Automatic operation lunar ladder modeling method and system based on gravitational siphon effect

Abstract

The invention discloses an automatic operation lunar ladder modeling method and system based on a gravitational siphon effect. The method comprises the following steps: constructing a gravitational siphon lunar ladder model; performing bead point simplification processing on the gravitational siphon moon ladder model to obtain a multi-body dynamics simplified model of the gravitational siphon moon ladder; and performing coordinate system construction processing and dynamic analysis on the multi-body dynamic simplified model of the gravitational siphon moon ladder to obtain a gravitational siphon effect moon ladder dynamic model. By using the system, the transfer of substances from the surface of a rotating body to an orbit collection spacecraft can be realized by utilizing a gravitational siphon effect, so that the requirement of a traditional propulsion system is avoided, and the energy consumption required for improving the load is greatly reduced. The automatic operation lunar ladder modeling method and system based on the gravitational siphon effect can be widely applied to the technical field of aerospace modeling.

Description

Technical Field

[0001] The present invention relates to the technical field of aerospace modeling, and in particular to a method and system for modeling an automatically operated lunar ladder based on a gravitational siphon effect. Background Art

[0002] At present, the development of space resources by human beings mainly depends on rocket launches, which consumes a lot of fuel and is extremely costly. In addition, the technology involved in the development of space resources is complex, including deep space exploration, sample collection and return, in-situ resource utilization, etc., which is technically difficult and risky. As a possible means of space transportation, the space elevator has great potential and important strategic significance. It is considered to be an efficient and sustainable mode of transportation between the earth and the moon, which can provide infrastructure support for space travel, resource development and future human habitation in space. The basic principle of the space elevator is to use a tether from the surface of the earth to the Earth-Moon L1 point close to the earth to establish a long rope suspension state between the earth and the moon, and realize space navigation through the tension of the rope. Compared with traditional rocket launch methods, the space elevator has many advantages such as low cost, low energy consumption, and reusability. It is considered to be one of the important breakthroughs in future space exploration. However, the current method has the need for a propulsion system, which greatly increases the consumption of the payload. Summary of the invention

[0003] In order to solve the above technical problems, the purpose of the present invention is to provide an automatically operated lunar ladder modeling method and system based on the gravitational siphon effect, which can utilize the gravitational siphon effect to realize the transfer of matter from the surface of a rotating body to an orbital collection spacecraft, thereby avoiding the need for a traditional propulsion system and greatly reducing the energy consumed by lifting the load.

[0004] The first technical solution adopted by the present invention is: a method for modeling an automatically operated lunar ladder based on the gravitational siphon effect, comprising the following steps: Construct a gravitational siphon lunar ladder model; The gravity siphon lunar ladder model is simplified by bead point processing to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder. The coordinate system construction and dynamic analysis of the simplified multi-body dynamics model of the gravitational siphon lunar ladder are carried out to obtain the dynamics model of the gravitational siphon effect lunar ladder.

[0005] Furthermore, the gravity siphon lunar ladder model specifically includes a closed-loop rope, a fixed pulley, a movable pulley and a cargo box, wherein the fixed pulley is distributed on the near-earth surface of the moon, the movable pulley is distributed on the near-earth surface of the earth, the closed-loop rope runs around both ends of the fixed pulley and the movable pulley respectively, the closed-loop rope running toward the moon is defined as the upward direction, and the closed-loop rope running toward the earth is defined as the downward direction, and the cargo boxes are evenly distributed on the upper surface of the closed-loop rope.

[0006] Furthermore, the step of performing bead point simplification processing on the gravity siphon lunar ladder model to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder specifically includes: The closed-loop rope in the gravity siphon lunar ladder model is divided into several segments with equal spacing, and each segment of the closed-loop rope is regarded as a node; Assume that adjacent nodes are connected by elastic straight rods, and the fixed pulley and movable pulley in the gravitational siphon lunar ladder model are regarded as nodes; Assume that the fixed pulley node is connected to the closed-loop rope node and the movable pulley node is connected to the closed-loop rope node, and set the previous node of the fixed pulley in the gravity siphon lunar ladder model to , the next node of the fixed pulley in the gravitational siphon lunar ladder model is , the previous node of the movable pulley in the gravitational siphon lunar ladder model is , the next node of the movable pulley in the gravitational siphon lunar ladder model is , and a simplified multi-body dynamics model of the gravitational siphon lunar ladder is obtained.

[0007] Furthermore, the step of constructing a coordinate system and conducting dynamic analysis on the simplified multi-body dynamics model of the gravity siphon lunar ladder to obtain the dynamics model of the gravity siphon lunar ladder specifically includes: Based on the Earth-Moon rotating coordinate system, a simplified multi-body dynamics model of the gravitational siphon lunar ladder with a coordinate system is constructed to obtain the position vectors of the model parameters; Based on the position vector of the model parameters, the dynamic equations of the node parameters are constructed by considering the interaction force factors, gravity factors, centrifugal force factors, Coriolis force factors and damping force factors; Characteristic node identification rules are introduced, and the dynamic equations of node parameters are transformed to obtain the dynamic model of the lunar ladder with gravitational siphon effect.

[0008] Furthermore, the position vector of the model parameter specifically includes the closed-loop rope node The position vector is , the Earth's position vector , the moon's position vector , the position vector of the fixed pulley , the position vector of the movable pulley is , the position vector of the previous node of the fixed pulley , the position vector of the next node of the fixed pulley , the position vector of the previous node of the movable pulley The position vector of the next node after the movable pulley .

