Dynamics modeling method for aluminum alloy friction stir welding industrial robot system

Abstract

The invention discloses a dynamic modeling method for an aluminum alloy friction stir welding industrial robot system, which comprises the following steps of: (1) establishing a stable welding stress model of a stirring needle system, and solving the tail end stress of the welding industrial robot system; (2) establishing a kinematic model of the welding industrial robot; (3) establishing a flexible joint model of the welding industrial robot; (4) establishing a joint friction model of the welding industrial robot, and solving the joint friction torque of the robot; (5) establishing a nonlinear dynamic equation set of the aluminum alloy friction stir welding industrial robot system; (6) solving nonlinear response characteristics of the system; the method has the beneficial effects that the nonlinear dynamic response characteristics of the aluminum alloy friction stir welding industrial robot system can be solved, the vacancy of the current research method for the aluminum alloy friction stir welding industrial robot system is filled, and the method has good universality.

Description

Technical Field

[0001] The invention relates to the technical field of aluminum alloy friction stir welding, and in particular to a dynamics modeling method for an aluminum alloy friction stir welding industrial robot system. Background Art

[0002] As core equipment for achieving complex spatial trajectory welding, industrial friction stir welding robots play a key role in the automated production of three-dimensional curved surface components, such as large aerospace cabins and battery trays for new energy vehicles. Compared with traditional machine tool-type friction stir welding equipment, industrial robots, with their multi-degree-of-freedom operation characteristics, can achieve high-precision tracking of variable curvature welds. However, the inherent weak stiffness characteristics of the industrial robot body structure and the strong multi-physics field coupling during the friction stir welding process make the system prone to nonlinear dynamic problems such as multi-axis coordinated motion instability during high-speed welding, which directly affects the quality of weld formation. In particular, during the welding of thin-walled aluminum alloy components, the nonlinear interaction effect between the system dynamic characteristics and process parameters is more significant. Current research focuses on the optimization of robot path planning algorithms or experimental analysis of welding process parameters, lacking in-depth research on the nonlinear dynamic mechanism of the robot-welding tool-workpiece coupling system.

[0003] In order to solve the above problems, the present invention establishes a dynamic modeling method for the aluminum alloy friction stir welding industrial robot system, which can effectively reveal the interaction mechanism between the flexible deformation of the robot arm and the nonlinear load of the stirring head during the welding process, and provide theoretical support for the robot's dynamic precision compensation control and process parameter optimization matching. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies and fill a gap in related technologies, this paper provides a dynamic modeling method for an industrial robot system for aluminum alloy friction stir welding. This method constructs a robot-welding tool-workpiece dynamic model, taking into account multiple factors such as flexible deformation of the robot arm, nonlinear friction in the joints, and process loads on the stir head. The Runge-Kutta integration method is then used to solve the system's differential dynamics equations, revealing the nonlinear response characteristics of the system under the influence of external excitations and internal factors.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows: a method for dynamic modeling of an aluminum alloy friction stir welding industrial robot system, characterized by comprising the following steps:

[0006] Step (1): Establish a stable welding force model of the stirring needle system and solve the force on the end of the welding industrial robot system; the industrial robot system is subjected to force F in the x-axis direction. 6x for:

[0007]

[0008] Where, l j is the stirring needle length, k j is the force coefficient, x(t) is the vibration displacement, v is the stirring needle feed speed, Ω is the stirring needle rotation angular velocity, R j is the radius of the stirring needle, is the rotation angle of the stirring needle when the displacement is x, σ Z is the yield strength of the workpiece material, F f0 is the friction force in the feed direction, R d is the radius of the bottom surface of the stirring needle shoulder, μ0 and k0 are the friction coefficient and force coefficient of the shear friction model respectively, σ N is the compressive stress between the stirring needle and the workpiece, v a is the relative sliding velocity between point A on the stirring needle and the workpiece, θ a With r a is the polar coordinate of point A at the bottom of the stirring needle, and C is the adjustment parameter;

[0009] Step (2): Establish kinematic model of welding industrial robot; improve Denavit-Hartenberg matrix by welding industrial robot

[0010]

[0011] Where, χ q is the rotation angle of the x-axis around the z-axis of the coordinate systems of two adjacent links, is the angle between two adjacent joint axes along the connecting rod direction, S q-1 is the distance between two adjacent joint axes, D q is the displacement of two adjacent links along the x-axis;

[0012] The robot end effector position matrix can be obtained

[0013]

[0014] Where, Improved Denavit-Hartenberg matrix for the q-link of welding industrial robots;

[0015] Step (3): Establish a flexible joint model of the welding industrial robot; use the Spong model to approximate the joint flexibility, insert a torsion spring at the joint to simulate the flexible connection, and solve the flexible joint torque τ r :

[0016] τ r =k r (θ c -θ n );

