A 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 initial values of design variables of the initial space flywheel; S2, performing modal analysis and harmonic response analysis on the initial space flywheel based on the input conditions and the technical requirements, judging whether the initial space flywheel meets the design requirements, taking the mass and the harmonic amplification factor of the space flywheel as optimization objectives, and obtaining initial values of the two optimization objectives of the initial space flywheel meeting the design requirements; the space flywheel optimization design method is used for optimizing design of the space flywheel with respect to two or more evaluation index parameters or optimization objectives in conflict, and an optimal space flywheel model meeting input conditions and technical requirements required by a space environment is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of space flywheel technology, in particular to a space flywheel optimization design method. BACKGROUND

[0002] Space flywheel, also known as angular momentum wheel, in the satellite attitude control system, the space flywheel adjusts the attitude of the spacecraft by changing its rotation speed, according to the controller instruction, accelerates or decelerates rotation in the predetermined direction, so as to exchange angular momentum with the satellite, realize accurate directional control or absorb the change of satellite angular momentum caused by space disturbance torque, and then realize the correction of satellite platform attitude deviation, or complete some predetermined attitude change.

[0003] In the active stage of satellite launch, the flywheel will be in a harsh dynamic environment under the joint action of vibration, impact, acceleration overload and various dynamic loads. In this case, the flywheel structure will produce obvious flexible deformation, and even have the risk of impact failure. The resonance amplification factor defined as the ratio of the response acceleration of the flywheel rim to the acceleration load of the flywheel body center can effectively indicate the load bearing capacity of the flywheel. Reducing the resonance amplification factor can effectively reduce the deformation degree of the wheel body rim, increase the impact resistance and overload resistance of the flywheel, and make it better maintain the stability and reliability of the structure in the harsh launch environment. The lightweight design of the satellite can significantly improve the reliability of the satellite. Lightweight makes the satellite structure more simple and efficient. On the other hand, lightweight design can increase the effective payload of the satellite. Under the limited space and carrying capacity, a lighter satellite body can provide the possibility for carrying more key equipment and instruments. At the same time, lightweight can greatly reduce the expensive launch cost.

[0004] Under the requirements of enhancing the impact resistance and overload resistance of the flywheel and the lightweight design of the wheel body, more stringent design requirements are put forward for the mass and resonance amplification factor of the space flywheel, so the mass and resonance amplification factor need to be optimized as evaluation index parameters.

[0005] In the flywheel design process, multiple optimization objectives such as moment of inertia, mass and resonance amplification factor need to be considered at the same time. However, there is a conflict relationship between the optimization objectives, for example: the moment of inertia of the flywheel mainly depends on the rim mass and radius, but with the increase of the rim mass and radius, the flywheel harmonic response will be amplified. At the same time, the flywheel resonance amplification factor and mass are constrained by the moment of inertia and cannot be reduced indefinitely. In the current flywheel optimization design, the multi-objective optimization problem is transformed into single objective or multi-objective optimization is carried out by experience through weighting method or transformation constraint method. However, such transformation inevitably brings problems such as difficulty in determining the weight value by weighting method, difficulty in determining the size of constraint by transformation constraint method, and inability to reflect optimality by empirical direct multi-objective method. SUMMARY

[0006] The purpose of this invention is to propose a space flywheel optimization design method, which optimizes the space flywheel for two or more conflicting evaluation index parameters or optimization objectives, and obtains an optimal space flywheel model that meets the input conditions and technical requirements of the space environment.

[0007] The technical solution adopted in this invention is: a space flywheel optimization design method, comprising the following steps:

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

[0009] S2. Based on the input conditions and technical requirements, perform modal analysis and harmonic response analysis on the initial space flywheel to determine whether the initial space flywheel meets the design requirements. With the optimization of the mass and resonance amplification factor of the space flywheel as the goal, obtain the initial values ​​of the two optimization objectives of the initial space flywheel that meet the design requirements.

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

[0011]

[0012] Where: X = (h,t,r1,r2,L,b,α);

[0013] In the formula W weight (X) represents the mass of the space flywheel; f RAF (X) is the resonant amplification factor; h j (X) is the equality constraint function; g k (X) is the inequality constraint function; where X is a decision vector composed 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 radius of the de-weighting hole, L is the distance from the center of the de-weighting hole to the rim, b is the spoke thickness, and α is the spoke inclination angle.

[0014] The boundary conditions and design variables of the space flywheel are determined based on equality constraint functions and inequality constraint functions. The parameter space is designed using the central experimental design method, and a space flywheel design variable database is established.

