Numerical simulation method and device for capturing space debris by flexible rope net

Abstract

The invention provides a numerical simulation method and device for capturing space debris through a flexible rope net, and belongs to the field of spaceflight. The method comprises the following steps: respectively dividing a flexible rope net and space debris to be captured into rope segment basic units and spherical basic units; calculating the internal force of each rope segment basic unit in the flexible rope net, and further establishing a mechanical simulation model of the flexible rope net; establishing a mechanical simulation model of the space debris; and based on the mechanical simulation model of the flexible rope net and the mechanical simulation model of the space debris, in combination with the division result of the space debris, establishing a contact mechanical simulation model of the space debris and the flexible rope net, thereby realizing numerical simulation of capturing the space debris by the flexible rope net. According to the method, flexible rope net simulation of million node orders of magnitude can be carried out, and irregular fragments can be described in the form of a ball cluster combination model while the simulation precision is maintained, so that the calculation amount is greatly reduced, and efficient and accurate simulation of the process of capturing highly irregular fragments by the rope net is realized.

Description

Technical Field

[0001] The invention belongs to the field of aerospace, and in particular relates to a numerical simulation method and a device for capturing space debris with a flexible rope net. Background Art

[0002] With the rapid development of space exploration and commercial space activities, the number of spacecraft in orbit is also increasing. Currently, there are thousands of spacecraft in orbit, and this number is expected to continue to grow in the next decade. The possibility of failed spacecraft colliding with other objects in orbit gradually increases, which dramatically increases the amount of space debris and aggravates the deterioration of the near-Earth space environment.

[0003] In order to ensure that the space environment will not continue to deteriorate in the future, active removal of space debris has been put on the development agenda of space technology in various countries. At present, the use of dedicated spacecraft for space-based capture is a relatively mature method. Among them, the space flexible rope net capture is based on the idea of ​​fault-tolerant capture. The space flexible rope net is composed of multiple sub-agents and irregular flexible nets. The flexible rope net is controlled to unfold and wrap the target in space to improve the capture success rate. This method can be applied to capture multiple space debris of different shapes and sizes, has a greater fault-tolerant advantage, and has become a research hotspot in the current field of space debris removal.

[0004] However, the flexible rope net system has a complex parallel topological structure, and the topological configuration changes in real time. The dynamic behavior of the coupling system composed of irregular flexible rope nets and non-cooperative targets is very complex, including flexible body dynamics, rigid-flexible coupling dynamics, and rigid-flexible coupling body collision dynamics, etc., showing multi-scale, high-dimensional, and strongly nonlinear dynamic behaviors, which poses a great challenge to the prediction of the dynamic behavior of the capture process. In particular, existing methods can only handle space debris with simple shapes such as spheres, and cannot consider the complex geometric shapes of real space debris. Therefore, a more efficient and accurate numerical simulation method for the capture of space debris by flexible rope nets is urgently needed. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and propose a numerical simulation method and device for capturing space debris with a flexible rope net. The present invention can simulate a flexible rope net with millions of nodes, and can depict irregular debris in the form of a ball cluster combination model while maintaining the simulation accuracy, thereby greatly reducing the amount of calculation and achieving efficient and accurate simulation of the process of capturing highly irregular debris with a rope net. The simulation results can guide the design of the space debris capture process to improve its success rate and efficiency, and meet the needs of the space debris removal mission.

[0006] The first embodiment of the present invention provides a numerical simulation method for capturing space debris using a flexible rope net, comprising:

[0007] Each rope of the flexible rope net is evenly divided into a plurality of rope segment basic units, wherein each rope segment basic unit includes nodes at both ends of the rope segment and a spring damper connecting the two nodes, the mass of the rope segment is evenly distributed on the nodes at both ends, and the non-shared nodes of adjacent rope segments are also connected by spring dampers; the surface of the space debris to be captured is divided into a plurality of adjacent spherical basic units, and all the spherical basic units form a spherical cluster combination model;

[0008] Based on the division result of the flexible rope net, the internal force of each basic unit of the rope segment is calculated, and then a mechanical simulation model of the flexible rope net is established;

[0009] Establishing a mechanical simulation model of the space debris;

[0010] Based on the mechanical simulation model of the flexible rope net and the mechanical simulation model of the space debris, combined with the division result of the space debris, a contact mechanical simulation model of the space debris and the flexible rope net is established, thereby realizing the numerical simulation of the flexible rope net capturing the space debris.

[0011] In a specific embodiment of the present invention, the establishment of the mechanical simulation model of the flexible rope net includes:

[0012] 1) Calculate the internal force of each basic unit of rope segment;

[0013] The tension T of any rope segment p is p The constitutive model of is expressed as:

[0014]

[0015] in, is the stiffness of the rope segment p; E is Young's modulus; is the cross-sectional area of ​​the rope segment; is the initial length of segment p; is the damping coefficient of segment p, ρ s is the density of the rope segment p, ζ is the rope segment damping ratio, Δr p is the relative displacement of two nodes in segment p, is the relative velocity of the two nodes of segment p, is the diameter of the rope segment p;

[0016] 2) Based on the results of step 1), the dynamic equation of the flexible rope net is established;

[0017] Based on formula (1), the dynamic equation of any node i is established as:

[0018]

[0019] Where i = 1, 2, 3...n; n is the total number of nodes of the flexible rope net; m i represents the quality of the i-th node; r i , and are the position, velocity and acceleration vector of node i respectively; n e is the total number of adjacent rope segments of node i; N i,T is the normal contact force on node i from the space debris T, f i,T is the friction force exerted on node i by space debris T; η i,T represents the contact identification function between node i and space debris T. When node i comes into contact with space debris T, η i,T =1, otherwise η i,T =0;

[0020] Equations (1) and (2) constitute the mechanical simulation model of the flexible rope net.

