Method for adjusting end stiffness of hybrid robot for thin-walled structure machining

Abstract

This invention discloses a method for adjusting the end effector stiffness of a hybrid robot used in the machining of thin-walled structural parts. The method first collects the proportional gain of each active branch servo drive system as the axial servo stiffness; secondly, it establishes a mapping model based on the robot configuration to solve for the equivalent axial servo stiffness of the end effector in the reference coordinate system; subsequently, it introduces stiffness weighting coefficients and combines them with the mechanical stiffness and electromechanical coupling stiffness performance evaluation index; finally, it uses a one-dimensional discrete search algorithm to traverse and filter redundant rotation angles that satisfy displacement and rotation constraints while keeping the end effector pose unchanged, aiming to maximize the electromechanical coupling stiffness index and generate an optimal sequence of redundant rotation angles. This invention establishes an electromechanical coupling model integrating mechanical and servo systems and adaptively adjusts the end effector stiffness using redundant degrees of freedom, which can effectively suppress cutting deformation and chatter during the machining of thin-walled parts while reducing computational complexity, significantly improving machining quality.

Description

Technical Field

[0001] This invention belongs to the field of robot motion control and relates to a method for adjusting the end effector stiffness of a hybrid robot used for machining thin-walled structural parts. Background Technology

[0002] With the rapid development of high-end equipment manufacturing industries such as aerospace and automobile manufacturing, thin-walled structural components have been widely used due to their advantages such as lightweight and high specific strength. However, thin-walled structural components are characterized by low stiffness and easy deformation. During milling, cutting forces can easily cause workpiece deformation and chatter, seriously affecting machining accuracy and surface quality. Therefore, improving the overall stiffness of the robot-workpiece system during machining has become the key to ensuring the machining quality of thin-walled components.

[0003] The end effector stiffness of a robotic machining system is jointly determined by the mechanical structural stiffness and the servo system stiffness. Existing research mainly focuses on the analysis and optimization of mechanical structural stiffness, improving mechanical stiffness by improving mechanism design or optimizing robot pose. However, for hybrid robots, the stiffness of the servo drive system also has a significant impact on end effector performance, especially in high-load, variable-condition machining processes, where the compliance characteristics of the servo system cannot be ignored.

[0004] Chinese patent CN107545127B discloses "A Method for Modeling the Joint Stiffness of Industrial Robots Considering Contact." This method extracts key contact structural features of industrial robot joints, assuming the contact structures to be spring structures with a certain torsional stiffness, and establishes equivalent system models for each joint. Based on measurement data, it calculates three-dimensional surface fractal parameters and surface roughness parameters using the power spectral density method. Force analysis is performed on each contact structure, calculating the contact pressure values ​​corresponding to different joint input torques. An equivalent torsional stiffness model of parallel springs is established, and the equivalent torsional stiffness of the joints is calculated by connecting the contact stiffnesses and the reducer stiffness in parallel. This method combines fractal theory and structural force analysis to establish a joint stiffness model for industrial robots. By considering contact stiffness, it provides a more accurate theoretical estimate of joint stiffness, offering a methodological basis for dynamic error compensation analysis of robot end effects. The problem with this structure is that the method only applies to the joints of serial industrial robots and does not involve the parallel mechanism of hybrid robots. At the same time, the method focuses on static stiffness modeling and does not consider the coupling effect between the stiffness of the servo system and the stiffness of the mechanical structure, so it cannot be directly applied to the dynamic stiffness optimization in the processing.

[0005] Chinese patent CN111444644B discloses "A method for optimizing the overall stiffness of an industrial robot based on finite element method," with the following specific steps: S1: Initial model finite element modeling; S2: Substructure division; S3: Adjusting substructure stiffness parameters; S4: Calculating the overall stiffness change; S5: Judging the rationality of the design; S6: Structural optimization. Using finite element methods to establish an overall model to analyze the design rationality of the overall stiffness and component stiffness significantly improves analysis efficiency and shortens the robot design and development cycle. By using finite element technology and normalization methods to expose design problems and defects in advance, fatal problems are avoided in the prototype stage, development costs are reduced, and the method can be applied to the design and development of any industrial robot. It improves the overall stiffness level of the robot while ensuring a lightweight design. The problem with this structure is that the method is an offline design optimization method, which requires finite element modeling and calculation in the design stage. It cannot be applied to online stiffness adjustment in the machining process of robots that have already been put into use. In addition, the method only considers the stiffness of the mechanical structure and does not include the stiffness of the servo system in the optimization system, making it difficult to adapt to the dynamic working conditions in actual machining.

