Design method of spacecraft sinusoidal test conditions based on time-frequency characteristics of interface loads

Abstract

The present invention discloses a method for designing sinusoidal test conditions for spacecraft based on the time-frequency characteristics of interface loads, the method comprising the following steps: obtaining low-frequency transient acceleration loads at the satellite-rocket interface at a critical stage during actual flight; performing time-frequency characteristic analysis on transient loads; calculating the frequency spectrum of transient loads based on the time-frequency characteristics; designing sinusoidal test conditions based on an envelope method; generating sinusoidal swept frequency loads based on sinusoidal test conditions; obtaining actual true responses and test responses; using a rain flow counting method based on mechanical environmental effects to compare true responses with test conditions, and completing a rationality assessment of test conditions; if the mechanical environmental effects of the test conditions on the structure are equivalent to the real mechanical environmental effects, the test condition design is completed. The present invention effectively alleviates the problem of over-testing during the sinusoidal test of spacecraft, and provides a theoretical and technical basis for reducing the design cost of spacecraft against mechanical environment.

Description

Technical Field

[0001] The invention belongs to the technical field of spacecraft sinusoidal mechanical environmental testing, and in particular relates to a spacecraft sinusoidal test condition design method based on the time-frequency characteristics of interface loads. Background Art

[0002] Sine vibration test is one of the main items of mechanical environment test for spacecraft, which mainly tests the ability of spacecraft to withstand low-frequency transient loads in the critical stage of launch process. However, due to the overly conservative design of test conditions and the mismatch of interface impedance during ground test, the actual sinusoidal test has prominent problems of over-testing. The whole satellite or single machine can pass the actual flight test but cannot pass the ground sinusoidal test. In order to ensure that the whole satellite or single machine can pass the ground sinusoidal test smoothly, the designers need to reinforce the whole satellite or single machine, which increases the cost of mechanical environment design for the whole satellite or single machine.

[0003] There are two main reasons for the over-test problem of spacecraft sinusoidal tests. First, the sinusoidal acceleration test conditions obtained based on the shock response spectrum design of transient loads are too conservative. At the same time, there are problems such as the applicability of the single-degree-of-freedom assumption and the lack of basis for the selection of the amplification factor in the shock response spectrum. Second, the test interface of the ground vibration table does not match the impedance of the actual satellite-rocket interface. Although the force-limited passive concave technology can be used in engineering to alleviate the over-test problem caused by the interface impedance mismatch, there is currently no sinusoidal force limit condition design method available for engineering. Summary of the invention

[0004] Research on the design and evaluation methods of sinusoidal test conditions based on the time-frequency characteristics of interface loads can not only optimize the spacecraft sinusoidal acceleration test conditions and reduce the design cost of the spacecraft's mechanical environment caused by unreasonable test conditions, but also guide the design of sinusoidal force limit conditions based on the time-frequency characteristics of transient interface forces, and then use force limit technology to alleviate the over-test of the sinusoidal test caused by interface impedance mismatch, thereby reducing the risk of damage to the entire satellite or a single machine during the sinusoidal test.

[0005] With the surge in demand for the development of large and new spacecraft in my country, such as large SAR antennas and large optical platforms, the structural size of spacecraft is getting larger, the configuration is getting more complex, and the fundamental frequency is getting lower. This puts forward more stringent requirements on the design and testing of the mechanical environment, especially the sinusoidal mechanical environment test. Since the dynamic characteristics of new aerospace are very different from those of previous models, the reference value of the relevant historical test data and model experience accumulated in the past has become very limited. Therefore, there is an urgent need for a refined sinusoidal test condition method for spacecraft to guide the design of spacecraft and the design of sinusoidal mechanical environment test conditions for spacecraft, and to provide technical support for the development of new spacecraft.

[0006] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art and provide a method for designing spacecraft sinusoidal test conditions based on the time-frequency characteristics of interface loads, which can not only realize the refinement of spacecraft sinusoidal test conditions, but also provide a basis for designing sinusoidal test force limit conditions based on interface force loads, alleviate the over-test problem caused by overly conservative test condition design, effectively ensure the scientificity, effectiveness and rationality of the spacecraft sinusoidal test condition design, and provide technical support for improving the level of spacecraft design in my country.

