Intelligent main shaft twinning control method for robot milling

Abstract

The invention belongs to the field of intelligent manufacturing, and particularly relates to an intelligent spindle twinning control method for robot milling, which comprises the following steps of: firstly, predicting frequency response functions of other processing positions by utilizing nonlinear mapping of a large number of simulation frequency response functions and a small number of measurement frequency response functions; therefore, the predicted frequency response function is higher in precision and wider in range. And then, the frequency domain error is used as the target function to optimize the obtained cutting force coefficient and the cutter jumping parameter, so that the influence of noise interference on the existing cutting force coefficient and cutter jumping parameter identification optimization index is overcome. And finally, the twinning control strategy of the next stage is designed on line by adopting a model updated in real time, the machining performance limit of the industrial robot is thoroughly exerted, and the situation that parameters are manually adjusted and cutting force is suddenly changed under variable working conditions is overcome. The situation that machining quality and efficiency are affected by sudden change of cutting force caused by changes of machining parameters such as cutting width and cutting depth is avoided, and therefore the machining performance of the industrial robot is fully exerted.

Description

Technical Field

[0001] This application belongs to the field of intelligent manufacturing, and particularly relates to an intelligent spindle twin control method for robot milling machining. Background Art

[0002] Aerospace structural parts are gradually becoming larger and more complex, which has accelerated the development of manufacturing equipment. The top priority is to consider using new equipment and technologies to replace the traditional machine tools that adopt the processing method of "fixed mother machine and flowing workpieces". Industrial robots are flexible in operation, have a large working space, strong parallel coordination ability, and good reconfigurability, and can provide "transformative" means for the processing of large components.

[0003] Due to the action of cutting force, deformation and vibration will occur at the end of the robot, resulting in poor part accuracy and low processing efficiency. For typical milling machining, the machining error of industrial robots can reach more than 1 mm. Compared with the spindle of traditional numerically controlled machine tools, the spindle配套 with industrial robots is not only a machining execution component, but should also support the robot control system to accurately monitor and make intelligent decisions on the machining state online, so as to improve the machining quality.

[0004] The intelligent spindle is the core functional component of the new generation of intelligent industrial robots and also the development direction of future spindles. The biggest difference between the intelligent spindle and the ordinary spindle is that the intelligent spindle has the functions of perception, decision-making and execution. Through the real-time monitoring and control of working condition signals such as vibration, temperature, rotational speed, and torque, the intelligent spindle can achieve higher speed, accuracy and reliability than the ordinary spindle, and realize higher machining efficiency.

[0005] So far, most intelligent spindles are embedded with model-based control methods (model predictive control, linear quadratic regulator, etc.). This type of control method mainly designs the controller through an offline model. The offline model is difficult to accurately reflect the real situation of the system. For example: when the working condition, machining parameters, posture, etc. change, the offline model is quite different from the actual system. Therefore, the controller designed based on the offline model has poor effect, and even the controller failure may occur.

[0006] At present, it is necessary to design an intelligent spindle twin control method for robot milling machining to ensure the reliability of the controller, so that the industrial robot配套 with the intelligent spindle "becomes smarter during machining" and fully发挥 its machining performance. Summary of the Invention

[0007] The purpose of this application is to provide an intelligent spindle twin control method for robot milling machining to solve the problem of low reliability of the existing intelligent spindle control.

[0008] The technical solution of this application is: an intelligent spindle twin control method for robot milling machining, including: A hammer impact experiment was conducted to collect the input impact force and output acceleration signals at each discrete processing point, and the actual measured frequency response function was established. The simulated frequency response function in the simulation environment is calculated based on the equation of motion, and the objective function is established by the error between the actual measured frequency response function and the simulated frequency response function. A BP neural network is trained using a small proportion of the actual measured frequency response function and a large proportion of the simulated frequency response function to obtain a nonlinear mapping. The predicted frequency response function at each processing point is then predicted based on the simulated frequency response function and the nonlinear mapping. A cutting force model based on cutting force model coefficients and tool skip parameters is established, and the simulated cutting force is calculated by combining the predicted frequency response function at each machining point. Based on the predicted frequency response function and the simulated cutting force output by the cutting force model at each machining point, the vibration response at each machining parameter and the tool tip at the machining position is predicted by combining the Duhamel integral. Milling is performed based on vibration response. Modal analysis is used to obtain the actual frequency response function at the machining point. The nonlinear mapping is updated based on the actual frequency response function at the machining point, and then the actual frequency response function at the machining point is continuously optimized. Using frequency domain error as the objective function for time-energy optimization, the particle swarm optimization algorithm is used to find the optimal tool jump parameters and initial entry angle, and the optimal cutting force parameters are obtained to update the cutting force model. Based on the predicted frequency response function and the cutting force output by the cutting force model at each machining point, the optimal machining parameters and position for the next stage are obtained. The output amplitude is continuously controlled by the machining parameters and position, and the predicted frequency response function and cutting force model are continuously optimized.