[0017] Where, τ r is the torque of the flexible joint, k r is the Spong model stiffness, θ c is the theoretical joint angle, θ n is the actual joint angle;

[0018] Step (4): Establish a joint friction model of the welding industrial robot and solve the friction torque of the robot joint; use the Coulomb-viscous friction model and combine it with the Stribeck effect to describe the joint friction and solve the joint friction torque:

[0019]

[0020] Where, τ st is the joint friction torque, τ s is the Coulomb friction torque, τ c is the static friction torque, v δ is the relative sliding velocity, v s is the Stribeck velocity, ζ is the velocity proportional coefficient, k v is the viscous friction coefficient;

[0021] Step (5): Establishing a nonlinear dynamic equation group of the aluminum alloy friction stir welding industrial robot system;

[0022] Based on the end force F of the welding industrial robot system obtained in step (1) 6x , the kinematic model of the welding industrial robot system obtained in step (2), the torque τ of the welding industrial robot flexible joint obtained in step (3) r , the friction torque τ obtained in step (4) st , establish the nonlinear dynamic equations of the aluminum alloy friction stir welding industrial robot system: the nonlinear dynamic equation of the aluminum alloy friction stir welding industrial robot link 1 is:

[0023]

[0024] Where m1 is the mass of the welding industrial robot link 1, λ1(λ∈{x,y,z}) is the vibration displacement of link 1 along the λ axis, λ2(λ∈{x,y,z}) is the vibration displacement of link 2 along the λ axis, and k 01λ (λ∈{x,y,z}) is the contact stiffness between link 0 and link 1 along the λ axis, c 01λ (λ∈{x,y,z}) is the contact damping between link 0 and link 1 along the λ axis, k 12λ (λ∈{x,y,z}) is the contact stiffness between link 1 and link 2 along the λ axis, c 12λ (λ∈{x,y,z}) is the contact damping between link 1 and link 2 along the λ axis, F 01λ(λ∈{x,y,z}) is the interaction force between link 0 and link 1 along the λ axis, F 12λ (λ∈{x,y,z}) is the interaction force between link 1 and link 2 along the λ axis, J 1j (j∈{x,y,z}) is the moment of inertia of connecting rod 1 around axis j, θ 1j (j∈{x,y,z}) is the rotation angle of connecting rod 1 around axis j, θ 2j (j∈{x,y,z}) is the rotation angle of connecting rod 2 around axis j, κ 01j (j∈{x,y,z}) is the torsional stiffness around the j-axis at the joint 1 between link 0 and link 1, κ 12j (j∈{x,y,z}) is the torsional stiffness around the j-axis at the joint 2 between link 1 and link 2, ξ 01j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 1, ξ 12j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 2, l1 is the length of link 1, α1 is the angle between link 1 and plane xOy, T 01 Output torque for joint 1, T f01 is the friction torque of joint 1, T 12 Output torque for joint 2, T f12 is the friction torque of joint 2, h1 is the distance between the axis of joint 2 and plane xOy;

[0025] The nonlinear dynamic equation of the link 2 of the aluminum alloy friction stir welding industrial robot is:

[0026]

[0027] Where m2 is the mass of the connecting rod 2 of the welding industrial robot, λ2(λ∈{x,y,z}) is the vibration displacement of the connecting rod 2 along the λ axis, and k 23λ (λ∈{x,y,z}) is the contact stiffness between link 2 and link 3 along the λ axis, c 23λ (λ∈{x,y,z}) is the contact damping between link 2 and link 3 along the λ axis, F 23λ (λ∈{x,y,z}) is the interaction force between connecting rod 2 and connecting rod 3 along the λ axis, J 2j (j∈{x,y,z}) is the moment of inertia of connecting rod 2 around axis j, θ 3j (j∈{x,y,z}) is the rotation angle of connecting rod 3 around axis j, κ 23j (j∈{x,y,z}) is the torsional stiffness of the joint 3 between link 2 and link 3 around the j axis, ξ 23j (j∈{x,y,z}) is the torsional damping around the j axis at joint 3, l2 is the length of link 2, α2 is the angle between link 2 and plane xOy, T 23 Output torque for joint 3, T f23 is the friction torque of joint 3;

[0028] The nonlinear dynamic equation of the link 3 of the aluminum alloy friction stir welding industrial robot is:

[0029]

[0030] Where m3 is the mass of the connecting rod 3 of the welding industrial robot, λ3 (λ∈{x,y,z}) is the vibration displacement of the connecting rod 3 along the λ axis, and k 34λ (λ∈{x,y,z}) is the contact stiffness between connecting rod 3 and connecting rod 4 along the λ axis, c 34λ (λ∈{x,y,z}) is the contact damping between connecting rod 3 and connecting rod 4 along the λ axis, F 34λ (λ∈{x,y,z}) is the interaction force between connecting rod 3 and connecting rod 4 along the λ axis, J 3j (j∈{x,y,z}) is the moment of inertia of connecting rod 3 around axis j, θ 4j (j∈{x,y,z}) is the rotation angle of connecting rod 4 around axis j, κ 34j (j∈{x,y,z}) is the torsional stiffness of the joint 4 between link 3 and link 4 around the j axis, ξ 34j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 4, l3 is the length of link 3, α3 is the angle between link 3 and plane xOy, T 34 Output torque for joint 4, T f34 is the friction torque of joint 4;

