A circular or spherical part layout system convergence judgment method, electronic equipment and storage medium

Abstract

The application discloses a kind of circular or spherical part layout system convergence judgment method, electronic equipment and storage medium, using discrete element method to be dispersed into independent unit with each circle or ball in container;According to the degree of collision deformation selection model;Based on impulse principle, the contact force between circle or ball is calculated;The motion differential equation of single circle or ball in vertical direction is established, and the second-order transfer function is obtained;Respectively, time domain model and complex frequency domain model are established, and the convergence under single disturbance and multiple disturbance is simulated and verified;By adjusting the disturbance amount value, the angle between the center line of the two intersecting circles and the horizontal direction, repeat the steps to predict the convergence under different conditions. Different types of circular (spherical) objects can be used to provide efficient and accurate convergence determination for layout optimization, maximize the use of raw materials and reduce waste. Avoid the problem of layout divergence caused by unstable object movement.

Description

Technical Field

[0001] This invention relates to the field of layout technology, and in particular to a layout system for equal-circular (spherical) parts or a convergence analysis and judgment method for solving the motion convergence of circular (spherical) parts, electronic equipment and storage medium. Background Technology

[0002] Layout technology is a key technology for optimizing material utilization in manufacturing. It is mainly applied in fields such as sheet metal cutting, garment tailoring, logistics packaging and transportation, and furniture manufacturing. For example, in sheet metal manufacturing industries such as shipbuilding, aircraft, and automobiles, a large number of curved sheet metal parts need to be processed. For instance, when laser cutting rectangular sheet metal to obtain round parts of pre-defined dimensions, to save material, these round parts are arranged on the raw material sheet before cutting, aiming to achieve a higher material utilization rate during material cutting. Its core objective is to reduce resource waste, lower costs, and improve economic efficiency by efficiently arranging parts on the raw material.

[0003] Current nesting algorithms generally rely on satisfying geometric constraints, achieving the nesting goal through the design of appropriate nesting strategies and optimization algorithms. The improvements are mainly reflected in computational techniques, with limited gains in computational efficiency and performance. In recent years, research on nesting problems has encountered a bottleneck, lacking new breakthroughs.

[0004] Inspired by the phenomenon that loose objects become denser after being vibrated and compacted, this method transforms the layout of graphic parts into the movement of a group of disturbed objects within a confined area. Adjusting the position and orientation of each graphic element is equivalent to the planar motion of a single object, and the optimization process of graphic layout can be viewed as the motion evolution of an object system. This is a novel approach completely different from traditional layout algorithms. Preliminary research shows that this method can solve the graphic layout problem, with promising computational speed and layout results.

[0005] Currently, it is possible to simulate and study real-world physical phenomena using computer graphics and computer simulation technologies, thereby simulating object motion and solving layout problems. The objects to be arranged can be transformed into the movement of a group of disturbed animals within a restricted area. Under the condition of satisfying geometric constraints (no overlap, no exceeding boundaries), adjusting the position and orientation of the objects to be arranged is equivalent to the movement of a single object. The layout optimization process can be viewed as the motion evolution of an object system. By adjusting the position and orientation of the objects to be arranged, the goal of optimal arrangement can be achieved. Whether the object motion converges will affect the final layout result. If the object motion is not convergent, meaning the moving object will continue to move indefinitely, the layout result will likely be divergent. Therefore, it is essential to determine the convergence of the object motion before using computer simulation.

[0006] Currently, no existing technologies have addressed the convergence problem of nesting systems. For example, Chinese patent CN116719320A proposes a method and system for trajectory tracking control and obstacle avoidance of wheeled robots, which can improve the motion control accuracy and stability of robots, but does not address the convergence problem of group motion. Chinese patent CN114676904A proposes a nesting and approaching method for two-dimensional irregular parts based on relational rectangles, which can efficiently and accurately complete local approaching in the nesting process based on blank discretization methods. However, this invention solves the problem of primitive overlap in graphic nesting, which is a static geometric positional relationship problem and does not address the dynamic convergence problem of the motion system. Another Chinese patent provides a nesting method and system for two-dimensional irregular parts based on contour matching, which effectively enhances the diversity of parts in the nesting process and achieves efficient nesting layout while ensuring optimal matching between parts. Although this patent has advantages in the field of two-dimensional irregular part nesting, it lacks a specific method to solve the motion convergence problem of circular (spherical) parts. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to overcome the above-mentioned technical defects and provide a convergence judgment method, electronic device and storage medium for a circular or spherical parts layout system, so as to analyze and judge the convergence of the motion of circular (spherical) parts in a container. It can provide efficient and accurate convergence judgment for different types of circular (spherical) objects in the field of layout optimization, maximize the utilization of raw materials and reduce waste.