[0006] CN112380726B discloses "A method for predicting the critical stable depth of cut in robot milling based on modal coupling chatter." The method includes the following steps: S1. Establishing a general prediction model for robot milling force. S2. Establishing a modal coupling dynamic model of the robot, and then using eigenvalue analysis based on the model to provide a method for determining the stability of modal coupling chatter and a method for calculating the critical depth of cut. S3. Conducting stiffness tests on the robot to obtain the joint stiffness and the Cartesian stiffness matrix of the robot's end effector wrist. S4. Determining the robot's machining trajectory and feed direction, and calculating the critical depth of cut along the machining path. S5. Optimizing the robot's milling parameters by changing the robot's milling trajectory and feed direction. This invention can quantitatively predict the critical stable depth of cut along the entire path of the robot during milling, thereby guiding the robot to change the machining path or machining parameters such as the axial depth of cut, thus preventing modal chatter. The problem with this structure is that the method focuses on flutter stability prediction rather than stiffness performance optimization; its stiffness analysis relies on joint stiffness obtained from experimental identification and does not establish a mapping relationship from servo system parameters to end-effector stiffness; at the same time, the method does not consider the redundant degrees of freedom unique to hybrid robots and cannot achieve stiffness adjustment through pose optimization.

[0007] CN113183181A discloses a "rigid-flexible coupling robotic arm," comprising an internal skeleton formed by several connected skeleton units and several sets of pneumatic muscles surrounding the internal skeleton and disposed between adjacent skeleton units; adjacent skeleton units are movably connected; each skeleton unit has several pairs of pneumatic muscle interfaces arranged circumferentially, with each set of pneumatic muscles correspondingly disposed on the pneumatic muscle interfaces of adjacent skeleton units; the pneumatic muscle interfaces on adjacent skeleton units include a sealing and fixing interface and an inflation interface for inflating the pneumatic muscles; each skeleton unit also has an air pipe interface circumferentially connected to the corresponding inflation interface. This invention, by arranging flexible pneumatic muscles around the internal skeleton, enables the robotic arm to possess the advantages of both rigid and flexible robots, while also exhibiting high flexibility. The problem with this structure is that this solution is a hardware structural innovation, achieving rigid-flexible coupling by changing the robotic arm's body structure, rather than optimizing the rigidity performance of existing robots through control algorithms; its application scenarios are in non-industrial fields such as service and medical, which are fundamentally different from the rigidity requirements of heavy-duty working conditions such as milling; furthermore, this solution cannot be applied to the optimization of the processing of traditional rigid hybrid robots.

[0008] The structure of a six-DOF hybrid robot with redundant degrees of freedom can be found in the structure of the six-DOF hybrid robot disclosed in patent CN111604885A, published on September 1, 2020, entitled "A Six-DOF Hybrid Robot with a Multi-Axis Rotary Support". This patent discloses a robot comprising a first fixed axis seat, a first rotating support, a second fixed axis seat, a second rotating support, a first length adjustment device, a second length adjustment device, a third length adjustment device, a fourth length adjustment device, a moving platform, and a positioning head connected to the moving platform. The first and second rotating supports are rotatably connected to the first and second fixed axis seats, respectively; the first three length adjustment devices are all rotatably connected to the first rotating support; the fourth length adjustment device is rotatably connected to the second rotating support; and the ends of the four length adjustment devices are connected to the moving platform via hinges. Specifically, the first length adjustment device is a first RPS active branch, the second length adjustment device is an RP branch, the third length adjustment device is a second RPS active branch, and the fourth length adjustment device is a UPS active branch. Furthermore, Shen Sitong's publicly available paper, "Research on Friction Compensation Method of a Novel Hybrid Robot" [D]. Tianjin University of Technology, 2025, on CNKI, further describes the mechanism composition, coordinate system establishment, and kinematic model of the aforementioned six-DOF TriMule hybrid robot. This robot consists of a 1T2R three-DOF parallel mechanism and a three-DOF serial rotating head, where T represents translational motion and R represents rotational motion. The parallel mechanism mainly includes two sets of fixed bearings, a rotating support, a moving platform, and two R... P S-chain, a U PS-branch and one RP driven branch; where R represents a revolute joint, P represents a prismatic joint, U represents a Hooke's joint, and S represents a ball joint. Two R-branch branches P One end of the S-branch is connected to the rotating support via a revolute joint, and the other end is connected to the moving platform via a ball joint; U P One end of the S-branch is connected to the fixed shaft via a Hooke's joint, and the other end is connected to the moving platform via a ball joint. One end of the RP driven branch is connected to the rotating bracket via a compound hinge, and the other end is fixedly connected to the moving platform. A series rotary head is mounted at the end of the moving platform and includes three axes: the fourth, fifth, and sixth axes. The fourth axis is perpendicular to the moving platform, the fifth axis is perpendicular to the fourth axis, and the sixth axis is perpendicular to the fifth axis. These six axes are connected in series and driven by servo motors and reducers. To describe the robot's motion relationships, a reference coordinate system, a moving platform coordinate system, a tool coordinate system, and a workpiece coordinate system are established.

