A method and system for predicting low-frequency chatter stability in robot milling

Abstract

The present invention belongs to the technical field related to robot milling processing, and discloses a method and system for predicting the stability of low-frequency chatter in robot milling. The method comprises the following steps: (1) establishing an instantaneous cutting force calculation model considering surface renewal based on the robot milling process; (2) establishing a low-frequency chatter stability prediction model considering the modal coupling effect based on the impulse response function method, and then using the low-frequency chatter stability prediction model to predict low-frequency chatter. The present invention calculates dynamic cutting thickness based on surface renewal (SR), adopts a dynamic modeling strategy based on the impulse response function method (IRF), combines SR and IRF, and considers the milling intermittent cutting characteristics and modal coupling effects at the same time, so as to achieve accurate prediction of low-frequency chatter.

Description

Technical Field

[0001] The present invention belongs to the technical field related to robot milling processing, and more specifically, relates to a method and system for predicting low-frequency vibration stability of robot milling. Background Art

[0002] Chatter is the main obstacle to the quality and efficiency of robot milling. At present, the research on chatter is mainly divided into high-frequency chatter and low-frequency chatter. Unlike the machine tool processing system, the stiffness of the machine tool is usually much higher than the stiffness of the tool structure. Therefore, in the chatter research, only the high-frequency chatter dominated by the tool mode is generally considered. For robot milling, when performing some large excess processing, in order to improve the processing efficiency, large-sized tools with stiffness much greater than the robot structure are usually used. Under such processing conditions, the robot body is very prone to low-frequency chatter, and the existing stability models cannot achieve reasonable low-frequency chatter prediction. Therefore, the mechanism and prediction model of low-frequency chatter need to be studied. Establishing a low-frequency chatter stability prediction model can effectively improve the robot processing efficiency and ensure the stability of robot milling.

[0003] For low-frequency chatter in robot milling, some scholars have tried to explain the chatter mechanism and predict stability by introducing modal coupling effect. In 2006, Pan et al. predicted the stability boundary of low-frequency chatter in robot milling based on modal coupling effect. In this study, they ignored the influence of damping and established a 2-DOF modal coupling dynamic model. The stability prediction results showed that the stability limit of the robot considering modal coupling chatter depends on the angle between the machining force vector and the main stiffness direction. Liu et al. measured the accuracy of modal coupling chatter stability prediction using reliability theory. In addition, many scholars have also studied modal coupling chatter, all with different focuses, which will not be repeated here. The modal coupling effect can explain the occurrence of low-frequency chatter to a certain extent, but the existing model uses a cutting force modeling method similar to the turning model, ignoring the dynamic changes in the cutting force direction and the intermittent cutting characteristics of milling.

[0004] In 2021, based on the above existing robot milling stability research methods, Celikag et al. established modal coupling and regenerative chatter prediction models for robot low-frequency chatter analysis, and verified them through milling experiments. The results show that: 1. The stability boundary obtained by the existing modal coupling chatter mechanism is inconsistent with the experimental results. The existing modal coupling chatter mechanism ignores the intermittent cutting characteristics of milling, and the stability prediction results are not related to the rotational speed, which has obvious defects. 2. The stability boundary obtained by the existing regenerative chatter mechanism is inconsistent with the experimental results, but there is a certain speed correlation in the low-speed zone (0-500rpm). It can be seen that the existing modal coupling chatter theory is not suitable for milling operations, and the stability prediction results of the regenerative chatter theory at medium and high speeds show serious deviations.