[0008] At the same time, the present invention can also solve the problem of layout dispersion caused by unstable object movement when dealing with the layout problem of round (spherical) parts.

[0009] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0010] A method for determining the convergence of a circular or spherical parts layout system includes the following steps:

[0011] S1: Discrete each circle or sphere in the container into independent units using the discrete element method;

[0012] S2: Select either a hard sphere model or a soft sphere model based on the degree of collision deformation;

[0013] S3: Calculate the normal and tangential contact forces between circles or spheres based on the impulse principle;

[0014] S4: Determine the average number of contacts using the contact number theory;

[0015] S5: Establish the differential equation of motion for a single circle or sphere in the vertical direction, and obtain it through the Laplace transform.

[0016] To a second-order transfer function;

[0017] S6: Based on the aforementioned equation of motion and the aforementioned transfer function, establish the time-domain model and the complex frequency domain model, respectively.

[0018] The model is used to simulate and verify its convergence under single and multiple perturbations.

[0019] S7: By adjusting the perturbation value, the duration of action, and the angle between the line connecting the centers of the two intersecting circles and the horizontal direction, repeat steps S1–S6 to predict convergence under different conditions.

[0020] In the above technical solutions, the hard ball model is used for instantaneous collisions, scenarios with no continuous contact time, and no deformation during collision; the soft ball model is used for scenarios with continuous contact time, simultaneous collisions of three or more circles or spheres, and scenarios where objects are allowed to overlap or undergo virtual deformation.

[0021] In the above technical solution, the normal contact force is represented by the instantaneous impulse I and the Dirac function, and the tangential contact force is determined by the product of the normal contact force and the static friction coefficient.

[0022] In the above technical solution, the average number of contacts is 2N under frictionless conditions and N+1 when friction is considered, where N is the translational degree of freedom of the circle or sphere.

[0023] In the above technical solution, when establishing the differential equation of motion of a single circle or sphere in the vertical direction, the final position and height of the circle are regarded as the output of the nesting system, while the various forces affecting the motion state of the circle are regarded as the input of the system. The various forces include at least contact force and gravity.

[0024] In the above technical solution, the second-order transfer function is: Where m is the mass of the circle or sphere, d is the air drag coefficient, and k is the stiffness coefficient.

[0025] In the above technical solution, the time-domain model is used to output the final position and height of the circle and the kinetic energy of the circle after the disturbance.

[0026] In the above technical solution, the time-domain model outputs position-time curves and kinetic energy-time curves to verify energy dissipation and steady-state convergence.

[0027] In the above technical solution, the complex frequency domain model verifies whether the system response asymptotically reverts to the equilibrium state through step, ramp, and continuous signal inputs.

[0028] An electronic device includes a processor, a memory, and a program stored in the memory and executable on the processor, wherein the program, when executed by the processor, performs the steps of any of the methods described above.

[0029] A computer-readable storage medium, characterized in that the storage medium stores a program, which, when executed by a processor, implements the steps of any of the methods described above.

[0030] The beneficial effects of this invention are:

[0031] The present invention provides a method for determining the convergence of a circular or spherical arrangement system, an electronic device, and a storage medium for analyzing and determining the motion convergence of circular (spherical) parts within a container.

[0032] The method of this invention uses the discrete element method, solves dynamic differential equations and system transfer functions, and uses time-domain and complex frequency-domain models for simulation to intuitively present energy dissipation and steady-state convergence, and makes an accurate judgment on the convergence of the sorting system.

[0033] Compared with existing technologies, this invention enables the effective prediction of the convergence of the layout results when dealing with the layout problem of circular (spherical) parts, and avoids the layout divergence problem caused by the instability of the object's motion.