[0007] The object of the present invention is achieved through the following technical scheme: a method for designing sinusoidal test conditions for spacecraft based on the time-frequency characteristics of interface loads, the method comprising the following steps: step one: obtaining the transient acceleration load A(t) of the spacecraft satellite-rocket interface according to actual flight telemetry data, wherein the variable t is time; step two: using a time-frequency analysis method to perform time-frequency analysis on the transient acceleration load A(t) of the spacecraft satellite-rocket interface to obtain the time-frequency spectrum TF(t,f) of the spacecraft satellite-rocket interface acceleration load, wherein f represents frequency; step three: according to the time-frequency spectrum TF(t,f) of the spacecraft satellite-rocket interface acceleration load obtained in step two, using peak projection or The energy equivalent method is used to obtain the frequency spectrum A(f) of the acceleration load on the spacecraft-satellite-rocket interface; Step 4: According to the frequency spectrum A(f) of the acceleration load on the spacecraft-satellite-rocket interface obtained in Step 3, a certain envelope method is used to establish the sinusoidal test condition C(f); Step 5: According to the sinusoidal test condition C(f) obtained in Step 4, a sinusoidal test swept frequency load A0(t) is generated according to the swept frequency algorithm; Step 6: According to the transient acceleration load A(t) of the spacecraft-satellite-rocket interface obtained in Step 1 and the sinusoidal test swept frequency signal A0(t) obtained in Step 5, two loads are used to perform transient dynamic analysis to obtain the acceleration response a under the action of the transient load A(t) true (t) and stress response σ true (t), acceleration response a under the action of sinusoidal test sweep signal A0(t) test (t) and stress response σ test (t); Step 7: Stress response σ under the transient load A(t) obtained in step 6 true (t) and the stress response σ under the action of the scanning signal A0(t) test (t), the rain flow counting method is used to obtain the amplitude-cycle number σ of the response of the structure under the transient load at the spacecraft-rocket interface m, t rue (c) and mean-cycle number result σ v, t rue (c) Amplitude of the structure’s response under sine sweep loads – number of cycles σ m, t est (c) and mean-cycle number result σ v,test(c); Step 8: According to the amplitude-cycle number σ of the response of the structure under the transient load of the spacecraft-rocket interface m,true (c) and mean-cycle number result σ v,true (c) Amplitude of the structure’s response under sine sweep loads – number of cycles σ m,test (c) and mean-cycle number result σ v,test (c) Use the peak failure criterion or low-cycle fatigue failure criterion for evaluation. If both meet the error requirements of the test conditions, the test condition design is completed.

[0008] In the above-mentioned spacecraft sinusoidal test condition design method based on the time-frequency characteristics of interface loads, in step 3, the peak projection method is obtained by the following formula:

[0009] A(f) = max(TF(t,f));

[0010] Among them, A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load, TF(t,f) is the time-frequency spectrum of the spacecraft-rocket interface acceleration load, f is frequency, and t is time.

[0011] In the above-mentioned spacecraft sinusoidal test condition design method based on the time-frequency characteristics of interface loads, in step 3, the energy equivalent method is obtained by the following formula:

[0012] A(f)=∫TF(t,f)dt / t n ;

[0013] Among them, t n is the total duration of the signal, TF(t,f) is the time-frequency spectrum of the spacecraft-rocket interface acceleration load, f is the frequency, t is the time, and A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load.

[0014] In the above-mentioned spacecraft sinusoidal test condition design method based on the time-frequency characteristics of interface loads, in step 4, the certain envelope method is obtained by the following formula:

[0015] C(f)=max(A(f))*(1+η)

[0016] Among them, η is the envelope margin, C(f) is the sinusoidal test condition, A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load, and f is the frequency.

[0017] In the above-mentioned spacecraft sinusoidal test condition design method based on the time-frequency characteristics of interface loads, in step eight, the peak failure criterion is:

[0018] For the first penetration failure, if the yield stress of the structural material is σ0, and both the real load and the test load are the first penetration failure, that is, σ0>max(σ v,true,σ v,test ), define the allowable structural damage margin of the test as β, and the allowable design margin error as ε, then:

[0019]

[0020] In the above formula, the condition max(σ v,test )>max(σ v,true )(1+β+ε) indicates that the damage caused by the sinusoidal test exceeds the design allowable error, that is, an unacceptable over-test occurs. It is necessary to reduce the envelope margin η to reduce the over-test, and then return to step 4 for analysis; the condition max(σ v,test ) <max(σ v,true )(1+β-ε) indicates that the damage caused by the sinusoidal test is lower than the design allowable error, that is, there is a risk of under-testing, and it is necessary to increase the envelope margin to increase the test intensity η, and then return to step 4 for analysis; condition max(σ v,true )(1+β-ε) <max(σ v,test ) <max(σ v,true )(1+β+ε) indicates that the damage is within the allowable error range, the test conditions are reasonable, and the test is exited.

[0021] In the above-mentioned spacecraft sinusoidal test condition design method based on the time-frequency characteristics of interface loads, in step eight, the low-cycle fatigue failure criterion is:

[0022] For low-cycle fatigue damage, the Miner criterion of linear fatigue cumulative damage theory is used. When a component is subjected to a constant amplitude alternating stress load S, the cyclic damage life is N. Then the damage after n cycles is D = n / N. For K stress cycles, the total damage can be expressed as

[0023] The fatigue damage SN curve of the spacecraft structural material is preset to be B=S 2 N, then the following sine test condition damage assessment method is established:

[0024] definition: and are the low cycle fatigue damage caused by real load and sine sweep test, respectively. i represents the i-th statistical result in rain flow counting, defines the allowable structural damage margin of the test as β, and the allowable design margin error as ε, then:

[0025]

[0026] In the above formula, condition D test >D true(1+β+ε) indicates that the low-cycle fatigue damage caused by the sinusoidal test exceeds the design allowable error, that is, an unacceptable over-test occurs. It is necessary to reduce the envelope margin η to reduce the over-test, and then return to step 4 for analysis; Condition D test <D true (1+β-ε) indicates that the low-frequency damage caused by the sinusoidal test is lower than the design allowable error, that is, there is a risk of under-testing, and it is necessary to increase the envelope margin to increase the test intensity η, and then return to step 4 for analysis; Condition D true (1+β-ε) <D test <D true (1+β+ε) shows that the low-cycle fatigue damage is within the allowable error range, the test conditions are reasonable, and the test is exited.

