A method for synchronously predicting the stability and surface topography error of robot milling

Abstract

This invention discloses a method for simultaneously predicting the stability and surface topography error of robotic milling, belonging to the field of robotic precision machining and digital manufacturing technology. It includes constructing a non-homogeneous dynamic model considering regenerative effects and static cutting force vectors. The robotic milling system is described as a non-homogeneous time-delay differential equation containing modal parameter matrices, periodic dynamic cutting force coefficient matrices, and static cutting force vectors. This invention simultaneously outputs two key process indicators—machining stability and surface topography error—in a single calculation process. It directly solves for the steady-state fixed point through analytical matrix operations, increasing the calculation speed by tens of times. By including non-homogeneous constant excitation terms caused by static cutting forces in the model, it accurately captures the tool deformation and forced vibration effects of a weakly rigid robot under cutting forces, making the predicted surface error more consistent with actual machining conditions.

Description

Technical Field

[0001] This invention belongs to the field of robot precision machining and digital manufacturing technology, specifically referring to a method for synchronously predicting the stability and surface topography error of robot milling. Background Technology

[0002] Industrial robots are increasingly used in the milling of large and complex components in aerospace, automotive manufacturing and other fields due to their large working space, high flexibility and cost advantages. However, due to the serial linkage structure of industrial robots, their end stiffness is much lower than that of traditional CNC machine tools. Under the action of cutting force, the robot is very prone to low-frequency modal coupling chatter, which leads to the deterioration of the machined surface quality.

[0003] Existing robotic milling dynamics analysis techniques suffer from the following shortcomings: Limited prediction metrics: Most existing methods focus solely on machining stability, primarily outputting stability lobe diagrams. However, in actual machining, even under stable cutting parameters, the low stiffness of the robot means that forced vibrations caused by cutting forces and static tool deflection can still lead to tool deviations from the theoretical trajectory, resulting in significant surface topography errors. Existing models often neglect the prediction of this crucial metric. Oversimplification: Traditional dynamics modeling typically ignores static cutting force components or treats them as constants, failing to accurately describe the periodic forced response terms in non-homogeneous time-delay differential equations, leading to significant prediction errors in machining accuracy. Low computational efficiency: To obtain surface topography errors, time-domain iterative simulation methods are commonly used, which are extremely time-consuming and cannot meet the demands of large-scale, rapid optimization of process parameters in industrial settings. Therefore, this paper proposes a method for simultaneously predicting robotic milling machining stability and surface topography errors. Summary of the Invention

[0004] The purpose of this invention is to provide a method for synchronously predicting the stability and surface topography error of robot milling, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for synchronously predicting the stability and surface topography error of robot milling, comprising the following steps:

[0006] S1. Construct a non-homogeneous dynamic model that considers regeneration effect and static cutting force vector, and describe the robot milling system as a non-homogeneous time-delay differential equation containing modal parameter matrix, periodic dynamic cutting force coefficient matrix and static cutting force vector;

[0007] S2. The cutting cycle is discretized using a semi-discretization method. The state transfer relationship within a single time step is derived, and then the state affine transformation relationship containing the state transition matrix and constant displacement vector within the complete cutting cycle is constructed.

[0008] S3. Determine the stability of the machining process by calculating the eigenvalues ​​of the state transition matrix. Under the premise of stability, solve the steady-state response vector based on the fixed point principle, extract the tool tip displacement and calculate the surface morphology error by combining the tool geometric motion trajectory.

[0009] S4. Define the dynamic roughness index. Quantitatively evaluate the dynamic waviness of the machined surface by calculating the average peak-to-valley difference of the tool tip trajectory envelope within the steady-state period.

[0010] Preferably, the specific process of constructing the non-homogeneous dynamic model in S1 is as follows: The modal parameter matrix M, damping matrix C, and stiffness matrix K of the robot milling system are defined. The modal parameter matrix is ​​obtained by testing the dynamic characteristics of the tool tip under a specific robot posture. A periodic dynamic cutting force coefficient matrix related to cutting parameters, tool geometry parameters, and workpiece material properties is introduced. This dynamic cutting force coefficient matrix fluctuates periodically with the change in the cutting position of the cutting teeth. A static cutting force vector is introduced. The static cutting force vector is calculated based on the shear strength of the workpiece material, the contact characteristics between the tool and the workpiece, and the cutting parameters. The final non-homogeneous time-delay differential equation can simultaneously characterize the dynamic cutting response caused by the regeneration effect and the forced response caused by the static cutting force. The non-homogeneous time-delay differential equation is as follows:

[0011] ,

[0012] Where M, C, and K are modal parameter matrices. This is a periodic dynamic cutting force coefficient matrix. This is the static cutting force vector.