[0015] S4. After using Python to call the space flywheel design variable database, connect to ANSYS for parametric modeling and simulation, and store the objective function values ​​corresponding to the sample geometric parameters into the solution set of the objective function.

[0016] S5. Using MATLAB, the design variables are fitted to the objective functions of the two optimization objectives respectively, and the root mean square error of the obtained functions and simulation results is verified.

[0017] S6. Based on the NSGA-II multi-objective optimization algorithm, the two optimization objectives are solved, and the Pareto front solution set of the two optimization objectives is output. Based on the root mean square error, the finite element simulation output is used to verify the multiple possible optimization results at the Pareto front, and finally the optimal space flywheel design scheme is obtained.

[0018] As a preferred option, the input conditions include the rotational speed, angular momentum, and moment of inertia under the operating conditions;

[0019] The technical requirements include the envelope size of the space flywheel, its maximum mass, and the mechanical environment it will experience during launch.

[0020] As a preferred option, the basic acceleration method is used for harmonic response analysis. 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 under the input condition and the first natural frequency under the first mode are compared based on the modal analysis results.

[0021] If the rotation frequency is greater than the first natural frequency, return to step S1 to redesign the initial space flywheel; if the rotation frequency is less than the first 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 option, the equality constraint function includes the mandatory constraint h1(X); the inequality constraint function includes the geometric dimension constraint g2(X), stiffness constraint g3(X), strength constraint g4(X), centroid constraint g5(X), inertia constraint g1(X), and stability constraint g6(X).

[0023] As a preferred approach, in S4, the parameter space is divided into multiple non-overlapping parameter subspaces, and the subspaces are called by multi-process Python for batch computation via multi-threading.

[0024] As a preferred option, in S5, 80% of the data in the space flywheel design variable database is fitted, and 20% of the data is used to test the accuracy of the model using root mean square error.

[0025] As a preferred approach, 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 approach, in S6, the root mean square error (RMSE) of the Pareto front solution set and simulation results is used to determine the effectiveness of the model. If the RMSE is less than 5%, the model is considered effective. If the RMSE is greater than 5%, S4 is repeated to increase the sample size.

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

[0028] Compared with the prior art, the beneficial effects of the present invention are:

[0029] 1. By combining NSGA-II and finite element simulation, the optimization algorithm of NSGA-II can ensure the diversity of solutions and quickly approximate the real Pareto front, thereby improving optimization efficiency and quality.

[0030] 2. Achieve efficient utilization of hardware resources and reduce labor costs through parametric modeling and multi-threaded batch simulation.

[0031] 3. This optimized design method is applicable to all types of flywheel designs. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a design variable diagram of the flywheel in this invention;

[0034] Figure 2 This is a schematic diagram illustrating the application of an acceleration load to a space flywheel according to the present invention;

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

[0036] Figure 4 This is a diagram showing the flywheel harmonic response analysis before optimization in this invention.

[0037] Figure 5 This is a schematic diagram of the Pareto front solution set of the present invention;

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

[0039] Figure 7 This is a schematic diagram illustrating the multi-objective optimization principle of the space flywheel of the present invention. Detailed Implementation

[0040] The present invention will now be described in detail through exemplary embodiments. However, it should be understood that, without further description, elements, structures, and features in one embodiment may be advantageously incorporated into other embodiments.

[0041] It should be noted that, unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "a," "an," or "the," etc., used in the specification and claims of this patent application do not express a limitation on quantity, but rather indicate the presence of at least one; the terms "first," "second," and "third," as used herein, should not be considered as a limitation on the order of components, but are merely for distinguishing different components; the terms "comprising," "including," etc., indicate that the elements or objects preceding "comprising" or "including" encompass the elements or objects listed following "comprising" or "including" and their equivalents, but do not exclude other elements or objects having the same function.

[0042] To more clearly describe the optimized design method of this space flywheel, in conjunction with the attached... Figures 1-7 This embodiment is described as follows:

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

[0044] S1. Based on the input conditions of the space flywheel (including the rotational 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 launch, etc.), design the initial space flywheel and obtain the initial values ​​of the design variables of the initial space flywheel.

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

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

[0047] The specific judgment method is as follows: harmonic response analysis is performed using the basic acceleration method, and axial fixed support is applied to the bottom of the initial space flywheel, such as... Figure 2 As shown, a local acceleration load (acceleration applied at the center) is applied at the fixed support boundary condition, and the rotational frequency under the input condition is compared with the first natural frequency under the first mode based on the modal analysis results.

