Stacked satellite bearing cylinder parameter optimization design method

Abstract

The invention discloses a stacked satellite bearing cylinder parameter optimization design method, which comprises the following steps of: carrying out mechanical simulation on a stacked multi-satellite assembly, and analyzing bearing cylinder parameters which influence the fundamental frequency k of the assembly; selecting different values for mechanical simulation according to the parameters of the bearing cylinder to obtain a corresponding combination fundamental frequency k, and fitting a binary polynomial function about the parameters of the bearing cylinder and the combination fundamental frequency k; different values are selected for the outer diameter d of the bearing cylinder and the wall thickness h of the bearing cylinder to carry out three-dimensional model design, and the corresponding weight m is obtained; fitting a binary polynomial function about the parameters of the bearing cylinder and the weight m of the bearing cylinder; according to the allowable stress sigma0 of the bearing cylinder material, a bearing cylinder strength constraint function is established; according to the method, the parameters of the stacked satellite bearing cylinder are optimized, the outer diameter and the wall thickness of the bearing cylinder are taken as design variables, the fundamental frequency of the assembly and the strength of the bearing cylinder are taken as constraint conditions, and the weight of the bearing cylinder is taken as an optimization target.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite structure design, and specifically to an optimized design method for the parameters of a stacked satellite load-bearing cylinder. Background Art

[0002] Low-Earth orbit satellite Internet constellations usually adopt a stacked multi-satellite combination for launch, which can make full use of the space in the fairing of the launch vehicle, improve the launch efficiency. At the same time, there is no need for a dedicated satellite-rocket adapter, reducing the redundant weight and improving the carrying capacity. In the stacked configuration, satellites are stacked and connected to each other by load-bearing cylinders. The structural parameters of the load-bearing cylinders affect both the fundamental frequency of the stacked multi-satellite combination and their own weight, and thus affect the weight of the satellite body. If one blindly increases the fundamental frequency of the combination to ensure launch safety, it will increase the weight of the satellite body, increase the launch cost, and reduce the launch efficiency. However, if one blindly reduces the weight of the load-bearing cylinder, it will reduce the fundamental frequency of the combination and weaken the strength of the load-bearing cylinder, posing a potential safety hazard for launch. Therefore, it is of great significance to optimize the parameters of the load-bearing cylinder. Summary of the Invention

[0003] Aiming at the deficiencies of the existing technology, the present invention provides an optimized design method for the parameters of a stacked satellite load-bearing cylinder. The present invention aims to solve the problem that when designers carry out the structural design of the load-bearing cylinder in the existing technology, they usually consider the requirements of the fundamental frequency of the combination, the requirements of structural strength, and the requirements of lightweighting. To increase the fundamental frequency of the combination and the structural strength, it is necessary to sacrifice the weight of the load-bearing cylinder, and it is difficult to obtain the optimal parameters of the load-bearing cylinder.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] An optimized design method for the parameters of a stacked satellite load-bearing cylinder, comprising the following steps:

[0006] Step S1: Conduct a mechanical simulation on the stacked multi-satellite combination to analyze the load-bearing cylinder parameters that affect the fundamental frequency k of the combination;

[0007] Step S2: Select different values for the load-bearing cylinder parameters to conduct a mechanical simulation to obtain the corresponding fundamental frequency k of the combination, and fit the binary polynomial function f k (d, h) of the load-bearing cylinder parameters and the fundamental frequency k of the combination, that is, the constraint function is: f k (d, h) = k0, where h is the wall thickness of the load-bearing cylinder and d is the outer diameter of the load-bearing cylinder;

[0008] Step S3: Select different values for the outer diameter d and the wall thickness h of the load-bearing cylinder to conduct a 3D model design to obtain the corresponding weight m;

[0009] Step S4: Fit the binary polynomial function f m (d, h) of the load-bearing cylinder parameters and the weight m of the load-bearing cylinder, that is, the optimization objective function: min f m(d, h) = [d, h] T ;

[0010] Step S5: Based on the allowable stress σ0 of the load-bearing cylinder material, establish the strength constraint function f of the load-bearing cylinder σ (d, h) < σ0; and use the fmincont algorithm in Matlab to find the minimum value of the objective function and obtain the corresponding design variables.