[0013] Preferably, the regeneration effect considered in S1 is specifically the interference effect between the residual texture formed on the workpiece surface in the previous cutting cycle and the cutting edge motion trajectory in the current cutting cycle. The interference effect is characterized by introducing a time delay term in the non-homogeneous time delay differential equation. The time delay is equal to the cutting cycle, that is, the time corresponding to one rotation of the spindle. The cutting cycle is determined by the spindle speed and the number of tool teeth.

[0014] Preferably, the specific process of discretizing the cutting cycle using a semi-discretization method in S2 is as follows: based on the spindle speed, the number of tool teeth, and the required calculation accuracy, a single cutting cycle is divided into N equally spaced time steps, with the time step ranging from 0.0001s to 0.001s, to ensure accurate capture of the periodic changes in dynamic cutting force; for each time step, based on the linearization assumption and numerical integration method, the local state transition matrix and local load term within the time step are calculated. The local state transition matrix characterizes the evolution law of the system state within the time step, and the local load term characterizes the excitation effect of the static cutting force on the system within the time step.

[0015] Preferably, the specific process of constructing the affine transformation relationship of the state within the complete cutting cycle in S2 is as follows: by performing iterative multiplication operations on the local state transition matrix of each time step, a global state transition matrix within the complete cutting cycle is obtained. The global state transition matrix comprehensively reflects the dynamic evolution characteristics of the system within a cutting cycle. By accumulating the local load terms of each time step, a constant displacement vector within the complete cutting cycle is obtained. The constant displacement vector characterizes the cumulative forced response caused by the static cutting force within a cutting cycle. The final constructed affine transformation relationship is as follows:

[0016] ,

[0017] in, The state transition matrix characterizes the dynamic evolution characteristics of the system. It is a constant displacement vector, representing the displacement caused by static cutting force. The cumulative forced response caused within a cycle.

[0018] Preferably, the method for determining the number of time steps N in S2 is as follows: based on the frequency characteristics of the dynamic cutting force and the system's natural frequency, and combined with the computational efficiency requirements, the value of N is optimized while ensuring computational accuracy, so that computational time and accuracy are balanced.

[0019] Preferably, the specific process for determining the stability of the processing in S3 is as follows: using the eigenvalue solving algorithm in linear algebra, the eigenvalues ​​of the global state transition matrix Φ obtained in step S2 are calculated; the modulus of each eigenvalue is calculated one by one; if the modulus of all eigenvalues ​​is less than 1, the processing is determined to be stable and no chatter occurs; if there is at least one eigenvalue whose modulus is greater than or equal to 1, the processing is determined to be unstable and chatter will occur.

[0020] Preferably, the specific process of solving the steady-state response vector under the premise of stability in S3 is as follows: Based on the fixed-point principle, when the system reaches steady state, the system state vector at the end of two adjacent cutting cycles is... Equal, that is The linear equation is solved by matrix inversion or Gaussian elimination to obtain the steady-state response vector. The vibration displacement components of the tool tip are extracted from the steady-state response vector, including displacement components in the X, Y and Z directions. The displacement components are the superposition of dynamic vibration displacement and static tool deflection displacement.

[0021] Preferably, the specific process for calculating the surface topography error in S3 is as follows: Calculate the ideal geometric motion trajectory of the tool based on the tool's geometric parameters and machining process parameters; superimpose the extracted tool tip vibration displacement component onto the tool's ideal geometric motion trajectory to generate the actual motion trajectory envelope of the tool tip; calculate the distance between the actual motion trajectory envelope of the tool tip and the ideal machined surface along the normal direction of the machined surface. This distance is the surface topography error SLE, where the ideal machined surface is determined based on the part's design model and machining path planning, and the normal direction is calculated by differentiating the surface equation of the ideal machined surface.

[0022] Preferably, the specific process of quantifying and evaluating the dynamic waviness of the machined surface in S4 is as follows: Define the Dynamic Roughness Index (DRI) as a quantification index, where the DRI is the average peak-to-valley difference of the tool tip trajectory envelope within a steady-state period; select multiple consecutive cutting cycles after the system reaches steady state as calculation cycles; within each calculation cycle, extract all peak and valley points of the tool tip trajectory envelope, and calculate the distance between each peak point and its adjacent valley point as the peak-to-valley difference; perform an arithmetic mean calculation on all peak-to-valley differences to obtain the Dynamic Roughness Index (DRI). The smaller the DRI value, the smaller the dynamic waviness of the machined surface and the better the surface quality. The extraction of peak and valley points uses extreme value detection, determining extreme points by comparing the magnitudes of adjacent displacement data points.