[0005] In summary, the existing stability model cannot achieve reasonable prediction for the low-frequency chatter of robots whose chatter frequency (10-30Hz) is much lower than the tooth-passing frequency (100-600Hz). In view of the above technical problems, it is urgent to propose a low-frequency chatter prediction method for robot milling to achieve reasonable stability boundary prediction, so as to support the optimization and improvement of robot milling efficiency and processing stability. Summary of the invention

[0006] In response to the above defects or improvement needs of the prior art, the present invention provides a method and system for predicting the stability of low-frequency chatter in robot milling, which calculates the dynamic cutting thickness based on surface renewal (SR), adopts a dynamic modeling strategy based on the impulse response function method (IRF), combines SR and IRF, and considers the intermittent cutting characteristics of milling and the modal coupling effect, thereby realizing accurate prediction of low-frequency chatter.

[0007] To achieve the above object, according to one aspect of the present invention, a method for predicting low-frequency chatter stability of robot milling is provided, the method comprising the following steps:

[0008] (1) Based on the robot milling process, an instantaneous cutting force calculation model considering surface renewal is established. The expression of the instantaneous cutting force calculation model is:

[0009]

[0010] In the formula, x T,ij,n (t),y T,ij,n (t) is the coordinate of the cutting interference point on the workpiece surface at time t in the tool coordinate system; T,ij (t),y T,ij (t) is the coordinate of the tool edge element in the tool coordinate system when the tool is in the cutting state at time t; represents the instantaneous radial contact angle; g ij (t) is the unit step function for determining whether cutting occurs; N is the number of teeth; M is the discrete number of blade elements;

[0011] K x,ij , K y,ij , K z,ij is the equivalent cutting force coefficient in x, y, and z directions, as shown below, where K tc is the tangential cutting force coefficient, K rc is the radial cutting force coefficient K ac is the axial cutting force coefficient;

[0012]

[0013] (2) Based on the impulse response function method, a low-frequency flutter stability prediction model considering the modal coupling effect is established, and then the low-frequency flutter stability prediction model is used to predict the low-frequency flutter. The expression of the low-frequency flutter stability prediction model is:

[0014]

[0015] In the formula, τ is a discrete time interval; k is a discrete number; f ij is the unit impulse response function within a given bandwidth, containing all modal information within the selected bandwidth. The subscripts i and j represent the response in the i direction caused by the excitation in the j direction. i (nτ) is the cutting force in the i direction at time t=nτ.

[0016] Furthermore, in the tool coordinate system XOY, the tool tip coordinate B at any time is expressed as:

[0017]

[0018] Where R represents the tool radius, t represents time, and x lev,ij (t),y lev,ij (t) represents the additional vibration displacement caused by low-frequency flutter, represents the instantaneous radial contact angle;

[0019] When cutting occurs, the coordinates of the tool tip need to be recorded as cutting point A. At this time, the formula for the coordinates of the cutting point in the tool coordinate system changing with the cutting process is:

[0020]

[0021] Where, f represents the feed rate; t n is the moment when cutting occurs; (x lev,ij (t n ), y lev,ij (t n )) is the additional vibration displacement caused by low-frequency flutter.

[0022] Furthermore, the angle of the cutting point in the tool coordinate system also changes with the cutting process as follows:

[0023]

[0024] Furthermore, point Bn(x T,ij ,y T,ij ) is the coordinate of the blade element in the tool coordinate system at the current moment; is the instantaneous radial contact angle at the current moment, The cutting point corresponding to the angle at this time is called the cutting interference point at this time; the cutting interference point is on the same straight line as the tool tip point B and the tool center point O.

[0025] Furthermore, the judgment function for determining whether cutting occurs is:

[0026]

[0027] In the formula, g ij (t) is the unit step function to determine whether cutting occurs, g ij (t) = 1 means cutting occurs, g ij (t) = 0 means that no cutting occurs.

[0028] Furthermore, when cutting occurs, the workpiece surface needs to be updated, and the cutting interference point A3 is replaced by the current tool edge element B3 as a new cutting interference point for subsequent calculations.

[0029] Furthermore, in the modeling of the modal coupling effect, an impulse response function with a predetermined bandwidth is used to characterize the modal characteristics in each direction.