[0048] If the rotation frequency is greater than the first natural frequency, return to step S1 to redesign the initial space flywheel; if the rotation frequency is less than the first 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] The rotational frequency f at the rated speed n is calculated to be 11.67 Hz based on f = n / 60. Comparing with Table 1, it can be seen that under the operating condition of 700 r / min, the rotational frequency of the flywheel is much smaller than the first natural frequency, indicating that there is no risk of resonance in the flywheel. Therefore, it can be used as the initial spatial flywheel model. The mass of the initial spatial flywheel is calculated to be 10.91 kg by the modeling software. The results of the harmonic response analysis are as follows... Figure 4 As shown, the response frequency is 310Hz and the resonant amplification factor is 25.62.

[0050] Table 1. Natural Frequency of Flywheel

[0051]

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

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

[0054]

[0055] Where: X = (h,t,r1,r2,L,b,α);

[0056] In the formula W weight (X) represents the mass of the space flywheel; f RAF (X) is the resonant amplification factor; h j (X) is the equality constraint function; g k (X) is the inequality constraint function; where X is a decision vector composed 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 radius of the de-weighting hole, L is the distance from the center of the de-weighting hole to the rim, b is the spoke thickness, and α is the spoke inclination angle.

[0057] The boundary conditions and design variables of the space flywheel are determined based on equality constraint functions and inequality constraint functions. The parameter space is designed using the central experimental design method, and a space flywheel design variable database is established.

[0058] Specifically, the equality constraint function includes (1) a mandatory constraint h1(X). The actual assembly requirements of the flywheel with the bearing assembly, housing, and other components, as well as the dimensions of the bearing assembly and the enclosing housing, have been determined. Therefore, the inner diameter of the flywheel and the radial dimensions of the wheel body radius become mandatory constraints. In this example:

[0059] Table 2 Forced Constraints of Flywheel

[0060]

[0061] The inequality constraint functions include geometric dimension constraint g2(X), stiffness constraint g3(X), strength constraint g4(X), centroid constraint g5(X), inertia constraint g1(X), and stability constraint g6(X).

[0062] (2) Moment of inertia constraint

[0063] The flywheel needs to output 25.7 Nm of angular momentum at its rated speed of 700 r / min, and its moment of inertia needs to be ≥0.35 kgm. 2 ;

[0064] (3) Geometric constraints

[0065] Due to the size limitations of the flywheel's sealing cover outer envelope, bearing support, bearing assembly cover, 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 constraints

[0070] The flywheel body should be a rigid rotor within the operating speed range, and its first-order resonant frequency needs to be greater than 1.5 times the rotational frequency of the rotor's highest operating speed.

[0071] (5) Strength constraints

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

[0073] (6) Centroid constraint

[0074] Under operating conditions, the flywheel's center of mass must be located at the axial center of the two 7005 bearings.

[0075] (7) Stability constraints

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

[0077] Refer to steps S4-S6 Figure 7 ;

[0078] S4. After using Python to call the space flywheel design variable database, connect to ANSYS for parametric modeling and simulation. Store the objective function values ​​corresponding to the obtained sample geometric parameters into the solution set of the objective function. Divide the parameter space into multiple non-overlapping parameter subspaces and perform batch calculations on the subspaces through multi-process Python calls and multi-threaded processing.

[0079] S5. Using MATLAB, the design variables are fitted to the objective functions of the two optimization objectives (resonance amplification factor and flywheel mass), and the root mean square error of the obtained functions and simulation results is verified. If the error is greater than 5%, the sample size is increased and the fitting is continued. If the error is less than 5%, the NSGA-II genetic algorithm is used to solve the objective function. The objective function program is run using MATLAB software, where there are 2 objective functions and 7 decision variables. 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 the fitting process, 80% of the data from the space flywheel design variable database is used for fitting, and 20% of the data is used to test the accuracy of the model using root mean square error.

[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, and verify the multiple possible optimization results at the Pareto front based on the root mean square error, and finally obtain the optimal space flywheel design scheme.

[0085] The effectiveness of the model is determined by comparing the Pareto front solution set with the simulation results using root mean square error (RMSE). If the RMS error is less than 5%, the model is considered effective. If the RMS error is greater than 5%, step S4 is repeated with an increased 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 space flywheel model for harmonic response analysis, and the harmonic response analysis results before and after optimization are compared and verified.