[0023] Compared with the prior art, the beneficial effects of the present invention are:

[0024] 1. This invention overcomes the limitation of traditional methods that can only predict chatter, and can simultaneously output two key process indicators, processing stability and surface morphology error (SLE), in a single calculation, providing process engineers with a more comprehensive basis for decision-making.

[0025] 2. This invention directly solves for the steady-state fixed point through analytical matrix operations, replacing the traditional long-period time-domain simulation. The calculation speed is increased by tens of times, making it possible to complete the optimization of process parameters across the entire speed range within minutes.

[0026] 3. This invention includes a non-homogeneous constant excitation term caused by static cutting force in the model, which accurately captures the tool deformation and forced vibration effect of a weakly rigid robot under the action of cutting force, making the predicted surface error more consistent with the actual machining situation. Attached Figure Description

[0027] Figure 1 This invention provides the operational flow of a method for simultaneously predicting the stability and surface topography error in robot milling. Figure 1 ;

[0028] Figure 2 This invention provides the operational flow of a method for simultaneously predicting the stability and surface topography error in robot milling. Figure 2 ;

[0029] Figure 3 This invention provides the operational flow of a method for simultaneously predicting the stability and surface topography error in robot milling. Figure 3 ;

[0030] Figure 4 This invention provides the operational flow of a method for simultaneously predicting the stability and surface topography error in robot milling. Figure 4 . Detailed Implementation

[0031] 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.

[0032] Example

[0033] Please see Figures 1-4 As shown, the present invention provides a technical solution comprising the following steps:

[0034] S1. Construct a non-homogeneous dynamic model that considers regeneration effect and static cutting force vector, and describe the robot milling system as a non-homogeneous time-delay differential equation containing modal parameter matrix, periodic dynamic cutting force coefficient matrix and static cutting force vector;

[0035] S2. The cutting cycle is discretized using a semi-discretization method. The state transfer relationship within a single time step is derived, and then the state affine transformation relationship containing the state transition matrix and constant displacement vector within the complete cutting cycle is constructed.

[0036] S3. Determine the stability of the machining process by calculating the eigenvalues ​​of the state transition matrix. Under the premise of stability, solve the steady-state response vector based on the fixed point principle, extract the tool tip displacement and calculate the surface morphology error by combining the tool geometric motion trajectory.

[0037] S4. Define the dynamic roughness index. Quantitatively evaluate the dynamic waviness of the machined surface by calculating the average peak-to-valley difference of the tool tip trajectory envelope within the steady-state period.

[0038] In this embodiment, the specific process of constructing the non-homogeneous dynamic model in S1 is as follows: the modal parameter matrix M, damping matrix C, and stiffness matrix K of the robot milling system are defined. The modal parameter matrix is ​​obtained by testing the dynamic characteristics of the tool tip under a specific robot posture. A periodic dynamic cutting force coefficient matrix related to cutting parameters, tool geometry parameters, and workpiece material properties is introduced.

[0039] The dynamic cutting force coefficient matrix fluctuates periodically with the change of the cutting position of the cutting teeth; a static cutting force vector is introduced. The static cutting force vector is calculated based on the shear strength of the workpiece material, the contact characteristics between the tool and the workpiece, and the cutting parameters. The final non-homogeneous time-delay differential equation can simultaneously characterize the dynamic cutting response caused by the regeneration effect and the forced response caused by the static cutting force. The non-homogeneous time-delay differential equation is as follows:

[0040] ,

[0041] Where M, C, and K are modal parameter matrices. This is a periodic dynamic cutting force coefficient matrix. This is the static cutting force vector.

[0042] In this embodiment, the regeneration effect considered in S1 is specifically the interference effect between the residual texture formed on the workpiece surface in the previous cutting cycle and the cutting edge movement trajectory in the current cutting cycle. The interference effect is characterized by introducing a time delay term in the non-homogeneous time delay differential equation. The time delay is equal to the cutting cycle, that is, the time corresponding to one rotation of the spindle. The cutting cycle is determined by the spindle speed and the number of tool teeth.