[0021] In a specific embodiment of the present invention, the step of establishing the mechanical simulation model of the space debris comprises:

[0022]

[0023] Among them, r T , are the position and acceleration vector of the center of mass of space debris T; m T is the mass of space debris T; is the normal contact moment from node i of the flexible rope net; is the friction torque of node i of the flexible rope network; ntotal represents the total number of nodes of the flexible rope network in contact with the space debris T; I T represents the inertia matrix of space debris; ω T , are the angular velocity and angular acceleration of the space debris T respectively.

[0024] In a specific embodiment of the present invention, the step of establishing a contact mechanics simulation model between the space debris and the flexible rope net comprises:

[0025] 1) According to the flexible rope net node position vector r i and the space debris center of mass position vector r T , calculate the relative distance between the flexible rope net node i and each spherical basic unit in the ball cluster combination model;

[0026] 2) Based on the result of step 1), determine:

[0027] If the relative distance between node i and any spherical basic unit is less than or equal to 0, it is determined that node i is in contact with the spherical cluster combination model; otherwise, no contact occurs;

[0028] 3) Based on the result of step 2), the contact force is calculated for the contacting flexible rope net node and ball cluster combined model;

[0029] Among them, the calculation expression of the normal contact force generated during contact is as follows:

[0030]

[0031] Among them, N i,k is the normal contact force between the node i of the flexible rope net and the spherical basic unit k in the ball cluster combination model; is the stiffness coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model, is the damping coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model; is the penetration depth of the flexible rope net node i in contact with the spherical basic unit k in the ball cluster combination model, is the speed at which the flexible rope net node i contacts the spherical basic unit k in the ball cluster combination model; is the normal contact vector of the flexible rope net node i in contact with the spherical basic unit k in the spherical cluster combination model; nd is the number of spherical basic units in the spherical cluster combination model that are in contact with node i;

[0032] The friction force generated during contact is calculated as follows:

[0033]

[0034] Among them, f i,k is the tangential friction force between the flexible rope net node i and the spherical basic unit k in the ball cluster combination model, expressed as:

[0035]

[0036] Among them, μ s is the static friction coefficient, μ d is the coefficient of dynamic friction, and ε is the transition value of the conversion between static and dynamic friction.

[0037] In a specific embodiment of the present invention, it also includes:

[0038] According to the displacement vector and velocity vector of each node in the flexible rope net at the current moment, the internal force of the flexible rope net at the current moment is calculated based on formula (1), and then the fourth-order Runge-Kutta method is used to solve formula (2) to obtain the position vector and velocity vector of each node in the flexible rope net at the next moment; according to the position vector and velocity vector of each node in the flexible rope net at the current moment, and the position vector and velocity vector of each spherical basic unit in the space debris at the current moment, the contact friction force between the flexible rope net and the space debris at the current moment is calculated based on formula (5)-(6), and the normal contact force between the flexible rope net and the space debris at the current moment is calculated according to formula (4), and then the fourth-order Runge-Kutta method is used to solve formula (3) to obtain the position vector and velocity vector of the space debris at the next moment, thereby realizing the simulation of the motion process of the flexible rope net capturing the space debris.

[0039] The second embodiment of the present invention provides a numerical simulation device for capturing space debris using a flexible rope net, comprising:

[0040] The unit division module is used to evenly divide each rope of the flexible rope net into a plurality of rope segment basic units, wherein each rope segment basic unit includes nodes located at both ends of the rope segment and a spring damper connecting the two nodes, the mass of the rope segment is evenly distributed on the nodes at both ends, and the non-shared nodes of adjacent rope segments are also connected by spring dampers; the surface of the space debris to be captured is divided into a plurality of adjacent spherical basic units, and all the spherical basic units form a spherical cluster combination model;

[0041] A flexible rope net mechanical simulation module is used to calculate the internal force of each basic unit of the rope segment based on the division result of the flexible rope net, and then establish a mechanical simulation model of the flexible rope net;

[0042] A space debris mechanics simulation module, used to establish a mechanics simulation model of the space debris;

[0043] The contact mechanics simulation module of space debris and flexible rope net is used to establish the contact mechanics simulation model of the space debris and flexible rope net based on the mechanics simulation model of the flexible rope net and the mechanics simulation model of the space debris, combined with the division result of the space debris, so as to realize the numerical simulation of the flexible rope net capturing the space debris.

[0044] In a specific embodiment of the present invention, the establishment of the mechanical simulation model of the flexible rope net includes:

[0045] 1) Calculate the internal force of each basic unit of rope segment;

[0046] The tension T of any rope segment p is p The constitutive model of is expressed as:

[0047]

[0048] in, is the stiffness of the rope segment p; E is Young's modulus; is the cross-sectional area of ​​the rope segment; is the initial length of segment p; is the damping coefficient of segment p, ρ s is the density of the rope segment p, ζ is the rope segment damping ratio, Δr p is the relative displacement of two nodes in segment p, is the relative velocity of the two nodes of segment p, is the diameter of the rope segment p;

[0049] 2) Based on the results of step 1), the dynamic equation of the flexible rope net is established;

[0050] Based on formula (1), the dynamic equation of any node i is established as:

[0051]

[0052] Where i = 1, 2, 3...n; n is the total number of nodes of the flexible rope net; m i represents the quality of the i-th node; r i , and are the position, velocity and acceleration vector of node i respectively; n e is the total number of adjacent segments of node i; N i,T is the normal contact force on node i from the space debris T, f i,T is the friction force exerted on node i by space debris T; η i,T represents the contact identification function between node i and space debris T. When node i comes into contact with space debris T, η i,T =1, otherwise η i,T =0;

[0053] Equations (1) and (2) constitute the mechanical simulation model of the flexible rope net.