[0031] The nonlinear dynamic equation of the link 4 of the aluminum alloy friction stir welding industrial robot is:

[0032]

[0033] Where m4 is the mass of the connecting rod 4 of the welding industrial robot, λ4 (λ∈{x,y,z}) is the vibration displacement of the connecting rod 4 along the λ axis, and k 45λ (λ∈{x,y,z}) is the contact stiffness between connecting rod 4 and connecting rod 5 along the λ axis, c 45λ (λ∈{x,y,z}) is the contact damping between connecting rod 4 and connecting rod 5 along the λ axis, F 45λ (λ∈{x,y,z}) is the interaction force between connecting rod 4 and connecting rod 5 along the λ axis, J 4j (j∈{x,y,z}) is the moment of inertia of connecting rod 4 around axis j, θ 5j (j∈{x,y,z}) is the rotation angle of connecting rod 5 around axis j, κ 45j (j∈{x,y,z}) is the torsional stiffness of the joint 5 between link 4 and link 5 around the j axis, ξ 45j (j∈{x,y,z}) is the torsional damping of joint 5 around axis j, l4 is the length of link 4, α4 is the angle between link 4 and plane xOy, T 45Output torque for joint 5, T f45 is the friction torque of joint 5;

[0034] The nonlinear dynamic equation of the connecting rod 5 of the aluminum alloy friction stir welding industrial robot is:

[0035]

[0036] Where m5 is the mass of the connecting rod 5 of the welding industrial robot, λ5 (λ∈{x,y,z}) is the vibration displacement of the connecting rod 5 along the λ axis, and k 56λ (λ∈{x,y,z}) is the contact stiffness between connecting rod 5 and connecting rod 6 along the λ axis, c 56λ (λ∈{x,y,z}) is the contact damping between connecting rod 5 and connecting rod 6 along the λ axis, F 56λ (λ∈{x,y,z}) is the interaction force between connecting rod 5 and connecting rod 6 along the λ axis, J 5j (j∈{x,y,z}) is the moment of inertia of connecting rod 5 around axis j, θ 6j (j∈{x,y,z}) is the rotation angle of connecting rod 6 around axis j, κ 56j (j∈{x,y,z}) is the torsional stiffness around the j-axis at the joint 6 between link 5 and link 6, ξ 56j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 6, l5 is the length of link 5, α5 is the angle between link 5 and plane xOy, T 56 Output torque for joint 6, T f56 is the friction torque of joint 6;

[0037] The nonlinear dynamic equation of the connecting rod 6 of the aluminum alloy friction stir welding industrial robot is:

[0038]

[0039] Where m6 is the mass of the welding industrial robot link 6, λ6 (λ∈{x,y,z}) is the vibration displacement of the link 6 along the λ axis, and F 6λ (λ∈{x,y,z}) is the interaction force between the connecting rod 6 and the workpiece along the λ axis, J 6j (j∈{x,y,z}) is the moment of inertia of connecting rod 6 around axis j, l6 is the length of connecting rod 6, and T6 is the torque between connecting rod 6 and the workpiece;

[0040] Step (6): Solve the nonlinear response characteristics of the system; select the stirring needle feed speed v, stirring needle speed n, stirring needle length l p , stirring needle pressure depth e tThe nonlinear response characteristics of the vibration displacement of the end effector in the feed direction of the stir friction welding industrial robot system are solved; by analyzing the nonlinear response characteristic curve of the vibration displacement, the parameter configuration for stable operation of the system is determined; the system operates stably under the periodic motion state, which can improve the working efficiency and quality of the aluminum alloy stir friction welding industrial robot.

[0041] Compared with the prior art, the present invention has the following beneficial effects: This method addresses the quantitative characterization of the multi-body coupled dynamic characteristics of an aluminum alloy friction stir welding industrial robot and addresses the shortcomings of traditional modeling methods in revealing the interaction mechanism between time-varying stiffness and nonlinear vibration. A robot-welding tool-workpiece dynamic model is constructed, taking into account multiple factors such as flexible deformation of the robotic arm, nonlinear friction of the joints, and process loads on the stirring head. Based on the improved Denavit-Hartenberg kinematic model and Spong flexible joint theory, a set of nonlinear dynamic differential equations is established, including a stirring needle force model, a multi-link contact stiffness matrix, and a Coulomb-Stribeck friction model. The Runge-Kutta integral algorithm is then used to solve the system's differential dynamic equations, obtaining the nonlinear response characteristics of the system under the influence of external excitation and internal factors. This method fills the technical gap in the calculation of aluminum alloy friction stir welding industrial robot systems, helps provide a scientific basis for optimizing welding processes, and improves welding quality. Furthermore, the dynamic model established by the present invention can also provide a reference for structural optimization and control strategy design of the robot system, thereby promoting the further development of aluminum alloy friction stir welding industrial robot technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of the nonlinear dynamic modeling method of the aluminum alloy friction stir welding industrial robot system;