[0009] For the aforementioned six-DOF hybrid robot, five degrees of freedom are needed to control the tool movement during machining, resulting in one redundant degree of freedom. The position coordinates of the tool tip in the robot's reference coordinate system and the rotation angles A, B, and C of the tool coordinate system relative to the robot's reference coordinate system around the X, Y, and Z axes together determine the robot's position and orientation. Among these, the rotation angle C around the Z axis constitutes a redundant rotational degree of freedom, which is a redundant rotation angle. During machining, by adjusting the redundant rotation angle C, the robot's configuration can be changed without altering the tool end effector's pose, thereby adjusting the end effector stiffness. How to fully utilize this redundant degree of freedom, comprehensively considering the coupling effect of mechanical stiffness and servo stiffness, to achieve stiffness performance optimization for the machining characteristics of thin-walled structural parts is a pressing technical problem that needs to be solved. Summary of the Invention

[0010] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for adjusting the end effect stiffness of a hybrid robot used for machining thin-walled structural parts. This method can fully consider the coupling effect between the mechanical structure stiffness and the servo system stiffness, and adaptively adjust the robot pose according to the machining characteristics of thin-walled structural parts, thereby significantly improving the end effect stiffness performance during the machining process.

[0011] The present invention provides a method for adjusting the end effector stiffness of a hybrid robot used for machining thin-walled structural components, comprising the following steps: Step S1: Collect the proportional gain of the PID controller of the servo drive system of each active branch of the hybrid robot, and define the value of the proportional gain as the axial servo stiffness of the active branch. Step S2: Using the axial servo stiffness of each active branch obtained in Step S1 as input, and based on the specific configuration and kinematic geometry of the hybrid robot, establish a mapping model from the axial servo stiffness of each active branch to the end effector direction stiffness. Solve the equivalent axial servo stiffness of the end effector in three orthogonal directions in the reference coordinate system using the mapping model, denoted as follows: , , ; Step S3: Establish a calculation model for the stiffness weighting coefficients, and calculate the stiffness weighting coefficients of the hybrid robot end effector in the X, Y, and Z directions of the reference coordinate system, denoted as follows: , , ; Step S4, Computer-aided evaluation index for electrical coupling stiffness performance, formula as follows:

[0012] In the formula, , , These represent the mechanical stiffness of the end effector of the hybrid robot in the X, Y, and Z axes, respectively. Step S5: Using a one-dimensional discrete search algorithm, the candidate redundant rotation angles C of the six-degree-of-freedom hybrid robot are discretely traversed. The feasibility constraint of each candidate redundant rotation angle is checked in turn. Infeasible solutions that violate the boundary constraints of parallel branch displacement and series joint rotation are eliminated. In the set of feasible solutions that satisfy all constraints, the electromechanical coupling stiffness performance evaluation index calculated in step S4 is used as the optimization objective to solve for the redundant rotation angle sequence when the stiffness performance of the hybrid robot is optimal for the entire machining trajectory.

[0013] The present invention has the following beneficial effects: 1. This invention establishes an electromechanical coupling stiffness model, which comprehensively considers the series effect of mechanical structure stiffness and servo system stiffness, breaking through the limitation of traditional methods that only consider mechanical stiffness, and making stiffness evaluation more consistent with actual processing conditions. 2. This invention proposes a stiffness weight coefficient calculation method oriented towards the processing technology, which is designed for the processing characteristics of thin-walled structural components. It can adaptively adjust the weight according to the degree of influence of processing deformation in different directions on quality, thereby achieving global optimization of processing quality. 3. This invention fully utilizes the redundant degrees of freedom of the hybrid robot, and achieves optimal electromechanical coupling stiffness performance by optimizing the rotation angle without changing the spatial position and attitude of the tool end point. 4. This invention employs a one-dimensional discrete search algorithm, which simplifies the complex electromechanical coupling stiffness optimization problem into a single-variable search problem. While ensuring the optimization accuracy, it significantly reduces the computational complexity and is suitable for online or offline planning of actual machining trajectories. 5. This invention can adaptively adjust the robot's pose according to the specific processing requirements of thin-walled structural parts, effectively improving the end effector stiffness during processing, suppressing cutting deformation and chatter, and improving the processing quality of thin-walled parts. Attached Figure Description

[0014] Figure 1 This is a flowchart of a method for adjusting the electromechanical coupling stiffness performance of a hybrid robot for machining thin-walled structural parts according to the present invention; Figure 2 This is a schematic diagram of a six-degree-of-freedom hybrid robot with redundant degrees of freedom, using the method of this invention. Figure 3 This is a geometric diagram showing the projection of the intersection point of the rotating R-joint onto the plane of the center point of the branch U / R-joint; Figure 4 This is a diagram of a triangular pyramid model for calculating the equivalent axial servo stiffness at the end. Figure 5 This is a flowchart of the one-dimensional discrete search algorithm of the present invention; Figure 6 This is a schematic diagram of a thin-walled structural component processed using the method of the present invention to adjust the stiffness performance of an existing hybrid robot. Figure 7 This is a front view of the grid markings on a thin-walled structural component; Figure 8 It is a cross-sectional drawing showing the wall thickness of a thin-walled structural component. Detailed Implementation

[0015] To make the technical solution of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific examples described herein are only for explaining the present invention, but are not limited to these examples.