[0054] In a specific embodiment of the present invention, the step of establishing the mechanical simulation model of the space debris comprises:

[0055]

[0056] Among them, r T , are the position and acceleration vector of the center of mass of space debris T; m T is the mass of space debris T; is the normal contact moment from node i of the flexible rope net; is the friction torque of node i of the flexible rope network; ntotal represents the total number of nodes of the flexible rope network in contact with the space debris T; I T represents the inertia matrix of space debris; ω T , are the angular velocity and angular acceleration of the space debris T respectively.

[0057] In a specific embodiment of the present invention, the step of establishing a contact mechanics simulation model between the space debris and the flexible rope net comprises:

[0058] 1) According to the flexible rope net node position vector r i and the space debris center of mass position vector r T , calculate the relative distance between the flexible rope net node i and each spherical basic unit in the ball cluster combination model;

[0059] 2) Based on the result of step 1), determine:

[0060] If the relative distance between node i and any spherical basic unit is less than or equal to 0, it is determined that node i is in contact with the spherical cluster combination model; otherwise, no contact occurs;

[0061] 3) Based on the result of step 2), the contact force is calculated for the contacting flexible rope net node and ball cluster combined model;

[0062] Among them, the calculation expression of the normal contact force generated during contact is as follows:

[0063]

[0064] Among them, N i,k is the normal contact force between the node i of the flexible rope net and the spherical basic unit k in the ball cluster combination model; is the stiffness coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model, is the damping coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model; is the penetration depth of the flexible rope net node i in contact with the spherical basic unit k in the ball cluster combination model, is the speed at which the flexible rope net node i contacts the spherical basic unit k in the ball cluster combination model; is the normal contact vector of the flexible rope net node i in contact with the spherical basic unit k in the spherical cluster combination model; nd is the number of spherical basic units in the spherical cluster combination model that are in contact with node i;

[0065] The friction force generated during contact is calculated as follows:

[0066]

[0067] Among them, fi,k is the tangential friction force between the flexible rope net node i and the spherical basic unit k in the ball cluster combination model, expressed as:

[0068]

[0069] Among them, μ s is the static friction coefficient, μ d is the coefficient of dynamic friction, and ε is the transition value of the conversion between static and dynamic friction.

[0070] In a specific embodiment of the present invention, it also includes:

[0071] According to the displacement vector and velocity vector of each node in the flexible rope net at the current moment, the internal force of the flexible rope net at the current moment is calculated based on formula (1), and then the fourth-order Runge-Kutta method is used to solve formula (2) to obtain the position vector and velocity vector of each node in the flexible rope net at the next moment; according to the position vector and velocity vector of each node in the flexible rope net at the current moment, and the position vector and velocity vector of each spherical basic unit in the space debris at the current moment, the contact friction force between the flexible rope net and the space debris at the current moment is calculated based on formula (5)-(6), and the normal contact force between the flexible rope net and the space debris at the current moment is calculated according to formula (4), and then the fourth-order Runge-Kutta method is used to solve formula (3) to obtain the position vector and velocity vector of the space debris at the next moment, thereby realizing the simulation of the motion process of the flexible rope net capturing the space debris.

[0072] A third aspect of the present invention provides an electronic device, including:

[0073] at least one processor; and a memory communicatively coupled to the at least one processor;

[0074] The memory stores instructions executable by the at least one processor, and the instructions are configured to execute the above-mentioned numerical simulation method for capturing space debris by a flexible rope net.

[0075] A fourth aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the above-mentioned numerical simulation method for capturing space debris with a flexible rope net.

[0076] The characteristics and beneficial effects of the present invention are:

[0077] The present invention establishes a high-precision and efficient calculation model for highly irregular debris by means of a ball cluster combination model, and combines it with a flexible dynamics model of a complex topological rope net, thereby realizing a fast and accurate simulation of the capture of irregular debris by a space flexible rope net. The present invention can depict complex space debris of any shape, while having a low amount of calculation, and can perform coupled dynamic calculations of a rope net with millions of nodes and highly irregular debris, and can obtain the changes in factors such as the rope net's internal force, envelope, debris speed, and position during the debris capture process at a low cost. The present invention can be used in scenarios such as the design of space debris removal missions in the future, and has a high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 The present invention is an overall flow chart of a numerical simulation method for capturing space debris using a flexible rope net according to an embodiment of the present invention.

[0079] Figure 2 It is a schematic diagram of a basic unit of a discrete rope segment in a specific embodiment of the present invention.

