Incremental self-excitation method for identifying low-frequency frequency response function of a milling robot

Abstract

The present application belongs to the technical field of milling processing, and discloses an incremental self-excitation method for identifying the low-frequency frequency response function of a milling robot. The method comprises the following steps: S1, in a preset standard posture, an incremental self-excitation experiment is performed by using a mass block, then a modal test is performed at a tool center point of the robot to obtain a frequency response function of the robot in the preset standard posture, and the frequency response function is used to solve an inertial self-excitation of the robot in the preset standard posture; S2, the robot again performs an incremental self-excitation experiment by using the mass block in a target posture in which the frequency response function needs to be identified, and the impulse and impulse moment of the mass block at the end of the robot during the experiment are calculated; S3, the frequency response function of the robot in the target posture is solved by using the impulse and impulse moment of the mass block and the inertial self-excitation of the robot in the preset standard posture. Through the present application, the identification of the frequency response function of the robot in any posture is solved.

Description

Technical Field

[0001] This invention belongs to the technical field of milling machining, and more specifically, relates to an incremental self-excitation method for identifying the low-frequency response function of a milling robot. Background Technology

[0002] Milling robots offer a large workspace, flexible structure, and high reconfigurability, making them widely used in the machining of large components in the aerospace field. However, the serial structure of the robot results in lower dynamic stiffness, leading to low-frequency chatter during milling, which significantly limits machining efficiency. The robot's frequency response function is a crucial foundation for predicting low-frequency chatter during milling; therefore, identifying the robot's attitude-dependent frequency response function is essential for improving the robot's machining efficiency over a wide range.

[0003] Methods for identifying the frequency response function of robots can generally be divided into modeling methods and experimental methods. Regarding modeling methods, Huynh et al. (2020) established a dynamic model based on the Lagrange equation, which showed good predictive performance for the frequency, damping ratio, and mode shape of most modes. Chen et al. (2020) considered the coupling effect between the tool holder and the tool and used a displacement admittance coupled substructure analysis method to calculate the tool tip frequency response of a milling robot in any posture. Wu et al. (2020) proposed a semi-analytical method for predicting low-order dynamics of robots based on finite element analysis. Regarding experimental methods, Sun et al. (2020) used joint angles as input variables and obtained a regression model of the natural frequencies of a six-DOF robot using the partial least squares method. Li et al. (2022) proposed a method for predicting the natural frequencies of industrial robots based on a blind Kriging model using Latin hypercube sampling technology. Wang et al. (2022) combined machine learning methods and modal recognition theory to propose a multimodal prediction method based on random forests.

[0004] However, for complex electromechanical systems, it is generally difficult to establish a comprehensive and effective dynamic model because deviations are ubiquitous and difficult to predict. For example, the stiffness, damping, and friction characteristics of robot joints often exhibit complex nonlinear variations with joint angles. Therefore, although modeling methods are universal for any robot posture, deviations in the model and its parameters limit their accuracy. While experimental methods have high accuracy near the experimental space, obtaining actual dynamic data often relies on manual experimentation, and achieving accurate predictions over a large spatial range requires considerable time and manpower. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides an incremental self-excitation method for identifying the low-frequency response function of a milling robot, thereby solving the problem of identifying the frequency response function of a robot in any posture.

[0006] To achieve the above objectives, according to the present invention, an incremental self-excitation method for identifying the low-frequency response function of a milling robot is provided, the method comprising the following steps:

[0007] S1 Incremental self-excitation experiment is conducted using a mass block under the preset standard posture of the robot. The impulse and impulse moment of the mass block at the end of the robot under the preset standard posture are calculated. Then, modal test is performed at the tool center point of the robot to obtain the frequency response function of the robot under the preset standard posture. The inertial self-excitation of the robot under the preset standard posture is solved using the frequency response function and the impulse and impulse moment of the mass block at the end of the robot under the preset standard posture.

[0008] S2 again uses the mass block to conduct an incremental self-excitation experiment in the target posture of the robot, and calculates the impulse and impulse moment of the mass block at the end of the robot in the target posture.

[0009] S3. Using the impulse and impulse moment of the mass block in the target posture obtained in step S2, and the inertial self-excitation of the robot in the preset standard posture in step S1, solve for the robot frequency response function in the target posture.

