collection node and sent to the collection node, and the collection node is ready to start collecting data. After collecting the signal, the data is identified on the smart gateway node, and the identification result is fed back to the big data platform, and then the data is sent to the cloud center for data processing via WIFI.

[0065] 1.2.2 Intelligent Gateway

[0066] Compared with wired data acquisition methods, wireless sensor networks have the advantages of flexibility and mobility brought by wireless communication and wireless passivity. At present, the most widely used wireless communication method in wireless sensor networks is radio frequency communication (RFC). Compared with wireless communication methods such as infrared and laser, wireless RFC is more in line with the requirements of wireless sensors for network environment, distance and bandwidth. With the development of RFC technology, some practical wireless RFC protocols and technologies have appeared in WSNs in different application scenarios, including Wi-Fi, ZigBee, LoRa, Bluetooth, UWB, NB-IOT, etc. The above wireless RFC technologies have different transmission performances. According to the actual data perception and acquisition requirements, reasonable communication modules are selected to meet the needs of different application scenarios. First of all, wireless sensor networks are usually used in inconvenient wired connection scenarios in the field of information perception of small and medium-sized enterprises, and the accuracy of sampling triggering directly affects the subsequent analysis and processing of collected data. Therefore, the requirements for low power consumption and synchronization performance of wireless RFC are very high. The low-power ZigBee transmission protocol based on IEEE 802.15.4 has a beacon mechanism and excellent synchronization performance. Therefore, ZigBee wireless sensor networks are a reasonable choice. In addition, data collection has high requirements on frequency and accuracy. The amount of data generated per unit time is very large. The transmission of large-capacity data poses a severe challenge to the bandwidth of wireless sensor networks. Wi-Fi, which has the highest transmission speed in the above RFC, becomes the best choice.

[0067] The working environment of wireless sensor networks is very harsh. The layout of the collection nodes is very complex. The collection nodes in the network topology need to maintain synchronous trigger accuracy. The sensor nodes communicate with the ZigBee protocol, and the data center is responsible for command sending and result display. Therefore, the data center should have a high transmission bandwidth and interact with the cloud platform. This embodiment uses the Wi-Fi protocol for communication. The intelligent gateway node is in a link position in the network topology, responsible for information exchange and data transmission between the sensor nodes and the data center, and should have a corresponding communication module. At the same time, the deployment location of the intelligent gateway node is far away from the sensor node, so the intelligent gateway node needs to be smaller than the collection node. Miniaturization, and can carry a large-capacity battery as a power source, the number of intelligent gateway nodes is far less than the number of collection nodes, and the requirement for low power consumption is not strict. Therefore, the intelligent gateway node designed for edge computing is equipped with ZigBee and Wi-Fi dual communication modules, which communicate with the sensor nodes and the data center respectively.

[0068] Embedding a deep learning neural network in the intelligent gateway node is necessary for processing and training the collected data. This embodiment uses XILINX ZYNQ7020 as the main control chip. Figure 3 The FPGA XC7Z020-2CLG400I and ARM Cortex-A9 used in XILINX ZYNQ7020 are shown. The processing model associated with the DLNN model is embedded in the FPGA XX7Z020-2-CLG400i and the post-processing model is embedded in the ARM Cortex-A9. FPGA development is done using Python. Using Python, FPGA development is done through Jupyter. Figure 3 As shown, in this embodiment, the intelligent gateway node includes a processor module, a ZigBee communication module, a WIFI communication module and a power management module. The ZigBee communication module is used to communicate with each data acquisition node of the data acquisition system, and the WIFI communication module is used to exchange information with the cloud center. The processor module uses XILINX ZYNQ7020 as the main control chip.

[0069] 1.3 Intelligent processing subsystem

[0070] 1.3.1 Working principle of intelligent processing subsystem

[0071] The architecture of the Intelligent Machining Subsystem (IMS) is as follows: Figure 4As shown. In input layer I, modeling input is provided to IMS. Input layer I mainly includes bearing position and support stiffness and the size of ME. In addition, material properties are also used as input. In modeling layer I, the finite element model of the machine tool system (MTS) is established, and then the finite element equation of the machine tool system is established; the finite element model of the workpiece system is established, and the finite element equation is established; the machining process of the machine tool system is subjected to finite element analysis based on the created machine tool model and workpiece model. Decision layer I predicts the frequency response function (FRF) of the MTS at the tool tip based on the finite element analysis results, and the cutting stability is obtained based on the frequency response function (FRF) to evaluate the machining performance. If the machining performance is satisfactory, the machining process is kept unchanged; if the machining performance does not meet the requirements, corresponding measures need to be taken. For spindle designers, the goal is to design a spindle with reasonable dynamic stiffness to meet specific machining conditions. Therefore, parameters such as spindle structure and bearing preload will be optimized based on the evaluation results of machining performance. For spindle users, since the spindle design has been completed, it is impossible to change its structural parameters, and the machining performance of the existing spindle can be improved by optimizing cutting parameters.

[0072] 1.3.2 Intelligent Processing Computing Kernel

[0073] According to the structural parameters of the machine tool, a dynamic model of the spindle is established, and then a cutting process model is established according to the current process. The interaction between the spindle dynamic model and the cutting process model is studied to optimize the cutting parameters and achieve efficient processing. This embodiment establishes a dynamic model of the milling process, such as Figure 5 Specifically, the optimization method of cutting parameters is:

[0074] Differential equations of the milling dynamics model:

[0075]

[0076] Among them, m x 、c x and k x Respectively represent the mass, damping and stiffness in the X direction; m y 、c y and k y They represent the mass, damping and stiffness in the Y direction respectively; F xj and F yj represents the cutting force components along the X and Y directions on the jth tooth; F x (t) and F y (t) represents the cutting force along the X and Y directions;

[0077] The dynamic displacement in the cutting direction is:

[0078]

[0079] Where x and y represent dynamic displacement; Indicates the tooth rotation angle;

[0080] The window function is used to determine whether a tool tooth is in or out of cutting:

[0081]

[0082] in, and denote the cut-in angle and cut-out angle respectively;

[0083] The dynamic cutting thickness in the cutting direction is:

[0084]

[0085] Among them, f z Indicates the feed amount of each tooth; Δx = x j -x j-1 ; Δy=y j -y j-1 ;(x j ,y j ) and (x j-1 ,y j-1 ) represent j th Tooth and (j-1) th Dynamic displacement at the tooth; v 0 represents the initial position; v represents the dynamic displacement in the cutting direction; g j represents the cutting state of the jth tool tooth;

