Cooperative machining track planning method for double-beam module three-dimensional laser cutting machine

Abstract

The invention discloses a collaborative processing track planning method for a double-beam module three-dimensional laser cutting machine. The collaborative processing track planning method comprises the following steps: establishing kinematic models of two sets of beam modules; performing kinematics analysis on the two sets of cross beam modules, and establishing a forward kinematics equation and an inverse kinematics solving equation set of the cross beam modules; and a step of planning the cooperative processing track of the two sets of cross beam modules by improving the chaotic particle swarm optimization. By the adoption of the collaborative processing track planning method for the double-beam module three-dimensional laser cutting machine, the collaborative processing track planning efficiency of the two sets of beam modules can be greatly improved, so that the collaborative processing time is shortened, and the collaborative processing efficiency of the two sets of beam modules is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of laser cutting, and particularly relates to a collaborative machining trajectory planning method for a three-dimensional laser cutting machine with a double beam module. Background Art

[0002] A three-dimensional laser cutting machine is a high-end equipment integrating optics, mechanics, electricity, and pneumatics, and is regarded as the pearl on the crown of laser processing equipment. It is mainly used for hole cutting and edge trimming of complex stamping parts, and is widely used in fields such as aerospace and new energy vehicles. To achieve high-efficiency laser cutting, it is necessary to plan the cutting path of the workpiece to reduce the idle travel distance during the laser cutting process. Currently, in both two-dimensional and three-dimensional laser cutting equipment, the solution of carrying a single cutting head is mainly adopted. Since it does not involve key technical issues such as collaborative cutting control and anti-collision, the technical difficulty is relatively low, but the improvement of the overall cutting efficiency is not obvious enough.

[0003] Currently, researchers have carried out a large number of studies on the forward and inverse kinematics, workspace, and joint space trajectory optimization of robotic arms. Xie Jun et al. carried out mathematical modeling and kinematic simulation on a 3P2R type assembly robot, explored the changes in the motion trajectory, the speed and acceleration of each joint, verified the rationality of the robot structure parameters, and provided an important basis for the subsequent control system design and trajectory planning. Zhao Zhiyuan et al. improved the Monte Carlo method for obtaining the workspace of the robot by using the normal distribution, proposed a voxelization algorithm to calculate the workspace volume, reduced the volume calculation error by continuously refining the boundary part, and finally the calculation error was less than 1%, providing a theoretical basis for motion analysis; Zeng Qingfei et al. used a fifth-order B-spline curve to interpolate the joint variables of a double-beam laser welding robot, and established a trajectory optimization model for the collaborative welding operation of the robot with the goal of high-efficiency and stable motion. Finally, the NSGA Ⅲ multi-objective optimization algorithm was used to solve the problem of the end trajectory optimization of a multi-arm collaborative robot for welding operations on complex welds; Wang Binqi took a six-axis serial robotic arm as the research object, and proposed a time-optimal 3-5-3 polynomial interpolation trajectory planning algorithm based on an improved particle swarm algorithm. The results show that the improved particle swarm algorithm has a faster convergence time and a shorter running time compared with traditional algorithms such as simulated annealing and genetic algorithms.

[0004] The kinematic analysis of the beam module is of great significance to the research, design, and application of three-dimensional laser cutting machines. However, at present, there are very few studies on the kinematics or trajectory planning of the double beam module of three-dimensional laser cutting machines, especially very few studies on the trajectory planning of the double beam module in collaborative machining, resulting in the working efficiency of three-dimensional laser cutting machines with double beam modules being always unsatisfactory. Summary of the Invention

[0005] In view of this, the present invention provides a collaborative machining trajectory planning method for a three-dimensional laser cutting machine with a double beam module.

[0006] The technical solution is as follows:

[0007] The first aspect of the present application relates to a collaborative machining trajectory planning method for a three-dimensional laser cutting machine with a double beam module, which is carried out according to the following steps:

[0008] S1. Establish the kinematic models of two sets of beam modules;

[0009] S2. Conduct kinematic analysis on two sets of beam modules, and establish the forward kinematic equation and the inverse kinematic solution equation set of the beam modules;

[0010] S3. Utilize the improved chaotic particle swarm optimization algorithm to plan the collaborative machining trajectory of two sets of beam modules, which is carried out according to the following steps:

[0011] S31. Obtain the initial poses and end poses of two sets of beam modules;

[0012] S32. Construct a machining trajectory between the initial pose and the end pose;

[0013] S33. Divide the machining trajectory into a first segment trajectory, a second segment trajectory, and a third segment trajectory according to time sequence, and the first segment trajectory, the second segment trajectory, and the third segment trajectory are all constructed by interpolation polynomial functions;

[0014] S34. Optimize the first segment trajectory, the second segment trajectory, and the third segment trajectory according to the improved chaotic particle swarm optimization algorithm to obtain the collaborative machining trajectory planning with the shortest time.

[0015] By adopting the above collaborative machining trajectory planning method for a three-dimensional laser cutting machine with a double beam module, first, by establishing kinematic models and conducting kinematic analysis, it provides a theoretical basis for the rapid collaborative machining trajectory planning of two sets of beam modules of the three-dimensional laser cutting machine with a double beam module and for avoiding collisions between two laser cutting heads. Then, the first segment trajectory, the second segment trajectory, and the third segment trajectory are constructed between the initial pose and the end pose by interpolation polynomial functions. Finally, the first segment trajectory, the second segment trajectory, and the third segment trajectory are optimized by the improved chaotic particle swarm optimization algorithm to obtain the collaborative machining trajectory planning with the shortest time, which can greatly improve the efficiency of the collaborative machining trajectory planning of two sets of beam modules, thereby shortening the collaborative machining time and improving the efficiency of the collaborative machining of two sets of beam modules. Description of the Drawings

[0016] Figure 1 The DH coordinate system for the three-dimensional laser cutting machine with a double beam module;

[0017] Figure 2Spatial trajectory planning diagram of the structures of each degree of freedom for a fifth-degree polynomial;

[0018] Figure 3 Curves of displacement, velocity, and acceleration obtained by using the improved chaotic particle swarm optimization algorithm for the structures from the first degree of freedom to the sixth degree of freedom;

[0019] Figure 4 Comparison curve of fitness obtained by using the improved chaotic particle swarm optimization algorithm and the standard chaotic particle swarm optimization algorithm for the structures from the first degree of freedom to the sixth degree of freedom;

[0020] Figure 5 Schematic diagram of the structure of the double-beam module three-dimensional laser cutting machine when the positioning tooling extends outwards to the side inlet and outlet;

[0021] Figure 6 Schematic diagram of the structure of the double-beam module three-dimensional laser cutting machine when the positioning tooling is fully retracted on the sliding table;

[0022] Figure 7 Schematic diagram of the double-beam module three-dimensional laser cutting machine after removing the track sliding table conveying mechanism;

[0023] Figure 8 Schematic diagram of the structure of the bed;

[0024] Figure 9 Schematic diagram of the structure of the crossbeam module;

[0025] Figure 10 Schematic diagram of the structure of the crossbeam;

[0026] Figure 11 Schematic diagram of the structure of the crossbeam after removing the second linear guide and the second rack;

[0027] Figure 12 Schematic diagram of the structure of the Z-axis sleeve from one perspective;

[0028] Figure 13 Schematic diagram of the structure of the Z-axis sleeve from another perspective;

[0029] Figure 14 Schematic diagram of the structure of the Z-axis sleeve, Y-axis slide, and laser cutting head from one perspective;

[0030] Figure 15 Schematic diagram of the structure of the Z-axis sleeve, Y-axis slide, and laser cutting head from another perspective;

[0031] Figure 16 Schematic diagram of the structure of the Y-axis slide;

[0032] Figure 17 Schematic diagram of the structure of one of the slider mounting components;

[0033] Figure 18 It is a schematic structural diagram of another slider mounting component;

[0034] Figure 19 It is a schematic structural diagram of a sleeve slider mounting seat;

[0035] Figure 20 It is a schematic structural diagram of a buckle. Specific embodiments

[0036] The present invention will be further described below in conjunction with embodiments and drawings.

[0037] Embodiment 1:

[0038] As Figures 9 - 20 shown, a crossbeam module mainly includes a crossbeam 6, a Y-axis slide 2, a Z-axis sleeve 1, and a laser cutting head 5.

[0039] Please refer to Figures 9 - 11 , the crossbeam 6 is composed of two strip-shaped slides 6b and two end connecting seats 6c. The two strip-shaped slides 6b and the two end connecting seats 6c are preferably integrally formed by a casting process, with high structural strength. Both of the two strip-shaped slides 6b are columnar or strip-shaped structures, and the two strip-shaped slides 6b are parallel to each other. The two end connecting seats 6c are arranged at both ends of the two strip-shaped slides 6b, that is: one end connecting seat 6c is fixedly connected to one end of the two strip-shaped slides 6b, and the other end connecting seat 6c is fixedly connected to the other end of the two strip-shaped slides 6b.