[0034] This method can quickly simulate nesting systems for different types of circular (spherical) objects, as well as boundary conditions and constraints, and effectively predict the convergence of circular (spherical) nesting systems. It provides an efficient and accurate convergence determination method for the field of nesting optimization, maximizes the utilization of raw materials, reduces waste, and has significant practical application value. Attached Figure Description

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0036] Figure 1 This is a flowchart of a convergence analysis and judgment method for a circular (spherical) nesting system according to an embodiment of the present invention.

[0037] Figure 2 It is a time-domain model established based on the dynamic differential equation of the circle according to the present invention.

[0038] Figure 3 It is a complex frequency domain model established based on the transfer function of the system according to the present invention.

[0039] Figure 4 This is a schematic diagram of the results of multiple perturbation locations in the time-domain model of the present invention.

[0040] Figure 5 This is a schematic diagram of the kinetic energy results under multiple perturbations in the time-domain model of the present invention.

[0041] Figure 6 This is a schematic diagram of the position result of a single perturbation in the complex frequency domain model of the present invention. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0043] Example 1

[0044] The present invention provides a convergence analysis and judgment method for a circular (spherical) parts layout system, belonging to the field of intelligent optimization layout in mechanical processing. For example, in laser cutting, when it is necessary to cut several circular parts with known part parameters from a raw material plate, the raw material can be maximized and waste reduced by using a layout method based on motion simulation. At the same time, the method of the present invention is used to judge whether the layout system has convergence, thereby making an advance judgment on the layout result.

[0045] The specific process is as follows: Figure 1 As shown, the circles (spheres) in the entire circular (spherical) part layout system are discretized using the discrete element method. A suitable collision model is selected, and the collision separation process between circles is handled using the impulse principle. In the mechanical analysis stage, the resultant external force and average number of contacts for each circle are calculated, the dynamic differential equation is established, and the corresponding transfer function is solved. Finally, based on the dynamic differential equation and transfer function, a time-domain model and a complex frequency-domain model are established. The motion of the circles is simulated under different conditions of single and multiple disturbances to verify the dynamic response of the system under different disturbances. This method can effectively predict the convergence of the circular (spherical) part layout system, and has the characteristics of high computational efficiency and reliable accuracy. It is suitable for the field of industrial layout optimization and has significant practical application value. The method of this invention includes the following steps:

[0046] I. Analysis of the circles within the container using the discrete element method. The discrete element method simulates the mechanical behavior of a discrete system by establishing a contact force model between the circles. During the simulation, the motion state of each circular element is determined by the contact forces it experiences. The accumulation of these discrete mechanical behaviors ultimately manifests as the macroscopic mechanical properties of the system. This method studies the dynamic behavior between the circles within the container by accurately describing their interactions.

[0047] 2. Select a suitable collision model based on the deformation of the circle during collision.

[0048] If the stress on the surface of the circle during the collision is small, there is no sustained contact time, and no deformation occurs during the collision, a hard sphere model can be used. This model treats the collision as an instantaneous event, disregarding the duration of the collision; it also assumes that the circle does not deform during the entire collision process. This model only considers pairwise collisions and ignores the case of multiple circles colliding simultaneously.

[0049] The soft sphere model is often used in scenarios where circles overlap or virtually deform during collisions. It replaces actual physical deformation by allowing numerical overlap between circles. The collisions between circles need to last for a certain time, and the number of colliding circles is not just two, but three or more circles colliding simultaneously.

[0050] During a collision, the circle undergoes both translation and rotation. After the collision, not only does its velocity change, but its relative velocity also changes, and energy is also lost.

[0051] III. Force analysis of the circle: The surface contact force is the impact force caused by the impulse applied to the circle. This analysis method is applicable to both hard and soft ball models, handling both high-speed collisions and static friction between circles. Taking any two contacting circles in the system as an example, the magnitude of the normal contact force is equal to the instantaneous force generated by the impulse I required to separate the two circles. The Dirac function is then introduced. The Dirac delta function (δ function for short) can express an impact force of impulse I as:

[0052]

[0053] In summary, the normal contact force is:

[0054] F n =F(t)=Iδ(t-t0);

[0055] In the formula: t is the time variable, and t0 is the time during which the impulse is applied.