[0043] Figure 2 It is the improved Denavit-Hartenberg kinematic model diagram of the industrial robot system for aluminum alloy friction stir welding;

[0044] Figure 3 It is a nonlinear dynamic model of the aluminum alloy friction stir welding industrial robot system;

[0045] Figure 4 It is the time domain diagram of the dimensionless-frequency nonlinear response characteristics of the system. DETAILED DESCRIPTION

[0046] The embodiments of the present invention are described below with reference to the accompanying drawings. Figure 1 — Figure 4 The specific embodiments of the present invention are described in detail.

[0047] Figure 1Shown is a flow chart of the nonlinear dynamic modeling method for the aluminum alloy friction stir welding industrial robot system;

[0048] A method for dynamics modeling of an aluminum alloy friction stir welding industrial robot system, characterized by comprising the following steps:

[0049] Step (1): Establish a stable welding force model of the stirring needle system and solve the end force of the welding industrial robot system;

[0050] The industrial robot system is subjected to force F in the x-axis direction 6x for:

[0051]

[0052] Where, l j is the stirring needle length, k j is the force coefficient, x(t) is the vibration displacement, v is the stirring needle feed speed, Ω is the stirring needle rotation angular velocity, R j is the radius of the stirring needle, is the rotation angle of the stirring needle when the displacement is x, σ Z is the yield strength of the workpiece material, F f0 is the friction force in the feed direction, R d is the radius of the bottom surface of the stirring needle shoulder, μ0 and k0 are the friction coefficient and force coefficient of the shear friction model respectively, σ N is the compressive stress between the stirring needle and the workpiece, v a is the relative sliding velocity between point A on the stirring needle and the workpiece, θ a With r a is the polar coordinate of point A at the bottom of the stirring needle, and C is the adjustment parameter;

[0053] Step (2): Establish a kinematic model of the welding industrial robot;

[0054] Figure 2 The figure shows the improved Denavit-Hartenberg kinematic model of the aluminum alloy friction stir welding industrial robot system. γ ,Y γ ,Z γ (γ∈{1,2,3,4,5,6}) are the coordinate axes of the improved Denavit-Hartenberg kinematic model of the robot system.

[0055] Improvement of the Denavit-Hartenberg matrix by means of welding industrial robots

[0056]

[0057] Where, χ qis the rotation angle of the x-axis around the z-axis of the coordinate systems of two adjacent links, is the angle between two adjacent joint axes along the connecting rod direction, S q-1 is the distance between two adjacent joint axes, D q is the displacement of two adjacent links along the x-axis;

[0058] The robot end effector position matrix can be obtained

[0059]

[0060] Where, Improved Denavit-Hartenberg matrix for the q-link of welding industrial robots;

[0061] Step (3): Establish a flexible joint model of the welding industrial robot;

[0062] The Spong model is used to approximate the joint flexibility, and a torsion spring is inserted at the joint to simulate the flexible connection to solve the torque τ of the flexible joint. r :

[0063] τ r =k r (θ c -θ n );

[0064] Where, τ r is the torque of the flexible joint, k r is the Spong model stiffness, θ c is the theoretical joint angle, θ n is the actual joint angle;

[0065] Step (4): Establish a joint friction model of the welding industrial robot and solve the friction torque of the robot joint;

[0066] The Coulomb-viscous friction model is used in combination with the Stribeck effect to describe joint friction and solve the joint friction torque:

[0067]

[0068] Where, τ st is the joint friction torque, τ s is the Coulomb friction torque, τ c is the static friction torque, v δ is the relative sliding velocity, v s is the Stribeck velocity, ζ is the velocity proportional coefficient, k v is the viscous friction coefficient;

[0069] Step (5): Establishing a nonlinear dynamic equation group of the aluminum alloy friction stir welding industrial robot system;

[0070] Figure 3 A nonlinear dynamic model of the industrial robot system for aluminum alloy friction stir welding.

[0071] Based on the end force F of the welding industrial robot system obtained in step (1) 6x , the kinematic model of the welding industrial robot system obtained in step (2), the torque τ of the welding industrial robot flexible joint obtained in step (3) r , the friction torque τ obtained in step (4) st , combined with Figure 3 The model shown is used to establish the nonlinear dynamic equations of the aluminum alloy friction stir welding industrial robot system.