[0086] The cutting force of each cutting tooth in the cutting direction is:

[0087] F t =K t a p h

[0088] F r =K r F t

[0089] Among them, K t and K r represents the cutting force coefficient (CFC); a p and h represent cutting depth and cutting thickness respectively; F t Indicates tangential cutting force; F r represents radial cutting force;

[0090] The cutting force per tooth is:

[0091]

[0092] in, represents the tool pitch angle, express……; represents the tool pitch angle, and z represents the number of teeth;

[0093] The total cutting force is:

[0094]

[0095] Where N represents the number of teeth;

[0096] The total dynamic milling force is:

[0097]

[0098] in, Representation and Related dynamic milling force factor matrix; a p represents the depth of cut; and:

[0099]

[0100] Then the dynamic milling force in the time domain is:

[0101]

[0102] in, represents the dynamic displacement at time t; A(t) is a periodic function of the tool tooth passing angular frequency ω=NΩ; and:

[0103]

[0104] in, T represents the passing period and T=2π / ω; r represents the harmonic number at the passing angular frequency ω; i represents the imaginary unit;

[0105] Depending on the cutting conditions and the number of teeth involved in the cutting, the harmonic order r of the determined cutting frequency is reduced and is an exact reconstruction of A(t):

[0106]

[0107] Where N represents the number of tool teeth; For climb milling, For upward milling; R represents the tool radius; a represents the cutting depth; a e Indicates cutting width;

[0108] The directivity coefficient is expressed as:

[0109]

[0110] in, Indicates the tool rotation angle;

[0111] The dynamic milling force equation is expressed as:

[0112]

[0113] The frequency response function of the machine tool system is:

[0114]

[0115] Among them, G xx (iω), G yy (iω), G xy (iω) and G yx (iω) represents the frequency response function of the tool-workpiece system;

[0116] The vibration vector of the cutting cycle of the tool tooth at the current time t and the previous time tT is:

[0117] r = [x(t)y(t)] T

[0118] r 0 =[x(tT)y(tT)] T

[0119] Where r represents the vibration vector at time t; x(t) represents the vibration vector in the x direction at time t; y(t) represents the vibration vector in the y direction at time t; r 0 represents the vibration vector at time tT; x(tT) represents the vibration vector in the x direction at time tT; y(tT) represents the vibration vector in the y direction at time tT;

[0120] Using the harmonic function, the flutter frequency ω is obtained in the frequency domain c The vibration function is:

[0121]

[0122] Δ=[xx 0 yy 0 ] T After substitution, the regeneration displacement is obtained:

[0123]

[0124] Among them, ω c T represents the phase value of the vibration between subsequent tooth periods T; ω c represents the chatter frequency; F represents the cutting force;

[0125] The dynamic milling force equation is written as:

[0126]

[0127] When the determinant is 0, there exists a non - zero solution, that is:

[0128]

[0129] where I represents the identity matrix:

[0130]

[0131] The characteristic roots are expressed as:

[0132] det|I - ΛG 0 (iω c )| = 0

[0133] where G 0 (iω c ) represents the characteristic frequency function;

[0134] The eigenvalues are expressed as:

[0135]

[0136] For a given flutter frequency, cutting force coefficient K t and K r , the cutting limit angle is obtained:

[0137] For a given flutter frequency, cutting force coefficient K t and K r , cutting limit angle and as well as the frequency response function of the machining system; if the cross - frequency response function of the machine tool system is not considered, then:

[0138] G xy (iω c ) = 0

[0139] G yx (iω c ) = 0

[0140] The eigenvalues are obtained, and the eigenvalue equation is expressed as:

[0141] a 0 Λ 2 +a 1 Λ + 1 = 0

[0142] where a 0 = G xx (iω c )G yy (iω c )(α xx α yy -αxy α yx );a 1 =α xx G xx (iω c )+α yy G yy (iω c );

[0143] In order to analyze and determine the stability of the system and solve the eigenvalue equation, the characteristic root of the eigenvalue equation is in complex form:

[0144] Λ=Λ R +iΛ I

[0145] Among them, Λ R and Λ I denote the real and imaginary parts of the characteristic roots respectively;

[0146] According to Lyapunov's first-order approximate stability theorem, the stability criterion of the system is obtained: when Λ R <0, the system is stable; when Λ R >0, the system is unstable; when Λ R = 0, the system is in a critical state; according to Euler equation, the flutter frequency ω c The axial cutting depth under the critical condition of stable cutting is expressed as:

[0147]

[0148] Due to a plim is a real number in the actual cutting, and its imaginary part is 0. but:

[0149]

[0150] Then: c T=π-2Ψ+2kπ=ε+2kπ

[0151] Where Ψ represents the characteristic phase angle, and Ψ = arctanκ; ε represents the phase difference between internal and external modulation, ε = π-2Ψ; k represents the tooth chatter frequency; T represents the integer wave number of all chatter; then the spindle speed is expressed as: n = 60 / NT

[0152] Further we get:

[0153]

[0154] 1.4 Error Control Subsystem

[0155] 1.4.1 Working principle of the error control subsystem

[0156] Since thermal information is dynamic and real-time data, the real-time performance of ECS is very high. However, the training of the error model is very time-consuming, which makes traditional cloud-based systems unsuitable. In addition, prediction and feedback control should be real-time. In order to solve the above problems, this embodiment designs a powerful computing architecture that can efficiently transmit, store and process a large amount of temperature and error data in real time. The architecture consists of four layers, such as Figure 6 Table 1 lists the hardware, software, and corresponding functions of each layer. Directly importing and exporting the collected data from the cloud layer is time-consuming, and frequent data operations should not be performed on the cloud layer. Historical data should be imported into the cloud and used to train the proposed TF-IGLSTM model.

[0157] Table 1 System architecture components

[0158]

[0159] The input layer as a physical entity is the bottom layer of the entire architecture. Input layer II mainly completes data acquisition and conversion. Machine tools, tools, workpieces, sensors, acquisition systems and other components together constitute this layer. Sensors are used to collect temperature and error. At the same time, the real-time data collected by the sensor is transmitted to the decision layer II through the router EC-20-CE and the designed gateway for data cleaning and selection. In addition, historical error data will be transmitted to the control layer II for status monitoring and analysis.

