Intelligent spindle twin control method for robot milling

Abstract

The application belongs to the field of intelligent manufacturing, and particularly relates to an intelligent spindle twin control method for robot milling processing. Firstly, a nonlinear mapping of a large number of simulation frequency response functions and a small number of measured frequency response functions is used to predict the frequency response functions of the remaining processing positions, which makes the predicted frequency response functions more accurate and wider in range. Then, the cutting force coefficients and the tool jump parameters obtained by optimizing the frequency domain error as a target function are used to overcome the influence of noise interference on the existing cutting force coefficient and tool jump parameter identification optimization index. Finally, a real-time updated model is used to design the twin control strategy of the next stage online, which completely gives play to the processing performance limit of the industrial robot, and overcomes the situation of manual parameter adjustment and cutting force mutation under variable working conditions. The cutting force mutation caused by the change of processing parameters such as cutting width and cutting depth is avoided to affect the processing quality and efficiency, so that the processing performance of the industrial robot itself is fully played.

Description

TECHNICAL FIELD

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

[0002] Aerospace structures are gradually becoming larger and more complex, which accelerates the development of manufacturing equipment. It is urgent to consider using new equipment and technology to replace the traditional machine tool processing mode of "iron mother machine and water workpiece". Industrial robots are flexible, have large workspaces, strong parallel coordination work capabilities, and good reconfigurability, and can provide "revolutionary" means for large component machining.

[0003] Due to the action of cutting force, the robot end will produce deformation and vibration, resulting in poor part precision and low machining efficiency. For typical milling machining, the machining error of an industrial robot can be more than 1 mm. Compared with the spindle of a traditional numerical control machine tool, the spindle matched with the industrial robot is not only a machining execution component, but also should support the online accurate monitoring and intelligent decision of the machining state by the robot control system, so as to improve the machining quality.

[0004] The intelligent spindle is a core functional component of a new generation of intelligent industrial robots, and is 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 and execution. Through real-time monitoring and control of working condition signals such as vibration, temperature, 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 of the intelligent spindles are embedded with model-based control methods (model predictive control, linear quadratic regulator, etc.). This kind of control method mainly designs a 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 parameter and posture 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 may fail.

[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 matched with the intelligent spindle can become "smarter" with machining, and fully play its machining performance. SUMMARY

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

[0008] The technical solution of the present application is: an intelligent spindle twin control method for robot milling machining, comprising:

[0009] A hammering experiment is performed to collect input impact force and output acceleration signals of each discrete machining point, and an actual measured frequency response function is established;

[0010] A simulation frequency response function in a simulation environment is calculated based on a motion equation, and a target function is established through an error between the actual measured frequency response function and the simulation frequency response function;

[0011] A nonlinear mapping is obtained by training a BP neural network using a small-scale actual measured frequency response function and a large-scale simulation frequency response function, and a predicted frequency response function at each machining point is predicted according to the simulation frequency response function and the nonlinear mapping;

[0012] A cutting force model based on cutting force model coefficients and tool jump parameters is established, and a simulation cutting force is calculated in combination with the predicted frequency response function at each machining point;

[0013] Based on the predicted frequency response function at each machining point and the simulation cutting force output by the cutting force model, the vibration response at each machining parameter and tool tip position is predicted in combination with Duhamel integral;

[0014] Based on the vibration response, milling machining is performed, and an actual frequency response function at the machining point is obtained by using a modal analysis method; the nonlinear mapping is updated based on the actual frequency response function at the machining point, and the actual frequency response function at the machining point is continuously optimized;

[0015] The frequency domain error is used as a time-energy optimal target function, and a particle swarm algorithm is used to find optimal tool jump parameters and initial cutting angle, so as to obtain optimal cutting force parameters and update the cutting force model;

[0016] Based on the predicted frequency response function at each machining point and the cutting force output by the cutting force model, the optimal machining parameters and position in the next stage are obtained, the output amplitude is continuously controlled through the machining parameters and position, and the predicted frequency response function and the cutting force model are continuously optimized.

[0017] Preferably, the motion equation is designed as follows: an industrial robot system modeling is performed to obtain a robot simulation model, and a motion equation of the robot simulation model is acquired;

[0018] The motion equation expression is as follows:

[0019] ;

[0020] wherein, , , respectively represent a system mass matrix, a damping matrix and a stiffness matrix, is an external force, is the joint angle vector, is the vibration response, is the first derivative of is the second derivative of

[0021] The system mass matrix is:

[0022]

[0023] wherein and are Jacobian matrices, is the mass of the ith link, is the number of links, is the inertia tensor of the ith link, is a rotation matrix.

[0024] Preferably, the objective function is:

[0025]

[0026] wherein is the actual measured frequency response function, is the simulated frequency response function, is a weight, i , j , k all are quantity numbers, x , y , z all are directions, is the total number of frequency samples.