[0080] Figure 3 It is a schematic diagram of the original space debris and the spherical cluster combination model after discretization in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0081] The present invention provides a numerical simulation method and device for capturing space debris with a flexible rope net. The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0082] The first embodiment of the present invention provides a numerical simulation method for capturing space debris with a flexible rope net, comprising:

[0083] Each rope of the flexible rope net is evenly divided into a plurality of rope segment basic units, wherein each rope segment basic unit includes nodes at both ends of the rope segment and a spring damper connecting the two nodes, the mass of the rope segment is evenly distributed on the nodes at both ends, and the non-shared nodes of adjacent rope segments are also connected by spring dampers; the surface of the space debris to be captured is divided into a plurality of adjacent spherical basic units, and all the spherical basic units form a spherical cluster combination model;

[0084] Based on the division result of the flexible rope net, the internal force of each basic unit of the rope segment is calculated, and then a mechanical simulation model of the flexible rope net is established;

[0085] Establishing a mechanical simulation model of the space debris;

[0086] Based on the mechanical simulation model of the flexible rope net and the mechanical simulation model of the space debris, combined with the division result of the space debris, a contact mechanical simulation model of the space debris and the flexible rope net is established, thereby realizing the numerical simulation of the flexible rope net capturing the space debris.

[0087] In a specific embodiment of the present invention, the numerical simulation method for capturing space debris with a flexible rope net has the following overall process: Figure 1 As shown, the following steps are included:

[0088] 1) Divide the flexible rope net and the space debris to be captured into rope segment basic units and spherical basic units respectively; the specific steps are as follows:

[0089] 1-1) Divide the flexible rope net into basic units of rope segments.

[0090] In this embodiment, each rope of the flexible rope net is evenly discretized into a plurality of rope segment basic units, each rope segment basic unit includes nodes at both ends of the rope segment and a spring damper connecting the two nodes. The mass of the rope segment is evenly distributed on the nodes at both ends; the mass of the common node of adjacent rope segments is half of the sum of the masses of the rope segments where the node is located. The non-common nodes of adjacent rope segments are also connected by spring dampers.

[0091] Figure 2 Schematic diagram of a basic unit of a discrete rope segment in a specific embodiment of the present invention. Figure 2 In the example, there are two adjacent rope segment basic units, which contain three nodes i, i+1 and i+2, and the node masses are m i 、m i+1 and m i+2 . Figure 2 The two rope segments shown in the figure are composed of node i to node i+1 and node i+1 to node i+2, respectively. Node i and node i+1 are connected by a spring damper, and the elastic coefficient of the spring is k. p , the viscosity coefficient of damping is c p (If the material and thickness of the rope net are uniform, then the k between all nodes p and c p are the same), describing the tensile stress of the rope segment. Nodes i+1 and i+2 are connected by spring damping to describe the tensile stress of the rope segment. In addition, spring damping also exists between non-shared nodes of adjacent rope segments, such as Figure 2 As shown, node i and node i+2 are connected by a spring damper, which describes the bending force between adjacent rope segments.

[0092] In this embodiment, by Figure 2 In the manner shown, the flexible rope net will be divided into a plurality of rope segment basic units, the entire flexible rope net is composed of a plurality of nodes and spring dampers connecting the nodes, and the mass of the entire flexible rope net is concentrated on the nodes.

[0093] 1-2) Divide the space debris to be captured into spherical basic units.

[0094] In this embodiment, the surface of the irregular space debris is discretized into a number of adjacent spherical basic units, and all the spherical basic units form a spherical cluster combination model. Figure 3 Schematic diagram of the original space debris and its discretized spherical cluster combination model in a specific embodiment of the present invention. Figure 3 (a) is the original image of irregular fragments. Figure 3 (b) is a discrete ball cluster combination model. In this embodiment, the smaller the volume of the spherical basic unit and the greater the number, the more accurate the simulation effect.

[0095] 2) Based on the division results of the flexible rope net in step 1), the internal force of each basic unit of the rope segment is calculated, and then the mechanical simulation model of the flexible rope net is established; the specific steps are as follows:

[0096] 2-1) Calculate the internal force of each basic unit of the rope segment.

[0097] In this embodiment, the tension T of any rope segment p p The constitutive model of is expressed as:

[0098]

[0099] in, is the stiffness of the rope segment p; E is Young's modulus, which takes different values ​​depending on the material of the rope net. is the cross-sectional area of ​​the rope segment; is the initial length of segment p. is the damping coefficient of segment p, ρ s is the density of the rope segment p, ζ is the rope segment damping ratio, Δr p is the relative displacement of two nodes in segment p, is the relative velocity of the two nodes of segment p, is the diameter of the rope segment p.

[0100] 2-2) Based on the results of step 2-1), the dynamic equation of the flexible rope net is established.

[0101] In this embodiment, based on formula (1), the dynamic equation of any node i is established as:

[0102]

[0103] Where i = 1, 2, 3...n; n is the total number of nodes of the flexible rope net. i represents the quality of the i-th node; r i , and are the position, velocity and acceleration vector of node i respectively. eis the total number of adjacent segments to node i. i,T is the normal contact force on node i from the space debris T, f i,T is the friction force exerted on node i by space debris T. η i,T represents the contact identification function between node i and space debris T. When node i comes into contact with space debris T, η i,T =1, otherwise η i,T =0.

[0104] In this embodiment, equations (1) and (2) constitute a mechanical simulation model of the flexible rope net.

