Method and equipment for identifying weak joints of whole working space body of robot under milling excitation

Abstract

The invention belongs to the related technical field of milling machining, and discloses a method and equipment for identifying weak joints of a whole-working-space body of a robot under milling excitation, and the method comprises the following steps: (1) carrying out dynamic characteristic sensitivity analysis on a target working space so as to select standard postures, and carrying out whole machine modal test on each determined standard posture; (2) calculating a modal-weak joint weight coefficient of each standard attitude based on a whole machine modal test result and an MFMS method; meanwhile, the modal contribution degree of each standard attitude under milling excitation is calculated; (3) reconstructing the configuration of the target attitude, calculating a configuration similarity index between the target attitude and the standard attitude, and further calculating to obtain an M-WJWC matrix and MCI of the target attitude; and (4) recognizing the robot-weak joint weight coefficient of the target posture, and further realizing online recognition of the weak joint of the robot body under milling excitation. According to the method, the R-WLWC prediction of any attitude in the target working space can be realized.

Description

Technical Field

[0001] The present invention belongs to the technical field related to milling processing, and more specifically, relates to a method and device for identifying weak joints of a robot body in the entire workspace under milling excitation. Background Art

[0002] Vibration is a major obstacle to the application of robots in the field of milling processing. Compared with the vibration of the tool, the vibration of the robot structure is more likely to occur and has a more severe impact. However, the complexity of the robot's structural mode and the posture dependence of the dynamic characteristics have caused great trouble in suppressing the robot's structural vibration, and the milling excitation will further change the distribution of the robot's structural vibration. The combined effect of these factors will make it difficult for engineers to locate the weak links that are prone to vibration, thereby achieving targeted vibration suppression. Therefore, it is necessary to clarify the structural vibration characteristics of the robot under cutting excitation and identify the weak links of the structure.

[0003] At present, the research objects of weak links are mostly machine tool structures, and the research on the weak links of robot milling structural vibration is still relatively preliminary. In order to more effectively realize the robot structure vibration suppression, improve the processing efficiency and ensure the processing accuracy, it is necessary to study the distribution law of the robot structure vibration weak links in the whole space. Summary of the invention

[0004] In view of the above defects or improvement needs of the prior art, the present invention provides a method and device for identifying weak joints of a robot's entire workspace body under milling excitation, which aims to solve the problem that it is difficult to identify weak links in the robot's structural vibration.

[0005] To achieve the above object, according to one aspect of the present invention, a method for identifying weak joints of a robot body in the entire workspace under milling excitation is provided, the method comprising the following steps:

[0006] (1) Determine the target workspace range where the weak joints of the robot body need to be identified, perform dynamic characteristic sensitivity analysis on the target workspace and then select a standard posture, and perform whole machine modal testing on each determined standard posture;

[0007] (2) Based on the modal test results of the whole machine and the MFMS method, the contribution of each joint degree of freedom to the vibration of the tool center point is calculated, and then the modal-weak joint weight coefficient (M-WJWC) of each standard posture is calculated based on the corresponding contribution of each joint degree of freedom; at the same time, the state space model of the standard posture is established according to the modal test results, and then the modal contribution (MCI) of each standard posture under milling excitation is calculated based on the Kalman filter method (KF);

[0008] (3) Reconstruct the configuration of the target posture and calculate the configuration similarity index (CSI) between the target posture and the standard posture. Then, based on the obtained configuration similarity index, the modal-weak joint weight coefficient of the standard posture and the modal contribution of the standard posture, the M-WJWC matrix and MCI of the target posture are calculated.

[0009] (4) Based on the M-WJWC matrix of the target posture and MCI, the robot-weak joint weight coefficient (R-WJWC) of the target posture is identified, and then the online identification of the weak joints of the robot body under milling excitation is realized based on the robot-weak joint weight coefficient of the target posture.

[0010] Furthermore, based on the robot frequency response curve and correlation coefficient, the dynamic characteristic sensitivity coefficient is proposed, and the corresponding formula is:

[0011]

[0012] where h i and h j Represents the frequency response vector at the sampling point, cov() represents the covariance operation, and var[] represents the variance operation;

[0013] Based on formula (1), the dynamic characteristic sensitivity coefficient matrix is ​​obtained, and then the standard posture of the robot is determined based on the dynamic characteristic sensitivity coefficient matrix.

[0014] Furthermore, the multi-joint full-degree-of-freedom vibration mode is used to represent the multi-order modal vibration mode of the robot structure, and the modal vibration mode of joint j is obtained expression:

[0015]

[0016] In the formula For CS j The origin coordinates under CS0, CS0 to CS j The rotation matrix of is the six-degree-of-freedom deformation amplitude of joint j under CS0; according to formula (2), the vibration mode of each joint of the robot is calculated to obtain X MFMS :

[0017]

[0018] X-based MFMS , calculate the contribution of each joint degree of freedom to the vibration of the tool center point, and the calculation expression of the contribution of each joint degree of freedom to the vibration of the tool center point is:

[0019]

[0020] Where j represents the robot joint, j = 1, 2, ..., 6, and k represents the 6 degrees of freedom of each joint (X, Y, Z, ω X ,ω Y ,ω Z ,),k=1,2,…,6;X MFMS,j,k Represents X MFMS The j-th row and k-th column element of Indicates the CS0 coordinate system and the CS j The unit vector with the same direction as the k-th coordinate axis, and Represents CS T and CS j The origin of the coordinate system in the CS0 coordinate system, Represents the contribution of the k degree of freedom of the j joint to the vibration of the tool center point.