[0027] A spacecraft sinusoidal test condition design system based on the time-frequency characteristics of interface loads, comprising: a first module, used to obtain a transient acceleration load A(t) of a spacecraft satellite-rocket interface according to actual flight telemetry data, wherein the variable t is time; a second module, used to perform a time-frequency analysis on the transient acceleration load A(t) of the spacecraft satellite-rocket interface using a time-frequency analysis method to obtain a time-frequency spectrum TF(t,f) of the spacecraft satellite-rocket interface acceleration load, wherein f represents frequency; a third module, used to obtain a spacecraft satellite-rocket interface acceleration load according to the time-frequency spectrum TF(t,f) of the spacecraft satellite-rocket interface acceleration load obtained by the second module using a peak projection or energy equivalent method. The fourth module is used to establish the sinusoidal test condition C(f) by a certain envelope method according to the spectrum A(f) of the acceleration load on the spacecraft-satellite-rocket interface obtained in the third module; the fifth module is used to generate the sinusoidal test swept frequency load A0(t) according to the swept frequency algorithm based on the sinusoidal test condition C(f) obtained in the fourth module; the sixth module is used to perform transient dynamic analysis using the transient acceleration load A(t) of the spacecraft-satellite-rocket interface obtained in the first module and the sinusoidal test swept frequency signal A0(t) obtained in the fifth module, and obtain the acceleration response a under the action of the transient load A(t) true (t) and stress response σ true (t), acceleration response a under the action of sinusoidal test sweep signal A0(t) test (t) and stress response σ test (t); The seventh module is used to calculate the stress response σ under the transient load A(t) obtained in the sixth module. true (t) and the stress response σ under the action of the scanning signal A0(t) test (t), the rain flow counting method is used to obtain the amplitude-cycle number σ of the response of the structure under the transient load at the spacecraft-rocket interface m,true (c) and mean-cycle number result σ v,true(c) Amplitude of the structure’s response under sine sweep loads – number of cycles σ m,test (c) and mean-cycle number result σ v,test (c) The eighth module is used to calculate the amplitude-cycle number σ of the response of the structure under the transient load of the spacecraft-rocket interface m,true (c) and mean-cycle number result σ v,true (c) Amplitude of the structure’s response under sine sweep loads – number of cycles σ m,test (c) and mean-cycle number result σ v,test (c) Use the peak failure criterion or low-cycle fatigue failure criterion for evaluation. If both meet the error requirements of the test conditions, the test condition design is completed.

[0028] In the above-mentioned spacecraft sinusoidal test condition design system based on the time-frequency characteristics of interface loads, the peak projection method is obtained by the following formula:

[0029] A(f) = max(TF(t,f));

[0030] Among them, A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load, TF(t,f) is the time-frequency spectrum of the spacecraft-rocket interface acceleration load, f is frequency, and t is time.

[0031] In the above-mentioned spacecraft sinusoidal test condition design system based on the time-frequency characteristics of interface loads, the energy equivalent method is obtained by the following formula:

[0032] A(f)=∫TF(t,f)dt / t n ;

[0033] Among them, t n is the total duration of the signal, TF(t,f) is the time-frequency spectrum of the spacecraft-rocket interface acceleration load, f is the frequency, t is the time, and A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load.

[0034] In the above-mentioned spacecraft sinusoidal test condition design system based on the time-frequency characteristics of interface loads, the certain envelope method is obtained by the following formula:

[0035] C(f)=max(A(f))*(1+η);

[0036] Among them, η is the envelope margin, C(f) is the sinusoidal test condition, A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load, and f is the frequency.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] (1) The present invention proposes a sinusoidal test condition design method based on the time-frequency characteristics of the interface load, which does not have the problems of parameter selection and applicability of assumed conditions, while meeting the requirements of the force limit condition design method;

[0039] (2) The present invention proposes a sinusoidal test condition evaluation method based on mechanical environmental effects to evaluate the rationality of sinusoidal test conditions from the perspective of structural damage;

[0040] (3) The present invention provides a sinusoidal test condition design method and process based on time-frequency characteristics, which can not only realize the refinement of spacecraft sinusoidal test conditions, but also provide a basis for designing sinusoidal test force limit conditions based on interface force loads, alleviate the over-test problem caused by overly conservative test condition design, and effectively ensure the scientificity, effectiveness and rationality of spacecraft sinusoidal test condition design, providing technical support for improving the level of spacecraft design in my country. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0042] Figure 1 It is a flow chart of a method for designing spacecraft sinusoidal test conditions based on the time-frequency characteristics of interface loads provided by an embodiment of the present invention;

[0043] Figure 2 is a schematic diagram of an interface transient acceleration load for a verification method provided by an embodiment of the present invention;

[0044] FIG3( a ) is a schematic diagram of a sinusoidal test condition based on an impulse response spectrum design provided in an embodiment of the present invention;

[0045] FIG3( b ) is a schematic diagram of a sinusoidal test condition designed based on time-frequency characteristics (short-time Fourier transform) according to an embodiment of the present invention;

[0046] FIG4( a ) is a schematic diagram of a sine test condition swept frequency time domain load based on an impulse response spectrum design provided in an embodiment of the present invention;

[0047] FIG4( b ) is a schematic diagram of a time domain load under a sine test condition swept frequency based on a time-frequency feature design provided in an embodiment of the present invention;

[0048] FIG5( a ) is a schematic diagram of rain flow counting results of an actual load provided by an embodiment of the present invention;