[0016] The method of this invention is applicable to six-degree-of-freedom hybrid robots with redundant degrees of freedom. The mechanical structure can be found in the relevant structure disclosed in Shen Sitong's "Research on a Novel Friction Compensation Method for Hybrid Robots" [D]. Tianjin University of Technology, 2025. Figure 2 The diagram shows a six-DOF hybrid robot with redundant degrees of freedom. In the figure: 1 is the moving platform, 2 is the serial rotating head, 3 is the rotating support, and 4 is the first R... P S is an active branch, and 5 is the second R. P S is the active branch chain, 6 is the RP branch chain, and 7 is the U branch chain. P S is the active branch chain, and 8 is the fixed axis support. The main drive mechanism of the hybrid robot is a parallel mechanism, with the first R... PS active branch 4, second R P S active branch 5 and U P S active branches and 7 together constitute the active branch. The parallel joint includes the first R P S active branch 4, second R P S active branch 5, U P The kinematic pairs formed between the S-active branch 7, RP-active branch 6, moving platform 1, rotating support 3, and fixed bearing 8. The series joints include the fourth, fifth, and sixth axes on the rotating support 3 and the series rotating head 2. The left and right ends of the rotating support 3 are connected to the fixed bearing 8 via revolute joints. The Hooke's joint (U-joint) in the UPS active branch 7 comprises two mutually perpendicular and intersecting revolute joints; the center point of the Hooke's joint in the UPS active branch 7 is the intersection of its two mutually perpendicular rotation axes.

[0017] The present invention provides a method for adjusting the end effector stiffness of a hybrid robot used for machining thin-walled structural components, comprising the following steps: Step S1: Collect the proportional gain of the PID controller of each active branch servo drive system of the hybrid robot, and define the value of the proportional gain as the axial servo stiffness of that active branch. The specific steps are as follows: The lengths of each active branch in the parallel mechanism of the hybrid robot are adjusted by servo motors. The servo drive system of each servo motor uses a PID controller for position control. The proportional gain of each PID controller is collected. ( The proportional gain directly reflects the response stiffness of the servo drive system to position errors, and the value of the proportional gain is directly defined as the axial servo stiffness of each active branch.

[0018] Step S2: Using the axial servo stiffness of each active branch obtained in step S1 as input, and based on the specific configuration of the hybrid robot (i.e., the parallel mechanism includes two R...), P S active branch chain, one U P S is the active branch and RP is the driven branch. The cascaded rotary head includes three rotary joints: the fourth, fifth, and sixth axes. Based on their kinematic geometry, a mapping model is established from the axial servo stiffness of each active branch to the end effector stiffness. The equivalent axial servo stiffness of the end effector in three orthogonal directions in the reference coordinate system is obtained using this mapping model, denoted as follows: , , .

[0019] Specifically, establish a reference coordinate system. ,origin Located at the intersection of the axis of RP branch 6 and the axis of rotating bracket 3, The axis of the rotating pair connected to the shaft, rotating bracket 3, and fixed shaft seat 8 coincides. P The center point of the Hooke hinge (U-joint) in the active branch 7 of S, the first R P The first intersection point of the active branch chain 4 axis and the rotating support 3 axis, and the second R P The three points at the second intersection of the axis of the active branch 5 and the axis of the rotating bracket 3 are coplanar and determine a reference plane. The center point of the Hooke hinge in the active branch 7 of the UPS is the intersection of its two mutually perpendicular rotation axes. The axis passes through the origin. Perpendicular to the reference plane, The axis is determined by the right-hand rule. The aforementioned... The axis coincides with the line connecting the first and second intersection points in the reference plane.

[0020] The mapping model is as follows:

[0021]

[0022]

[0023] , ,

[0024]

[0025]

[0026] , , In the formula: Point P is the intersection of the axes of the four and five rotational joints of the serial rotating head 2 on the end effector and the axis of the sixth joint of the robot end effector, which is the center point of the serial rotating head; For U P The center point of the Hooke hinge (U-joint) in the active branch 7 of S; and The first R P S active branch 4, second R P The intersection of the axes of each of the active branches 5 and the axis of the rotating support 3; For point In plane Projection on; Points on the three active chains of the hybrid robot on the aforementioned reference plane , and Forming a base triangle, point P is located above the base triangle. Draw a line through point P onto the plane. Projection on Construct a triangular pyramid P- The geometric model.

[0027] , , These represent the equivalent axial servo stiffness of the end-effector in the X, Y, and Z axes of the reference coordinate system, respectively. , , The first R obtained in step S1 is respectively P S active branch 4, second R P S active branch 5, U P Axial servo stiffness of S active branch 7; , , Representing points respectively In the reference coordinate system The coordinates in the X, Y, and Z axes; Origin of the reference coordinate system With the second R P The rotational center point of active branch 5 (i.e., the second R) P The length of the line segment formed by connecting the intersection of the axis of the active branch 5 and the axis of the rotating support 3, and with reference to the origin of the coordinate system and the first R P S active branch 4 rotating subcenter point (i.e.: first R) P The length of the line segment formed by connecting the intersection of the axis of active branch 4 and the axis of rotating support 3 is also equal to... The origin Connect respectively and Forming line segments and , =line segment Length = line segment The length.