[0072] The nonlinear dynamic equation of the link 1 of the aluminum alloy friction stir welding industrial robot is:

[0073]

[0074] Where m1 is the mass of the welding industrial robot link 1, λ1(λ∈{x,y,z}) is the vibration displacement of link 1 along the λ axis, λ2(λ∈{x,y,z}) is the vibration displacement of link 2 along the λ axis, and k 01λ (λ∈{x,y,z}) is the contact stiffness between link 0 and link 1 along the λ axis, c 01λ (λ∈{x,y,z}) is the contact damping between link 0 and link 1 along the λ axis, k 12λ (λ∈{x,y,z}) is the contact stiffness between link 1 and link 2 along the λ axis, c 12λ (λ∈{x,y,z}) is the contact damping between link 1 and link 2 along the λ axis, F 01λ (λ∈{x,y,z}) is the interaction force between link 0 and link 1 along the λ axis, F 12λ (λ∈{x,y,z}) is the interaction force between link 1 and link 2 along the λ axis, J 1j (j∈{x,y,z}) is the moment of inertia of connecting rod 1 around axis j, θ 1j (j∈{x,y,z}) is the rotation angle of connecting rod 1 around axis j, θ 2j (j∈{x,y,z}) is the rotation angle of connecting rod 2 around axis j, κ 01j (j∈{x,y,z}) is the torsional stiffness around the j-axis at the joint 1 between link 0 and link 1, κ 12j (j∈{x,y,z}) is the torsional stiffness around the j-axis at the joint 2 between link 1 and link 2, ξ 01j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 1, ξ 12j(j∈{x,y,z}) is the torsional damping around the j-axis at joint 2, l1 is the length of link 1, α1 is the angle between link 1 and plane xOy, T 01 Output torque for joint 1, T f01 is the friction torque of joint 1, T 12 Output torque for joint 2, T f12 is the friction torque of joint 2, h1 is the distance between the axis of joint 2 and plane xOy;

[0075] The nonlinear dynamic equation of the link 2 of the aluminum alloy friction stir welding industrial robot is:

[0076]

[0077] Where m2 is the mass of the connecting rod 2 of the welding industrial robot, λ2(λ∈{x,y,z}) is the vibration displacement of the connecting rod 2 along the λ axis, and k 23λ (λ∈{x,y,z}) is the contact stiffness between link 2 and link 3 along the λ axis, c 23λ (λ∈{x,y,z}) is the contact damping between link 2 and link 3 along the λ axis, F 23λ (λ∈{x,y,z}) is the interaction force between connecting rod 2 and connecting rod 3 along the λ axis, J 2j (j∈{x,y,z}) is the moment of inertia of connecting rod 2 around axis j, θ 3j (j∈{x,y,z}) is the rotation angle of connecting rod 3 around axis j, κ 23j (j∈{x,y,z}) is the torsional stiffness of the joint 3 between link 2 and link 3 around the j axis, ξ 23j (j∈{x,y,z}) is the torsional damping around the j axis at joint 3, l2 is the length of link 2, α2 is the angle between link 2 and plane xOy, T 23 Output torque for joint 3, T f23 is the friction torque of joint 3;

[0078] The nonlinear dynamic equation of the link 3 of the aluminum alloy friction stir welding industrial robot is:

[0079]

[0080] Where m3 is the mass of the connecting rod 3 of the welding industrial robot, λ3 (λ∈{x,y,z}) is the vibration displacement of the connecting rod 3 along the λ axis, and k 34λ (λ∈{x,y,z}) is the contact stiffness between connecting rod 3 and connecting rod 4 along the λ axis, c 34λ (λ∈{x,y,z}) is the contact damping between connecting rod 3 and connecting rod 4 along the λ axis, F 34λ (λ∈{x,y,z}) is the interaction force between connecting rod 3 and connecting rod 4 along the λ axis, J 3j (j∈{x,y,z}) is the moment of inertia of connecting rod 3 around axis j, θ4j (j∈{x,y,z}) is the rotation angle of connecting rod 4 around axis j, κ 34j (j∈{x,y,z}) is the torsional stiffness of the joint 4 between link 3 and link 4 around the j axis, ξ 34j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 4, l3 is the length of link 3, α3 is the angle between link 3 and plane xOy, T 34 Output torque for joint 4, T f34 is the friction torque of joint 4;

[0081] The nonlinear dynamic equation of the link 4 of the aluminum alloy friction stir welding industrial robot is:

[0082]

