CN115879386A - Three-node flexible detector and dynamics modeling method thereof - Google Patents
Three-node flexible detector and dynamics modeling method thereof Download PDFInfo
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Abstract
The invention provides a three-node flexible detector and a dynamics modeling method thereof, and belongs to the field of asteroid detection. The three-node flexible probe includes: the flexible connection structure is embedded in the flexible connection structure, and three prismatic rigid nodes with the same size are distributed in a rotational symmetry mode relative to the center of the detector; the height of the rigid node is equal to the distance between the upper bottom surface and the lower bottom surface of the flexible connecting structure; the flexible connecting structure is used for connecting three rigid nodes and buffering in the process that the detector lands on the small planet; the rigid node is used for providing control force and control moment of the detector and protecting equipment placed in the rigid node. The three-node flexible detector can improve the success rate of asteroid landing detection, and the dynamics modeling method can carry out dynamics simulation solving on the three-node flexible detector to obtain physical quantities such as displacement, speed and the like of the three-node flexible detector in the asteroid landing process, so that technical support is provided for asteroid landing tasks.
Description
Technical Field
The invention belongs to the field of asteroid detection, and particularly relates to a three-node flexible detector and a dynamics modeling method thereof.
Background
The structure and composition information of the asteroid probably contain the evolution track of the solar system, and meanwhile, part of the asteroids contain a large amount of platinum, iridium and other rare metal resources. The asteroid exploration and development has great scientific research value and economic value.
Currently, landing and exploring asteroids is the most direct and effective way to study asteroids. However, in actual tasks, due to the weak gravity environment and irregular surface of the small planet, the traditional rigid detector is easy to rebound and escape and overturn out of control, and the login task fails. Meanwhile, the surface information of the asteroid mastered by human beings at present is very limited, a flat landing site is difficult to determine when the detector logs in, and large-scale movement is difficult to carry out after logging in, so that the logging in detection task fails.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a three-node flexible detector and a dynamic modeling method thereof. The three-node flexible detector can improve the success rate of asteroid landing detection, and the corresponding dynamic modeling method can perform dynamic simulation solving on the three-node flexible detector, so that physical quantities such as displacement, speed and the like of the three-node flexible detector in the asteroid landing process are obtained, and technical support is provided for the research of a control method of the three-node flexible detector and the asteroid landing task.
An embodiment of a first aspect of the present invention provides a three-node flexible detector, including: the flexible connection structure is embedded in the flexible connection structure, and three prismatic rigid nodes with the same size are embedded in the flexible connection structure and are distributed in a rotational symmetry mode relative to the center of the detector; the height of the rigid node is equal to the distance between the upper bottom surface and the lower bottom surface of the flexible connecting structure; the weight and the moment of inertia of each rigid node are equal;
the flexible connecting structure is used for connecting the three rigid nodes and buffering the detector in the process of landing the small planet; the rigid node is used for providing control force and control moment of the detector and protecting equipment placed in the rigid node.
In a specific embodiment of the present invention, the flexible connection structure is composed of two disks with the same size and a ring with an inner diameter equal to the diameter of the disks, the disks and the ring are both made of the same flexible material and have the same thickness, and the two disks respectively form the upper and lower bottom surfaces of the semicircular ring; the rigid nodes are hexagonal prism-shaped, and the flexible connecting structures are connected with the side faces of the three rigid nodes through rubber adhesives.
In a specific embodiment of the present invention, the rigid node comprises: a rigid housing, a tank, and a jet conduit; the gas tank is fixed at the central position inside the rigid node through a connecting framework inside the rigid shell; the gas tank is a hollow sphere; the upper and lower poles of the gas tank are respectively connected with one section of the gas injection guide pipe, and the two sections of the gas injection guide pipes vertically penetrate through the upper and lower bottom surfaces of the rigid shell in the rigid shell and are connected with the rigid shell in a welding mode;
the gas tank is used for storing high-pressure gas which provides control force and control torque during the landing process of the detector;
the gas injection conduit is used for guiding out the high-pressure gas stored in the gas tank.
In a specific embodiment of the invention, a payload for the detector to detect asteroid is also placed inside the rigid housing.