[0028] Origin of the robot's reference coordinate system with U PThe length of the line segment formed by connecting the center points of the active branch and the Hooke hinge (S), i.e., the origin. With point The line segments formed by connecting The length is .

[0029] Equivalent angle express and The angle between them, where express and The angle between them express and The angle between them express and The angle between them; Equivalent angle Point With plane The angle between the line and the plane, where express and The angle between them express and The angle between them express and The angle between them; , , These represent the UPS active branch 7, the second RPS active branch 5, and the first RPS active branch 6, respectively. P S active branch 4 connection point , , arrive The distance.

[0030] In this step, the servo stiffness acts along the branch axis and needs to be mapped to the orthogonal direction of the end coordinate system through geometric projection, so an equivalent angle is introduced.

[0031] Step S3: Establish a calculation model for the stiffness weighting coefficients, and calculate the stiffness weighting coefficients of the hybrid robot end effector in the X, Y, and Z directions of the reference coordinate system, denoted as follows: , , To eliminate the influence of the difference in dimensions of different machining accuracy indicators on the weight calculation results, the machining contour dimension accuracy, machining surface roughness, and wall thickness accuracy are first processed to be dimensionless. The specific calculation model is as follows: , , In the formula: This serves as a reference value for the machining contour dimensions accuracy. This serves as a reference value for the surface roughness of the machined surface. This serves as a reference value for the accuracy of the machining wall thickness. The machining contour dimensional accuracy (unit: mm) is defined as the maximum permissible deviation between the actual machined contour and the designed contour, and is determined according to the requirements of the part drawing. Surface roughness of the machined structural part (unit: ), used to characterize the micro-geometric errors of the machined surface; The wall thickness accuracy (unit: mm) of the machined structural part is defined as the maximum permissible deviation between the actual wall thickness and the designed wall thickness, and is determined according to the requirements of the part drawing.

[0032] , , These are the dimensionless machining accuracy parameters corresponding to the machining contour dimension accuracy, machining surface roughness, and machining wall thickness accuracy, respectively.

[0033] Based on dimensionless machining accuracy parameters, a calculation model for the initial stiffness weighting coefficients in the X, Y, and Z directions is established: , , In the formula: , , These represent the initial stiffness weighting coefficients in the X, Y, and Z axes, respectively.

[0034] Furthermore, the initial stiffness weighting coefficients in each direction are normalized to obtain the final stiffness weighting coefficients:

[0035]

[0036] In the formula: , , These are the stiffness weighting coefficients in the X, Y, and Z axes, respectively, and satisfy the following conditions:

[0037] In the above formula: machining contour dimensional accuracy and Towards (feed direction) and perpendicular to the feed direction Related to the (horizontal) direction, therefore , Stiffness weighting coefficient in the direction , Follow The wall thickness accuracy of the machined structural parts increases with the increase of the size; and Related to (tool axis), therefore Stiffness weighting coefficient in the direction Follow The surface roughness of the machined surface increases as the surface roughness decreases. Then and , , All three directions are correlated, that is , , All follow It increases as it decreases.

[0038] In this step, a comprehensive evaluation of the equivalent axial servo stiffness performance of the end effector in each direction obtained in step S2 is performed in order to meet the machining task. Therefore, based on the specific machining accuracy requirements of the thin-walled structural parts, the stiffness weight coefficients of the robot end effector in the X, Y, and Z directions of the reference coordinate system are calculated.

[0039] Step S4, Computer-aided evaluation index for electrical coupling stiffness performance, formula as follows:

[0040] In the formula, , , These represent the mechanical stiffness of the end effector of the hybrid robot in the X, Y, and Z axes, respectively, and can be calculated using finite element analysis software.

[0041] The following example illustrates the mechanical stiffness analysis process: The 3D CAD model of the hybrid robot (including the fixed platform, rotating support, branches, moving platform, and tandem rotor) is imported into the finite element analysis software, and the material parameters of each component (elastic modulus E, Poisson's ratio) are defined. ,density After (etc.), mesh generation is performed and key connection parts are locally refined. Then, fixed constraints are applied to the bottom surface of the fixed platform, and unit forces in the X, Y, and Z directions are applied at the end tool reference point P. , , The displacement response of the end point P under forces in various directions was obtained by statics solution. , , Finally, according to the definition of stiffness Calculate the mechanical stiffness in each direction, i.e., the X-direction. , Y direction Z direction .