[0021] Furthermore, the contribution of each degree of freedom of each joint under each order mode to the vibration of the tool center point is quantitatively evaluated by the modal-weak joint weight coefficient. The calculation expression is:

[0022]

[0023] Based on the definition of MFMS, the modal vibration data of each mode of the robot are substituted into formula (4) to obtain the contribution of each degree of freedom of each joint to the vibration of the tool center point under different postures and modes of the robot structure; and then the M-WJWC of each standard posture is obtained by formula (5): j,k,l,m ; Among them, j, k = 1, 2, ..., 6; l = 1, 2, ..., 5; m = 1, 2, ..., 27; l is the modal order, and m is the standard posture index.

[0024] Furthermore, the contribution of each mode to the vibration is considered in the modal space, and the state space model is established. The model is expanded and reorganized, and the cutting force term is also included in the system state variable. The state variable is set to The state space model of the system is expressed as:

[0025]

[0026] In the formula, w and v are the process noise and observation noise of the system respectively. The equation satisfies w~N(0,Q) and v~N(0,R), Q is the process noise variance, R is the observation noise variance, A and B are the state matrix and input matrix of the system equation.

[0027] Furthermore, the KF method combines the modal parameters obtained from the modal test with the vibration data y observed at a single measuring point j on the robot structure. k+1, to achieve the optimal estimation of the modal vibration displacement vector q, the vibration displacement signal A = [A1, A2, A3, A4, A5] of each mode of the robot structure is obtained by the following formula:

[0028] A=Φq (9)

[0029] Using the amplitude of the vibration signal |A l |To characterize the contribution of each mode in the robot structure vibration process, so as to obtain the MCI of each standard posture.

[0030] Furthermore, the coordinate similarity S of multiple coordinates corresponding to each standard posture is taken g,m The average value of the target posture is the CSI between the target posture and the standard posture; the M-WJWC matrix of the CSI and the standard posture Multiply and add the elements at the corresponding positions to get the M-WJWC matrix of the target posture

[0031] Furthermore, the modal contribution of the calculated standard posture is weighted with CSI as the weight to obtain the MCI of the target posture.

[0032] The present invention also provides a system for identifying weak joints of a robot's entire workspace body under milling excitation. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it executes the method for identifying weak joints of a robot's entire workspace body under milling excitation as described above.

[0033] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the method for identifying weak joints of the robot's entire workspace body under milling excitation as described above.

[0034] In general, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:

[0035] 1. Based on the modal test results of the whole machine and the MFMS method, the contribution of each joint degree of freedom to the vibration of the tool center point is calculated, and then the modal-weak joint weight coefficient (M-WJWC) of each standard posture is calculated based on the corresponding contribution of each joint degree of freedom; at the same time, the state space model of the standard posture is established according to the modal test results, and then the modal contribution (MCI) of each standard posture under milling excitation is calculated based on the Kalman filter method (KF), so as to realize the prediction of R-WLWC of the standard posture of the robot.

[0036] 2. The present invention proposes a robot configuration similarity evaluation index, which can realize the prediction of R-WLWC of any posture in the target workspace based on the modal test of limited standard postures.

[0037] 3. Take the coordinate similarity S of multiple coordinates corresponding to each standard posture g,m The average value of the CSI (S g,m ), which not only avoids the problem of amplified terminal coordinate differences caused by the series structure, but also reasonably considers the influence of each joint on the robot configuration.

[0038] 4. Take the coordinate similarity S of multiple coordinates corresponding to each standard posture g,m The average value of the target posture is the CSI between the target posture and the standard posture; the M-WJWC matrix of the CSI and the standard posture Multiply and add the elements at the corresponding positions to get the M-WJWC matrix of the target posture Realize the identification of weak joints in each mode of arbitrary posture in the target space. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of a method for identifying weak joints of a robot body in the entire workspace under milling excitation provided by the present invention;

[0040] Figure 2 (a), (b), and (c) are the robot dynamic characteristic sensitivity coefficient matrices in different directions respectively;

[0041] Figure 3 It is a schematic diagram of the standard posture distribution of the robot in the target workspace;

[0042] Figure 4 (a), (b), (c), (d), and (e) are schematic diagrams of the 1st to 5th order mode vibration modes, respectively;

[0043] Figure 5 (a), (b), (c), (d), and (e) are schematic diagrams of weak joint distribution of the robot in the first to fifth order modes in standard posture 8, respectively;

[0044] Figure 6 (a), (b), and (c) are schematic diagrams of MCI distribution under spindle speeds of 4800 rpm, 5400 rpm, and 6000 rpm, respectively;

[0045] Figure 7 is the parallel coordinate diagram of R-WJWC under milling excitation (standard posture 8);

[0046] Figure 8 This is a schematic diagram of the weak joint distribution of the robot body when the spindle speed is 4800rpm and the radial cutting depth is 4mm (standard posture 8);

[0047] Fig. 9 is a schematic diagram of the experimental setup for joint vibration testing to verify the prediction accuracy of R-WJWC;

[0048] Fig.10 (a), (b), and (c) are schematic diagrams of the calculation process of the joint vibration displacement corresponding to the acceleration signal of the link 2, the acceleration signal of the link 1, and the displacement signal of the link 1, respectively;

[0049] Fig.11 The experimental test results and prediction results of R-WJWC are in ω Z Schematic diagram of the comparison results on the degrees of freedom;