[0043] In this embodiment, the specific process of using a semi-discretization method to discretize the cutting cycle in S2 is as follows: based on the spindle speed, the number of tool teeth and the calculation accuracy requirements, a single cutting cycle is divided into N equally spaced time steps, with the time step value ranging from 0.0001s to 0.001s, to ensure that the periodic changes of dynamic cutting force can be accurately captured.

[0044] Specifically, for each time step, based on the linearization assumption and numerical integration method, the local state transition matrix and local load terms within the time step are calculated. The local state transition matrix characterizes the evolution law of the system state within the time step, and the local load terms characterize the excitation effect of the static cutting force on the system within the time step.

[0045] In this embodiment, the specific process of constructing the affine transformation relationship of the state within the complete cutting cycle in S2 is as follows: by performing iterative multiplication operations on the local state transition matrix of each time step, the global state transition matrix within the complete cutting cycle is obtained.

[0046] Specifically, the global state transition matrix comprehensively reflects the dynamic evolution characteristics of the system within a cutting cycle; by accumulating the local load terms for each time step, the constant displacement vector within the complete cutting cycle is obtained.

[0047] The constant displacement vector characterizes the cumulative forced response caused by the static cutting force within one cutting cycle, and the final affine transformation relationship is as follows:

[0048] ,

[0049] in, The state transition matrix characterizes the dynamic evolution characteristics of the system. It is a constant displacement vector, representing the displacement caused by static cutting force. The cumulative forced response caused within a cycle.

[0050] In this embodiment, the method for determining the number of time steps N in S2 is as follows: based on the frequency characteristics of the dynamic cutting force and the inherent frequency of the system, and combined with the computational efficiency requirements, the value of N is optimized while ensuring computational accuracy, so that computational time and accuracy are balanced.

[0051] In this embodiment, the specific process of determining the stability of the processing in step S3 is as follows: using the eigenvalue solving algorithm in linear algebra, the eigenvalues ​​of the global state transition matrix Φ obtained in step S2 are calculated; the modulus of each eigenvalue is calculated one by one; if the modulus of all eigenvalues ​​is less than 1, the processing is determined to be stable and no chatter occurs; if there is at least one eigenvalue with a modulus greater than or equal to 1, the processing is determined to be unstable and chatter will occur.

[0052] In this embodiment, the specific process of solving the steady-state response vector under the premise of stability in S3 is as follows: Based on the fixed-point principle, when the system reaches steady state, the system state vector at the end of two adjacent cutting cycles is... Equal, that is The steady-state response vector can be obtained by solving the linear equation through matrix inversion or Gaussian elimination.

[0053] The vibration displacement components of the tool tip are extracted from the steady-state response vector, including displacement components in the X, Y and Z directions. The displacement components are the superposition values ​​of dynamic vibration displacement and static tool deflection displacement.

[0054] In this embodiment, the specific process of calculating the surface topography error in S3 is as follows: calculate the ideal geometric motion trajectory of the tool based on the tool's geometric parameters and machining process parameters.

[0055] The extracted tool tip vibration displacement components are superimposed onto the ideal geometric motion trajectory of the tool to generate the actual motion trajectory envelope of the tool tip. The distance between the actual motion trajectory envelope of the tool tip and the ideal machining surface is calculated along the normal direction of the machined surface. This distance is the surface topography error SLE. The ideal machining surface is determined according to the part design model and machining path planning, and the normal direction is calculated by differentiating the surface equation of the ideal machining surface.

[0056] In this embodiment, the specific process of quantifying and evaluating the dynamic waviness of the machined surface in S4 is as follows: the dynamic roughness index DRI is defined as the quantitative index, which is the average value of the peak-valley difference of the tool tip trajectory envelope within the steady-state period; and multiple consecutive cutting cycles after the system reaches steady state are selected as the calculation cycle.

[0057] Within each calculation cycle, all peak and valley points of the tool tip trajectory envelope are extracted, and the distance between each peak point and its adjacent valley point is calculated as the peak-valley difference. The arithmetic mean of all peak-valley differences is calculated to obtain the dynamic roughness index (DRI). The smaller the DRI value, the smaller the dynamic waviness of the machined surface and the better the surface quality. The extraction of peak and valley points adopts extreme value detection, and the extreme points are determined by comparing the magnitude of adjacent displacement data points.

[0058] In this embodiment, the synchronous prediction of the aluminum alloy milling process of the six-axis industrial robot is as follows:

[0059] Step 1: System Parameter Identification and Setting:

[0060] First, the modal parameters of the robot's blade tip in a specific posture, including the modal mass matrix, were obtained through hammer impact experiments. Damping matrix and stiffness matrix Set machining process parameters: spindle speed axial depth radial cut width Feed per tooth Set tool geometry parameters: number of teeth helix angle ,radius .