[0040] In this embodiment, the gap between the two strip-shaped slides 6b forms a Z-axis sleeve relief groove 6a extending in the horizontal direction, and both ends of the Z-axis sleeve relief groove 6a are defined by the two strip-shaped slides 6b. Moreover, Y-direction sliding component mounting structures 6b1 are arranged on the upper parts of the strip-shaped slides 6b, and X-direction driving device mounting structures 6c1 are arranged on the end connecting seats 6c, so that the centers of gravity of the Y-axis slide 2 and the Z-axis sleeve 1 are located at the center position of the crossbeam 6, greatly improving the stability and reliability of the Y-axis slide 2 and the Z-axis sleeve 1. It is neither necessary to frequently perform alignment debugging nor likely to cause torsional deformation of the crossbeam 6, making the static and dynamic characteristics of the three-dimensional laser cutting machine excellent. Therefore, the crossbeam 6 in this embodiment enables the Y-axis slide 2 to be mounted on the two Y-direction sliding component mounting structures 6b1, and at the same time, the Z-axis sleeve 1 can be inserted into the Z-axis sleeve relief groove 6a, so as to be able to cooperate with the Y-axis slide 2 to achieve a central straddle-mounted installation method on the crossbeam 6.

[0041] Further, the upper parts of the two strip-shaped sliding seats 6b have upper support surfaces 6b2 that are both inclined-plane structures. The two upper support surfaces 6b2 are symmetrically inclined downward away from each other, that is: the two upper support surfaces 6b2 together form an "eight" - shaped structure. At the same time, the Y - direction sliding component mounting structures 6b1 each include mounting bosses 6b11 protruding from the corresponding upper support surfaces 6b2. The mounting bosses 6b11 extend along the length direction of the corresponding upper support surfaces 6b2. On the sides of the two mounting bosses 6b11 away from each other, support ribs 6b12 protrude. Second linear guide rails 7 extending along their length directions are installed on the mounting bosses 6b11. The slide rails of the respective second linear guide rails 7 are respectively supported on the corresponding support ribs 6b12. Therefore, not only is the reliable installation of the second linear guide rails 7 ensured, but the two second linear guide rails 7 also together form an "eight" - shaped structure.

[0042] In this embodiment, at least one of the upper support surfaces 6b2 forms a rack mounting horizontal plane 6b3 extending in the horizontal direction on the side close to the Z - axis sleeve relief groove 6a. A rack mounting pad 11 extending along the length direction of the Z - axis sleeve relief groove 6a is installed on one of the rack mounting horizontal planes 6b3. On the top surface of the rack mounting pad 11, a rack support rib 11a protrudes on the side away from the Z - axis sleeve relief groove 6a. A second rack 8 extending along its length direction is installed on the rack mounting pad 11. The side of the second rack 8 away from the Z - axis sleeve relief groove 6a is supported on the rack support rib 11a, ensuring the reliable installation of the second rack 8.

[0043] Further, the interiors of the strip-shaped sliding seats 6b are all hollow structures extending along their length directions to meet the requirements of lightweight design. At the same time, a number of reinforcing support ribs 6b4 distributed along their length directions are provided inside the strip-shaped sliding seats 6b, thus ensuring the structural strength of the strip-shaped sliding seats 6b.

[0044] Moreover, a number of weight - reducing openings 6b5 distributed along their length directions are formed on the side walls of the strip-shaped sliding seats 6b close to each other. The respective reinforcing support ribs 6b4 are located at both ends of the corresponding weight - reducing openings 6b5, not only meeting the requirements of lightweight design, but also facilitating the welding of the reinforcing support ribs 6b4.

[0045] In this embodiment, the X - direction driving device mounting structures 6c1 are respectively motor mounting grooves formed by concave - down from the top surfaces of the corresponding end connectors 6c to facilitate the installation of the motors. At the same time, a number of triangular reinforcing ribs 6c2 are provided on the groove walls of the two motor mounting grooves, ensuring the structural strength at the positions of the motor mounting grooves.

[0046] Further, triangular reinforcing ribs 6d are provided at the four corners of the Z - axis sleeve relief groove 6a to improve the structural strength at the connection between the strip-shaped sliding seat 6b and the end connector 6c.

[0047] Please refer to Figure 9 and Figures 12 - 15 The Z-axis sleeve 1 includes a flat tube portion 1a and a cylindrical tube portion 1b that are integrally formed, and has high structural strength. Among them, the flat tube portion 1a is a flat tubular structure, and the flat tube portion 1a extends in the vertical direction. The cylindrical tube portion 1b is a cylindrical structure, and the cylindrical tube portion 1b also extends in the vertical direction. At the same time, the cylindrical tube portion 1b is located at the lower end of the flat tube portion 1a.

[0048] In this embodiment, the flat tube portion 1a and the cylindrical tube portion 1b are coaxially arranged. Most importantly, lifting guide planes 1a1 that both extend in the vertical direction are provided parallel to each other on both sides in the width direction of the flat tube portion 1a. Moreover, the distance between the two lifting guide planes 1a1 is smaller than the diameter of the cylindrical tube portion 1b. At the same time, the cylindrical tube portion 1b protrudes radially from the two lifting guide planes 1a1. In addition, lifting control component mounting structures that extend in the vertical direction are provided on the lifting guide planes 1a1.

[0049] The flat tube portion 1a is used to cooperate with the Y-axis slide 2, that is: the flat tube portion 1a can move up and down along the Y-axis slide 2. The cylindrical tube portion 1b is used to install the laser cutting head 5. Specifically, the laser cutting head 5 extends downward from the cylindrical tube portion 1b. Among them, the laser cutting head 5 uses a traditional laser cutting head that can excite laser, and usually has one or two or more rotational degrees of freedom, which can be selected according to actual needs. In this embodiment, the laser cutting head 5 has three degrees of freedom, including two rotational degrees of freedom and one degree of freedom for lifting and moving. Specifically, the laser cutting head 5 includes a first laser head base rotatably installed at the lower end of the Z-axis sleeve 1 along the vertical axis, a second laser head base rotatably installed on the first laser head base along the length direction of the bed 12, and a laser installed on the second laser head base capable of lifting. That is: the first laser head base can be rotatably installed on the first laser head base along the Z-axis, the second laser head base can be rotatably installed on the first laser head base along the X-axis, and the laser can be installed on the second laser head base capable of lifting along the Z-axis. Among them, the laser uses a follow-up control system adjustment mechanism, and the working principle is that the monitoring system quickly detects the capacitance value between the laser nozzle and the metal cutting part to dynamically adjust the focal length during the cutting process, ensuring the efficiency and quality of laser cutting processing. Therefore, on the premise of meeting the wiring requirements, the flat tube portion 1a can achieve an ultra-thin design, that is: the distance between the two lifting guide planes 1a1 can be designed to be very small. Therefore, the width of the Y-axis slide 2 that cooperates with it can also be very small, thereby reducing the size and weight of the Y-axis slide 2, meeting the requirements of lightweight design. And because the Z-axis sleeve 1 and the Y-axis slide 2 form an irregular shaft-hole fit through the flat tube portion 1a, there will be no relative rotation between them, so there will be no misassembly problem during assembly, and the assembly tolerance can be greatly reduced, shortening the assembly and debugging cycle; at the same time, because the widths of the flat tube portion 1a and the Y-axis slide 2 are both very small, the width of the Z-axis sleeve relief groove 6a of the beam 6 that cooperates with them can be greatly reduced, thereby effectively improving the structural strength of the beam 6, not easily having the problem of bending deformation, and reducing the maintenance frequency and use cost.

[0050] On the inner wall of the flat tube portion 1a, two wire routing relief grooves 1a2 facing each other are recessed. Both of the two wire routing relief grooves 1a2 are arranged inside the corresponding lifting guide plane 1a1 along the vertical direction. Therefore, while ensuring the structural strength of the flat tube portion 1a itself, the middle part of the flat tube portion 1a forms two wire routing relief grooves 1a2 through the diameter-expanded profile, which is convenient for wire routing. Further, the cross-section of the flat tube portion 1a is approximately rectangular. Specifically, the circumferential outer wall of the flat tube portion 1a is enclosed by two relatively arranged lifting guide planes 1a1 and two relatively arranged arc-shaped surfaces 1a5. The lifting guide planes 1a1 are both planar structures, and the arc-shaped surfaces 1a5 are both arc-shaped surfaces protruding outward. The lifting guide planes 1a1 and the arc-shaped surfaces 1a5 both extend along the vertical direction. Among them, since the arc-shaped surface 1a5 is an arc-shaped thin plate structure, it is not only easy to cast, but also has higher structural strength compared with the conventional flat plate structure.

[0051] In this embodiment, since both of the two lifting guide planes 1a1 protrude laterally from the cylindrical tube portion 1b along the horizontal direction, the internal space of the flat tube portion 1a can be effectively increased, so that more wire harnesses can pass through without increasing the width of the flat tube portion 1a.

[0052] The Z-axis sleeve 1 of this embodiment is integrally formed by a casting process, and has high structural strength.