[0042] Step S5: Using a one-dimensional discrete search algorithm, the candidate redundant rotation angles C of the six-degree-of-freedom hybrid robot are discretely traversed. Feasibility constraints are checked for each candidate redundant rotation angle, eliminating infeasible solutions that violate the parallel branch displacement boundary constraints and the series joint rotation angle boundary constraints. In the set of feasible solutions that satisfy all constraints, the electromechanical coupling stiffness performance evaluation index calculated in step S4 is used as the optimization objective to obtain the sequence of redundant rotation angles that achieve the optimal stiffness performance of the hybrid robot for the entire machining trajectory. The specific steps are as follows: Step S51, Trajectory Discretization and Variable Initialization: Divide the entire machining trajectory into... m +1 blade position point, for the first individual knife sites Set the search range for redundant corners ,in , These are the lower and upper limits of the redundant rotation angle, respectively. The lower and upper limits of the redundant rotation angle are determined based on the range of motion of the robot's joints, and are typically [values ​​to be filled in]. Set redundant corner step size Where n is the number of parts into which the redundant rotation angle range is uniformly discretized. Its value needs to take into account accuracy requirements, computational efficiency, and stiffness variation characteristics. Generally, a step size is required. To ensure optimization accuracy while also considering computational efficiency; define the first... The optimal redundant rotation angle for each tool position is ,when At that time, set the optimal redundant rotation angle of the initial tool position. .

[0043] Step S52: Discretely traverse the redundant rotation angles at each tool position according to the step size to obtain the candidate redundant rotation angle sequence, and simultaneously set the optimal index for evaluating the current electromechanical coupling stiffness performance. , Set to 0: ; in: For the first Candidate redundant corner sequences for each knife site, The numbers are discrete indices, starting from 0 and increasing until... , Preferred satisfaction To ensure that the optimization step size does not exceed ;at the same time It should not be too large, it is recommended This is to control the computational load within a reasonable range. and As independent loop variables, Control the traversal of candidate corners within a single tool position (inner loop). Control the traversal of tool positions along the entire trajectory (outer loop); Step S53, Inverse Position Analysis: For candidate redundant corner sequences Each candidate redundant rotation angle is combined with the position coordinates of the tool tip in the robot reference coordinate system under the current pose. Given the rotation angles A and B of the tool coordinate system relative to the robot reference coordinate system around the X and Y axes, solve for the displacements of the three active chains of the parallel mechanism. The rotation angle of the three rotating joints of the series rotating head For specific calculation methods, please refer to Chapter 2, Kinematics and Rigid Body Dynamics Modeling of Hybrid Robots, in (Liu Qi. Research on CNC Key Technologies of a Novel Five-Axis Hybrid Robot [D]. Tianjin University, 2019).

[0044] Step S54, Constraint check: For each candidate redundant corner sequence in step S53 The displacements of the three active branches of the parallel mechanism are obtained by solving for each candidate redundant rotation angle. The rotation angle of the three rotating joints of the series rotating head Substitute the following parallel joint displacement constraint model and series joint rotation constraint model into the model in sequence, and determine whether the constraint conditions are met: Parallel joint displacement constraint model:

[0045] in For U P S active branch 7, second R P S Active Branch 5, First R P The displacement, or expansion / contraction, of active branch 4 S. , The first The lower and upper limits of displacement for each active branch (determined based on the mechanical structure).

[0046] Series joint rotation constraint model:

[0047] in These are the fourth, fifth, and sixth axis joint angles of the tandem rotary head, respectively. .

[0048] If the constraints are not met, the candidate redundant corner is discarded, and the above constraint judgment is continued for the next candidate redundant corner. If the above constraints are met, the candidate is marked as a qualified candidate redundant corner, and the next step is executed.

[0049] In this step, at each machining trajectory point, the redundant rotation angles are judged one by one from the minimum to the maximum value to determine the constraints. Infeasible solutions that violate the boundary constraints of parallel branch displacement and series joint rotation are eliminated, and the remaining qualified angles are then compared for stiffness.

[0050] Step S55: Calculate the corresponding electromechanical coupling stiffness performance evaluation index: The displacements of the three active branches corresponding to the qualified candidate redundant rotation angles after screening. The rotation angle of the three rotating joints of the series rotating head Substituting the values ​​into the forward kinematics model of the robot (Reference: Liu Qi. Research on key CNC technologies of a novel five-axis hybrid robot [D]. Tianjin University, 2019. CNKI), the points can be solved. In the reference coordinate system Coordinates in the X, Y, and Z axes , , Then, calculate the current pose based on the mapping model in step S2. , , Then, the current electromechanical coupling stiffness performance evaluation index is calculated according to the formula in step S4. .

[0051] Step S56, Optimal Redundancy Rotation Angle Update: If the current electromechanical coupling stiffness performance evaluation index Better than the recorded best value ,Right now Then update makes And will be with the current best The corresponding value of the qualified candidate redundant angle is assigned to the optimal redundant angle. Otherwise keep and Unchanged (i.e., not updated, maintaining the historical best stiffness index and best redundancy angle record).

[0052] Step S57, Tool position traversal completion judgment and optimal output: After traversing all candidate redundant corners of the current tool position, the optimal output is obtained. Optimal redundant rotation angle at each tool position That is, the first Among all qualified candidate redundant corners at each tool position, make The largest redundant corner.