[0030] Furthermore, the vibration displacement of each mode in the x direction caused by the cutting force in the x, y, and z directions corresponds to the formula:

[0031]

[0032] Where X(kτ+τ) is the response of the system in the x direction at time (k+1)τ, τ is the discrete time interval, and k is a discrete number; f ab It is the unit impulse response function within a given bandwidth and contains all modal information within the selected bandwidth. The subscripts a and b here represent the response in the a direction caused by the excitation in the b direction.

[0033] Furthermore, in step (2), the cutting force and IRF of the first k steps are used to calculate the response signal x of the k+1th step. lev,ij ((k+1)τ),y lev,ij ((k+1)τ),z lev,ij ((k+1)τ); then, according to the vibration response signal at this time, the current cutting edge element (x T,ij ((k+1)τ),y T,ij ((k+1)τ)) and the cutting interference point (x T,ij,n ((k+1)τ),y T,ij,n ((k+1)τ)) coordinates; then, determine whether cutting is currently occurring. If cutting is occurring, calculate the current cutting force F x ((k+1)τ),F y ((k+1)τ),F z((k+1)τ), and the cutting interference points on the workpiece surface are updated; if no cutting occurs, the cutting force is zero, and the cutting interference points on the workpiece surface do not need to be updated.

[0034] According to another aspect of the present invention, a robot milling vibration stability prediction system is provided, wherein the system uses the robot milling low-frequency vibration stability prediction method as described above to predict low-frequency vibration and sends the prediction result to the robot.

[0035] In general, compared with the prior art, the above technical solution conceived by the present invention, the method and system for predicting the stability of low-frequency chatter in robot milling provided by the present invention mainly have the following beneficial effects:

[0036] 1. An instantaneous cutting force calculation model considering surface renewal was established to calculate the size of the dynamic cutting thickness from a geometric level, thereby solving the problem that the intermittent cutting characteristics caused by low-frequency chatter in the model are difficult to accurately calculate.

[0037] 2. A dynamic modeling strategy based on the impulse response function (IRF) method is adopted, and the frequency response function used in traditional modeling is replaced by the time domain response signal, thereby taking into account all the dynamic performance of the robot, making the model more accurate, and then making the vibration prediction more accurate, while reducing the amount of calculation and omitting modal identification, simplifying the process and reducing the generation of errors.

[0038] 3. Combining SR and IRF, the intermittent cutting characteristics and modal coupling effects of milling are considered simultaneously, achieving accurate prediction of low-frequency chatter. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a geometrical schematic diagram of the instantaneous cutting force calculation model considering surface renewal constructed by the present invention;

[0040] Figure 2 (a) and (b) are schematic diagrams of the instantaneous cutting force calculation model considering surface renewal;

[0041] Figure 3 (a) to (i) are schematic diagrams of impulse response functions in various directions;

[0042] Figure 4 It is a schematic diagram of the modal coupling effect of the robot;

[0043] Figure 5 This is a schematic diagram of the vibration response solution process based on IRF;

[0044] Figure 6 (a) and (b) are schematic diagrams of milling stability prediction under low-frequency chatter. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0046] The present invention provides a method for predicting the stability of low-frequency chatter in robot milling, and the method mainly comprises the following steps:

[0047] Step 1: Based on the robot milling process, an instantaneous cutting force calculation model considering surface renewal is established. The expression of the instantaneous cutting force calculation model is:

[0048]

[0049] In the formula, x T,ij,n (t),y T,ij,n (t) is the coordinate of the cutting interference point on the workpiece surface at time t in the tool coordinate system; T,ij (t),y T,ij (t) is the coordinate of the tool edge element in the tool coordinate system when the tool is in the cutting state at time t; represents the instantaneous radial contact angle; g ij (t) is the unit step function for determining whether cutting occurs; N is the number of teeth; M is the discrete number of blade elements;

[0050] K x,ij , K y,ij , K z,ij is the equivalent cutting force coefficient in x, y, and z directions, as shown below, where K tc is the tangential cutting force coefficient, K rc is the radial cutting force coefficient K ac is the axial cutting force coefficient.