The embodiment of the second aspect of the invention provides a dynamic modeling method based on the three-node flexible detector, which comprises the following steps:
dispersing the surface of the flexible connecting structure into a plurality of triangular units;
based on the triangle unit, solving the internal force when the flexible structure deforms, comprising: the stretching internal force of each vertex when the triangular unit is subjected to stretching deformation and the bending internal force of each vertex when the triangular unit is subjected to bending deformation;
and establishing a dynamic model of the three-node flexible detector according to the internal force when the flexible structure deforms.
In a specific embodiment of the present invention, the discretizing the surface of the flexible connecting structure into a plurality of triangular units further includes:
and equating the material quality of the flexible connection structure to the vertex of each triangular unit according to the area of each triangular unit, wherein the expression is as follows:
wherein m is i Representing the quality of the ith vertex, N representing the number of triangle elements connected by the ith vertex, A j And the area of the jth triangular unit connected with the ith vertex is shown, rho is the density of the flexible material at the position of the triangular unit, and h is the thickness of the flexible material at the position of the triangular unit.
In an embodiment of the present invention, the method for calculating the tensile internal force of each vertex when the triangle unit is subjected to tensile deformation includes:
respectively marking three vertexes of any triangular unit as x in the counterclockwise direction i 、x j And x k Then the triangle unit is stretched and deformed at the vertex x i The resulting tensile internal force calculation expression is as follows:
wherein,
is represented by vertex x i 、x j And x k When the composed triangular units are subjected to tensile deformation, the vertex x is i Tensile internal force generated, /) i 、l j 、l k Respectively representing the vertexes x after the deformation of the triangular units i 、x j And x k Respective opposite sides, i.e. sides x j x k 、x i x k 、x i x j Length of (L) i 、L j 、L k Respectively representing the deformation of a triangular unitFront edge x j x k 、x i x k 、x i x j Length of (a) r xi Representing vertex x i Position vector of r xj Representing a vertex x j A position vector of (a); k ij 、K i And K j Respectively represent an edge x i x j Angle of included stiffness, edge x j x k Tensile stiffness, edge x of i x k The expressions are calculated as follows:
wherein E is the Young modulus of the flexible structure material, mu is the Poisson's ratio of the flexible structure material, and alpha i Representing the deformed front edge x of the triangular element i x k And x i x j Angle of (a) of j Representing the deformed front edge x of the triangular element j x k And x i x j Angle of (a) of k Representing the deformed front edge x of the triangular element j x k And x i x k A represents the area of the triangular unit before deformation;
and calculating the stretching internal force generated at each vertex when each triangular unit is stretched and deformed, and summing the stretching internal forces generated at the same vertex to obtain the final stretching internal force of the vertex.
In a specific embodiment of the present invention, the method for calculating the bending internal force of each vertex when the triangular unit is subjected to bending deformation includes:
let the common edge of any two adjacent triangle units be x 0 x 1 One of the triangular units f 0 Has a vertex of x 0 、x 1 And x 2 Another triangular unit f 1 Has a vertex of x 0 、x 1 And x 3 Then, the bending internal force generated by each vertex when the two triangular units are subjected to bending deformation is as follows:
wherein,
respectively represent triangle units f 0 And f 1 At the vertex x when bending deformation occurs 0 、x 1 、x 2 、x 3 Resulting bending internal force, n 0 、n 1 Respectively representing triangular units f 0 And a triangle unit f 1 Unit normal vector of (A) f0 And A f1 Respectively represent triangle units f 0 And f 1 Area of (a), theta e Representing n after deformation 0 And n 1 Is included angle of (B)>
Representing n before deformation 0 And n 1 In the angle of (B) is greater than or equal to>
Indicating the current time n 0 And n 1 Speed of change of angle, e 0 Representing the deformed common edge x 0 x 1 Is greater than or equal to>
Denotes x before deformation 0 x 1 Length of (a), a 01 Represents an edge x 0 x 1 And x 0 x 2 Angle of (a) of 02 Represents an edge x 0 x 1 And x 0 x 3 Angle of (a) 03 Represents x 0 x 1 And x 1 x 2 Angle of (a) 04 Represents an edge x 0 x 1 And x 1 x 3 ；/>
Wherein->
As a unit of triangle f 0 Relative to the edge x 0 x 1 Is high,. Sup.,>
is a triangular unit f 1 Relative to the edge x 0 x 1 C is the damping coefficient of the flexible connecting structure material;
and calculating the bending internal force generated at each vertex when each adjacent triangular unit is subjected to bending deformation, and summing the bending internal forces generated at the same vertex to obtain the final bending internal force of the vertex.