[0010] More preferably, in steps S1 and S2, the incremental self-excitation experiment is performed according to the following steps:

[0011] (a) The robot end joint runs at a constant speed at a preset speed and then stops suddenly. The acceleration time-domain signal at the tool center point of the robot end is measured and acquired when the robot stops suddenly.

[0012] (b) Attach a mass block with its center of mass located at the center point of the tool to the end of the robot and repeat step (a) to obtain the time-domain acceleration signal at the center point of the tool with the mass block attached.

[0013] More preferably, in step S1, the robot's inertial self-excitation in the preset standard posture is obtained according to the following steps:

[0014] S11. Determine the total modal order based on the robot's frequency response function in the preset standard posture as described in step S1. E , No. e First-order modal angular frequency ;

[0015] S12 converts the acceleration time-domain signals obtained in steps (a) and (b) of the incremental self-excitation experiment into acceleration frequency-domain signals, respectively, and subtracts the two acceleration frequency-domain signals to obtain the subtracted acceleration frequency-domain signal in the first step. e First-order modal angular frequency The amplitude below, i.e. ;

[0016] S13 Calculate the spectral density function of the frequency response function under the preset standard attitude and the... The sum of squared residuals between them;

[0017] S14 The identification result of the standard deviation is obtained by calculating the sum of squared residuals;

[0018] S15 Substitute the identification result of the standard deviation and the impulse of the mass block in the preset standard posture obtained in step S1 into the inertial self-excitation function to obtain the robot's inertial self-excitation in the preset standard posture.

[0019] More preferably, in step S13, the sum of squared residuals is determined according to the following relationship:

[0020]

[0021] in, It is the sum of squared residuals. for standard deviation For incremental self-excitation, e Indicates the modal angular frequency order. Indicates the first e First-order modal angular frequency, For identification The number of modes, For joints i The impulse generated by the mass block during runtime. To calculate the self-excitation based on the measured response and frequency response. The amplitude at that point;

[0022] More preferably, in step S14, the identification result of the standard deviation is:

[0023]

[0024] in, It is the sum of squared residuals.

[0025] More preferably, in step S15, the inertial self-excitation function Perform according to the following formula:

[0026]

[0027] in, t It represents time, and 'e' represents the base of the exponent. For joints i The impulse generated by the mass block during runtime. This indicates calculating the magnitude of a vector.

[0028] More preferably, in steps S1 and S2, the impulse and impulse moment of the mass block are both determined according to the following relationship:

[0029]

[0030] in, It is the impulse of the robot's end effector mass block. It is the impulse moment of the robot's end effector mass. and These are the momentum and angular momentum of the robot's end effector mass, respectively. , These are the mass and inertia tensor of the mass block, respectively. The mass block follows the joint i The velocity of the center of mass during motion, For preset joints i angular velocity, i It is the number of the robot's joint.

[0031] More preferably, in step S3, the frequency response function of the robot in the target posture is obtained by solving the following steps:

[0032] S31 converts the robot's inertial self-excitation in the preset standard posture obtained in step S1 into a frequency domain signal, and obtains... ,according to and Relationship, to obtain to obtain the direction ;

[0033] S32 uses sensor measurement , For joints i During self-excitation, the frequency domain expression of the difference in translational response along the X, Y, and Z directions at TCP before and after the addition of the mass block is based on... get , and ,right and , , Perform modal analysis to obtain the first modal value in three different directions. e Frequency response function of first mode , and ;

[0034] S33 According to The relationship between the frequency response and the terminal frequency response is used to construct the first e Modal vibration direction of the robot tool center under first mode Relationship;

[0035] S34 Utilizing the , , , and The relationship between the frequency response function of the robot under the target posture is constructed to obtain the required frequency response function of the robot under any posture.

[0036] More preferably, in step S33, the first e Modal vibration direction of the robot tool center under first mode The relational expression is as follows:

[0037]

[0038] in, , , respectively with As input, with , , For output, the first modal fit is obtained through modal analysis. e The frequency response function of the first mode.