[0009] Preferably, the motion equations are designed as follows: modeling the industrial robot system to obtain a robot simulation model, and then obtaining the motion equations of the robot simulation model; The equation of motion is expressed as follows: ; in, , , These are represented as the system mass matrix, damping matrix, and stiffness matrix, respectively. It is an external force. Joint angle vector, For vibration response, for The first derivative, for The second derivative; The system quality matrix for: ; in and For Jacobian matrices, Let the mass of the i-th link be... The number of links. Let be the inertia tensor of the i-th link. It is a rotation matrix.

[0010] Preferably, the objective function for: ; in It is the actual measured frequency response function. It is a simulated frequency response function. As weight, i , j , k All are quantity numbers. x , y , z All are directions. This represents the total number of frequency samples.

[0011] Preferably, the particle swarm optimization algorithm is used in conjunction with elastic parameters to optimize the objective function to obtain the minimum error, and the simulation frequency response function corresponding to the minimum error is calculated.

[0012] Preferably, the specific method for optimizing the objective function using the particle swarm optimization algorithm is as follows: Based on existing data, the maximum and minimum values ​​of stiffness and damping are obtained to establish a search domain. Then, the initial values ​​and step sizes of stiffness and damping are set respectively. The initial value is the maximum or minimum value of stiffness or damping. The particle swarm optimization algorithm is used to first calculate the error values ​​of stiffness and damping at the initial values. Then, the values ​​of stiffness and damping are adjusted by adjusting the step size until the entire search domain is traversed to obtain different error values. Finally, the simulation frequency response function corresponding to the minimum error value is obtained by calculating the minimum error value.

[0013] Preferably, the mapping corresponding to the simulated frequency response function output by simulation is a low-level mapping. The mapping corresponding to the actual measured frequency response function obtained through actual measurement is a high-level mapping. The trained BP neural network and low-level mapping Combining yields higher-level mappings High-level mapping It can be directly converted into the actual measured frequency response function; then, low-level mappings within the simulated frequency response function are established respectively. High-level mapping within the actual measured frequency response function .

[0014] Preferably, the specific design method for the simulated cutting force is as follows: The static chip thickness, including radial jump cutter thickness, is obtained by calculating the impact of the imbalance during the actual spindle rotation process. The dynamic chip thickness is calculated based on the vibration response of the robot's multi-mode output and the static chip thickness. The simulated cutting force on the entire milling cutter is calculated based on static cutting thickness, dynamic cutting thickness, initial entry angle, jump cutter parameters, and cutting force coefficient.

[0015] Preferably, the cutting force model is: ; In the formula: ; ; The cutting force is in the x-direction. The cutting force is in the y-direction. The cutting thickness is determined by the tool switching parameters and the robot modal parameters. The number of teeth. The number of iterations for the cutting depth. For the first j The initial angle of entry for each cutting tooth. This is the cutting force coefficient.

[0016] Preferably, the vibration response is specifically designed as follows: Based on the predicted frequency response function at each machining point and the simulated cutting force output by the cutting force model, the vibration response at each machining parameter and the tool tip at the machining position is obtained by solving in the time domain. The vibration and cutting force signals are collected in real time to update the nonlinear mapping and cutting force model coefficients, and further update the predicted frequency response function and cutting force model to predict the machining parameters and vibration response at different times and machining points.

[0017] Preferably, during the hammer impact experiment, a hammer is used to strike the tool tip along the x, y, and z directions respectively, and the output signals of the three-dimensional accelerometer at the spindle housing are collected. Using the input impact force and the output acceleration signal, the cross power spectral density of the input and output and the input self power spectral density are calculated respectively, and the actual measured frequency response functions in the x, xy, xz, yx, yy, yz, zx, zy, and zz directions are obtained.