[0027] Preferably, the particle swarm algorithm is adopted to optimize the objective function to obtain the minimum error value, and the simulated frequency response function corresponding to the minimum error value is calculated.

[0028] Preferably, the specific method for optimizing the objective function by the particle swarm algorithm is:

[0029] The maximum and minimum values of the stiffness and the damping are obtained according to the existing data to establish a search domain, and then the initial value and the step size of the stiffness and the damping are set, and the initial value is the maximum or minimum value of the stiffness or the damping; the particle swarm algorithm is adopted to calculate the error value corresponding to the stiffness and the damping at the initial value, and then the values of the stiffness and the damping are adjusted through the step size until the entire search domain is traversed to obtain different error values; and the simulated frequency response function corresponding to the minimum error value is obtained by calculating the minimum value of the error values.

[0030] ​​Preferably, the mapping corresponding to the simulation frequency response function output by simulation is a low-level mapping , and the mapping corresponding to the actual measurement frequency response function obtained by actual measurement is a high-level mapping ; the trained BP neural network and the low-level mapping are combined to obtain a high-level mapping , and the high-level mapping can be directly converted into an actual measurement frequency response function; and then a low-level mapping within the simulation frequency response function and a high-level mapping within the actual measurement frequency response function are respectively established.

[0031] Preferably, the simulation cutting force specific design method is:

[0032] According to the influence calculation of the actual spindle rotation process unbalance, the static chip thickness containing radial jump tool is obtained;

[0033] According to the vibration response output by the robot body structure multi-order modal and the static chip thickness, the dynamic chip thickness is calculated;

[0034] Based on the static cutting thickness, the dynamic cutting thickness, the initial cutting angle, the jump tool parameter and the cutting force coefficient, the simulation cutting force of the entire milling cutter is calculated.

[0035] Preferably, the cutting force model is:

[0036] ;

[0037] In the formula:

[0038] ;

[0039] ;

[0040] is the x-direction cutting force, is the y-direction cutting force, is the cutting thickness determined by the jump tool parameter and the robot modal parameter, is the number of teeth, is the cutting depth iteration step number, is the initial cutting angle of the j th tooth, is the cutting force coefficient.

[0041] Preferably, the vibration response is specifically designed as:

[0042] Based on the predicted frequency response function at each machining point and the simulation cutting force output by the cutting force model, the vibration response at each machining parameter and machining position tool tip is obtained by time domain solution;

[0043] Real-time acquisition of vibration signals and cutting force signals updates the nonlinear mapping and cutting force model coefficients, further updates the predicted frequency response function and cutting force model, and predicts the machining parameters and vibration response at the machining point at different times.

[0044] Preferably, when performing hammering experiments, a force hammer is used to strike the tool tip along the x, y and z directions, respectively, and the output signals of the three-axis acceleration sensors at the spindle box are collected; the input and output cross-power spectral densities and the input self-power spectral density are calculated using the input impact force and output acceleration signals, respectively, to obtain the actual measured frequency response functions in the xx, xy, xz, yx, yy, yz, zx, zy and zz directions.

[0045] The intelligent spindle twin control method for robot milling processing provided in the present application first uses the nonlinear mapping of a large number of simulation frequency response functions and a small number of measured frequency response functions to predict the frequency response functions of the remaining machining positions, which makes the predicted frequency response functions more accurate and have a wider range. Then, the cutting force coefficients and tool jump parameters obtained by optimization using the frequency domain error as the target function overcome the influence of noise interference on the existing cutting force coefficient and tool jump parameter identification optimization indicators. Finally, the model updated in real time is used to design the twin control strategy of the next stage online, which completely gives play to the processing performance limit of the industrial robot and overcomes the situation of manual adjustment of parameters and sudden changes in cutting force under varying working conditions. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the technical solutions provided by the present application, the following will briefly introduce the drawings. Obviously, the drawings described below are only some embodiments of the present application.

[0047] Figure 1 The schematic diagram of the overall process of the present application;

[0048] Figure 2 The overall process flow chart of the twin control of the present application. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0050] Although industrial robots cannot completely replace machine tools, they have advantages in machining large and complex parts. In the same workspace, the cost of industrial robots is much lower than that of machine tools. In addition, the portability of industrial robots can improve productivity. Compared with machine tools, the rigidity of industrial robots is extremely low, which limits its application in mechanical processing. The randomly adopted processing parameters can easily make the industrial robot produce unstable vibration in the processing process, thereby affecting the processing quality and efficiency.

[0051] Therefore, an intelligent spindle twin control method for robot milling is designed to realize the design of twin control strategy in virtual space, so as to further exert the processing performance of industrial robots and realize high-precision and high-efficiency processing of industrial robots.