[0039] More preferably, the frequency response function of the robot in the target posture is expressed according to the following formula:

[0040]

[0041] in, It is the first e Frequency response function of first mode , It is the first e The modal vibration direction of the robot tool center under the first modal mode. It is the direction of the mass block excitation. , , They are the first in three directions e The frequency response function of the first mode.

[0042] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0043] 1. This invention obtains a fully knowable and controllable excitation increment by adding a mass block at the center of the robot tool. Based on the linear relationship between the response increment and the excitation impulse increment brought about by the added mass block, it bypasses the complex robot inertial parameters and uses the excitation increment and response increment to identify the frequency response of the robot end effector with high identification accuracy.

[0044] 2. Based on the momentum theorem, this invention establishes a model of incremental self-excitation impulse (moment). To address the issue that the frequency response calculation process is highly sensitive to noise, the incremental self-excitation is assumed to be a Gaussian pulse, and a simplified analytical expression of its spectrum is given. Based on this, a method for identifying incremental self-excitation using measured frequency response functions is provided.

[0045] 3. This invention establishes a relationship model between the impulse response increment and the incremental self-excitation, and provides a method for calculating the frequency response function based on the modal directionality of the end effector of a milling robot. The results include all direct terms and cross terms. The verification results of the examples show that this method can effectively identify the low-frequency response function at the TCP of the milling robot. Attached Figure Description

[0046] Figure 1 This is a flowchart of an incremental self-excitation method for identifying the low-frequency response function of a milling robot, constructed according to a preferred embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram of the device in the robot incremental self-excitation method constructed according to a preferred embodiment of the present invention, wherein (a) is a schematic diagram of the robot self-excitation structure, and (b) is a schematic diagram of the robot end effector with and without mass increment;

[0048] Figure 3 This refers to the geometric information of the cylindrical-spherical tool and cutting tool constructed according to a preferred embodiment of the present invention;

[0049] Figure 4 These are error sum-of-squares curves calculated from experimental results under usage postures 1 to 3, constructed according to a preferred embodiment of the present invention;

[0050] Figure 5 The TCP frequency response identification result of attitude 4 constructed according to the preferred embodiment of the present invention is shown in the following: (a) is the frequency response of X-direction excitation and X-direction response, (b) is the frequency response of Y-direction excitation and X-direction response, (c) is the frequency response of Z-direction excitation and X-direction response, (d) is the frequency response of X-direction excitation and Y-direction response, (e) is the frequency response of Y-direction excitation and Y-direction response, (f) is the frequency response of Z-direction excitation and Y-direction response, (g) is the frequency response of X-direction excitation and Z-direction response, (h) is the frequency response of Y-direction excitation and Z-direction response, and (i) is the frequency response of Z-direction excitation and Z-direction response. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0052] like Figure 1 As shown, the steps of the robot incremental self-excitation method are as follows:

[0053] (1) When the robot end joint stops running at a constant speed according to a preset speed, measure the acceleration a1 of the center point of the robot end tool when it stops suddenly;

[0054] (2) A mass block with its center of mass located at the tool center point TCP is attached to the end of the robot; the end of the robot carrying the mass block m runs at a constant speed v at a preset speed and then stops suddenly. The acceleration a2 of the tool center point of the end of the robot caused by the sudden stop is measured.

[0055] The specific steps for obtaining the frequency response function are as follows:

[0056] S1. Calculation of Incremental Self-Excited Impulse (Moment)

[0057] Joint movement is a macroscopic motion. When the end joint, which is running at a preset constant speed, suddenly stops, the macroscopic motion is converted into microscopic motion—vibration and dynamic deformation—due to the concentration of flexibility in the joint. This process occurs within an extremely short time. Therefore, the excitation force causing deformation within the joint during cessation can be considered as an impulse. According to the momentum theorem, the magnitude of this impulse is precisely the momentum of the robot's moving parts just before the joint stops moving.