[0051]

[0052] In this embodiment, the geometric model of the surface update is as follows: Figure 1 As shown, in the tool coordinate system (XOY), the tool tip coordinate B at any time can be expressed as:

[0053]

[0054] Where R represents the tool radius, t represents time, and x lev,ij (t),y lev,ij (t) represents the additional vibration displacement caused by low-frequency flutter, represents the instantaneous radial contact angle, i and j represent the number of cutting elements and the number of teeth, respectively. During the cutting process, the position coordinates of the cutting point in the tool coordinate system where effective cutting occurs and the time A(x T,ij (t n ),y T,ij (t n )). Since the cutting point A is located on the workpiece, the coordinates of the cutting point in the tool coordinate system change with the cutting process and can be expressed as:

[0055]

[0056] Where f represents the feed rate; t n is the moment when cutting occurs; (x lev,ij (t n ), y lev,ij (t n )) is the additional vibration displacement caused by low-frequency chatter. It can be seen that the angle of the cutting point in the tool coordinate system also changes with the cutting process, which can be expressed as:

[0057]

[0058] This gives the angles of all cutting points on the workpiece surface in the tool coordinate system. and coordinates A(x T,ij,n (t),y T,ij,n (t)).

[0059] See also Figure 2 , point Bn(x T,ij ,y T,ij ) is the coordinate of the tool edge element in the tool coordinate system at the current moment. is the instantaneous radial contact angle at the current moment, and n = 2 or 3 in the figure. For the convenience of expression, The cutting point corresponding to the angle at this time is called the cutting interference point A2. The cutting interference point is on the same straight line as the tool tip point B2 and the tool center point O2.

[0060] If the tool tip point B2 is between the cutting interference point A2 and the tool center point O2, no cutting occurs at this time, and the current instantaneous cutting thickness h ij (t) and cutting force are zero. When the tool rotates a tooth angle, the cutting interference point A3 is the same as A2. Because the previous tooth did not cut into the current workpiece surface, at this time, the cutting interference point A3 is between the blade element B3 and the tool center point O3, and cutting occurs at this time. The instantaneous cutting thickness is composed of the cutting interference point A3 and the blade element B3. The judgment function for determining whether cutting occurs is as follows:

[0061]

[0062] Among them, g ij (t) is the unit step function to determine whether cutting occurs, g ij (t) = 1 means cutting occurs, g ij (t) = 0 means that no cutting occurs.

[0063] On the other hand, when cutting occurs, the workpiece surface needs to be updated. As shown in formula (2), the cutting interference point A3 is replaced by the current blade element B3 as the new cutting interference point for subsequent calculations.

[0064] The calculation model of instantaneous cutting force considering surface renewal is expressed as follows:

[0065]

[0066] In the formula, x T,ij,n (t),y T,ij,n (t) is the coordinate of the cutting interference point on the workpiece surface at time t in the tool coordinate system, x T,ij (t),y T,ij (t) is the coordinate of the tool edge element in the tool coordinate system when the tool is in the cutting state at time t.

[0067] Step 2: Based on the impulse response function method, a low-frequency flutter stability prediction model considering the modal coupling effect is established, and then the low-frequency flutter stability prediction model is used to predict the low-frequency flutter. The expression of the low-frequency flutter stability prediction model is:

[0068]

[0069] In the formula, τ is a discrete time interval; k is a discrete number; f ij is the unit impulse response function within a given bandwidth, containing all modal information within the selected bandwidth. The subscripts i and j represent the response in the i direction caused by the excitation in the j direction. i (nτ) is the cutting force in the i direction at time t=nτ.