[0053] Please refer to Figure 4 、 Figures 16 - 20 , the Y-axis slide 2 is of an annular structure. Specifically, the Y-axis slide 2 is enclosed by two relatively arranged slider mounting components and two relatively arranged buckle components, that is: the two slider mounting components face each other, the two buckle components face each other, and the two slider mounting components and the two buckle components are arranged in a rectangular layout, thus jointly forming an annular structure. Each slider mounting component includes a cross beam slider mounting seat 2a and two sleeve slider mounting seats 2b. The cross beam slider mounting seat 2a includes a vertically extending vertical mounting plate 2a1 and a slider connecting plate 2a2 bent outward from the bottom of the vertical mounting plate 2a1. The two slider connecting plates 2a2 are respectively parallel to the corresponding upper support surface 6b2, and Y-direction slider connection structures 2a21 are provided on both of the two slider connecting plates 2a2. Among them, the slider connecting plate 2a2 can be arranged perpendicular to the vertical mounting plate 2a1 or inclined to the vertical mounting plate 2a1.

[0054] Further, the slider connecting plate 2a2 of this embodiment is preferably extended outward from the lower edge of the corresponding vertical mounting plate 2a1 and inclined downward, so that the two slider connecting plates 2a2 of the two slider mounting components jointly form a "V"-shaped structure (matched with the second linear guide 7).

[0055] Therefore, when the Y-axis slider 2 is translated, the pressure can be applied to the cross beam 6 in a way of slope cooperation. Compared with the structure that the slider connecting plate 2a2 is perpendicular to the vertical mounting plate 2a1 and applies pressure to the cross beam 6, the method of this embodiment can reduce the pressure borne by the cross beam 6, so that the structural stability of the cross beam 6 is better, and the risk of the middle part of the cross beam 6 being concave and bent is reduced. Further, at least one triangular reinforcing rib 2a3 is provided between the outer surface of the vertical mounting plate 2a1 and the upper surface of the slider connecting plate 2a2, so that the structural strength of the cross beam slider mounting seat 2a can be effectively improved and deformation can be avoided.

[0056] Z-axis slider connection structures 2b1 are provided on all four sleeve slider mounting seats 2b. Connection bosses 2b2 adapted to the corresponding vertical mounting plates 2a1 are provided on the outer sides of the sleeve slider mounting seats 2b, and the connection bosses 2b2 can be respectively adjustably mounted on the inner sides of the corresponding vertical mounting plates 2a1. The buckle assemblies are each composed of at least one vertically arranged buckle 2c. Both ends of each buckle 2c are bent inward to form buckle connection arms 2c1. Connection arm slots 2b21 adapted to the corresponding buckle connection arms 2c1 are provided on the side walls of the connection bosses 2b2, and the buckle connection arms 2c1 can be respectively adjustably mounted in the corresponding connection arm slots 2b21. Therefore, the size of the Y-axis slider 2 in the circumferential direction can be adjusted.

[0057] The Y-axis slider 2 of this embodiment can be connected to the cross beam 6 by adopting a central-mounted straddle mounting method by providing two Y-axis slider connection structures 2a21. Compared with the existing offset mounting structure of the Y-axis slider, the Y-axis slider 2 of this embodiment not only makes the overall center of gravity in the central position, so that the installation of the Y-axis slider 2 is stable and reliable, without the need for frequent alignment debugging, and is not likely to cause torsional deformation of the cross beam 6, making the static and dynamic characteristics of the three-dimensional laser cutting machine excellent. At the same time, since the Y-axis slider adopts a split structure, it can be very conveniently assembled with the Z-axis sleeve 1, and can also adapt to Z-axis sleeves 1 of different sizes by replacing buckles 2c of different sizes or adjusting the connection positions of the buckle connection arms 2c1 and the connection arm slots 2b21, with good versatility. Moreover, the split-structured Y-axis slider can very conveniently correct the assembly error by adjusting the connection positions of the buckle connection arms 2c1 and the connection arm slots 2b21 and the connection positions of the connection bosses 2b2 and the vertical mounting plates 2a1, and cooperate with the processing precision debugging of the later equipment.

[0058] On the outer sides of the connecting bosses 2b2, there is a first bolt hole array 2b22 composed of bolt holes distributed in an array, that is: the first bolt hole array 2b22 is composed of bolt holes distributed in multiple rows and multiple columns in an array, and the inner ends of the bolt holes of the first bolt hole array 2b22 all penetrate through to the corresponding connecting arm slots 2b21. At the same time, on the straight mounting plates 2a1, there are two second bolt hole arrays 2a11 composed of bolt holes distributed in an array, that is: the second bolt hole array 2a11 is composed of bolt holes distributed in multiple rows and multiple columns in an array. On the buckle connecting arms 2c1, there is a bolt hole linear array 2c11 composed of bolt holes evenly distributed along the length direction.

[0059] The apertures and spacings of adjacent bolt holes in the first bolt hole array 2b22, adjacent bolt holes in the second bolt hole array 2a11, and adjacent bolt holes in the bolt hole linear array 2c11 are all the same, and at least one bolt hole in each bolt hole linear array 2c11 communicates with the bolt holes in the corresponding first bolt hole array 2b22 and second bolt hole array 2a11, and they are locked into one body by bolts (not shown in the figure). When it is necessary to adjust the size and structure of the Y-axis slider 2, only need to take out the bolts, then adjust the relative positions of the sleeve slider mounting seat 2b and the crossbeam slider mounting seat 2a, and the relative position of the buckle 2c and the sleeve slider mounting seat 2b. After it is in place, lock the bolts again, which is simple and reliable.

[0060] Please refer to Figure 9 , in this embodiment, two first linear guides 1c extending in the vertical direction are installed on both of the two lifting guide planes 1a1, a first rack 1d extending in the vertical direction is installed on one of the lifting guide planes 1a1, two slider mounting assemblies are correspondingly arranged on the outer sides of the two lifting guide planes 1a1, two buckle assemblies are correspondingly arranged on the outer sides of the two arc surfaces 1a5, four Z-axis slider connection structures 2b1 are fixedly connected to the sliders of the four first linear guides 1c correspondingly, a first driving motor 3 is installed on the crossbeam slider mounting seat 2a close to the first rack 1d, and a first driving gear 4 meshing with the first rack 1d is sleeved on the motor shaft of the first driving motor 3 in a synchronously rotating manner.

[0061] Therefore, by driving the first driving gear 4 to rotate forward and backward by the motor shaft of the first driving motor 3, the Z-axis sleeve 1 can be lifted or lowered along the Y-axis slider, and the control accuracy is high. Further, the first driving motor 3 is preferably a servo motor, which can further improve the accuracy control of the lifting of the Z-axis sleeve 1.

[0062] Among them, the Y-direction slider connection structure 2a21 includes a Y-direction slider limiting rib 2a211 integrally formed on the lower side of the slider connection plate 2a2 and a third bolt hole array 2a212 penetrating the slider connection plate 2a2 in the thickness direction. The third bolt hole array 2a212 is composed of bolt holes distributed in an array. After the slider of the first linear guide 1c is positioned on the Y-direction slider limiting rib 2a211, it is connected to the third bolt hole array 2a212 through bolts, which is simple and reliable. Similarly, two Y-direction slider connection structures 2a21 are fixedly connected to the sliders of two second linear guides 7 in a one-to-one correspondence. A second driving motor 9 is installed on the crossbeam slider mounting seat 2a far from the first rack 1d, and a second driving gear 10 meshing with the second rack 8 is sleeved on the motor shaft of the second driving motor 9 in a synchronous rotation manner.

[0063] Therefore, by driving the second driving gear 10 to rotate forward and backward through the motor shaft of the second driving motor 9, the Y-axis slide can be translated along the crossbeam 6, and the control precision is high. Further, the second driving motor 9 is preferably a servo motor, which can further improve the precision control of the translation of the Y-axis slide.

[0064] Among them, the Z-direction slider connection structure 2b1 includes a Z-direction slider limiting rib 2b11 integrally formed on the side of the sleeve slider mounting seat 2b far from the slider connection plate 2a2 and a fourth bolt hole array 2b12 penetrating the sleeve slider mounting seat 2b in the thickness direction. The fourth bolt hole array 2b12 is composed of bolt holes distributed in an array. After the slider of the second linear guide 7 is positioned on the Z-direction slider limiting rib 2b11, it is connected to the fourth bolt hole array 2b12 through bolts, which is simple and reliable.

[0065] In this embodiment, the first rack 1d and each first linear guide 1c are respectively installed on the corresponding lifting control component installation structures. Specifically, a plurality of flat cylinder part reinforcing ribs 1a3 are convexly formed on the lifting guide plane 1a1, which improves the structural strength of the flat cylinder part 1a. At the same time, some of the flat cylinder part reinforcing ribs 1a3 extending in the vertical direction are the lifting control component installation structures, and the first rack 1d and each first linear guide 1c are respectively installed on the corresponding flat cylinder part reinforcing ribs 1c extending in the vertical direction, ensuring the installation accuracy of the first rack 1d and each first linear guide 1c.

[0066] Further, a circular reinforcing flange 1a4 is convexly formed along the circumference at the top of the flat cylinder part 1a, thereby improving the structural strength at the entrance of the flat cylinder part 1a. At the same time, the upper parts of the flat cylinder part reinforcing ribs 1a3 extending in the vertical direction all extend to the circular reinforcing flange 1a4, improving the overall structural strength of the flat cylinder part 1a. And the upper ends of the first rack 1d and each first linear guide 1c are both abutted against the circular reinforcing flange 1a4, thereby further improving the installation accuracy of the first rack 1d and each first linear guide 1c.