[0049] FIG5( b ) is a schematic diagram of rain flow counting results under the impact response spectrum test conditions provided by an embodiment of the present invention;

[0050] FIG5( c ) is a schematic diagram of rain flow counting results under the time-frequency characteristic test conditions provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0051] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present disclosure and to be able to fully convey the scope of the present disclosure to those skilled in the art. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features described in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0052] Figure 1 1 is a flow chart of a method for designing spacecraft sinusoidal test conditions based on the time-frequency characteristics of interface loads provided by an embodiment of the present invention. Figure 1 As shown, the method comprises the following steps:

[0053] Step 1: Obtain the transient acceleration load A(t) of the spacecraft-rocket interface based on actual flight telemetry data or ground tests, where the variable t is time;

[0054] Step 2: Based on the transient acceleration load A(t) of the spacecraft-rocket interface obtained in step 1, a time-frequency analysis method is used to perform a time-frequency analysis on the transient acceleration load A(t) to obtain the time-frequency spectrum TF(t,f) of the spacecraft-rocket interface acceleration load, where f represents frequency;

[0055] Step 3: Based on the time-frequency spectrum TF(t,f) of the spacecraft-rocket interface acceleration load obtained in step 2, the spectrum A(f) of the spacecraft-rocket interface acceleration load is obtained by using the peak projection or energy equivalent method;

[0056] Construct the spectrum using the peak projection method:

[0057] A(f)=max(TF(f,t))

[0058] The frequency is established using the energy equivalent method:

[0059] A(f)=∫TF(f,t)dt / t n

[0060] where t n is the total duration of the signal, and max() is the maximum value function.

[0061] Step 4: Based on the frequency spectrum A(f) of the spacecraft-rocket interface acceleration load obtained in step 3, the following envelope method is used to establish the sinusoidal test condition C(f):

[0062] C(f)=max(A(f))*(1+η)

[0063] Where η is the envelope margin, and its value range is 0≤η.

[0064] Step 5: Based on the sinusoidal test condition C(f) obtained in step 4, generate the sinusoidal test swept frequency load A0(t) according to the swept frequency algorithm;

[0065] Step 6: Based on the transient acceleration load A(t) of the spacecraft-rocket interface obtained in step 1 and the sinusoidal test sweep signal A0(t) obtained in step 5, two loads are used to perform transient dynamic analysis on the specific spacecraft structure to obtain the response of the spacecraft structure. The acceleration response and stress response under the transient load A(t) are respectively recorded as a true (t) and σ true (t), the acceleration response and stress response under the action of the scanning signal A0(t) are denoted as a test (t) and σ test (t);

[0066] Step 7: Stress response σ under transient load A(t) obtained in step 6 true (t) and the stress response under the action of the scanning signal A0(t) and σ test (t), the rain flow counting method is used to obtain the amplitude-cycle number and mean-cycle number results of the structure response under the transient load of the spacecraft-rocket interface and the sine sweep load, which are recorded as: σ m,true (c),σ v,true (c), σ m,test (c),σ v,test (c), c is the number of cycles;

[0067] Step 8: According to the amplitude-cycle number and mean-cycle number results σ obtained in step 7 m,true (c),σ v,true (c) and σ m,test (c),σ v,test (c) Use the peak failure criterion or low-cycle fatigue failure criterion to evaluate the difference between the two. If the two meet the error requirements of the test conditions, the test condition design is completed. Otherwise, return to step 4 to re-envelope and design.

[0068] Evaluation criterion 1: For the first penetration failure, if the yield stress of the structural material is σ0, and both the real load and the test load are the first penetration failure, that is, σ0>max(σv,true ,σ v,test ), the structural damage margin allowed by the test will be set as β, and the allowable design margin error will be ε, then:

[0069]

[0070] In the above formula, the condition max(σ v,test )>max(σ v,true )(1+β+ε) indicates that the damage caused by the sinusoidal test exceeds the design allowable error, that is, an unacceptable over-test occurs. It is necessary to reduce the envelope margin η to reduce the over-test, and then return to step 4 for analysis; the condition max(σ v,test ) <max(σ v,true )(1+β-ε) indicates that the damage caused by the sinusoidal test is lower than the design allowable error, that is, there is a risk of under-testing, and it is necessary to increase the envelope margin to increase the test intensity η, and then return to step 4 for analysis; condition max(σ v,true )(1+β-ε) <max(σ v,test ) <max(σ v,true )(1+β+ε) indicates that the damage is within the allowable error range, the test conditions are reasonable, and the test is exited.

[0071] Evaluation criterion 2: For low-cycle fatigue damage, the linear fatigue cumulative damage theory Miner criterion is used. When a component is subjected to a constant amplitude alternating stress load S, the cyclic damage life is N, and the damage after n cycles is D = n / N. For K stress cycles, the total damage can be expressed as Assume that the fatigue damage SN curve of the spacecraft structural material is B = S 2 N, then the following sine test condition damage assessment method can be established:

[0072] definition: and are the low cycle fatigue damage caused by real load and sine sweep test, respectively. i represents the i-th statistical result in rain flow counting. Similarly, the allowable structural damage margin of the test is defined as β, and the allowable design margin error is ε, then:

[0073]

[0074] The meaning of the relevant conditions is the same as that of evaluation method 1 and will not be repeated here.

