Industrial robot tail end vibration response calculation method and system

Abstract

The invention discloses an industrial robot tail end vibration response calculation method and system, solves the problem of how to improve industrial robot tail end dynamic response prediction accuracy, and belongs to the field of industrial robot dynamics analysis. According to the method, elements of the industrial robot are regarded as rigid bodies or flexible bodies, all assemblies are integrated into a rigid-flexible coupling dynamic model in combination with a robot kinematic model, step-by-step parameter identification is conducted on the decoupled rigid body dynamic model and structural dynamic model, inertial parameters are identified by considering the influence of nonlinear joint friction, and the method is suitable for industrial robot control. Further identifying a rotational inertia matrix in the robot milling kinetic model; joint elastic parameters are identified by considering the influence of non-linear joint rigidity, and a damping matrix in a robot milling kinetic model is further identified. And the torque fluctuation of each joint is predicted, the vibration response of each joint is calculated in combination with a robot milling kinetic model, and finally the robot tail end vibration response is calculated in combination with robot kinematics.

Description

Technical Field

[0001] The present invention relates to a method and system for calculating the vibration response of an industrial robot terminal, and belongs to the field of industrial robot dynamics analysis. Background Art

[0002] Industrial robots have been widely used in milling and drilling operations on various components due to their high machining efficiency, wide working range, low operating costs, and high system flexibility. However, since industrial robots are inherently composed of a series of joints and links, they inevitably suffer from weak rigidity and poor positioning accuracy, which impact machining quality and, in severe cases, can cause irreversible damage to the robot. Therefore, it is necessary to study the vibration characteristics of robots to enhance the dynamic performance of robotic machining systems and provide theoretical guidance for improving positioning accuracy and suppressing chatter. One existing method uses the inertial load of an industrial robot as a load term in the dynamic model. Inputting load parameters modifies the overall dynamic model when the load changes. During identification, the end links are identified first, followed by the front links. While this improves collision detection efficiency and reduces the cumulative error introduced by sequential identification, it fails to account for the complex effects of coupling factors such as nonlinear joint friction and operating states, which affects the accuracy of inertial parameter identification. This method increases the difficulty of identification without providing a comprehensive understanding of dynamic parameters.

[0003] Another method breaks down the overall structure of an industrial robot into several components with transfer relationships, establishes transfer matrices and transfer equations for each component, and forms the overall system transfer matrix and transfer equation based on the component transfer chain. The system characteristic equation is then solved based on the system boundary conditions to obtain the natural frequencies and natural vibration shapes of the industrial robot at each order. Finally, the robot's vibration response is solved using the principles of augmented eigenvector orthogonality and modal superposition. While this method offers advantages in computational efficiency, it does not take the robot's internal excitations into account when solving for the robot's end-point vibration response. Therefore, the calculated vibration response may not match the actual end-point vibration response of the industrial robot. Summary of the Invention

[0004] In order to improve the accuracy of prediction of the dynamic response of an industrial robot terminal, the present invention provides a method and system for calculating the vibration response of an industrial robot terminal.

[0005] A method for calculating the vibration response of an industrial robot terminal of the present invention includes:

[0006] Step 1: Consider the links of the industrial robot as rigid bodies and the joints as flexible bodies. By modeling the mass, stiffness, and damping of each component, and combining it with the robot kinematic model, the components are integrated into a rigid-flexible coupling dynamic model.

[0007] Step 2: Establish a nonlinear joint friction model and a nonlinear joint stiffness model for the industrial robot, conduct parameter identification experiments under variable working conditions, and obtain nonlinear joint friction parameters related to speed and load, and nonlinear joint stiffness parameters related to operating state and load;

[0008] Step 3: Decouple the rigid-flexible coupling dynamics model into a rigid body dynamics model and a structural dynamics model in the joint space for step-by-step parameter identification. Considering the nonlinear joint friction parameters, the inertia parameters of the robot are identified, and then the moment of inertia matrix in the robot milling dynamics model is obtained.

[0009] The joint elastic parameters of the robot are identified by running modal experiments, and the nonlinear joint stiffness parameters are used as the stiffness matrix in the robot milling dynamics model. The influence of the nonlinear joint stiffness is considered and the damping matrix in the robot milling dynamics model is further obtained by combining the joint elastic parameters.

