Recognition method for micro-vibration source of reaction wheel

Abstract

The invention discloses a method for identifying a micro-vibration source of a reaction wheel, which comprises the following steps of: firstly, testing micro-vibration signals of the reaction wheel under a plurality of rotating speed working conditions, then carrying out noise reduction processing on the micro-vibration signals under each rotating speed working condition, converting the micro-vibration signals into frequency domain signals, and identifying the micro-vibration source of the reaction wheel on the basis of amplitude-frequency response under each rotating speed working condition. The method comprises the steps that firstly, a three-dimensional frequency spectrum waterfall plot with micro-vibration changing along with the rotating speed is formed, then, based on theoretical values and test values of modal frequency characteristics, a characteristic peak value is extracted, modal characteristics in the three-dimensional frequency spectrum waterfall plot are recognized and verified, and finally, a vibration source is positioned based on the characteristic peak value, the modal characteristics and rotor-bearing vibration frequency characteristics. According to the recognition method, theoretical calculation and operation modal testing are fused, so that the modal frequency of the reaction wheel system can be more comprehensively obtained, damage of a force measurement method to the reaction wheel and modal distortion in simulation are avoided, the recognition error of a harmonic coefficient is reduced, the fitting precision of high-order harmonics is improved according to multi-order resonance response characteristics, and the recognition accuracy of the reaction wheel system is improved. Therefore, the contribution of the reaction wheel vibration source component and the structure thereof under transmission can be effectively evaluated.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and particularly to a method for identifying the micro-vibration vibration source of a reaction wheel. Background Art

[0002] When a satellite is in orbit, it may generate micro-vibrations due to external space environment and internal on-board disturbances. The frequency of micro-vibrations is usually in the range of 0 to 1000 Hz, and the vibration amplitude is in the range of 10 -3 to 10 -6 g or even smaller, showing characteristics such as wide frequency band, low amplitude, and long duration, which are likely to have an adverse impact on the working performance of sensitive on-board payloads. Through a large number of studies and on-orbit experiments, it has been verified that among the on-board attitude control components, the reaction wheel is one of the main vibration sources causing satellite micro-vibrations. Therefore, the analysis of the characteristics and suppression of reaction wheel micro-vibrations is the key to improving the overall working performance of the satellite, and is of great significance for the development of ultra-precision and ultra-stable technologies of spacecraft.

[0003] Currently, the analysis of the micro-vibration characteristics of reaction wheels is based on dynamic modeling and micro-vibration tests, and combines finite element simulation and signal processing methods to reveal its action mechanism. The vibration source and transmission law of the reaction wheel are obtained through theoretical modeling, micro-vibration signal acquisition, feature extraction, and parameter identification. Although the binning algorithm based on the steady-state empirical model can identify the harmonic disturbances caused by rotor imbalance and bearing geometric defects, it ignores the structural elasticity factor and cannot describe the resonance effect between the vibration source and the structural mode. The feature identification method based on the five-degree-of-freedom rotor-bearing dynamic model and the mathematical analytical extended model only considers the flexible support effect of the rotor-bearing, and there are certain errors in the high-order harmonic fitting and identification. Incomplete consideration of disturbance factors and loss of key characteristic frequencies lead to a decrease in the accuracy of existing identification methods in feature extraction and parameter identification, and it is difficult to quantitatively evaluate the contribution of each disturbance component to the overall micro-vibration. Furthermore, it is impossible to reasonably and effectively guide the vibration isolation design and structural optimization of the reaction wheel. Summary of the Invention

[0004] In view of some or all of the problems in the prior art, the present invention provides a method for identifying the micro-vibration vibration source of a reaction wheel, including:

[0005] Testing the micro-vibration signals of the reaction wheel under multiple rotational speed conditions, where the micro-vibration signals include the magnitudes of three-direction disturbing forces and torques;

[0006] Performing noise reduction processing on the micro-vibration signals under each rotational speed condition, converting them into frequency-domain signals, and forming a three-dimensional spectral waterfall diagram of the micro-vibration varying with the rotational speed based on the amplitude-frequency response under each rotational speed condition;

[0007] Extract the characteristic peaks based on the theoretical values and test values of the modal frequency characteristics, identify and verify the modal characteristics in the three-dimensional spectral waterfall diagram; and

[0008] Locate the vibration source based on the characteristic peaks, modal characteristics, and vibration frequency characteristics of the rotor-bearing.

[0009] Further, evenly divide the maximum rotational speed range of the reaction wheel at a specified interval to obtain the multiple rotational speed conditions.

[0010] Further, perform noise reduction processing on the micro-vibration signals under each rotational speed condition based on the AIC-SVD algorithm.