[0086] In a specific example, three sets of Pareto candidate solutions are shown in Table 5. The third set of Pareto candidate solutions is selected, and harmonic response analysis is performed on the optimized space flywheel model. The optimized harmonic response analysis is shown below. Figure 6 As shown, compared with the original Figure 4 The comparison shows that the optimized mass is 10.58 kg, while the unoptimized mass is 10.91 kg, a reduction of 0.33 kg, or approximately 3.02%; the optimized resonant amplification factor is 18.55, while the unoptimized resonant amplification factor is 25.62, a reduction of 7.07, or approximately 27.59%; and the optimized response frequency is 322 Hz, while the unoptimized response frequency is 310 Hz, an increase of 12 Hz.

[0087] Table 5. Three sets of Pareto candidate solutions

[0088]

[0089] The parts not described in detail in the above embodiments are existing technologies.

[0090] It should be noted that although the present invention has been described through the above embodiments, the present invention may have many other embodiments. Without departing from the spirit and scope of the present invention, those skilled in the art can obviously make various corresponding changes and modifications to the present invention, but all such changes and modifications should fall within the scope of protection of the appended claims and their equivalents.

Claims

1. A method for optimizing the design of a space flywheel, characterized in that, Includes the following steps: S1. Design the initial space flywheel based on the input conditions and technical requirements of the space flywheel, and obtain the initial values ​​of the initial space flywheel design variables; S2. Based on the input conditions and technical requirements, perform modal analysis and harmonic response analysis on the initial space flywheel to determine whether the initial space flywheel meets the design requirements. Take the mass and resonance amplification factor of the space flywheel as optimization objectives, and obtain the initial values ​​of the two optimization objectives of the initial space flywheel that meet the design requirements. S3. After determining the design variables and constraints, establish the following optimization model: Where: X = (h,t,r1,r2,L,b,α); In the formula W weight (X) represents the mass of the space flywheel; f RAF (X) is the resonant amplification factor; h j (X) is the equality constraint function; g k (X) is the inequality constraint function; where X is a decision vector composed 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 radius of the de-weighting hole, L is the distance from the center of the de-weighting hole to the rim, b is the spoke thickness, and α is the spoke inclination angle. The boundary conditions and design variables of the space flywheel are determined based on equality constraint functions and inequality constraint functions. The parameter space is designed using the central experimental design method, and a space flywheel design variable database is established. S4. After using Python to call the space flywheel design variable database, connect to ANSYS for parametric modeling and simulation, and store the objective function values ​​corresponding to the sample geometric parameters into the solution set of the objective function. S5. Using MATLAB, the design variables are fitted to the objective functions of the two optimization objectives respectively, and the root mean square error of the obtained functions and simulation results is verified. S6. Based on the NSGA-II multi-objective optimization algorithm, the two optimization objectives are solved, and the Pareto front solution set of the two optimization objectives is output. Based on the root mean square error, the finite element simulation output is used to verify the multiple possible optimization results at the Pareto front, and finally the optimal space flywheel design scheme is obtained.

2. The space flywheel optimization design method according to claim 1, characterized in that: Input conditions include rotational speed, angular momentum, and moment of inertia under operating conditions; The technical requirements include the envelope size of the space flywheel, its maximum mass, and the mechanical environment it will experience during launch.

3. The space flywheel optimization design method according to claim 1, characterized in that: Harmonic response analysis was performed using the basic acceleration method. An axial fixed support was applied to the bottom of the initial space flywheel, and a local acceleration load was applied at the fixed support boundary condition. The rotational frequency under the input condition and the first natural frequency under the first mode were compared based on the modal analysis results. If the rotation frequency is greater than the first natural frequency, return to step S1 to redesign the initial space flywheel; If the rotation frequency is less than the first natural frequency, it means that the initial space flywheel of the design has no risk of resonance. The mass and resonance amplification factor of the initial space flywheel can then be obtained.

4. The space flywheel optimization design method 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 centroid constraint g5(X), and the stability constraint g6(X).

5. The space flywheel optimization design method 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 by multi-process Python and batched by multi-threading.

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

7. The space flywheel optimization design method 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 space flywheel optimization design method according to claim 1, characterized in that: In S6, the root mean square error (RMSE) of the Pareto front solution set and simulation results is used to determine the effectiveness of the model. If the RMSE is less than 5%, the model is considered effective. If the RMSE is greater than 5%, S4 is repeated to increase the sample size.

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

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