[0067] Furthermore, a plurality of annular reinforcing ribs 1b1 arranged side by side in the axial direction and axial reinforcing ribs 1b2 evenly distributed in the circumferential direction of each annular reinforcing rib 1b1 are convexly formed on the outer peripheral surface of the cylindrical portion 1b. The annular reinforcing ribs 1b1 and the axial reinforcing ribs 1b2 together form a grid-like structure, thereby effectively improving the structural strength of the cylindrical portion 1b.

[0068] Furthermore, a first motor mounting seat 2a4 is provided on the crossbeam slider mounting seat 2a close to the first rack 1d, and the first driving motor 3 is mounted on the first motor mounting seat 2a4, ensuring the reliable mounting of the first driving motor 3. A second motor mounting seat 2a5 is provided on the crossbeam slider mounting seat 2a close to the second rack 8, and the second driving motor 9 is mounted on the second motor mounting seat 2a5, ensuring the reliable mounting of the second driving motor 9.

[0069] Embodiment 2:

[0070] Please refer to Figures 5 - 8 , a three-dimensional laser cutting machine with a double crossbeam module, including a bed 12, a rail slider conveying mechanism 17, and two sets of crossbeam modules described in Embodiment 1. Please refer to Figure 7 and Figure 8 , sliding table inlets and outlets 12c are provided at both ends of the bed 12 in the length direction, and a side inlet and outlet 12d is provided on one side of the bed 12 in the width direction. Specifically, the bed 12 includes five columns 12a and a top frame 12b simultaneously mounted on the tops of the five columns 12a. Among them, the top frame 12b is a rectangular frame structure. Specifically, the top frame 12b is formed by enclosing a rectangular structure by two relatively arranged main beams 12b1 and two relatively arranged side beams 12b2. Four of the columns 12a are respectively supported at the four corners of the top frame 12b, that is: the four corners of the top frame 12b are respectively fixedly connected to the tops of the four columns 12a. Another column 12a is supported at the middle position of one of the main beams 12b1, so that sliding table inlets and outlets 12c are formed below both side beams 12b2 of the bed 12, that is: the two sliding table inlets and outlets 12c are located at both ends of the bed 12 in the length direction; at the same time, a side inlet and outlet 12d is formed below the main beam 12b1 of the bed 12 supported on two columns 12a, that is: the side inlet and outlet 12d is located on one side of the bed 12 in the width direction. Among them, the extending direction of the two main beams 12b1 is the length direction of the bed 12, the extending direction of the two side beams 12b2 is the width direction of the bed 12, and the extending direction of the column 12a is the height direction of the bed 12.

[0071] The above design not only ensures the structural strength of the bed but also facilitates the expansion and arrangement of functions at the position of the side inlet and outlet 12d.

[0072] In this embodiment, each column 12a includes a column body 12a1 extending in the vertical direction, and a column top plate 12a2 and a column bottom plate 12a3 respectively fixedly installed at the top and bottom of the column body 12a1. A number of column strengthening plates 12a4 extending in the vertical direction are installed on the circumference of the column body 12a1. The top parts of the column strengthening plates 12a4 are respectively fixedly connected to the corresponding column top plates 12a2, and the bottom parts of the column strengthening plates 12a4 are respectively fixedly connected to the corresponding column bottom plates 12a3. Therefore, the structural strength of each column 12a is greatly improved, and thus the structural strength of the bed body 12 is further improved. Further, in order to improve the structural strength of the bed body 12, top frame strengthening triangular ribs 12b3 are installed at the boundaries of the top frame 12b, thereby improving the structural strength of the top frame 12b. At the same time, in order to improve the connection strength between the top frame 12b and each column 12a, top frame strengthening triangular plates 12b4 are also provided at the connection positions between the top frame 12b and each column 12a.

[0073] In this embodiment, two mutually parallel third linear guide rails 13 are installed on the top of the bed body 12. A third rack 14 parallel to each of the two third linear guide rails 13 is installed beside them, that is: a third linear guide rail 13 and a third rack 14 are installed on the top of the main beam 12b1 along its length direction. At the same time, third driving motors 15 are installed on each end connecting seat 6c of the two sets of cross beam modules. Third driving gears 16 respectively meshing with the corresponding third racks 14 are synchronously rotatably sleeved on the motor shafts of the two third driving motors 15 of each set of cross beam modules.

[0074] The cross beams 6 of the two sets of cross beam modules are installed on the corresponding sliders of the two third linear guide rails 13 in parallel, and the extending directions of the two cross beams 6 are perpendicular to the extending directions of the two third linear guide rails 13. Generally, the extending direction of the third linear guide rail 13 is the X direction, the extending direction of the cross beam 6 is the Y direction, and the extending direction of the Z-axis sleeve 1 is the Z direction. Therefore, by driving the third driving gear 16 to rotate forward and backward through the motor shaft of the third driving motor 15, the translation of the cross beam 6 can be controlled with high control precision. Further, the third driving motor 15 is preferably a servo motor, which can further improve the precision control of the translation of the cross beam 6.

[0075] Please refer to Figure 5 and Figure 6, the rail slide table conveying mechanism 17 includes a slide table rail 17a and two slide tables 17b that can slide along the slide table rail 17a driven by a slide table drive assembly. The slide table rail 17a extends along the length direction of the bed body 12, and the slide table rail 17a passes through the two slide table inlets and outlets 12c at the same time. Positioning jigs 18 that can move along the width direction of the bed body 12 driven by a tooling translation assembly 19 are installed on both of the slide tables 17b. In this embodiment, driven by their respective slide table drive assemblies, the two slide tables 17b can not only independently enter and exit from the adjacent slide table inlets and outlets 12c, but also synchronously enter and exit from any one of the slide table inlets and outlets 12c. Moreover, when any one of the slide tables 17b is located beside the side inlet and outlet 12d, the positioning jig 18 on this slide table 17b can extend outwards from the side inlet and outlet 12d driven by the tooling translation assembly 19.

[0076] Therefore, when the two slide tables 17b cooperate to load and unload large workpieces, any two of the side inlet and outlet 12d and the two slide table inlets and outlets 12c can be used as the loading position and the unloading position; when the two slide tables 17b independently load and unload two groups of small workpieces (the two groups of small workpieces can be the same workpieces or different workpieces), the side inlet and outlet 12d and the corresponding one slide table inlet and outlet 12c can be used as the loading position and the unloading position respectively; therefore, not only can the manipulator or the automatic loading mechanism (including the stacking mechanism) be very conveniently arranged, but also the problem of misplacing during loading and unloading can be avoided. At the same time, because the side inlet and outlet is very close to the processing position, the loading and unloading efficiency is improved; and because the positioning jig increases the freedom of translation along the width direction of the bed body, the whole slide table has two degrees of freedom, and then combined with the multiple degrees of freedom (usually 5 degrees of freedom) realized on the bed body and the two sets of crossbeam modules, a redundant processing mode with super multiple degrees of freedom can be realized, which can not only perform laser cutting processing more efficiently, but also perform laser cutting processing more flexibly, so that it can be applied to more complex processing profiles and obtain higher processing accuracy.

[0077] The tooling translation assemblies 19 each include a tooling base 19a fixedly installed on the corresponding slide table 17b, a fourth rack 19b installed on the tooling base 19a and extending along the width direction of the bed body 12, and two fourth linear guide rails 19c. Among them, the fourth rack 19b is usually adjacent to one of the fourth linear guide rails 19c. The tooling base 19a can be an integral structure or a split structure, and can be flexibly selected according to the actual situation. The positioning toolings 18 each include a driving carriage 18a and a driven carriage 18b that are parallel to each other. The driving carriage 18a and the driven carriage 18b are respectively fixedly installed on the sliders of the corresponding fourth linear guide rails 19c. A fourth motor 19d is installed on the driving carriage 18a, and a fourth driving gear 19e meshing with the fourth rack 19b is synchronously rotatably sleeved on the motor shaft of the fourth motor 19d. When the workpiece is fixed on the driving carriage 18a and the driven carriage 18b, the driving carriage 18a and the driven carriage 18b move synchronously.

[0078] Therefore, by driving the fourth driving gear 19e to rotate forward and backward through the motor shaft of the fourth motor 19d, the translation of the positioning tooling 18 can be controlled, and the control accuracy is high. Further, the fourth motor 19d is preferably a servo motor, which can further improve the accuracy control of the translation of the positioning tooling 18.

[0079] The driving carriage 18a includes a driving carriage base 18a1 fixedly installed on the slider of the corresponding fourth linear guide rail 19c, and a driving carriage fixed mounting plate 18a2 and a driving carriage movable mounting plate 18a3 both installed on the driving carriage base 18a1. The driving carriage fixed mounting plate 18a2 is fixedly installed at one end of the driving carriage base 18a1 close to the side inlet / outlet 12d. A first elongated hole 18a11 extending along the width direction of the bed body 12 is provided in the middle of the driving carriage base 18a1. The driving carriage movable mounting plate 18a3 is slidably installed in the first elongated hole 18a11 through at least two bolts that can be locked or unlocked. The fourth motor 19d is installed at one end of the driving carriage base 18a1 away from the side inlet / outlet 12d.