[0010] Step 4: Obtain the joint torque fluctuations induced by multi-factor coupling, calculate the vibration response of each joint based on the robot milling dynamics model, and calculate the vibration response of the robot end by converting the vibration response of each joint in the joint space to the Cartesian space.

[0011] Preferably, in step 2, the method for obtaining nonlinear joint friction parameters related to speed and load includes:

[0012] The Stribeck friction model was used to collect joint angle and joint torque data in a uniform swing experiment, and the speed-related nonlinear joint friction parameter F was identified using a function fitting method. c ,F s ,v s ,F v , and obtain the friction torque related to speed F c is the Coulomb friction force, F s represents the static friction, v s represents the Stribeck velocity, F v represents the viscous friction coefficient, represents the joint angular velocity, δ represents the empirical coefficient;

[0013] Adding load terms to the Stribeck friction model, the model is expressed as in It represents the nonlinear joint friction parameter related to speed and load, F l represents the end load, is the empirical coefficient, μ is the load-related parameter to be identified;

[0014] μ is identified based on the variable load joint uniform swing experiment and function fitting method.

[0015] Preferably, in step 3, the nonlinear joint friction parameters are considered to identify the inertia parameters of the robot, and then a method for obtaining the moment of inertia matrix in the robot milling dynamics model is as follows:

[0016] Combined with the constraints, the objective function is the minimum condition number of the observation matrix, and the optimal excitation trajectory is designed;

[0017] The constraints are:

[0018]

[0019] Among them, t0 and t f Represent the start and end time respectively, W(q(t)) represents the Cartesian position of the robot end, W0 represents the robot workspace, J(q(t)) represents the Jacobian matrix of the robot at time t, q i (t) represents the angle of joint i at time t, represents the angular velocity of joint i at time t, represents the angular acceleration of joint i at time t, q max represents the maximum joint angle, represents the maximum joint angular velocity, represents the maximum joint angular acceleration;

[0020] The robot collects data according to the optimal excitation trajectory, and identifies the robot's inertia parameters based on the least squares method of the residual, and obtains:

[0021] p=(Y T Z -1 Y)Y T Z -1 τ rb

[0022] Among them, p is the minimum inertia parameter set, Y is the observation matrix in the rigid body dynamics model, Z is the residual matrix, which contains the inverse of the mean square error of each joint torque, τ rb It is the joint torque in the collected data minus the nonlinear joint friction parameter related to speed and load.

[0023] The inertia parameters of the robot CAD model are used as the initial values. Combined with the nonlinear programming algorithm, constraints are imposed on the mass and moment of inertia in the inertia parameters based on the initial values of the inertia parameters and the actual situation. The p is decoupled to obtain independent inertia parameters, and finally the moment of inertia matrix M in the robot milling dynamics model in the joint space is obtained. q .

[0024] Preferably, in step 2, the method for obtaining nonlinear joint stiffness parameters related to the operating state and load includes:

[0025] Through the variable load experiment under running state, the joint torque is collected while the end deformation data is collected synchronously with the laser tracker to calculate the stiffness of each joint of the robot and obtain the nonlinear joint stiffness matrix K q , nonlinear joint stiffness matrix K q The nonlinear joint stiffness parameters related to the running state and load are calculated by transforming the nonlinear joint stiffness matrix K into q As the stiffness matrix in the robot milling dynamics model in joint space.

[0026] Preferably, in step 3, the method of further obtaining the damping matrix in the robot milling dynamics model by considering the influence of nonlinear joint stiffness and combining joint elastic parameters includes:

[0027] A modal experiment is conducted in the running state to obtain the joint motor current signal I during the robot milling process. q , I q The vibration signal θ generated during milling q Satisfy I q =H(ω)θ q The relationship between the two is that H(ω) is the transfer function of the system. The joint elastic parameters of the robot, namely the damping ratio ζ, are identified by the least squares complex frequency domain method. Combined with the moment of inertia matrix M in the robot milling dynamics model in the joint space, q and the stiffness matrix K q , calculate the damping matrix C in the robot milling dynamics model in joint space q :

[0028]

[0029] Preferably, in step 4, the method for obtaining the joint torque fluctuation induced by multi-factor coupling includes:

[0030] An LSTM deep learning network model is used, with joint angle, joint velocity, joint acceleration, and joint torque as input, and joint torque fluctuation as output, to construct a training set for training.