[0011] As a further solution of the present invention, in step S1, it specifically includes performing a mechanical simulation on the stacked multi-star combination body, analyzing the load-bearing cylinder parameters that have a greater impact on the fundamental frequency k of the combination body, and finding the vector p: p = [d, h] T .

[0012] As a further solution of the present invention, in step S1: The specific process of obtaining the corresponding fundamental frequency k of the combination body by performing mechanical simulations with different values selected for the load-bearing cylinder parameters is as follows: Perform mechanical simulations with different values selected for the outer diameter d of the load-bearing cylinder and the wall thickness h of the load-bearing cylinder to obtain the corresponding fundamental frequency k of the combination body, and establish a fitting relationship matrix:

[0013] As a further solution of the present invention, step S2 specifically includes: Fitting the binary polynomial function f of the load-bearing cylinder parameters and the fundamental frequency k of the combination body k (d, h); f k (d, h) = p0 + p1 * d + p2 * h, where p0, p1, and p2 are the binary polynomial constant coefficients obtained by fitting.

[0014] As a further solution of the present invention, in step S3, it specifically includes performing 3D model designs with different values selected for the outer diameter d of the load-bearing cylinder and the wall thickness h of the load-bearing cylinder to obtain the corresponding weight m, and establishing a fitting relationship matrix:

[0015] As a further solution of the present invention, in step S4, it specifically includes fitting the binary polynomial function f of the load-bearing cylinder parameters and the weight m of the load-bearing cylinder m (d, h); f m (d, h) = q0 + q1 * d + q2 * h; where q0, q1, and q2 are the binary polynomial constant coefficients obtained by fitting.

[0016] As a further solution of the present invention, in step S5, based on the allowable stress σ0 of the load-bearing cylinder material, the specific process of establishing the strength constraint function f σ (d, h) < σ0 is as follows: Establish the strength constraint function f of the load-bearing cylinder σ (d, h);

[0017] f σ (d, h) = (f n + n * M * g) / (π * ((d / 2)^2 - (d / 2 - h)^2)), where f n is the pre-tightening force on the load-bearing cylinder during multi-satellite stacking; n is the overload coefficient given by the launch vehicle; M is the weight of the stacked multi-satellite combination borne by each load-bearing cylinder on average; g is the acceleration due to gravity.

[0018] As a further solution of the present invention, in step S5, the specific process of using the fmincont algorithm in Matlab to find the minimum value of the objective function and obtain the corresponding design variables is as follows: Using the fmincont algorithm in Matlab to find the minimum value of the objective function: min f m (d, h) = [d, h] T , and obtaining the corresponding design variables: d min 、h min .

[0019] The present invention has the following beneficial effects:

[0020] The present invention optimizes the parameters of the stacked satellite load-bearing cylinder. Taking the outer diameter and wall thickness of the load-bearing cylinder as design variables, the fundamental frequency of the combination and the strength of the load-bearing cylinder as constraint conditions, and the weight of the load-bearing cylinder as the optimization objective. The optimal outer diameter and wall thickness parameters of the load-bearing cylinder are obtained under the conditions that the fundamental frequency requirement of the combination by the launch vehicle is met, the stress of the load-bearing cylinder meets the allowable stress of the material and there is a certain safety margin. It meets the fundamental frequency requirement of the combination by the launch vehicle, reduces the mass of the satellite body, and thus reduces the launch cost.

[0021] To more clearly illustrate the structural features and effects of the present invention, the following will combine the drawings with specific embodiments to detail the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a schematic diagram of the structure of the load-bearing cylinder mentioned in the present invention.

[0023] Figure 2 is a schematic diagram of the stacked multi-satellite combination mentioned in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] The following will further illustrate the present invention in combination with the drawings and relevant knowledge, and describe it clearly and completely. Obviously, the described applications are only a part of the embodiments of the present invention, rather than all the embodiments.

[0025] The parameter optimization design method of the stacked satellite load-bearing cylinder of the present invention solves the problem that when designers carry out the structural design of the load-bearing cylinder, they usually consider the requirements of the combined body's fundamental frequency, structural strength, and lightweight. To increase the combined body's fundamental frequency and structural strength, the weight of the load-bearing cylinder must be sacrificed, making it difficult to obtain the optimal parameters of the load-bearing cylinder. In Figure 1 and Figure 2 In the figure, the mark 1 is the wall thickness h of the load-bearing cylinder, 2 is the outer diameter d of the load-bearing cylinder, 3 is the satellite, and 4 is the load-bearing cylinder.

