Friction torque prediction method based on deep learning

Abstract

The invention discloses a friction torque prediction method based on deep learning, and belongs to the technical field of intelligent manufacturing and machining, and the method comprises the following steps: analyzing the kinematic characteristics of the overall structure of a numerical control machine tool machining center, and describing the dynamic response characteristics of a servo motor by combining the milling process of a numerical control machine tool and referring to a classical Stribeck friction model; the method comprises the following steps: respectively constructing system dynamic models related to X and Y feed axes, determining a dynamic relationship between excitation and response under the action of time-varying disturbance, solving the problems of nonlinear dynamic system modeling and parameter identification under a time-lag condition, and taking a servo system mechanism as a model architecture, introducing a deep neural network as a function approximation model, so as to realize the nonlinear dynamic system modeling and parameter identification. And the problem of quantitative characterization of friction parameters is effectively solved. Prediction conditions of different driving shaft friction torques are systematically evaluated from a time domain perspective, and results show that the method has better prediction precision and stability.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent manufacturing and processing technology, and involves the state identification and dynamic characterization of nonlinear dynamic parameters of CNC machine tools during milling. Specifically, it is a friction torque prediction method based on deep learning. Background Art

[0002] The servo feed system of a CNC machine tool is central to achieving high-precision machining. Its motion accuracy directly impacts part geometric errors and surface quality. Under high-load, high-speed, and high-acceleration machining scenarios, wear, temperature variations, and nonlinear friction torque due to lubrication conditions can cause system positioning lag, vibration, and even instability, limiting the machine tool's machining performance and reliability. Therefore, accurately predicting friction torque in the servo feed system is crucial for improving machining accuracy and dynamic performance.

[0003] The complexity of friction torque mainly comes from the coupling of multiple sources such as ball screws, bearings, guide rails and lubrication conditions, which makes the friction torque show highly nonlinear and time-varying characteristics with speed, load, temperature and wear conditions (such as reference C. Hsu, J. Kahn. Parameter Identification in Dynamic Friction Models. ASME J. Dyn. Syst., Meas., Control. 2002: 124(1): 30-37.). Establishing a dynamic model of a CNC machine tool servo system, identifying the key structures that generate friction torque, and using mechanical sensing components to obtain friction torque is an efficient method. However, this technology adds additional experimental costs and has certain requirements for the experimental environment. In particular, the signal attenuation obtained under high-speed and high-load conditions is significant (for example, the literature Z. Wang, S. Liu, H. Li, J. Ou, D. Peng, Z. Li, A Novel Method for Updating Time-Varying Information of Milling Thin-Walled Components Based on Digital Twin Model, IEEE Sensors Journal, 24(2024)2531-2546). To this end, relevant researchers have developed a series of technologies and methods for solving friction torque by studying the motion feedback mechanism of machine tool servo systems.Among them, in terms of mechanism models, traditional friction models such as the Coulomb friction model (such as K. Johnson. Friction and Wear Characteristics in Precision Machine Tools. Tribology Int. 2007; 40(7): 1068–1075.), the Dahl model (such as P. Dahl. Solid friction damping of mechanical vibrations. AIAA Journal. 1976; 14(12): 1675–1682.), and the LuGre model (such as E. Anderson, M. Tuma. Hybrid LuGre Friction Model and Experimental Validation. Journal of Sound and Vibration. 2015; 345: 78–94.) can capture some friction characteristics under ideal working conditions. However, since parameter identification relies on simplified assumptions and nonlinear updates are complex, it is difficult to meet the real-time requirements of high-speed and high-precision machining (such as McCarthy M. Temperature-Dependent Friction Modeling for Servo Systems, Mechanical Systems and Signal Processing, vol. 30, pp. 35–45, 2012.). Chen et al. obtained friction torque by combining servo motor current and kinematic parameters. However, this method relies on an accurate dynamic model, and the coupling of inertia torque and cutting force leads to high model complexity and is susceptible to noise interference in practical applications (e.g., Chen Lumeng. Online Monitoring and Fault Diagnosis of High-end CNC Machine Tool Feed Systems [D]. Beijing Information Science and Technology University, 2023. DOI: 10.26966 / d.cnki.gbjjc.2023.000019.). In terms of data models, Zhou et al. used a multi-layer feedforward neural network to achieve a relative error of less than 5% in friction prediction of key components (e.g., X. Zhou, Z. Li, Friction Torque Prediction of Rolling Bearings Using Deep Neural Networks. Mechanical Systems and Signal Processing. 2021: 152: 107-123.).Chen et al. combined CNN with a timing model, reducing the relative error of friction in the servo system from 20% to 3.5% (e.g., Y. Chen, S. Ma, Huang H. Mechanism-Informed Friction-Dynamics Coupling GRU Neural Network. Control Engineering Practice. 2024: 152: 104917.). Li et al. introduced the constraints of the friction constitutive equation into the PINN model, achieving stable prediction under high-dimensional input (e.g., Q. Li, J. Sun, Friction Modelling with Physics-Informed Neural Networks. International Journal for Numerical Methods in Engineering. 2023: 125(5): 1234-1250.). However, the above complex models still have high computational costs and overfitting. In summary, in the face of complex milling processing environments, it is urgent to study an efficient and stable friction torque prediction method to solve the problem of dynamic characterization of friction torque under lightweight and small sample conditions. Summary of the Invention