[0160] Modeling layer II has a powerful cloud server and is a key component of the entire system. According to the characteristics of modeling layer II, this layer is used to implement the basic functions of the entire architecture. The cloud server model is SS100G-24S / R, and a large database is established to store the collected data. In addition, a database is established in modeling layer II for model training, and multiple GPUs (whose model is GeForce RTX 3080Ti12G) are used to speed up the training efficiency. Modeling layer II has abundant computing resources, and error mechanism modeling is also completed in the modeling layer. One of the most important tasks of modeling layer II is to train the hyperparameters of the proposed model, and then pass the updated hyperparameters of the TF-IGLSTM network to control layer II to ensure that the prediction accuracy of the system remains high after long-term operation. The continuous interaction between modeling layer II and control layer II and decision layer II ensures real-time performance.

[0161] Control layer II adopts a distributed architecture with very low computing latency, which can achieve low-latency service response. Under this architecture, control layer II is used for data cleaning and real-time prediction tasks, and control layer II uses a designed gateway with input variables for real-time control. FGPA is used for control layer II, and its model is Versal ACAP Virtex UltraScale&VU19P. The TF-IGLSTM network is embedded into FGPA to achieve real-time prediction, thereby reducing the computing pressure of the cloud layer and alleviating bandwidth limitations. Control layer II has low latency and fast response rate, and can undertake real-time control tasks. The prediction data is fed back to the PLC, and the controller reads the RAM of the PLC to superimpose the prediction data with the processing instructions. The feed drive system is then driven to drive the tool or workpiece to move in the opposite direction.

[0162] The error threshold is set in the decision layer II. Historical data, including thermal error and temperature, are used as training data. The updated parameters are sent to the control layer to ensure that the latest model is effective in the control layer II. If the predicted data is less than the threshold, the current TF-IGLSTM model is sufficient to maintain normal execution; otherwise, the TF-IGLSTM network is retrained and the data is used to determine whether the ME in the input layer II is faulty.

[0163] 1.4.2 Error Mechanism

[0164] The heat transfer model of the spindle is as follows: Figure 7 The one-dimensional heat transfer equation is

[0165]

[0166] Among them, λ, ρ, c, h, d 0 , x and t represent conductivity, density, specific heat, convection coefficient, diameter, axial position and time respectively; u(x,t) represents temperature; u 0 Indicates the ambient temperature.

[0167] The non-stationary heating process is mainly characterized by rapid heating, and its internal heat transfer efficiency plays a dominant role. Therefore, ignoring the heat transfer term, the heat transfer equation becomes:

[0168]

[0169] The initial condition is: u(x,0)=u 0

[0170] The temperature response of a single heat source is as follows:

[0171]

[0172] Thermal elongation is expressed as:

[0173]

[0174] Wherein, L represents the length; α represents the thermal expansion coefficient;

[0175] The thermal expansion at Δt and 2Δt is:

[0176]

[0177] The thermal expansion at time kΔt is:

[0178]

[0179] but:

[0180] It can be seen that the thermal error shows nonlinearity in the time domain, and the thermal elongation error at the moment ΔL(kΔt) is closely related to the thermal errors at the moments before ΔL((k-1)Δt)…, ΔL(2Δt) and ΔL(Δt). This reveals the characteristics of memory. Therefore, it is necessary to choose a model that characterizes its memory characteristics.

[0181] 1.4.3TF-IGLSTM Thermal Error Prediction Model

[0182] like Figure 8 As shown, the TF-IGLSTM thermal error prediction model of this embodiment includes a data input layer, a Transformer encoder block, an IGLSTM module, a linear layer and a data output layer which are arranged in sequence.

[0183] (1)IGLSTM module

[0184] RNN has storage capacity and can be used to process serial and time series data. LSTM is a variant of RNN and inherits the storage capacity of RNN. LSTM processes current and historical information through the joint operation of three gates. Therefore, excellent performance is achieved when processing long sequence data. The error includes long-term change trends and short-term transient change trends. The long-term change trend is caused by the continuous temperature increase during operation. The transient change trend is caused by environmental noise. The resulting model needs to have a reasonable understanding of the long-term and short-term information of the thermal error. LSTM model such as Fig. 9 As shown. The state of each gate is controlled by training the parameter matrix of each gate with gradient descent. The forget gate is one of the most important gates in LSTM, which is used to judge the importance of information and assign corresponding weights to the information. The principle of traditional LSTM is:

[0185] f t =σ(W f [h t-1 ,x t ]+b f)

[0186] i t =σ(W i [h t-1 ,x t ]+b i )

[0187]

[0188] o t =σ(W o [h t-1 ,x t ]+b o )

[0189]

[0190] h t =o t ·tanh(c t )

[0191] Among them, x t 、h t-1 、c t-1 , c t and h t They represent the input at time t, the output at time t-1, the unit state at time t-1, the state to be updated, the unit state at time t, and the output at time t respectively; f t 、i t and t represents three information processing gates; σ and represent the sigmoid function and tanh function respectively; W f , W i , W o and W c represents the weight matrix; b f 、b i 、b o and b c Represents the bias matrix. The parameters of the weight and bias matrices are automatically updated during the training process.

[0192] Fig.10 In the IGLSTM structure designed for this embodiment, the forget gate and the input gate are integrated into a new gate, which no longer learns the information to be forgotten and the new input information separately, thereby reducing the number of parameters to be learned. In addition, the design of this gate is to make the processing of unit information more intensive and orderly while selecting the unit information to be forgotten and updated. In order to improve the training efficiency, IGLSTM further integrates the input information x at the current moment t With h t It adopts the same tSimilar update mechanisms enable the model to focus on the information of the previous moment, thereby further enhancing the short-term memory behavior. Therefore, the IGLSTM proposed in this embodiment is more suitable for describing the error mechanism than the traditional LSTM. The results show that the IGLSTM improves the short-term memory capacity of the traditional LSTM without increasing the model learning parameters. The IGLSTM module includes several IGLSTM units connected in series, and the principle of the IGLSTM unit is:

[0193]

[0194] i t =σ(W i [h t-1 ,x t ]+b i )

[0195]

[0196] m t =σ(W m [h t-1 ,x t ]+b m )

[0197]

[0198] Among them, x t , h t-1 、c t-1 , c t and h t Respectively represent the input at time t, the weighted input at time t, the output at time t-1, the unit state at time t-1, the unit state to be updated at time t, the unit state at time t, and the output at time t; i t and m t Respectively represent the input gate and output gate; W, W i , W c and W m Represents the weight matrices of input variables, input gate variables, unit states, and output variables respectively; b i 、b c and b m denote the bias matrices of input variables, unit states, and output variables, respectively; σ and tanh denote the sigmoid function and tanh function, respectively; · denotes the product operator.