[0050] Fig.12 It is a schematic diagram of the configuration similarity of the robot in 27 standard postures and 1 target posture;

[0051] Fig.13 (a), (b), and (c) are schematic diagrams of MCI distribution under spindle speeds of 4800 rpm, 5400 rpm, and 6000 rpm, respectively (non-standard posture);

[0052] Fig.14 is the parallel coordinate diagram of R-WJWC under milling excitation (non-standard posture);

[0053] Fig.15 This is a schematic diagram of the weak joint distribution of the robot body when the spindle speed is 4800rpm and the radial cutting depth is 4mm (non-standard posture);

[0054] Fig.16 The experimental test results and prediction results of R-WJWC are in ω Z Schematic diagram of the comparison results on degrees of freedom (non-standard posture). DETAILED DESCRIPTION

[0055] 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.

[0056] The present invention provides a method for identifying weak joints of the robot's entire workspace under milling excitation. The identification method combines milling excitation to quantitatively evaluate weak links corresponding to different cutting parameters and different robot configurations, thereby providing a theoretical basis for targeted suppression of robot structural vibration in a certain workspace and cutting parameter domain. At the same time, the identification method can accurately identify the distribution of weak links of the robot under any posture and working condition.

[0057] See also Figure 1 , the identification method mainly includes the following steps:

[0058] Step 1: Determine the target workspace range where the weak joints of the robot body need to be identified, perform dynamic characteristic sensitivity analysis on the target workspace and then select a standard posture, and perform whole machine modal testing on each determined standard posture.

[0059] First, according to the workspace where the processing operation needs to be performed, determine the target workspace range where the weak joints of the robot body need to be identified, and select the standard posture.

[0060] Taking the 800mm×400mm×400mm cuboid space in the robot workspace as an example to select the standard posture, considering that the frequency response curve reflects the dynamic characteristics of the robot's current posture to a certain extent. Therefore, based on the robot's frequency response curve and correlation coefficient, the dynamic characteristic sensitivity coefficient is proposed:

[0061]

[0062] where h i and h j represents the frequency response vector at the sampling point, cov() represents the covariance operation, and var[] represents the variance operation. Therefore, r i,j The closer it is to 0, the greater the change in the dynamic characteristics from sampling point i to j, and vice versa.

[0063] According to formula (1), the dynamic characteristic sensitivity coefficient matrix can be obtained, as follows: Figure 2 As shown in the figure, it can be found that the dynamic characteristics of the robot are most sensitive in the X direction, followed by the Z direction, and the least sensitive is the Y direction. Therefore, when distributing discrete sampling points, the discrete spacing in the Y direction is set to 400mm, and the X and Z directions are set to a smaller 200mm. A total of 27 robot standard postures were selected, and the distribution of the standard postures, i.e., the serial number, is as follows: Figure 3As shown in the figure, modal tests were conducted on 27 standard postures of the selected robot. A sine sweep frequency excitation was performed using an exciter, and a force sensor was installed at the end of the exciter to synchronously measure the exciting force. A three-dimensional scanning laser Doppler vibrometer was used to measure the vibration response of the robot structure, and 120 measuring points were evenly arranged on each connecting rod of the robot structure.

[0064] According to the measured results, modal analysis can be performed to obtain the modal parameters of the robot structure under the above 27 standard postures. Taking standard posture 8 as an example, the modal vibration shape of the robot body is as follows: Figure 4 As shown, Figure 4 The circular point in the middle represents the original position of the robot, and the arrow vector represents the direction and magnitude of the mode shape.

[0065] Step 2: Based on the modal test results of the whole machine and the MFMS method, the contribution of each joint degree of freedom to the vibration of the tool center point is calculated, and then the modal-weak joint weight coefficient (M-WJWC) of each standard posture is calculated based on the corresponding contribution of each joint degree of freedom; at the same time, the state space model of the standard posture is established according to the modal test results, and then the modal contribution (MCI) of each standard posture under milling excitation is calculated based on the Kalman filter method (KF).

[0066] The flexibility of the robot structure mainly comes from the joints. Considering the flexibility of the joints, the multi-joint and full-DOF Mode Shape (MFMS) can be used to represent the multi-order mode shapes of the robot structure, and the mode shape of joint j can be obtained. expression:

[0067]

[0068] In the formula For CS j The origin coordinates under CS0, CS0 to CS j The rotation matrix of is the six-degree-of-freedom deformation amplitude of joint j under CS0. According to formula (2), the vibration mode of each joint of the robot can be obtained: MFMS :

[0069]

[0070] X-based MFMS , the contribution of each joint degree of freedom to the vibration of the tool center point can be calculated. The calculation expression for the contribution of each joint degree of freedom to the vibration of the tool center point is:

[0071]

[0072] Where j (j = 1, 2, ..., 6) represents the robot joint, k (k = 1, 2, ..., 6) represents the 6 degrees of freedom (X, Y, Z, ω X ,ω Y ,ω Z ,),X MFMS,j,k Represents X MFMS The j-th row and k-th column element of Indicates the CS0 coordinate system and the CS j The unit vector with the same direction as the k-th coordinate axis, and Represents CS T and CS j The origin of the coordinate system in the CS0 coordinate system, Represents the contribution of the k degree of freedom of the j joint to the vibration of the tool center point.

