A Method for Selecting Measurement Points in Modal Testing of Industrial Robots Based on Modal Kinetic Energy Method

Abstract

This invention discloses a method for selecting measurement points for modal testing of industrial robots based on modal kinetic energy, relating to the technical field of modal testing of industrial robots. Based on the traditional modal kinetic energy method, a comprehensive modal kinetic energy weighting index is introduced, which includes a modal kinetic energy weighting factor and a directional effectiveness coefficient. This addresses the problems of neglecting local modes, insufficient sensor directional matching, and equal weighting of modes in different parts in traditional methods applied to industrial robots. Nodes with higher modal kinetic energy are selected through iterative updates, and the optimal measurement points are chosen. Finally, accelerometers are deployed to complete the experimental modal testing. This invention can effectively identify local modes, improve the rationality of measurement point placement and the accuracy of modal parameter identification, avoid mode loss, and provide reliable data support for industrial robot structural optimization and dynamic performance improvement.

Description

Technical Field

[0001] This invention relates to the technical field of modal testing of industrial robots, and in particular to a method for selecting test points during the testing process, specifically a method for selecting test points for modal testing of industrial robots based on the modal kinetic energy method. Background Technology

[0002] With the rapid development of intelligent manufacturing and automation technologies, industrial robots have been widely used in high-precision, high-efficiency production scenarios such as automobile manufacturing, electronic assembly, welding, and material handling. Their dynamic performance during operation directly affects processing accuracy, equipment lifespan, and production safety.

[0003] Therefore, in-depth research on the dynamic characteristics of industrial robots, especially their modal parameters (fixed frequency, mode shape, damping ratio), is of great significance for optimizing structural design and improving operational stability. Modal testing, as an important means of obtaining structural dynamic characteristics, has been widely used in the field of industrial robots. Through modal testing, resonant frequencies and weak points that may occur during robot operation can be identified, thus providing a basis for structural optimization and vibration control.

[0004] However, the accuracy of modal testing largely depends on the rationality of the measurement point arrangement. An inappropriate measurement point arrangement can lead to missing modal information, low signal-to-noise ratio, and even misjudgment of structural dynamic characteristics. Currently, commonly used measurement point selection methods include the effective independence method and the modal kinetic energy method. Among these, the modal kinetic energy method has gradually attracted researchers' attention because it can preferentially select locations with higher modal kinetic energy as measurement points, thereby improving the signal-to-noise ratio of the test signal and the accuracy of modal identification. Compared with other methods, the modal kinetic energy method can retain key dynamic information of the structure while reducing the number of measurement points, making it particularly suitable for modal testing of complex structures.

[0005] The traditional modal kinetic energy method for modal testing of industrial robots still has the following shortcomings: 1. The traditional method tends to select global modal measurement points with large amplitudes, while the local modes such as wrists and forearms that exist in many industrial robots, although having small overall kinetic energy, have a significant impact on end-effector accuracy; 2. When performing weighing calculations, the traditional method does not consider the degree of matching between the actual measurement direction of the accelerometer and the mode shape direction; 3. The traditional method treats all parts of the modality equally, without considering the differences in the actual impact of different parts of the modality on the performance of the industrial robot.

[0006] This invention selects measurement points in modal testing of industrial robots based on the modal kinetic energy method. On this basis, a weighted improvement is made by introducing a comprehensive modal kinetic energy weight index to weight the measurement points in different regions of the robot, which significantly improves the recognition accuracy of modal parameters and provides reliable data support for the structural optimization and performance improvement of industrial robots. Summary of the Invention

[0007] To achieve the above objectives, the technical solution adopted by this invention is as follows: a method for selecting test points for modal testing of industrial robots based on modal kinetic energy method, comprising the following steps:

[0008] Step 1: Create a 3D model of the industrial robot and import it into the finite element analysis software. Mesh the model, set constraint and boundary condition parameters, and obtain the simulation modal parameters of the 3D model of the industrial robot.

