A method and device for identifying weak joints of a robot's entire workspace under milling excitation

Abstract

The present invention belongs to the technical field related to milling processing, and discloses a method and device for identifying weak joints of a robot body in the entire workspace under milling excitation, comprising the following steps: (1) performing a dynamic characteristic sensitivity analysis on a target workspace and then selecting a standard posture, and performing a whole-machine modal test on each determined standard posture; (2) calculating the modal-weak joint weight coefficient of each standard posture based on the whole-machine modal test results and the MFMS method; and at the same time, calculating the modal contribution of each standard posture under milling excitation; (3) reconstructing the configuration of the target posture, and calculating the configuration similarity index between the target posture and the standard posture, and then calculating the M-WJWC matrix and MCI of the target posture; (4) identifying the robot-weak joint weight coefficient of the target posture, and then realizing online identification of weak joints of the robot body under milling excitation. The present invention can realize the prediction of the R-WLWC of any posture in the target workspace.

Description

Technical Field

[0001] The present invention belongs to the technical field related to milling processing, and more specifically, relates to a method and equipment 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 milling machining. Compared to tool vibration, robot structural vibration is more likely to occur and has a more severe impact. However, the complexity of the robot's structural modes and the posture-dependence of its dynamic characteristics pose significant challenges in suppressing the robot's structural vibration. Milling excitation further alters the distribution of the robot's structural vibration. These combined factors make it difficult for engineers to locate weak links prone to vibration and achieve targeted vibration suppression. Therefore, it is necessary to clarify the structural vibration characteristics of the robot under cutting excitation and identify the weak links in the structure.

[0003] Currently, the research on weak links in machine tool structures is mostly focused on them. Research on weak links in robot milling machining is still relatively preliminary. To more effectively suppress robot structural vibration, improve machining efficiency, and ensure machining accuracy, it is necessary to study the distribution of weak links in robot structural vibration across the entire space. Summary of the Invention

[0004] In response to the above defects or improvement needs of the prior art, the present invention provides a method and device for identifying weak joints of the 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 objectives, according to one aspect of the present invention, a method for identifying weak joints in a robot's entire workspace under milling excitation is provided, the method comprising the following steps:

[0006] (1) Determine the target workspace range where weak joints of the robot body need to be identified, perform dynamic sensitivity analysis on the target workspace, and then select a standard posture. Perform a whole-machine modal test 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 tool center vibration 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's 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] Based on X MFMS , calculate the contribution of each joint degree of freedom to the tool center point vibration, the calculation expression of each joint degree of freedom to the tool center point vibration contribution 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 in 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 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 a 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] Where 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, and 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 and 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 | is used to characterize the contribution of each mode during the robot structure vibration process, thereby obtaining 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 pose and the standard pose is the CSI; the CSI is combined with the M-WJWC matrix of the standard pose 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 the entire workspace body of a robot 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 the entire workspace body of a robot 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 solutions conceived by the present invention provide a method and device for identifying weak joints in the entire workspace of a robot under milling excitation, which 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), which can realize the prediction of the R-WLWC of the robot's standard posture.

[0036] 2. This paper 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 a limited number of 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 serial 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 pose and the standard pose is the CSI; the CSI is combined with the M-WJWC matrix of the standard pose 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 This 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 shapes, respectively;

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

[0044] Figure 6 (a), (b), and (c) are schematic diagrams of MCI distribution at 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 4800 rpm and the radial cutting depth is 4 mm (standard posture 8);

[0047] Figure 9 Schematic diagram of the experimental setup for joint vibration testing to verify the prediction accuracy of R-WJWC;

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

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

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

[0051] Figure 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] Figure 14 is the parallel coordinate diagram of R-WJWC under milling excitation (non-standard posture);

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

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

[0055] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is 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 for the purpose of explaining 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 may be combined with each other as long as they do not conflict with each other.

[0056] This paper provides a method for identifying weak joints in a robot's entire workspace under milling excitation. This method, combined with milling excitation, quantitatively evaluates weak links corresponding to different cutting parameters and robot configurations, providing a theoretical basis for targeted suppression of robot structural vibration within a specific workspace and cutting parameter domain. Furthermore, this method can accurately identify the distribution of weak links in a 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 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, the target workspace range where the weak joints of the robot body need to be identified is determined, and a standard posture is selected.

[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, such as 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 in 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 spacing of 200mm. A total of 27 standard robot postures were selected, and the distribution of the standard postures, i.e., the serial numbers, are as follows: Figure 3Modal tests were conducted on 27 standard robot postures. A shaker was used for sinusoidal sweep excitation, with a force sensor installed at the end of the shaker to synchronously measure the excitation force. A 3D scanning laser Doppler vibrometer was used to measure the vibration response of the robot structure. 120 measurement points were evenly distributed across each link of the robot structure.