[0009] Furthermore, the dynamic equation of the node parameters specifically includes the closed-loop rope node The dynamic equation of the fixed pulley, the dynamic equation of the movable pulley, the dynamic equation of the previous node of the fixed pulley, the dynamic equation of the next node of the fixed pulley, the dynamic equation of the previous node of the movable pulley and the dynamic equation of the next node of the movable pulley, where: The closed loop rope node The expression of the kinetic equation is:

[0010] In the above formula, represents the i-th closed-loop rope node The concentrated mass, represents the i-th closed-loop rope node The second derivative of the position vector with respect to time, represents the gravitational force of the earth on the nodes of the closed-loop rope, represents the gravitational force of the moon on the nodes of the closed-loop rope, , represents the elastic force of the connecting rod between adjacent closed-loop rope nodes, represents the centrifugal force on the closed-loop rope node, represents the Coriolis force on the closed-loop rope node, represents the damping force on the closed-loop rope node; The dynamic equation of the movable pulley is expressed as:

[0011] In the above formula, represents the concentrated mass of the movable pulley, represents the second-order derivative of the position vector of the movable pulley with respect to time, represents the gravitational force on the movable pulley, represents the gravitational force of the moon on the movable pulley, is the centrifugal force on the movable pulley, is the Coriolis force on the movable pulley, is the friction force on the movable pulley, represents the elastic force of the connecting rod between the movable pulley and the previous node of the movable pulley, It represents the elastic force of the connecting rod between the movable pulley and the next node of the movable pulley; The expression of the dynamic equation of the previous node of the fixed pulley is:

[0012] In the above formula, represents the concentrated mass of the previous rope node of the fixed pulley, represents the second-order derivative of the position vector of the previous rope node of the fixed pulley with respect to time, represents the earth's gravitational force on the previous node of the fixed pulley, represents the gravitational force of the moon on the previous node of the fixed pulley, represents the centrifugal force on the previous node of the fixed pulley, represents the Coriolis force on the previous node of the fixed pulley, represents the friction force on the previous node of the fixed pulley, represents the elastic force of the connecting rod between the previous node and the adjacent node of the fixed pulley, represents the elastic force of the connecting rod between the adjacent node of the previous node of the fixed pulley and a node further away; The expression of the dynamic equation of the next node of the fixed pulley is:

[0013] In the above formula, represents the concentrated mass of the next rope node of the fixed pulley, represents the second-order derivative of the position vector of the next rope node of the fixed pulley with respect to time, represents the earth's gravitational force on the next node of the fixed pulley, represents the lunar gravitational force on the next node of the fixed pulley, represents the centrifugal force on the next node of the fixed pulley, represents the Coriolis force on the next node of the fixed pulley, represents the friction force on the next node of the fixed pulley, represents the elastic force of the connecting rod between the next node of the fixed pulley and the adjacent node, represents the elastic force of the connecting rod between the adjacent node of the next node of the fixed pulley and a node further away; The expression of the dynamic equation of the previous node of the movable pulley is:

[0014] In the above formula, represents the concentrated mass of the previous rope node of the movable pulley, represents the second-order derivative of the position vector of the previous rope node of the movable pulley with respect to time, represents the earth's gravitational force on the previous node of the movable pulley, represents the gravitational force of the moon on the previous node of the movable pulley, represents the centrifugal force on the previous node of the movable pulley, represents the Coriolis force on the previous node of the movable pulley, represents the friction force on the previous node of the movable pulley, represents the elastic force of the connecting rod between the previous node and the adjacent node of the movable pulley, represents the elastic force of the connecting rod between the adjacent node of the previous node of the movable pulley and a node further away; The expression of the dynamic equation of the next node of the movable pulley is:

[0015] In the above formula, represents the concentrated mass of the next rope node of the movable pulley, represents the second-order derivative of the position vector of the next rope node of the movable pulley with respect to time, represents the gravitational force of the earth on the next node of the movable pulley, represents the gravitational force of the moon on the last node of the movable pulley, represents the centrifugal force on the next node of the movable pulley, represents the Coriolis force on the next node of the movable pulley, represents the friction force on the next node of the movable pulley, represents the elastic force of the connecting rod between the next node of the movable pulley and the adjacent node, Represents the elastic force of the connecting rod between the adjacent node of the rear node of the movable pulley and a node further away.

[0016] Furthermore, the introduced characteristic node identification rule is specifically as follows: Determine the closed-loop rope node closest to the pulley, number it, and determine the target node, the pulley is a fixed pulley or a movable pulley; Determine the next node of the target node and the previous node of the target node, determine the distance between the next node of the target node and the pulley, and determine the distance between the previous node of the target node and the pulley; Determine the distance between the next node of the target node and the pulley and the distance between the previous node of the target node and the pulley; If the distance between the next node of the target node and the pulley is less than the distance between the previous node of the target node and the pulley, then the next node of the target node is determined to be the previous node of the pulley and the target node is the next node of the pulley; If the distance between the next node of the target node and the pulley is greater than the distance between the previous node of the target node and the pulley, the target node is determined to be the previous node of the pulley and the previous node of the target node is the next node of the pulley.

[0017] The second technical solution adopted by the present invention is: an automatic operation lunar ladder modeling system based on the gravitational siphon effect, comprising: The first module is used to construct a gravitational siphon lunar ladder model; The second module is used to simplify the gravitational siphon lunar ladder model by beads to obtain a simplified multi-body dynamics model of the gravitational siphon lunar ladder; The third module is used to construct the coordinate system and conduct dynamic analysis on the simplified multi-body dynamics model of the gravitational siphon lunar ladder, and obtain the dynamics model of the gravitational siphon effect lunar ladder.