[0058] First, an incremental self-excitation experiment was conducted on the robot, focusing on the joints. i For example ( i = 1, 2, …, n , n Explaining the number of robot-driven joints. Establish the joint coordinate system using the Denavit-Hartenberg method, and denote the joint coordinate system. i for ( The robot's base coordinate system is The tool coordinate system is Its origin Located at TCP. When only joints are present. i At runtime, and These represent the momentum and angular momentum of the robot's moving parts, respectively. A mass block with its center of mass located at the tool's center point TCP is attached to the robot's end effector. and Let their momentum and angular momentum be represented by , respectively. Let the total momentum and angular momentum be denoted as . and Then we have:

[0059]

[0060] The variables are all based on This serves as the benchmark (unless otherwise specified below). As mentioned earlier, and Related to complex robot inertial parameters, which are difficult to obtain, but and It can be calculated using the following formula:

[0061]

[0062] in , These are the mass and inertia tensor of the mass block, respectively. For mass blocks to follow joints i The velocity of the center of mass during motion, For preset joints i The angular velocity satisfies:

[0063]

[0064] in, The origin of the joint coordinate system is represented by the point. Time The vector.

[0065] According to the momentum (angular momentum) theorem, the momentum (angular momentum) of the mass block will be converted into impulse (angular momentum), thus:

[0066]

[0067] in, These represent the corresponding impulse and impulse moment, respectively.

[0068] S2, Incremental Self-Excitation Identification Method

[0069] The frequency domain expression for incremental self-excitation is a necessary condition for calculating the frequency response through the incremental response. Clearly, the (incremental) self-excitation of a robot cannot be directly measured. This paper proposes a method to identify incremental self-excitation by combining the measured frequency response function.

[0070] By combining the response increment and the frequency response obtained from hammering along the direction of incremental self-excitation, the actual spectrum of incremental self-excitation can be obtained. Specifically, the spectrum of the response increment is divided by the measured frequency response at each frequency. However, since the amplitude of the frequency response is very small at most frequencies, the result obtained is highly sensitive to noise and is therefore invalid. Therefore, this invention assumes that incremental self-excitation is a pulse signal with a fixed form, and then identifies the pulse parameters using the small amount of discrete data provided by the response increment and the frequency response at the modal frequencies.

[0071] In robotic milling, only forces are generally considered, not torques. Therefore, the following section focuses only on the identification of forces in self-excitation. Let inertial self-excitation be denoted as... Assuming it is a Gaussian pulse. Standard Gaussian pulse. Represented as:

[0072]

[0073] in, For time, The standard deviation is denoted as .

[0074] Only exists .because The main part is Within the scope, here is for The starting point, that is:

[0075]

[0076] in For joints i The impulse generated by the mass block during runtime can be obtained according to equation (4).

[0077] spectral density function for:

[0078]

[0079] The above formula can be simplified to:

[0080]

[0081] when ,Right now At that time, there were:

[0082]

[0083] Then there is:

[0084]

[0085] And when hour, decay to At approximately 1%, the incremental self-excitation is unlikely to produce an effective response. Therefore, when using response increment to identify incremental self-excitation, equation (10) is applicable. In actual implementation, it is possible to first identify the incremental self-excitation based on the amplitude of the response increment at the lowest frequency mode. Then, based on all less than The amplitude at the modal angular frequency can be used to improve identification accuracy. The modal frequency can be identified from the response increment using the least squares complex exponential method.

[0086] The following is an introduction The identification method. From equation (10), it can be seen that... It can be seen as about and The function. It can be identified based on the least squares principle. Suppose it is used to identify The modal frequencies are total If there are 1, then the sum of squared residuals (SSE) is expressed as:

[0087]

[0088] in, Indicates the first e First-order modal angular frequency, The frequency domain signal representing (a2-a1) is in... The amplitude and frequency response function at the point The ratio of the amplitude at a given point (obtained from the frequency response function). Where " The reason is that modal frequencies are generally considered only for the positive frequencies, while Regarding vertical axis symmetry, the amplitude needs to be multiplied by 2 when only considering positive frequencies.

[0089] This section focuses only on the identification of incremental self-excitation. The specific calculation method is as follows: Measure the three-dimensional frequency response of the hammer impact along the incremental self-excitation direction at the TCP (Transient Coulomb) point; since the robot's end-effector modal response has directionality, use the L2 norm of the three-dimensional frequency response amplitude at the calculated modal frequency as the synthetic dynamic compliance of the corresponding mode; calculate the synthetic amplitude of the response increment at each modal frequency using the same method; then divide the synthetic amplitude by the synthetic dynamic compliance to obtain the amplitude of the incremental self-excitation at each modal frequency. .