In a specific embodiment of the present invention, the establishing a dynamic model of the three-node flexible probe according to the internal force when the flexible structure is deformed includes:
1) Constructing a node dynamic equation of the three-node flexible detector:
wherein m is ci Denotes the quality of the ith node, r ci Representing the centroid position vector of the ith node, F ci Representing the control force, I, acting on the ith node i Inertia matrix, ω, representing the ith node i Indicating the rotational angular velocity of the i-th node, M ci Representing the control torque acting on the ith node;
2) Constructing a dynamic equation of a flexible connection structure of the three-node flexible detector:
wherein Np represents the number of rear vertexes of the flexible connection structure dispersed into triangular units, and m i Denotes the mass of the ith vertex, r i A position vector representing the ith vertex;
represents the sum of all tensile internal forces acting on the ith vertex,
represents the sum of all bending internal forces acting on the ith vertex;
3-3) applying rigid constraint to the vertex of the position occupied by the node on the surface of the flexible connecting structure:
φ i ＝R c (r φi -r c )+C i ＝0 i＝1,…N φ (7)
wherein, N φ The total number of vertices, phi, representing the positions occupied by the nodes at the surface of the flexible joint structure i A rigid constraint equation corresponding to the ith vertex representing the position occupied by the node on the surface of the flexible connection structure, r φi A position vector of the ith vertex representing the position occupied by the node at the surface of the flexible joint structure, r c Centroid position vector, R, of corresponding node connected to ith vertex representing the position occupied by the node at the surface of the flexible connection structure c An attitude transformation matrix, C, representing the inertial system to the nodal body coordinate system i And a vector from the ith vertex of the position occupied by the node on the surface of the flexible connecting structure to the centroid of the corresponding node under the undeformed condition.
In a specific embodiment of the present invention, the method further comprises:
and solving the dynamic model to obtain the displacement vector and the velocity vector of each triangular unit vertex and the angular velocity, the centroid displacement vector and the velocity vector of the three rigid nodes.
The invention has the characteristics and beneficial effects that:
the invention provides a three-node flexible detector suitable for asteroid landing detection. In the landing process, the three-node flexible detector can dissipate energy through deformation and collision of the flexible material, so that the collision rebound speed is reduced, and the rebound and escape phenomena are avoided.
The symmetrical structural design of the three-node flexible detector can ensure that the detector can still work normally in a turnover state, and the phenomenon of out-of-control overturning is avoided. Three nodes of the three-node flexible detector can carry different detection instruments respectively, failure of the whole task caused by damage of a single node is avoided, and success rate of detection tasks is improved.
The invention introduces a discrete curvature model and establishes an internal force solving model of the flexible material of the three-node flexible detector. By introducing a constraint violation stability law, the coupling relation between the flexible material in the three-node flexible detector and the three nodes is established, so that a dynamic model of the three-node flexible detector is established and calculated, and a new scheme is provided for asteroid landing detection.
The invention can be used for asteroid detection tasks such as asteroid landing detection, asteroid surface inspection detection and the like in the future, and has high application value.
Drawings
Fig. 1 is an overall structural diagram of a three-node flexible detector in an embodiment of the invention.
FIG. 2 is a cross-sectional view of a three-node flexible probe and a node in accordance with an embodiment of the present invention.
FIG. 3 is a flowchart illustrating a method for modeling the dynamics of a three-node flexible probe according to an embodiment of the present invention.
FIG. 4 is a diagram illustrating triangle unit segmentation according to an embodiment of the present invention.
FIG. 5 is a schematic diagram of adjacent triangle units in accordance with one embodiment of the present invention.