[0018] This application presents an intelligent spindle twin control method for robotic milling. First, it uses a nonlinear mapping of numerous simulated frequency response functions and a small number of measured frequency response functions to predict the frequency response functions of other machining positions. This results in higher accuracy and a wider range of predicted frequency response functions. Then, it uses frequency domain error as the objective function to optimize the obtained cutting force coefficient and tool jump parameters, overcoming the influence of noise interference on the identification and optimization indices of existing cutting force coefficient and tool jump parameters. Finally, it employs a real-time updated model to design the next stage of twin control strategy online, fully utilizing the machining performance limits of the industrial robot and overcoming the challenges of manual parameter adjustments and sudden changes in cutting force under varying operating conditions. Attached Figure Description

[0019] To more clearly illustrate the technical solutions provided in this application, the accompanying drawings will be briefly described below. Obviously, the drawings described below are merely some embodiments of this application.

[0020] Figure 1 This is a schematic diagram of the overall process of this application; Figure 2 This is the overall flowchart of the twin control in this application. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] While industrial robots cannot completely replace machine tools, they have advantages in machining large and complex parts. Industrial robots are significantly less expensive than machine tools within the same workspace. Furthermore, the portability of industrial robots can improve productivity. However, compared to machine tools, industrial robots have extremely low rigidity, which limits their application in machining. Arbitrarily applied machining parameters can easily cause unstable vibrations in industrial robots during processing, thus affecting machining quality and efficiency.

[0023] Therefore, an intelligent spindle twin control method for robotic milling is designed to realize the design of twin control strategies in virtual space, thereby further enhancing the machining performance of industrial robots and achieving high-precision and high-efficiency machining.

[0024] Taking the commonly used industrial robot milling as an example, such as Figure 1 Specifically, it includes the following steps: Step S100: Conduct hammer impact experiments at a small number of discrete processing points, collect the input impact force and output acceleration signals at each discrete processing point, and establish the actual measured frequency response function. The selection of discrete processing points covers all directions in three-dimensional space.

[0025] The frequency response function is simplified as FRF.

[0026] During the impact test, a hammer was used to strike the tool tip along the x, y, and z directions, and the output signals of the triaxial accelerometers at the spindle housing were collected. Using the input impact force and output acceleration signals, the cross-power spectral density of the input and output, and the input self-power spectral density were calculated, respectively, to obtain the actual measured frequency response functions in the x, xy, xz, yx, yy, yz, zx, zy, and zz directions.

[0027] Step S200: Perform industrial robot system modeling to obtain robot simulation model and obtain the motion equations of robot simulation model; The simulated frequency response function in the simulation environment is calculated based on the equation of motion, and the objective function is established by the error between the actual measured frequency response function and the simulated frequency response function.

[0028] Preferably, the industrial robot system is modeled based on parameters such as system mass, damping, and stiffness, and the resulting equations of motion are as follows:

[0029] in , , These are represented as the system mass matrix, damping matrix, and stiffness matrix, respectively. It is an external force. Joint angle vector, For vibration response, for The first derivative, for The second derivative of .

[0030] System quality matrix for:

[0031] in and For Jacobian matrices, Let the mass of the i-th link be... The number of links. Let be the inertia tensor of the i-th link. It is a rotation matrix.

[0032] Preferably, the objective function As shown below:

[0033] in It is the actual measured frequency response function. It is a simulated frequency response function. As weight, i , j , k All are quantity numbers. x , y , z All are directions. This represents the total number of frequency samples.

[0034] Preferably, a particle swarm optimization algorithm is used in conjunction with elastic parameters to optimize the objective function to obtain the minimum error, and the simulated frequency response function corresponding to the minimum error is calculated. The elastic parameters include damping and stiffness.

[0035] The specific method for optimizing the objective function using the particle swarm optimization algorithm is as follows: Based on existing data, the maximum and minimum values ​​of stiffness and damping are obtained to establish a search domain. Then, initial values ​​and step sizes for stiffness and damping are set, with the initial value being the maximum or minimum value of either stiffness or damping. A particle swarm optimization algorithm is used to first calculate the error values ​​corresponding to the stiffness and damping at the initial values. Then, the values ​​of stiffness and damping are adjusted by changing the step size until the entire search domain is traversed, obtaining different error values. Finally, the simulated frequency response function corresponding to the minimum error value is obtained by calculating the minimum error value. It should be noted that stiffness and damping must be positive values.

[0036] Step S300: Train a BP neural network using a small proportion of the actual measured frequency response function and a large proportion of the simulated frequency response function to obtain a nonlinear mapping. Predict the predicted frequency response function at each processing point based on the simulated frequency response function and the nonlinear mapping.