[0031] The collected joint angle, joint velocity, joint acceleration and joint torque data are input into the trained LSTM deep learning network model, and the LSTM deep learning network model outputs the joint torque fluctuations induced by multi-factor coupling.

[0032] Preferably, in step 4, the method for calculating the vibration response of the robot end includes:

[0033] The dynamic model of robot milling in joint space is: T q,ex and T q,in The joint torques are respectively the external milling force excitation and the internal joint torque fluctuation excitation, and then the vibration response of each joint is calculated and q represent the acceleration, velocity, and angle of the joint;

[0034] Will and q are converted from the joint space to the Cartesian space, and the vibration response of the robot end is finally calculated and x = J -T qJ -1 , x represents the vibration acceleration, vibration velocity, and vibration displacement of the robot end, and J represents the Jacobian matrix.

[0035] As a preferred option, the rigid-flexible coupling dynamic model is:

[0036]

[0037] Where M(q) represents the inertia matrix, represents the centrifugal force and Coriolis force matrix, G(q) represents the mass matrix, D represents the joint damping matrix, K represents the stiffness matrix, q represents the joint angle, represents the joint angular velocity, represents the joint acceleration, represents the torsion angular velocity, dq represents the torsion angle, τ f represents the friction torque, τ represents the generalized torque;

[0038] Preferably, in step 3, the rigid-flexible coupling dynamics model is decoupled into a rigid body dynamics model and a structural dynamics model in the joint space;

[0039] The rigid body dynamics model is τ m is the external torque that combines the driving, resistance, and gravity compensation torques;

[0040] The structural dynamics model is τ s To consider the relatively high frequency part of the external torque.

[0041] The present invention also provides an industrial robot terminal vibration response calculation system, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor. The processor executes the computer program to implement the steps of the above-mentioned industrial robot terminal vibration response calculation method.

[0042] The beneficial effects of the present invention are as follows: in terms of dynamic parameter identification, the present invention identifies inertial parameters and elastic parameters separately. The identification of inertial parameters in rigid body dynamics takes into account the influence of nonlinear joint friction, and the identification of joint elastic parameters in the structural dynamics model takes into account the influence of nonlinear joint stiffness. In addition, in terms of the prediction of the terminal vibration response, the influence of the robot's internal excitation is taken into account, that is, by constructing a deep learning network to predict the joint torque fluctuation, which has higher accuracy. It is used as the input of the dynamic model to predict the vibration response of each joint, and then the vibration response of the robot terminal is obtained, which improves the accuracy of the terminal dynamic response prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is an overall flow chart of the method of the present invention;

[0044] Figure 2 This is a model diagram of each component of the industrial robot;

[0045] Figure 3 This is a schematic diagram of the gravity compensation mechanism;

[0046] Figure 4 is the optimal excitation trajectory diagram for the design;

[0047] Figure 5 The torque map of joint 2 is predicted based on the least squares residual. DETAILED DESCRIPTION

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0049] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0050] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0051] The method for calculating the vibration response of an industrial robot terminal in this embodiment includes:

[0052] Step 1: Consider the components of the industrial robot as rigid or flexible bodies, model the mass, stiffness, and damping of each component, and integrate the components into a rigid-flexible coupling dynamic model based on the robot kinematic model.

[0053] Specifically, an industrial robot can be divided into several components, such as connecting rods and joints. The connecting rods are regarded as rigid bodies and the joints are regarded as flexible bodies. The kinetic energy and potential energy of each rigid connecting rod can be expressed as:

[0054]

[0055] Among them, T i and V i denote the kinetic energy and potential energy of connecting rod i, m i 、v i and r i They represent the mass, velocity and center of mass position of link i, g represents the acceleration of gravity, and the elastic torque and damping torque of each joint can be expressed as:

[0056]

[0057] where τ e,i and τ d,i are the elastic moment and damping moment of joint i, k i ,θ e,i and c i are the stiffness, damping and flexible deformation of joint i, respectively.