[0056] For tangential contact forces, assuming that when a unit circle is subjected to an impulse, only static friction occurs between the circles, and kinetic friction is neglected, then the tangential contact force and the normal contact force satisfy the following relationship:

[0057] F t =μ·F n =μ·Iδ(t-t0);

[0058] In the formula: μ is the static friction coefficient.

[0059] IV. Determining the average number of contacts between circles within the container using contact number theory. Based on the internal structural characteristics of the nesting system, this parameter is calculated by statistically analyzing the contact relationships between adjacent circles. Since circles possess perfect rotational symmetry, only their translational degrees of freedom need to be considered in the analysis, without special treatment of rotational degrees of freedom. Specifically, under frictionless conditions, the average number of contacts in the system is 2N; however, when considering frictional effects, the average number of contacts simplifies to the number of degrees of freedom plus N+1, where N represents the number of degrees of freedom of the circle.

[0060] V. Establish the differential equation of motion for the circle and solve for the transfer function. Based on the force analysis and average contact number calculation results of the circle, the differential equation of motion for the circle can be established. First, sum the net external forces acting on a single circle and calculate the net force components in the X and Y directions respectively.

[0061]

[0062] In the formula: F x The net force acting on the circle in the X direction;

[0063] F y The net force acting on the circle in the X direction;

[0064] I represents the magnitude of the impulse applied to the circle;

[0065] t0 is the duration of the impulse.

[0066] It is the angle between the line connecting the centers of two intersecting circles and the horizontal direction.

[0067] After determining the net external force acting on the circle, its differential equation of motion can be solved. To simplify the analysis model, this method only considers the case where the circle collides with the bottom boundary of the container. Since the analysis of motion in the horizontal direction is similar to that in the vertical direction, except that the influence of gravity is omitted, the horizontal motion of the unit circle is not considered; only its vertical motion is considered. Combining Newton's second law, the differential equation of motion of the circle is obtained:

[0068]

[0069] In the formula: m is the mass of the circle; d is the air resistance; k is the stiffness coefficient; and μ is the static friction coefficient.

[0070] By introducing control theory, the final position and height y of the circle is considered as the output of the system, while the various forces affecting the circular motion state (including contact forces, gravity, etc.) are considered as the inputs of the system. A Laplace transform is then performed on the system's dynamic differential equations.

[0071]

[0072] In the formula: s is a complex variable;

[0073] Under zero initial conditions, the transfer function of the system is obtained after simplification:

[0074]

[0075] From the obtained transfer function of the system, we can see that the motion of the circle inside the container is a second-order system. Therefore, the convergence of the system can be analyzed by analyzing the transfer function.

[0076] VI. Establishing Time-Domain and Complex Frequency-Domain Models: The time-domain model directly solves the differential equations to verify energy dissipation and steady-state convergence; the complex frequency-domain model verifies the response characteristics of the transfer function to different disturbances. The simulation process is based on the modular simulation platform MATLAB / Simulink. Time-domain and complex frequency-domain models are constructed according to the dynamic differential equations and transfer functions, respectively.

[0077] (1) Time-domain model

[0078] The time-domain model is used to output the final position and height of the circle, as well as its kinetic energy after the disturbance. The position-time curve reflects the change characteristics of the circle's position and height, while the kinetic energy-time curve reflects the energy dissipation law of the system. From the simulation results, the magnitude of each value at different times can be observed intuitively, thus obtaining specific information about the changes in output over time.

[0079] Figure 2 It is a time-domain model established based on the dynamic differential equation of a circle, which defines three perturbation effects: perturbation 1 is a boundary constraint force. When the circle contacts the bottom of the container, it prevents the circle from penetrating the boundary and reverses the direction of motion through an instantaneous impulse. Perturbation 2 and 3 are used to simulate multi-body interactions, including the magnitude of the impulse applied when separating intersecting circles and the angular relationship between the circles. The duration of each perturbation is controlled by condition triggering.