[0073] By comparing the contribution of each joint degree of freedom, the modal weak joint weight coefficient (M-WJWC) can be determined to quantitatively evaluate the contribution of each degree of freedom of each joint under each order mode to the vibration of the tool center point. The calculation expression is:

[0074]

[0075] Based on the definition of MFMS, the modal vibration data of each mode of the robot are substituted into formula (4), and the contribution of each degree of freedom of each joint to the vibration of the tool center point under different postures and modes of the robot structure can be obtained; and then the M-WJWC of each standard posture is obtained by formula (5): j,k,l,m (j,k=1,2,…,6;l=1,2,…,5;m=1,2,…,27), where l is the modal order and m is the standard posture index.

[0076] Taking standard posture 8 as an example, the distribution of weak joints under each mode is plotted according to M-WJWC, as shown in Figure 5 As shown. It can be found that the Z-axis rotational freedom (ω Z ) contributes more to the vibration of the tool center point. In the first-order mode, the Z-axis rotational freedom (ω Z ) contributes most to the vibration of the tool center point. In the second-order mode, the Z-axis rotational freedom (ω Z ) contributes most to the vibration of the tool center point. In the third-order mode, the Z-axis rotational freedom (ω Z ) and the X-axis rotational freedom of the 6 joints (ω X ) contributes most to the vibration of the tool center point. In the 4th and 5th order modes, the Z-axis rotational freedom (ωZ ) contributes most to the vibration of the tool center point.

[0077] During the robot milling process, milling excitation will cause the multi-order modes of the robot structure to participate in vibration to varying degrees. In order to accurately identify the weak joints of the robot body under milling excitation, the vibration participation of each order mode under milling excitation, namely the Modal Contribution Index (MCI), is accurately identified based on the Kalman Filter (KF).

[0078] The dynamic model of the robot in modal coordinates can be expressed as:

[0079]

[0080] Where q is the modal vibration displacement vector, M, C, K and Φ are the mass matrix, damping matrix, stiffness matrix and modal matrix respectively, and F is the exciting force vector.

[0081] Consider the contribution of each mode to vibration in the modal space, establish the state space model, expand and reorganize it, and include the cutting force term in the system state variables. Set the state variable to The state space model of the system can be expressed as:

[0082]

[0083] In the formula, w and v are the process noise and observation noise of the system respectively. The equation satisfies w~N(0,Q) and v~N(0,R), Q is the process noise variance, R is the observation noise variance, A and B are the state matrix and input matrix of the system equation.

[0084] The observed data is in discrete form, so the state space model of the system is discretized and can be rewritten as follows:

[0085]

[0086] Where, X k and X k+1 denote the state variables of the system at time k and k+1 respectively, T is the discrete time interval, y k+1 represents the speed of the observation point at time k+1, w k and v k+1 are process noise and observation noise, respectively.

[0087] The KF method combines the modal parameters obtained from the modal test with the vibration data y observed at a single measuring point j on the robot structure. k+1, the optimal estimation of the modal vibration displacement vector q can be achieved. The vibration displacement signal A = [A1, A2, A3, A4, A5] of each mode of the robot structure can be obtained by the following formula:

[0088] A=Φq (9)

[0089] On this basis, the amplitude of the vibration signal |A l | is used to characterize the contribution of each mode in the robot structure vibration process, so as to obtain the MCI of each standard posture. The expression is as follows, where l represents the modal order and m represents the robot posture index:

[0090]

[0091] Step three, reconstruct the configuration of the target posture, and calculate the configuration similarity index (CSI) between the target posture and the standard posture, and then calculate the M-WJWC matrix and MCI of the target posture based on the obtained configuration similarity index, the modal-weak joint weight coefficient of the standard posture and the modal contribution of the standard posture.

[0092] The robot configuration largely determines the distribution of the body's dynamic characteristics, that is, the distribution of weak joints. By reconstructing the configuration characteristics of the robot's posture at the sampling point, the Configuration Similarity Index (CSI) is proposed to achieve the identification of M-WJWC and MCI in the whole space. The specific steps are as follows:

[0093] (1) Reconstruct the configuration features of 27 typical postures in three-dimensional space based on DH parameters and joint angles. Taking posture 8 as an example, the homogeneous coordinate transformation matrix is ​​used to calculate the coordinate system CS0 of each joint under the robot base coordinate system CS0. j and the origin coordinates of the tool coordinate system CS7 It is the origin of the reference coordinate system CS0.

[0094] (2) Interpolate n coordinates based on the coordinates at both ends of each connecting rod Indicates the position of the connecting rod. The size of n will affect the judgment accuracy of CSI to a certain extent. According to experience, n=25 is taken here. At this time, according to the robot posture and DH parameters, the coordinates of the 8 endpoints under any posture m can be reconstructed and 175 link coordinates A total of 183 coordinates are used Describe the configuration of the robot under any posture m. The specific expression is:

[0095]

[0096] (3) Based on the joint configuration of the target posture, reconstruct the configuration of the target posture according to the method in step (2)

[0097] (4) First, the 183 coordinates of the target posture are matched one by one with the coordinates of the 27 standard postures with the same index, and the Euclidean distance ρ between each coordinate of the target posture and the corresponding coordinate of each standard posture with the same index is calculated. p,m (p=1,2,…,183;m=1,2,…,27), the calculation expression is:

[0098]

[0099] (5) The Euclidean distance ρ between the target posture corresponding to each posture index m and the standard posture p,m As the coordinate similarity S between the target pose coordinates and the standard pose coordinates under index m p,m (p=

[0100] 1,2,…,183; m=1,2,…,27), the calculation expression is:

[0101]

[0102] In the formula, Uni p,m is the normalized Euclidean distance, expressed as:

[0103]

[0104] (6) Take the coordinate similarity S of the 183 coordinates corresponding to each standard posture g,m The average value of the CSI (S g,m (m=1,2,…,27)). This not only avoids the problem of amplification of the end coordinate difference caused by the series structure, but also reasonably considers the influence of each joint on the robot configuration. The expression is:

[0105]

[0106] (7) CSI reflects the similarity of the dynamic characteristics of the robots to a large extent. It is compared with the M-WJWC matrix λ of the 27 standard postures. m Multiply and add the elements at the corresponding positions to get the M-WJWC matrix of the target posture To realize the identification of weak joints in each mode of any posture in the target space, the calculation expression is:

[0107]

[0108] (8) Based on the modal test results of 27 standard postures, the corresponding state space model is established according to formula (8).

[0109] (9) The KF method is used to achieve the optimal estimation of the modal vibration displacement vector q with 27 standard postures as reference postures, and the corresponding vibration displacement signal is solved according to formula (9).

[0110] (10) Taking the 27 standard postures as reference, the reference MCI of each standard posture is calculated according to formula (10), η l,m (l=1,2,...,5; m=1,2,...,27).

[0111] (11) Using CSI as the weight, the calculated reference MCI is weighted to obtain the MCI of the target posture:

[0112]

[0113] Step 4: Based on the M-WJWC matrix and MCI of the target posture, the robot-weak joint weight coefficient (R-WJWC) of the target posture is identified, and then the online identification of the weak joints of the robot body under milling excitation is realized based on the robot-weak joint weight coefficient of the target posture.

[0114] According to the M-WJWC matrix under any posture in the target workspace and MCI The identification of the weak joint R-WJWC of the robot body in any posture in the target workspace under milling excitation can be realized. The calculation formula is:

[0115]

[0116] in:

[0117]

[0118] During the cutting process, each mode will participate in the vibration to varying degrees (assessed using MCI, which is a one-dimensional value). The vibration of each mode is composed of the 6 degrees of freedom vibration of the 6 joints with different degrees of participation, totaling 36 vibration components (expressed using the M-WJWC matrix = , which is a 6×6×5 matrix). Therefore, as shown in formula (18), R-WJWC is a 6×6 matrix, which represents the contribution ratio of each degree of freedom (36 in total) of each joint of the robot to the end vibration under milling excitation. Based on R-WJWC, the distribution of the weak joints of the robot under any posture and any milling parameters can be intuitively identified, and the weak joints in the current working state can be effectively located, so as to perform targeted vibration suppression.

[0119] The present invention is further described in detail below with reference to specific embodiments.

[0120] Based on the above process, the weak joints of the robot body under milling excitation are completely identified for two different types of instances of standard posture and non-standard posture.

[0121] Example 1:

[0122] Standard posture 8: 17.04°, 17.12°, 41.61°, 24.77°, -44.34°, -18.25°)

[0123] First, the vibration signal measurement points in the milling process are selected. Since the KF method is used in MCI identification, in the vibration signal test, it is only necessary to collect the vibration signal of any measuring point in the modal test experiment. The experiment uses the DYTRAN 3263A2T acceleration sensor to collect the vibration signal during the robot milling process, and the sampling frequency is set to 3125Hz. The tool used in the experiment is a SANDVIKΦ16 end mill with a tool length of 115mm and 4 teeth. The cutting material is 7075 aluminum alloy, which has a smaller cutting force and a more stable cutting process than nickel-aluminum bronze, which can ensure the effectiveness of the weak link identification results.

[0124] Based on the above experimental settings, spindle speeds of 4800 rpm, 5400 rpm, and 6000 rpm, axial cutting depth of 3 mm, radial cutting depth of 1 mm-6 mm, and increment of 1 mm were selected for milling experiments, and the other cutting parameters remained unchanged. The specific experimental parameters are shown in Table 1.

[0125] Table 1 Cutting parameter settings for the robot body weak joint identification experiment

[0126]

[0127] In order to identify the weak joints of the robot body, the posture of the robot must be determined first. In Example 1, the standard posture 8 is selected as the target posture.

[0128] The first step is to calculate the CSI. Considering that the target posture selected in this example is standard posture 8, the parameters of standard posture 8 can be directly used as the predicted value of the target posture. Therefore, the CSI of the posture can be expressed as follows:

[0129]

[0130] The second step is to calculate the MCI of each mode. The KF method and formula (10) are used to calculate the MCI of each mode of the robot in this posture under different cutting parameters. Since the standard posture 8 is selected as the target posture in this example, The results are as follows Figure 6 As shown in the figure, the influence trend of cutting parameters on MCI can be observed. As the cutting volume increases, the low-frequency structural mode of the robot is excited, and the corresponding MCI also increases sharply. At this time, the end of the robot shows a more violent low-frequency vibration.

[0131] The third step is to calculate M-WJWC. According to equations (16) and (20), the M-WJWC of the target posture of instance 1 can be calculated, that is, the M-WJWC of the standard posture 8.

[0132] The fourth step is to calculate R-WJWC. R-WJWC is calculated according to formula (18), and the change trend of R-WJWC under different cutting parameters is displayed in the form of parallel coordinates. Figure 7 As shown. Taking the spindle speed of 4800rpm and the radial cutting depth of 4mm as an example, the R-WJWC distribution diagram under this cutting condition is as follows Figure 8 shown.