[0009] Step 2: Based on the simulation modal parameters of key parts of the industrial robot 3D model obtained in Step 1, the modal kinetic energy distribution of the industrial robot 3D model is automatically obtained using finite element analysis software; a comprehensive modal kinetic energy weight index is introduced, which includes a modal kinetic energy weight factor and a directional effectiveness coefficient;

[0010] Step 3: Use the modal contribution index to select the point with the largest contribution and iteratively update to obtain the optimal point. Continuously filter the points with the largest contribution through the iterative method until the number of remaining points equals the number of measurement points.

[0011] Step 4: Based on the final optimized measurement point results obtained in Step 3, deploy sensors to conduct modal experiments and complete the modal experimental analysis of the industrial robot.

[0012] Furthermore, the modal kinetic energy weighting factor is processed with unequal weights based on the existing modal kinetic energy method; the modal kinetic energy weighting factor is determined by frequency importance, mode shape importance, and energy balance (avoiding low-frequency dominance).

[0013] Furthermore, the modal kinetic energy weighting factor is denoted as ,

[0014]

[0015] Where k is the modal order, F is the frequency, T is the modal type, and E is the kinetic energy.

[0016] Frequency importance factor is denoted as The importance factor of mode type is denoted as The energy balance factor is denoted as ;

[0017] .

[0018] Furthermore, in the frequency importance ranking, modes within the industrial robot's operating bandwidth should be assigned high weights, while modes outside the industrial robot's operating bandwidth should be assigned low weights; that is:

[0019]

[0020] in, This represents the frequency of the k-th mode; This indicates the center frequency of the main operating frequency band of the industrial robot; This represents the attenuation coefficient (controlling the bandwidth range).

[0021] Furthermore, in the importance of mode type, a higher weight is given to the mode of the end effector; that is:

[0022]

[0023]

[0024] Right now:

[0025] in This represents the proportion of modal kinetic energy of the end effector at the k-th joint; This represents the sum of the kinetic energies of the k-th joint of all end effectors; This represents the sum of the kinetic energies of the k-th joint among all joints; This is the adjustment coefficient.

[0026] Furthermore, in energy equilibrium, the weights of rigid body modes with high modal kinetic energy or their first few low-frequency modes can be appropriately reduced to avoid low-order modes masking local higher-order modes; that is:

[0027]

[0028] in, This represents the total kinetic energy of the k-th mode; This represents the maximum kinetic energy value among all modes; This represents the adjustment coefficient.

[0029] Furthermore, the directional effectiveness coefficient is denoted as ,but:

[0030]

[0031] Where n represents the normal direction of sensor installation at the node; For the first Node number The first-order mode shape vector.

[0032] Furthermore, the comprehensive modal kinetic energy weight index measures the modal contribution of the measurement points, and the combination of measurement points with the largest modal contribution is used as the preset measurement points for experimental modal analysis;

[0033] The integrated modal kinetic energy weight index is defined as follows: ,but:

[0034]

[0035] in, For modal order index; This represents the total number of modes; It is the first The object in the first Modal kinetic energy weighting factor in first-order modes; It is the first The object in the first Effective directional coefficients in first-order modes;

[0036] The modal contribution index is marked as ,but:

[0037]

[0038] in, This represents the modal kinetic energy value.

[0039] Furthermore, in step three, the measurement points selected for the modal contribution index are iteratively screened using the modal confidence criterion (MAC criterion). After selecting the node with the largest modal contribution index each time, the modal guarantee criterion value of the remaining nodes and all selected nodes is calculated, and the contribution index of the remaining nodes is updated based on this value.

[0040] Furthermore, the modal experimental analysis process includes setting up experimental equipment, using a force hammer to traverse all measuring points, and obtaining modal parameters and information.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1. This invention selects measurement points in modal testing of industrial robots based on the modal kinetic energy method. On this basis, a weighted improvement is made by introducing a comprehensive modal kinetic energy weight index to weight the measurement points in different regions of the robot, which can significantly improve the recognition accuracy of modal parameters and accurately obtain a series of modal parameters of industrial robots.