[0053] Step S58, Generation of the optimal pose sequence for the entire trajectory: For all m +1 tool positions repeat steps S51 to S57, and finally obtain the optimal redundant rotation sequence corresponding to the machining trajectory. This sequence is the robot posture planning scheme that optimizes the electromechanical coupling comprehensive stiffness performance of the entire machining trajectory.

[0054] The present invention and its embodiments have been described above illustratively. This description is not restrictive, and the figures shown are only one embodiment of the present invention; the actual structure is not limited thereto. Therefore, if those skilled in the art are inspired by this description and, without departing from the spirit of the invention, devise structural methods and embodiments similar to this technical solution in terms of component shape and connection method without creative design, all such embodiments should fall within the protection scope of the present invention.

Claims

1. A method for adjusting the end effector stiffness of a hybrid robot used in the machining of thin-walled structural parts, characterized in that... Includes the following steps: Step S1: Collect the proportional gain of the PID controller of the servo drive system of each active branch of the hybrid robot, and define the value of the proportional gain as the axial servo stiffness of the active branch. Step S2: Using the axial servo stiffness of each active branch obtained in Step S1 as input, and based on the specific configuration and kinematic geometry of the hybrid robot, establish a mapping model from the axial servo stiffness of each active branch to the end effector direction stiffness. Solve the equivalent axial servo stiffness of the end effector in three orthogonal directions in the reference coordinate system using the mapping model, denoted as follows: , , ; Step S3: Establish a calculation model for the stiffness weighting coefficients, and calculate the stiffness weighting coefficients of the hybrid robot end effector in the X, Y, and Z directions of the reference coordinate system, denoted as follows: , , ; Step S4, Computer-aided evaluation index for electrical coupling stiffness performance, formula as follows: ； In the formula, , , These represent the mechanical stiffness of the end effector of the hybrid robot in the X, Y, and Z axes, respectively. Step S5: Using a one-dimensional discrete search algorithm, the candidate redundant rotation angles C of the six-degree-of-freedom hybrid robot are discretely traversed. The feasibility constraint of each candidate redundant rotation angle is checked in turn. Infeasible solutions that violate the boundary constraints of parallel branch displacement and series joint rotation are eliminated. In the set of feasible solutions that satisfy all constraints, the electromechanical coupling stiffness performance evaluation index calculated in step S4 is used as the optimization objective to solve for the redundant rotation angle sequence when the stiffness performance of the hybrid robot is optimal for the entire machining trajectory.

2. The method for adjusting the end effector stiffness of a hybrid robot for machining thin-walled structural parts according to claim 1, characterized in that: The specific process of step S1 is as follows: The length of each active branch of the parallel mechanism of the hybrid robot is adjusted by a servo motor. The servo drive system of each servo motor uses a PID controller for position control, and the proportional gain of each PID controller is collected. ( The proportional gain directly reflects the response stiffness of the servo drive system to position errors, and the value of the proportional gain is directly defined as the axial servo stiffness of each active branch.

3. The method for adjusting the end effector stiffness of a hybrid robot for machining thin-walled structural parts according to claim 1 or 2, characterized in that: The specific process of step S2 is as follows: Establish a reference coordinate system ,origin Located at the intersection of the RP branch axis and the rotating support axis, The axis of the rotating pair connecting the shaft to the rotating bracket and the fixed shaft seat coincides. P The center point of the Hooke's hinge in the active branch S, the first R P The first intersection point of the active branch axis and the rotating support axis, and the second R P The three points of the second intersection of the active branch axis and the rotating support axis are coplanar and determine a reference plane. The center point of the Hooke hinge in the UPS active branch is the intersection of its two mutually perpendicular rotating axes. The axis passes through the origin. Perpendicular to the reference plane, The axis is determined by the right-hand rule; The mapping model is as follows: ； ； ； ， ， ； ； ； ； , , ； In the formula: Point P is the intersection of the axes of the two rotary joints of the series-connected rotary head on the end effector, namely the fourth and fifth axes, and the axis of the sixth axis joint of the robot end effector, which is the center point of the series-connected rotary head; For U P The center point of the Hooke hinge in the active branch of S; and The first R P S active branch, second R P The intersection of the axes of each active branch and the axis of the rotating support; For point In plane Projection on; Points on the three active chains of the hybrid robot on the aforementioned reference plane , and Forming a base triangle, point P is located above the base triangle. Draw a line through point P onto the plane. Projection on Construct a triangular pyramid P- Geometric model; , , These represent the equivalent axial servo stiffness of the end-effector in the X, Y, and Z axes of the reference coordinate system, respectively. , , The first R obtained in step S1 is respectively P S active branch, second R P S active branch chain, U P Axial servo stiffness of the active branch; , , Representing points respectively In the reference coordinate system The coordinates in the X, Y, and Z axes; The origin of the reference coordinate system With the second R P The length of the line segment formed by connecting the center points of the rotating joints of the active branch S, and the reference coordinate system origin and the first R P The length of the line segment formed by connecting the center points of the active branch's rotating sub-branch is also equal to... ; Origin of the robot's reference coordinate system with U P The length of the line segment formed by connecting the center points of the active branch Hooke hinge; Equivalent angle express and The angle between them, where express and The angle between them express and The angle between them express and The angle between them; Equivalent angle Point With plane The angle between the line and the plane, where express and The angle between them express and The angle between them express and The angle between them; , , These represent the UPS active branch, the second RPS active branch, and the first R... P S active branch connection point , , arrive The distance.