[0090] The identification result is:

[0091]

[0092] Equation (12) is a nonlinear least squares problem, which can be solved using methods such as the Gauss-Newton method and the Levenberg-Marquardt method. Since the deceleration performance of different joints may be different, their incremental self-excitation needs to be identified separately.

[0093] S3. Robot Frequency Response Function Identification Method

[0094] Robot TCP q Directional motivation p The unit impulse response function of the directional response is denoted as: ( p, q = x,y, z, Ω x , Ω y , Ω z , respectively represent (The coordinate axis directions and the directions of rotation around the coordinate axes), for ease of representation, ... When the movement of the I-th joint stops, the excitation forces generated by the mass block in six directions are as follows: , Using superscripts "Ⅰ" and "Ⅱ" to represent no mass block and with mass block respectively, joints are used. i TCP during self-excitation p directional response and for:

[0095]

[0096] Subtract equation (13) from equation (14) and transform to the frequency domain:

[0097]

[0098] in,

[0099] similar, Indicates Fourier transform, Let represent the angular frequency. Equation (15) can be transformed into the following form:

[0100]

[0101] in The latter refers to the change in the frequency response at the TCP level after adding a quality block.

[0102] Milling robots typically have a body mass exceeding one ton, while the mass of the mass block is relatively small, and its impact on the TCP frequency response is often negligible. On the other hand, in common industrial robot structures, the links near the base often account for the majority of the mass, while the end effector links account for a very small percentage. This means that when using end effector joints for motion-stop self-excitation, the self-excitation provided by the mass block must be considered, as the resulting response increment can be effectively captured. In other words, after adding the mass block, the rate of change of the TCP frequency response is much smaller than the rate of change of the self-excitation. Let represent the changes in frequency response and self-excitation at the TCP after the addition of the mass block, respectively. Based on the above discussion, we have:

[0103]

[0104] Equation (16) can be simplified to:

[0105]

[0106] The above formula is the relationship model between the impulse response increment and the incremental self-excitation.

[0107] The frequency response function of the robot's end effector is calculated below.

[0108] Equation (18) can be expressed in the following matrix form:

[0109]

[0110] in , They are respectively based on , It is a 6-dimensional column vector of elements. Therefore The vectors and matrices in equation (19) are 6×6 dimensional matrices. The vectors and matrices in equation (19) are divided into sub-vectors and sub-matrices representing linear displacement / force and angular displacement / moment:

[0111]

[0112] In robotic milling research, the focus is generally on the end-effector linear displacement, while the influence of end-effector angular displacement can be ignored. Therefore, we will only consider... Without considering It satisfies:

[0113]

[0114] In the study of the dynamic characteristics of milling robots, the end effector frequency response generally refers to... This refers to the transfer function between linear displacement and force. In robot self-excitation experiments, It can be measured using a triaxial accelerometer. It is unknown, but it and Within the same order of magnitude (this is because the flexible parts of the robot are at the joints, and the torques caused by the forces and moments acting on the robot's end effector, resulting in joint deformation, are obviously of the same order of magnitude). Since the magnitude of the impulse moment in the self-excitation of the mass block should be much smaller than the magnitude of the impulse:

[0115]

[0116] Equation (21) can be simplified to:

[0117]

[0118] The following provides a method for calculating the frequency response based on the modal directionality of the end effector of a milling robot.

[0119] The cross frequency response of a milling robot's end effector is essentially a manifestation of the directionality of its end-effector modal vibrations under different excitation and measurement directions. The direction and magnitude are respectively unit vectors and ,satisfy , Obviously with They are in the same direction. Yes and , , Perform modal analysis and record the fitted modality. e The frequency response functions of the first mode are respectively , , Modal analysis can be performed using the least squares complex exponential method. Based on equation (23), the... e Modal vibration direction of the robot TCP under first mode It can be calculated using the following formula:

[0120]

[0121] in For the first e First-order modal angular frequency.

[0122] but Direction first e Frequency response function of first mode It can be calculated using the following formula:

[0123]

[0124] And there are:

[0125]

[0126] in, for elements, .

[0127] The present invention will be further described below with reference to specific embodiments.

[0128] The method was validated using ABB's IRB6660 heavy-duty milling robot.