[0083] Where m4 is the mass of the connecting rod 4 of the welding industrial robot, λ4 (λ∈{x,y,z}) is the vibration displacement of the connecting rod 4 along the λ axis, and k 45λ (λ∈{x,y,z}) is the contact stiffness between connecting rod 4 and connecting rod 5 along the λ axis, c 45λ (λ∈{x,y,z}) is the contact damping between connecting rod 4 and connecting rod 5 along the λ axis, F 45λ (λ∈{x,y,z}) is the interaction force between connecting rod 4 and connecting rod 5 along the λ axis, J 4j (j∈{x,y,z}) is the moment of inertia of connecting rod 4 around axis j, θ 5j (j∈{x,y,z}) is the rotation angle of connecting rod 5 around axis j, κ 45j (j∈{x,y,z}) is the torsional stiffness of the joint 5 between link 4 and link 5 around the j axis, ξ 45j (j∈{x,y,z}) is the torsional damping of joint 5 around axis j, l4 is the length of link 4, α4 is the angle between link 4 and plane xOy, T 45 Output torque for joint 5, T f45 is the friction torque of joint 5;

[0084] The nonlinear dynamic equation of the connecting rod 5 of the aluminum alloy friction stir welding industrial robot is:

[0085]

[0086] Where m5 is the mass of the connecting rod 5 of the welding industrial robot, λ5 (λ∈{x,y,z}) is the vibration displacement of the connecting rod 5 along the λ axis, and k 56λ (λ∈{x,y,z}) is the contact stiffness between connecting rod 5 and connecting rod 6 along the λ axis, c 56λ (λ∈{x,y,z}) is the contact damping between connecting rod 5 and connecting rod 6 along the λ axis, F 56λ (λ∈{x,y,z}) is the interaction force between connecting rod 5 and connecting rod 6 along the λ axis, J 5j(j∈{x,y,z}) is the moment of inertia of connecting rod 5 around axis j, θ 6j (j∈{x,y,z}) is the rotation angle of connecting rod 6 around axis j, κ 56j (j∈{x,y,z}) is the torsional stiffness around the j-axis at the joint 6 between link 5 and link 6, ξ 56j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 6, l5 is the length of link 5, α5 is the angle between link 5 and plane xOy, T 56 Output torque for joint 6, T f56 is the friction torque of joint 6;

[0087] The nonlinear dynamic equation of the connecting rod 6 of the aluminum alloy friction stir welding industrial robot is:

[0088]

[0089] Where m6 is the mass of the welding industrial robot link 6, λ6 (λ∈{x,y,z}) is the vibration displacement of the link 6 along the λ axis, and F 6λ (λ∈{x,y,z}) is the interaction force between the connecting rod 6 and the workpiece along the λ axis, J 6j (j∈{x,y,z}) is the moment of inertia of connecting rod 6 around axis j, l6 is the length of connecting rod 6, and T6 is the torque between connecting rod 6 and the workpiece;

[0090] Step (6): Solve the nonlinear response characteristics of the system; select the stirring needle feed speed v, stirring needle speed n, stirring needle length l p , stirring needle pressure depth e t The nonlinear response characteristics of the vibration displacement of the end effector in the feed direction of the stir friction welding industrial robot system are solved; by analyzing the nonlinear response characteristic curve of the vibration displacement, the parameter configuration for stable operation of the system is determined; the system operates stably under the periodic motion state, which can improve the working efficiency and quality of the aluminum alloy stir friction welding industrial robot.

[0091] In this example, the parameters selected for the system are shown in Table 1. Using the above method, the nonlinear response of the system is obtained. The results are as follows: Figure 4 As shown;

[0092] Table 1 Parameters of aluminum alloy friction stir welding industrial robot system

[0093]

[0094] Figure 4 It is the time domain diagram of the system dimension-frequency nonlinear response characteristics; Figure 4In the figure, (a) is the vibration displacement x of the aluminum alloy stir friction welding system over time when the dimensionless frequency is 0.3505, and (b) is the vibration displacement x of the aluminum alloy stir friction welding system over time when the dimensionless frequency is 0.4153. It can be seen from the time domain of the system response that at this time, the time domain graph in (a) shows one amplitude and is stable; the time domain graph in (b) shows two amplitudes and is stable. In this state, the system performance can be improved, the noise can be reduced, and the service life of the structure can be increased.

[0095] The above description is only a preferred embodiment of the invention and does not limit the invention in any way. Any modifications, changes and equivalent changes made to the above embodiments based on the essence of the invention shall still fall within the scope of protection of the technology of the invention.