[0064] Based on the measured results, the modal parameters of the robot structure under the above 27 standard postures can be obtained by modal analysis. 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 circle in the middle represents the original position of the robot, and the arrow vector represents the direction and magnitude of the mode shape.

[0065] In the second step, 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 calculated to obtain X MFMS :

[0069]

[0070] Based on X MFMS , the contribution of each joint degree of freedom to the tool center vibration can be calculated. The calculation expression of the contribution of each joint degree of freedom to the tool center vibration 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 in 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 to the tool center point vibration under each order mode. 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 pose index.

[0076] Taking standard posture 8 as an example, the distribution of weak joints under each mode is drawn according to M-WJWC, as shown in the following figure: Figure 5 As shown in Figure 2, 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 of the two joints (ω Z ) contributes most to the vibration of the tool center point. In the second-order mode, the Z-axis rotational freedom of the three joints (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 of the 6 joints (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) method.

[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 a 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] Where 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, and 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 velocity 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 and 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, thereby obtaining the MCI of each standard posture. Its expression is as follows, where l represents the modal order and m represents the robot posture index:

[0090]

[0091] Step 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.

[0092] The robot's configuration largely determines the distribution of its dynamic characteristics, namely the distribution of weak joints. By reconstructing the configuration characteristics of the robot's posture at the sampling point, a configuration similarity index (CSI) is proposed to achieve full-space M-WJWC and MCI identification. 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 CS 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. Based on experience, n = 25 is taken here. At this time, the 8 endpoint coordinates under any posture m can be reconstructed based on the robot posture and DH parameters. 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 amplified end coordinate differences 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 27 standard postures. m Multiply and add the elements at the corresponding positions to get the M-WJWC matrix of the target posture To achieve the identification of weak joints in each mode of arbitrary 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] In step 4, the robot-weak joint weight coefficient (R-WJWC) of the target posture is identified based on the M-WJWC matrix and MCI of the target posture, 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 (using MCI for evaluation, MCI is a one-dimensional value). The vibration of each mode is composed of the 6 degrees of freedom vibration of 6 joints with different degrees of participation, totaling 36 vibration components (using the M-WJWC matrix ( denoted by , which is a 6 × 6 × 5 matrix). Therefore, as shown in Equation (18), R-WJWC is a 6 × 6 matrix that represents the contribution ratio of each degree of freedom of each joint of the robot (a total of 36) to the end vibration under milling excitation. Based on R-WJWC, the distribution of weak joints in the robot body under any posture and any milling parameters can be intuitively identified, and the weak joints in the current working state can be effectively located, thereby performing 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 with standard and non-standard postures.

[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 during the milling process were selected. Since the KF method is used in MCI identification, vibration signal testing only requires collecting the vibration signal from any one measurement point during the modal test experiment. The experiment used a DYTRAN 3263A2T accelerometer to collect vibration signals during the robot milling process, with a sampling frequency set to 3125 Hz. The tool used in the experiment was a SANDVIK Φ16 end mill with a tool length of 115 mm and four teeth. The cutting material used was 7075 aluminum alloy, which has lower cutting forces and a more stable cutting process than nickel-aluminum bronze, ensuring the effectiveness of the weak link identification results.

[0124] Based on the above experimental settings, milling experiments were conducted at spindle speeds of 4800 rpm, 5400 rpm, and 6000 rpm, with an axial depth of cut of 3 mm and radial depths of cut ranging from 1 mm to 6 mm in 1 mm increments. The remaining 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 robot's posture 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 obtained are as follows Figure 6 As shown in the figure, the impact of cutting parameters on MCI can be observed. As the cutting volume increases, the robot's low-frequency structural modes are excited, and the corresponding MCI increases sharply. At this time, the robot end exhibits more intense low-frequency vibrations.

[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 a parallel coordinate graph, as shown in the figure below: 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, the distribution 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 are 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 other joint degrees of freedom are 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 a targeted manner according to the degree of freedom, thereby greatly improving the vibration reduction efficiency of the robot.