[0018] The beneficial effects of the method and system of the present invention are as follows: the present invention constructs a gravity siphon lunar ladder model, uses gravity siphon as a power system with a power source, and then realizes the use of the rotational kinetic energy of asteroids to achieve propellant-free payload transfer, and realizes the transfer of materials from the lunar surface to the orbital collection spacecraft. The gravity siphon lunar ladder model is simplified by bead points to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder, and the continuous ladder structure is discretized into a series of nodes and elastic connecting segments. The simplified multi-body dynamics model of the gravity siphon lunar ladder is then subjected to coordinate system construction processing and dynamic analysis, and a criterion for determining the nodes coupled with the pulley is designed. The differential algebraic equation is converted into a pure differential equation through continuous determination, and the uninterrupted continuous practical process integral solution of the differential equation is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a flow chart of the steps of the method for automatically operating the lunar ladder modeling based on the gravitational siphon effect of the present invention; Figure 2 It is a structural block diagram of the automatic operation lunar ladder modeling system based on the gravitational siphon effect of the present invention; Figure 3 is a schematic diagram of an automatically operated lunar ladder based on the gravitational siphon effect provided by a specific embodiment of the present invention; Figure 4 is a schematic diagram of kinetic modeling provided by a specific embodiment of the present invention; Figure 5 It is a schematic diagram of a simplified multi-body dynamics model of a siphon lunar ladder provided by a specific embodiment of the present invention; Figure 6 It is a schematic diagram of force analysis of a node in an overall inertial coordinate system provided by a specific embodiment of the present invention; Figure 7 Schematic diagram of two results of special node judgment provided by a specific embodiment of the present invention; Figure 8 It is a schematic diagram of a special node judgment process provided by a specific embodiment of the present invention; Fig. 9 It is a schematic diagram of the instantaneous configuration of the system at 0 o'clock every day in a typical example provided by a specific embodiment of the present invention. DETAILED DESCRIPTION

[0020] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only provided for the convenience of explanation and description, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0021] Reference Figure 1 The present invention provides a method for modeling an automatically operated lunar ladder based on the gravitational siphon effect, the method comprising the following steps: S100, construct a gravitational siphon lunar ladder model; Specifically, the gravity siphon lunar ladder model specifically includes a closed-loop rope, a fixed pulley, a movable pulley and a cargo box, wherein the fixed pulley is distributed on the near-earth surface of the moon, and the movable pulley is distributed on the near-earth surface of the earth. The closed-loop rope runs around the two ends of the fixed pulley and the movable pulley respectively. The closed-loop rope running toward the moon is defined as the upward direction, and the closed-loop rope running toward the earth is defined as the downward direction. Cargo boxes are evenly spaced on the upper surface of the closed-loop rope.

[0022] In this embodiment, if Figure 3 As shown in the figure, this ladder can be regarded as an extra-long closed-loop rope running around a binary pulley set, similar to a conveyor belt. A fixed pulley is installed at the center of the lunar surface facing the earth, and the movable pulley is arranged near the earth. Combining statics and material mechanics analysis, the movable pulley cannot be too close to the earth, nor can it be more than 110,000 kilometers away from the earth, to ensure that the internal force of the system as a whole is tension, so that it can maintain its shape and not fall to the moon. An extra-long rope is connected end to end and runs around these two pulleys. Obviously, one side will run toward the moon, called the upward direction, and the other side will run toward the earth, called the downward direction. On the entire rope, a series of cargo boxes are arranged at equal intervals. When the cargo box reaches the lunar surface and turns downward (from the moon, it is upward and away from the lunar surface), it is loaded with a certain mass of cargo; when the cargo box reaches the terminal fixed pulley, the cargo is unloaded and placed in the terminal space station, or the cargo is simply directly separated from the ladder system, and then these cargoes will fall to the earth under the action of gravity. This forms the gravitational siphon lunar ladder, which will be referred to as the "siphon ladder" or "ladder" hereinafter.

[0023] S200, performing bead point simplification processing on the gravity siphon lunar ladder model to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder; Specifically, the closed-loop rope in the gravity siphon lunar ladder model is divided into several segments with equal spacing, and each segment of the closed-loop rope is regarded as a node; it is assumed that adjacent nodes are connected by elastic straight rods, and the fixed pulley and movable pulley in the gravity siphon lunar ladder model are both regarded as nodes; it is assumed that the fixed pulley node is connected to the closed-loop rope node and the movable pulley node is connected to the closed-loop rope node, and the previous node of the fixed pulley in the gravity siphon lunar ladder model is set to , the next node of the fixed pulley in the gravitational siphon lunar ladder model is , the previous node of the movable pulley in the gravitational siphon lunar ladder model is , the next node of the movable pulley in the gravitational siphon lunar ladder model is , and a simplified multi-body dynamics model of the gravitational siphon lunar ladder is obtained.

[0024] In this embodiment, if Figure 4 As shown, first simplify the model, assuming the total number of cargo boxes is , the model is assumed to distribute the mass of the cargo box and the goods inside evenly to the upper rope in the counterclockwise direction, and then divide the entire rope into equally spaced segment, each segment The mass (the collection of ropes, boxes, and cargo) is concentrated at its nodes In this process, Not necessarily Equal, but in principle cannot be greater than , in order to facilitate higher precision simulation calculations. In actual engineering, The number should not be too small to facilitate the smooth operation of the system as a whole; of course, it should not be too large to take into account the carrying capacity of the system. For example, if a cargo box is set up approximately every 1,000 kilometers, then when the terminal movable pulley is about 50,000 kilometers from the ground, Set to 700, at the same time The value is also set to 700, which can basically guarantee the calculation accuracy and make each node correspond to a container. They are numbered in sequence. For convenience, the node closest to the fixed pulley on the lunar surface can be numbered 1 at the initial moment. On the uplink side, the mass of each node is , on the downstream side, the quality of each node is . Contains the mass of ropes and empty containers in the node set, The quality of the goods is increased. .

[0025] Furthermore, the two pulleys are also simplified into two nodes. Considering that the pulley radius is much smaller than the overall system, its radius is not considered. The mass of the fixed pulley PM (M represents the lunar side) does not need to be considered, because its movement is known and moves with the lunar surface; and the gravitational force on its mass is also balanced by the reaction force of the lunar surface and will not be transmitted to other nodes. As for the movable pulley PE (E represents the earth side), the mass of its simplified node is set to the total mass of the pulley and the space station closely connected to it.

[0026] It is also necessary to explain that the model needs to treat the four nodes closest to the two pulleys in the clockwise and counterclockwise directions specially. Although these two pairs of nodes are actually directly connected by ropes passing around the pulleys, since the rod is assumed to be a straight rod without bending, these two pairs of nodes are connected to the pulley nodes, and the forces between them and the pulleys are transmitted through the rod. The node before the fixed pulley PM is (b stands for before), the next node is (a stands for after); the node before the movable pulley PE is , the next node is , the corresponding four-link section is marked as , , , Of course we know that and It is actually connected directly around the pulley and The two points are only considered as two sections due to our setting here. and The situation is similar. Figure 5 As shown in the figure , , , As the name suggests, it represents a previous or next node.