[0075] Obtain the low-frequency transient acceleration load of the satellite-rocket interface during actual flight:

[0076] The sine test mainly simulates the ability of the spacecraft to withstand low-frequency transient loads. Therefore, the test conditions must be designed based on the transient loads that the real spacecraft will experience, including the loads of the launch release, engine ignition, engine shutdown, booster separation, and interstage separation. The loads can be obtained through the telemetry data of the actual flight. Assume that the telemetered interface transient acceleration is A(t), t∈[0,t n ], where variable t is time, t n is the signal duration.

[0077] Perform time-frequency characteristic analysis on transient loads:

[0078] For the real interface transient acceleration load A(t), time-frequency analysis methods such as short-time Fourier transform (STFT) and continuous wavelet transform are used. Here, short-time Fourier transform is taken as an example to perform time-frequency analysis on the transient acceleration load, and its time-frequency spectrum can be obtained as follows:

[0079]

[0080] Where TF is the time-frequency spectrum, f is the frequency in Hz, w is the window function, and j is the imaginary unit.

[0081] The window function can be a Hamming window function, and T is the period of the window function.

[0082]

[0083] Calculate the frequency spectrum of the transient load based on the time-frequency characteristics:

[0084] The present invention proposes two methods for determining transient load spectra based on time-frequency characteristics.

[0085] Method 1: Use the peak projection method to establish the spectrum:

[0086] A(f)=max(TF(f,t),for 0≤t≤t n );

[0087] Method 2: Use energy equivalent method to establish frequency:

[0088] A(f)=∫TF(f,t)dt / t n ;

[0089] Design of sinusoidal test conditions based on the envelope method:

[0090] For the spectrum obtained in step 3, the envelope method is used to establish the sinusoidal test conditions. Here, only the spectrum peak value is used to take the margin envelope to establish the sinusoidal test conditions for explanation. The specific implementation is as follows:

[0091] C(f)=max(A(f))*(1+η);

[0092] Where η is the envelope margin, and its value range is 0≤η.

[0093] Generate a swept sine load based on a sinusoidal test condition:

[0094] For the designed test condition C(f), the sweep rate is specified as m octaves / minute, the start and end frequencies of the sweep are f0 and f1 respectively, and the total sweep time is:

[0095] t tot =60ln(f1 / f0) / ln(2 m );

[0096] Then the frequency and phase of the swept time domain load can be determined as:

[0097]

[0098] The generated swept frequency load is:

[0099]

[0100] Where A0(t) is the generated sinusoidal test frequency sweep signal.

[0101] For specific spacecraft structures, actual transient load data and designed sine swept loads are used to perform structural dynamics analysis to obtain actual real response and test response:

[0102] In order to evaluate whether the test conditions can reasonably and accurately reflect the mechanical environmental effects of the real load on the spacecraft, it is necessary to carry out simulation analysis based on the swept frequency time domain signal to obtain the real transient load data and the real response of the spacecraft structure under the sine swept frequency load. The specific implementation method is as follows:

[0103] Assume that the dynamic equation of the spacecraft structure is described by the following equation:

[0104] Ma(t)+Cv(t)+Kx(t)=F(t);

[0105] Where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, a is the node acceleration response vector, v is the velocity response vector, x is the displacement response vector, F is the external load vector, and for the sinusoidal base excitation F(t) = 0. Assuming that in the spacecraft model, the degree of freedom of the satellite-rocket interface is b, and the non-interface degree of freedom is i, the above formula can be rewritten as:

[0106]

[0107] Written in equation form and using the integral operator Γ instead of the differential, we get:

[0108]

[0109] Simplified to:

[0110]

[0111] If the acceleration response of the interface is known and used as a constraint, it is assumed to be Then the equation can be established from the second line of the above formula:

[0112]

[0113] The real load A(t) and the swept frequency time domain load A0(t) are respectively b Substituting into the above equations, we can obtain the true response of the spacecraft structure under the base excitation and the influence of the sine frequency sweep result, which are denoted as a and true (t) and a test (t), the corresponding structural stress is σ true (t) and σ test (t).

[0114] Based on the mechanical environmental effect, the rain flow counting method is used to compare the actual response with the test conditions to complete the rationality evaluation of the test conditions:

[0115] The rain flow counting method was proposed by M. Matsuiki and T. Endo in the 1950s. It is a dual-parameter technical method that records the amplitude and mean of the load and has a good mechanical foundation. Since its theory is mature, it will not be repeated here. After rain flow counting, the amplitude-cycle number and mean-cycle number results of the structure's response under the real load and the sine sweep load can be obtained, which are recorded as: σ m,true (c),σ v,true (c), σ m,test (c),σ v,test (c), c is the number of cycles.