[0080] Similarly, the driven carriage 18b includes a driven carriage base 18b1 fixedly mounted on the slider corresponding to the fourth linear guide 19c, and a driven carriage fixed mounting plate 18b2 and a driven carriage movable mounting plate 18b3 both mounted on the driven carriage base 18b1. The driven carriage fixed mounting plate 18b2 is fixedly mounted at one end of the driven carriage base 18b1 close to the side inlet / outlet 12d. A second elongated hole 18b11 extending in the width direction of the bed 12 is provided in the middle of the driven carriage base 18b1. The driven carriage movable mounting plate 18b3 is slidably fitted in the second elongated hole 18b11 through at least two bolts that can be locked or unlocked. Therefore, by adjusting the position of the active carriage movable mounting plate 18a3 on the active carriage base 18a1 and the position of the driven carriage movable mounting plate 18b3 on the driven carriage base 18b1, workpieces of different sizes can be adapted, and the versatility is good. Further, in the active carriage fixed mounting plate 18a2 and the driven carriage fixed mounting plate 18b2, a bolt hole array composed of bolt holes distributed in an array is provided on one of them, and a slot hole array composed of slot holes distributed in an array is provided on the other, further improving the applicability to workpieces of different sizes.

[0081] In this embodiment, the slide table drive assembly includes a fifth rack 21 and two fifth linear guides 20 that are installed in parallel on the slide table track 17a, and a fifth motor 22 respectively installed on the slide tables 17b. The two slide tables 17b are respectively fixedly mounted on the corresponding sliders of the two fifth linear guides 20. Fifth drive gears 23 meshing with the fifth rack 21 are synchronously rotated and sleeved on the motor shafts of the fifth motors 22. Therefore, by driving the fifth drive gears 23 to rotate forward and backward by the motor shafts of the fifth motors 22, the translation of the slide tables 17b can be achieved, and the control accuracy is high. Further, the fifth motor 22 is preferably a servo motor, which can further improve the precision control of the translation of the slide tables 17b.

[0082] Embodiment 3:

[0083] Please refer to Figures 1 - 4 , a collaborative processing trajectory planning method for a double-beam module three-dimensional laser cutting machine, characterized in that it is carried out according to the following steps:

[0084] S1. Establish the kinematic models of two sets of beam modules, and carry out according to the following steps:

[0085] S11. Establish a mechanical model. First, establish as Figure 5 and Figure 6The mechanical model of the double-beam module three-dimensional laser cutting machine shown. The first degree-of-freedom structure is the crossbeam 6, which translates along the X-axis; the second degree-of-freedom structure is the Y-axis slide 2, which translates along the Y-axis; the third degree-of-freedom structure is the Z-axis sleeve 1, which moves up and down along the Z-axis; the fourth degree-of-freedom structure is the first base of the laser, which rotates around the Z-axis; the fifth degree-of-freedom structure is the second base of the laser, which rotates around the X-axis; the sixth degree-of-freedom structure is the laser, which moves up and down along the Z-axis.

[0086] S12. Simplify the mechanical model to obtain the kinematic model. The kinematic model includes the DH coordinate systems and the DH parameter table of two sets of crossbeam modules. Specifically, the forward kinematic model is established by the MDH method, and the mechanism kinematic diagram and joint coordinate system are established as Figure 1 shown, where, x i y i z i (i = 1 to 6) represents the coordinate system of one set of crossbeam modules, and (x i )(y i )(z i )(i = 1 to 6) represents the coordinate system of the other set of crossbeam modules.

[0087] The DH parameters of the coordinate systems of two sets of crossbeam modules are obtained by the MDH representation method. The DH parameters of the two sets of crossbeam modules are the same, and the specific values of any set of crossbeam modules are shown in Table 1.

[0088] Table 1 DH parameter table of crossbeam modules

[0089]

[0090] S2. Conduct kinematic analysis on two sets of crossbeam modules, and establish the forward kinematic equation and the inverse kinematic solution equation set of the crossbeam modules.

[0091] Specifically, step S2 is carried out according to the following steps:

[0092] S21. Establish the forward kinematic equation of the crossbeam module, and carry out according to the following steps:

[0093] S211. Use the coordinate transformation matrix to represent the homogeneous transformation of coordinate system i to coordinate system i - 1, and obtain according to the MDH parameter method:

[0094]

[0095] In formula (1), a i-1 represents the length of the previous degree-of-freedom structure, that is: the offset distance along the x i-1 axis from the (i - 1)-th degree-of-freedom structure to the i-th degree-of-freedom structure of the crossbeam module; θ iRepresents the rotation angle of the current degree - of - freedom structure, that is: the angle of rotation of the \(i\) - th degree - of - freedom structure of the cross - beam module around the \(z\) i axis. For the moving joints of the cross - beam module, \(\theta\) i is a constant. For the rotating joints of the cross - beam module, \(\theta\) i is a variable; \(d\) i Represents the offset of the current degree - of - freedom structure, that is: the displacement of the \(i\) - th degree - of - freedom structure of the cross - beam module relative to the \((i - 1)\) - th degree of freedom along the \(z\) i-1 axis; for the moving joints of the cross - beam module, \(d\) i is a variable, and for the rotating joints of the cross - beam module, \(d\) i is a constant; \(s\) and \(c\) represent the abbreviations of the Sin and Cos functions respectively.

[0096] S212. Substitute the DH parameter table into Equation (1) to obtain:

[0097]

[0098] In Equation (2), \(l\) c represents the translation distance of the 4 - th degree - of - freedom structure of the cross - beam module along the \(z\) axis, and \(l\) a represents the translation distance of the 5 - th degree - of - freedom structure of the cross - beam module along the \(z\) axis, \(s\) i represents \(\sin\theta\) i , \(c\) i represents \(\cos\theta\) i .

[0099] S213. Multiply the matrices in Equation (2) successively on the right by to obtain the forward kinematic equation of the cross - beam module:

[0100]

[0101] S22. Establish the inverse kinematic solution equations of the cross - beam module and proceed as follows:

[0102] S221. Since the motions of the cross - beam 6, the Y - axis slide 2, and the Z - axis sleeve 1 are decoupled from each other, the analytical method is used to solve the joint variables \(d\) 1 , \(d\) 2 , \(d\) 3 , \(\theta\) 4 and \(\theta\) 5 . The desired pose of the 6 - th degree - of - freedom structure (i.e., the laser) of the cross - beam module is expressed as:

[0103]

[0104] In Equation (4), the upper - left 3×3 sub - matrix (\(R\)) represents the attitude of the laser cutting head; among them, each column corresponds to the unit direction vector of the end - effector coordinate system: the first column \([r\) 11 , \(r\)21 , r 31 T : Laser cutting head X-axis direction vector (relative to the base coordinate system); The second column [r 12 , r 22 , r 32 T : Laser cutting head Y-axis direction vector (relative to the base coordinate system); The third column [r 13 , r 23 , r 33 T : Laser cutting head Z-axis direction vector (relative to the base coordinate system); The rightmost column 3×1 vector (p) represents the translation vector p, that is: the position of the laser cutting head in the base coordinate system: P x : The position of the laser cutting head in the X direction; P y : The position of the laser cutting head in the Y direction; P z : The position of the laser cutting head in the Z direction; The 1 in the lower right corner indicates that the matrix is a homogeneous transformation matrix, which is used to maintain the consistency of coordinate transformation.

[0105] S222. There are 12 elements in the matrix in Equation (3), and there are 6 independent parameters. By making the corresponding elements of the matrices in Equation (3) and Equation (4) equal, we get:

[0106]

[0107] S223. Solving Equation (5) gives the inverse kinematics solution equations for the crossbeam module:

[0108]

[0109] S3. Use the improved chaotic particle swarm optimization algorithm to plan the collaborative processing trajectories of two sets of crossbeam modules, and proceed according to the following steps:

[0110] In order to make the structures of each degree of freedom operate stably and meet the constraint conditions, it is necessary to control the speed and acceleration of the movement of the structures of each degree of freedom. The commonly used method for the spatial trajectory planning of the structures of each degree of freedom is cubic or quintic polynomial interpolation. However, the former cannot make the acceleration change smoothly, and the latter has a large computational amount.

[0111] Therefore, the polynomial interpolation adopted in this embodiment better combines the advantages of both, and has certain advantages in multi-trajectory point planning. The process is as follows: In the first section of the trajectory (time t 1 ), cubic polynomial interpolation is used. In the second section of the trajectory (time t 2 ), quintic polynomial interpolation is used. In the third section of the trajectory (time t 3 ), cubic polynomial interpolation is used. Specifically, it is carried out according to the following steps S31 - S33. ​​​

[0112] S31. Obtain the initial poses and end poses of two sets of crossbeam modules.

[0113] S32. Construct a machining trajectory between the initial pose and the end pose.