[0105] 3) Establish a mechanical simulation model of space debris, as follows:

[0106] In the capture mission, the forces on a single space debris include microgravity, disturbance force, and contact force. Microgravity and disturbance force can be ignored in the process of capturing debris. Contact force includes the normal reaction force and tangential friction force from the flexible rope net. Secondly, contact force will also affect the rotational motion of the debris. Therefore, the dynamic equation of space debris can be expressed as:

[0107]

[0108] Among them, r T , are the position and acceleration vector of the center of mass of space debris T. T is the mass of space debris T; is the normal contact moment from node i of the flexible rope net; is the friction torque of node i of the flexible rope network; ntotal represents the total number of nodes of the flexible rope network in contact with the space debris T. T Represents the inertia matrix of space debris. ω T , are the angular velocity and angular acceleration of the space debris T respectively.

[0109] 4) Based on the results of steps 1)-3), a contact mechanics simulation model of space debris and flexible rope net is established. The specific steps are as follows:

[0110] 4-1) Based on the results of the spatial debris division in step 1), according to the flexible rope net node position vector r i and the space debris center of mass position vector r T , calculate the relative distance between the flexible rope net node i and each spherical basic unit in the ball cluster combination model.

[0111] 4-2) Based on the result of step 4-1), determine:

[0112] If the relative distance between node i and any spherical basic unit is less than or equal to 0, it is determined that node i is in contact with the spherical cluster combination model; otherwise, no contact occurs.

[0113] 4-3) Based on the result of step 4-2), the contact force is calculated for the contacting flexible rope net node and ball cluster combined model.

[0114] Among them, the normal contact force generated during contact is calculated using the linear Hertz model:

[0115]

[0116] Among them, N i,k is the normal contact force between the node i of the flexible rope net and the spherical basic unit k in the ball cluster combination model; is the stiffness coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model, is the damping coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combined model. is the penetration depth of the flexible rope net node i in contact with the spherical basic unit k in the ball cluster combination model, is the speed at which the flexible rope net node i contacts the spherical basic unit k in the ball cluster combination model, which needs to be recalculated in each calculation step; is the normal contact vector of the flexible rope net node i in contact with the spherical basic unit k in the spherical cluster combination model. nd is the number of spherical basic units in the spherical cluster combination model that are in contact with node i;

[0117] The friction force generated during contact is calculated using a simplified Coulomb friction model:

[0118]

[0119] Among them, f i,k is the tangential friction force between the flexible rope net node i and the spherical basic unit k in the ball cluster combination model, expressed as:

[0120]

[0121] Among them, μ s is the static friction coefficient, μ d is the dynamic friction coefficient, and ε is the transition value of static-dynamic friction conversion. s With μ d The value of ε should refer to the friction properties of the space rope net material in contact with metal space debris. ε is generally taken as 10 -6 m / s.

[0122] 5) In the embodiment of the present invention, according to the displacement vector and velocity vector of each node in the flexible rope net at the current moment, the internal force of the flexible rope net at the current moment is calculated based on formula (1), and then the fourth-order Runge-Kutta method is used to solve formula (2), so as to obtain the position vector and velocity vector of each node in the flexible rope net at the next moment; according to the position vector and velocity vector of each node in the flexible rope net at the current moment, and the position vector and velocity vector of each spherical basic unit in the space debris at the current moment, the contact friction force between the flexible rope net and the space debris at the current moment is calculated based on formulas (5)-(6), and the normal contact force between the flexible rope net and the space debris at the current moment is calculated according to formula (4), and then the fourth-order Runge-Kutta method is used to solve formula (3), so as to obtain the position vector and velocity vector of the space debris at the next moment, thereby realizing the simulation of the motion process of the flexible rope net capturing irregular space debris.

[0123] To implement the above embodiment, a second aspect of the present invention provides a numerical simulation device for capturing space debris using a flexible rope net, comprising:

[0124] The unit division module is used to evenly divide each rope of the flexible rope net into a plurality of rope segment basic units, wherein each rope segment basic unit includes nodes located at both ends of the rope segment and a spring damper connecting the two nodes, the mass of the rope segment is evenly distributed on the nodes at both ends, and the non-shared nodes of adjacent rope segments are also connected by spring dampers; the surface of the space debris to be captured is divided into a plurality of adjacent spherical basic units, and all the spherical basic units form a spherical cluster combination model;

[0125] A flexible rope net mechanical simulation module is used to calculate the internal force of each basic unit of the rope segment based on the division result of the flexible rope net, and then establish a mechanical simulation model of the flexible rope net;

[0126] A space debris mechanics simulation module, used to establish a mechanics simulation model of the space debris;

[0127] The contact mechanics simulation module of space debris and flexible rope net is used to establish the contact mechanics simulation model of the space debris and flexible rope net based on the mechanics simulation model of the flexible rope net and the mechanics simulation model of the space debris, combined with the division result of the space debris, so as to realize the numerical simulation of the flexible rope net capturing the space debris.

[0128] In a specific implementation of the present invention, the establishment of the mechanical simulation model of the flexible rope net includes:

[0129] 1) Calculate the internal force of each basic unit of rope segment;

[0130] The tension T of any rope segment p is p The constitutive model of is expressed as:

[0131]

[0132] in, is the stiffness of the rope segment p; E is Young's modulus; is the cross-sectional area of ​​the rope segment; is the initial length of segment p; is the damping coefficient of segment p, ρ s is the density of the rope segment p, ζ is the rope segment damping ratio, Δr p is the relative displacement of two nodes in segment p, is the relative velocity of the two nodes of segment p, is the diameter of the rope segment p;

[0133] 2) Based on the results of step 1), the dynamic equation of the flexible rope net is established;

[0134] Based on formula (1), the dynamic equation of any node i is established as:

[0135]

[0136] Where i = 1, 2, 3...n; n is the total number of nodes of the flexible rope net; m i represents the quality of the i-th node; r i , and are the position, velocity and acceleration vector of node i respectively; n e is the total number of adjacent segments of node i; N i,T is the normal contact force on node i from the space debris T, f i,T is the friction force exerted on node i by space debris T; η i,T represents the contact identification function between node i and space debris T. When node i comes into contact with space debris T, η i,T =1, otherwise η i,T =0;

[0137] Equations (1) and (2) constitute the mechanical simulation model of the flexible rope net.