[0199] (2) Transformer encoder block

[0200] The Transformer encoder block includes a multi-head attention layer, a connection layer, an Add&Norm layer I, an FFN layer, and an Add&Norm layer II. A linear module for linearly projecting the input data is provided between the multi-head attention layer and the data input layer.

[0201] Specifically, the encoder block of the Transformer is used to extract and enhance long-term trends and short-term features. The Transformer model consists of an attention structure that achieves parallel computation by using a self-attention mechanism. Fig.11 As shown in Figure 2, the encoder of the Transformer usually consists of a deep network structure with multiple identical encoder blocks. The network is optimized using multi-head self-attention layers and fully connected feed-forward layers with residual connections and normalization.

[0202] The multi-head attention layer is formed by combining multiple self-attention layers. The principle of the self-attention layer is:

[0203]

[0204] Among them, q, k, and v represent matrices obtained by linear transformation of input variables; softmax represents the activation function used as output node; d k Represents the dimension of the kth vector.

[0205] In order to learn features without additional calculations, the above three vectors of q, k and v are projected into multiple dimensions through different linear transformations, different features are obtained independently in each dimension, and the results are connected to obtain the final result. The connection layer is used to splice the outputs of multiple self-attention layers together. The principle is:

[0206] MultiHead(q,k,v)=Concat(head 1 ,…,head n )·W

[0207] head i =Attention(qW i q ,kW i k ,vW i v )

[0208] Among them, head i represents the output of the i-th self-attention layer; W i q , W i k and W i v represents the weight matrix; W represents the weight matrix corresponding to the output.

[0209] The Add&Norm layer consists of two parts. The existence of the residual connection structure prevents the problem of gradient disappearance and network degradation. The function of the normalization layer is to calculate the mean and variance of samples of different channels, which is also called the normalization operation. When the network is optimized using gradient descent, it ensures the stability of the uniform distribution of data features, thereby speeding up the convergence process. This embodiment combines the Transformer encoder block with the IGLSTM module to construct a new TF-IGLSTM model. The IGLSTM module is connected to the encoder block of the Transformer and then connected to the linear layer as the output layer.

[0210] The modeling process of the TF-IGLSTM model is as follows:

[0211] Step 1: Filter the raw data to obtain smooth temperature and thermal error curves while eliminating noise;

[0212] Step 2: Use the filtered temperature and error variables as input information, and use the Transformer module to extract the spatial feature extractor to mine and enhance the global and local features hidden in the input information to obtain enhanced data;

[0213] Step 3: Input the enhanced data into the IGLSTM module to express the nonlinear, time-varying and non-steady-state characteristics of thermal error;

[0214] Step 4: Use linear layer processing to obtain output data.

[0215] The feature extraction and enhancement capabilities of Transformer can improve the convergence speed, and the capabilities of Transformer are combined with the representation capabilities of IGLSTM in the time domain to achieve high prediction accuracy. The model is trained using supervised learning methods. The time complexity and number of parameters of each part of the model are shown in Table 2.

[0216] Table 2 Complexity of each module

[0217]

[0218] Where h, D, and n represent the number of head size, neurons, and input features, respectively.

[0219] 2. Case Study

[0220] 2.1 Optimization of high-speed milling processing parameters

[0221] 2.1.1 Input Layer I

[0222] At present, researchers still rely on trial cutting methods, and overly conservative cutting parameters limit the processing performance and production efficiency of processing equipment. The fundamental purpose of intelligent processing is to improve the processing efficiency and quality of parts and reduce the scrap rate. The structure of the processed parts is as follows: Fig.12 As shown in the figure, the material of the part to be processed is titanium alloy Ti600, and the part has features such as end face, cylindrical surface and top surface. The processing is carried out on the milling machine VMC850D.

[0223] Fig.13 The structure of the spindle WZ15B90-30SE used in VMC850D is shown. It is a mechanical spindle with a rated speed of 8000rpm. Belt drive is used to drive the spindle, and the supporting bearing model is 7014CTYNSULP4. The overall back-to-back configuration is used for positioning preload, the grease type is NSK MTE, the cooling water is not passed, and the vibration displacement sensor and thermal sensor are also installed inside the spindle. Rough milling and fine milling processes are used to machine the parts, using a carbide spiral end mill. The unoptimized cutting parameters are shown in Table 3.

[0224] Table 3 Unoptimized cutting parameters

[0225]

[0226] 2.1.2 Modeling Layer I

[0227] The MTS model and cutting process model were established. For ease of application, a user interface was developed using Visual C++ to visualize the finite element modeling process. The rough milling and fine milling processes were analyzed and an integrated model was established. The FRF was calculated using the integrated model. and cutting angle Determined according to the milling method, tool diameter and radial cutting depth. Then the cutting force coefficient (CFC) is calculated. It is determined by the average cutting force of the full gear milling experiment. That is, K is obtained by linear regression tc , K rc , K te and K re Table 4 lists the calculated CFC for coarse and fine grinding.

[0228] Table 4 Cutting force coefficient

[0229]

[0230] Based on CFC and and The cutting angle and cutting angle of the directional milling coefficient matrix A(0) are calculated, and the transfer function matrix is ​​obtained by using the integral model:

[0231]

[0232] 2.1.3 Decision-making level I

[0233] Fig.14 Shows G xx , G yy and G xy The FRFs of the tool tip are obtained by using the MTS model for the rough and fine milling processes. It is found that the system stiffness decreases with increasing rotational speed, which leads to a decrease in the natural frequency. In addition, the FRF of the tool tip will move toward the low frequency direction. Fig.14 (a) and 14(b). Fig.14 (c) shows that due to the gyroscopic torque, the cross FRF G xy .

[0234] When the transfer function matrix Φ(iω,Ω) is obtained, the chatter stability region calculation method is used to calculate the chatter stability lobe diagrams for rough milling and fine milling processes, such as Fig.15 As shown. In the spindle speed range of 0 to 20,000 r / min, for rough milling, the most ideal processing area is the lobe near the spindle speed n = 5950 r / min, and the maximum axial stable cutting depth a plim Reach 8.7mm. For fine milling, the ideal spindle speed for machining convex angles is 5560r / min, and the maximum stable cutting depth is a plim It is 6.7mm.

[0235] 2.1.4 Control Layer I

[0236] According to the lobe diagram of chatter stability, considering the maximum output power, the spindle speed and axial cutting depth are optimized. The optimized parameters are listed in Table 5. For rough milling, the optimized spindle speed reaches 5950r / min, the axial cutting depth increases to 8.0mm, and the processing efficiency is improved by about 167% after optimization. For fine milling, the spindle speed increases from 3500r / min to 5500r / min, and the axial cutting depth increases from 2.0mm to 6.0mm, and the processing efficiency is improved by 200%.