[0037] The nonlinear mapping is represented as:

[0038] in For robot posture, For robot posture in The values ​​of the real and imaginary parts corresponding to the frequency band.

[0039] The mapping corresponding to the simulated frequency response function output by the simulation is a low-level mapping. The mapping corresponding to the actual measured frequency response function obtained through actual measurement is a high-level mapping. The trained BP neural network and low-level mapping Combining yields higher-level mappings High-level mapping It can be directly converted into the actual measured frequency response function; then, low-level mappings within the simulated frequency response function are established respectively. High-level mapping within the actual measured frequency response function ; High-level mapping The formula for calculation is:

[0040] in It is a BP neural network.

[0041] Step S400: Establish a cutting force model based on the cutting force model coefficients and the tool jumper parameters, and calculate the simulated cutting force by combining the predicted frequency response function at each machining point. The initial values ​​of the cutting force model coefficients and the tool jumper parameters are determined by the workpiece material parameters.

[0042] The static chip thickness in the cutting force model takes into account radial jump cutter movement, while the dynamic chip thickness in the cutting force model considers both the robot's dynamic characteristics and the static chip thickness. The simulated cutting force on the entire milling cutter is calculated based on the chip thickness (static cutting thickness + dynamic cutting thickness), cutting force coefficient, jump cutter parameters, and initial approach angle.

[0043] The specific design method for simulated cutting force is as follows: Step S410: Calculate the impact of the unbalance during the actual spindle rotation to obtain the static chip thickness including the radial jump cutter. Step S420: Calculate the dynamic chip thickness based on the vibration response of the multi-mode output of the robot body structure and the static chip thickness. Step S430: Calculate the simulated cutting force on the entire milling cutter based on the chip thickness (static cutting thickness + dynamic cutting thickness), initial entry angle, jump cutter parameters, and cutting force coefficient.

[0044] Preferably, the cutting thickness, number of teeth, depth of cut iteration deployment, initial entry angle, and cutting force coefficient of the industrial robot boring tool are obtained based on the cutting force model coefficients and the tool jumper parameters, resulting in the following cutting force model:

[0045] In the formula:

[0046] The cutting force is in the x-direction. The cutting force is in the y-direction. The cutting thickness is determined by the tool switching parameters and the robot modal parameters. The number of teeth. The number of iterations for the cutting depth. For the first j The initial angle of entry for each cutting tooth. This is the cutting force coefficient.

[0047] Preferably, during the processing, vibration signals are collected and the robot-milling dynamics model is updated in real time. The robot-milling dynamics model can accurately predict the processing performance at each processing position. Based on this high-fidelity model and actual processing requirements, a twin control strategy is designed in the virtual space.

[0048] Step S500: Based on the predicted frequency response function at each machining point and the simulated cutting force output by the cutting force model, the vibration response at each machining parameter and the tool tip at the machining position is predicted by combining the Duhamel integral. The vibration response is specifically designed as follows: Step S510: Based on the predicted frequency response function at each machining point and the simulated cutting force output by the cutting force model, the vibration response at each machining parameter and the tool tip at the machining position is obtained by solving in the time domain. Step S520: Real-time acquisition of vibration signals and cutting force signals to update nonlinear mapping and cutting force model coefficients, further updating the predicted frequency response function and cutting force model, and predicting machining parameters and vibration response at machining points at different times.

[0049] Step S600: Milling is performed based on vibration response, and acceleration and milling force signals are measured in real time during the milling process; Based on the measured acceleration and milling force signals, the actual frequency response function at the machining point is obtained using modal analysis. A BP neural network is trained and the nonlinear mapping is updated based on the actual frequency response function at the machining point, thereby continuously optimizing the actual frequency response function at the machining point.

[0050] Extensive robotic milling experiments revealed significant white noise in the measured cutting force, highlighting the potential of operational modal analysis methods for acquiring modal parameters in robotic milling.

[0051] Preferably, the frequency response function at the processing point is: (7) In the formula, It is the robot's frequency response function matrix. It is the cross-power spectral density matrix of cutting force and vibration acceleration. It is the cutting force power spectral density matrix.

[0052] Step S700: Based on the frequency domain error between the real-time measured cutting force and the simulated cutting force output by the cutting force model, the frequency domain error is used as the objective function for time-energy optimization. The particle swarm optimization algorithm is used to find the optimal tool jump parameters and initial entry angle, and the optimal cutting force parameters are obtained to update the cutting force model.