[0004] To effectively address the challenges of the prior art, the present invention provides a deep learning-based friction torque prediction method. This method, targeting the feed drive system of a CNC machine tool, constructs system dynamics models for the X and Y feed axes, determining the dynamic relationship between excitation and response under time-varying disturbances. This method addresses the modeling and parameter identification of nonlinear dynamic systems under time-delay conditions. Using the servo system mechanism as the model architecture, a deep neural network is introduced as a function approximation model to effectively address the characterization of friction parameters. A systematic evaluation of the friction torque predictions for different drive shafts from a time-domain perspective demonstrates that the present invention offers improved prediction accuracy and stability.

[0005] The technical solution of the present invention is:

[0006] A friction torque prediction method based on deep learning includes the following steps:

[0007] Step 1: Mechanism analysis of CNC machine tools and servo feed systems;

[0008] First, the kinematic characteristics of the overall structure of the CNC machine tool machining center are analyzed. Combined with the CNC machine tool milling process, the dynamic response characteristics of the servo motor are described. The dynamic response characteristics refer to the output torque and the action on the motion chain of the servo feed system, which then generates acceleration and rotation and transmits them to the worktable. Then, referring to the classic Stribeck friction model, the friction torque τ in the transmission chain of the servo feed system is described. f Nonlinear relationships with relevant kinetic parameters.

[0009] Step 2: Determination of end-to-end relationships;

[0010] Combined with the monitoring characteristics of the machine tool servo signal in the actual production process, a dynamic model with time discrete characteristics is constructed, and the friction torque τ in the transmission chain of the servo feed system obtained in step 1 is obtained. f The nonlinear relationship between the relevant dynamic parameters is used to determine the end-to-end relationship between the angular velocity and friction torque of the servo motor of the CNC machine tool.

[0011] Step 3: Establishment of friction torque prediction model;

[0012] Based on the mechanism model and the characteristics of solving the servo feed system dynamics model, a DNN prediction method is introduced as a function approximator to effectively address the nonlinearity of the signal variation process. The DNN is trained using the angular velocity and friction torque of the servo motor of a CNC machine tool, and the trained DNN is used to predict the friction torque.

[0013] The beneficial effects of the present invention are as follows: the present invention is a friction torque prediction method based on deep learning. By constructing a dynamic model of the CNC machine tool feed system, the dynamic relationship between excitation and response under time-varying disturbances is determined, and the problems of nonlinear dynamic system modeling and parameter identification are sorted out. The servo system mechanism is used as the model architecture, and the DNN model is introduced as a function approximation model for different feed axes, effectively solving the problem of characterizing friction parameters and realizing a quantitative description of the key nonlinear dynamic characteristics in the servo system. The friction torque prediction of different drive axes is comprehensively evaluated. The results show that the present invention has better prediction accuracy and stability. Specifically, in both Scheme A and Scheme B, the DNN prediction models for the X and Y feed axes maintain excellent performance, that is, the friction torque prediction values ​​show periodic changes, and the absolute value of the friction torque prediction error is stably distributed within 0.5%. Therefore, the present invention has excellent prediction accuracy and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flow chart of a friction torque prediction method based on a deep learning model provided in a specific embodiment of the present invention;

[0015] Figure 2 This is the research method of the present invention;

[0016] Figure 3 This is a comparison chart of the prediction effects of different methods on the X-axis in solution A of the present invention;

[0017] Figure 4 This is a comparison chart of the prediction effects of different methods on the Y axis in solution A of the present invention;

[0018] Figure 5 This is a comparison chart of the prediction effects of different methods on the X-axis in Solution B of the present invention;

[0019] Figure 6 This is a comparison chart of the prediction effects of different methods on the Y-axis in Solution B of the present invention. DETAILED DESCRIPTION

[0020] The specific implementation of the present invention is described in detail below in conjunction with the technical solutions and drawings.