Claims

1. A dynamic modeling method for an aluminum alloy friction stir welding industrial robot system, characterized in that: The following steps are involved: Step (1): Establish a stable welding force model of the stirring needle system and solve the force on the end of the welding industrial robot system; the industrial robot system is subjected to force F in the x-axis direction. 6x for: Where, l j is the stirring needle length, k j is the force coefficient, x(t) is the vibration displacement, v is the stirring needle feed speed, Ω is the stirring needle rotation angular velocity, R j is the radius of the stirring needle, is the rotation angle of the stirring needle when the displacement is x, σ Z is the yield strength of the workpiece material, F f0 is the friction force in the feed direction, R d is the radius of the bottom surface of the stirring needle shoulder, μ0 and k0 are the friction coefficient and force coefficient of the shear friction model respectively, σ N is the compressive stress between the stirring needle and the workpiece, v a is the relative sliding velocity between point A on the stirring needle and the workpiece, θ a With r a is the polar coordinate of point A at the bottom of the stirring needle, and C is the adjustment parameter; Step (2): Establish kinematic model of welding industrial robot; improve Denavit-Hartenberg matrix by welding industrial robot Where, χ q is the rotation angle of the x-axis around the z-axis of the coordinate systems of two adjacent links, is the angle between two adjacent joint axes along the connecting rod direction, S q-1 is the distance between two adjacent joint axes, D q is the displacement of two adjacent links along the x-axis; The robot end effector position matrix can be obtained Where, Improved Denavit-Hartenberg matrix for the q-link of welding industrial robots; Step (3): Establish a flexible joint model of the welding industrial robot; use the Spong model to approximate the joint flexibility, insert a torsion spring at the joint to simulate the flexible connection, and solve the flexible joint torque τ r : t r =k r (i c -θ n ); Where, τ r is the torque of the flexible joint, k r is the Spong model stiffness, θ c is the theoretical joint angle, θ n is the actual joint angle; Step (4): Establish a joint friction model of the welding industrial robot and solve the friction torque of the robot joint; use the Coulomb-viscous friction model and combine it with the Stribeck effect to describe the joint friction and solve the joint friction torque: Where, τ st is the joint friction torque, τ s is the Coulomb friction torque, τ c is the static friction torque, v δ is the relative sliding velocity, v s is the Stribeck velocity, ζ is the velocity proportional coefficient, k v is the viscous friction coefficient; Step (5): Establishing a nonlinear dynamic equation group of the aluminum alloy friction stir welding industrial robot system; Based on the end force F of the welding industrial robot system obtained in step (1) 6x , the kinematic model of the welding industrial robot system obtained in step (2), the torque τ of the welding industrial robot flexible joint obtained in step (3) r , the friction torque τ obtained in step (4) st , establish the nonlinear dynamic equations of the aluminum alloy friction stir welding industrial robot system: the nonlinear dynamic equation of the aluminum alloy friction stir welding industrial robot link 1 is: Where m1 is the mass of the welding industrial robot link 1, λ1(λ∈{x,y,z}) is the vibration displacement of link 1 along the λ axis, λ2(λ∈{x,y,z}) is the vibration displacement of link 2 along the λ axis, and k 01λ (λ∈{x,y,z}) is the contact stiffness between link 0 and link 1 along the λ axis, c 01λ (λ∈{x,y,z}) is the contact damping between link 0 and link 1 along the λ axis, k 12λ (λ∈{x,y,z}) is the contact stiffness between link 1 and link 2 along the λ axis, c 12λ (λ∈{x,y,z}) is the contact damping between link 1 and link 2 along the λ axis, F 01λ (λ∈{x,y,z}) is the interaction force between link 0 and link 1 along the λ axis, F 12λ (λ∈{x,y,z}) is the interaction force between link 1 and link 2 along the λ axis, J 1j (j∈{x,y,z}) is the moment of inertia of connecting rod 1 around axis j, θ 1j (j∈{x,y,z}) is the rotation angle of connecting rod 1 around axis j, θ 2j (j∈{x,y,z}) is the rotation angle of connecting rod 2 around axis j, κ 01j (j∈{x,y,z}) is the torsional stiffness around the j-axis at the joint 1 between link 0 and link 1, κ 12j (j∈{x,y,z}) is the torsional stiffness around the j-axis at the joint 2 between link 1 and link 2, ξ 01j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 1, ξ 12j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 2, l1 is the length of link 1, α1 is the angle between link 1 and plane xOy, T 01 Output torque for joint 1, T f01 is the friction torque of joint 1, T 12 Output torque for joint 2, T f12 is the friction torque of joint 2, h1 is the distance between the axis of joint 2 and plane xOy; The nonlinear dynamic equation of the link 2 of the aluminum alloy friction stir welding industrial robot is: Where m2 is the mass of the connecting rod 2 of the welding industrial robot, λ2(λ∈{x,y,z}) is the vibration displacement of the connecting rod 2 along the