[0026] The present invention provides a parameter optimization design method for a stacked satellite load-bearing cylinder, including the following steps:

[0027] Step S1: Conduct a mechanical simulation on the stacked multi-satellite combination to analyze the load-bearing cylinder parameters that affect the fundamental frequency k of the combination;

[0028] Step S2: Select different values for the load-bearing cylinder parameters and conduct a mechanical simulation to obtain the corresponding fundamental frequency k of the combination, and fit the binary polynomial function f k (d, h) of the load-bearing cylinder parameters and the fundamental frequency k of the combination, that is, the constraint function is: f k (d, h) = k0, where h is the wall thickness of the load-bearing cylinder and d is the outer diameter of the load-bearing cylinder;

[0029] Step S3: Select different values for the outer diameter d and the wall thickness h of the load-bearing cylinder to conduct a 3D model design to obtain the corresponding weight m;

[0030] Step S4: Fit the binary polynomial function f m (d, h) of the load-bearing cylinder parameters and the weight m of the load-bearing cylinder, that is, the optimization objective function: min f m (d, h) = [d, h] T ;

[0031] Step S5: According to the allowable stress σ0 of the load-bearing cylinder material, establish the load-bearing cylinder strength constraint function f σ (d, h) < σ0; and use the fmincont algorithm in Matlab to find the minimum value of the objective function and obtain the corresponding design variables.

[0032] Further preferably, conduct a mechanical simulation on the stacked multi-satellite combination to analyze the load-bearing cylinder parameters that have a greater impact on the fundamental frequency k of the combination - the outer diameter d of the load-bearing cylinder and the wall thickness h of the load-bearing cylinder, that is, the optimization problem is to find a vector p: p = [d, h] T .

[0033] Further preferably, select different values for the outer diameter d and the wall thickness h of the load-bearing cylinder to conduct a mechanical simulation to obtain the corresponding fundamental frequency k of the combination, and establish a fitting relationship matrix:

[0034]

[0035] Further preferably, according to the corresponding combined body fundamental frequency k obtained above, a binary polynomial function f of the load-bearing cylinder parameters (outer diameter d, wall thickness h) and the combined body fundamental frequency k is fitted k (d, h): f k (d, h) = p0 + p1*d + p2*h, where p0, p1, and p2 are the binary polynomial constant coefficients obtained by fitting. The fundamental frequency constraint function is: f k (d, h) = k0;

[0036] Further preferably, different values are selected for the outer diameter d of the load-bearing cylinder and the wall thickness h of the load-bearing cylinder for 3D model design, and the corresponding weight m is obtained, and a fitting relationship matrix is established:

[0037]

[0038] Further preferably, according to the corresponding weight m obtained above, a binary polynomial function f of the load-bearing cylinder parameters (outer diameter d, wall thickness h) and the load-bearing cylinder weight m is fitted m (d, h): f m (d, h) = q0 + q1*d + q2*h; where q0, q1, and q2 are the binary polynomial constant coefficients obtained by fitting;

[0039] Further preferably, a load-bearing cylinder strength constraint function f is established σ (d, h):

[0040] f σ (d, h) = (f n + n*M*g) / (π*((d / 2)^2 - (d / 2 - h)^2)), where f n is the pre-tightening force received by the load-bearing cylinder during multi-star stacking; n is the overload coefficient given by the launch vehicle; M is the weight of the stacked multi-star combined body borne by each load-bearing cylinder on average; g is the acceleration due to gravity.

[0041] In addition, according to the allowable stress σ0 of the load-bearing cylinder material, a load-bearing cylinder strength constraint function is established, and the strength constraint function is: f σ (d, h) < σ 0。

[0042] Further preferably, the fmincont algorithm in Matlab is used to find the minimum value of the objective function: min f m (d, h) = [d, h] T , and the corresponding design variables: d min 、h min .

[0043] The technical principle of the present invention has been described above in combination with specific embodiments, which are only the preferred embodiments of the present invention. The protection scope of the present invention is not limited to the above embodiments. Any technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. Those skilled in the art can readily conceive of other specific embodiments of the present invention without creative efforts, and these embodiments will all fall within the protection scope of the present invention.