[0058] Each rigid link and flexible joint are connected through robot kinematics. Based on the Lagrange equation and combined with the total kinetic energy, total potential energy and damping dissipation of the system, the Lagrange equation is expanded to obtain the rigid-flexible coupling dynamic model of the robot:

[0059]

[0060] Where M(q) represents the inertia matrix, represents the centrifugal force and Coriolis force matrix, G(q) represents the mass matrix, D represents the joint damping matrix, K represents the stiffness matrix, q represents the joint angle, represents the joint angular velocity, represents the joint acceleration, represents the torsion angular velocity, dq represents the torsion angle, τ f represents the friction torque, τ represents the generalized torque;

[0061] Inertia matrix M(q), centrifugal force and Coriolis force matrix The mass matrix G(q) is obtained through the inertia parameters of the robot; the joint damping matrix D is obtained through the joint elastic parameters of the robot.

[0062] Step 2: Establish a nonlinear joint friction model and a nonlinear joint stiffness model for the industrial robot, conduct parameter identification experiments under variable working conditions, and obtain nonlinear joint friction parameters related to speed and load, and nonlinear joint stiffness parameters related to operating state and load;

[0063] Specifically, the nonlinear joint friction model takes into account the influence of speed and load: when identifying speed-related parameters, the Stribeck friction model is used. In the joint uniform swing experiment, the joint angle and joint torque data are collected, and the speed-related nonlinear joint friction parameter F is identified using the function fitting method. c ,F s ,v s ,F v , and obtain the friction torque related to speed F c is the Coulomb friction force, F s represents the static friction, v s represents the Stribeck velocity, F v represents the viscous friction coefficient, represents the joint angular velocity, δ represents the empirical coefficient;

[0064] When identifying the load-related parameters, the load term is added to the Stribeck friction model, and the model is expressed as in represents the friction torque considering speed and load terms, F f represents the friction torque in the Stribeck friction model, F l represents the end load, is the empirical coefficient, μ is the load-related parameter of the robot joint friction to be identified, combined with the identified F f , μ is identified based on the variable load joint uniform swing experiment and function fitting method.

[0065] The nonlinear joint stiffness model takes into account the influence of operating state and load. The nonlinearity of joint stiffness is mainly reflected in the process of gear meshing between the rigid wheel and the flexible wheel in each joint harmonic reducer, and the joint elastic torque τ when the gear teeth alternate between non-meshing, partial meshing and full meshing. e,i =f(Δq i ) is a nonlinear function of the joint angle. The nonlinear joint stiffness model can be described as a nonlinear model. Considering the influence of the nonlinear stiffness of the joint, the nonlinear joint stiffness matrix K is obtained by collecting the joint torque and the end deformation data synchronously with the laser tracker through the variable load experiment under the running state. q , nonlinear joint stiffness matrix K q is the nonlinear joint stiffness parameter related to the running state and load. It is worth mentioning that the influence of the gravity compensation mechanism needs to be considered when calculating the torque of joint 2. The structural diagram of the gravity compensation mechanism is as follows: Figure 3 shown.

[0066] Step 3: Decouple the rigid-flexible coupling dynamic model into a rigid body dynamic model and a structural dynamic model in the joint space for step-by-step parameter identification. Considering the nonlinear joint friction parameters, the inertia parameters of the robot are identified, and then the moment of inertia matrix in the robot milling dynamic model is obtained. The joint elastic parameters of the robot are identified by running a modal experiment, and the nonlinear joint stiffness parameters are used as the stiffness matrix in the robot milling dynamic model. Considering the influence of the nonlinear joint stiffness, the damping matrix in the robot milling dynamic model is further obtained in combination with the joint elastic parameters. Considering the nonlinear joint stiffness parameters, specifically, the nonlinear stiffness is introduced to calculate the frequency response function and then the elastic parameters are identified through the algorithm to obtain the joint elastic parameters of the robot. According to the joint elastic parameters of the robot, the damping matrix M in the robot milling dynamic model is identified. q ;

[0067] Specifically, the dynamic model of robot milling in joint space is: T q,ex and T q,in The joint torques excited by external milling force and internal joint torque fluctuations, and the vibration responses of each joint are and q represent the acceleration, velocity, and angle of the joint;

[0068] Specifically, the rigid-flexible coupling dynamics model is decoupled into a rigid body dynamics model and a structural dynamics model for step-by-step parameter identification:

[0069] The rigid body dynamics model is τ m is the external torque relative to the driving, drag, and gravity compensation torques;

[0070] The structural dynamics model is τ s To consider the relatively high frequency part of the external torque.