[0053] like Figure 2 In step S800, based on the predicted frequency response function and the cutting force output by the cutting force model at each machining point, considering the milling conditions during the machining process, the optimal machining parameters (feed speed, rotation speed and attitude) and position for the next stage are obtained with time-energy optimization as the objective function. The output amplitude is continuously controlled by the machining parameters and position, and the predicted frequency response function and cutting force model are continuously optimized.

[0054] In robotic milling operations under constant conditions, the industrial robot uses the measured cutting force as the output and employs a twin control strategy. It continuously controls the output amplitude through machining parameters (feed rate, spindle speed, and attitude) and position, obtaining new acceleration and cutting force signals. These new signals are then used to optimize the predicted frequency response function and the cutting force model. This process is repeated, continuously updating the nonlinear mapping, cutting force coefficient, and tool jump parameters to achieve continuous optimization control. The output amplitude is equal to the amplitude of the simulated cutting force.

[0055] By using a twin control strategy that updates the cutting force model in real time, control parameters can be optimized in the virtual space. Furthermore, it can prevent sudden changes in cutting force caused by variations in machining parameters such as cutting width and depth from affecting machining quality and efficiency, thus fully leveraging the machining performance of the industrial robot itself.

[0056] Based on the predicted frequency response function at the machining location and the cutting force output by the updated cutting force model, the optimal machining parameters and trajectory are obtained through the time-energy optimal objective function. The amplitude control of the cutting force is achieved by using the feedforward control strategy of trajectory tracking.

[0057] During milling operations, industrial robots continuously optimize the output amplitude by repeating steps S600-S800, further improving the accuracy of the simulated cutting force output by the cutting force model. This achieves the goal of "becoming smarter with each machining operation." However, data updates that are abnormal require cleaning; that is, data showing significant changes in frequency response functions, cutting force coefficients, or tool skipping parameters need to be manually filtered.

[0058] In summary, this application first utilizes a nonlinear mapping of numerous simulated frequency response functions and a small number of measured frequency response functions to predict the frequency response functions of the remaining machining positions, resulting in higher accuracy and a wider range of predicted frequency response functions. Then, it uses frequency domain error as the objective function to optimize the obtained cutting force coefficient and tool jump parameters, overcoming the influence of noise interference on the existing cutting force coefficient and tool jump parameter identification and optimization indices. Finally, it employs a real-time updated model to design the next stage of the twin control strategy online, fully utilizing the machining performance limits of the industrial robot and overcoming the challenges of manual parameter adjustments and sudden changes in cutting force under varying working conditions.

[0059] Finally, it should be noted that the accompanying drawings of the embodiments disclosed in this invention only involve the structures involved in the embodiments disclosed in this invention. Other structures can refer to the general design. In the absence of conflict, the same embodiment and different embodiments of this invention can be combined with each other. In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A smart spindle twin control method for robotic milling, characterized in that, include: A hammer impact experiment was conducted to collect the input impact force and output acceleration signals at each discrete processing point, and the actual measured frequency response function was established. The simulated frequency response function in the simulation environment is calculated based on the equation of motion, and the objective function is established by the error between the actual measured frequency response function and the simulated frequency response function. A BP neural network is trained using a small proportion of the actual measured frequency response function and a large proportion of the simulated frequency response function to obtain a nonlinear mapping. The predicted frequency response function at each processing point is then predicted based on the simulated frequency response function and the nonlinear mapping. A cutting force model based on cutting force model coefficients and tool skip parameters is established, and the simulated cutting force is calculated by combining the predicted frequency response function at each machining point. Based on the predicted frequency response function and the simulated cutting force output by the cutting force model at each machining point, the vibration response at each machining parameter and the tool tip at the machining position is predicted by combining the Duhamel integral. Milling is performed based on vibration response. Modal analysis is used to obtain the actual frequency response function at the machining point. The nonlinear mapping is updated based on the actual frequency response function at the machining point, and then the actual frequency response function at the machining point is continuously optimized. Using frequency domain error as the objective function for time-energy optimization, the particle swarm optimization algorithm is used to find the optimal tool jump parameters and initial entry angle, and the optimal cutting force parameters are obtained to update the cutting force model. Based on the predicted frequency response function and the cutting force output by the cutting force model at each machining point, the optimal machining parameters and position for the next stage are obtained. The output amplitude is continuously controlled by the machining parameters and position, and the predicted frequency response function and cutting force model are continuously optimized.

