Space mechanism on-orbit expansion elastic load calculation method

Abstract

The invention relates to a spatial mechanism in-orbit unfolding elastic load calculation method, which aims at solving the problem that a locking motor may fail due to elastic vibration caused by the interference force of an attitude control engine of an aircraft after a multi-degree-of-freedom space, carding the in-orbit working mode of the aircraft, and calculating the elastic load of the spatial mechanism based on a dynamic model. After dynamics simulation is carried out, attitude motion information and generalized coordinates of a space mechanism aircraft are obtained, joint rigid body and elastic load analysis research is carried out, a foundation is further laid for structural design of the space mechanism, and finally the load working condition of the space mechanism is obtained.

Description

Technical Field

[0001] The invention relates to a method for calculating elastic loads of an on-orbit deployment of a space mechanism, and belongs to the field of aerospace vehicle structural loads and mechanical environment. Background Art

[0002] In recent years, large flexible attachment aircraft has become a research hotspot in the aerospace field. Large flexible attachment space mechanisms have the structural characteristics of large area, low stiffness, and low damping, which leads to complex dynamic characteristics. Once low-order modes are excited by external interference torque, it will affect the normal operation of the aircraft at the least, and even lead to the failure of the mission at the worst. Therefore, the study of its elastic vibration is of great significance. Summary of the invention

[0003] 1. Technical issues to be resolved

[0004] In response to the needs and deficiencies of the above-mentioned prior art, the present invention aims at the problem that elastic vibration caused by the interference force of the aircraft attitude control engine in multi-degree-of-freedom space may lead to failure of the locking motor, sorts out the on-orbit working mode of the aircraft, and obtains the attitude motion information and generalized coordinates of the space mechanism aircraft after carrying out dynamic simulation based on the dynamic model, so as to conduct joint rigid body and elastic load analysis and research, further lay the foundation for the structural design of the space mechanism, and finally derive its load working condition.

[0005] (II) Technical solution

[0006] A method for calculating elastic loads of an on-orbit deployment of a space mechanism comprises the following steps:

[0007] S1. Determine the structural scheme and build a finite element model:

[0008] Based on the specific structure, mechanism scheme and mass characteristics of the spatial mechanism, a finite element model of the spatial mechanism is established, and the boundary condition is root fixation;

[0009] S2. Obtain mass matrix, coordinate matrix, modal moment and modal analysis:

[0010] The mass matrix [M] of all finite element nodes of the on-orbit rotating part of the space mechanism and the coordinate matrix [r] of the local coordinate system of the rotation point are obtained by the finite element method, wherein the mass matrix [M] is an n×1 matrix, and the coordinate matrix [r] is an n×3 matrix, wherein n is the number of all finite element nodes of the on-orbit rotating part of the space mechanism; modal analysis is performed to extract the modal frequency [F] and modal vibration shape [Φ], wherein the modal frequency [F] is an m×1 matrix, and the modal vibration shape [Φ] is an m×n×6 matrix, wherein m is the modal order, and modal damping is selected;

[0011] S3. According to the on-orbit mission of the spacecraft, the main mission conditions are sorted out and attributed to the on-orbit engine switch combination. The on-orbit mission of the spacecraft includes orbit transfer and orbit control. The on-orbit engine switch combination is related to the actual engine configuration of the spacecraft;

[0012] S4. According to the on-orbit dynamics model of the spacecraft and the main mission conditions, dynamic simulation is carried out to obtain the modal coordinates [q], the acceleration of the spacecraft body [A], the angular acceleration [a] and the angular velocity [w]. The modal coordinates [q] are m×t×1 matrices, and the acceleration of the spacecraft body [A], the angular acceleration [a] and the angular velocity [w] are all t×3 matrices, where t is the time step.

[0013] S5. See Figure 2-3 , obtain joint torque: take the modal vibration shape [Φ], modal coordinates [q], aircraft body acceleration [A], angular acceleration [a], angular velocity [w], mass matrix [M], coordinate matrix [r] as input conditions, use the elastic method to calculate the corresponding joint torque Ma and Mb; take the modal bending moment and modal coordinates [q] as input conditions, use the modal bending moment method to calculate the joint torque Ma and Mb again, where Ma and Mb are both t×3 matrices;

[0014] S6. Compare the consistency of Ma and Mb. If the error of Ma and Mb calculated by the two methods at the same time is within 5%, they are considered consistent, otherwise they are considered inconsistent. If they are consistent, it means that the calculation is correct; if they are inconsistent, it means that there is a problem in the calculation process, and the calculation process needs to be reviewed step by step until the calculation process is consistent.

[0015] S7. Obtain the maximum absolute value of Ma and Mb to obtain the load condition of the space mechanism under a certain mission condition. The calculation is then completed.