4. The method for adjusting the end effector stiffness of a hybrid robot for machining thin-walled structural parts according to claim 3, characterized in that: The calculation model for step S3 is as follows: ； ； ； ； ， ， ； ， ， ； In the formula: This serves as a reference value for the machining contour dimensions accuracy. This serves as the reference value for the surface roughness of the machined surface. This serves as a reference value for the accuracy of the machining wall thickness. For machining contour dimensional accuracy, it is defined as the maximum permissible deviation between the actual machined contour and the designed contour; The surface roughness of the machined structural part is used to characterize the micro-geometric errors of the machined surface. The wall thickness accuracy of the machined structural component is defined as the maximum permissible deviation between the actual wall thickness and the designed wall thickness. , , These are the dimensionless machining accuracy parameters corresponding to the machining contour dimension accuracy, machining surface roughness, and machining wall thickness accuracy, respectively. , , These represent the initial stiffness weighting coefficients in the X, Y, and Z axes, respectively.

5. The method for adjusting the end effector stiffness of a hybrid robot for machining thin-walled structural parts according to claim 4, characterized in that: The calculation model for step S5 is as follows: Step S51, Trajectory Discretization and Variable Initialization: Divide the entire machining trajectory into... m +1 blade position point, for the first individual knife sites Set the search range for redundant corners ,in , These are the lower and upper limits of the redundant angle, respectively, and the step size of the redundant angle is set. Where n is the number of parts into which the redundant rotation angle range is uniformly discretized; the first is defined as... The optimal redundant rotation angle for each tool position is ,when At that time, set the optimal redundant rotation angle of the initial tool position. ; Step S52: Discretely traverse the redundant rotation angles at each tool position according to the step size to obtain the candidate redundant rotation angle sequence, and simultaneously set the optimal index for evaluating the current electromechanical coupling stiffness performance. , Set to 0: ； in: For the first Candidate redundant corner sequences for each knife site The numbers are discrete indices, starting from 0 and incrementing until... ; Step S53, Inverse Position Analysis: For candidate redundant corner sequences Each candidate redundant rotation angle is combined with the position coordinates of the tool tip in the robot reference coordinate system under the current pose. Given the rotation angles A and B of the tool coordinate system relative to the robot reference coordinate system around the X and Y axes, solve for the displacements of the three active chains of the parallel mechanism. The rotation angle of the three rotating joints of the series rotating head ; Step S54, Constraint check: For each candidate redundant corner sequence in step S53 The displacements of the three active branches of the parallel mechanism are obtained by solving for each candidate redundant rotation angle. The rotation angle of the three rotating joints of the series rotating head Substitute the following parallel joint displacement constraint model and series joint rotation constraint model into the model in sequence, and determine whether the constraint conditions are met: Parallel joint displacement constraint model: ； in For U P S active branch, second R P S-active branch, first R P The displacement, or stretching, of the active branch S. , The first The lower and upper limits of displacement for each active branch; Series joint rotation constraint model: ； in These are the fourth, fifth, and sixth axis joint angles of the cascaded rotary heads. ; If the constraints are not met, the candidate redundant corner is discarded, and the above constraint judgment is continued for the next candidate redundant corner. If the above constraints are met, the candidate is marked as a qualified candidate redundant corner, and the next step is executed. Step S55: Calculate the corresponding electromechanical coupling stiffness performance evaluation index: The displacements of the three active branches corresponding to the qualified candidate redundant rotation angles after screening. The rotation angle of the three rotating joints of the series rotating head Substitute the points into the forward kinematics model of the robot and solve for the points. In the reference coordinate system Coordinates in the X, Y, and Z axes , , Then, calculate the current pose based on the mapping model in step S2. , , Then, the current electromechanical coupling stiffness performance evaluation index is calculated according to the formula in step S4. ; Step S56, Optimal Redundancy Rotation Angle Update: If the current electromechanical coupling stiffness performance evaluation index Better than the recorded best value ,Right now Then update makes And will be with the current best The corresponding value of the qualified candidate redundant angle is assigned to the optimal redundant angle. Otherwise keep and constant; Step S57, Tool position traversal completion judgment and optimal output: After traversing all candidate redundant corners of the current tool position, the optimal output is obtained. Optimal redundant rotation angle at each tool position That is, the first Among all qualified candidate redundant corners at each tool position, make Maximum redundant angle; Step S58, Generation of the optimal pose sequence for the entire trajectory: For all m +1 tool positions repeat steps S51 to S57, and finally obtain the optimal redundant rotation sequence corresponding to the machining trajectory. This sequence is the robot posture planning scheme that optimizes the electromechanical coupling comprehensive stiffness performance of the entire machining trajectory.

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