[0027] S300. Perform coordinate system construction and dynamic analysis on the simplified multi-body dynamics model of the gravity siphon lunar ladder to obtain a dynamics model of the gravity siphon lunar ladder.

[0028] S310, based on the Earth-Moon rotating coordinate system, construct a simplified multi-body dynamics model of a gravitational siphon lunar ladder with a coordinate system, and obtain position vectors of model parameters; Among them, it should be noted that the position vector of the model parameter specifically includes the closed-loop rope node The position vector is , the Earth's position vector , the moon's position vector , the position vector of the fixed pulley , the position vector of the movable pulley is , the position vector of the previous node of the fixed pulley , the position vector of the next node of the fixed pulley , the position vector of the previous node of the movable pulley The position vector of the next node of the movable pulley .

[0029] Furthermore, in this embodiment, the Earth-Moon rotating coordinate system is used, that is, the origin is set at the common center of mass of the Earth and the Moon, the x-axis points to the Moon and rotates with the revolution of the Moon, the z-axis is the direction of the angular velocity of the revolution of the Earth-Moon system, and finally the y-axis is determined by the right-hand rule of the three-dimensional coordinate system, as follows: Figure 2 In such a coordinate system, the positions of the Earth and the Moon remain fixed, but the coordinate system rotates around the z-axis as a whole, so the inertial force (centrifugal force, Coriolis force) needs to be explicitly given in the dynamic equations.

[0030] The main dynamic activities in the Earth-Moon system occur in the ecliptic plane, so the present invention does not consider the movement in the z direction. Therefore, in this coordinate system, the node The position vector is , the Earth's position vector , the moon's position vector , the position vector of the fixed pulley PM are all constant vectors, and the position vector of the movable pulley is Then the position vector of the special node connected to the pulley is recorded as , , , Etc. Each of the above vectors contains components in two directions, for example .

[0031] S320, based on the position vector of the model parameter, considering the interaction force factor, the gravitational force factor, the centrifugal force factor, the Coriolis force factor and the damping force factor, constructing the dynamic equation of the node parameter; Among them, it should be noted that the dynamic equation of the node parameters specifically includes the closed-loop rope node The dynamic equation of the fixed pulley, the dynamic equation of the movable pulley, the dynamic equation of the node before the fixed pulley, the dynamic equation of the node after the fixed pulley, the dynamic equation of the node before the movable pulley and the dynamic equation of the node after the movable pulley.

[0032] like Figure 6 As shown, the closed-loop rope node The expression of the kinetic equation is:

[0033] In the above formula, represents the i-th closed-loop rope node The concentrated mass, represents the i-th closed-loop rope node The second derivative of the position vector with respect to time, represents the gravitational force of the earth on the nodes of the closed-loop rope, represents the gravitational force of the moon on the nodes of the closed-loop rope, , represents the elastic force of the connecting rod between adjacent closed-loop rope nodes, represents the centrifugal force on the closed-loop rope node, represents the Coriolis force on the closed-loop rope node, represents the damping force on the closed-loop rope node; Among them, the expression of the earth's gravitational force on the closed-loop rope node is:

[0034] The expression of the moon's gravitational force on the closed-loop rope node is:

[0035] represent and The connecting rod between The elastic force points to , then the expression of the elastic force of the connecting rod between adjacent closed-loop rope nodes is:

[0036] represent and The connecting rod between The elastic force points to , then the expression of the elastic force of the connecting rod between adjacent closed-loop rope nodes is:

[0037] The expression of the centrifugal force on the closed-loop rope node is:

[0038] The expression of the Coriolis force on the closed-loop rope node is:

[0039] In the absence of air, sunlight pressure and other external forces, the main source of damping force is the viscosity of the material. Its specific expression can be obtained through material mechanics experiments. This structure directly uses the linear damping assumption, that is, the damping force is proportional to the speed, and the viscosity coefficient is set to , the direction is always opposite to the direction of node movement, so the damping force on the closed-loop rope node is expressed as:

[0040] In addition, it should be noted that, for the fixed pulley PM, its position remains unchanged in the selected coordinate system, and its velocity and acceleration remain at 0.

[0041] The dynamic equation of the movable pulley is expressed as:

[0042] In the above formula, represents the concentrated mass of the movable pulley, represents the second-order derivative of the position vector of the movable pulley with respect to time, represents the gravitational force of the earth on the movable pulley, represents the gravitational force of the moon on the movable pulley, represents the centrifugal force on the movable pulley, is the Coriolis force on the movable pulley, represents the friction force on the movable pulley, represents the elastic force of the connecting rod between the movable pulley and the previous node of the movable pulley, It represents the elastic force of the connecting rod between the movable pulley and the next node of the movable pulley; in, and They represent PE and the two nodes before and after respectively. , Between connecting rods , The two connecting rods are actually the same rope that goes around the pulley, so their elastic forces should be equal and point to , , whose expression is:

[0043]

[0044] Represents the elongation of a rope around a pulley, and its expression is:

[0045] That is, after the length of this section is less than the original length after deformation, the elastic force is set to 0 to ensure that the rope as a whole is not under pressure. All have this provision, namely .