[0043] 2. This invention is based on a weighted improved modal kinetic energy method. This method can more accurately identify the weak links and vibration-sensitive areas of the robot structure, thereby providing a theoretical basis for targeted structural optimization, lightweight design and dynamic performance improvement, and enhancing the guiding value of modal testing in engineering practice. Attached Figure Description

[0044] Figure 1 This is an overall flowchart of the improved modal kinetic energy method of the present invention;

[0045] Figure 2 This is a 3D model diagram of an industrial six-axis robot in an embodiment of the present invention;

[0046] Figure 3 This is a finite element mesh diagram of an industrial six-axis robot in an embodiment of the present invention;

[0047] Figure 4 This is the first simulation result of the industrial six-axis robot modality in this embodiment of the invention;

[0048] Figure 5 This is the second simulation result of the industrial six-axis robot partial mode in the embodiment of the present invention;

[0049] Figure 6 This is the third simulation result of the industrial six-axis robot in this embodiment of the invention;

[0050] Figure 7 This is a distribution diagram of the frequency response function of an industrial six-axis robot before optimization in an embodiment of the present invention;

[0051] Figure 8 This is a distribution diagram of the optimized frequency response function of an industrial six-axis robot in an embodiment of the present invention. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] The present invention provides a method for selecting test points for modal testing of industrial robots based on the modal kinetic energy method, comprising the following steps:

[0054] Step 1: Create a 3D model of the industrial robot and import it into the finite element analysis software. Mesh the model, set constraint and boundary condition parameters, and obtain the simulation modal parameters of the 3D model of the industrial robot.

[0055] Step 2: Based on the simulation modal parameters of the key parts of the industrial robot 3D model obtained in Step 1, the modal kinetic energy distribution of the industrial robot 3D model is automatically obtained using finite element analysis software; a comprehensive modal kinetic energy weight index is introduced, including modal kinetic energy weight factor and directional effectiveness coefficient; among which, the key parts of the industrial robot 3D model include the upper arm, forearm, wrist joint, and fuselage;

[0056] Step 3: Use the modal contribution index to select the point with the largest contribution (the node with the highest modal contribution index) and iteratively update to obtain the optimal point. Continuously filter the points with the largest contribution through the iterative method until the number of remaining points equals the number of measurement points.

[0057] Step 4: Based on the final optimized measurement point results obtained in Step 3, deploy sensors to conduct modal experiments and complete the modal experimental analysis of the industrial robot.

[0058] The specific steps are as follows:

[0059] Step 1: Based on the appearance and structural characteristics of the selected industrial robot, create a 3D model of the robot using SOLIDWORKS and import it into finite element analysis software such as ANSYS. Then, ANSYS automatically meshes the imported 3D model. Next, set the material properties in ANSYS (in this example, structural steel with a density of 7850 kg / m³, Poisson's ratio of 0.3, and an elastic modulus of 200 GPa is selected). Then, set constraints in ANSYS (in this example, the contact characteristics of each joint of the imported 3D model are set to bonded constraints). Next, set boundary conditions in ANSYS (in this example, the four threaded holes on the base of the imported 3D model are fixed). Finally, ANSYS automatically obtains the simulation modal parameters of the imported 3D model (including the first N modes (e.g., N=6) and natural frequencies; the mode shape of each node should include components in the X, Y, and Z directions).

[0060] It should be noted that modal kinetic energy distribution refers to the distribution calculated by extracting the mode shape components (X, Y, Z) of each node using finite element analysis software and applying the modal kinetic energy formula.

[0061] Modal kinetic energy method is an energy criterion with good sensitivity and noise resistance. It can be easily obtained through finite element methods. The original formula principle of modal kinetic energy method is as follows:

[0062]

[0063] in Represents the k-th modal component of the i-th degree of freedom. This represents the value in the i-th row and j-th column of the mass matrix. This represents the k-th modal component of the j-th degree of freedom.

[0064] Step 2: Introduce a comprehensive modal kinetic energy weighting index, including a modal kinetic energy weighting factor and a directional effectiveness coefficient:

[0065] It needs to be explained that, theoretically, the standard modal kinetic energy method treats the kinetic energy contribution of all components of the tested device (such as a 3D model of an industrial robot) equally. However, in actual engineering, testers focus on the vibration of specific locations (such as the upper arm, forearm, wrist joint, and body) or the response in specific directions (such as the vertical direction that affects accuracy). The comprehensive modal kinetic energy weight index is used to amplify modes with large contributions (such as the upper arm, forearm, wrist joint, and body at specific locations) and weaken modes with small contributions; that is, the greater the contribution of a mode, the higher its weight.