[0114] S33. Divide the machining trajectory into a first-segment trajectory, a second-segment trajectory, and a third-segment trajectory in chronological order. The first-segment trajectory, the second-segment trajectory, and the third-segment trajectory are all constructed by interpolation polynomial functions. Among them, the following interpolation polynomial functions are used to construct the first-segment trajectory, the second-segment trajectory, and the third-segment trajectory:

[0115]

[0116] In Equation (7), t represents time, a j10 , a j11 , a j12 , a j13 , a j20 , a j21 , a j22 , a j23 , a j24 , a j25 , a j30 , a j31 , a j32 , a j33 all represent coefficients and jointly form a coefficient matrix a;

[0117] Use t 1 , t 2 , t 3 to represent the times of interpolation of the three-segment polynomial functions of the i-th degree-of-freedom structure of the crossbeam module respectively, and x ij represents the displacement of the i-th degree-of-freedom structure of the crossbeam module at the j-th segment of interpolation. Given the initial points x j0 , interpolation nodes x j1 and x j2 as well as the displacements of the end points x j3 , and the displacements, velocities, and accelerations between path points are all continuous, and the velocities and accelerations of the initial point and the end point are both 0, the following equations (8)-(10) can be obtained:

[0118]

[0119] θ = [0 0 0 0 0 0 x j3 0 0 x j0 0 0 x j2 x j1 T (9)

[0120] a = A -1 θ = [a​j13 a j12 a j11 a j10 a j25 a j24 a j23 a j22 a j21 a j20 a j33 a j32 a j31 a j30 T (10)

[0121] t 1 、t 2 、t 3 The sum of them is the total time for the crossbeam module to move along the collaborative processing trajectory. Equation (10) can also be written as Aa = θ.

[0122] S34. Optimize the first trajectory, the second trajectory, and the third trajectory according to the improved chaotic particle swarm optimization algorithm to obtain the collaborative processing trajectory planning with the shortest time.

[0123] Specifically, step S34 is carried out according to the following steps:

[0124] S341. Initialize the parameters, where the parameters include the number of particles M, the particle dimension D, the number of iterations T, the particle velocity range, the particle initial position range, the adaptive inertia weight, the dynamic learning factor, and the chaotic mapping function.

[0125] S342. Randomly generate M particles (a total of M×3), and substitute them into the interpolation polynomial functions of equations (8)-(10) for the first trajectory, the second trajectory, and the third trajectory to obtain the coefficient matrix of the polynomial, and at the same time obtain the interpolation polynomial function of each degree-of-freedom structure.

[0126] S343. Based on the interpolation polynomial function of each degree-of-freedom structure, calculate the fitness value of each particle, and judge whether its velocity and acceleration meet the constraint conditions: if not, eliminate the particle; if so, proceed to the next step.

[0127] Specifically, the function for calculating the fitness value of each particle is:

[0128]

[0129] In equation (11), t i1 represents the running time of the i-th degree-of-freedom structure of the crossbeam module on the first trajectory, t i2 represents the running time of the i-th degree-of-freedom structure of the crossbeam module on the second trajectory, t i3 ​Represents the running time of the i-th degree of freedom structure of the crossbeam module in the third segment of the trajectory, v ij Represents the velocity of the i-th degree of freedom structure of the crossbeam module varying with time in the j-th polynomial, v max Represents the maximum speed limit for the operation of each degree of freedom structure, a ij Represents the acceleration of the i-th degree of freedom structure varying with time in the j-th polynomial, a max Represents the maximum acceleration limit for the operation of each degree of freedom structure.

[0130] The particle velocity and particle position are determined by the following formula (12):

[0131]

[0132] In formula (12), Is the d-th dimensional component of the velocity of particle i in the t-th generation; Is the d-th dimensional component (after update) of the velocity of particle i in the (t + 1)-th generation; c 1 r 1 (p id -x id ) and c 2 r 2 (p gd -x id ) are the cognitive factor and social factor causing the change of particle velocity respectively; ω is the inertia weight; c 1 Is the self-learning factor, which measures the ability of the particle to learn from its own experience; c 2 Is the social learning factor, which measures the ability of the particle to learn from the global optimal solution; r 1 and r 2 Represent random numbers between [0, 1], used to introduce randomness and improve the search ability; p id Is the d-th dimensional component of the best position (individual extreme value) found by particle i so far; p gd Is the d-th dimensional component of the best position (global extreme value) found by the entire population.

[0133] S344. Compare the current fitness value of each particle with the fitness value of the optimal position it has experienced: If the current fitness value of the particle is better than the fitness value of the optimal position it has experienced, update the current position to the optimal position of the particle; If the current fitness value of the particle is not better than the fitness value of the optimal position it has experienced, do not update the optimal position of the particle.

[0134] S345. Compare the optimal position of the current particle population with the optimal position experienced by the particle population: If the optimal position of the current particle population is better than the optimal position experienced by the particle population, update the optimal position of the current particle population to the optimal position of the particle population.

[0135] S346. Reconstitute the particle population with new positions and velocities according to the improved chaotic particle swarm algorithm.

[0136] Specifically, the inertia weight is determined by the following formula (13):

[0137]

[0138] In formula (13), ω max represents the maximum inertia weight, and ω min represents the minimum inertia weight. represent the minimum fitness, maximum fitness, and average fitness of all particles at the d-th iteration, respectively.

[0139] To solve the problem of the shortest trajectory running time, the smaller the fitness, the closer the particle is to the optimal solution, and local search is needed to reduce the fitness; the larger the fitness, the farther the particle is from the optimal solution, and global search is needed to increase the fitness. ω is related to the iteration number and fitness of each particle, and is more flexible and efficient compared to the standard chaotic particle swarm algorithm (abbreviated as PSO).

[0140] The self-learning factor c 1 and the social learning factor c 2 also have an important impact on the performance of the algorithm. In the standard chaotic particle swarm algorithm, the learning factor is fixed. The smaller the value of the learning factor, the slower the speed change of the particle, which will lead to a slower convergence speed of the algorithm and more iteration times are required to reach the optimal solution. The larger the value of the learning factor, the faster the speed change of the particle, and the particle is likely to jump out of the current local optimal solution, but at the same time, it is also likely to skip the global optimal solution. Therefore, the selection of the learning factor needs to balance global search and local search.

[0141] In this embodiment, the learning factors are determined by the following formulas (14) and (15):

[0142] c 1 = c 1i -(c 1i - c 1f )*k / N max (14)

[0143] c 2 = c 2i +(c 2f - c 2i )*k / N max (15)

[0144] In formulas (14) and (15), c 1 and c 2 represent the self-learning factor and the social learning factor respectively, and c 1iand c 2i respectively represent the initial value of c 1 and c 2 The final value of c 1f and c 2f respectively represent the final value of c 1 and c 2 k represents the number of iteration steps, and N max represents the maximum number of iteration steps. The self-learning factor c of this embodiment 1 decreases as the number of iterations increases, and the social learning factor c 2 increases as the number of iterations increases. The dynamically changing learning factor enables the search to quickly reach the global optimum in the early stage and quickly reach the local optimum in the later stage, improving the search efficiency.

[0145] In each iteration process, the current group-optimal particle is used as the initial position of the new group, and a set of new random positions are generated through the chaotic sequence. Then, one particle in the original group is replaced with the optimal particle of the new group. In this way, the position of the group changes in each iteration process. Due to the randomness and ergodicity of the chaotic sequence, the chaotic particle swarm algorithm can effectively search the entire solution space and avoid falling into the local optimal solution. The chaotic sequence is generated by the Logistic equation as shown in Equation (16) below:

[0146] z n+1 = μz n (1 - z n ), n = 0, 1, 2,... (16)

[0147] In Equation (16), z n represents the value of the chaotic sequence at the nth iteration, and z n+1 represents the value of the chaotic sequence at the (n + 1)th iteration, and μ represents the control parameter.

[0148] When μ = 4 and 0 < z 0 < 1, the sequence generated by Equation (17) is completely in a chaotic state. Therefore, from any initial value z 0 ∈(0, 1), a chaotic sequence z 1 , z 2 , z 3 ,... can be iterated.

[0149] S347. First, use the optimal position of the particle population as the initial condition to generate the optimal position of the new chaotic particle population, and then replace the optimal position of the particle population with the optimal position of the new chaotic particle population.

[0150] Specifically, the optimal position P of the particle population g =(P g1 , P g2 , P g3 …PgD ) Map to the domain (0, 1) of the Logistic equation, and determine the new particle position using the following formula (17):

[0151]

[0152] In formula (17), a i and b i respectively represent the lower and upper limits of the value of the i-th dimensional particle position;

[0153] Taking z i0 as the initial state, generate a new chaotic sequence Z i = [z i1 , z i2 ,... z im T , and map the new chaotic sequence to the solution space through formula (12) to obtain M new chaotic particle positions

[0154]

[0155] Calculate the fitness value of the newly generated chaotic particle positions , find the optimal particle position and use to randomly replace a particle in the current particle population using the rand function.

[0156] S348. Judge whether the stop iteration condition is satisfied: If yes, output the optimal first trajectory, second trajectory, and third trajectory to obtain the collaborative processing trajectory planning with the shortest time; if not, return to step S344.