Detailed Description
The invention provides a three-node flexible detector and a dynamics modeling method thereof, and the invention is further described in detail below by combining the attached drawings and specific embodiments.
An embodiment of a first aspect of the present invention provides a three-node flexible detector, including: the flexible connection structure is embedded in the flexible connection structure, and three rigid nodes which are same in size and are rotationally symmetrical relative to the center of the detector are embedded in the flexible connection structure; the height of the rigid node is equal to the distance between the upper bottom surface and the lower bottom surface of the flexible connecting structure. The flexible connecting structure is used for connecting three rigid nodes and plays a role in buffering when the detector lands on a small planet so as to prevent the detector from rebounding and escaping. The rigid node is used for placing equipment which is easy to damage, such as a payload, a gas tank, a gas injection guide pipe and the like, and is used for providing control force and control torque for the detector and protecting the equipment for detection.
It should be noted that each node may carry a different payload or probe device. In order to ensure the symmetry of the whole detector, the weights and the rotational inertia of the three nodes are required to be ensured to be the same.
In a specific embodiment of the invention, the overall structure of the three-node flexible detector is shown in fig. 1, the flexible connection structure is specifically composed of two disks with the diameter of 2m and the thickness of 5mm, and a semicircular ring with the inner diameter of 2m, the outer diameter of 2.8m and the thickness of 5mm, the disks respectively form the upper bottom surface and the lower bottom surface of the semicircular ring, and the distance between the upper ground surface and the lower ground surface is 0.4m. The flexible connection structure is connected with three rigid nodes which are rotationally symmetrical relative to the center of the detector and are respectively marked as a node (1), a node (2) and a node (3). It should be noted that the shape and size of the flexible connection structure can be modified according to the specific detection task, such as proportional enlargement or a cube shape. The flexible connection structure can be made of materials with low Young modulus, such as vulcanized rubber and silicon rubber, and the silicon rubber is adopted as the flexible connection material in the embodiment. In the embodiment, three rigid nodes are all rigid hexagonal prisms with the height of 0.4m and the side length of 0.2m, the rigid hexagonal prisms are rotationally and symmetrically distributed relative to the center of the detector, each rigid node is 0.6m away from the center of the detector, and the flexible connecting structure is connected with the side faces of the three rigid nodes through rubber adhesives. The shape and size of the rigid nodes can be modified according to the specific detection task, but the rigid nodes are prism-shaped, such as a quadrangular prism or a pentagonal prism, and the three nodes are consistent in shape.
In an embodiment of the present invention, a cross-sectional view of a three-node flexible detector and a node is shown in fig. 2, where each node has the same structure, and includes: rigid shell, gas tank, air injection pipe. In this embodiment, the rigid casing is a hexagonal prism casing having a wall thickness of 2mm or more. The cross section of the middle embedding in the rigid shell is a connecting framework and is used for fixing the gas tank in the center position inside the rigid node, the connecting framework is integrated with the rigid shell, and the gas tank and the connecting framework are fixed in a welding mode. The gas tank is in the shape of a hollow sphere, and the specific size and volume can be adjusted according to the control requirements of the deep space exploration task. The upper and lower two poles of the gas tank are respectively connected with a section of gas injection conduit, and the two sections of gas injection conduits respectively vertically penetrate to the upper and lower bottom surfaces of the rigid shell in the rigid shell; the gas tank is connected with the gas injection guide pipe in a welding mode, and the rigid shell is connected with the gas injection guide pipe in a welding mode.
In a specific embodiment of the invention, the rigid shell material of each node is an impact-resistant alloy material, such as any one of steel alloy, aluminum alloy and magnesium alloy, and the embodiment adopts 16Mn steel alloy for protecting the payload, the gas tank and the gas injection conduit. The gas tank material inside the node is a light alloy material, such as any one of steel alloy, aluminum alloy and magnesium alloy, in the embodiment, 1a95 aluminum alloy is adopted, and the gas tank material is used for storing high-pressure gas, such as 10MPa high-pressure nitrogen, which provides control force and control torque in the landing process of the three-node flexible detector. The material of the gas injection conduit of the node can be any one of steel alloy, aluminum alloy and magnesium alloy, the 16Mn steel alloy is adopted in the embodiment, and the gas injection conduit is used for guiding out the high-pressure gas stored in the gas tank. Further, the remaining space in the node may also be used for installing payloads such as radar, communication equipment, sampling devices, etc. for asteroid detection.