[0061] Step 2: Calculation of cutting force coefficient matrix:

[0062] Discretize the tool along the axial direction. Each infinitesimal element; based on the shear force coefficient ( ) and plowing shear force coefficient ( The time-varying dynamic cutting force coefficient matrix is ​​calculated using numerical integration methods. and static cutting force vector In this step, a window function is used. Determine whether the cutting teeth have cut into the workpiece.

[0063] Step 3: Construct the augmented state space:

[0064] Introducing state vectors The second-order dynamic equations are transformed into first-order form:

[0065] ,

[0066] Among them, non-homogeneous terms This is a key feature of this implementation method, which introduces the influence of static forces on the system.

[0067] Step 4: Calculate the periodic state transition matrix and constant displacement vector:

[0068] Cutting cycle Divided into time interval .

[0069] For each time interval Calculate the local transition matrix and local load terms .

[0070] Construct the full-cycle state transition matrix through iterative multiplication (or matrix assembly). :

[0071] ,

[0072] Simultaneous calculation of the cumulative constant displacement vector throughout the entire period :

[0073] .

[0074] Step 5: Output the results:

[0075] Stability assessment: Calculation The eigenvalues ​​are determined. If the magnitude of all eigenvalues ​​is less than 1, the output is stable; otherwise, the output exhibits chattering.

[0076] SLE prediction: If the system is stable, solve the linear equations. Obtain the steady-state vibration response .Will The displacement components are superimposed onto the rigid body motion trajectory of the tool, generating the tool tip envelope. The distance between the maximum value of the envelope and the ideal surface is calculated, which is the SLE value.

[0077] Based on the prediction results, adjust the spindle speed or depth of cut until the minimum and stable combination of process parameters for SLE is found.

[0078] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their likenesses.

[0079] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for synchronously predicting the stability and surface topography error of robot milling, characterized in that, Includes the following steps: S1. Construct a non-homogeneous dynamic model that considers regeneration effect and static cutting force vector, and describe the robot milling system as a non-homogeneous time-delay differential equation containing modal parameter matrix, periodic dynamic cutting force coefficient matrix and static cutting force vector; S2. The cutting cycle is discretized using a semi-discretization method. The state transfer relationship within a single time step is derived, and then the state affine transformation relationship containing the state transition matrix and constant displacement vector within the complete cutting cycle is constructed. S3. Determine the stability of the machining process by calculating the eigenvalues ​​of the state transition matrix. Under the premise of stability, solve the steady-state response vector based on the fixed point principle, extract the tool tip displacement and calculate the surface morphology error by combining the tool geometric motion trajectory. S4. Define the dynamic roughness index. Quantitatively evaluate the dynamic waviness of the machined surface by calculating the average peak-to-valley difference of the tool tip trajectory envelope within the steady-state period.

2. The method for synchronously predicting the stability and surface topography error of robot milling as described in claim 1, characterized in that: The specific process of constructing the non-homogeneous dynamic model in S1 is as follows: the modal parameter matrix is ​​obtained by testing the dynamic characteristics of the tool tip under a specific robot posture; a periodic dynamic cutting force coefficient matrix related to cutting parameters, tool geometry parameters, and workpiece material properties is introduced, and the dynamic cutting force coefficient matrix fluctuates periodically with the change of the cutting position of the tool teeth; a static cutting force vector is introduced. The static cutting force vector is calculated based on the shear strength of the workpiece material, the contact characteristics between the tool and the workpiece, and the cutting parameters. The final non-homogeneous time-delay differential equation can simultaneously characterize the dynamic cutting response caused by the regeneration effect and the forced response caused by the static cutting force. The non-homogeneous time-delay differential equation is as follows: ， Where M, C, and K are modal parameter matrices. This is a periodic dynamic cutting force coefficient matrix. This is the static cutting force vector.

3. The method for synchronously predicting the stability and surface topography error of robot milling as described in claim 2, characterized in that: The regeneration effect considered in S1 is specifically the interference effect between the residual texture formed on the workpiece surface in the previous cutting cycle and the cutting edge movement trajectory in the current cutting cycle. The interference effect is characterized by introducing a time delay term in the non-homogeneous time delay differential equation. The time delay is equal to the cutting cycle, that is, the time corresponding to one rotation of the spindle. The cutting cycle is determined by the spindle speed and the number of tool teeth.