[0021] In this embodiment, a friction torque prediction method based on deep learning is described. The specific process is as follows: Figure 1 As shown, it mainly includes the following steps:

[0022] Step 1: Mechanism analysis of CNC machine tools and servo feed systems;

[0023] A complete five-axis feed system mainly consists of three sets of linear axes and two sets of rotary axes, of which the linear axes are driven by ball screws. Taking the ball screw of a machine tool as an example, an analysis of the linear axis of its feed system shows that there is a close and complex relationship between the dynamic parameters and the CNC servo signal. Referring to the classic Stribeck friction model, the τ described f It can be specifically expressed as follows:

[0024]

[0025] Among them, τ coul is the Coulomb friction torque; τ stat is the static friction torque; ω stri is the Stribeck velocity; σ ω is the viscous friction coefficient, and the positive and negative signs represent the direction of the servo motor's operation, respectively. ω represents the continuous motor angular velocity. At the same time, since the servo motor is in a non-stationary state during CNC machining, ω = 0 is not considered.

[0026] Step 2: Determination of end-to-end relationships;

[0027] The above-mentioned dynamic model for friction torque prediction has the characteristics of time continuity. However, in actual production and processing, CNC servo signals are usually tracked in a discrete form. Therefore, the end-to-end model with time discrete characteristics is as follows:

[0028] τ f (k) = f dis (ω c (k))(2)

[0029] Among them, f dis is the nonlinear relationship between the predicted friction torque and angular velocity shown in formula (1), k is the discrete moment; ω c (k) represents the angular velocity of the discrete servo motor;

[0030] Step 3: Establishment of friction torque prediction model;

[0031] According to the milling force derivation process described above, the input angular velocity ω c (k) and friction torque τ f There is a complex nonlinear relationship between them, and the traditional mechanism model has uncertainty in the parameter identification process. Therefore, the DNN model with powerful fitting function is introduced to efficiently solve the nonlinear friction torque τ f It is worth noting that if the DNN used to solve this problem contains L hidden layers, the input layer of the model can be expressed as:

[0032] h 0 =ω c (k)(3)

[0033] Therefore, the i-th hidden layer can be expressed as:

[0034] h i =σ i (W i h i-1 +b i )(4)

[0035] Among them, h i is the vector of the i-th hidden layer; σ i is the activation function, and τ f The prediction process of (ω) is regressive, so the Tanh function is selected as the activation function; W i is the weight matrix between the (i-1)th layer and the i-th layer; b i is the bias vector. At the same time, since the output layer has no activation function, the linear layer of the model can be expressed as:

[0036] DNN(ω(k))=W out h L+b out (5)

[0037] Among them, W out is the weight matrix between connections; b out is the set vector.

[0038] h i =σ i (W i h i-1 +b i )(6)

[0039] The research ideas of the prediction model are as follows: Figure 2 shown.

[0040] Step 4: Model validation;

[0041] This study used a horizontal boring and milling machine in the rotor power workshop of a certain group company as the research context. Considering ideal conditions, a Simulink simulation platform was built based on the dynamic parameters of the linear axis servo system. A series of angular velocity and friction torque signals were obtained. The relevant dynamic parameters are shown in Table 1 below.

[0042] Table 1 Dynamic parameters of servo feed system

[0043]

[0044]

[0045] At the same time, referring to the workshop machine tool parameters, the system sampling frequency is set to 333Hz. The angular velocity ω in solution A is required to be a multi-frequency sine signal, as shown below:

[0046] ω(k)=220sin(100πk)+110sin(200πk)(6)

[0047] Combined with the dynamic parameters in Table 1, two sets of data sets related to the X and Y feed axes are obtained in turn. Then, according to the input and output relationship, the steps of data division, model training, model verification, and model testing are completed.

[0048] Subsequently, an error term with Gaussian characteristics is introduced to construct a dynamic model considering error compensation, and the τ f The derivation formula of * is as follows:

[0049]

[0050] At the same time, considering the modeling error conditions, a series of angular velocity and friction torque signals of Scheme B are obtained based on the Simulink simulation platform. According to the input-output relationship, the steps of data partitioning, model training, model verification, and model testing are completed. Where ω is a multi-frequency sinusoidal signal, as shown in formula (6).