[0133] like Figure 7 As shown in Figure 8, in standard posture 8, the distribution law of the weak joints of the robot body under milling excitation can be intuitively expressed in the form of a parallel coordinate diagram. In this posture, the main weak joints are concentrated at joints 2 and 3. Z At the degrees of freedom, R-WJWC is between 0.14-0.16 and 0.16-0.18 respectively; the second weakest joint is concentrated at ω of joint 5 Z Degrees of freedom and ω of joint 6 X and ω Z The R-WJWC of the degrees of freedom of the joints is between 0.10 and 0.12. The R-WJWC of the degrees of freedom of the other joints is almost all less than 0.05. It can be seen that when performing robot milling vibration suppression in this posture, the ω of joints 2, 3, 5, and 6 can be focused on. Z Degrees of freedom and ω of joint 6 X The robot can suppress vibrations in different degrees of freedom in a targeted manner, thereby greatly improving the robot's vibration reduction efficiency.

[0134] Specifically, under the working posture of 4800rpm rotation speed and 4mm radial cutting depth, the distribution of the robot's weak joints is as follows: Figure 8 As shown. Figure 5 It can be seen that although the corresponding M-WJWC distributions are different under different modes, after considering the influence of milling excitation, the R-WJWC distribution will be concentrated on the several degrees of freedom with the largest vibration, which can intuitively indicate the weak joints of the robot body under the current working conditions. Figure 8 It can be seen that under the working conditions of spindle speed of 4800rpm and radial cutting depth of 4mm, the maximum vibration degrees of freedom of the robot are ω of joints 2, 3, and 5 respectively. Z Degrees of freedom and ω of joint 6 X degrees of freedom, which is similar to Figure 8 The analysis conclusions are consistent with those of Figure 5 The difference is, Figure 8 It represents the weakness of each joint and its degrees of freedom of the robot body under this working condition, integrates the contribution of each order mode, and can reflect the distribution of weak joints of the robot body, which is of guiding significance for formulating targeted vibration reduction strategies.

[0135] In order to verify the correctness of the R-WJWC recognition results, a milling experiment was carried out under the conditions of a spindle speed of 4800 rpm and a radial cutting depth of 4 mm. Twelve acceleration sensors were used to simultaneously measure the ω values ​​of the six joints. Z Degrees of freedom vibration, such as Fig. 9 According to the above measurement scheme, joint vibration is calculated by taking joint 1 as an example.

[0136] The calculation process of joint vibration displacement is as follows: Fig.10 As shown, Fig.10 (a) is the joint tangential vibration acceleration signal on the joint 1 of the connecting rod 2. Fig.10 (b) is the joint tangential vibration acceleration signal on the connecting rod 1 joint 1, respectively. and The difference between the two is used to obtain the vibration acceleration signal of joint 1. The acceleration signal of joint 1 is integrated twice to obtain the displacement signal d1 of joint 1. The vibration displacement signal d of joints 2-6 can be obtained by the same method. 2～6 .

[0137] Due to the different spatial positions of different joints, the amplification factor of joint vibration on the end vibration is also different. In the above calculation, only the vibration displacement signal of the measuring point position is obtained, which should be calculated based on the distance D between the measuring point and the corresponding joint axis. 1～6 Calculate the joint angle A j (j=1,2,…,6), the calculation expression is:

[0138]

[0139] Among them, D1=0.565m, D2=0.310m, D3=0.160m, D4=0.270m, D5=0.170m, D6=0.180m.

[0140] Then, according to the Jacobian matrix corresponding to the current robot posture, the amplification factor of the vibration angular displacement of each joint to the terminal vibration is calculated. Since only the translational degrees of freedom of the terminal TCP in the X, Y, and Z directions are considered in the experiment, three TCP amplification factors can be calculated for each joint, and the expression is as follows:

[0141]

[0142] In the formula, represents the unit angular vibration of each joint, ν j Indicates that the unit angle vibration of each joint is mapped to the vibration of the end TCP. In the experiment, only ν needs to be considered j The first three elements of are expressed as follows:

[0143]

[0144] Space Movement The amplification factor is expressed by the 2-norm, and its expression is:

[0145]

[0146] Finally, according to the joint angle A j and magnification factor The contribution of each joint to the robot end vibration during the cutting process is obtained as j (j=1,2,...,6). After normalization, the R-WJWC under the current working condition can be approximately obtained, and the calculation expression is:

[0147]

[0148]

[0149] Among them, sum() is the sum calculation, that is, the sum calculation of each element in the vector; Ave() is the arithmetic mean calculation, that is, the sum of the elements in the vector divided by the number of elements, σ ​​can be expressed as:

[0150] σ=[σ1 σ2…σ6] (29)

[0151] Thus, the ω of R-WJWC with a spindle speed of 4800 rpm and a radial cutting depth of 4 mm in standard posture 8 of Example 1 was obtained: Z The relative contribution of degrees of freedom And compared with the ω of R-WJWC under this condition Z The relative size of the predicted degrees of freedom ( Figure 8 ) for comparison, such as Fig.11 shown.

[0152] Example 2:

[0153] Non-standard posture (-16.63°, 5.44°, 43.54°, -23.45°, -46.02°, 16.77°)

[0154] In the second example, a non-standard posture is selected to analyze and verify the distribution law of R-WJWC. This example focuses on verifying the rationality of CSI-based reasoning. Except for the different postures, the settings of all experimental parameters in this example are consistent with those in Example 1.