[0138] In a specific implementation of the present invention, the step of establishing the mechanical simulation model of the space debris includes:

[0139]

[0140] Among them, r T , are the position and acceleration vector of the center of mass of space debris T; m T is the mass of space debris T; is the normal contact moment from node i of the flexible rope net; is the friction torque of node i of the flexible rope network; ntotal represents the total number of nodes of the flexible rope network in contact with the space debris T; I T represents the inertia matrix of space debris; ω T , are the angular velocity and angular acceleration of the space debris T respectively.

[0141] In a specific implementation of the present invention, the step of establishing a contact mechanics simulation model between the space debris and the flexible rope net includes:

[0142] 1) According to the flexible rope net node position vector r i and the space debris center of mass position vector r T , calculate the relative distance between the flexible rope net node i and each spherical basic unit in the ball cluster combination model;

[0143] 2) Based on the result of step 1), determine:

[0144] If the relative distance between node i and any spherical basic unit is less than or equal to 0, it is determined that node i is in contact with the spherical cluster combination model; otherwise, no contact occurs;

[0145] 3) Based on the result of step 2), the contact force is calculated for the contacting flexible rope net node and ball cluster combined model;

[0146] Among them, the calculation expression of the normal contact force generated during contact is as follows:

[0147]

[0148] Among them, N i,k is the normal contact force between the node i of the flexible rope net and the spherical basic unit k in the ball cluster combination model; is the stiffness coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model, is the damping coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model; is the penetration depth of the flexible rope net node i in contact with the spherical basic unit k in the ball cluster combination model, is the speed at which the flexible rope net node i contacts the spherical basic unit k in the ball cluster combination model; is the normal contact vector of the flexible rope net node i in contact with the spherical basic unit k in the spherical cluster combination model; nd is the number of spherical basic units in the spherical cluster combination model that are in contact with node i;

[0149] The friction force generated during contact is calculated as follows:

[0150]

[0151] Among them, fi,k is the tangential friction force between the flexible rope net node i and the spherical basic unit k in the ball cluster combination model, expressed as:

[0152]

[0153] Among them, μ s is the static friction coefficient, μ d is the coefficient of dynamic friction, and ε is the transition value of the conversion between static and dynamic friction.

[0154] In a specific implementation of the present invention, it also includes:

[0155] According to the displacement vector and velocity vector of each node in the flexible rope net at the current moment, the internal force of the flexible rope net at the current moment is calculated based on formula (1), and then the fourth-order Runge-Kutta method is used to solve formula (2) to obtain the position vector and velocity vector of each node in the flexible rope net at the next moment; according to the position vector and velocity vector of each node in the flexible rope net at the current moment, and the position vector and velocity vector of each spherical basic unit in the space debris at the current moment, the contact friction force between the flexible rope net and the space debris at the current moment is calculated based on formula (5)-(6), and the normal contact force between the flexible rope net and the space debris at the current moment is calculated according to formula (4), and then the fourth-order Runge-Kutta method is used to solve formula (3) to obtain the position vector and velocity vector of the space debris at the next moment, thereby realizing the simulation of the motion process of the flexible rope net capturing the space debris.

[0156] To implement the above embodiment, a third aspect of the present invention provides an electronic device, including:

[0157] at least one processor; and a memory communicatively coupled to the at least one processor;

[0158] The memory stores instructions executable by the at least one processor, and the instructions are configured to execute the above-mentioned numerical simulation method for capturing space debris by a flexible rope net.

[0159] To implement the above-mentioned embodiment, the fourth aspect of the present invention proposes a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the above-mentioned numerical simulation method for capturing space debris with a flexible rope net.

[0160] It should be noted that the computer-readable medium disclosed above may be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present disclosure, a computer-readable storage medium may be any tangible medium containing or storing a program that may be used by or in combination with an instruction execution system, device or device. In the present disclosure, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, in which a computer-readable program code is carried. This propagated data signal may take a variety of forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. The computer readable signal medium may also be any computer readable medium other than a computer readable storage medium, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. The program code contained on the computer readable medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (radio frequency), etc., or any suitable combination of the above.

[0161] The computer readable medium may be included in the electronic device, or may exist independently without being installed in the electronic device. The computer readable medium carries one or more programs. When the one or more programs are executed by the electronic device, the electronic device executes the numerical simulation method of the flexible rope net capturing space debris in the above embodiment.

[0162] Computer program code for performing the operations of the present disclosure may be written in one or more programming languages, or a combination thereof, including object-oriented programming languages, such as Java, Smalltalk, C++, and conventional procedural programming languages, such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0163] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0164] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0165] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code that includes one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

[0166] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute the instructions), or in combination with these instruction execution systems, devices or apparatuses. For the purpose of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in combination with these instruction execution systems, devices or apparatuses. More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk box (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or otherwise processing in a suitable manner if necessary, and then stored in a computer memory.