The embodiment of the second aspect of the present invention further provides a dynamics modeling method based on the above three-node flexible detector, and the overall flow is shown in fig. 3, and includes the following steps:
1) Flexible connection structure meshing:
the surface of the flexible connection structure is discretized into a plurality of triangular units, wherein the positions occupied by the nodes on the surface of the flexible connection structure also participate in discretization, the areas of the triangular units can be different, and the discretization process can be completed by means of finite element commercial software. In an embodiment of the present invention, a schematic diagram of the flexible connection structure after the triangle units are divided is shown in fig. 4.
The material quality of the flexible connection structure is equivalent to the top point of each triangular unit according to the area of each divided triangular unit, and the specific expression is as follows:
wherein m is i Representing the quality of the ith vertex, N representing the number of triangle elements connected by the ith vertex, A j And the area of the jth triangular unit connected with the ith vertex is shown, rho is the density of the flexible material at the position of the triangular unit, and h is the thickness of the flexible material at the position of the triangular unit.
It should be noted that values of ρ and h may be different in different units. For cells falling at a node, ρ and h may be taken as a large fixed value.
2) Solving the internal force when the flexible connection structure deforms, including; the method comprises the following specific steps:
2-1) obtaining the Young modulus E, the Poisson ratio mu, the density rho and the damping coefficient c of the material (vulcanized rubber in the example) of the flexible connecting structure by methods such as experimental verification or reference of documents and the like
2-2) calculating the tensile internal force of each vertex when the triangular unit is subjected to tensile deformation;
FIG. 5 shows two adjacent triangle units f after being dispersed according to an embodiment of the present invention 0 And f 1 Schematic representation of (a). The three vertexes of each triangular unit are respectively marked as x in the counterclockwise direction i 、x j And x k 。
In this embodiment, the basic triangle unit f 0 For example, the three vertices of the triangle unit in FIG. 5 are respectively marked as x 0 、x 1 And x 2 When the triangular unit is subjected to tensile deformation, the tensile internal force generated at any vertex is as follows:
wherein,
is represented by vertex x i 、x j And x k When the composed triangular units are subjected to tensile deformation, the vertex x is i Tensile internal force generated, /) i 、l j 、l k Respectively representing the vertexes x after the deformation of the triangular units i 、x j And x k Respective opposite side, i.e. side x j x k 、x i x k 、x i x j Length of (L) i 、L j 、L k Respectively representing the deformed front edges x of the triangular elements j x k 、x i x k 、x i x j Length of (a) r xi Representing a vertex x i Position vector of r xj Representing a vertex x j The position vector of (a); k is ij 、K i And K j Respectively represent an edge x i x j Angle of included stiffness, edge x j x k Tensile stiffness, edge x of i x k The calculated expression for the tensile stiffness of (a) is:
wherein alpha is i Representing the deformed front edge x of the triangular element i x k And x i x j Angle of (a) j Representing the deformed front edge x of the triangular element j x k And x i x j Angle of (a) of k Representing the deformed front edge x of the triangular element j x k And x i x k A represents a triangular unit (f in this embodiment) 0 ) Area before deformation;
and calculating the stretching internal force generated at each vertex when each triangle unit is subjected to stretching deformation, and summing the stretching internal forces generated at the same vertex to obtain the final stretching internal force of the vertex.