[0116] If the mechanical environment effect of the test condition on the structure is equivalent to the real mechanical environment effect and meets the test condition design requirements, the test condition design is completed. Otherwise, return to step 4 to re-envelope and design

[0117] There are two main failure modes of the sinusoidal test: one is the stress peak failure with first-through failure as the failure mode, and the other is the fatigue failure with low-cycle fatigue failure as the failure mode. In order to evaluate the damage caused by the test conditions to the structure, two evaluation methods are proposed for the two failure modes:

[0118] Evaluation criterion 1: For the first penetration failure, it is assumed that the yield stress of the structural material is σ0, and both the actual load and the test load are the first penetration failure, that is, σ0>max(σ true ,σ test ), the structural damage margin allowed by the test will be set as β, and the allowable design margin error will be ε, then:

[0119]

[0120] In the above formula, the condition max(σ test )>max(σ true )(1+β+ε) indicates that the damage caused by the sinusoidal test exceeds the design allowable error, that is, an unacceptable over-test occurs. It is necessary to reduce the envelope margin η to reduce the over-test, and then return to step 4 for analysis; the condition max(σ test ) <max(σ true )(1+β-ε) indicates that the damage caused by the sinusoidal test is lower than the design allowable error, that is, there is a risk of under-testing, and it is necessary to increase the envelope margin to increase the test intensity η, and then return to step 4 for analysis; condition max(σ true )(1+β-ε) <max(σ test ) <max(σ true )(1+β+ε) indicates that the damage is within the allowable error range, the test conditions are reasonable, and the test is exited.

[0121] Evaluation criterion 2: For low-cycle fatigue damage, the linear fatigue cumulative damage theory Miner criterion is used. When a component is subjected to a constant amplitude alternating stress load S, the cyclic damage life is N, and the damage after n cycles is D = n / N. For K stress cycles, the total damage can be expressed as Assume that the fatigue damage SN curve of the spacecraft structural material is B = S 2 N, then the following sine test condition damage assessment method can be established:

[0122] definition: and They are low-cycle fatigue damage caused by real load and sine sweep test respectively. Similarly, the allowable structural damage margin of the test is defined as β, and the allowable design margin error is ε, then:

[0123]

[0124] In the above formula, condition D test >D true (1+β+ε) indicates that the low-cycle fatigue damage caused by the sinusoidal test exceeds the design allowable error, that is, an unacceptable over-test occurs. It is necessary to reduce the envelope margin η to reduce the over-test, and then return to step 4 for analysis; Condition Dtest <D true (1+β-ε) indicates that the low-frequency damage caused by the sinusoidal test is lower than the design allowable error, that is, there is a risk of under-testing, and it is necessary to increase the envelope margin to increase the test intensity η, and then return to step 4 for analysis; Condition D true (1+β-ε) <D test <D true (1+β+ε) shows that the low-cycle fatigue damage is within the allowable error range, the test conditions are reasonable, and the test is exited.

[0125] In order to verify the method proposed in the present invention, the method proposed in the present invention is used to carry out sinusoidal test condition design for a transient low-frequency load. Figure 2 is the interface transient acceleration load used to verify the method. Figure 3(a) is the sinusoidal test condition designed by the traditional method (impact response spectrum), Figure 3(b) is the sinusoidal test condition obtained based on the time-frequency characteristics (short-time Fourier analysis), Figure 4 generates the corresponding swept frequency load, Figure 5(a) is the rainflow counting result of the original load, (b) is the rainflow counting result of the structural response after the sinusoidal test condition is designed by the traditional method, and (c) is the rainflow counting result designed by the time-frequency characteristic method. By comparison, it can be seen that according to the evaluation criterion one, the test conditions designed by the method proposed in the present invention are about 1 times less damaging to the structure than the test conditions designed by the traditional method.

[0126] The present invention proposes a sinusoidal test condition design method based on the time-frequency characteristics of interface loads, which does not have the problems of parameter selection, applicability of assumed conditions, etc., and at the same time can meet the requirements of force limit condition design methods; the present invention proposes a sinusoidal test condition evaluation method based on mechanical environment effects, and evaluates the rationality of sinusoidal test conditions from the perspective of structural damage; the present invention provides a sinusoidal test condition design method and process based on time-frequency characteristics, which can not only realize the refinement of spacecraft sinusoidal test conditions, but also provide a basis for designing sinusoidal test force limit conditions based on interface force loads, alleviate the over-test problem caused by overly conservative test condition design, effectively ensure the scientificity, effectiveness and rationality of spacecraft sinusoidal test condition design, and provide technical support for improving the level of spacecraft design in my country.