[0016] (III) Beneficial effects

[0017] The advantage of the elastic load calculation method for the on-orbit deployment of a space mechanism of the present invention compared with the prior art is that in the prior art, there are many studies on the dynamic simulation of aircraft with flexible attachments, especially the in-depth research on excessive vibration control, but there are few studies on the elastic load of the space mechanism itself. It is of great practical significance to study the on-orbit load condition determination method of multi-degree-of-freedom space mechanism considering elastic vibration, which can provide the necessary input conditions for the design and experimental verification of space mechanisms and improve flight reliability and safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Flow chart of calculation of elastic load of on-orbit deployment of a space mechanism of the present invention

[0019] Figure 2 Aircraft model with space mechanism of the present invention

[0020] Figure 3 Multi-degree-of-freedom solar cell array of the present invention DETAILED DESCRIPTION

[0021] See also Figure 1 A method for calculating elastic loads of a space mechanism deployed on-orbit in the present invention comprises the following steps:

[0022] S1. Determine the structural scheme and build a finite element model:

[0023] Based on the specific structure, mechanism scheme and mass characteristics of the spatial mechanism, a finite element model of the spatial mechanism is established, and the boundary condition is root fixation;

[0024] S2. Obtain mass matrix, coordinate matrix, modal moment and modal analysis:

[0025] The mass matrix [M] of all finite element nodes of the on-orbit rotating part of the space mechanism and the coordinate matrix [r] of the local coordinate system of the rotation point are obtained by the finite element method, wherein the mass matrix [M] is an n×1 matrix, and the coordinate matrix [r] is an n×3 matrix, wherein n is the number of all finite element nodes of the on-orbit rotating part of the space mechanism; modal analysis is performed to extract the modal frequency [F] and modal vibration shape [Φ], wherein the modal frequency [F] is an m×1 matrix, and the modal vibration shape [Φ] is an m×n×6 matrix, wherein m is the modal order, and modal damping is selected;

[0026] S3. According to the on-orbit mission of the spacecraft, the main mission conditions are sorted out and attributed to the on-orbit engine switch combination. The on-orbit mission of the spacecraft includes orbit transfer and orbit control. The on-orbit engine switch combination is related to the actual engine configuration of the spacecraft;

[0027] S4. According to the on-orbit dynamics model of the spacecraft and the main mission conditions, dynamic simulation is carried out to obtain the modal coordinates [q], the acceleration of the spacecraft body [A], the angular acceleration [a] and the angular velocity [w]. The modal coordinates [q] are m×t×1 matrices, and the acceleration of the spacecraft body [A], the angular acceleration [a] and the angular velocity [w] are all t×3 matrices, where t is the time step.

[0028] S5. See Figure 2-3 , obtain joint torque: take the modal vibration shape [Φ], modal coordinates [q], aircraft body acceleration [A], angular acceleration [a], angular velocity [w], mass matrix [M], coordinate matrix [r] as input conditions, use the elastic method to calculate the corresponding joint torque Ma and Mb; take the modal bending moment and modal coordinates [q] as input conditions, use the modal bending moment method to calculate the joint torque Ma and Mb again, where Ma and Mb are both t×3 matrices;

[0029] S6. Compare the consistency of Ma and Mb. If the error of Ma and Mb calculated by the two methods at the same time is within 5%, they are considered consistent, otherwise they are considered inconsistent. If they are consistent, it means that the calculation is correct; if they are inconsistent, it means that there is a problem in the calculation process, and the calculation process needs to be reviewed step by step until the calculation process is consistent.

[0030] S7. Obtain the maximum absolute value of Ma and Mb to obtain the load condition of the space mechanism under a certain mission condition. The calculation is then completed.

[0031] The spatial structure is a solar cell array having multiple degrees of freedom, and elastic vibration is considered in the calculation.

[0032] In step S1, a finite element model of the spatial mechanism is established, a sailboard model of the spatial mechanism is simulated by using shell elements, and a specific structure of the spatial mechanism is simulated by using beam elements.

[0033] In step S2, the modal analysis software used is MSC.Nastran SOL103, which automatically generates an f06 file, and extracts the modal frequency and modal vibration shape from the f06 file.

[0034] In step S2, the modal damping is set to 0.005.

[0035] In step S2, after obtaining the coordinates of all points in the root coordinate system, the following formula 1 is used to obtain the coordinate matrix [r] in the local coordinate system of the rotation point:

[0036] [r]=[r0]-O (1)

[0037] In formula 1, O is the coordinate of the rotation point in the root coordinates.