[0046] The expression of the dynamic equation of the previous node of the fixed pulley is:

[0047] In the above formula, represents the concentrated mass of the previous rope node of the fixed pulley, represents the second-order derivative of the position vector of the previous rope node of the fixed pulley with respect to time, represents the earth's gravitational force on the previous node of the fixed pulley, represents the gravitational force of the moon on the previous node of the fixed pulley, represents the centrifugal force on the previous node of the fixed pulley, represents the Coriolis force on the previous node of the fixed pulley, represents the friction force on the previous node of the fixed pulley, represents the elastic force of the connecting rod between the previous node and the adjacent node of the fixed pulley, represents the elastic force of the connecting rod between the adjacent node of the previous node of the fixed pulley and a node further away; The expression of the dynamic equation of the next node of the fixed pulley is:

[0048] In the above formula, represents the concentrated mass of the next rope node of the fixed pulley, represents the second-order derivative of the position vector of the next rope node of the fixed pulley with respect to time, represents the earth's gravitational force on the next node of the fixed pulley, represents the lunar gravitational force on the next node of the fixed pulley, represents the centrifugal force on the next node of the fixed pulley, represents the Coriolis force on the next node of the fixed pulley, represents the friction force on the next node of the fixed pulley, represents the elastic force of the connecting rod between the next node of the fixed pulley and the adjacent node, represents the elastic force of the connecting rod between the adjacent node of the next node of the fixed pulley and a node further away; The expression of the dynamic equation of the previous node of the movable pulley is:

[0049] In the above formula, represents the concentrated mass of the previous rope node of the movable pulley, represents the second-order derivative of the position vector of the previous rope node of the movable pulley with respect to time, represents the earth's gravitational force on the previous node of the movable pulley, represents the gravitational force of the moon on the previous node of the movable pulley, represents the centrifugal force on the previous node of the movable pulley, represents the Coriolis force on the previous node of the movable pulley, represents the friction force on the previous node of the movable pulley, represents the elastic force of the connecting rod between the previous node and the adjacent node of the movable pulley, represents the elastic force of the connecting rod between the adjacent node of the previous node of the movable pulley and a node further away; The expression of the dynamic equation of the next node of the movable pulley is:

[0050] In the above formula, represents the concentrated mass of the next rope node of the movable pulley, represents the second-order derivative of the position vector of the next rope node of the movable pulley with respect to time, represents the gravitational force of the earth on the next node of the movable pulley, represents the gravitational force of the moon on the last node of the movable pulley, represents the centrifugal force on the next node of the movable pulley, represents the Coriolis force on the next node of the movable pulley, represents the friction force on the next node of the movable pulley, represents the elastic force of the connecting rod between the next node of the movable pulley and the adjacent node, Represents the elastic force of the connecting rod between the adjacent node of the rear node of the movable pulley and a node further away.

[0051] Finally, it should be noted that , , , Each item represents the elastic force of the connecting rod between the adjacent node and a further node, and all points in the counterclockwise direction of the node.

[0052] S330, introducing characteristic node identification rules, transforming the dynamic equations of node parameters, and obtaining the gravitational siphon effect lunar ladder dynamics model.

[0053] First of all, it should be noted that the numbers corresponding to special nodes will obviously change during the movement process, and a certain mechanism is needed to determine the numbers of these special nodes at a specific moment. The judgment mechanism is not unique, and it has a critical impact on the execution mode and operation efficiency of the algorithm. The existing method is to establish a global variable that stores the numbers of these special nodes, which is an array type, and judge whether the next node in the running direction has become the corresponding special node during the calculation process. This method is highly efficient, but it has requirements for the smoothness of the dynamic process, especially in the early transient stage, the system jitters violently, and it is easy to have the situation that the next node does not arrive at the pulley in sequence, resulting in singularity and causing operation failure. In order to overcome this difficulty, the interrupt integration method can be used to handle it. When it is determined that a singularity occurs, the time history integral calculation is stopped, the current result is stored as the initial value of the next stage calculation, and then the position and speed of the singular node are forcibly adjusted, and the integration is started again. However, this method will seriously affect the calculation efficiency.

[0054] Therefore, the embodiment of the present invention introduces a characteristic node discrimination rule, specifically, determines the closed-loop rope node closest to the pulley, and numbers it, determines the target node, and the pulley is a fixed pulley or a movable pulley; determines the next node of the target node and the previous node of the target node, determines the distance between the next node of the target node and the pulley, and the distance between the previous node of the target node and the pulley; judges the distance between the next node of the target node and the pulley, and the distance between the previous node of the target node and the pulley; if the distance between the next node of the target node and the pulley is less than the distance between the previous node of the target node and the pulley, then determines that the next node of the target node is the previous node of the pulley, and the target node is the next node of the pulley; if the distance between the next node of the target node and the pulley is greater than the distance between the previous node of the target node and the pulley, then determines that the target node is the previous node of the pulley, and the previous node of the target node is the next node of the pulley.

[0055] In this embodiment, if Figure 7 and Figure 8 As shown, take the PE side of the movable pulley as an example. First determine the node closest to PE and get its number , then calculate , The distance between two nodes and PE, when the ladder runs in order (i.e. the node with a smaller number moves towards the adjacent node with a larger number), if Compare If the distance to PE is closer, for , For Pea, for On the contrary, if Compare Farther from PE, Pmin is , For Pea, is .

[0056] A similar method is used to determine the PM side of the fixed pulley. , The number of the node.

[0057] In addition, in Python and most programming languages, node numbers can only be one-dimensional arrays, so you need to pay attention to the problem of connecting the beginning and the end. The last number plus one returns to the first number, and the first number minus one is defined as the last number.

[0058] Finally, the embodiment of the present invention also discloses that when a node passes over the pulley, that is, from ( )become ( ), its velocity is no longer given by the integral of the acceleration according to the dynamic equation, but is directly set to a constant velocity, and the direction changes directly from toward the pulley PM (PE) to toward ( ). Without affecting the accuracy, for the sake of simplicity, we can even directly specify its speed as ( ) speed. This setting directly gives the equation ( ) are as follows:

[0059]

[0060] When a node is become When the quality is changed from become ; When a node mass is become When become That is to say, and The node masses between , while the masses of other nodes are all .exist and The relationship in the ordinal array is Greater than When the quality of the uplink node is guaranteed, it is necessary to carefully define the difference between the two as [1~Pea]U[Pmb~N]. This is actually to ensure that the quality of the uplink node is , the downstream node is loaded with goods Increase to .