4. The method for synchronously predicting the stability and surface topography error of robot milling as described in claim 3, characterized in that: The specific process of discretizing the cutting cycle using the semi-discretization method in S2 is as follows: Based on the spindle speed, the number of tool teeth, and the calculation accuracy requirements, a single cutting cycle is divided into N equally spaced time steps; for each time step, based on the linearization assumption and numerical integration method, the local state transition matrix and local load terms within the time step are calculated. The local state transition matrix represents the evolution law of the system state within the time step, and the local load terms represent the excitation effect of the static cutting force on the system within the time step.

5. The method for synchronously predicting the stability and surface topography error of robot milling according to claim 4, characterized in that: The specific process of constructing the affine transformation relationship of the state within the complete cutting cycle in S2 is as follows: By performing iterative multiplication on the local state transition matrix of each time step, the global state transition matrix within the complete cutting cycle is obtained. This global state transition matrix comprehensively reflects the dynamic evolution characteristics of the system within a cutting cycle. By accumulating the local load terms of each time step, the constant displacement vector within the complete cutting cycle is obtained. This constant displacement vector characterizes the cumulative forced response caused by the static cutting force within a cutting cycle. The final constructed affine transformation relationship is as follows: ， in, The state transition matrix characterizes the dynamic evolution characteristics of the system. It is a constant displacement vector, representing the displacement caused by static cutting force. The cumulative forced response caused within a cycle.

6. The method for synchronously predicting the stability and surface topography error of robot milling as described in claim 5, characterized in that: The method for determining the number of time steps N in S2 is as follows: based on the frequency characteristics of the dynamic cutting force and the system's natural frequency, and combined with the computational efficiency requirements, the value of N is optimized while ensuring computational accuracy, so that computational time and accuracy are balanced.

7. The method for synchronously predicting the stability and surface topography error of robot milling as described in claim 6, characterized in that: The specific process for determining the stability of the processing in S3 is as follows: using the eigenvalue solving algorithm in linear algebra, the eigenvalues ​​of the global state transition matrix Φ obtained in step S2 are calculated; the modulus of each eigenvalue is calculated one by one. If the modulus of all eigenvalues ​​is less than 1, the processing is determined to be stable and no chatter occurs; if there is at least one eigenvalue whose modulus is greater than or equal to 1, the processing is determined to be unstable and chatter will occur.

8. The method for synchronously predicting the stability and surface topography error of robot milling according to claim 7, characterized in that: The specific process of solving the steady-state response vector under the premise of stability in S3 is as follows: Based on the fixed-point principle, when the system reaches steady state, the system state vector at the end of two adjacent cutting cycles is... Equal, that is By solving the linear equation, the steady-state response vector is obtained; the vibration displacement components of the tool tip are extracted from the steady-state response vector, including displacement components in the X, Y and Z directions, and the displacement components are the superposition values ​​of dynamic vibration displacement and static tool deflection displacement.

9. The method for synchronously predicting the stability and surface topography error of robot milling as described in claim 8, characterized in that: The specific process for calculating the surface topography error in S3 is as follows: Calculate the ideal geometric motion trajectory of the tool based on the tool's geometric parameters and machining process parameters; superimpose the extracted tool tip vibration displacement component onto the tool's ideal geometric motion trajectory to generate the actual motion trajectory envelope of the tool tip; calculate the distance between the actual motion trajectory envelope of the tool tip and the ideal machining surface along the normal direction of the machined surface, and this distance is the surface topography error.

10. The method for synchronously predicting the stability and surface topography error of robot milling according to claim 9, characterized in that: The specific process of quantitatively evaluating the dynamic waviness of the machined surface in S4 is as follows: Define the dynamic roughness index DRI as a quantitative index, wherein the dynamic roughness index is the average value of the peak-valley difference of the tool tip trajectory envelope within the steady-state period. Multiple consecutive cutting cycles after the system reaches steady state are selected as the calculation cycle. Within each calculation cycle, all peak and valley points of the tool tip trajectory envelope are extracted, and the distance between each peak point and the adjacent valley point is calculated as the peak-valley difference. The arithmetic mean of all peak-valley differences is calculated to obtain the dynamic roughness index (DRI). The smaller the DRI value, the smaller the dynamic waviness of the machined surface and the better the surface quality. The extraction of peak and valley points adopts extreme value detection, and the extreme points are determined by comparing the magnitude of adjacent displacement data points.

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