[0052] Taking the commonly used industrial robot milling as an example, Figure 1 , specifically comprising the following steps:

[0053] Step S100, hammering experiments are carried out at a small number of discrete machining points, input impact forces and output acceleration signals of each discrete machining point are collected, and actual measurement frequency response functions are established. The selection of discrete machining points covers all directions in three-dimensional space.

[0054] The frequency response function is simplified as FRF.

[0055] When performing hammering experiments, a force hammer is used to knock the tool tip along the x, y and z directions, and the output signals of the three-direction acceleration sensors at the spindle box are collected. Using the input impact force and the output acceleration signal, the cross-power spectral density of the input and output and the self-power spectral density of the input are calculated respectively, and the actual measurement frequency response functions in the xx, xy, xz, yx, yy, yz, zx, zy and zz directions are obtained.

[0056] Step S200, industrial robot system modeling is performed to obtain a robot simulation model, and the motion equation of the robot simulation model is obtained.

[0057] Based on the motion equation, the simulation frequency response function in the simulation environment is calculated, and the target function is established by the error between the actual measurement frequency response function and the simulation frequency response function.

[0058] Preferably, the industrial robot system is modeled based on the system mass, damping and stiffness parameters of the industrial robot, and the obtained motion equation expression is as follows:

[0059]

[0060] wherein , , respectively represent the system mass matrix, the damping matrix and the stiffness matrix, is an external force, is an angle vector of a joint, is a vibration response, is a first derivative of is a second derivative of

[0061] a system mass matrix is:

[0062]

[0063] wherein and is a Jacobian matrix, is a mass of the ith link, is a number of links, is an inertia tensor of the ith link, is a rotation matrix.

[0064] Preferably, the objective function is as follows:

[0065]

[0066] wherein is an actual measured frequency response function, is a simulated frequency response function, is a weight, i , j , k all are number indexes, x , y , z all are directions, is a total number of frequency samples.

[0067] Preferably, a particle swarm algorithm is adopted to optimize the objective function with respect to elastic parameters to obtain a minimum error value, and a simulated frequency response function corresponding to the minimum error value is calculated. The elastic parameters include damping and stiffness.

[0068] A specific method for optimizing the objective function by the particle swarm algorithm is as follows:

[0069] 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.

[0070] 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.

[0071] The nonlinear mapping is represented as:

[0072]

[0073] in For robot posture, For robot posture in The values ​​of the real and imaginary parts corresponding to the frequency band.

[0074] 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 ;

[0075] High-level mapping The formula for calculation is:

[0076]

[0077] in It is a BP neural network.

[0078] 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.

[0079] The static chip thickness in the cutting force model considers the radial runout, and the dynamic chip thickness in the cutting force model considers the dynamic characteristics of the robot itself and the static chip thickness. The simulation cutting force of the entire milling cutter is calculated based on the chip thickness (static cutting thickness + dynamic cutting thickness), the cutting force coefficient, the runout parameter and the initial cutting angle.

[0080] The specific design method of the simulation cutting force is:

[0081] In step S410, the static chip thickness with radial runout is obtained by calculating the influence according to the unbalance amount in the actual spindle rotation process;

[0082] In step S420, the dynamic chip thickness is calculated according to the vibration response output by the multi-modal modal of the robot body structure and the static chip thickness.

[0083] In step S430, the simulation cutting force of the entire milling cutter is calculated based on the chip thickness (static cutting thickness + dynamic cutting thickness), the initial cutting angle, the runout parameter and the cutting force coefficient.

[0084] Preferably, the cutting thickness, the number of teeth, the cutting depth iteration deployment, the initial cutting angle and the cutting force coefficient of the industrial robot boring cutter are obtained according to the cutting force model coefficient and the runout parameter, and the obtained cutting force model is:

[0085]

[0086] In the formula:

[0087]

[0088] is the x-direction cutting force, is the y-direction cutting force, is the cutting thickness determined by the runout parameter and the modal parameter of the robot, is the number of teeth, is the cutting depth iteration step number, is the initial cutting angle of the j th tooth, is the cutting force coefficient.

[0089] Preferably, during the machining process, the vibration signal is collected to update the robot-milling dynamics model in real time, the robot-milling dynamics model can accurately predict the machining performance at each machining position, and the twin control strategy is designed in the virtual space according to the high-fidelity model and the actual machining requirements.

[0090] In step S500, based on the predicted frequency response function at each machining point and the simulation cutting force output by the cutting force model, the vibration response at the tool tip at each machining parameter and machining position is predicted by combining the Duhamel integral.

[0091] The vibration response is specifically designed as:

[0092] In step S510, based on the predicted frequency response function at each machining point and the simulation cutting force output by the cutting force model, the vibration response at the tool tip of each machining parameter and machining position is obtained by time domain solution;

[0093] In step S520, the vibration signal and the cutting force signal are collected in real time to update the nonlinear mapping and the cutting force model coefficients, further update the predicted frequency response function and the cutting force model, and predict the machining parameters and the vibration response at the machining point at different times.