2. The intelligent spindle twin control method for robotic milling as described in claim 1, characterized in that, The motion equations are designed as follows: model the industrial robot system to obtain a robot simulation model, and then obtain the motion equations of the robot simulation model. The equation of motion is expressed as follows: ； in, , , These are represented as the system mass matrix, damping matrix, and stiffness matrix, respectively. It is an external force. Joint angle vector, For vibration response, for The first derivative, for The second derivative; The system quality matrix for: ； in and For Jacobian matrices, Let the mass of the i-th link be... The number of links. Let be the inertia tensor of the i-th link. It is a rotation matrix.

3. The intelligent spindle twin control method for robotic milling as described in claim 2, characterized in that, The objective function for: ； in It is the actual measured frequency response function. It is a simulated frequency response function. As weight, i , j , k All are quantity numbers. x , y , z All are directions. This represents the total number of frequency samples.

4. The intelligent spindle twin control method for robotic milling as described in claim 1, characterized in that: The objective function is optimized by using a particle swarm optimization algorithm combined with elastic parameters to obtain the minimum error value, and the simulated frequency response function corresponding to the minimum error value is calculated.

5. The intelligent spindle twin control method for robotic milling as described in claim 4, characterized in that, The specific method for optimizing the objective function using the particle swarm optimization algorithm is as follows: Based on the existing data, the maximum and minimum values ​​of stiffness and damping are obtained to establish the search domain. Then, the initial values ​​and step sizes of stiffness and damping are set respectively. The initial value is the maximum or minimum value of stiffness or damping. The particle swarm algorithm is used to first calculate the error values ​​of stiffness and damping at the initial values. Then, the values ​​of stiffness and damping are adjusted by the step size until the entire search domain is traversed to obtain different error values. The simulated frequency response function corresponding to the minimum error value is then obtained by calculating the minimum error value.

6. The intelligent spindle twin control method for robotic milling as described in claim 1, characterized in that: The mapping corresponding to the simulated frequency response function output by the simulation is a low-level mapping. The mapping corresponding to the actual measured frequency response function obtained through actual measurement is a high-level mapping. The trained BP neural network and low-level mapping Combining yields higher-level mappings High-level mapping It can be directly converted into the actual measured frequency response function; then, low-level mappings within the simulated frequency response function are established respectively. High-level mapping within the actual measured frequency response function .

7. The intelligent spindle twin control method for robotic milling as described in claim 1, characterized in that, The specific design method for the simulated cutting force is as follows: The static chip thickness, including radial jump cutter thickness, is obtained by calculating the impact of the imbalance during the actual spindle rotation process. The dynamic chip thickness is calculated based on the vibration response of the robot's multi-mode output and the static chip thickness. The simulated cutting force on the entire milling cutter is calculated based on static cutting thickness, dynamic cutting thickness, initial entry angle, jump cutter parameters, and cutting force coefficient.

8. The intelligent spindle twin control method for robotic milling as described in claim 3, characterized in that, The cutting force model is as follows: ； In the formula: ； ； The cutting force is in the x-direction. The cutting force is in the y-direction. The cutting thickness is determined by the tool switching parameters and the robot modal parameters. The number of teeth. The number of iterations for the cutting depth. For the first j The initial angle of entry for each cutting tooth. This is the cutting force coefficient.

9. The intelligent spindle twin control method for robotic milling as described in claim 1, characterized in that, The vibration response is specifically designed as follows: Based on the predicted frequency response function at each machining point and the simulated cutting force output by the cutting force model, the vibration response at each machining parameter and the tool tip at the machining position is obtained by solving in the time domain. The vibration and cutting force signals are collected in real time to update the nonlinear mapping and cutting force model coefficients, and further update the predicted frequency response function and cutting force model to predict the machining parameters and vibration response at different times and machining points.

10. The intelligent spindle twin control method for robotic milling as described in claim 1, characterized in that: During the hammer impact experiment, a hammer was used to strike the tool tip along the x, y, and z directions, and the output signals of the three-dimensional accelerometer at the spindle housing were collected. Using the input impact force and the output acceleration signal, the cross power spectral density of the input and output and the input self power spectral density were calculated respectively, and the actual measured frequency response functions in the x, xy, xz, yx, yy, yz, zx, zy, and zz directions were obtained.

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