[0080] Figure 2It is a time-domain model established according to the dynamic differential equation of a circle. The solid line in the figure indicates that this module will be in a triggered state from the start of the simulation until the end of the simulation; the dashed line indicates that this module will only be triggered when the conditions are met. Among them, the initial height y is the position height x0 of the circle at time zero; the kinetic energy of the circle is related to the speed and position of the circle, and is visualized with the position of the circle through the result display module; the system stiffness k·u is a unique property of the system itself, and u is the position of the circle; the air resistance when the circle moves is d·v, where v is the speed of the circle; the gravity m·g is the external force acting on the circle; m·a is the acceleration of the circle; the disturbance quantity 1 (shown as module D1 in the figure) is the boundary constraint force. When the circle touches the bottom of the container, it prevents penetration through an instantaneous impulse and reverses the direction of motion. The triggering condition of the illustrated condition module 1 is that the position height of the circle is less than 1. When the action condition of condition module 1 is satisfied, the condition control subsystem 1 will control the action of the disturbance quantity 1 (module D1); the disturbance quantities 2 and 3 (shown as modules D2 and D3 in the figure) are used to simulate multi-body interactions, including the magnitude of the impulse applied when separating and intersecting circles and the angular relationship between circles, and the action time of the disturbance quantities is controlled through condition modules 2 and 3. The triggering time of the illustrated disturbance quantity 2 (module D2) is 10 ≤ u1 < 11, and the triggering time of the disturbance quantity 3 (module D3) is 40 ≤ u1 < 41. When the action conditions of condition modules 2 and 3 are satisfied, the condition control subsystems 2 and 3 will control the action of the disturbance quantities 2 and 3 (modules D2 and D3), where clocks 1 and 2 are the inputs of condition modules 2 and 3.

[0081] (2) Complex frequency-domain model

[0082] The complex frequency-domain model is used to study the dynamic response characteristics of the system under the action of different excitation signals. When all excitation signals disappear, if the system output can asymptotically return to the initial equilibrium state, the system is determined to be stable.

[0083] Figure 3 It is a complex frequency-domain model established according to the transfer function of the system. Among them, m·y represents the gain magnitude of the constant signal, and the value of the constant signal does not change with time; d·y represents the gain magnitude of step signal 1. Step signal 1 has a step at t = 0. When t < 0, its value is 0, and when t > 0, its value is d·y; m·g is the slope of the ramp signal, and the ramp signal is represented as a signal that linearly increases with time starting from zero; the D module represents the disturbance quantity, which is the gain magnitude of step signal 2. The step time of step signal 2 is t = t0. When t < t0, its value is 0, and when t > t0, its value is the magnitude of the disturbance quantity (module D). And it is not inherent to the system but comes from external interference. This model is mainly used to verify the convergence problem of the system under the action of this step signal.

[0084] VII. Change the model parameters and repeat the simulation experiment.

[0085] The model analyzes different circles by dynamically adjusting three key parameters or disturbances: the magnitude of the impulse, the duration of its action, and the angle between the line connecting the centers of the circles and the horizontal direction. Within the entire system, each circle experiences different forces due to its different spatial location, and the duration of the impulse also varies. Therefore, different circles can be analyzed by adjusting these three key parameters.

[0086] Once convergence is determined, several circular parts with known part parameters can be cut from the raw material plate according to the layout results, maximizing the utilization of raw materials and reducing waste.

[0087] Example 2

[0088] In the time domain, different circular motion outcomes are simulated by changing the perturbation amount. At T = 10s and 40s, the circle is subjected to perturbation amounts d1(t) and d2(t) respectively. Figure 2 The diagram shows module D2), d2(t) (disturbance 3( Figure 2 The diagram shows the function of module D3.

[0089] Figure 4 The simulation results of the circle's position and height in the time-domain model are presented. The images show that the circle eventually comes to a stationary position, and its position and height no longer change over time. Therefore, the system is considered stable at this point.

[0090] Figure 5 Simulation results of the kinetic energy of the circle in the time-domain model are presented. The graphs show that the kinetic energy of the circle exhibits an oscillating decay trend. When the circle is subjected to a disturbance, its kinetic energy increases and then gradually decays to zero. At T = 10s and 40s, the circle is subjected to a disturbance, its kinetic energy increases, and then decreases to zero, remaining stationary. This indicates that the circle is not unable to remain stationary after being subjected to a disturbance; rather, its kinetic energy gradually decays to zero, and the circle remains stationary. Therefore, the system is considered stable at these times.