[0094] In step S600, milling is carried out based on the vibration response, and the acceleration and milling force signals are measured in real time during milling;

[0095] According to the measured acceleration and milling force signals, the modal analysis method is used to obtain the actual frequency response function at the machining point; the BP neural network is trained according to the actual frequency response function at the machining point and the nonlinear mapping is updated, and then the actual frequency response function at the machining point is continuously optimized.

[0096] Through a large number of robot milling experiments, it is found that there is obvious white noise in the measured cutting force, which makes the operating modal analysis method have potential in robot milling modal parameter acquisition.

[0097] Preferably, the frequency response function at the machining point is:

[0098] (7)

[0099] In the formula, is the robot frequency response function matrix, is the cross power spectral density matrix of cutting force and vibration acceleration, is the cutting force self-power spectral density matrix.

[0100] In step S700, according to the frequency domain error between the real-time measured cutting force and the simulation cutting force output by the cutting force model, the frequency domain error is used as the target function of time-energy optimization, and the particle swarm algorithm is used to find the optimal tool jump parameters and initial cutting angle, and the optimal cutting force parameters are obtained to update the cutting force model.

[0101] As Figure 2, step S800, based on the predicted frequency response function at each machining point and the cutting force model output cutting force, considering the milling working condition in the machining process, taking the time-energy optimal as the objective function to obtain the optimal machining parameters (feed speed, rotation speed and posture) and position of the next stage, and continuously control the output amplitude through the machining parameters and position, and continuously optimize the predicted frequency response function and the cutting force model.

[0102] The industrial robot in the robot milling process with constant working condition, taking the measured cutting force as the output, adopts the twin control strategy, continuously controls the output amplitude through the machining parameters (feed speed, rotation speed and posture) and position, obtains new acceleration signal and cutting force signal, and optimizes the predicted frequency response function and the cutting force model through the new acceleration signal and the cutting force signal; so repeatedly, continuously update the nonlinear mapping, cutting force coefficient and tool jump parameter, realize continuous optimization control. The output amplitude is equal to the amplitude of the simulated cutting force.

[0103] The twin control strategy designed by updating the cutting force model in real time not only can optimize the control parameters in the virtual space, but also can avoid the influence of cutting force mutation caused by the change of cutting width, cutting depth and other machining parameters on the machining quality and efficiency, so as to fully exert the machining performance of the industrial robot itself.

[0104] According to the predicted frequency response function at the machining position 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, and the amplitude control of the cutting force is realized by using the feedforward control strategy of trajectory tracking.

[0105] Through repeating steps S600-S800, the industrial robot can continuously optimize the output amplitude during milling, and further improve the precision of the simulated cutting force output by the cutting force model. The demand of "the more you process, the smarter you are" is realized. If the data involved in the update is abnormal, it needs to be cleaned, that is, the frequency response function or the cutting force coefficient and the tool jump parameter which changes greatly compared with before needs to be manually screened.

[0106] In summary, the present application firstly uses the nonlinear mapping of a large number of simulated frequency response functions and a small number of measured frequency response functions to predict the frequency response functions of the remaining machining positions, which makes the predicted frequency response functions more accurate and the range wider. Then, the cutting force coefficient and the tool jump parameter obtained by optimizing the frequency domain error as the objective function overcome the influence of noise interference on the existing cutting force coefficient and tool jump parameter identification optimization index. Finally, the model updated in real time is used to design the twin control strategy of the next stage online, which completely releases the processing performance limit of the industrial robot, and overcomes the situation of cutting force mutation under manual parameter adjustment and variable working condition.

[0107] Finally, it needs to be explained that: the present application discloses the embodiment in the drawing, only relates to the structure involved in the present application, other structures can refer to the usual design, under the condition of not conflicting, the same embodiment and different embodiments of the present application can be combined with each other;

[0108] Finally: the above only for the preferred embodiment of the present application, and not for limiting the present application, any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application, should be included in the protection scope of the present application.

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. The objective function is optimized by combining the particle swarm optimization algorithm with elastic parameters to obtain the minimum error, and the simulated frequency response function corresponding to the minimum error is calculated. 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, with the initial value being 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 the step size until the entire search domain is traversed to obtain different error values. Finally, the simulated frequency response function corresponding to the minimum error value is obtained by calculating the minimum error value. 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.

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. Let i, j, and k represent the weights, i, j, and k be the quantity indices, and x, y, and z be the 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 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 .

5. 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. Let be the initial entry angle of the j-th cutting tooth. This is the cutting force coefficient.

6. 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.

7. 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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