[0038] In step S4, in the on-orbit dynamics model of the aircraft, assuming that the aircraft is a rigid body, the aircraft dynamics equation expressed by vectors is simplified to the following formula 2-4:

[0039]

[0040]

[0041] In formula 2-4:

[0042] m—total mass of the aircraft;

[0043] —The aircraft acceleration matrix, which is a 3×1 matrix;

[0044] B t —The solar wing translation coupling system coefficient matrix, which is a 3×n matrix;

[0045] q—modal generalized coordinates, which is an n×1 matrix;

[0046] —modal generalized velocity, which is an n×1 matrix;

[0047] — modal generalized acceleration, which is an n×1 matrix;

[0048] F—control force matrix, which is a 3×1 matrix;

[0049] I—vehicle inertia matrix, which is a 3×3 matrix;

[0050] —The aircraft angular acceleration matrix, which is a 3×1 matrix;

[0051] B r — Solar wing rotation coupling system matrix, which is a 3×n matrix;

[0052] T—control torque matrix, which is a 3×1 matrix;

[0053] ξ—damping coefficient matrix, which is an n×1 matrix;

[0054] —modal frequencies, which are n×1 matrices;

[0055] n—modal order.

[0056] When calculating the joint moments Ma and Mb by the elastic method in step S5, the elasticity of the spatial mechanism and the rigidity of the aircraft body are taken into account. Similarly, the absolute acceleration of each point of the spatial mechanism is calculated according to the linear acceleration, angular acceleration, angular velocity and elastic motion of the aircraft body, the mass of each point is superimposed, and then the distance of the intersection of the A axis and the B axis is taken, and the inertia moment of the A axis and the B axis is obtained by summing them; the A axis is a horizontal axis, and the B axis is a longitudinal axis, and the two axes intersect vertically;

[0057] Considering the elasticity of the mass point dm, the displacement r of dm relative to the elastic system OeXeYeZe after vibration deformation e , relative speed v e , relative acceleration a e , relative angular velocity w e , relative angular acceleration a e , the generalized coordinate is q, see the following formula 5:

[0058]

[0059] Considering the elastic state of the spatial mechanism, the absolute acceleration a of the moving point dm relative to the static system OXYZ ism See the following formula 6:

[0060]

[0061] To calculate the distance between the intersection of the A-axis and the B-axis, refer to the following formula 7:

[0062]

[0063] In formula 7:

[0064] R—position vector of each point to the intersection of A axis and B axis;

[0065] dm—The mass of each point.

[0066] When the modal bending moment method in step S5 calculates the joint moments Ma and Mb, the unit modal bending moment w and the unit internal moment F are extracted by the finite element method:

[0067]

[0068] In the above formula 8-9:

[0069] M—unit internal moment;

[0070] w—unit modal bending moment.

[0071] In step S7, when obtaining the maximum absolute value of Ma and Mb, Matlab is used for solving.

Claims

1. A method for calculating elastic loads of on-orbit deployment of a space mechanism, characterized in that: The following steps are involved: S1. Determine the structural scheme and build a finite element model; S2. Obtain mass matrix, coordinate matrix, modal bending moment and modal analysis; S3. According to the on-orbit mission of the spacecraft, the main mission conditions are sorted out and attributed to the on-orbit engine switch combination. The on-orbit mission of the spacecraft includes orbit transfer and orbit control. The on-orbit engine switch combination is related to the actual engine configuration of the spacecraft; S4. According to the on-orbit dynamics model of the spacecraft and the main mission conditions, dynamic simulation is carried out to obtain the modal coordinates [q], the acceleration of the spacecraft body [A], the angular acceleration [a] and the angular velocity [w]. The modal coordinates [q] are m×t×1 matrices, and the acceleration of the spacecraft body [A], the angular acceleration [a] and the angular velocity [w] are all t×3 matrices, where t is the time step. S5. Obtain joint torque; S6. Compare the consistency of Ma and Mb. If the error of Ma and Mb calculated by the two methods at the same time is within 5%, they are considered consistent, otherwise they are considered inconsistent. If they are consistent, it means that the calculation is correct; if they are inconsistent, it means that there is a problem in the calculation process, and the calculation process needs to be reviewed step by step until the calculation process is consistent. S7. Obtain the maximum absolute value of Ma and Mb to obtain the load condition of the space mechanism under a certain mission condition. The calculation is then completed.

2. The method for calculating elastic loads of a space mechanism deployed on-orbit as claimed in claim 1, characterized in that: The spatial structure is a solar cell array having multiple degrees of freedom, and elastic vibration is considered in the calculation.

3. The method for calculating elastic loads of a space mechanism on-orbit deployment as claimed in claim 2, characterized in that: The step S1 specifically includes: establishing a finite element model of the spatial mechanism based on the specific structure, mechanism scheme, and mass characteristics of the spatial mechanism, with the boundary condition being root fixation.