λ axis, and k 23λ (λ∈{x,y,z}) is the contact stiffness between link 2 and link 3 along the λ axis, c 23λ (λ∈{x,y,z}) is the contact damping between link 2 and link 3 along the λ axis, F 23λ (λ∈{x,y,z}) is the interaction force between connecting rod 2 and connecting rod 3 along the λ axis, J 2j (j∈{x,y,z}) is the moment of inertia of connecting rod 2 around axis j, θ 3j (j∈{x,y,z}) is the rotation angle of connecting rod 3 around axis j, κ 23j (j∈{x,y,z}) is the torsional stiffness of the joint 3 between link 2 and link 3 around the j axis, ξ 23j (j∈{x,y,z}) is the torsional damping around the j axis at joint 3, l2 is the length of link 2, α2 is the angle between link 2 and plane xOy, T 23 Output torque for joint 3, T f23 is the friction torque of joint 3; The nonlinear dynamic equation of the link 3 of the aluminum alloy friction stir welding industrial robot is: Where m3 is the mass of the connecting rod 3 of the welding industrial robot, λ3 (λ∈{x,y,z}) is the vibration displacement of the connecting rod 3 along the λ axis, and k 34λ (λ∈{x,y,z}) is the contact stiffness between connecting rod 3 and connecting rod 4 along the λ axis, c 34λ (λ∈{x,y,z}) is the contact damping between connecting rod 3 and connecting rod 4 along the λ axis, F 34λ (λ∈{x,y,z}) is the interaction force between connecting rod 3 and connecting rod 4 along the λ axis, J 3j (j∈{x,y,z}) is the moment of inertia of connecting rod 3 around axis j, θ 4j (j∈{x,y,z}) is the rotation angle of connecting rod 4 around axis j, κ 34j (j∈{x,y,z}) is the torsional stiffness of the joint 4 between link 3 and link 4 around the j axis, ξ 34j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 4, l3 is the length of link 3, α3 is the angle between link 3 and plane xOy, T 34 Output torque for joint 4, T f34 is the friction torque of joint 4; The nonlinear dynamic equation of the link 4 of the aluminum alloy friction stir welding industrial robot is: Where m4 is the mass of the connecting rod 4 of the welding industrial robot, λ4 (λ∈{x,y,z}) is the vibration displacement of the connecting rod 4 along the λ axis, and k 45λ (λ∈{x,y,z}) is the contact stiffness between connecting rod 4 and connecting rod 5 along the λ axis, c 45λ (λ∈{x,y,z}) is the contact damping between connecting rod 4 and connecting rod 5 along the λ axis, F 45λ (λ∈{x,y,z}) is the interaction force between connecting rod 4 and connecting rod 5 along the λ axis, J 4j (j∈{x,y,z}) is the moment of inertia of connecting rod 4 around axis j, θ 5j (j∈{x,y,z}) is the rotation angle of connecting rod 5 around axis j, κ 45j (j∈{x,y,z}) is the torsional stiffness of the joint 5 between link 4 and link 5 around the j axis, ξ 45j (j∈{x,y,z}) is the torsional damping of joint 5 around axis j, l4 is the length of link 4, α4 is the angle between link 4 and plane xOy, T 45 Output torque for joint 5, T f45 is the friction torque of joint 5; The nonlinear dynamic equation of the connecting rod 5 of the aluminum alloy friction stir welding industrial robot is: Where m5 is the mass of the connecting rod 5 of the welding industrial robot, λ5 (λ∈{x,y,z}) is the vibration displacement of the connecting rod 5 along the λ axis, and k 56λ (λ∈{x,y,z}) is the contact stiffness between connecting rod 5 and connecting rod 6 along the λ axis, c 56λ (λ∈{x,y,z}) is the contact damping between connecting rod 5 and connecting rod 6 along the λ axis, F 56λ (λ∈{x,y,z}) is the interaction force between connecting rod 5 and connecting rod 6 along the λ axis, J 5j (j∈{x,y,z}) is the moment of inertia of connecting rod 5 around axis j, θ 6j (j∈{x,y,z}) is the rotation angle of connecting rod 6 around axis j, κ 56j (j∈{x,y,z}) is the torsional stiffness around the j-axis at the joint 6 between link 5 and link 6, ξ 56j (j∈{x,y,z}) is the torsional damping around the j-axis at joint 6, l5 is the length of link 5, α5 is the angle between link 5 and plane xOy, T 56 Output torque for joint 6, T f56 is the friction torque of joint 6; The nonlinear dynamic equation of the connecting rod 6 of the aluminum alloy friction stir welding industrial robot is: Where m6 is the mass of the welding industrial robot link 6, λ6 (λ∈{x,y,z}) is the vibration displacement of the link 6 along the λ axis, and F 6λ (λ∈{x,y,z}) is the interaction force between the connecting rod 6 and the workpiece along the λ axis, J 6j (j∈{x,y,z}) is the moment of inertia of connecting rod 6 around axis j, l6 is the length of connecting rod 6, and T6 is the torque between connecting rod 6 and the workpiece; Step (6): solve the nonlinear response characteristics of the system; Select the stirring needle feed speed v, stirring needle speed n, stirring needle length l p , stirring needle pressure depth e t The nonlinear response characteristics of the vibration displacement of the end effector in the feed direction of the stir friction welding industrial robot system are solved; by analyzing the nonlinear response characteristic curve of the vibration displacement, the parameter configuration for stable operation of the system is determined; the system operates stably under the periodic motion state, which can improve the working efficiency and quality of the aluminum alloy stir friction welding industrial robot.

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