Claims

1. A method for optimizing the design of stacked satellite bearing cylinder parameters, characterized in that: The following steps are involved: Step S1: Perform mechanical simulation on the stacked multi-satellite assembly to analyze the bearing cylinder parameters that affect the assembly fundamental frequency k; Step S2: Select different values ​​according to the load-bearing cylinder parameters to perform mechanical simulation, obtain the corresponding assembly fundamental frequency k, and fit the bivariate polynomial function f about the load-bearing cylinder parameters and the assembly fundamental frequency k k (d,h), that is, the constraint function is: f k (d,h)=k0, where h is the wall thickness of the bearing cylinder and d is the outer diameter of the bearing cylinder; Step S3: Select different values ​​for the outer diameter d and the wall thickness h of the load-bearing cylinder to design a 3D model and obtain the corresponding weight m; Step S4: Fitting a bivariate polynomial function f about the load-bearing cylinder parameters and the load-bearing cylinder weight m m (d,h), that is, the optimization objective function: min f m (d,h)=[d,h] T ; Step S5: According to the allowable stress σ0 of the bearing cylinder material, establish the bearing cylinder strength constraint function f σ (d,h)<σ0; and use the fmincont algorithm in Matlab to find the minimum value of the objective function and obtain the corresponding design variables.

2. The stacked satellite bearing cylinder parameter optimization design method according to claim 1, characterized in that: In step S1, the mechanical simulation of the stacked multi-satellite assembly is specifically performed to analyze the bearing cylinder parameters that have a greater impact on the fundamental frequency k of the assembly, and to find the vector p; p = [d, h] T .

3. The stacked satellite bearing cylinder parameter optimization design method according to claim 2, characterized in that: In step S1, different values ​​are selected according to the load-bearing cylinder parameters for mechanical simulation to obtain the corresponding combination fundamental frequency k. The specific process is: different values ​​are selected for the load-bearing cylinder outer diameter d and the load-bearing cylinder wall thickness h for mechanical simulation to obtain the corresponding combination fundamental frequency k, and establish a fitting relationship matrix:

4. The stacked satellite bearing cylinder parameter optimization design method according to claim 3, characterized in that: Step S2 specifically includes: fitting a bivariate polynomial function f about the bearing cylinder parameters and the fundamental frequency k of the assembly k (d,h);f k (d,h)=p0+p1*d+p2*h, where p0, p1, and p2 are the constant coefficients of the bivariate polynomial obtained by fitting.

5. The stacked satellite bearing cylinder parameter optimization design method according to claim 4, characterized in that: In the step S3, specifically, different values ​​are selected for the outer diameter d of the load-bearing cylinder and the wall thickness h of the load-bearing cylinder to perform 3D model design, obtain the corresponding weight m, and establish a fitting relationship matrix:

6. The stacked satellite bearing cylinder parameter optimization design method according to claim 5, characterized in that: The step S4 specifically includes fitting a bivariate polynomial function f about the load-bearing cylinder parameters and the load-bearing cylinder weight m m (d,h);f m (d,h)=q0+q1*d+q2*h; where q0, q1, q2 are the constant coefficients of the bivariate polynomial obtained by fitting.

7. The stacked satellite bearing cylinder parameter optimization design method according to claim 6, characterized in that: In step S5, the bearing tube strength constraint function f is established according to the allowable stress σ0 of the bearing tube material. σ The specific process of (d,h)<σ0 is as follows: Establish the strength constraint function f of the load-bearing cylinder σ (d,h); f σ (d,h)=(f n +n*M*g) / (π*((d / 2)^2-(d / 2-h)^2)), where f n is the preload force on the load-bearing cylinder when multiple satellites are stacked; n is the overload coefficient given by the launch vehicle; M is the average weight of the stacked multi-satellite assembly borne by each load-bearing cylinder; g is the gravitational acceleration.

8. The stacked satellite bearing cylinder parameter optimization design method according to claim 7, characterized in that: In step S5, the specific process of finding the minimum value of the objective function by using the fmincon algorithm in Matlab and obtaining the corresponding design variables is as follows: finding the minimum value of the objective function by using the fmincon algorithm in Matlab: min f m (d,h)=[d,h] T , and obtain the corresponding design variables: d min 、h min .

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