Space flywheel optimization design method

Abstract

A space flywheel optimization design method comprises the following steps: S1, designing an initial space flywheel based on input conditions and technical requirements of the space flywheel, and obtaining an initial value of an initial space flywheel design variable; s2, performing modal analysis and harmonic response analysis on the initial space flywheel based on input conditions and technical requirements, judging whether the initial space flywheel meets design requirements or not, taking the mass of the space flywheel and a resonance amplification factor as optimization targets, and obtaining initial values of two optimization targets of the initial space flywheel meeting the design requirements; according to the space flywheel optimization design method, optimization design is carried out on a space flywheel according to two or more evaluation index parameters or optimization targets with the conflict relation, and an optimal space flywheel model meeting input conditions and technical requirements required by a space environment is obtained.

Description

Technical Field

[0001] The invention relates to the technical field of space flywheels, and in particular to a space flywheel optimization design method. Background Art

[0002] Space flywheels, also known as angular momentum wheels, adjust the attitude of spacecraft in satellite attitude control systems by changing their own rotation speed. According to controller instructions, they accelerate or decelerate in a predetermined direction, thereby exchanging angular momentum with celestial bodies to achieve precise directional control or absorb changes in satellite angular momentum caused by space interference torque, thereby correcting the attitude deviation of the satellite platform or completing certain predetermined attitude changes.

[0003] In the active phase of satellite launch, the flywheel will be in a harsh dynamic environment with vibration, impact, acceleration overload and multiple dynamic loads. In this case, the flywheel structure will produce obvious flexural deformation and even risk of impact failure. The resonance amplification factor is defined as the ratio of the response acceleration of the flywheel rim to the acceleration load at the center of the flywheel body, which can effectively indicate the ability of the flywheel to withstand loads. Reducing the resonance amplification factor can effectively reduce the deformation of the wheel rim, increase the impact resistance and overload resistance of the flywheel, and better maintain the stability and reliability of the structure in a harsh launch environment. The lightweight design of the satellite can significantly improve the reliability of the satellite, and the lightweight design makes the satellite structure more concise and efficient. On the other hand, the lightweight design can increase the payload of the satellite. Under limited space and carrying capacity, a lighter satellite body can provide the possibility of carrying more key equipment and instruments. At the same time, lightweight can also significantly reduce the expensive launch cost.

[0004] Under the requirements of enhancing the flywheel's impact resistance and overload resistance as well as lightweight design of the wheel body, more stringent design requirements are placed on the mass and resonance amplification factor of the space flywheel. Therefore, it is necessary to optimize the mass and resonance amplification factor as evaluation index parameters.

[0005] In the flywheel design process, multiple optimization objectives need to be taken into account at the same time, such as moment of inertia, mass and resonance amplification factor. However, there are conflicts between the optimization objectives. For example, the moment of inertia of the flywheel mainly depends on the rim mass and radius, but as the rim mass and radius increase, the harmonic response of the flywheel will be amplified. At the same time, the resonance amplification factor and mass of the flywheel are subject to the constraints of the moment of inertia and cannot be reduced indefinitely. At present, in the flywheel optimization design, the multi-objective optimization problem is mainly converted into a single objective or multi-objective optimization is performed using experience through weighted methods or transfer constraint methods. However, such a conversion inevitably brings problems such as the difficulty in determining the weight value by the weighted method, the difficulty in determining the size of the constraint by the transfer constraint method, and the inability of the empirical direct multi-objective method to reflect the optimality. Summary of the invention

[0006] The purpose of the present invention is to propose a space flywheel optimization design method, to optimize the design of the space flywheel according to two or more conflicting evaluation index parameters or optimization objectives, and to obtain the optimal space flywheel model that meets the input conditions and technical requirements of the space environment.

[0007] The technical solution adopted by the present invention is: a method for optimizing the design of a space flywheel, comprising the following steps:

[0008] S1. designing an initial space flywheel based on input conditions and technical requirements of the space flywheel, and obtaining initial values ​​of design variables of the initial space flywheel;

[0009] S2. Perform modal analysis and harmonic response analysis on the initial space flywheel based on input conditions and technical requirements to determine whether the initial space flywheel meets the design requirements, optimize the mass and resonance amplification factor of the space flywheel, and obtain the initial values ​​of the two optimization objectives of the initial space flywheel that meets the design requirements;

[0010] S3. After determining the design variables and constraints, the following optimization model is established:

[0011]

[0012] Where: X = (h, t, r 1 ,r 2 ,L,b,α);