[0127] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for designing sinusoidal test conditions for spacecraft based on the time-frequency characteristics of interface loads, characterized in that: The method comprises the following steps: Step 1: Obtain the transient acceleration load A(t) of the spacecraft-rocket interface based on the actual flight telemetry data, where the variable t is time; Step 2: Use the time-frequency analysis method to perform time-frequency analysis on the transient acceleration load A(t) of the spacecraft-satellite-rocket interface to obtain the time-frequency spectrum TF(t,f) of the acceleration load of the spacecraft-satellite-rocket interface, where f represents frequency; Step 3: Based on the time-frequency spectrum TF(t,f) of the spacecraft-rocket interface acceleration load obtained in step 2, the spectrum A(f) of the spacecraft-rocket interface acceleration load is obtained by using the peak projection or energy equivalent method; Step 4: Based on the frequency spectrum A(f) of the spacecraft-rocket interface acceleration load obtained in step 3, a certain envelope method is used to establish the sinusoidal test condition C(f); Step 5: Based on the sinusoidal test condition C(f) obtained in step 4, generate the sinusoidal test swept frequency load A0(t) according to the swept frequency algorithm; Step 6: Based on the transient acceleration load A(t) of the spacecraft-rocket interface obtained in step 1 and the sinusoidal test sweep signal A0(t) obtained in step 5, two loads are used to perform transient dynamic analysis to obtain the acceleration response a under the action of the transient load A(t). true (t) and stress response σ true (t), acceleration response a under the action of sinusoidal test sweep signal A0(t) test (t) and stress response σ test (t); Step 7: Stress response σ under transient load A(t) obtained in step 6 true (t) and the stress response σ under the action of the scanning signal A0(t) test (t), the rain flow counting method is used to obtain the amplitude-cycle number σ of the response of the structure under the transient load at the spacecraft-rocket interface m,true (c) and mean-cycle number result σ v,true (c) Amplitude of the structure’s response under sine sweep loads – number of cycles σ m,test (c) and mean-cycle number result σ v,test (c); Step 8: According to the amplitude-cycle number σ of the structure response under the transient load of the spacecraft-rocket interface m，true (c) and mean-cycle number result σ v，true (c) Amplitude of the structure’s response under sine sweep loads – number of cycles σ m，text (c) and mean-cycle number result σ v，text (c) Use the peak failure criterion or low-cycle fatigue failure criterion for evaluation. If both meet the error requirements of the test conditions, the test condition design is completed; The peak failure criterion is: For the first penetration failure, if the yield stress of the structural material is σ0, and both the real load and the test load are the first penetration failure, that is, σ0>max(σ v，true , σ v，test ), define the allowable structural damage margin of the test as β, and the allowable design margin error as ε, then: In the above formula, the condition max(σ v，text )>max(σ v，true )(1+β+ε) indicates that the damage caused by the sinusoidal test exceeds the design allowable error, that is, an unacceptable over-test occurs. It is necessary to reduce the envelope margin η to reduce the over-test, and then return to step 4 for analysis; the condition max(σ v，test )<max(σ v，true )(1+β-ε) indicates that the damage caused by the sinusoidal test is lower than the design allowable error, that is, there is a risk of under-testing, and it is necessary to increase the envelope margin to increase the test intensity η, and then return to step 4 for analysis; condition max(σ v，true )(1+β-ε) <max(σ v，test )<max(σ v，true )(1+β+ε) indicates that the damage is within the allowable error range, the test conditions are reasonable, and the test is exited; The low cycle fatigue failure criterion is: For low-cycle fatigue damage, the Miner criterion of linear fatigue cumulative damage theory is used. When a component is subjected to a constant amplitude alternating stress load S, the cyclic damage life is N. Then the damage after n cycles is D = n / N. For K stress cycles, the total damage can be expressed as The fatigue damage SN curve of the spacecraft structural material is preset to be B=S 2 N, then the following sine test condition damage assessment method is established: definition: and are the low cycle fatigue damage caused by real load and sine sweep test, respectively. i represents the i-th statistical result in rain flow counting, defines the allowable structural damage margin of the test as β, and the allowable design margin error as ε, then: if(D test >D true (1+b+e)) else if(max(σ test )<max(σ true (1+b-e)) else if(D true (1+β-ε)<D test <D true (1+b+e)) break; end; In the above formula, condition D test >D true (1+β+ε) indicates that the low-cycle fatigue damage caused by the sinusoidal test exceeds the design allowable error, that is, an unacceptable over-test occurs. It is necessary to reduce the envelope margin η to reduce the over-test, and then return to step 4 for analysis; Condition D test <D true (1+β-ε) indicates that the low-frequency damage caused by the sinusoidal test is lower than the design allowable error, that is, there is a risk of under-testing, and it is necessary to increase the envelope margin to increase the test intensity η, and then return to step 4 for analysis; Condition D true (1+β-ε)<D test <D true (1+β+ε) shows that the low-cycle fatigue damage is within the allowable error range, the test conditions are reasonable, and the test is exited.

2. The method for designing spacecraft sinusoidal test conditions based on the time-frequency characteristics of interface loads according to claim 1 is characterized in that: In step three, the peak projection method is obtained by the following formula: A(f) = max(TF(t,f)); Among them, A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load, TF(t,f) is the time-frequency spectrum of the spacecraft-rocket interface acceleration load, f is frequency, and t is time.

3. The method for designing spacecraft sinusoidal test conditions based on the time-frequency characteristics of interface loads according to claim 1 is characterized in that: In step three, the energy equivalent method is obtained by the following formula: A(f)=∫TF(t,f)dt / t n ; Among them, t n is the total duration of the signal, TF(t,f) is the time-frequency spectrum of the spacecraft-rocket interface acceleration load, f is the frequency, t is the time, and A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load.

4. The method for designing spacecraft sinusoidal test conditions based on the time-frequency characteristics of interface loads according to claim 1 is characterized in that: In step 4, the certain envelope method is obtained by the following formula: C(f)=max(A(f))*(1+η); Among them, η is the envelope margin, C(f) is the sinusoidal test condition, A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load, and f is the frequency.