[0061] The first node after passing the fixed pulley , provided to the cargo in motion Momentum, thus receiving a reaction force. Until the cargo and the node have the same speed. The actual loading process of this force is relatively complicated, and this section uses the overall analysis method to approximate it. First, it is assumed that the cargo just uses one section of travel to reach the same linear speed as the system. This assumption is to avoid dealing with multiple nodes and cargo coupling processes at the same time. In addition, only the steady state is considered, and the final overall linear speed of the system is , that is, the speed of the cargo increases from 0 to , assuming that the force on the cargo remains constant during acceleration, is , then:

[0062] and It is mainly composed of the gravity of the earth, the moon, cargo and nodes. The force between The three items are composed of the following: At this time, the earth's gravity is in the same direction as the movement, and the moon's gravity is in the opposite direction of the movement. In addition, when dealing with gravity, it is considered that the cargo and the node At the same location, we have:

[0063] Therefore, the above expression needs to be further modified to become:

[0064] It should be said that The symbol represents assignment, which means modifying the variable based on the previous expression, which can be conveniently expressed in a sequentially compiled programming language. The expression of In computing practice, its direction is always defined as The direction of motion acceleration is opposite. Of course, such approximate processing is reasonable and convenient, and the error can be ignored.

[0065] By combining the above equations, we can get the dynamic equation of the system. This dynamic equation is a differential algebraic equation. Then it can be further degenerated into an ordinary differential equation:

[0066] In addition, since the embodiment of the present invention adopts a rotating coordinate system and does not study the situation of the moon's revolution elliptical orbit, the equation does not explicitly contain the time independent variable t, and it is a nonlinear autonomous system.

[0067] Furthermore, a simulation experiment is conducted on the embodiment of the present invention. First, a typical reasonable working condition is selected for simulation and post-processing analysis. The natural parameters of the Earth-Moon system are shown in Table 1: Table 1 Parameter values ​​used in static calculations

[0068] Its main material indicators are shown in Table 2 below: Table 2 Material index data table

[0069] The movable pulley end of the siphon ladder is located at Ten thousand kilometers, that is, about 63,000 kilometers above the ground, which means that the one-way length of the siphon ladder is about 313,260 kilometers.

[0070] The ladder is divided into 340 nodes in one direction according to the method in Section 5.3, and there are 680 nodes in both directions. An empty cargo box is set at each node. In the simulation, the mass of the cargo box and the mass of the material of the next section of the ladder counterclockwise are combined and assigned to the node, which is This is equivalent to the density of the material or a corresponding increase in value. In this example, the length of each segment is calculated , the quality of each node . Because each container is loaded with Unchanged, for the convenience of general comparison, the goods and nodes are given the quality A ratio, called the cargo-box mass ratio , in this example =0.1, then the corresponding =9343kg.

[0071] In order to start the numerical simulation smoothly, all nodes are given an initial velocity of 10 in the counterclockwise direction. The Rouge-Kutta 4-5 method is used for simulation, and the time history is from time 0 to day 120. Fig. 9As shown in the figure, it is a typical moment screenshot of the simulation result of the embodiment of the present invention, as well as the post-processing of the results of some important parameters, and a brief analysis is performed. The results show that the gravity siphon lunar ladder can be successfully started and operated under the working conditions of this typical example, and can smoothly reach a stable operating state, can effectively implement cargo transportation, and achieve the design goal. The ladder starts from a small preset initial speed, and under the action of the gravity siphon, the operating speed gradually increases. During its operation, the Coriolis forces on the upward and downward parts are in opposite directions, so that the two sides of the ladder are opened in opposite directions, just avoiding opposite collisions. In the early stage of operation, the opening degree of the ladder is opened and closed under the action of the elastic force, but because the elastic force is the reaction force caused by the Coriolis force, it is not enough to cause a collision, and when the ladder reaches a certain speed, the opening degree will remain in a larger state. Finally, the ladder will reach its steady-state operating speed, and maintain long-term stable operation in the process of continuous loading and unloading.

[0072] Finally, the relationship between steady-state speed and ladder length The above results show that the steady-state speed It has little to do with the cargo-to-box mass ratio, which is the most important operating indicator. Which design or operating parameters are mainly affected and what is the relationship? The following attempts to use the principle of conservation of energy for a brief analysis.

[0073] Since in most cases the opening The total length of the ladder is very small, and the deflection angles relative to the Earth-Moon line are also very small. The opening will be ignored in this analysis. , the system is approximately regarded as moving up and down along the Earth-Moon line.

[0074] First, in steady-state operation, the speed of all nodes in the siphon ladder is the steady-state speed. , the distance between adjacent nodes remains unchanged, and it can be considered that the total elastic potential energy of the system remains unchanged.

[0075] Secondly, the overall gravitational potential energy of the cargo in the downlink section decreases from the lunar surface to the end, which is converted into the kinetic energy of the cargo, increasing the overall kinetic energy of the system.

[0076] Finally, the cargo is thrown away at the end, which is equivalent to the system losing kinetic energy. The lost kinetic energy is equal to the kinetic energy increased by the conversion of potential energy, so that the overall kinetic energy of the system remains unchanged, that is, the system movement maintains a stable speed. .

[0077] Further, the quality of the empty node , the quality of a single box of goods Evenly distributed on the siphon ladder system, there is a corresponding line density , , in unit time The overall potential energy of the system The changes are as follows:

[0078] The first term on the right side of the above formula represents the upward direction, and the second term represents the downward direction. The integral directions of the two are opposite. is the gravitational field intensity gradient of the Earth-Moon system, that is, the gravitational acceleration. The above formula can be simplified to:

[0079] In unit time The kinetic energy lost by the system as follows:

[0080] equal , perform the integral operation, and we can get:

[0081] In the above formula, , , , , , are all constants, only the coordinates of the end movable pulley are is a variable, that is, the steady-state speed of the gravitational siphon lunar ladder It's only about its length.

[0082] It can be seen that the steady-state speed and internal force of the ladder system decrease as the length of the ladder decreases, which is basically consistent with the results of the calculation integration. The difference between the numerical simulation results and the theoretical analysis results is mainly caused by the neglect of the opening in the theoretical analysis. The opening is more complicated, and the opening is the largest when the end of the ladder is 70,000 to 80,000 kilometers away from the earth.