2-2) calculating the bending internal force of each vertex when the triangular unit is subjected to bending deformation;
in this embodiment, as shown in fig. 5, let the common edge of any two adjacent triangle units be x 0 x 1 One of the triangular units f 0 Has a vertex of x 0 、x 1 And x 2 Another triangular unit f 1 Has a vertex of x 0 、x 1 And x 3 Then, the bending internal force generated by each vertex when the two triangular units are subjected to bending deformation is as follows:
wherein,
respectively representing triangular units f 0 And f 1 At the vertex x when bending deformation occurs 0 、x 1 、x 2 、x 3 Resulting bending internal force, n 0 、n 1 Respectively representing triangular units f 0 And a triangle unit f 1 Unit normal vector of (A) f0 And A f1 Respectively representing triangular units f 0 And f 1 Area of (a), theta e Denotes n after deformation 0 And n 1 Is included angle of (B)>
Representing n before deformation 0 And n 1 Is included angle of (B)>
Indicating the current time n 0 And n 1 Speed of change of angle, e 0 Representing the deformed common edge x 0 x 1 In the length of (b), in combination with>
Denotes x before deformation 0 x 1 Length of (a) 01 Represents an edge x 0 x 1 And x 0 x 2 Angle of (a) 02 Represents an edge x 0 x 1 And x 0 x 3 Angle of (a) 03 Denotes x 0 x 1 And x 1 x 2 Angle of (a) 04 Represents an edge x 0 x 1 And x 1 x 3 。/>
Wherein->
Is a triangular unit f 0 Relative to the edge x 0 x 1 Is high,. Sup.,>
is a triangular unit f 1 Relative to the edge x 0 x 1 Is high.
And calculating the bending internal force generated at each vertex when each adjacent triangular unit is subjected to bending deformation, and summing the bending internal forces generated at the same vertex to obtain the final bending internal force of the vertex.
3) Establishing a dynamic model of the three-node flexible detector;
3-1) constructing a node dynamic equation of the three-node flexible detector;
in this embodiment, for each node of the three-node flexible detector, a kinetic equation is constructed as follows:
wherein m is ci Denotes the quality of the ith node, r ci Representing the centroid position vector of the ith node, F ci Representing the control force, I, acting on the ith node i Inertia matrix, ω, representing the ith node i Indicating the rotational angular velocity, M, of the i-th node ci Representing the control torque acting on the ith node.
3-2) constructing a dynamic equation of a flexible connection structure of the three-node flexible detector;
in this embodiment, for the flexible connection structure, a kinetic equation is constructed as follows:
wherein Np represents the number of rear vertexes of the flexible connection structure dispersed into triangular units, and m i Denotes the mass of the ith vertex, r i Representing the position vector of the ith vertex.
Represents the sum of all tensile internal forces acting on the ith vertex>
The sum of all bending internal forces, which are expressed at the ith vertex, is obtained by step 2).
3-3) applying rigid constraint to the vertex of the position occupied by the node on the surface of the flexible connecting structure;
in this embodiment, the stiffness constraint equation is:
φ i ＝R c (r φi -r c )+C i ＝0 i＝1,…N φ (7)
wherein N is φ The total number of vertices, phi, representing the positions occupied by the nodes at the surface of the flexible joint structure i A rigid constraint equation, r, corresponding to the ith vertex representing the position occupied by the node on the surface of the flexible connection structure φi A position vector of the ith vertex representing the position occupied by the node at the surface of the flexible joint structure, r c Centroid position vector, R, of corresponding node connected to ith vertex representing the position occupied by the node at the surface of the flexible connection structure c (the value is independent of i and is determined by a node dynamic equation) represents an attitude transformation matrix from an inertia system to the node body coordinate system, C i And a vector representing the ith vertex of the position occupied by the node on the surface of the flexible connection structure under the undeformed condition to the centroid of the corresponding node.
4) And solving a third dynamic model of the three-node flexible detector.
In the embodiment of the invention, the equations (5), (6) and (7) are solved by adopting a four-order Runge Kutta method and a constraint violation stabilizing method, so that the displacement vector and the velocity vector of each triangular unit vertex, which are obtained by dividing the dispersed flexible connecting structure in the three-node flexible detector at each moment, and the angular velocity, the centroid displacement vector and the velocity vector of three rigid nodes can be obtained through settlement, and the dynamic simulation of the three-node flexible detector is realized.