5. A spacecraft sinusoidal test condition design system based on the time-frequency characteristics of interface loads, characterized by include: The first module is used to obtain the transient acceleration load A(t) of the spacecraft-rocket interface based on the actual flight telemetry data, where the variable t is time; The second module is used to perform time-frequency analysis on the transient acceleration load A(t) of the spacecraft-satellite-rocket interface using the time-frequency analysis method to obtain the time-frequency spectrum TF(t,f) of the acceleration load of the spacecraft-satellite-rocket interface, where f represents frequency; The third module is used to obtain the frequency spectrum A(f) of the spacecraft-rocket interface acceleration load by using the peak projection or energy equivalent method according to the time-frequency spectrum TF(t,f) of the spacecraft-rocket interface acceleration load obtained in the second module; The fourth module is used to establish the sinusoidal test condition C(f) using a certain envelope method based on the frequency spectrum A(f) of the spacecraft-rocket interface acceleration load obtained in the third module; The fifth module is used to generate the sinusoidal test swept frequency load A0(t) according to the sinusoidal test condition C(f) obtained in the fourth module and the swept frequency algorithm; The sixth module is used to perform transient dynamic analysis based on the transient acceleration load A(t) of the spacecraft-rocket interface obtained in the first module and the sinusoidal test sweep signal A0(t) obtained in the fifth module, and obtain the acceleration response a under the action of the transient load A(t). true (t) and stress response σ true (t), acceleration response a under the action of sinusoidal test sweep signal A0(t) test (t) and stress response σ test (t); The seventh module is used to calculate the stress response σ under the transient load A(t) obtained in the sixth module. true (t) and the stress response σ under the action of the scanning signal A0(t) test (t), the rain flow counting method is used to obtain the amplitude-cycle number σ of the response of the structure under the transient load at the spacecraft-rocket interface m,true (c) and mean-cycle number result σ v,true (c) Amplitude of the structure’s response under sine sweep loads – number of cycles σ m,test (c) and mean-cycle number result σ v,test (c); The eighth module is used to calculate the amplitude-cycle number σ of the response of the structure under the transient load of the spacecraft-rocket interface m,true (c) and mean-cycle number result σ v,true (c) Amplitude of the structure’s response under sine sweep loads – number of cycles σ m,test (c) and mean-cycle number result σ v,test (c) Use the peak failure criterion or low-cycle fatigue failure criterion for evaluation. If both meet the error requirements of the test conditions, the test condition design is completed; The peak failure criterion is: For the first penetration failure, if the yield stress of the structural material is σ0, and both the real load and the test load are the first penetration failure, that is, σ0>max(σ v,true ,σ v,test ), define the allowable structural damage margin of the test as β, and the allowable design margin error as ε, then: In the above formula, the condition max(σ v,test )>max(σ v,true )(1+β+ε) indicates that the damage caused by the sinusoidal test exceeds the design allowable error, that is, an unacceptable over-test occurs. It is necessary to reduce the envelope margin η to reduce the over-test, and then return to step 4 for analysis; the condition max(σ v,test )<max(σ v,true )(1+β-ε) indicates that the damage caused by the sinusoidal test is lower than the design allowable error, that is, there is a risk of under-testing, and it is necessary to increase the envelope margin to increase the test intensity η, and then return to step 4 for analysis; condition max(σ v,true )(1+β-ε)<max(σ v,test )<max(σ v,true )(1+β+ε) indicates that the damage is within the allowable error range, the test conditions are reasonable, and the test is exited; The low cycle fatigue failure criterion is: For low-cycle fatigue damage, the Miner criterion of linear fatigue cumulative damage theory is used. When a component is subjected to a constant amplitude alternating stress load S, the cyclic damage life is N. Then the damage after n cycles is D = n / N. For K stress cycles, the total damage can be expressed as The fatigue damage SN curve of the spacecraft structural material is preset to be B=S 2 N, then the following sine test condition damage assessment method is established: definition: and are the low cycle fatigue damage caused by real load and sine sweep test, respectively. i represents the i-th statistical result in rain flow counting, defines the allowable structural damage margin of the test as β, and the allowable design margin error as ε, then: if(D test >D true (1+b+e)) else if(max(σ test )<max(σ true (1+b-e)) else if(D true (1+β-ε)<D test <D true (1+b+e)) break; end; In the above formula, condition D test >D true (1+β+ε) indicates that the low-cycle fatigue damage caused by the sinusoidal test exceeds the design allowable error, that is, an unacceptable over-test occurs. It is necessary to reduce the envelope margin η to reduce the over-test, and then return to step 4 for analysis; Condition D test <D true (1+β-ε) indicates that the low-frequency damage caused by the sinusoidal test is lower than the design allowable error, that is, there is a risk of under-testing, and it is necessary to increase the envelope margin to increase the test intensity η, and then return to step 4 for analysis; Condition D true (1+β-ε)<D test <D true (1+β+ε) shows that the low-cycle fatigue damage is within the allowable error range, the test conditions are reasonable, and the test is exited.

6. The spacecraft sinusoidal test condition design system based on the time-frequency characteristics of interface loads according to claim 5 is characterized in that: The peak projection method is obtained by the following formula: A(f) = max(TF(t,f)); Among them, A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load, TF(t,f) is the time-frequency spectrum of the spacecraft-rocket interface acceleration load, f is frequency, and t is time.

7. The spacecraft sinusoidal test condition design system based on the time-frequency characteristics of interface loads according to claim 5 is characterized in that: The energy equivalent method is obtained by the following formula: A(f)=∫TF(t,f)dt / t n ; Among them, t n is the total duration of the signal, TF(t,f) is the time-frequency spectrum of the spacecraft-rocket interface acceleration load, f is the frequency, t is the time, and A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load.

8. The spacecraft sinusoidal test condition design system based on the time-frequency characteristics of interface loads according to claim 5 is characterized in that: The certain envelope method is obtained by the following formula: C(f)=max(A(f))*(1+η); Among them, η is the envelope margin, C(f) is the sinusoidal test condition, A(f) is the frequency spectrum of the spacecraft-rocket interface acceleration load, and f is the frequency.

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