[0167] It should be understood that the various parts of the present application can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0168] A person skilled in the art may understand that all or part of the steps in the method for implementing the above-mentioned embodiment may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiment.

[0169] In addition, each functional unit in each embodiment of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0170] The storage medium mentioned above may be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application. A person of ordinary skill in the art may change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A numerical simulation method for capturing space debris with a flexible rope net, characterized in that: include: Each rope of the flexible rope net is evenly divided into a plurality of rope segment basic units, wherein each rope segment basic unit includes nodes at both ends of the rope segment and a spring damper connecting the two nodes, the mass of the rope segment is evenly distributed on the nodes at both ends, and the non-shared nodes of adjacent rope segments are also connected by spring dampers; the surface of the space debris to be captured is divided into a plurality of adjacent spherical basic units, and all the spherical basic units form a spherical cluster combination model; Based on the division result of the flexible rope net, the internal force of each basic unit of the rope segment is calculated, and then a mechanical simulation model of the flexible rope net is established; Establishing a mechanical simulation model of the space debris; Based on the mechanical simulation model of the flexible rope net and the mechanical simulation model of the space debris, combined with the division result of the space debris, a contact mechanical simulation model of the space debris and the flexible rope net is established, thereby realizing the numerical simulation of the flexible rope net capturing the space debris.

2. The method according to claim 1, characterized in that The step of establishing the mechanical simulation model of the flexible rope net comprises: 1) Calculate the internal force of each basic unit of rope segment; The tension T of any rope segment p is p The constitutive model of is expressed as: in, is the stiffness of the rope segment p; E is Young's modulus; is the cross-sectional area of ​​the rope segment; is the initial length of segment p; is the damping coefficient of segment p, ρ s is the density of the rope segment p, ζ is the rope segment damping ratio, Δr p is the relative displacement of two nodes in segment p, is the relative velocity of the two nodes of segment p, is the diameter of the rope segment p; 2) Based on the results of step 1), the dynamic equation of the flexible rope net is established; Based on formula (1), the dynamic equation of any node i is established as: Where i = 1, 2, 3...n; n is the total number of nodes of the flexible rope net; m i represents the quality of the i-th node; r i , and are the position, velocity and acceleration vector of node i respectively; n e is the total number of adjacent rope segments of node i; N i,T is the normal contact force on node i from the space debris T, f i,T is the friction force exerted on node i by space debris T; η i,T represents the contact identification function between node i and space debris T. When node i comes into contact with space debris T, η i,T =1, otherwise η i,T =0; Equations (1) and (2) constitute the mechanical simulation model of the flexible rope net.

3. The method according to claim 2, characterized in that The step of establishing the mechanical simulation model of the space debris comprises: Among them, r T , are the position and acceleration vector of the center of mass of the space debris T; m T is the mass of space debris T; is the normal contact moment from node i of the flexible rope net; is the friction torque of node i of the flexible rope network; ntotal represents the total number of nodes of the flexible rope network in contact with the space debris T; I T represents the inertia matrix of space debris; ω T , are the angular velocity and angular acceleration of the space debris T respectively.

4. The method according to claim 3, characterized in that The step of establishing a contact mechanics simulation model between the space debris and the flexible rope net comprises: 1) According to the flexible rope net node position vector r i and the space debris center of mass position vector r T , calculate the relative distance between the flexible rope net node i and each spherical basic unit in the ball cluster combination model; 2) Based on the result of step 1), determine: If the relative distance between node i and any spherical basic unit is less than or equal to 0, it is determined that node i is in contact with the spherical cluster combination model; otherwise, no contact occurs; 3) Based on the result of step 2), the contact force is calculated for the contacting flexible rope net node and ball cluster combined model; Among them, the calculation expression of the normal contact force generated during contact is as follows: Among them, N i,k is the normal contact force between the node i of the flexible rope net and the spherical basic unit k in the ball cluster combination model; is the stiffness coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model, is the damping coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model; is the penetration depth of the flexible rope net node i in contact with the spherical basic unit k in the ball cluster combination model, is the speed at which the flexible rope net node i contacts the spherical basic unit k in the ball cluster combination model; is the normal contact vector of the flexible rope net node i in contact with the spherical basic unit k in the spherical cluster combination model; nd is the number of spherical basic units in the spherical cluster combination model that are in contact with node i; The friction force generated during contact is calculated as follows: Among them, f i,k is the tangential friction force between the flexible rope net node i and the spherical basic unit k in the ball cluster combination model, expressed as: Among them, μ s is the static friction coefficient, μ d is the coefficient of dynamic friction, and ε is the transition value of the conversion between static and dynamic friction.

5. The method according to claim 4, characterized in that Also includes: According to the displacement vector and velocity vector of each node in the flexible rope net at the current moment, the internal force of the flexible rope net at the current moment is calculated based on formula (1), and then the fourth-order Runge-Kutta method is used to solve formula (2) to obtain the position vector and velocity vector of each node in the flexible rope net at the next moment; according to the position vector and velocity vector of each node in the flexible rope net at the current moment, and the position vector and velocity vector of each spherical basic unit in the space debris at the current moment, the contact friction force between the flexible rope net and the space debris at the current moment is calculated based on formula (5)-(6), and the normal contact force between the flexible rope net and the space debris at the current moment is calculated according to formula (4), and then the fourth-order Runge-Kutta method is used to solve formula (3) to obtain the position vector and velocity vector of the space debris at the next moment, thereby realizing the simulation of the motion process of the flexible rope net capturing the space debris.