[0051] The verification process of the model is mainly divided into four parts. The first part is to use the method of the present invention to evaluate the prediction results of the X axis in solution A. The results are as follows: Figure 3 As shown, that is τ f The label value and prediction error diagram of τ f The absolute values ​​of the prediction errors are all stably distributed within 0.5%. The second part is to evaluate the prediction results of the Y axis in solution A using the method of the present invention. The results are as follows Figure 4 As shown, that is τ f The label value and prediction error diagram of τ f The maximum absolute value of the prediction error is 0.5%. The third part is to use the method of the present invention to evaluate the prediction results of the X axis in solution B. The results are as follows Figure 5 As shown, that is τ f The label value and prediction error diagram of τ f The absolute value of the prediction error is less than 0.5%. The fourth part is to use the method of the present invention to evaluate the prediction results of the Y axis in solution B. The results are as follows: Figure 6 As shown, that is, τ f The label value and prediction error diagram of τ f The absolute value of the prediction error is controlled within 0.5%.In summary, the model of the present invention shows excellent performance in both prediction accuracy and stability.

Claims

1. A friction torque prediction method based on deep learning, characterized in that: The following steps are involved: Step 1: Mechanism analysis of CNC machine tools and servo feed systems; First, the kinematic characteristics of the overall structure of the CNC machine tool machining center are analyzed. Combined with the CNC machine tool milling process, the dynamic response characteristics of the servo motor are described. The dynamic response characteristics refer to the output torque and the action on the motion chain of the servo feed system, which then generates acceleration and rotation and transmits them to the worktable. Then, referring to the classic Stribeck friction model, the friction torque τ in the transmission chain of the servo feed system is described. f Nonlinear relationships with relevant kinetic parameters; Step 2: Determination of end-to-end relationships; Combined with the monitoring characteristics of the machine tool servo signal in the actual production process, a dynamic model with time discrete characteristics is constructed, and the friction torque τ in the transmission chain of the servo feed system obtained in step 1 is obtained. f The nonlinear relationship between the relevant dynamic parameters is used to determine the end-to-end relationship between the angular velocity and friction torque of the servo motor of the CNC machine tool; Step 3: Establishment of friction torque prediction model; Based on the mechanism model as the basic framework and in accordance with the solution characteristics of the servo feed system dynamics model, the DNN prediction method is introduced as a function approximator to effectively solve the nonlinear problem in the signal change process; the DNN is trained using the angular velocity and friction torque of the servo motor of the CNC machine tool, and the trained DNN is used to predict the friction torque.

2. The friction torque prediction method based on deep learning according to claim 1, characterized in that: In step 1, a complete five-axis feed system consists of three sets of linear axes and two sets of rotary axes, wherein the linear axes are driven by ball screws; referring to the classic Stribeck friction model, the τ f Specifically, it is expressed as follows: Among them, τ coul is the Coulomb friction torque; τ stat is the static friction torque; ω stri is the Stribeck velocity; σ ω is the viscous friction coefficient, and the positive and negative signs represent the running directions of the servo motor respectively; ω represents the continuous angular velocity of the servo motor; at the same time, since the servo motor is in a non-stationary state during CNC machining, ω = 0 is not considered.

3. The friction torque prediction method based on deep learning according to claim 2, characterized in that: In step 2, during the actual production process, the CNC servo signal is tracked in a discrete form; therefore, the end-to-end model with time discreteness characteristics is as follows: t f (k)=f dis (oh c (k) (2) Among them, f dis is the nonlinear relationship between the predicted friction torque and angular velocity shown in formula (1), k is the discrete moment; ω c (k) represents the discrete angular velocity of the servo motor.

4. The friction torque prediction method based on deep learning according to claim 3, characterized in that: In step 3, the input angular velocity ω is obtained by formula (2): c (k) and friction torque τ f The relationship between them is established, and a DNN model is trained between the two, and the trained DNN is used to predict the friction torque.

5. The friction torque prediction method based on deep learning according to claim 3, characterized in that: In step 3, the DNN model contains L hidden layers, and the input layer of the model is expressed as: h 0 =ω c (k)(3) Therefore, the i-th hidden layer is expressed as: h i =σ i (W i h i-1 +b i )(4) Among them, h i is the vector of the i-th hidden layer; σ i is the activation function, and τ f The prediction process of (ω) is regressive, so the Tanh function is selected as the activation function; W i is the weight matrix between the (i-1)th layer and the i-th layer; b i is the bias vector; at the same time, since the output layer has no activation function, the linear layer of the model is expressed as: DNN(ω(k))=W out h L +b out (5) Among them, W out is the weight matrix between connections; b out is the set vector; h i =σ i (W i h i-1 +b i )(6)。

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