[0157] Comparative example:

[0158] In Matlab, given the initial pose A, i.e., Theta0 = [0.5, 0.8, 0.7, pi, -pi / 4], the expected end pose D, i.e., Theta1 = [1.25, 0.2, 0.4, 0.1*pi, pi / 2], and the trajectory running time of 6 s, use fifth-order polynomial interpolation to perform trajectory planning in the joint space, and obtain the values of joint position, velocity, and acceleration by calling jtraj(Theta0, Theta1, step), as Figure 2 shown. From Figure 2It can be seen that the motion, velocity, and acceleration curves of the crossbeam module obtained by fifth-order polynomial interpolation change uniformly and smoothly in the space of each degree of freedom structure. The structure design of the three-dimensional laser cutting machine is reasonable and can meet the actual cutting requirements, but the current running time has not reached the optimal. Taking the three-dimensional laser cutting machine as the research object, 4 poses of the end of the robotic arm are taken within the working range, which respectively represent the trajectory points passed by each joint of the initial point A, the middle point B, the middle point C, and the end point D as shown in Table 2:

[0159] Table 2 Nodes Passed by Each Degree of Freedom Structure

[0160]

[0161] Use the method of Example 3 to perform iterative optimization on the first-degree-of-freedom structure to the fifth-degree-of-freedom structure of the crossbeam module respectively, and at the same time use the traditional particle swarm algorithm for comparison. In the standard chaotic particle swarm algorithm (abbreviation: PSO), set the inertia weight w = 0.9, learning factor c 1 = c 2 = 2, and the other parameters are the same as those of the improved chaotic particle swarm algorithm (abbreviation: CPSO) algorithm. The optimization results are as Figure 3 shown.

[0162] The optimal time for each joint optimized by the improved chaotic particle swarm algorithm (abbreviation: CPSO) is shown in Table 3. Since the motion of each degree of freedom structure of the crossbeam module is synchronous, the maximum time in each degree of freedom structure is selected as the interpolation time for each segment in each time period. It can be seen from Table 3 that: Max(t i1 ) = 0.924s, Max(t i1 ) = 0.319s, Max(t i3 ) = 0.924s, and the total time is 2.283s. Compared with before optimization, the trajectory interpolation time is shortened by 3.717s.

[0163] Table 3 Optimal Interpolation Time for Each Degree of Freedom Structure

[0164]

[0165] As can be seen from the above, the fitness functions of the improved chaotic particle swarm optimization algorithm for the displacement-degree-of-freedom structure and the rotation-degree-of-freedom structure can converge in about 50 generations, while the standard chaotic particle swarm optimization algorithm requires about 100 steps. The fitness values of the function for optimizing the trajectory running time of the first to fifth degree-of-freedom structures by the improved chaotic particle swarm optimization algorithm are 1.805 s, 1.443 s, 0.720 s, 2.166 s, and 1.805 s respectively. The optimization times by the standard chaotic particle swarm optimization algorithm are 1.834 s, 1.537 s, 0.737 s, 2.283 s, and 1.955 s respectively. The optimization rate of the improved chaotic particle swarm optimization algorithm compared with the standard chaotic particle swarm optimization algorithm is 4.55%, and the optimization effect is better. At the same time, it can be seen from Figure 3 that during the movement of the crossbeam module, each degree-of-freedom structure remains stable, and there are no sudden changes in the speed and acceleration. Moreover, under the constraint conditions of each degree-of-freedom structure of the crossbeam module, the high efficiency of the time-optimal trajectory planning method of the present invention is verified, and the working efficiency of the laser cutting machine tool is improved.

[0166] Finally, it should be noted that the above description is only the preferred embodiment of the present invention. Under the inspiration of the present invention, those of ordinary skill in the art can make various similar representations without departing from the purpose and claims of the present invention. Such transformations all fall within the protection scope of the present invention.

Claims

1. A collaborative processing trajectory planning method for a dual-beam module three-dimensional laser cutting machine, characterized in that: Follow these steps: S1. Establish kinematic models of two sets of beam modules; S2. Perform kinematic analysis on the two beam modules, and establish the forward kinematics equations and inverse kinematics solution equations of the beam modules; S3, which is conducive to improving the chaotic particle swarm algorithm to plan the collaborative processing trajectory of the two sets of beam modules, is carried out according to the following steps: S31, obtaining the initial position and terminal position of two sets of beam modules; S32, constructing a processing trajectory between the initial posture and the end posture; S33, dividing the processing trajectory into a first trajectory segment, a second trajectory segment and a third trajectory segment in chronological order, wherein the first trajectory segment, the second trajectory segment and the third trajectory segment are all constructed by an interpolation polynomial function; S34. Optimize the first trajectory, the second trajectory and the third trajectory according to the improved chaotic particle swarm algorithm to obtain the collaborative processing trajectory planning with the shortest time.

2. The method for collaborative processing trajectory planning of a dual-beam module three-dimensional laser cutting machine according to claim 1 is characterized in that: In the step S1, the kinematic model includes two sets of DH coordinate systems and DH parameter tables of the beam modules; The step S2 is performed according to the following steps: S21. Establish the forward kinematics equation of the beam module by following the steps below: S211, using coordinate system transformation matrix Represents the homogeneous transformation from coordinate system i to coordinate system i-1, which is obtained according to the MDH parameter method: In formula (1), a i-1 represents the length of the previous degree of freedom structure, θ i Indicates the rotation angle of the current degree of freedom structure, d i Indicates the offset of the current degree of freedom structure, s and c are the abbreviations of Sin and Cos functions respectively; S212, substituting the DH parameter table into formula (1) to obtain: In formula (2), l c Indicates the value of the translation distance of the fourth degree of freedom structure of the beam module along the z-axis, l a Indicates the translation distance of the fifth degree of freedom structure of the beam module along the z-axis, s i represents Sinθ i , c i Cosθ i ; S213, right-multiply the matrices in formula (2) The forward kinematic equation of the beam module is obtained: S22. Establish the inverse kinematics solution equations for the beam module, and proceed as follows: S221. The desired posture of the sixth degree of freedom structure of the beam module is expressed as: In formula (4), the first column [r 11 ,r 21 ,r 31 ] T Represents the X-axis direction vector of the laser cutting head. The second column [r 12 ,r 22 ,r 32 ] T Indicates the Y-axis direction vector of the laser cutting head. The third column [r 13 ,r 23 ,r 33 ] T Represents the Z-axis direction vector of the laser cutting head, P x Indicates the position of the laser cutting head in the X direction, P y Indicates the position of the laser cutting head in the Y direction, P z Indicates the position of the laser cutting head in the Z direction, 1 indicates that the matrix is ​​a homogeneous transformation matrix; S222. Since the elements corresponding to the matrices in equation (3) and equation (4) are equal, we get: S223. Solve equation (5) to obtain the inverse kinematics solution equation group of the beam module:

3. The method for collaborative processing trajectory planning of a dual-beam module three-dimensional laser cutting machine according to claim 2 is characterized in that: In step S33, the following interpolation polynomial function is used to construct the first trajectory, the second trajectory and the third trajectory: In formula (7), t represents time, a j10 、a j11 、a j12 、a j13 、a j20 、a j21 、a j22 、a j23 、a j24 、a j25 、a j30 、a j31 、a j32 、a j33 They all represent coefficients and together constitute the coefficient matrix a; Let t1, t2, and t3 represent the time of the three-segment polynomial function interpolation of the i-th degree of freedom structure of the beam module, respectively. ij represents the displacement of the i-th degree of freedom structure of the beam module at the j-th segment interpolation, given the initial points x of each segment of the beam module j0 , interpolation node x j1 and x j2 and the end point x j3 The displacement, velocity and acceleration between the path points are continuous, and the velocity and acceleration of the initial point and the end point are both 0. Therefore, equations (8) to (10) can be obtained: θ=[0 0 0 0 0 0 x j3 0 0 x j0 0 0 x j2 x j1 ] T (9) a=A -1 θ=[a j13 a j12 a j11 a j10 a j25 a j24 a j23 a j22 a j21 a j20 a j33 a j32 a j31 a j30 ] T (10) The sum of t1, t2, and t3 is the total time that the beam module moves along the collaborative processing trajectory.

4. The method for collaborative processing trajectory planning of a dual-beam module three-dimensional laser cutting machine according to claim 3 is characterized in that: The step S34 is performed according to the following steps: S341, initializing parameters, wherein the parameters include the number of particles, particle dimension, number of iterations, particle velocity range, particle initial position range, adaptive inertia weight, dynamic learning factor and chaos mapping function; S342, randomly generate M particles, and substitute them into the interpolation polynomial functions of equations (8) to (10) of the first trajectory, the second trajectory, and the third trajectory to obtain the coefficient matrix of the polynomial, and at the same time obtain the interpolation polynomial function of each degree of freedom structure; S343, based on the interpolation polynomial function of each degree of freedom structure, calculate the fitness value of each particle, and determine whether its speed and acceleration meet the constraint conditions: if not, eliminate the particle; if yes, proceed to the next step; S344, comparing the current fitness value of each particle with the fitness value of the optimal position it has experienced: if the current fitness value of the particle is better than the fitness value of the optimal position it has experienced, then the current position is updated to the optimal position of the particle; if the current fitness value of the particle is not better than the fitness value of the optimal position it has experienced, then the optimal position of the particle is not updated; S345, comparing the optimal position of the current particle population with the optimal position experienced by the particle population: if the optimal position of the current particle population is better than the optimal position experienced by the particle population, then updating the optimal position of the current particle population to the optimal position of the particle population; S346, reconstructing a particle population with a new position and velocity according to an improved chaotic particle swarm algorithm; S347, firstly taking the optimal position of the particle population as the initial condition, generating the optimal position of the new chaotic particle population, and then replacing the optimal position of the particle population with the optimal position of the new chaotic particle population; S348. Determine whether the conditions for stopping iteration are met: if yes, output the optimal first, second and third trajectories to obtain the collaborative processing trajectory planning with the shortest time; if no, return to step S344.