[0013] Where W weight (X) is the mass of the space flywheel; f RAF (X) is the resonance amplification factor; h j (X) is the equality constraint function; g k (X) is the inequality constraint function; where X is the design variables h, t, r 1 、r 2 , L, b, α, h is the rim height, t is the rim thickness, r 1 is the wheel rim radius, r 2 is the radius of the de-weighting hole, L is the distance from the center of the de-weighting hole to the wheel rim, b is the thickness of the spoke plate, and α is the inclination angle of the spoke plate;

[0014] Based on the equality constraint function and inequality constraint function, the boundary conditions and the range of design variables of the space flywheel are determined, the parameter space is designed using the central experimental design method, and the space flywheel design variable database is established;

[0015] S4, using Python to call the spatial flywheel design variable database and then connect to ANSYS for parametric modeling simulation, and storing the corresponding objective function values ​​under the sample geometric parameters into the solution set of the objective function;

[0016] S5. Fit the design variables to the objective functions of the two optimization objectives based on MATLAB, and verify the root mean square error between the obtained functions and the simulation results;

[0017] S6. Solve the two optimization objectives based on the NSGA-II multi-objective optimization algorithm, output the Pareto front solution set of the two optimization objectives, and verify the finite element simulation output of multiple possible optimization results on the Pareto front based on the root mean square error, and finally obtain the optimal space flywheel design scheme.

[0018] As a preferred solution, the input conditions include the rotation speed, angular momentum and moment of inertia under working conditions;

[0019] Technical requirements include the envelope size of the space flywheel, its maximum mass and the mechanical environment it will be subjected to during the launch phase.

[0020] As a preferred solution, the basic acceleration method is used to perform harmonic response analysis, an axial fixed support is applied to the bottom of the initial space flywheel, a local acceleration load is applied at the fixed support boundary condition, and the rotation frequency of the input condition is compared with the first-order natural frequency under the first-order mode according to the modal analysis results;

[0021] If the rotation frequency is greater than the first-order natural frequency, return to step S1 to redesign the initial space flywheel; if the rotation frequency is less than the first-order natural frequency, it means that the designed initial space flywheel has no risk of resonance, and the mass and resonance amplification factor of the initial space flywheel are obtained.

[0022] As a preferred solution, the equality constraint function includes a mandatory constraint h 1 (X); Inequality constraint functions include geometric size constraints g 2 (X), stiffness constraint g 3 (X), strength constraint g 4 (X), center of mass constraint g 5 (X), inertia constraint g 1 (X), stability constraint g 6 (X).

[0023] As a preferred solution, in S4, the parameter space is divided into multiple non-overlapping parameter subspaces, and the subspaces are called through multi-process Python and multi-threaded batch calculations.

[0024] As a preferred solution, in S5, 80% of the data in the spatial flywheel design variable database are fitted, and 20% of the data are used for root mean square error test of the accuracy of the model.

[0025] As a preferred solution, in the root mean square error verification of S5, if the error is greater than 5%, the sample size is increased to continue fitting. If the error is less than 5%, the NSGA-II genetic algorithm is used to solve the objective function, and the objective function program is run using MATLAB software.

[0026] As a preferred solution, in S6, the Pareto front solution set and the simulation results are subjected to root mean square error judgment to determine the validity of the model. If the root mean square error is less than 5%, the model is considered valid. If the root mean square error is greater than 5%, S4 is repeated to increase the sample size.

[0027] As a preferred solution, in S6, the best solution among the Pareto candidate solutions is taken as the optimized spatial flywheel model for harmonic response analysis, and the harmonic response analysis results before and after the optimization are compared and verified.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] 1. Combining NSGA-II and finite element simulation, the optimization algorithm of NSGA-II can not only ensure the diversity of solutions, but also quickly approach the real Pareto frontier, thereby improving the optimization efficiency and quality.

[0030] 2. Through parametric modeling and multi-threaded batch simulation, efficient use of hardware resources can be achieved and labor costs can be reduced.

[0031] 3. This optimization design method is applicable to all types of flywheel designs. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0033] Figure 1 A variable diagram for the flywheel design of the present invention;

[0034] Figure 2 It is a schematic diagram of applying acceleration load to a space flywheel according to the present invention;

[0035] Figure 3 is a modal analysis diagram of the flywheel of the present invention;

[0036] Figure 4 This is a flywheel harmonic response analysis diagram before optimization of the present invention;

[0037] Figure 5 Schematic diagram of the Pareto front solution set of the present invention;

[0038] Figure 6 This is the flywheel harmonic response analysis diagram after optimization of the present invention;

[0039] Figure 7 This is a multi-objective optimization principle diagram of the space flywheel of the present invention. DETAILED DESCRIPTION

[0040] The present invention is described in detail below by way of exemplary embodiments. However, it should be understood that, without further description, elements, structures and features in one embodiment may also be beneficially combined in other embodiments.