[0070] In order to consider the intermittent cutting characteristics, the surface renewal model is used instead of the traditional time-delay model to avoid the calculation error of the instantaneous cutting thickness caused by the separation of the cutter teeth and workpieces during multi-tooth cutting. In this way, the regeneration effect caused by intermittent cutting can be considered in the stability prediction of low-frequency chatter. Then, it is necessary to combine the modal coupling effect to achieve effective prediction of low-frequency chatter. In the modeling of the modal coupling effect, an IRF with a certain bandwidth is used to characterize the modal characteristics in all directions. Compared with multi-modal parameters, IRF can retain more modal information and is more convenient to combine with the SR model. The impulse response functions in each direction are as follows Figure 3 shown.

[0071] See also Figure 4 , considering the dynamic characteristics of the robot in three physical degrees of freedom (DOFs) and the modal coupling between each DOF, the vibration response of the robot in any direction will be affected by the force in each direction, and the expression is as follows:

[0072]

[0073] Where X(ω), Y(ω), and Z(ω) represent the vibration of the robot end in the x, y, and z directions, respectively. ij represents the frequency response function of the robot end in the i-th direction in response to the excitation in the j-th direction, F i (ω) represents the cutting force in the direction i of the robot end, and the expression is as follows:

[0074]

[0075] Figure 4 In the equation (6), m is the modal order. Taking the x direction as an example, the time domain expression is converted as follows:

[0076]

[0077]

[0078]

[0079] Where M n,ij , C n,ij , K n,ij are the modal parameters of each order in each direction, X xn , X yn , X zn They represent the vibration displacement of each mode in the x direction caused by the cutting force in the x, y, and z directions, respectively. The expressions are as follows:

[0080] X(t)=X x1 (t)+X y1 (t)+X z1 (t)+…+X xm (t)+X ym (t)+X zm (t) (9)

[0081] The IRF method is used for the time domain solution of vibration signals. Using IRF instead of multimodal parameters, formulas (8) and (9) can be rewritten as:

[0082]

[0083] where X(kτ+τ) is the response of the system in the x direction at time (k+1)τ, τ is the discrete time interval, and k is a discrete number; fij It is the unit impulse response function within a given bandwidth, containing all modal information within the selected bandwidth. The subscripts i and j represent the response in the i direction caused by the excitation in the j direction.

[0084] Similarly, the response expressions in the y and z directions can be obtained as follows:

[0085]

[0086]

[0087] In the formula, F x (nτ), F y (nτ), F z (nτ) are the cutting forces in the x, y, and z directions at t = nτ, respectively.

[0088] The three-dimensional vibration displacement response of the robot based on the impulse response function method and considering the modal coupling effect can be rewritten as follows:

[0089]

[0090] Where:

[0091] The iterative solution process of formula (5) and formula (12) is represented by a graph, as shown in Figure 5 First, the cutting force and IRF of the first k steps are used to calculate the response signal x of the k+1 step. lev,ij ((k+1)τ),y lev,ij ((k+1)τ),z lev,ij ((k+1)τ); then according to the vibration response signal at this time, the current cutting blade element (x T,ij ((k+1)τ),y T,ij ((k+1)τ)) and the cutting interference point (x T,ij,n ((k+1)τ),y T,ij,n The coordinates of ((k+1)τ)) can be calculated according to formula (1) and formula (2). Formula (4) is used to determine whether cutting is currently occurring. If cutting is occurring, formula (5) is used to calculate the current cutting force F x ((k+1)τ),F y ((k+1)τ),F z ((k+1)τ), and update the cutting interference point (x T,ij,k+1 (t),y T,ij,k+1 (t)). If no cutting occurs, the cutting force is zero and the cutting interference points on the workpiece surface do not need to be updated.

[0092] like Figure 5 Step T k+1 As shown in the calculation process, there is no tool-workpiece separation in the first k steps, and the vibration response calculation formula is shown in formula (12). According to the above process, the cutting interference points on the workpiece surface are updated, and the vibration displacement and cutting force of the k+1th step are calculated.