[0071] The method for obtaining the inertia parameters of the robot in the rigid-flexible coupling dynamics model specifically includes:

[0072] Combined with the constraints, the objective function is the minimum condition number of the observation matrix, and the optimal excitation trajectory is designed, such as Figure 4 As shown;

[0073] The excitation trajectory designed based on the rigid body dynamics model is a fifth-order Fourier series that meets the constraints:

[0074]

[0075] Among them, t0 and t fRepresent the start and end time respectively, W(q(t)) represents the Cartesian position of the robot end, W0 represents the robot workspace, J(q(t)) represents the Jacobian matrix of the robot at time t, q i (t) represents the angle of joint i at time t, represents the angular velocity of joint i at time t, represents the angular acceleration of joint i at time t, q max represents the maximum joint angle, represents the maximum joint angular velocity, represents the maximum joint angular acceleration;

[0076] The optimal excitation trajectory is the experimental part for identifying inertial parameters. By letting the robot run the excitation trajectory, it is easy to fully excite the robot, collect data during the excitation process, and then perform parameter identification. The robot collects data according to the optimal excitation trajectory, and the inertial parameters of the robot are identified based on the least squares method of residuals. The final form of the solution is:

[0077] p=(Y T Z -1 Y)Y T Z -1 τ rb

[0078] Among them, p is the solution of the inertial parameter set, Y is the observation matrix in the rigid body dynamics model, Z is the residual matrix, which contains the inverse of the mean square error of each joint torque, τ rb It is the joint torque in the collected data minus the nonlinear joint friction parameter related to speed and load. At this time, the torque of joint 2 needs to take into account the influence of the gravity compensation mechanism. The predicted torque of joint 2 is as follows: Figure 5 shown.

[0079] Each element in the minimum inertia parameter set p is the result of coupling of a single or multiple inertia parameters. Therefore, in order to obtain independent inertia parameters, it is necessary to combine the nonlinear programming algorithm. The inertia parameters of the robot CAD model are used as the initial values. Based on the initial values of the inertia parameters and the actual situation, the mass and moment of inertia in the inertia parameters are constrained by the nonlinear programming algorithm. The p is decoupled to obtain independent inertia parameters, and finally the moment of inertia matrix M in the robot milling dynamics model in the joint space is obtained. q .

[0080] The method for obtaining joint elastic parameters of a robot in a rigid-flexible coupling dynamics model includes:

[0081] A modal experiment is conducted in the running state to obtain the joint motor current signal I during the robot milling process. q , I q The vibration signal θ generated during millingq Satisfy I q =H(ω)θ q The relationship between the two is that H(ω) is the transfer function of the system. The joint elastic parameters of the robot, namely the damping ratio ζ, are identified by the least squares complex frequency domain method. Combined with the moment of inertia matrix M in the robot milling dynamics model in the joint space, q and the stiffness matrix K q , calculate the damping matrix C in the robot milling dynamics model in joint space q :

[0082]

[0083] In the process of calculating the vibration response, the joint torque fluctuations induced by multi-factor coupling must also be taken into account in order to perform more accurate vibration response calculations.

[0084] Step 4: Obtain the joint torque fluctuations induced by multi-factor coupling, calculate the vibration response of each joint based on the robot milling dynamics model, and calculate the vibration response of the robot end by converting the vibration response of each joint in the joint space to the Cartesian space.

[0085] The method for obtaining joint torque fluctuations induced by multi-factor coupling in this embodiment includes: using an LSTM deep learning network model, taking joint angles, joint velocities, joint accelerations, and joint torques as inputs of the LSTM deep learning network model, and using joint torque fluctuations as outputs, constructing a training set for training, and constructing a loss function:

[0086]

[0087] Where σ is the root mean square error of torque fluctuation, N is the number of samples, Δτ i is the difference between the actual torque fluctuation data and the predicted torque fluctuation data.

[0088] The real-time joint angle, joint velocity, joint acceleration and joint torque are input into the trained LSTM deep learning network model, and the LSTM deep learning network model outputs the joint torque fluctuations induced by multi-factor coupling.