[0041] It should be noted that: unless otherwise defined, the technical terms or scientific terms used in this document shall have the usual meanings understood by people with ordinary skills in the field to which the invention belongs. The words "one", "an" or "the" and the like used in the patent application specification and claims of the present invention do not express quantity restrictions, but indicate the existence of at least one; the words "first", "second" and "third" used in this document shall not be regarded as restrictions on the order of components, but are only used to distinguish different components; words such as "include" or "comprise" and the like indicate that the elements or objects appearing before "include" or "comprise" include the elements or objects listed after "include" or "comprise" and their equivalents, but do not exclude other elements or objects with the same function.

[0042] In order to describe the optimization design method of the space flywheel more clearly, Figure 1-7 Describe this embodiment:

[0043] A method for optimizing the design of a space flywheel comprises the following steps:

[0044] S1. Design an initial space flywheel based on the input conditions of the space flywheel (including the rotation speed, angular momentum and moment of inertia under working conditions) and technical requirements (including the envelope size, maximum mass and mechanical environment of the space flywheel during the launch phase, etc.), and obtain the initial values ​​of the initial space flywheel design variables;

[0045] In this example, the flywheel is required to output an angular momentum of 25.7Nms at a rated speed of 700r / min, and the moment of inertia is required to be ≥ 0.35kgm 2 .

[0046] S2. Perform modal analysis and harmonic response analysis on the initial space flywheel based on input conditions and technical requirements to determine whether the initial space flywheel meets the design requirements, determine the optimization target and obtain the initial values ​​of the two optimization targets (resonance amplification factor / rim acceleration g, flywheel mass) of the initial space flywheel that meets the design requirements; when the moment of inertia is determined, the smaller the flywheel mass, the greater the inertia-to-mass ratio;

[0047] The specific judgment method is: use the basic acceleration method to perform harmonic response analysis, and apply axial fixed support at the bottom of the initial space flywheel, such as Figure 2 As shown, a local acceleration load (centrally applied acceleration) is applied at the fixed support boundary condition, and the rotational frequency of the input condition is compared with the first-order natural frequency under the first-order mode according to the modal analysis results;

[0048] If the rotation frequency is greater than the first-order natural frequency, return to step S1 to redesign the initial space flywheel; if the rotation frequency is less than the first-order natural frequency, it means that the designed initial space flywheel has no risk of resonance, and the mass and resonance amplification factor of the initial space flywheel are obtained;

[0049] According to f=n / 60, the rotation frequency f at the rated speed n is calculated to be 11.67Hz. Compared with Table 1, under the working condition of 700r / min, the rotation frequency of the flywheel body is much smaller than the first-order natural frequency, indicating that the flywheel has no risk of resonance and can be used as the initial space flywheel model. The mass of the initial space flywheel is calculated by the modeling software to be 10.91Kg. The calculation results of the harmonic response analysis are as follows Figure 4 As shown, the response frequency is 310Hz and the resonance amplification factor is 25.62;

[0050] Table 1 Flywheel natural frequency

[0051]

[0052] Resonance amplification factor = rim acceleration / center acceleration.

[0053] S3. After determining the design variables and constraints, the following optimization model is established:

[0054]

[0055] Where: X = (h, t, r 1 ,r 2 ,L,b,α);

[0056] Where W weight (X) is the mass of the space flywheel; f RAF (X) is the resonance amplification factor; h j (X) is the equality constraint function; g k (X) is the inequality constraint function; where X is the design variables h, t, r 1 、r 2 , L, b, α, h is the rim height, t is the rim thickness, r 1 is the wheel rim radius, r 2is the radius of the de-weighting hole, L is the distance from the center of the de-weighting hole to the wheel rim, b is the thickness of the spoke plate, and α is the inclination angle of the spoke plate;

[0057] Based on the equality constraint function and inequality constraint function, the boundary conditions and the range of design variables of the space flywheel are determined, the parameter space is designed using the central experimental design method, and the design variable database of the space flywheel is established;

[0058] Specifically, the equality constraint function includes (1) the mandatory constraint h 1 (X), the actual assembly requirements of the flywheel, bearing assembly, housing and other components, as well as the dimensions of the bearing assembly and the envelope housing have been determined, so the flywheel inner diameter and the radial dimensions of the wheel body radius become mandatory constraints; in this example:

[0059] Table 2 Flywheel mandatory constraints

[0060]