[0091] In the complex frequency domain, the convergence of the system under external disturbances at different times is verified by changing the step time of the step signal. At T = 40s, the circle is subjected to a disturbance u1(t). The disturbance u1(t) is... Figure 3 The D module contains the disturbance quantity.

[0092] Figure 6 Simulation results of system convergence in the complex frequency domain model are presented. The step time of step signal 2 is t = 40s. When t < 40s, its value is 0; when t > 40s, its value is the magnitude of the disturbance (D module). This example illustrates that the system will deviate from its equilibrium position due to the disturbance, and after a period of time, it will return to its original equilibrium state. Therefore, the system is considered stable at this point.

[0093] The simulation results show that when the disturbance changes, the position and height of the circle also change. The motion state of the circle can be observed intuitively, and it can be judged whether its motion has convergence, as well as the position and height of the circle when it finally stays still after it tends to a steady state.

[0094] Once convergence is determined, several circular parts with known part parameters can be cut from the raw material plate according to the layout results, maximizing the utilization of raw materials and reducing waste.

[0095] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for determining the convergence of a circular or spherical parts layout system, characterized in that... The process includes the following steps: S1: Discretize each circle or sphere within the container into independent elements using the discrete element method; S2: Select a hard sphere model or a soft sphere model based on the degree of collision deformation; S3: Calculate the normal and tangential contact forces between the circles or spheres based on the impulse principle; S4: Determine the average number of contacts using contact number theory; S5: Establish the differential equation of motion for a single circle or sphere in the vertical direction, and obtain the second-order transfer function through Laplace transform; S6: Based on the differential equation of motion and the transfer function, establish a time-domain model and a complex frequency-domain model respectively, and perform simulation verification on the convergence under single and multiple perturbations. S7: By adjusting the perturbation value, the duration of action, and the angle between the line connecting the centers of the two intersecting circles and the horizontal direction, repeat steps S1–S6 to predict convergence under different conditions.

2. The convergence judgment method for a circular or spherical parts layout system according to claim 1, characterized in that... The hard ball model is used for instantaneous collisions with no sustained contact time and no deformation during the collision; the soft ball model is used for scenarios with sustained contact time, three or more circles or spheres colliding simultaneously, and where objects are allowed to overlap or undergo virtual deformation.

3. The convergence judgment method for a circular or spherical parts layout system according to claim 1, characterized in that... The normal contact force is represented by the instantaneous impulse I and the Dirac function, and the tangential contact force is determined by the product of the normal contact force and the static friction coefficient.

4. The convergence judgment method for a circular or spherical parts layout system according to claim 1, characterized in that... The average number of contacts is 2N under frictionless conditions and N+1 when friction is considered, where N is the translational degree of freedom of the circle or sphere.

5. The convergence judgment method for a circular or spherical parts layout system according to claim 1, characterized in that... The final position and height of the circle are considered as the output of the layout system, while the various forces affecting the state of the circle's motion are considered as the input of the system. These forces include at least contact force and gravity.

6. The convergence judgment method for a circular or spherical parts layout system according to claim 1, characterized in that... The second-order transfer function is: ； in The mass of a circle or sphere The air drag coefficient, This is the stiffness coefficient.

7. The convergence judgment method for a circular or spherical parts layout system according to claim 1, characterized in that... The time-domain model is used to output the final position and height of the circle and the kinetic energy of the circle after the perturbation. The position-time curve and kinetic energy-time curve are output to verify energy dissipation and steady-state convergence.

8. The convergence judgment method for a circular or spherical parts layout system according to claim 1, characterized in that... The complex frequency domain model verifies whether the system response asymptotically reverts to an equilibrium state through step, ramp, and continuous signal inputs.

9. An electronic device comprising a processor, a memory, and a program stored in the memory and executable on the processor, wherein the program, when executed by the processor, performs the steps of any of the methods described above.

10. A computer-readable storage medium, characterized in that, The storage medium stores a program that, when executed by a processor, implements the steps of the method described in any one of claims 1-8.

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