[0089] To calculate the vibration response of the robot terminal, the predicted joint torque fluctuations must first be input into the dynamic model, and then the vibration response of each joint is calculated. Finally, the robot terminal vibration response is calculated by combining the robot kinematic model.

[0090] The method for calculating the vibration response of the robot end includes:

[0091] The dynamic model of robot milling in joint space is: T q,ex and Tq,in The joint torques are respectively the external milling force excitation and the internal joint torque fluctuation excitation, and then the vibration response of each joint is calculated and q represent the acceleration, velocity, and angle of the joint;

[0092] Will and q are converted from the joint space to the Cartesian space, and the vibration response of the robot end is finally calculated and x = J -T qJ -1 , x represents the vibration acceleration, vibration velocity, and vibration displacement of the robot end, and J represents the Jacobian matrix.

[0093] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments.

Claims

1. A method for calculating the vibration response of an industrial robot terminal, characterized in that: include: Step 1: Consider the links of the industrial robot as rigid bodies and the joints as flexible bodies. By modeling the mass, stiffness, and damping of each component, and combining it with the robot kinematic model, the components are integrated into a rigid-flexible coupling dynamic model. Step 2: Establish a nonlinear joint friction model and a nonlinear joint stiffness model for the industrial robot, conduct parameter identification experiments under variable working conditions, and obtain nonlinear joint friction parameters related to speed and load, and nonlinear joint stiffness parameters related to operating state and load; Step 3: Decouple the rigid-flexible coupling dynamics model into a rigid body dynamics model and a structural dynamics model in the joint space for step-by-step parameter identification. Considering the nonlinear joint friction parameters, the inertia parameters of the robot are identified, and then the moment of inertia matrix in the robot milling dynamics model is obtained. The joint elastic parameters of the robot are identified by running modal experiments, and the nonlinear joint stiffness parameters are used as the stiffness matrix in the robot milling dynamics model. The influence of the nonlinear joint stiffness is considered and the damping matrix in the robot milling dynamics model is further obtained by combining the joint elastic parameters. Step 4: Obtain the joint torque fluctuations induced by multi-factor coupling, and calculate the vibration response of each joint based on the dynamic model of the robot milling process. By converting the vibration response of each joint in the joint space into the Cartesian space, the vibration response of the robot end is calculated.

2. The method for calculating the vibration response of an industrial robot terminal according to claim 1, characterized in that: In step 2, the method for obtaining nonlinear joint friction parameters related to speed and load includes: The Stribeck friction model was used to collect joint angle and joint torque data in a uniform swing experiment, and the speed-related nonlinear joint friction parameter F was identified using a function fitting method. c ,F s ,v s ,F v , and obtain the friction torque related to speed F c is the Coulomb friction force, F s represents the static friction, v s represents the Stribeck velocity, F v represents the viscous friction coefficient, represents the joint angular velocity, δ represents the empirical coefficient; Adding load terms to the Stribeck friction model, the model is expressed as in It represents the nonlinear joint friction parameter related to speed and load, F l represents the end load, is the empirical coefficient, μ is the load-related parameter to be identified; μ is identified based on the variable load joint uniform swing experiment and function fitting method.

3. The method for calculating the vibration response of an industrial robot terminal according to claim 2, characterized in that: In step 3, the nonlinear joint friction parameters are considered to identify the inertia parameters of the robot, and then the method of obtaining the moment of inertia matrix in the robot milling dynamics model is as follows: Combined with the constraints, the objective function is the minimum condition number of the observation matrix, and the optimal excitation trajectory is designed; The constraints are: Among them, t0 and t f Represent the start and end time respectively, W(q(t)) represents the Cartesian position of the robot end, W0 represents the robot workspace, J(q(t)) represents the Jacobian matrix of the robot at time t, q i (t) represents the angle of joint i at time t, represents the angular velocity of joint i at time t, represents the angular acceleration of joint i at time t, q max represents the maximum joint angle, represents the maximum joint angular velocity, represents the maximum joint angular acceleration; The robot collects data according to the optimal excitation trajectory, and identifies the robot's inertia parameters based on the least squares method of the residual, and obtains: p=(Y T Z -1 Y)Y T Z -1 τ rb Among them, p is the minimum inertia parameter set, Y is the observation matrix in the rigid body dynamics model, Z is the residual matrix, which contains the inverse of the mean square error of each joint torque, τ rb It is the joint torque in the collected data minus the nonlinear joint friction parameter related to speed and load. The inertia parameters of the robot CAD model are used as the initial values. Combined with the nonlinear programming algorithm, constraints are imposed on the mass and moment of inertia in the inertia parameters based on the initial values of the inertia parameters and the actual situation. The p is decoupled to obtain independent inertia parameters, and finally the moment of inertia matrix M in the robot milling dynamics model in the joint space is obtained. q .