[0093] T k+2 The calculation process of the step is similar to T k+1 The calculation process of the first step is the same, and the vibration response equation is as follows:

[0094]

[0095] According to formula (4), there is no cutting at present, the cutting force is zero, and there is no need to update the cutting interference point on the workpiece surface. The vibration displacement x is calculated. lev,ij ((k+2)τ),y lev,ij ((k+2)τ),z lev,ij ((k+2)τ).

[0096] When calculating step Tk+3, since the tool-workpiece separation occurred in step Tk+2, the cutting force of step Tk+2 does not need to be considered in the vibration response calculation. However, the IRF is still consistent with the calculation step and needs to be iterated backward one step. The calculation equation is as follows:

[0097]

[0098] in:

[0099] Finally, the cutting force F is calculated according to formula (5): x ((k+3)τ),F y ((k+3)τ),F z ((k+3)τ), and at the same time update the coordinates of the cutting interference points on the workpiece surface.

[0100] In calculating T k+4 Step time, T k+2 The cutting force of the step does not need to be considered, and the calculation expression is as follows:

[0101]

[0102] In the formula The cutting force is also calculated according to formula (5), and the cutting interference points on the workpiece surface are also updated accordingly. The following iterative calculation process is similar.

[0103] The present invention is further described in detail below with reference to specific examples.

[0104] Based on the LFC stability model, the intermittent characteristics of milling and the modal coupling effect of the robot structure are comprehensively considered to determine the low-frequency chatter stability boundaries in the low-speed area (100-350rpm) and the high-speed area (4000-5600rpm). The ball-end cutter (600-025A25-10H) was used in the simulation, and the cutting parameters are shown in Table 1. The radial cutting depth used in the simulation is 12mm, and the axial cutting depth is 0.1-2.0mm. The simulation results are shown in Figure 6 shown.

[0105] Table 1 Description of relevant parameters used in simulation

[0106]

[0107] The stability boundary obtained by simulation has a certain spindle speed correlation, which further confirms the intermittent cutting characteristics in low-frequency chatter in robot milling. Therefore, in robot milling, the low dynamic stiffness, low modal frequency and modal coupling effect of the robot body will lead to the occurrence of low-frequency chatter, and the correlation between the critical axial cutting depth and the spindle speed is related to the regeneration effect caused by intermittent cutting. The model proposed in this invention can effectively predict the stability boundary of low-frequency chatter in robot milling, which has important guiding significance for the actual processing process.

[0108] The present invention also provides a robot milling vibration stability prediction system, which uses the robot milling low-frequency vibration stability prediction method as described above to predict low-frequency vibration and sends the prediction result to the robot.

[0109] It will be easily understood by those skilled in the art that 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 and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting low-frequency chatter stability of robot milling, characterized in that: The method comprises the following steps: (1) Based on the robot milling process, an instantaneous cutting force calculation model considering surface renewal is established. The expression of the instantaneous cutting force calculation model is: In the formula, x T,ij,n (t),y T,ij,n (t) is the coordinate of the cutting interference point on the workpiece surface at time t in the tool coordinate system; T,ij (t),y T,ij (t) is the coordinate of the tool edge element in the tool coordinate system when the tool is in the cutting state at time t; represents the instantaneous radial contact angle; g ij (t) is the unit step function for determining whether cutting occurs; N is the number of teeth; M is the discrete number of blade elements; K x,ij , K y,ij , K z,ij is the equivalent cutting force coefficient in x, y, and z directions, where K tc is the tangential cutting force coefficient, K rc is the radial cutting force coefficient K ac is the axial cutting force coefficient; (2) Based on the impulse response function method, a low-frequency flutter stability prediction model considering the modal coupling effect is established, and then the low-frequency flutter stability prediction model is used to predict the low-frequency flutter. The expression of the low-frequency flutter stability prediction model is: In the formula, τ is a discrete time interval; k is a discrete number; f ij is the unit impulse response function within a given bandwidth, containing all modal information within the selected bandwidth. The subscripts i and j represent the response in the i direction caused by the excitation in the j direction. i (nτ) is the cutting force in the i direction at time t=nτ.