[0083] In addition, simulation results show that the ladder can still operate even at a distance of 120,000 kilometers from the Earth (and the position of the movable pulley after dynamic elastic extension still reaches 119,000 kilometers), although the running speed is very slow, that is, the end of the ladder is more than 110,000 kilometers away from the Earth, but it still does not fall to the moon. =125000km, the system fell onto the moon. This shows that the permissible length of the gravity siphon lunar ladder is shorter. The main reason is that the siphon ladder needs to be designed with a larger movable pulley at the end, which makes the earth's gravitational force on the whole system stronger and strengthens the overall stability of the system.

[0084] In summary, the embodiments of the present invention have the following advantages compared with the prior art: 1) The bead point simplification method is used to discretize the continuous ladder structure into a series of nodes and elastic connection segments, and the interaction force between nodes, the gravity of the earth and the moon, centrifugal force, Coriolis force, and material damping are comprehensively considered. The mechanical model of the coupling between the rope and the movable pulley and the fixed pulley is cleverly designed, and the criterion for determining the nodes coupled with the pulley is designed. Through continuous determination, the differential algebraic equation is converted into a pure differential equation, realizing the uninterrupted continuous practice process integral solution of the differential equation.

[0085] 2) Provide an effective power system for the ladder climber so that it can move smoothly on the cable. The present invention provides a power system method using gravitational siphon as a power source. Orbital siphon is an innovative physical mechanism that aims to use the rotational kinetic energy of an asteroid to achieve propellant-free payload transfer. The core of this concept is to achieve the transfer of material from the lunar surface to the orbital collection spacecraft through a load mass chain connected by a rope perpendicular to the surface of the asteroid.

[0086] 3) A detailed sensitivity analysis was conducted on key operating parameters such as cargo-to-container mass ratio and ladder length. The results show that the cargo-to-container mass ratio has little effect on the performance indicators of the ladder, such as steady-state speed, internal force and stress. The main performance indicators of the ladder operation depend on its total length. The present invention provides an analytical analysis of the relationship between steady-state speed and length based on a simplified model, and verifies it by comparing it with the numerical simulation results. The results show that the longer the total length of the siphon ladder, the greater its final steady-state operating rate.

[0087] 4) The speed of the ladder designed in the embodiment of the present invention reaches about 1600m / s, and it takes about 2.5 days to transport the goods from the lunar surface to the ground. Although the linear speed is much lower than that of the rocket, the distance is much closer than the lunar orbit of most rockets and is close to a straight line, so the efficiency is not low. It must be pointed out that the original intention of the gravity siphon lunar ladder was to mine lunar minerals and transport them to the earth. However, its uplink side does not have to run empty, and lighter payloads can be loaded and transported to the moon. Compared with using rockets throughout the journey, it can greatly save fuel, and the total transportation capacity is also much larger than that of rockets, and the control of operation control and landing and ascent processes is also much easier. The travel time of about 2.5 days makes this system also usable for manned travel, which is completely within the acceptable range of human interstellar travel.

[0088] Reference Figure 2 , an automatic lunar ladder modeling system based on the gravitational siphon effect, including: The first module 201 is used to construct a gravity siphon lunar ladder model; The second module 202 is used to perform bead point simplification processing on the gravity siphon lunar ladder model to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder; The third module 203 is used to construct a coordinate system and perform dynamic analysis on the simplified multi-body dynamics model of the gravity siphon lunar ladder to obtain a dynamics model of the gravity siphon lunar ladder.

[0089] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0090] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. The automatic operation lunar ladder modeling method based on the gravitational siphon effect is characterized by: The following steps are involved: Construct a gravitational siphon lunar ladder model; The gravity siphon lunar ladder model is simplified by bead point processing to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder. The coordinate system construction and dynamic analysis of the simplified multi-body dynamics model of the gravitational siphon lunar ladder are carried out to obtain the dynamics model of the gravitational siphon effect lunar ladder.

2. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 1 is characterized in that: The gravitational siphon lunar ladder model specifically includes a closed-loop rope, a fixed pulley, a movable pulley and a cargo box, wherein the fixed pulley is distributed on the near-earth surface of the moon, the movable pulley is distributed on the near-earth surface of the earth, the closed-loop rope runs around both ends of the fixed pulley and the movable pulley respectively, the closed-loop rope running toward the moon is defined as the upward direction, and the closed-loop rope running toward the earth is defined as the downward direction, and the cargo boxes are evenly spaced on the upper surface of the closed-loop rope.

3. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 2 is characterized in that: The step of performing bead point simplification processing on the gravity siphon lunar ladder model to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder specifically includes: The closed-loop rope in the gravity siphon lunar ladder model is divided into several segments with equal spacing, and each segment of the closed-loop rope is regarded as a node; Assume that adjacent nodes are connected by elastic straight rods, and the fixed pulley and movable pulley in the gravitational siphon lunar ladder model are regarded as nodes; Assume that the fixed pulley node is connected to the closed-loop rope node and the movable pulley node is connected to the closed-loop rope node, and set the previous node of the fixed pulley in the gravity siphon lunar ladder model to , the next node of the fixed pulley in the gravitational siphon lunar ladder model is , the previous node of the movable pulley in the gravitational siphon lunar ladder model is , the next node of the movable pulley in the gravitational siphon lunar ladder model is , and a simplified multi-body dynamics model of the gravitational siphon lunar ladder is obtained.

4. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 3 is characterized in that: The step of constructing a coordinate system and conducting dynamic analysis on the simplified multi-body dynamics model of the gravity siphon lunar ladder to obtain the dynamics model of the gravity siphon lunar ladder specifically includes: Based on the Earth-Moon rotating coordinate system, a simplified multi-body dynamics model of the gravitational siphon lunar ladder with a coordinate system is constructed to obtain the position vectors of the model parameters; Based on the position vector of the model parameters, the dynamic equations of the node parameters are constructed by considering the interaction force factors, gravity factors, centrifugal force factors, Coriolis force factors and damping force factors; Characteristic node identification rules are introduced, and the dynamic equations of node parameters are transformed to obtain the dynamic model of the lunar ladder with gravitational siphon effect.

5. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 4 is characterized in that: The position vector of the model parameter specifically includes a closed-loop rope node The position vector is , the Earth's position vector , the moon's position vector , the position vector of the fixed pulley , the position vector of the movable pulley is , the position vector of the previous node of the fixed pulley , the position vector of the next node of the fixed pulley , the position vector of the previous node of the movable pulley The position vector of the next node of the movable pulley .

6. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 5 is characterized in that: The dynamic equations of the node parameters specifically include the closed-loop rope node The dynamic equation of the fixed pulley, the dynamic equation of the movable pulley, the dynamic equation of the previous node of the fixed pulley, the dynamic equation of the next node of the fixed pulley, the dynamic equation of the previous node of the movable pulley and the dynamic equation of the next node of the movable pulley, where: The closed loop rope node The expression of the kinetic equation is: In the above formula, represents the i-th closed-loop rope node The concentrated mass, represents the i-th closed-loop rope node The second derivative of the position vector with respect to time, represents the gravitational force of the earth on the nodes of the closed-loop rope, represents the gravitational force of the moon on the nodes of the closed-loop rope, , represents the elastic force of the connecting rod between adjacent closed-loop rope nodes, represents the centrifugal force on the closed-loop rope node, represents the Coriolis force on the closed-loop rope node, represents the damping force on the closed-loop rope node; The dynamic equation of the movable pulley is expressed as: In the above formula, represents the concentrated mass of the movable pulley, represents the second-order derivative of the position vector of the movable pulley with respect to time, represents the gravitational force on the movable pulley, represents the gravitational force of the moon on the movable pulley, is the centrifugal force on the movable pulley, is the Coriolis force on the movable pulley, is the friction force on the movable pulley, represents the elastic force of the connecting rod between the movable pulley and the previous node of the movable pulley, It represents the elastic force of the connecting rod between the movable pulley and the next node of the movable pulley; The expression of the dynamic equation of the previous node of the fixed pulley is: In the above formula, represents the concentrated mass of the previous rope node of the fixed pulley, represents the second-order derivative of the position vector of the previous rope node of the fixed pulley with respect to time, represents the earth's gravitational force on the previous node of the fixed pulley, represents the gravitational force of the moon on the previous node of the fixed pulley, represents the centrifugal force on the previous node of the fixed pulley, represents the Coriolis force on the previous node of the fixed pulley, represents the friction force on the previous node of the fixed pulley, represents the elastic force of the connecting rod between the previous node and the adjacent node of the fixed pulley, represents the elastic force of the connecting rod between the adjacent node of the previous node of the fixed pulley and a node further away; The expression of the dynamic equation of the next node of the fixed pulley is: In the above formula, represents the concentrated mass of the next rope node of the fixed pulley, represents the second-order derivative of the position vector of the next rope node of the fixed pulley with respect to time, represents the earth's gravitational force on the next node of the fixed pulley, represents the lunar gravitational force on the next node of the fixed pulley, represents the centrifugal force on the next node of the fixed pulley, represents the Coriolis force on the next node of the fixed pulley, represents the friction force on the next node of the fixed pulley, represents the elastic force of the connecting rod between the next node of the fixed pulley and the adjacent node, represents the elastic force of the connecting rod between the adjacent node of the next node of the fixed pulley and a node further away; The expression of the dynamic equation of the previous node of the movable pulley is: In the above formula, represents the concentrated mass of the previous rope node of the movable pulley, represents the second-order derivative of the position vector of the previous rope node of the movable pulley with respect to time, represents the earth's gravitational force on the previous node of the movable pulley, represents the gravitational force of the moon on the previous node of the movable pulley, represents the centrifugal force on the previous node of the movable pulley, represents the Coriolis force on the previous node of the movable pulley, represents the friction force on the previous node of the movable pulley, represents the elastic force of the connecting rod between the previous node and the adjacent node of the movable pulley, represents the elastic force of the connecting rod between the adjacent node of the previous node of the movable pulley and a node further away; The expression of the dynamic equation of the next node of the movable pulley is: In the above formula, represents the concentrated mass of the next rope node of the movable pulley, represents the second-order derivative of the position vector of the next rope node of the movable pulley with respect to time, represents the earth's gravitational force on the next node of the movable pulley, represents the gravitational force of the moon on the last node of the movable pulley, represents the centrifugal force on the next node of the movable pulley, represents the Coriolis force on the next node of the movable pulley, represents the friction force on the next node of the movable pulley, represents the elastic force of the connecting rod between the next node of the movable pulley and the adjacent node, Represents the elastic force of the connecting rod between the adjacent node of the rear node of the movable pulley and a node further away.

7. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 6 is characterized in that: The introduced characteristic node identification rule is specifically as follows: Determine the closed-loop rope node closest to the pulley, number it, and determine the target node, the pulley is a fixed pulley or a movable pulley; Determine the next node of the target node and the previous node of the target node, determine the distance between the next node of the target node and the pulley, and determine the distance between the previous node of the target node and the pulley; Determine the distance between the next node of the target node and the pulley and the distance between the previous node of the target node and the pulley; If the distance between the next node of the target node and the pulley is less than the distance between the previous node of the target node and the pulley, then the next node of the target node is determined to be the previous node of the pulley and the target node is the next node of the pulley; If the distance between the next node of the target node and the pulley is greater than the distance between the previous node of the target node and the pulley, the target node is determined to be the previous node of the pulley and the previous node of the target node is the next node of the pulley.

8. The automatic operation lunar ladder modeling system based on the gravitational siphon effect is characterized by: Includes the following modules: The first module is used to construct a gravitational siphon lunar ladder model; The second module is used to simplify the gravitational siphon lunar ladder model by beads to obtain a simplified multi-body dynamics model of the gravitational siphon lunar ladder; The third module is used to construct the coordinate system and conduct dynamic analysis on the simplified multi-body dynamics model of the gravitational siphon lunar ladder, and obtain the dynamics model of the gravitational siphon effect lunar ladder.

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