[0237] Table 5 Cutting parameter optimization

[0238]

[0239] Optimized cutting parameters are used for machining, such as Fig.16 As shown in the figure. The machining process is monitored in real time, the cutting force signal is collected by Kistler 9257B, and the vibration signal is collected by the acceleration sensor on the spindle box. Then the fault feature extraction is performed on the collected working condition signal, and no abnormal state is found, indicating that the IMS machining parameter optimization is effective. The part size meets the standard, and the surface quality meets the requirement of roughness Ra<3.2μm.

[0240] 2.2 Thermal error control in profile gear grinding

[0241] 2.2.1 Input Layer II

[0242] The experimental platform is the high-speed spindle of the YK73200 tooth profile grinder, with a maximum speed of 9000r / min. Fig.17 As shown. The measurement system is used to measure the temperature and thermal error simultaneously. The temperature is obtained by the temperature sensors T1 to T11. The installation positions of the temperature and error sensors are shown in Table 6. The thermal error is obtained by the displacement sensors S1 to S5. The five-point method is used, such as Fig.18 As shown in Figure 2, the axial thermal extension is obtained by S5. The thermal yaw angle is measured by S1 and S3, and the thermal pitch angle is measured by S2 and S4.

[0243] In order to obtain realistic experimental results, the actual operating conditions were simulated. Acceleration and deceleration processes are common phenomena in the grinding process. Fig.19 Two working conditions are shown, condition 1 is random speed change, condition 2 is acceleration and deceleration change. The data is sampled once per second, and 10,000 data points can be obtained for each temperature and error. The collected signal is inevitably accompanied by noise, which is a serious interference. Therefore, A / D conversion is performed first, and then data preprocessing is considered. After removing high-frequency noise, such as Fig. 20 Under working condition 1, the temperature change obtained from the temperature sensor is as follows Fig. 20 As shown in (a), the thermal error is Fig. 20 As shown in (c). Fig.19 (a) shows an overall increase and subsequent decrease in the speed of operating condition 1. In addition, there is also an increase and decrease process in each cycle. From the collected temperature data, the overall trend of each temperature is also to increase first and then decrease. The temperature also shows an increase and decrease fluctuation in each cycle, which is consistent with the change in speed.

[0244] Under condition 2, the collected temperature changes as Fig. 20 As shown in (b), the thermal error is Fig. 20 As shown in (d). For operating condition 2, the increasing and subsequent decreasing trends of the speed distribution are obvious. As the operating time passes, the temperature increases and then slowly decreases, which reflects the change in speed. As the speed increases, the temperature increases. As the speed decreases, the temperature also decreases. It was found that the thermal error does not decrease significantly with the decrease in temperature, which further verifies the memory behavior shown in Section 1.4.2. From the historical thermal errors obtained, it is easy to find that the thermal error has dynamic and nonlinear characteristics. The thermal error is not prone to sudden changes because it is a historically related time series data and its changes are closely related to historical information. The collected data also verifies the thermal error memory behavior shown in Section 1.4.2.

[0245] 2.2.2 Modeling Layer II

[0246] The temperature and error data under working condition 1 are used as training data. The TF-IGLSTM model is built in the PyTorch architecture, the integrated development environment is PyCharm, and it is used under Intel(R) CORE(TM) i7-10700GPU@2.90GHz. Table 7 lists the model parameters. In order to save training time, only one encoder module is used to build the TF-IGLSTM model. The more attention heads in the transformer module, the stronger its ability to extract local and global features. The advantage is that the convergence speed is significantly improved. Therefore, the number of attention heads in the transformer module is 8. In order to further illustrate the feasibility of using the TF-IGLSTM network model, several different deep learning models are built, including LSTM, IGLSTM and TF-LSTM. To ensure the fairness of the comparison, the principle of the control variable method is adopted. That is, the parameters of LSTM, IGLSTM and TF-LSTM are the same as those of the TF-IGLSTM network model. LSSVM is a traditional and commonly used method for building error models, and it has excellent performance in nonlinear feature extraction. Therefore, it is selected as the traditional model for comparison, with the input variables being T1, T5, T6, T7, and T10, and the output being the axial thermal error.

[0247] Table 7 Model parameters

[0248]

[0249] There are three indicators that constitute the evaluation system of the error model to evaluate the fitting and prediction performance of the TF-IGLSTM network. The smaller these three indicators are, the higher the fitting and prediction accuracy is.

[0250]

[0251] Where N represents the statistical number; y i Indicates actual value; Represents the predicted value.

[0252] First, this embodiment constructs a TF-IGLSTM model, and the input temperature variables are selected from T1 to T11. Then the three selected temperature variables and thermal error are used as input features, the time step is set to 1, and the learning rate is set to 0.0005. During the training process, the role of the optimizer is to update the model parameters so as to minimize the loss function. During the optimization process, different optimizers are compared to select the most suitable optimizer. Fig.21The loss functions of the proposed model with five optimizers are shown. It is clear that the optimizer has a great impact on the loss. The loss curve of the stochastic gradient descent model (SGD) is difficult to converge, which shows that SGD is not suitable as an optimizer. The weight decay TF-IGLSTM model with adaptive momentum estimation (AdamW) has the smallest initial loss and the fastest convergence speed. In addition, this model achieves the best training efficiency. The adaptive gradient (AdaGrad) has the largest initial loss and the slowest convergence speed. It is found that if the model converges, the optimizer has little effect on the loss. Therefore, AdamW is selected to achieve the best performance. In the following comparison, AdamW is used as the optimizer.

[0253] The batch size setting has a great impact on the training speed and accuracy. This example studies the impact of batch size on model accuracy. If the batch size is too small and the amount of data is large enough, the training will be insufficient and the expected effect cannot be achieved. As the batch size increases, the training effect will first reach the optimal value and then gradually deteriorate. The training results are shown in Figure 2. Fig. 22 The results are consistent with the above statements. As the batch size increases, the model convergence becomes weaker and the model accuracy decreases significantly. When the batch size is 200, the convergence time is the shortest and the prediction performance is the best. Considering the amount of data collected when the batch size is less than 200, the training time is too long. Therefore, the batch size is taken as 200.