[0066] Among them, the modal kinetic energy weighting factor is processed with unequal weights based on the existing modal kinetic energy method.

[0067] In step one, the ANSYS finite element analysis software automatically calculates the first N modes and natural frequencies (i.e., modal kinetic energy distribution) of the industrial robot model using the modal kinetic energy method formula, and then uses these values ​​as the basis for subsequent calculation of the comprehensive modal kinetic energy weight index.

[0068] The weighting criteria are as follows:

[0069] (1) Frequency importance: Modes within the working bandwidth of the industrial robot should be given high weight, and modes outside the bandwidth should be given low weight;

[0070] (2) Importance of mode type: Give higher weight to modes that affect the positioning accuracy of the end effector (such as arm bending and end wrist twisting), even if their overall kinetic energy may not be large.

[0071] (3) Energy balance (avoiding low frequency dominance): For rigid body modes with large modal kinetic energy or their first few low-frequency modes, the weight can be appropriately reduced to prevent the local high-order modes from being masked.

[0072] Modal kinetic energy weighting factor is denoted as ,

[0073]

[0074] Where k is the modal order, F is the frequency, T is the modal type, and E is the kinetic energy.

[0075] Frequency importance factor is denoted as The importance factor of mode type is denoted as The energy balance factor is denoted as ;

[0076] .

[0077] In the frequency importance ranking, modes within the operating bandwidth of the industrial robot should be assigned high weights, while modes outside the operating bandwidth should be assigned low weights; that is:

[0078]

[0079] in, This represents the frequency of the k-th mode; This indicates the center frequency of the main operating frequency band of the industrial robot; This represents the attenuation coefficient (controlling the bandwidth range).

[0080] In the importance of mode type, higher weight is given to the modes of the end effector; that is:

[0081]

[0082]

[0083] Right now:

[0084] in This represents the proportion of modal kinetic energy of the end effector at the k-th joint; This represents the sum of the kinetic energies of the k-th joint of all end effectors; This represents the sum of the kinetic energies of the k-th joint among all joints; This is the adjustment coefficient.

[0085] In energy equilibrium, the weights of rigid body modes with high modal kinetic energy or their first few low-frequency modes can be appropriately reduced to prevent low-order modes from masking local high-order modes; that is:

[0086]

[0087] in, This represents the total kinetic energy of the k-th mode; This represents the maximum kinetic energy value among all modes; This represents the adjustment coefficient.

[0088] In another embodiment, the modal kinetic energy weighting factors for different parts of the industrial robot are set as follows: the upper arm bending mode σ is 1.2; the forearm bending mode σ is 1.3; the wrist joint torsion mode σ is 1.4; the body global mode σ is 1.0; and the other local modes σ is 1.1. These can be adjusted appropriately according to the actual engineering situation.

[0089] In this embodiment, to address the directionality issue of sensor placement, a directional effectiveness coefficient is defined for each node i and each mode k. :

[0090]

[0091] In the formula, n is the possible sensor mounting normal direction at the node (for example, considering the curved surface of the robot, n can be [1,0,0], [0,1,0], [0,0,1], representing the measurement X, Y, and Z directions respectively). The direction effectiveness coefficient is introduced to ensure that the selected measurement point has a sufficiently obvious response to the mode in its optimal measurement direction. For nodes next to robot joints, the possibility of motion interference should be considered, and the appropriate mounting direction should be adjusted. For the first Node number The first-order mode shape vector.

[0092] The integrated modal kinetic energy weight index is defined as follows: ,but:

[0093]

[0094] in, For modal order index; This represents the total number of modes; It is the first The object in the first Modal kinetic energy weighting factor in first-order modes; It is the first The object in the first The effective directional coefficients in the first mode.

[0095] Modal contribution is denoted as ,but:

[0096]

[0097] in, This represents modal kinetic energy.

[0098] In this embodiment, modal contribution index is used. (i.e., modal kinetic energy) With integrated modal kinetic energy weight index The product of the two factors is used as the basis for selecting measurement points.