[0129] The experimental attitudes are shown in Table 1. Using Equation (12), attitudes 1-3 are used to jointly identify incremental self-excitation, thereby reducing identification error. Attitude 4 is used to verify the proposed frequency response identification method.

[0130] Experimental site Figure 2 As shown. Figure 2 Image (a) illustrates a diagram of a robot's self-excitation, where the robot starts from a certain posture, rotates a certain end joint (here, a 6-joint) at a constant speed, and then suddenly stops after traversing a certain angle. It's important to note that the focus is only on the vibration signal after the joint stops. The reason for traversing a certain angle is to ensure that the vibration caused by the joint's initiation is attenuated before the joint stops, thus not affecting the vibration signal caused by the joint's cessation. A cylindrical-spherical tool is used as the mass increment, and a cutting tool is used as a reference; these can be seen in the magnified view of the robot's end effector. Figure 2 As seen in (b), the cylindrical-spherical tool is made of stainless steel with a density similar to the cutting tool, and its cylindrical portion has the same diameter as the cutting tool. The mass increment is the mass of the cylindrical-spherical tool minus the mass of the cutting tool, and its center of mass is approximately at the center of the sphere. The cutting tool is a SANDVIK 600-025A25-10H face milling cutter. The geometry of the cylindrical-spherical tool and the cutting tool is as follows: Figure 3 As shown, the masses of the two are 4.50 kg and 0.48 kg, respectively, resulting in a mass increment of 4.02 kg. A DYTRAN 3263A2 triaxial accelerometer was used to measure the response, placed near the center of the sphere. The frequency response was tested using a Dytran 5802A pulse hammer.

[0131] Tool coordinate system of The axis is aligned with the robot's 6 axes. The axis and the tool axis are in the same direction, such as Figure 2 As shown in (b), a 6-joint self-excitation system was used, with a joint operating speed of 16.7° / s. To fully attenuate the vibration caused by the initiation of the 6-joint system, the traversal angle of the self-excitation was set to -150°. The hammering direction was... , which is in the same direction as self-excitation.

[0132] The SSE curve for incremental self-excitation identification is as follows: Figure 4 As shown, the identification result is . Figure 5The frequency response identification results according to Equation (26) are shown in posture 4. Experimental results show that the proposed method is accurate in identifying the natural frequencies of the robot end effector, and the accuracy of amplitude identification is even higher for frequency responses with higher amplitudes. However, modes above 20Hz, such as 20.5Hz and 43Hz, were not identified in this experiment. This is because the effective frequency band of incremental self-excitation is lower than that of hammering, which cannot excite these modes. However, this does not affect the practicality of the proposed method, because the dynamic compliance of the milling robot generally decreases as the frequency increases, and the frequency of body chatter is generally below 20Hz. In most cases, the effective frequency band of incremental self-excitation is sufficient. In summary, the experimental results show that the proposed method can effectively identify the direct and cross low-frequency response functions at the TCP of the milling robot.

[0133] Table 1 Robot posture

[0134]

[0135] Those skilled in the art will readily understand that the above description is merely 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 within the scope of protection of the present invention.