[0061] The inequality constraint function includes the geometric size constraint g 2 (X), stiffness constraint g 3 (X), strength constraint g 4 (X), center of mass constraint g 5 (X), inertia constraint g 1 (X), stability constraint g 6 (X);

[0062] (2) Moment of inertia constraint

[0063] The flywheel needs to output an angular momentum of 25.7Nms at a rated speed of 700r / min, and the moment of inertia is required to be ≥0.35kgm 2 ;

[0064] (3) Geometric size constraints

[0065] Subject to the size restrictions of the flywheel's seal cover outer envelope, bearing support seat, bearing assembly upper gland, motor rotor, motor stator and Hall bracket, the specific geometric constraints given to the flywheel are shown in Table 3;

[0066] Table 3 Space flywheel parameter range

[0067]

[0068]

[0069] (4) Stiffness constraint

[0070] The flywheel body should be a rigid rotor within the operating speed range, and its first-order resonance frequency must be greater than 1.5 times the rotation frequency of the rotor's maximum operating speed.

[0071] (5) Strength constraint

[0072] Considering the actual working conditions of the flywheel rotation, under the condition of a safety factor of 2, the maximum Mises equivalent stress requirement of the flywheel at the highest speed must be met to ensure the safety and reliability of the flywheel during operation.

[0073] (6) Center of mass constraint

[0074] Under working conditions, the flywheel must have its center of mass located at the axial center of the two 7005 bearings.

[0075] (7) Stability constraints

[0076] Under the condition of safety factor of 2, the flywheel body is constrained by the elastic deformation under overload conditions during the launching process.

[0077] Steps S4-S6 refer to Figure 7 ;

[0078] S4. Use Python to call the spatial flywheel design variable database and then connect it to ANSYS for parametric modeling simulation. Store the corresponding objective function values ​​under the sample geometric parameters into the solution set of the objective function; divide the parameter space into multiple non-intersecting parameter subspaces, call the subspaces through multi-process Python, and perform multi-threaded batch calculations;

[0079] S5. Based on MATLAB, the design variables are fitted with the objective functions of the two optimization objectives (resonance amplification factor and flywheel quality) respectively, and the functions and simulation results are verified by root mean square error; if the error is greater than 5%, the sample size is increased to continue fitting, and if the error is less than 5%, the NSGA-Ⅱ genetic algorithm is used to solve the objective function, and the objective function program is run using MATLAB software, where the number of objective functions is 2, the number of decision variables is 7, and the relevant parameter settings of the genetic algorithm are shown in Table 4;

[0080] Table 4 NSGA-Ⅱ parameter settings

[0081]

[0082]

[0083] Specifically, during fitting, 80% of the data in the spatial flywheel design variable database are fitted, and 20% of the data are used for root mean square error testing of the accuracy of the model.

[0084] S6. Solve the two optimization objectives based on the NSGA-II multi-objective optimization algorithm, output the Pareto front solution set of the two optimization objectives, perform finite element simulation output verification on multiple possible optimization results on the Pareto front based on the root mean square error, and finally obtain the optimal space flywheel design solution;

[0085] The Pareto front solution set and the simulation results are compared by root mean square error to determine the validity of the model. If the root mean square error is less than 5%, the model is considered valid. If the root mean square error is greater than 5%, S4 is repeated to increase the sample size. The Pareto front solution set is as follows: Figure 5 As shown, the optimal solution among the Pareto candidate solutions is taken as the optimized spatial flywheel model for harmonic response analysis, and the harmonic response analysis results before and after optimization are compared and verified;

[0086] In the specific example, three groups of Pareto candidate solutions are taken as shown in Table 5. The third group of Pareto candidate solutions is selected, and the optimized spatial flywheel model is subjected to harmonic response analysis. The optimized harmonic response analysis is shown in Figure 6 As shown in the figure, compared with the Figure 4 By comparison, it can be seen that the mass after optimization is 10.58kg, and the mass before optimization is 10.91Kg, which is reduced by 0.33Kg, about 3.02%; the resonance amplification factor after optimization is 18.55, and the resonance amplification factor before optimization is 25.62, which is reduced by 7.07, about 27.59%; the response frequency after optimization is 322Hz, and the response frequency before optimization is 310Hz, which is increased by 12Hz;

[0087] Table 5 Three groups of Pareto candidate solutions

[0088]

[0089] The parts not described in detail in the above embodiments are prior art.

[0090] It should be noted that although the present invention is described by the above embodiments, the present invention may also have other various embodiments. Without departing from the spirit and scope of the present invention, it is obvious that those skilled in the art may make various corresponding changes and deformations to the present invention, but these changes and deformations should all fall within the scope of protection of the appended claims of the present invention and their equivalents.