2. The method for predicting low-frequency chatter stability of robot milling according to claim 1, characterized in that: In the tool coordinate system XOY, the tool tip coordinate B at any time is expressed as: Where R represents the tool radius, t represents time, and x lev,ij (t),y lev,ij (t) represents the additional vibration displacement caused by low-frequency flutter, represents the instantaneous radial contact angle; When cutting occurs, the coordinates of the tool tip need to be recorded as cutting point A. At this time, the formula for the coordinates of the cutting point in the tool coordinate system changing with the cutting process is: Where, f represents the feed rate; t n is the moment when cutting occurs; (x lev,ij (t n ), y lev,ij (t n )) is the additional vibration displacement caused by low-frequency flutter.

3. The method for predicting low-frequency chatter stability of robot milling according to claim 2, characterized in that: The angle of the cutting point in the tool coordinate system also changes with the cutting process. The formula is:

4. The method for predicting low-frequency chatter stability of robot milling according to claim 3, characterized in that: Point Bn(x T,ij ,y T,ij ) is the coordinate of the blade element in the tool coordinate system at the current moment; is the instantaneous radial contact angle at the current moment, The cutting point A corresponding to the angle at this time is called the cutting interference point at this time; the cutting interference point is on the same straight line as the tool tip point B and the tool center point O.

5. The method for predicting low-frequency chatter stability of robot milling according to claim 4, characterized in that: The judgment function to determine whether cutting occurs is: In the formula, g ij (t) is the unit step function to determine whether cutting occurs, g ij (t) = 1 means cutting occurs, g ij (t) = 0 means that no cutting occurs.

6. The method for predicting low-frequency chatter stability of robot milling according to claim 4, characterized in that: When cutting occurs, the workpiece surface needs to be updated and the cutting interference point A3 is replaced by the current tool edge element B3 as the new cutting interference point for subsequent calculations.

7. The method for predicting low-frequency chatter stability of robot milling according to claim 1, characterized in that: In the modeling of modal coupling effects, impulse response functions are used to characterize the modal characteristics in various directions.

8. The method for predicting low-frequency chatter stability of robot milling according to claim 1, characterized in that: The vibration displacement of each mode in the x direction caused by the cutting force in the x, y, and z directions is given by the following formula: Where X(kτ+τ) is the response of the system in the x direction at time (k+1)τ, τ is the discrete time interval, and k is a discrete number; f ab It is the unit impulse response function within a given bandwidth and contains all modal information within the selected bandwidth. The subscripts a and b here represent the response in the a direction caused by the excitation in the b direction.

9. The method for predicting low-frequency chatter stability of robot milling according to claim 8, characterized in that: In step (2), the cutting force and IRF of the previous k steps are used to calculate the response signal x of the k+1 step. lev,ij ((k+1)τ),y lev,ij ((k+1)τ),z lev,ij ((k+1)τ); then, according to the vibration response signal at this time, the current cutting edge element (x T,ij ((k+1)τ),y T,ij ((k+1)τ)) and the cutting interference point (x T,ij,n ((k+1)τ),y T,ij,n ((k+1)τ)) coordinates; then, determine whether cutting is currently occurring. If cutting is occurring, calculate the current cutting force F x ((k+1)τ),F y ((k+1)τ),F z ((k+1)τ), and the cutting interference points on the workpiece surface are updated; if no cutting occurs, the cutting force is zero, and the cutting interference points on the workpiece surface do not need to be updated.

10. A robot milling chatter stability prediction system, characterized in that: The system adopts the robot milling low-frequency chatter stability prediction method described in any one of claims 1 to 9 to predict low-frequency chatter, and sends the prediction result to the robot.

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