[0099] The comprehensive modal kinetic energy weight index of all candidate surface nodes is calculated based on the weight index.

[0100] In step three, the measurement points selected for the modal contribution index are iteratively screened using the modal confidence criterion. After selecting the node with the largest modal contribution index each time, the modal guarantee criterion value of the remaining nodes and all selected nodes is calculated, and the contribution index of the remaining nodes is updated based on this value.

[0101] Specifically, the point with the largest contribution is selected based on weight, and the process iteratively optimizes until the number of remaining measurement points equals the preset number of measurement points: the candidate measurement point set is initialized with nodes from all surfaces, and the set of already selected nodes is set to empty; all candidate points are calculated, and the point with the largest contribution is added to the node set; to avoid redundancy between newly selected and already selected point information, a modal confidence criterion is introduced for constraint. After each selection, the contribution index of the remaining candidate points is updated, and the update calculation process is as follows:

[0102]

[0103] In the formula The mode shape vector representing all selected measurement points; This represents the mode shape vector of the i-th measurement point.

[0104] If the mode shape of a candidate point is highly correlated with the mode shape of any selected point (i.e., the modal confidence criterion value is close to 1), it is considered to provide little new information, and its contribution index will be significantly reduced, thus decreasing the probability of it being selected in subsequent iterations. The maximum off-diagonal value of the modal confidence criterion matrix is ​​minimized as the criterion for optimizing the measurement points. A threshold is set (the threshold can be set to 0.1-0.2). If the threshold is met, iterative calculation continues. The steps are repeated through iterative iteration until the number of selected measurement points reaches the preset value.

[0105] In step four, the final optimized measurement point results are output, and sensors are deployed for modal testing: Based on the obtained iterative measurement point optimization results, triaxial accelerometers are deployed at these most critical nodes, connected to the corresponding channels of the data acquisition and analysis instrument, and a hammer impact test device is deployed. Modal testing software is connected to use the hammer to impact all measurement points to obtain the experimental modal parameters of the industrial robot, thus completing the experimental modal analysis of the robot.

[0106] In another embodiment, the test object was a Qianjiang brand industrial six-axis robot, model QJR6S-1, which is mainly used for assembly, sorting, and other operations. A 3D model of the robot was created using SOLIDWORKS (see attached image). Figure 2 ), and import it into ANSYS, then properly mesh it (see attached). Figure 3 The material properties (structural steel with a density of 7850 kg / m³, Poisson's ratio of 0.3, and elastic modulus of 200 GPa) and constraint conditions (fixed constraints are provided by the four threaded holes of the base, and the contact characteristics of each joint are bonded constraints) are set. The modal parameters are calculated, and the magnitudes of the first three natural frequencies and the modal shapes calculated by the finite element simulation are attached. Figure 4-6 As shown.

[0107] This embodiment focuses on the first three modes of the industrial robot, and two sensors are deployed. Therefore, the final iteration target number of nodes in this embodiment is two. The obtained surface nodes are weighted and iteratively calculated to obtain the final point selection scheme. Based on two different measurement point layout schemes, the force hammer excitation method experimental modal analysis is performed using the domestic Econ Test modal testing software. The first three natural frequencies of the two schemes before and after the improvement are observed. The final experimental modal test FRF frequency response function results before and after optimization are shown in the appendix. Figure 7 and attached Figure 8 As shown, the obtained results are compared with the simulation results, and the results data in the table below are obtained. The comparison shows that the point selection test results of the improved modal kinetic energy method are closer to the calculation results of finite element modal analysis than the point selection test results of engineering experience before optimization.

[0108]

[0109] The above charts are comparison tables of the results before and after optimization, as well as simulation results.