Claims

1. A method for optimizing the design of a space flywheel, characterized in that: The following steps are involved: S1. designing an initial space flywheel based on input conditions and technical requirements of the space flywheel, and obtaining initial values ​​of design variables of the initial space flywheel; S2. Perform modal analysis and harmonic response analysis on the initial space flywheel based on input conditions and technical requirements to determine whether the initial space flywheel meets the design requirements, take the mass and resonance amplification factor of the space flywheel as optimization targets, and obtain the initial values ​​of the two optimization targets of the initial space flywheel that meets the design requirements; S3. After determining the design variables and constraints, the following optimization model is established: Where: X = (h, t, r1, r2, L, b, α); Where W weight (X) is the mass of the space flywheel; f RAF (X) is the resonance amplification factor; h j (X) is the equality constraint function; g k (X) is the inequality constraint function; where X is a decision vector consisting of design variables h, t, r1, r2, L, b, and α, h is the rim height, t is the rim thickness, r1 is the rim radius, r2 is the deduplication hole radius, L is the distance from the deduplication hole center to the rim, b is the web thickness, and α is the web inclination angle; Based on the equality constraint function and inequality constraint function, the boundary conditions and the range of design variables of the space flywheel are determined, the parameter space is designed using the central experimental design method, and the space flywheel design variable database is established; S4, using Python to call the spatial flywheel design variable database and then connect to ANSYS for parametric modeling simulation, and storing the corresponding objective function values ​​under the sample geometric parameters into the solution set of the objective function; S5. Fit the design variables to the objective functions of the two optimization objectives based on MATLAB, and verify the root mean square error between the obtained functions and the simulation results; S6. Solve the two optimization objectives based on the NSGA-II multi-objective optimization algorithm, output the Pareto front solution set of the two optimization objectives, and verify the finite element simulation output of multiple possible optimization results on the Pareto front based on the root mean square error, and finally obtain the optimal space flywheel design scheme.

2. A method for optimizing the design of a space flywheel according to claim 1, characterized in that: Input conditions include rotational speed, angular momentum, and moment of inertia under operating conditions; Technical requirements include the envelope size of the space flywheel, its maximum mass and the mechanical environment it will be subjected to during the launch phase.

3. A method for optimizing the design of a space flywheel according to claim 1, characterized in that: The harmonic response analysis is carried out using the basic acceleration method. An axial fixed support is applied to the bottom of the initial space flywheel, and a local acceleration load is applied at the fixed support boundary condition. The rotation frequency of the input condition is compared with the first-order natural frequency under the first-order mode according to the modal analysis results. If the rotation frequency is greater than the first-order natural frequency, return to step S1 to redesign the initial spatial flywheel; If the rotation frequency is less than the first-order natural frequency, it means that the designed initial space flywheel has no risk of resonance, and the mass and resonance amplification factor of the initial space flywheel are obtained.

4. A method for optimizing the design of a space flywheel according to claim 1, characterized in that: The equality constraint function includes the mandatory constraint h1(X); the inequality constraint function includes the inertia constraint g1(X), the geometric dimension constraint g2(X), the stiffness constraint g3(X), the strength constraint g4(X), the center of mass constraint g5(X), and the stability constraint g6(X).

5. The method for optimizing the design of a space flywheel according to claim 1, characterized in that: In S4, the parameter space is divided into multiple non-overlapping parameter subspaces, and the subspaces are called through multi-process Python and multi-threaded batch calculations.

6. The method for optimizing the design of a space flywheel according to claim 1, characterized in that: In S5, 80% of the data in the spatial flywheel design variable database are fitted, and 20% of the data are used to test the accuracy of the model by the root mean square error.

7. The method for optimizing the design of a space flywheel according to claim 1, characterized in that: In the root mean square error verification of S5, if the error is greater than 5%, the sample size is increased to continue fitting. If the error is less than 5%, the NSGA-Ⅱ genetic algorithm is used to solve the objective function, and the objective function program is run using MATLAB software.

8. The method for optimizing the design of a space flywheel according to claim 1, characterized in that: In S6, the Pareto front solution set and the simulation results are compared by root mean square error to determine the validity of the model. If the root mean square error is less than 5%, the model is considered valid. If the root mean square error is greater than 5%, S4 is repeated to increase the sample size.

9. The method for optimizing the design of a space flywheel according to claim 1, characterized in that: In S6, the best solution among the Pareto candidate solutions is taken as the optimized spatial flywheel model for harmonic response analysis, and the harmonic response analysis results before and after optimization are compared and verified.

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