[0254] 2.2.3 Decision-making layer II

[0255] The data collected under processing condition 1 is used as fitting data. The preprocessed data can reflect the true error magnitude. Temperature and axial error are used as input variables, and then the TF-IGLSTM model is trained. The loss curves of LSTM, IGLSTM, TF-LSTM, and TF-IGLSTM models are obtained, as shown in Fig.23 (a) shown. Fig.23 The fitting curves in (b) show that the LSSVM, LSTM, IGLSTM, TF-LSTM, and TF-IGLSTM models fit the measured data well. This also shows that both the traditional model and the deep learning model can achieve good fitting performance. From a macroscopic perspective, both of the above models meet the fitting requirements. However, from the perspective of local magnification details, the traditional LSSVM model has no transformation turning point and cannot accurately reflect the thermal error, so the four deep learning models can achieve accurate expression of the transformation turning point.

[0256] The fitting accuracy of LSSVM, LSTM, IGLSTM, TF-LSTM and TF-IGLSTM is above 98%, as shown in Table 8. The MAE, MSE and RMSE of each model are relatively small, which shows that the traditional LSSVM model with temperature variables as input and the LSTM-based deep learning model with multiple factors as input have good fitting ability. The MAE, MSE and RMSE of the TF-IGLSTM algorithm model are the smallest, indicating that the TF-IGLST algorithm has the most outstanding fitting accuracy among the above models, and then the advantages of the proposed model are reflected by the evaluation indicators. In addition, the TF-IGLSTM and TF-LSTM models converge fastest during the fitting process, and their convergence points are reached when the number of iterations is 3 and 5 respectively. The convergence points of the IGLSTM and LSTM models appear when the number of iterations is 35 and 48 respectively. It can be seen that the training speed of the model without the transformer module is significantly lower than that of the model with this module. This verifies the effectiveness of the transformer-based design. As shown in Section 1.4.3, the designed transformer module can effectively extract multi-dimensional features due to its multi-head attention, and the captured features contain both global and local features. Then the convergence of the model is improved.

[0257] The fitting accuracy of IGLSTM and LSTM is 99.38% and 98.39% respectively. The loss curves of the above two models also show that the former has stronger convergence ability than the latter. Therefore, the advantage of IGLSTM in convergence is proved. The introduction of the attention mechanism based on LSTM enhances the attention to the information of the previous moment. IGLSTM integrates forgetting and input gates, highlighting the long-term change memory, thereby strengthening the connection between input and forgetting information. The number of parameters of IGLSTM has not increased, and m is the output h t This further shows that the improvement of IGLSTM over traditional LSTM is reasonable and effective, and the design of IGLSTM is consistent with the characterization and modeling of memory behavior.

[0258] Table 8 Fitting results evaluation

[0259]

[0260] The data under working condition 2 is used for model prediction. Fig.24The prediction results are shown. The prediction performance of the TF-IGLSTM model is better than that of the other four models. The design of the TF-IGLSTM model takes into account the error mechanism, that is, the strong correlation of short-term memory is reflected and the short-term memory is enhanced. In addition, the model also takes into account the auxiliary characteristics of the temperature variable, which improves the robustness and prediction accuracy. The IGLSTM layer in the model completes the in-depth description of the nonlinear, time-varying and non-steady-state characteristics of the thermal error, enabling it to learn the above characteristics. Due to the explicit representation of memory information, the TF-IGLSTM model outperforms the TF-LSTM model in terms of prediction performance. In the TF-IGLSTM model, the processing of forgetting and input information is reasonable, and both short-term and long-term memory are considered.

[0261] The results show that the Transformer module plays a good role in model convergence and verify the effectiveness of using Transformer for feature extraction and improving model convergence. The LSSVM model is prone to overfitting during training, showing good fitting performance but insufficient generalization ability. Compared with other models, it has the worst prediction accuracy and the lowest robustness. The LSTM model will have slight overfitting and memory behavior. Fig.24 At the beginning of the prediction, the performance of LSTM is relatively poor, and then the predicted data deviates seriously from the true value. The prediction performance gradually improves and is generally better than the traditional LSSVM model. This comparison also means that the LSSVM model with temperature variables as input cannot reflect the memory behavior, so a good fitting performance is obtained for condition 1 and a poor prediction performance is obtained for condition 2. The TF-IGLSTM model has good fitting and prediction performance. This once again proves that the model with memory behavior can well describe the thermal error.

[0262] The prediction performance indicators are shown in Table 9. The prediction accuracy of LSSVM is 76.5%, the lowest among all models, and its RMSE, MAE and MSE are the highest among all models. The TF-IGLSTM network has the highest prediction accuracy of 99.45%, and the RMSE, MAE and MSE are 0.15, 0.13 and 0.02 respectively. The input of the TF-IGLSTM model is the time series data of error and temperature. Using error and temperature data as input variables has perfect robustness. Therefore, the TF-IGLSTM model is the most suitable model to characterize the error mechanism.

[0263] Table 9 Prediction performance evaluation

[0264]

[0265] 2.2.4 Control Layer II

[0266] Fig.25(a) shows that the bed and turntable are warped, and the column is thermally bent, resulting in relative thermal deformation in the X direction. In addition, the spindle is thermally elongated, resulting in relative thermal deformation in the Y direction. Fig.25 (b) shows the thermal deformation and the resulting relative position error. Hαl (Δx T ,Δy T ) and f Hαr (Δx T ,Δy T ) is:

[0267]

[0268] Among them, k x and k y Represents the proportionality factor.

[0269]

[0270] in, Indicates the installation angle; Δx wT , Δy wT , Δx gT and Δy gT Relative position error.

[0271] Gear grinding process Fig.26 As shown. The gear to be processed has 60 teeth, a module of 25, and a tooth thickness of 200 mm. The maximum diameter of the grinding wheel is 400 mm. The rotation of the C axis puts the tooth groove in the predetermined position, and the vertical feed of the Z axis realizes the cutting along the tooth groove direction. During this process, the X, Y, A, and C axes always maintain a theoretical locking state. The processing of each tooth is fed four times along the tooth groove direction of the Z axis. In addition, two rough grindings and two fine grindings realize the processing of the gear. During the grinding process, ECS is performed and thermal errors are controlled.

[0272] Gear measurement report Fig. 27 As shown. Through error control, the f of the left and right tooth surfaces Hαl and f Hαr The maximum values ​​decreased from 17.4μm to 5.4μm and from 17.9μm to 5.8μm, respectively. αl and F αr The maximum values ​​of f decreased from 18.9μm to 6.1μm and from 18.2μm to 5.8μm, respectively. fαl and f fαr The maximum values ​​of decrease from 19.6μm to 16.8μm and from 18.3μm to 16.9μm respectively.