6. A numerical simulation device for capturing space debris using a flexible rope net, characterized in that: include: The unit division module is used to evenly divide each rope of the flexible rope net into a plurality of rope segment basic units, wherein each rope segment basic unit includes nodes located at both ends of the rope segment and a spring damper connecting the two nodes, the mass of the rope segment is evenly distributed on the nodes at both ends, and the non-shared nodes of adjacent rope segments are also connected by spring dampers; the surface of the space debris to be captured is divided into a plurality of adjacent spherical basic units, and all the spherical basic units form a spherical cluster combination model; A flexible rope net mechanical simulation module is used to calculate the internal force of each basic unit of the rope segment based on the division result of the flexible rope net, and then establish a mechanical simulation model of the flexible rope net; A space debris mechanics simulation module, used to establish a mechanics simulation model of the space debris; The contact mechanics simulation module of space debris and flexible rope net is used to establish the contact mechanics simulation model of the space debris and flexible rope net based on the mechanics simulation model of the flexible rope net and the mechanics simulation model of the space debris, combined with the division result of the space debris, so as to realize the numerical simulation of the flexible rope net capturing the space debris.

7. The device according to claim 6, characterized in that The step of establishing the mechanical simulation model of the flexible rope net comprises: 1) Calculate the internal force of each basic unit of rope segment; The tension T of any rope segment p is p The constitutive model of is expressed as: in, is the stiffness of the rope segment p; E is Young's modulus; is the cross-sectional area of ​​the rope segment; is the initial length of segment p; is the damping coefficient of segment p, ρ s is the density of the rope segment p, ζ is the rope segment damping ratio, Δr p is the relative displacement of two nodes in segment p, is the relative velocity of the two nodes of segment p, is the diameter of the rope segment p; 2) Based on the results of step 1), the dynamic equation of the flexible rope net is established; Based on formula (1), the dynamic equation of any node i is established as: Where i = 1, 2, 3...n; n is the total number of nodes of the flexible rope net; m i represents the quality of the i-th node; r i , and are the position, velocity and acceleration vector of node i respectively; n e is the total number of adjacent rope segments of node i; N i,T is the normal contact force on node i from the space debris T, f i,T is the friction force exerted on node i by space debris T; η i,T represents the contact identification function between node i and space debris T. When node i comes into contact with space debris T, η i,T =1, otherwise η i,T =0; Equations (1) and (2) constitute the mechanical simulation model of the flexible rope net.

8. The device according to claim 7, characterized in that The step of establishing the mechanical simulation model of the space debris comprises: Among them, r T , are the position and acceleration vector of the center of mass of the space debris T; m T is the mass of space debris T; is the normal contact moment from node i of the flexible rope net; is the friction torque of node i of the flexible rope network; ntotal represents the total number of nodes of the flexible rope network in contact with the space debris T; I T represents the inertia matrix of space debris; ω T , are the angular velocity and angular acceleration of the space debris T respectively.

9. The device according to claim 8, characterized in that The step of establishing a contact mechanics simulation model between the space debris and the flexible rope net comprises: 1) According to the flexible rope net node position vector r i and the space debris center of mass position vector r T , calculate the relative distance between the flexible rope net node i and each spherical basic unit in the ball cluster combination model; 2) Based on the result of step 1), determine: If the relative distance between node i and any spherical basic unit is less than or equal to 0, it is determined that node i is in contact with the spherical cluster combination model; otherwise, no contact occurs; 3) Based on the result of step 2), the contact force is calculated for the contacting flexible rope net node and ball cluster combined model; Among them, the calculation expression of the normal contact force generated during contact is as follows: Among them, N i,k is the normal contact force between the node i of the flexible rope net and the spherical basic unit k in the ball cluster combination model; is the stiffness coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model, is the damping coefficient of the contact between the flexible rope net node i and the spherical basic unit k in the spherical cluster combination model; is the penetration depth of the flexible rope net node i in contact with the spherical basic unit k in the ball cluster combination model, is the speed at which the flexible rope net node i contacts the spherical basic unit k in the ball cluster combination model; is the normal contact vector of the flexible rope net node i in contact with the spherical basic unit k in the spherical cluster combination model; nd is the number of spherical basic units in the spherical cluster combination model that are in contact with node i; The friction force generated during contact is calculated as follows: Among them, f i,k is the tangential friction force between the flexible rope net node i and the spherical basic unit k in the ball cluster combination model, expressed as: Among them, μ s is the static friction coefficient, μ d is the coefficient of dynamic friction, and ε is the transition value of the conversion between static and dynamic friction.

10. The device according to claim 9, characterized in that Also includes: According to the displacement vector and velocity vector of each node in the flexible rope net at the current moment, the internal force of the flexible rope net at the current moment is calculated based on formula (1), and then the fourth-order Runge-Kutta method is used to solve formula (2) to obtain the position vector and velocity vector of each node in the flexible rope net at the next moment; according to the position vector and velocity vector of each node in the flexible rope net at the current moment, and the position vector and velocity vector of each spherical basic unit in the space debris at the current moment, the contact friction force between the flexible rope net and the space debris at the current moment is calculated based on formula (5)-(6), and the normal contact force between the flexible rope net and the space debris at the current moment is calculated according to formula (4), and then the fourth-order Runge-Kutta method is used to solve formula (3) to obtain the position vector and velocity vector of the space debris at the next moment, thereby realizing the simulation of the motion process of the flexible rope net capturing the space debris.

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