Claims (10)
1. A three-node flexible probe, comprising: the flexible connection structure is embedded in the flexible connection structure, and three prismatic rigid nodes with the same size are distributed in a rotational symmetry mode relative to the center of the detector; the height of the rigid node is equal to the distance between the upper bottom surface and the lower bottom surface of the flexible connecting structure; the weight and the moment of inertia of each rigid node are equal;
the flexible connecting structure is used for connecting the three rigid nodes and buffering in the process that the detector logs in the little planet; the rigid node is used for providing control force and control moment of the detector and protecting equipment placed in the rigid node.
2. The three-node flexible probe of claim 1, wherein the flexible connection structure is composed of two disks of the same size and a ring of the same inner diameter as the diameter of the disks, the disks and the ring are both made of the same flexible material and have the same thickness, and the two disks respectively constitute the upper and lower bottom surfaces of the semicircular ring; the rigid nodes are hexagonal prism-shaped, and the flexible connecting structures are connected with the side faces of the three rigid nodes through rubber adhesives.
3. The three-node flexible probe of claim 1, wherein the rigid node comprises: a rigid housing, a tank, and a jet conduit; the gas tank is fixed at the central position inside the rigid node through a connecting framework inside the rigid shell; the gas tank is a hollow sphere; the upper and lower poles of the gas tank are respectively connected with one section of the gas injection guide pipe, and the two sections of the gas injection guide pipes vertically penetrate through the upper and lower bottom surfaces of the rigid shell in the rigid shell and are connected with the rigid shell in a welding mode;
the gas tank is used for storing high-pressure gas which provides control force and control torque during the landing process of the detector;
the gas injection conduit is used for guiding out the high-pressure gas stored in the gas tank.
4. A three-node flexible probe according to claim 3, wherein a payload for the probe to detect asteroid is also placed inside the rigid housing.
5. A dynamic modeling method based on a three-node flexible detector as claimed in any one of claims 1-4, characterized by comprising:
dispersing the surface of the flexible connecting structure into a plurality of triangular units;
based on the triangle unit, solving the internal force when the flexible structure deforms, comprising: the stretching internal force of each vertex when the triangular unit is subjected to stretching deformation and the bending internal force of each vertex when the triangular unit is subjected to bending deformation;
and establishing a dynamic model of the three-node flexible detector according to the internal force when the flexible structure deforms.
6. The method of claim 5, wherein the discretizing the surface of the flexible connecting structure into a plurality of triangular units further comprises:
and equating the material quality of the flexible connection structure to the vertex of each triangular unit according to the area of each triangular unit, wherein the expression is as follows:
wherein m is i Represents the quality of the ith vertex, N represents the number of triangle units connected by the ith vertex, A j And the area of the jth triangular unit connected with the ith vertex is shown, rho is the density of the flexible material at the position of the triangular unit, and h is the thickness of the flexible material at the position of the triangular unit.
7. The method of claim 6, wherein the method for calculating the stretching internal force of each vertex when the triangle unit is subjected to stretching deformation comprises the following steps:
respectively marking three vertexes of any triangular unit as x in the counterclockwise direction i 、x j And x k Then the triangle unit is stretched and deformed at the vertex x i The resulting tensile internal force calculation expression is as follows:
wherein,
is represented by vertex x i 、x j And x k When the formed triangular unit is subjected to tensile deformation, the vertex x is i Tensile internal force generated, /) i 、l j 、l k Respectively representing the vertexes x after the deformation of the triangular units i 、x j And x k Respective opposite sides, i.e. sides x j x k 、x i x k 、x i x j Length of (L) i 、L j 、L k Respectively representing the deformed front edge x of the triangular unit j x k 、x i x k 、x i x j Length of (a), r xi Representing a vertex x i Position vector of r xj Representing a vertex x j A position vector of (a); k ij 、K i And K j Respectively represent an edge x i x j Angle of included stiffness, edge x j x k Tensile stiffness, edge x of i x k The calculation expressions are respectively as follows:
wherein E is the Young modulus of the flexible structure material, mu is the Poisson's ratio of the flexible structure material, and alpha i Representing the deformed front edge x of the triangular element i x k And x i x j Angle of (a) j Representing the deformed front edge x of the triangular element j x k And x i x j Angle of (a) k Representing the deformed front edge x of the triangular element j x k And x i x k A represents the area of the triangular unit before deformation;
and calculating the stretching internal force generated at each vertex when each triangle unit is subjected to stretching deformation, and summing the stretching internal forces generated at the same vertex to obtain the final stretching internal force of the vertex.