[0273] 3. Conclusion

[0274] In order to achieve high-quality processing, ME's IMECA was built for Industry 4.0. The working principle of IMECA was analyzed by dividing the layers of IMECA. Then the architecture was divided into PF / EG, IMS and ECS. The implementation process of PF / EG, IMS and ECS was analyzed. The conclusions are as follows:

[0275] (1) IMECA was designed, and the implementation of PF / EG, IMS and ECS was studied. Finally, IMECA was applied to engineering practice. The effectiveness and practicality of the method were verified from the perspectives of milling processing parameter optimization and error control. The application results show that the designed system can achieve the optimization of high-speed milling processing parameters and greatly improve the processing efficiency. The error control of the gear profile grinder can effectively improve the geometric accuracy of the tooth surface, thereby ensuring the reliability of the intelligent processing process.

[0276] (2) An improvement plan is proposed from the perspective of data storage, processing, and transmission modes, and then the computing and storage tasks originally undertaken by the data center are allocated to locations close to the data source. In addition, the rationality and feasibility of using WSN gateway nodes for edge computing are analyzed. A design method for an edge computing intelligent gateway is proposed. Finally, the intelligent gateway and ZigBee wireless sensor network are used for data collection and reprocessing.

[0277] (3) The working principle of IMS was analyzed. IMS then simulated the machining process from the positive direction and gave the optimized cutting parameters from a theoretical perspective. IMS is a typical closed-loop system. The input of IMS is the structural parameters and cutting parameters. The finite element model of MTS and the cutting process was established, and the two models were integrated. Using the integrated model, the FRF of the tool tip was predicted. On this basis, the cutting stability was predicted.

[0278] (4) The working principle of ECS was analyzed. In the input layer, thermal information was collected. In the modeling layer, the TF-IGLSTM model was constructed to perform data fitting and model adjustment. Then the error control model was established. The position error and the tooth profile inclination deviation are proportional. Finally, the linear superposition principle was proposed, and the movement position of the X-axis and Y-axis was adjusted according to the relative position error to realize the control of the tooth profile inclination deviation, thereby effectively improving the overall processing accuracy of the tooth surface.

[0279] (5) The demonstration of historical data dependence provides guidance for the design of thermal error models. In addition, nonlinear, time-varying, and non-steady-state behaviors are demonstrated. The IGLSTM model is proposed based on LSTM and attention mechanism, and it has extraordinary advantages in characterizing the memory behavior of thermal errors compared with traditional LSTM. In order to improve the training efficiency, IGLSTM and Transformer are combined to propose a new TF-IGLSTM network. The Transformer module improves the convergence speed during training and uses its powerful feature extraction ability to achieve efficient prediction and avoid overfitting. IGLSTM achieves deep expression of long-term and short-term information in thermal data. In addition, temperature and error data are used as input, which is very different from previous studies. The geometric error of the tooth surface is reduced through error control.

[0280] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A TF-IGLSTM thermal error prediction model, characterized in that: it includes a data input layer, a Transformer encoder block, an IGLSTM module, a linear layer, and a data output layer arranged in sequence; the Transformer encoder block includes a multi-head attention layer, a connection layer, an Add&Norm layer Ⅰ, an FFN layer, and an Add&Norm layer Ⅱ, and a linear module for performing a linear transformation on the input data is provided between the multi-head attention layer and the data input layer; the IGLSTM module includes a number of IGLSTM units connected in series, and the principle of the IGLSTM unit is: i t = σ(W i [h t-1 , x t + b i ) m t = σ(W m [h t-1 , x t + b m ) Among them, x t 、 h t-1 、c t-1 、 c t and h t respectively represent the input at time t, the weighted input at time t, the output at time t - 1, the cell state at time t - 1, the cell state to be updated at time t, the cell state at time t, and the output at time t; i t and m t respectively represent the input gate and the output gate; W, W i 、W c and W m respectively represent the weight matrices of the input variable, the input gate variable, the cell state, and the output variable; b i 、b c and b m respectively represent the bias matrices of the input variable, the cell state, and the output variable; σ and tanh respectively represent the sigmoid function and the tanh function; · represents the product operator.

2. The TF-IGLSTM thermal error prediction model according to claim 1, characterized in that: the multi-head attention layer is formed by combining multiple self-attention layers, and the principle of the self-attention layer is: where q, k, and v represent matrices obtained by linear transformation of input variables; softmax represents the activation function used as the output node; d k represents the dimension of the k-th vector.

3. The TF-IGLSTM thermal error prediction model according to claim 2, characterized in that: the connection layer is used to splice the outputs of multiple self-attention layers together, and its principle is: MultiHead(q,k,v) = Concat(head 1 , …, head n ) · W head i = Attention(qW i q ,kW i k ,vW i v ) Among them, head i represents the output of the i-th self-attention layer; W i q , W i k and W i v represent weighted matrices; W represents the weight matrix corresponding to the output.

4. An intelligent processing and error control system, characterized in that: it includes a process flow / processing equipment group, an intelligent processing subsystem, and an error control subsystem; the process flow / processing equipment group includes a collection node for collecting data, an edge node for processing data, and a cloud center for storing data, and a data transmission system is provided between the collection node and the edge node and between the edge node and the cloud center; the intelligent processing subsystem includes an input layer Ⅰ, a modeling layer Ⅰ, a decision-making layer Ⅰ, and a control layer Ⅰ; the intelligent processing subsystem creates a finite element model and finite element equations of the machine tool system and a finite element model and finite element equations of the workpiece system in the modeling layer Ⅰ to perform finite element analysis on the machine tool processing process, and predicts the frequency response function at the tool tip according to the finite element analysis results and the real-time machining data of the machine tool in the decision-making layer Ⅰ, and evaluates the machining performance at the same time, and makes the machine tool process according to the set cutting parameters through the control layer Ⅰ; the error control subsystem includes an input layer Ⅱ, a modeling layer Ⅱ, a decision-making layer Ⅱ, and a control layer Ⅱ; the error control subsystem creates a TF-IGLSTM thermal error prediction model as described in any one of claims 1-3 in the modeling layer Ⅱ, and trains the TF-IGLSTM thermal error prediction model using historical thermal error data in the modeling layer Ⅱ, and transmits the trained TF-IGLSTM thermal error prediction model to the control layer Ⅱ to update the parameters of the TF-IGLSTM thermal error prediction model in the control layer Ⅱ, and performs real-time prediction of the machine tool thermal error according to the real-time thermal error data input by the input layer in the control layer Ⅱ, and controls the machine tool to compensate for the thermal error after obtaining the thermal error prediction data; the decision-making layer Ⅱ compares the real-time thermal error data input by the input layer with a set threshold, and if the reason for the real-time thermal error exceeding the set threshold is a machine tool failure, the machine tool is shut down; If the reason for the real-time thermal error exceeding the set threshold is the decline in the prediction accuracy of the TF-IGLSTM thermal error prediction model, the TF-IGLSTM thermal error prediction model is retrained through Modeling Layer II.