[0155] Then, the weak joints of the robot body are identified, and the non-standard postures (-16.63°, 5.44°, 43.54°, -23.45°, -46.02°, 16.77°) are selected as the target postures in Example 2.

[0156] The first step is to calculate the CSI. Based on equation (11), the configuration of 27 standard poses and 1 target pose is reconstructed. Based on equations (12)-(15), the CSI between the target pose and the 27 standard poses is calculated. The CSI can be expressed as Fig.12 The more similar the target posture is, the darker the line color of the standard posture configuration diagram is, and vice versa. The connecting rod structure is represented by a solid line, and the joint structure and the end TCP are represented by a circle.

[0157] The second step is to calculate the MCI of each mode. The KF method and formula (10) are used to calculate the MCI of each mode of 27 standard postures under different cutting parameters. According to CSI and formula (17), the MCI of each mode of the target posture under different cutting parameters is calculated. Finally, the MCI calculation result of the target posture is obtained, as shown in Fig.13 As shown in Figure 1, the effect of cutting parameter changes on MCI can also be observed. It is worth noting that under the same cutting parameters, there are significant differences in MCI for different postures, which further demonstrates the necessity of analyzing different modal MCIs in combination with milling parameters. This method can perform more accurate and targeted R-WJWC analysis, thereby better guiding the development of robot milling vibration suppression strategies.

[0158] The third step is to calculate M-WJWC. Based on equation (16) and CSI, the M-WJWC of the target posture can be calculated.

[0159] The fourth step is to calculate R-WJWC. R-WJWC is calculated according to formula (18), and the change trend of R-WJWC under different cutting parameters is shown in the form of parallel coordinate diagram, as shown in Fig.14 As shown in the figure, taking the spindle speed of 4800rpm and the radial cutting depth of 4mm as an example, the R-WJWC distribution diagram under this cutting condition is as follows: Fig.15 shown.

[0160] like Fig.14As shown in Figure 1, under the target posture, the distribution law of the weak joints of the robot body under milling excitation can be intuitively expressed in the form of a parallel coordinate diagram. In this posture, the main weak joints are concentrated at ω2 of joint 2 and joint 3. Z degrees of freedom, R-WJWC are between 0.11-0.13 and 0.13-0.15 respectively; the second weakest joint is concentrated at ω of joint 5 Z Degrees of freedom and ω of joint 6 X The R-WJWC of the degrees of freedom of the joints 2, 3, and 5 is between 0.09-0.11 and 0.07-0.09 respectively. The R-WJWC of all degrees of freedom of other joints is almost less than 0.04. It can be seen that when conducting a robot milling vibration suppression study under this posture, the ω of joints 2, 3, and 5 can be Z Degrees of freedom and ω of joint 6 X Targeted vibration control of the degrees of freedom can greatly improve the vibration suppression effect of the robot. Different from the R-WJWC distribution in the posture selected in Example 1, the ω of joint 6 in the posture selected in Example 2 is Z The R-WJWC at the degree of freedom is between 0 and 0.02, which is not a weak joint that needs attention. On the other hand, compared with the posture selected in Example 1, the R-WJWC of each degree of freedom of each joint in the posture selected in Example 2 has changed significantly. It can be seen that the robot posture dependence characteristics also have an important influence on the distribution of weak joints of the robot body. Therefore, the full workspace R-WJWC identification based on CSI is of great significance.

[0161] Specifically, under the conditions of 4800rpm and radial cutting depth of 4mm, the distribution of weak joints of the robot body is as follows: Fig.15 It can be seen that under the working conditions of spindle speed of 4800rpm and radial cutting depth of 4mm, the robot has the largest vibration degrees of freedom of joints 2, 3, and 5. Z Degrees of freedom and ω of joint 6 X degrees of freedom, which is similar to Fig.14 The analysis conclusions are consistent and more targeted.

[0162] Similar to Example 1, a verification experiment of R-WJWC was also conducted in Example 2. The experimental setting was spindle speed of 4800 rpm and radial cutting depth of 4 mm. Except for the posture, other parameters were consistent with Example 1. According to equations (21)-(29), the ω of R-WJWC when the spindle speed was 4800 rpm and the radial cutting depth was 4 mm under the selected posture in Example 2 can be calculated: Z Relative size of degrees of freedom And compared with the ω of R-WJWC under this condition Z The relative size of the degrees of freedom prediction ( Fig.15 ) for comparison, the comparison results are as follows Fig.16Compared with the sampling point posture with complete modal information, the recognition results of non-sampling point posture still have a certain degree of accuracy. Through the relative size of each joint R-WJWC, the weak links can be accurately located at the 2nd, 3rd, and 5th joints. Therefore, the recognition results have a certain reference value and can be used to locate the weak joints.

[0163] The present invention also provides a system for identifying weak joints of a robot's entire workspace body under milling excitation. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it executes the method for identifying weak joints of a robot's entire workspace body under milling excitation as described above.

[0164] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the method for identifying weak joints of the robot's entire workspace body under milling excitation as described above.