5. The method for collaborative processing trajectory planning of a dual-beam module three-dimensional laser cutting machine according to claim 4, characterized in that: In step S343, the function for calculating the fitness value of each particle is: In formula (11), t i1 represents the running time of the i-th degree of freedom structure of the beam module in the first trajectory, t i2 represents the running time of the i-th degree of freedom structure of the beam module in the second trajectory, t i3 represents the running time of the i-th degree of freedom structure of the beam module in the third trajectory, v ij represents the speed of the i-th degree of freedom structure of the beam module in the j-th segment polynomial changing with time, v max Indicates the maximum speed limit of each degree of freedom structure operation, a ij represents the acceleration of the i-th degree of freedom structure in the j-th segment of the polynomial changing with time, a max Indicates the maximum acceleration limit of each degree of freedom structure operation; The particle velocity and particle position are determined using the following formula (12): In formula (12), is the d-th component of the velocity of particle i in the tth generation, is the d-th component of the velocity of particle i in the t+1 generation, c1r1(p id -x id ) and c2r2(p gd -x id ) are cognitive factors and social factors that cause particle velocity changes, ω is the inertia weight, c1 is the self-learning factor, c2 is the social learning factor, r1 and r2 are random numbers between [0,1], p id represents the d-th dimension component of the best position found by particle i so far, p gd represents the d-th dimension component of the best position found by the entire population.

6. The method for collaborative processing trajectory planning of a dual-beam module three-dimensional laser cutting machine according to claim 5, characterized in that: In step S346, the inertia weight is determined using the following formula (13): In formula (13), ω max represents the maximum inertia weight, ω min represents the minimum inertia weight, They represent the minimum fitness, maximum fitness, and average fitness of all particles at the dth iteration respectively; The learning factor is determined using the following formulas (14) and (15): c1=c 1i -(c 1i -c 1f )*k / N max (14) c2=c 2i +(c 2f -c 2i )*f / n max (15) In formulas (14) and (15), c1 and c2 represent the self-learning factor and social learning factor, respectively. 1i and c 2i Represent the initial values ​​of c1 and c2 respectively, c 1f and c 2f Represent the final values ​​of c1 and c2 respectively, k represents the number of iterations, N max Indicates the maximum number of iteration steps; The chaotic sequence is generated using the Logistic equation of equation (16): z n+1 =μz n (1-z n ), n=0,1,2,... (16) In formula (16), z n represents the chaotic sequence value of the nth iteration, z n+1 represents the chaotic sequence value at the n+1th iteration, and μ represents the control parameter.

7. The method for collaborative processing trajectory planning of a dual-beam module three-dimensional laser cutting machine according to claim 6, characterized in that: In step S347, the optimal position P of the particle population is g =(P g1 , P g2 , P g3 …P gD ) is mapped to the domain of the Logistic equation (0, 1), and the new particle position is determined using the following equation (17): In formula (17), a i 、b i They represent the lower and upper limits of the particle position in the i-th dimension respectively; With z i0 As the initial state, the new chaotic sequence Z is generated by using the Logistic equation i =[z i1 ,z i2 ,...z im ] T , and map the new chaotic sequence to the solution space through equation (12), and obtain M new chaotic particle positions Calculate the position of newly generated chaotic particles The fitness value of Use with Use the rand function to randomly replace a particle in the current particle population.

8. The method for collaborative processing trajectory planning of a dual-beam module three-dimensional laser cutting machine according to claim 1, characterized in that: The double-beam module 3D laser cutting machine comprises a bed, a track slide conveying mechanism and two sets of beam modules, both ends of the bed in the length direction are provided with slide inlets and outlets, the track slide conveying mechanism comprises a slide track passing through the two slide inlets and outlets at the same time and two slides that can slide along the slide track driven by the slide drive assembly, the two sets of beam modules are parallel to each other and spanned on the top of the bed in the width direction, and both can move along the length direction of the bed; The crossbeam modules include a crossbeam, a Y-axis slide, a Z-axis sleeve and a laser cutting head. Two third linear guides are installed parallel to each other on the top of the bed, both extending in the length direction of the bed. Third racks parallel to the two third linear guides are installed next to the two third linear guides. The two crossbeams extend in the width direction of the bed and are installed parallel to each other on the corresponding sliders of the two third linear guides. The crossbeams include two strip slides parallel to each other and two end connecting seats fixedly connected to the two ends of the two strip slides. The gap between the two adjacent strip slides forms a Z-axis sleeve giving groove extending in the horizontal direction. The two strip slides are installed with a second linear guide extending in the length direction thereof, one of the strip slides is installed with a second rack extending in the length direction thereof, and a third driving motor is installed on the end connecting seat. The motor shaft of each third driving motor is synchronously rotatably provided with a third driving gear respectively meshing with the corresponding third rack. The laser cutting heads are respectively installed on the lower part of the corresponding Z-axis sleeves so as to extend downward. The upper part of the Z-axis sleeves is provided with a first rack and at least one first linear guide extending in the vertical direction. The Y-axis slides are respectively mounted on the upper part of the corresponding Z-axis sleeves and are respectively fixedly connected to the sliders of the corresponding first linear guide and the second linear guide. The Y-axis slides are respectively provided with a first driving motor and a second driving motor. The motor shafts of the first driving motors are provided with a first driving gear meshing with the corresponding first rack so as to rotate synchronously. The motor shafts of the second driving motors are provided with a second driving gear meshing with the corresponding second rack so as to rotate synchronously. The laser cutting head comprises a first laser head base which can be rotatably mounted on the lower end of the Z-axis sleeve along a rotating shaft in a vertical direction, a second laser head base which can be rotatably mounted on the first laser head base along a rotating shaft extending in the length direction of the bed, and a laser which can be lifted and lowered on the second laser head base.

9. The method for collaborative processing trajectory planning of a dual-beam module three-dimensional laser cutting machine according to claim 8, characterized in that: The Z-axis sleeves each include a flat cylinder portion with a cylindrical structure and a cylindrical portion coaxially integrally formed at the bottom of the flat cylinder portion, the cylindrical portion is provided with the laser cutting head extending downwardly, the outer walls on both sides of the width direction of the flat cylinder portion are lifting guide planes parallel to each other, the spacing between two adjacent lifting guide planes is smaller than the diameter of the corresponding cylindrical portion, each lifting guide plane is provided with at least one of the first linear guide rails extending in the vertical direction, one of the lifting guide planes of the Z-axis sleeve is provided with the first rack extending in the vertical direction, and the Y-axis slides are respectively mounted on the outside of the corresponding flat cylinder portion.

10. The method for collaborative processing trajectory planning of a dual-beam module three-dimensional laser cutting machine according to claim 9, characterized in that: The circumferential outer wall of the flat cylinder portion is formed by two oppositely disposed lifting guide planes and two oppositely disposed arcuate surfaces, the arcuate surfaces are all arcuate structures convex outward, and the lifting guide planes and the arcuate surfaces both extend in the vertical direction; The Y-axis sliding seat of the annular structure is surrounded by two relatively arranged slider mounting assemblies and two relatively arranged buckle assemblies. The slider mounting assemblies each include a crossbeam slider mounting seat and two sleeve slider mounting seats. The crossbeam slider mounting seat includes a vertical mounting plate extending vertically and a slider connecting plate formed by bending outward from the bottom of the vertical mounting plate. The two slider connecting plates are respectively parallel to the corresponding upper supporting surfaces and are each provided with a Y-direction slider connecting structure. The four sleeve slider mounting seats are each provided with a Z-direction slider connecting structure. The outer sides of the sleeve slider mounting seats are each provided with a connecting boss adapted to the corresponding vertical mounting plate, and each connecting boss can be respectively adjusted to be installed on the inner side of the corresponding vertical mounting plate. The buckle assemblies each consist of at least one vertically arranged buckle, and both ends of each buckle are bent inwardly to form a buckle connecting arm. The side walls of each connecting boss are each provided with a connecting arm slot adapted to the corresponding buckle connecting arm, and each buckle connecting arm can be respectively adjusted to be installed in the corresponding connecting arm slot. Two first linear guide rails extending in the vertical direction are installed on the two lifting guide planes, two slider mounting assemblies are arranged one-to-one on the outside of the two lifting guide planes, two buckle assemblies are arranged one-to-one on the outside of the two arc-shaped surfaces, four Z-direction slider connection structures are fixedly connected to the sliders of the four first linear guide rails one-to-one, and the first driving motor is installed on the beam slider mounting seat close to the first rack; The two Y-direction slider connection structures are fixedly connected to the sliders of the two second linear guide rails in a one-to-one correspondence, and the second driving motor is installed on the beam slider mounting seat away from the first rack.

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