Claims

1. An incremental self-excitation method for identifying the low-frequency response function of a milling robot, characterized in that, The method includes the following steps: S1 Incremental self-excitation experiment is conducted using a mass block under the preset standard posture of the robot. The impulse and impulse moment of the mass block at the end of the robot under the preset standard posture are calculated. Then, modal test is performed at the tool center point of the robot to obtain the frequency response function of the robot under the preset standard posture. The inertial self-excitation of the robot under the preset standard posture is solved using the frequency response function and the impulse and impulse moment of the mass block at the end of the robot under the preset standard posture. S2 again uses the mass block to conduct an incremental self-excitation experiment in the target posture of the robot, and calculates the impulse and impulse moment of the mass block at the end of the robot in the target posture. S3. Using the impulse and impulse moment of the mass block in the target posture obtained in step S2 and the inertial self-excitation of the robot in the preset standard posture in step S1, solve the robot frequency response function in the target posture. In steps S1 and S2, the incremental self-excitation experiment is performed according to the following steps: (a) The robot end joint runs at a constant speed at a preset speed and then stops suddenly. The acceleration time-domain signal at the tool center point of the robot end is measured and acquired when the robot stops suddenly. (b) Attach a mass block with its center of mass located at the center point of the tool to the end of the robot and repeat step (a) to obtain the time-domain acceleration signal at the center point of the tool with the mass block attached. In step S1, the robot's inertial self-excitation under the preset standard posture is obtained according to the following steps: S11. Determine the total modal order based on the robot's frequency response function in the preset standard posture as described in step S1. E , No. e First-order modal angular frequency ; S12 converts the acceleration time-domain signals obtained in steps (a) and (b) of the incremental self-excitation experiment into acceleration frequency-domain signals, respectively, and subtracts the two acceleration frequency-domain signals to obtain the subtracted acceleration frequency-domain signal in the first step. e First-order modal angular frequency The amplitude below, i.e. ; S13 Calculate the spectral density function of the frequency response function under the preset standard attitude and the... The sum of squared residuals between them; S14 The identification result of the standard deviation is obtained by calculating the sum of squared residuals; S15 Substitute the identification result of the standard deviation and the impulse of the mass block in the preset standard posture obtained in step S1 into the inertial self-excitation function to obtain the robot's inertial self-excitation in the preset standard posture. In step S13, the sum of squared residuals is determined according to the following relationship: in, It is the sum of squared residuals. for standard deviation For incremental self-excitation, e Indicates the modal angular frequency order. Indicates the first e First-order modal angular frequency, For identification The number of modes, For joints i The impulse generated by the mass block during runtime. To calculate the self-excitation based on the measured response and frequency response. The amplitude at that point; In step S15, the inertial self-excitation function Perform according to the following formula: in, t It represents time, and 'e' represents the base of the exponent. For joints i The impulse generated by the mass block during runtime. This indicates calculating the magnitude of a vector.

2. The incremental self-excitation method for identifying the low-frequency response function of a milling robot as described in claim 1, characterized in that, In step S14, the identification result of the standard deviation is: in, It is the sum of squared residuals.

3. The incremental self-excitation method for identifying the low-frequency response function of a milling robot as described in claim 1 or 2, characterized in that, In steps S1 and S2, the impulse and impulse moment of the mass block are both determined according to the following relationship: in, It is the impulse of the robot's end effector mass block. It is the impulse moment of the robot's end effector mass. and These are the momentum and angular momentum of the robot's end effector mass, respectively. , These are the mass and inertia tensor of the mass block, respectively. The mass block follows the joint i The velocity of the center of mass during motion, For preset joints i angular velocity, i It is the number of the robot's joint.

4. The incremental self-excitation method for identifying the low-frequency response function of a milling robot as described in claim 1 or 2, characterized in that, In step S3, the frequency response function of the robot in the target posture is obtained by solving the following steps: S31 converts the robot's inertial self-excitation in the preset standard posture obtained in step S1 into a frequency domain signal, and obtains... ,according to and Relationship, to obtain to obtain the direction ; S32 uses sensor measurement , For joints i During self-excitation, the frequency domain expression of the difference in translational response along the X, Y, and Z directions at TCP before and after the addition of the mass block is based on... get , and ,right and , , Perform modal analysis to obtain the first modal value in three different directions. e Frequency response function of first mode , and ; S33 According to The relationship between the frequency response and the terminal frequency response is used to construct the first e Modal vibration direction of the robot tool center under first mode Relationship; S34 Utilizing the , , , and The relationship between the frequency response function of the robot under the target posture is constructed to obtain the required frequency response function of the robot under any posture.

5. The incremental self-excitation method for identifying the low-frequency response function of a milling robot as described in claim 4, characterized in that, In step S33, the first e Modal vibration direction of the robot tool center under first mode The relational expression is as follows: in, , , respectively with As input, with , , For output, the first modal fit is obtained through modal analysis. e The frequency response function of the first mode.

6. The incremental self-excitation method for identifying the low-frequency response function of a milling robot as described in claim 5, characterized in that, The frequency response function of the robot in the target posture is expressed according to the following relationship: in, It is the first e Frequency response function of first mode , It is the first e The modal vibration direction of the robot tool center under the first modal mode. It is the direction of the mass block excitation. , , They are the first in three directions e The frequency response function of the first mode.

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