4. The method for calculating elastic loads of on-orbit deployment of a space mechanism according to claim 3, characterized in that: The step S2 specifically includes: obtaining the mass matrix [M] of all finite element nodes of the on-orbit rotating part of the space mechanism and the coordinate matrix [r] in the local coordinate system of the rotation point by the finite element method, wherein the mass matrix [M] is an n×1 matrix, and the coordinate matrix [r] is an n×3 matrix, wherein n is the number of all finite element nodes of the on-orbit rotating part of the space mechanism; performing modal analysis, extracting the modal frequency [F] and modal vibration shape [Φ], wherein the modal frequency [F] is an m×1 matrix, and the modal vibration shape [Φ] is an m×n×6 matrix, wherein m is the modal order, and selecting the modal damping.

5. The method for calculating elastic loads of on-orbit deployment of a space mechanism according to claim 4, characterized in that: The step S5 specifically includes: using the modal vibration shape [Φ], modal coordinates [q], aircraft body acceleration [A], angular acceleration [a], angular velocity [w], mass matrix [M], and coordinate matrix [r] as input conditions, and using the elastic method to calculate the corresponding joint moments Ma and Mb; using the modal bending moment and modal coordinates [q] as input conditions, and using the modal bending moment method to calculate the joint moments Ma and Mb again, where Ma and Mb are both t×3 matrices.

6. The method for calculating elastic loads of on-orbit deployment of a space mechanism according to claim 5, characterized in that: In the step S1, a finite element model of the spatial mechanism is established, a sailboard model of the spatial mechanism is simulated by using shell elements, and a specific structure of the spatial mechanism is simulated by using beam elements.

7. The method for calculating elastic loads of on-orbit deployment of a space mechanism according to claim 6, characterized in that: In step S2, after obtaining the coordinates of all points in the root coordinate system, the following formula 1 is used to obtain the coordinate matrix [r] in the local coordinate system of the rotation point: [r]=[r0]-O (1) In formula 1, O is the coordinate of the rotation point in the root coordinate.

8. The method for calculating elastic loads of on-orbit deployment of a space mechanism according to claim 7, characterized in that: In step S4, in the on-orbit dynamics model of the aircraft, assuming that the aircraft is a rigid body, the aircraft dynamics equation expressed by vectors is simplified to the following formula 2-4: In formula 2-4: m—total mass of the aircraft; —The aircraft acceleration matrix, which is a 3×1 matrix; B t —The solar wing translation coupling system coefficient matrix, which is a 3×n matrix; q—modal generalized coordinates, which is an n×1 matrix; —modal generalized velocity, which is an n×1 matrix; — modal generalized acceleration, which is an n×1 matrix; F—control force matrix, which is a 3×1 matrix; I—aircraft inertia matrix, which is a 3×3 matrix; —The aircraft angular acceleration matrix, which is a 3×1 matrix; B r — Solar wing rotation coupling system matrix, which is a 3×n matrix; T—control torque matrix, which is a 3×1 matrix; ξ—damping coefficient matrix, which is an n×1 matrix; —modal frequencies, which are n×1 matrices; n—modal order.

9. The method for calculating elastic loads of on-orbit deployment of a space mechanism according to claim 8, characterized in that: When calculating the joint moments Ma and Mb by the elastic method in step S5, the elasticity of the spatial mechanism and the rigidity of the aircraft body are taken into account. Similarly, the absolute acceleration of each point of the spatial mechanism is calculated according to the linear acceleration, angular acceleration, angular velocity and elastic motion of the aircraft body, the mass of each point is superimposed, and then the distance of the intersection of the A axis and the B axis is taken, and the inertia moment of the A axis and the B axis is obtained by summing them; the A axis is a horizontal axis, and the B axis is a longitudinal axis, and the two axes intersect vertically; Considering the elasticity of the mass point dm, the displacement r of dm relative to the elastic system OeXeYeZe after vibration deformation e , relative speed v e , relative acceleration a e , relative angular velocity w e , relative angular acceleration a e , the generalized coordinate is q, see the following formula 5: Considering the elastic state of the spatial mechanism, the absolute acceleration a of the moving point dm relative to the static system OXYZ is m See the following formula 6: To calculate the distance between the intersection of the A-axis and the B-axis, refer to the following formula 7: In formula 7: R—position vector of each point to the intersection of A axis and B axis; dm—The mass of each point.

10. The method for calculating elastic loads of on-orbit deployment of a space mechanism according to claim 9, characterized in that: When the modal bending moment method in step S5 calculates the joint moments Ma and Mb, the unit modal bending moment w and the unit internal moment M are extracted by the finite element method: In formula 8 above: M—unit internal moment; w—unit modal bending moment.

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