5. The intelligent machining and error control system according to claim 4, characterized in that: An intelligent network gateway node is provided inside the edge node. The intelligent network gateway node includes a processor module, a ZigBee communication module, a WIFI communication module, and a power management module. The ZigBee communication module is used to communicate with each data acquisition node of the data acquisition system, and the WIFI communication module is used to exchange information with the cloud center. The XILINX ZYNQ7020 is used as the main control chip inside the processor module.

6. The intelligent machining and error control system according to claim 4, characterized in that: The Decision-making Layer I predicts the frequency response function at the tool tip based on the finite element analysis results of the Modeling Layer and evaluates the machining performance; if the machining performance meets the requirements, the existing cutting parameters remain unchanged; if the machining performance does not meet the requirements, the cutting parameters are optimized.

7. The intelligent machining and error control system according to claim 6, characterized in that: The optimization method of the cutting parameters is as follows: Differential equation of the milling dynamics model: Among them, m x , c x and k x respectively represent the mass, damping, and stiffness in the X direction; m y , c y and k y respectively represent the mass, damping, and stiffness in the Y direction; F xj and F yj represent the cutting force components in the X and Y directions on the j-th tooth; F x (t) and F y (t) represent the cutting forces in the X and Y directions; Dynamic displacement in the cutting direction: where x and y represent dynamic displacements; represents the rotational angle of the j-th tooth; The window function is used to determine whether the tool tooth is in cutting or out of cutting: Among them, and respectively represent the cutting-in angle and the cutting-out angle; Dynamic cutting thickness in the cutting direction: where, f z represents the feed per tooth; Δx = x j - x j-1 ; Δy = y j - y j-1 ; (x j , y j ) and (x j-1 , y j-1 ) represent the dynamic displacements at the j-th tooth and the (j - 1)-th tooth respectively; v 0 represents the initial position; v represents the dynamic displacement in the cutting direction; g j represents the cutting state of the j-th tool tooth; Cutting force of each cutting tooth in the cutting direction: F t = K t a p h F r = K r F t where K t and K r represent the cutting force coefficients (CFCs); a p and h represent the cutting depth and the cutting thickness, respectively; F t represents the tangential cutting force; F r represents the radial cutting force; Cutting force of each tooth: Among them, represents the angular position of each tooth; represents the pitch angle of the tool, and z represents the number of teeth; Total cutting force: where N represents the number of teeth; Then the total dynamic milling force is: Among them, represents the dynamic milling force factor matrix related to ; a p represents the cutting depth; and: Then the dynamic milling force in the time domain is: Among them, represents the dynamic displacement at time t; A(t) is a periodic function of the tool tooth passing angular frequency ω = NΩ; and: Among them, T represents the passing period and T = 2π / ω; r represents the harmonic number at the angular frequency ω; i represents the imaginary unit; According to the cutting conditions and the number of teeth involved in cutting, the harmonic order r of the determined cutting frequency is reduced and is an exact reconstruction of A(t): Among them, N represents the number of teeth of the cutter; for climb milling, for up milling; R represents the cutter radius; a represents the cutting depth; a e represents the cutting width; The direction coefficient is expressed as: Among them, represents the rotational angle of the cutting tool; The dynamic milling force equation is expressed as: Frequency response function of the machine tool system: Among them, G xx (iω), G yy (iω), G xy (iω) and G yx (iω) represent the frequency response functions of the tool-workpiece system; Vibration vectors of the cutting cycles of the tool teeth at the current time t and the previous time t-T: r = [x(t) y(t)] T r 0 = [x(t - T) y(t - T)] T where r represents the vibration vector at time t; x(t) represents the vibration vector in the x direction at time t; y(t) represents the vibration vector in the y direction at time t; r 0 represents the vibration vector at time t-T; x(t-T) represents the vibration vector in the x direction at time t-T; y(t-T) represents the vibration vector in the y direction at time t-T; Obtain the vibration function at the flutter frequency ω in the frequency domain using harmonic functions c as follows: Substitute Δ = [x - x 0 y - y 0 T to obtain the regeneration displacement volume: where ω c T represents the phase value of the vibration between subsequent tooth cycles T; ω c represents the chatter frequency; F represents the cutting force; Write the dynamic milling force equation as: When the determinant is 0, there is a non-zero solution, that is: where I represents the identity matrix: The characteristic root is expressed as: det|I - ΛG 0 (iω c )| = 0 Among them, G 0 (iω c ) represents the characteristic frequency function; The eigenvalue is expressed as: For a given flutter frequency and cutting force coefficient K t and K r , the cutting limit angle is obtained as follows: For a given flutter frequency and cutting force coefficient K t and K r , cutting limit angle and and the frequency response function of the machining system; if the cross-frequency response function of the machine tool system is not considered, then: G xy (iω c ) = 0 G yx (iω c ) = 0 Get the eigenvalue, and the eigenvalue equation is expressed as: a 0 Λ 2 +a 1 Λ + 1 = 0 where a 0 = G xx (iω c )G yy (iω c )(α xx α yy -α xy α yx ) ; a 1 = α xx G xx (iω c )+α yy G yy (iω c ) ; To analyze and judge the stability of the system and solve the eigenvalue equation, the characteristic roots of the eigenvalue equation are in complex form: Λ = Λ R +iΛ I where, Λ R and Λ I represent the real part and the imaginary part of the characteristic root, respectively; According to Lyapunov's first-order approximation stability criterion theorem, the stability criterion of the system is obtained: when Λ R < 0, the system is stable; when Λ R > 0, the system is unstable; when Λ R = 0, the system is in a critical state; According to 's Euler equation, the flutter frequency ω c The axial cutting depth under the stable cutting critical condition is expressed as: Since a plim is a real number in actual cutting with an imaginary part of 0, let Then: Then: ω c T = π - 2Ψ + 2kπ = ε + 2kπ where Ψ represents the characteristic phase angle, and Ψ = arctanκ; ε represents the phase difference between internal and external modulation, ε = π - 2Ψ; k represents the tooth chatter frequency; T represents the integer wave number of all chattering; then the spindle speed is expressed as: n = 60 / NT. Further obtain:

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