[0110] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for selecting test points for modal testing of industrial robots based on modal kinetic energy method, characterized in that, Includes the following steps: Step 1: Create a 3D model of the industrial robot and import it into the finite element analysis software. Mesh the model, set constraint and boundary condition parameters, and obtain the simulation modal parameters of the 3D model of the industrial robot. Step 2: Based on the simulation modal parameters of key parts of the industrial robot 3D model obtained in Step 1, the modal kinetic energy distribution of the industrial robot 3D model is automatically obtained using finite element analysis software; a comprehensive modal kinetic energy weight index is introduced, which includes a modal kinetic energy weight factor and a directional effectiveness coefficient; Step 3: Use the modal contribution index to select the point with the largest contribution and iteratively update to obtain the optimal point. Continuously filter out the point with the largest contribution through the iterative method until the number of remaining points equals the number of measurement points. Step 4: Based on the final optimized measurement point results obtained in Step 3, deploy sensors to conduct modal experiments and complete the modal experimental analysis of the industrial robot.

2. The method for selecting test points for modal testing of industrial robots based on modal kinetic energy method according to claim 1, characterized in that: The modal kinetic energy weighting factor is based on the existing modal kinetic energy method and undergoes unequal weighting; the modal kinetic energy weighting factor is determined by frequency importance, mode shape importance, and energy balance.

3. The method for selecting test points for modal testing of industrial robots based on modal kinetic energy method according to claim 2, characterized in that: The modal kinetic energy weighting factor is denoted as , ； Where k is the modal order, F is the frequency, T is the modal type, and E is the kinetic energy. Frequency importance factor is denoted as The importance factor of mode type is denoted as The energy balance factor is denoted as ; 。 4. The method for selecting test points for modal testing of industrial robots based on modal kinetic energy method according to claim 3, characterized in that: In the frequency importance ranking, modes within the operating bandwidth of the industrial robot should be assigned high weights, while modes outside the operating bandwidth should be assigned low weights; that is: ； in, This represents the frequency of the k-th mode; This indicates the center frequency of the main operating frequency band of the industrial robot; This represents the attenuation coefficient.

5. The method for selecting test points for modal testing of industrial robots based on modal kinetic energy method according to claim 3, characterized in that: In the importance of mode type, higher weight is given to the modes of the end effector; that is: ； ； Right now: ; in This represents the proportion of modal kinetic energy of the end effector at the k-th joint; This represents the sum of the kinetic energies of the k-th joint of all end effectors; This represents the sum of the kinetic energies of the k-th joint among all joints; This is the adjustment coefficient.

6. The method for selecting test points for modal testing of industrial robots based on modal kinetic energy method according to claim 3, characterized in that: In energy equilibrium, the weights of rigid body modes with high modal kinetic energy or their first few low-frequency modes can be appropriately reduced to prevent low-order modes from masking local high-order modes; that is: ； in, This represents the total kinetic energy of the k-th mode; This represents the maximum kinetic energy value among all modes; This represents the adjustment coefficient.

7. The method for selecting test points for modal testing of industrial robots based on modal kinetic energy method according to claim 3, characterized in that: The directional effectiveness coefficient is denoted as ,but: ； Where n represents the normal direction of sensor installation at the node; For the first Node number The first-order mode shape vector.

8. The method for selecting test points for modal testing of industrial robots based on modal kinetic energy method according to claim 7, characterized in that: The comprehensive modal kinetic energy weight index measures the modal contribution of the measurement points, and the combination of measurement points with the largest modal contribution is used as the preset measurement points for experimental modal analysis. The integrated modal kinetic energy weight index is defined as follows: ,but: ； in, For modal order index; This represents the total number of modes; It is the first The object in the first Modal kinetic energy weighting factor in first-order modes; It is the first The object in the first Effective directional coefficients in first-order modes; The modal contribution index is marked as ,but: ； in, This represents modal kinetic energy.

9. The method for selecting test points for modal testing of industrial robots based on modal kinetic energy method according to claim 1, characterized in that: In step three, the measurement points selected for the modal contribution index are iteratively screened using the modal confidence criterion. After selecting the node with the largest modal contribution index each time, the modal guarantee criterion value of the remaining nodes and all selected nodes is calculated, and the contribution index of the remaining nodes is updated based on this value.

10. The method for selecting test points for modal testing of industrial robots based on modal kinetic energy method according to claim 1, characterized in that: The modal experimental analysis process includes setting up experimental equipment, using a force hammer to traverse all measuring points, and obtaining modal parameters and information.

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