[0165] 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 identifying weak joints of a robot body in the entire workspace under milling excitation, characterized in that: The method comprises the following steps: (1) Determine the target workspace range where the weak joints of the robot body need to be identified, perform dynamic characteristic sensitivity analysis on the target workspace and then select a standard posture, and perform whole machine modal testing on each determined standard posture; (2) Based on the modal test results of the whole machine and the MFMS method, the contribution of each joint degree of freedom to the vibration of the tool center point is calculated, and then the modal-weak joint weight coefficient (M-WJWC) of each standard posture is calculated based on the corresponding contribution of each joint degree of freedom; at the same time, the state space model of the standard posture is established according to the modal test results, and then the modal contribution (MCI) of each standard posture under milling excitation is calculated based on the Kalman filter method (KF); (3) Reconstruct the configuration of the target posture and calculate the configuration similarity index (CSI) between the target posture and the standard posture. Then, based on the obtained configuration similarity index, the modal-weak joint weight coefficient of the standard posture and the modal contribution of the standard posture, the M-WJWC matrix and MCI of the target posture are calculated. (4) Based on the M-WJWC matrix of the target posture and the MCI, the robot-weak joint weight coefficient of the target posture is identified, and then the online identification of the weak joints of the robot body under milling excitation is realized based on the robot-weak joint weight coefficient of the target posture.

2. The method for identifying weak joints of a robot body in the entire workspace under milling excitation as claimed in claim 1, characterized in that: Based on the robot frequency response curve and correlation coefficient, the dynamic characteristic sensitivity coefficient is proposed, and the corresponding formula is: where h i and h j Represents the frequency response vector at the sampling point, cov() represents the covariance operation, and var[] represents the variance operation; Based on formula (1), the dynamic characteristic sensitivity coefficient matrix is ​​obtained, and then the standard posture of the robot is determined based on the dynamic characteristic sensitivity coefficient matrix.

3. The method for identifying weak joints of a robot body in the entire workspace under milling excitation as claimed in claim 1, characterized in that: Use the multi-joint full-degree-of-freedom vibration mode to represent the multi-order modal vibration mode of the robot structure, and obtain the modal vibration mode of joint j expression: In the formula For CS j The origin coordinates under CS0, CS0 to CS j The rotation matrix of is the six-degree-of-freedom deformation amplitude of joint j under CS0; According to formula (2), the vibration mode of each joint of the robot is calculated, and X MFMS : X-based MFMS , calculate the contribution of each joint degree of freedom to the vibration of the tool center point, and the calculation expression of the contribution of each joint degree of freedom to the vibration of the tool center point is: Where j represents the robot joint, j = 1, 2, ..., 6, and k represents the 6 degrees of freedom of each joint (X, Y, Z, ω X, ω Y, ω Z, ),k=1,2,…,6;X MFMS,j,k Represents X MFMS The j-th row and k-th column element of Indicates the CS0 coordinate system and the CS j The unit vector with the same direction as the k-th coordinate axis, and Represents CS T and CS j The origin of the coordinate system in the CS0 coordinate system, Represents the contribution of the k degree of freedom of the j joint to the vibration of the tool center point.

4. The method for identifying weak joints of a robot body in the entire workspace under milling excitation as claimed in claim 3, characterized in that: The contribution of each degree of freedom of each joint under each order mode to the vibration of the tool center point is quantitatively evaluated by the modal-weak joint weight coefficient. The calculation expression is: Based on the definition of MFMS, the modal vibration data of each mode of the robot are substituted into formula (4) to obtain the contribution of each degree of freedom of each joint to the vibration of the tool center point under different postures and modes of the robot structure; and then the M-WJWC of each standard posture is obtained by formula (5): j,k,l,m ; Where j, k = 1, 2, …, 6; l = 1, 2, …, 5; m = 1, 2, …, 27; l is the modal order and m is the standard posture index.

5. The method for identifying weak joints of a robot body in the entire workspace under milling excitation as claimed in claim 1, characterized in that: Considering the contribution of each mode to vibration in the modal space, the state space model is established, expanded and reorganized, and the cutting force term is also included in the system state variables; Set the state variable to The state space model of the system is expressed as: In the formula, w and v are the process noise and observation noise of the system respectively. The equation satisfies w~N(0,Q) and v~N(0,R), Q is the process noise variance, R is the observation noise variance, A and B are the state matrix and input matrix of the system equation.

6. The method for identifying weak joints of a robot body in the entire workspace under milling excitation as claimed in claim 5, characterized in that: The KF method combines the modal parameters obtained from the modal test with the vibration data y observed at a single measuring point j on the robot structure. k+1 , to achieve the optimal estimation of the modal vibration displacement vector q, the vibration displacement signal A = [A1, A2, A3, A4, A5] of each mode of the robot structure is obtained by the following formula: A=Φq (9) Using the amplitude of the vibration signal |A l |To characterize the contribution of each mode in the robot structure vibration process, so as to obtain the MCI of each standard posture.

7. The method for identifying weak joints of a robot body in the entire workspace under milling excitation as claimed in claim 1, characterized in that: Take the coordinate similarity S of multiple coordinates corresponding to each standard posture g,m The average value of the target posture is the CSI between the target posture and the standard posture; the M-WJWC matrix of the CSI and the standard posture Multiply and add the elements at the corresponding positions to get the M-WJWC matrix of the target posture 8. The method for identifying weak joints of a robot body in the entire workspace under milling excitation as claimed in claim 7, characterized in that: Taking CSI as the weight, the modal contribution of the calculated standard posture is weighted to obtain the MCI of the target posture.

9. A system for identifying weak joints of a robot in the entire workspace under milling excitation, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the method for identifying weak joints of a robot body in the entire workspace under milling excitation as described in any one of claims 1 to 8 is executed.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the method for identifying weak joints of the robot's entire workspace body under milling excitation as described in any one of claims 1-8.

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