[0134] Specifically, at a working speed of 4800 rpm and a radial cutting depth of 4 mm, 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 represent 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 consistent with Figure 8 The conclusion of the analysis is consistent with that of Figure 5 The difference is, Figure 8 It represents the weakness of each joint and its degree 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 Figure 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 Figure 10 As shown, Figure 10 (a) is the joint tangential vibration acceleration signal on the connecting rod 2 joint 1, Figure 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] Since the spatial positions of different joints are different, the amplification coefficients of joint vibration on terminal vibration are also different. In the above calculation, only the vibration displacement signal of the measuring point position is obtained, and the distance D between the measuring point and the corresponding joint axis should be used. 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, based on the Jacobian matrix corresponding to the current robot posture, the amplification factor of the vibration angular displacement of each joint on the terminal vibration is calculated. Since the experiment only considers the translational degrees of freedom of the terminal TCP in the X, Y, and Z directions, three TCP amplification factors can be calculated for each joint, and the expression is as follows:

[0141]

[0142] Where, 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 amplification factor The contribution of each joint to the vibration of the robot end during the cutting process is obtained 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 spindle speed of 4800 rpm and 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 Figure 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 pose is selected to analyze and verify the distribution of R-WJWC. This example focuses on verifying the rationality of CSI-based reasoning. Aside from the different poses, all experimental parameters in this example are the same as 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 Figure 12 The more similar the standard posture is to the target posture, the darker the line color of the standard posture configuration diagram; vice versa, the line color is lighter. The connecting rod structure is represented by a solid line, and the joint structure and the end TCP are represented by circles.

[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 the figure. Figure 13 As shown in Figure 1, similar to Example 1, the effect of varying cutting parameters on MCI can also be observed. Notably, under the same cutting parameters, MCI varies significantly between different postures, further demonstrating the necessity of analyzing different modal MCIs in conjunction with milling parameters. This method enables more accurate and targeted R-WJWC analysis, thus better guiding the development of vibration suppression strategies for robotic milling.

[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 displayed in the form of a parallel coordinate graph, as shown in Figure 1. Figure 14 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 15 shown.

[0160] like Figure 14As shown in Figure 2, under the target posture, the distribution 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 are between 0.09-0.11 and 0.07-0.09 respectively. The R-WJWC of all degrees of freedom of the other joints are almost all less than 0.04. It can be seen that when studying the vibration suppression of robot milling in this posture, the ω of joints 2, 3, and 5 can be targeted. 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 each degree of freedom is between 0 and 0.02, indicating that it is not a weak joint requiring attention. On the other hand, the R-WJWC of each degree of freedom for each joint in the posture selected in Example 2 shows significant changes compared to the posture selected in Example 1. This shows that the robot's posture-dependent characteristics also have a significant impact on the distribution of weak joints in the robot body. Therefore, full-workspace R-WJWC identification based on CSI is of great significance.

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

[0162] Similar to Example 1, a R-WJWC verification experiment was also conducted in Example 2. The experimental setting was a spindle speed of 4800 rpm and a radial depth of cut of 4 mm. Except for the posture, other parameters were consistent with those in Example 1. According to equations (21)-(29), the ω of R-WJWC can be calculated when the spindle speed is 4800 rpm and the radial depth of cut is 4 mm under the posture selected in Example 2. 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 ( Figure 15 ) for comparison, the comparison results are as follows Figure 16Compared with the sampling point posture with complete modal information, the identification results of the 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 joints 2, 3, and 5. Therefore, the identification 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 the entire workspace body of a robot 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 the entire workspace body of a robot 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 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 in the scope of protection of the present invention.

Claims

1. A method for identifying weak joints in the entire workspace of a robot under milling excitation, characterized in that: The method comprises the following steps: (1) Determine the target workspace range where weak joints of the robot body need to be identified, perform dynamic sensitivity analysis on the target workspace, and then select a standard posture. Perform a whole-machine modal test 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 tool center vibration 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 and MCI of the target posture, 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 in the entire workspace of a robot under milling excitation according to claim 1, characterized in that: Based on the robot's 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 in the entire workspace of a robot under milling excitation according to 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 : Based on X MFMS , calculate the contribution of each joint degree of freedom to the tool center point vibration, the calculation expression of each joint degree of freedom to the tool center point vibration contribution 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 in 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 in the entire workspace of a robot under milling excitation according to claim 3, characterized in that: The contribution of each degree of freedom of each joint to the vibration of the tool center point under each order mode 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 in the entire workspace of a robot under milling excitation according to claim 1, characterized in that: Considering the contribution of each mode to vibration in the modal space, a 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: Where 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, and A and B are the state matrix and input matrix of the system equation.

6. The method for identifying weak joints in the entire workspace of a robot under milling excitation according to claim 5, characterized in that: The KF method combines the modal parameters obtained from the modal test and 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 | is used to characterize the contribution of each mode during the robot structure vibration process, thereby obtaining the MCI of each standard posture.

7. The method for identifying weak joints in the entire workspace of a robot under milling excitation according to 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 pose and the standard pose is the CSI; the CSI is combined with the M-WJWC matrix of the standard pose 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 in the entire workspace of a robot under milling excitation according to claim 7, characterized in that: Using 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 in the entire workspace of a robot under milling excitation, characterized by: The system includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, it executes the method for identifying weak joints of the robot's entire workspace body under milling excitation according to any one of claims 1 to 8.

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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