4. The method for calculating the vibration response of an industrial robot terminal according to claim 1, wherein: In step 2, the method for obtaining nonlinear joint stiffness parameters related to the operating state and load includes: Through the variable load experiment under running state, the joint torque is collected and the terminal deformation data is collected synchronously with the laser tracker to calculate the stiffness of each joint of the robot and obtain the joint stiffness matrix K q , joint stiffness matrix K q The nonlinear joint stiffness parameters related to the running state and load are calculated by transforming the nonlinear joint stiffness matrix K into q As the stiffness matrix in the dynamic model of the robot milling process in the joint space.

5. The method for calculating the vibration response of an industrial robot terminal according to claim 4, characterized in that: In step 3, the method of further obtaining the damping matrix in the robot milling dynamics model by considering the influence of nonlinear joint stiffness and combining joint elastic parameters includes: A modal experiment is conducted in the running state to obtain the joint motor current signal I during the robot milling process. q , which is related to the vibration signal θ generated during milling q Satisfy I q =H(ω)θ q The relationship between the two is that H(ω) is the transfer function of the system. The elastic parameter of the robot, namely the damping ratio ζ, is identified by the least squares complex frequency domain method. Combined with the rotational inertia matrix M in the robot milling dynamics model in the joint space, q and the stiffness matrix K q , calculate the damping matrix in the robot milling dynamics model in joint space:

6. The method for calculating the vibration response of an industrial robot terminal according to claim 1, wherein: In step 4, the method for obtaining the joint torque fluctuation induced by multi-factor coupling includes: An LSTM deep learning network model is used, with joint angle, joint velocity, joint acceleration, and joint torque as input, and joint torque fluctuation as output, to construct a training set for training. The collected joint angle, joint velocity, joint acceleration and joint torque data are input into the trained LSTM deep learning network model, and the LSTM deep learning network model outputs the joint torque fluctuations induced by multi-factor coupling.

7. The method for calculating the vibration response of an industrial robot terminal according to claim 1, wherein: In step 4, the robot terminal vibration response calculation method includes: The dynamic model of the robot milling process in joint space is: T q,ex and T q,in The joint torques are respectively the external milling force excitation and the internal joint torque fluctuation excitation, and then the vibration response of each joint is calculated and q, transforming it from the joint space to the Cartesian space, and finally calculating the vibration response of the robot end and x = J -T qJ -1 , respectively represent the vibration acceleration, vibration velocity and vibration displacement of the robot end.

8. The method for calculating the vibration response of an industrial robot terminal according to claim 1, wherein: The rigid-flexible coupling dynamic model is: Where M(q) represents the inertia matrix, represents the centrifugal force and Coriolis force matrix, G(q) represents the mass matrix, D represents the joint damping matrix, K represents the joint stiffness matrix, that is, the nonlinear joint stiffness parameter related to the running state and load, q represents the joint angle, represents the joint angular velocity, represents the joint acceleration, represents the torsion angular velocity, dq represents the torsion angle, τ f represents the friction torque, and τ represents the generalized torque.

9. The method for calculating the vibration response of an industrial robot terminal according to claim 8, characterized in that: In step 3, the rigid-flexible coupling dynamics model is decoupled into a rigid body dynamics model and a structural dynamics model in the joint space; The rigid body dynamics model is τ m is the external torque that combines the driving, resistance, and gravity compensation torques; The structural dynamics model is τ s To consider the relatively high frequency part of the external torque.

10. A system for calculating vibration response of an industrial robot terminal, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, wherein: The processor executes the computer program to implement the steps of the method for calculating the vibration response of an industrial robot terminal according to any one of claims 1 to 9.

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