8. The method of claim 7, wherein the method for calculating the bending internal force of each vertex when the triangular unit is subjected to bending deformation comprises the following steps:
let the common edge of any two adjacent triangle units be x 0 x 1 One of the triangular units f 0 Has a vertex of x 0 、x 1 And x 2 Another triangular unit f 1 Has a vertex of x 0 、x 1 And x 3 Then, the bending internal force generated by each vertex when the two triangular units are subjected to bending deformation is as follows:
wherein,
respectively representing triangular units f 0 And f 1 At the vertex x when bending deformation occurs 0 、x 1 、x 2 、x 3 Resulting bending internal force, n 0 、n 1 Respectively representing triangular units f 0 And a triangle unit f 1 Unit normal vector of (A) f0 And A f1 Respectively representing triangular units f 0 And f 1 Area of (a), theta e Representing n after deformation 0 And n 1 Is included angle of (B)>
Representing n before deformation 0 And n 1 Is included angle of (B)>
Indicating the current time n 0 And n 1 Speed of change of angle, e 0 Representing the deformed common edge x 0 x 1 Is greater than or equal to>
Denotes x before deformation 0 x 1 Length of (a) 01 Represents an edge x 0 x 1 And x 0 x 2 Angle of (a) 02 Represents an edge x 0 x 1 And x 0 x 3 Angle of (a) 03 Denotes x 0 x 1 And x 1 x 2 Angle of (a) 04 Represents an edge x 0 x 1 And x 1 x 3 ；/>
Wherein->
As a unit of triangle f 0 Relative to the edge x 0 x 1 High->
Is a triangular unit f 1 Relative to the edge x 0 x 1 C is the damping coefficient of the flexible connecting structure material;
and calculating the bending internal force generated at each vertex when each adjacent triangular unit is subjected to bending deformation, and summing the bending internal forces generated at the same vertex to obtain the final bending internal force of the vertex.
9. The method of claim 8, wherein the establishing a dynamic model of the three-node flexible probe according to the internal force of the flexible structure during deformation comprises:
1) Constructing a node dynamic equation of the three-node flexible detector:
wherein m is ci Denotes the quality of the ith node, r ci Representing the centroid position vector of the ith node, F ci Representing the control force, I, acting on the ith node i Inertia matrix, ω, representing the ith node i Indicating the rotational angular velocity of the i-th node, M ci Representing the control torque acting on the ith node;
2) Constructing a dynamic equation of a flexible connection structure of the three-node flexible detector:
wherein Np represents the number of rear vertexes of the flexible connection structure dispersed into triangular units, and m i Denotes the mass of the ith vertex, r i A position vector representing the ith vertex;
represents the sum of all tensile internal forces acting on the ith vertex>
Represents the sum of all bending internal forces acting on the ith vertex;
3-3) applying rigid constraint to the vertex of the position occupied by the node on the surface of the flexible connecting structure:
φ i ＝R c (r φi -r c )+C i ＝0 i＝1,…N φ (7)
wherein N is φ The total number of vertices, phi, representing the positions occupied by the nodes at the surface of the flexible joint structure i A rigid constraint equation, r, corresponding to the ith vertex representing the position occupied by the node on the surface of the flexible connection structure φi Position vector of i-th vertex representing the position occupied by the node at the surface of the flexible joint structure, r c Centroid position vector, R, of corresponding node connected to ith vertex representing position occupied by node at surface of flexible connection structure c An attitude transformation matrix, C, representing the inertial system to the nodal body coordinate system i And a vector representing the ith vertex of the position occupied by the node on the surface of the flexible connection structure under the undeformed condition to the centroid of the corresponding node.
10. The method of claim 9, further comprising:
and solving the dynamic model to obtain the displacement vector and the velocity vector of each triangular unit vertex and the angular velocity, the centroid displacement vector and the velocity vector of the three rigid nodes.
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