[0011] Further, the noise reduction processing includes:

[0012] Use an m×n-dimensional Hankel matrix as the attractor trajectory matrix of the micro-vibration signal, and determine the optimal number of rows and columns of the matrix according to the maximum singular value energy criterion;

[0013] Perform singular value decomposition on the Hankel matrix constructed by the micro-vibration signal to obtain the singular values of the matrix;

[0014] For the micro-vibration signal with colored noise, perform singular value correction, use the Akaike information criterion to order the singular values, calculate the AIC value of the singular values, and set the index k of the minimum AIC value as the effective order of the singular values;

[0015] Use the first k-order effective components to perform the inverse operation of singular value decomposition to obtain the construction matrix of the approximate signal; and

[0016] Restore the time series of the construction matrix of the approximate signal according to the averaging method to obtain the noise-reduced signal.

[0017] Further, the calculation of the theoretical values of the modal frequency characteristics includes:

[0018] Establish a five-degree-of-freedom rotor-bearing model of the reaction wheel; and

[0019] Calculate the structural modal frequencies of the rotor-bearing, where the structural modal frequencies include the radial translational frequency, the axial translational frequency, and the gyroscopic wobble frequency.

[0020] Further, the acquisition of the test values of the modal frequency characteristics includes:

[0021] Fix the reaction wheel on the platform and evenly arrange multiple acceleration sensors on its housing surface;

[0022] Control the reaction wheel to run to the maximum rotational speed and collect the response signals of the acceleration sensors after stabilization; and

[0023] Based on the response signal, the dynamic modal frequency of the housing is obtained through operational modal analysis.

[0024] Further, the platform is a marble platform.

[0025] Further, locating the vibration source based on the characteristic peak, modal characteristics, and vibration frequency characteristics of the rotor-bearing includes:

[0026] Removing the modal frequency in the characteristic peak;

[0027] Determining the effective harmonic coefficient through frequency normalization and parameter setting; and

[0028] Combining the vibration frequency characteristics of the rotor and bearing to identify the harmonic components caused by rotor imbalance and bearing geometric defects to locate the vibration source.

[0029] Further, determining the effective harmonic coefficient includes:

[0030] Combining the identified rotor-bearing and housing modal frequencies to discriminate the characteristic peak. If the frequency of the characteristic peak is not the system modal frequency, it is retained and normalized; and

[0031] Traverse the normalized frequency characteristics at all speeds, set the tolerance coefficient and peak ratio for screening, and extract the normalized frequencies within the micro-vibration attention frequency band, which are the effective harmonic coefficients.

[0032] Further, the identification method further includes determining the contribution magnitude of each vibration source, including:

[0033] Fitting the harmonic amplitude to obtain the amplitude coefficient of the harmonic excitation and its amplitude coefficient after resonance with the rotor-bearing; and

[0034] Calculating the contribution magnitude of each vibration source and its contribution under the action of structural transmission according to the frequency amplitude.

[0035] Further, obtaining the amplitude coefficient includes:

[0036] Based on the effective harmonic coefficient and the three-dimensional spectral waterfall diagram, extracting the harmonic amplitudes of each harmonic component;

[0037] Using a quadratic function fitting to obtain the amplitude coefficient of the harmonic excitation; and

[0038] Using a resonance function fitting to obtain the harmonic response amplitude coefficient of the excitation harmonic acting on the rotor-bearing mode.

[0039] A method for identifying the micro-vibration vibration source of a reaction wheel provided by the present invention integrates theoretical calculation and operational modal testing, so that the modal frequencies of the reaction wheel system can be obtained more comprehensively, avoiding the damage to the reaction wheel by the force measurement method and the modal distortion in simulation. The identification method uses the AI C-SVD algorithm to adaptively remove the noise components in the weak signal, filtering out white noise and colored noise in the vibration signal, and can avoid under-denoising and over-denoising. In addition, the identification method takes into account rotor imbalance, local defects and surface waviness of bearings, and elastic factors of the rotor-bearing and the housing, and can more comprehensively identify the vibration sources of high-order harmonics during feature extraction and parameter identification, improving the fitting accuracy of the harmonic amplitude coefficient. At the same time, through more complete theoretical analysis and parameter identification, the identification method can quickly calculate the contribution of the structural components of the reaction wheel to the micro-vibration, realize the visualization of the micro-vibration contribution ranking, and further specifically guide the structural optimization and vibration isolation design. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] To further clarify the above and other advantages and features of the embodiments of the present invention, more specific descriptions of the embodiments of the present invention will be presented with reference to the accompanying drawings. It can be understood that these drawings only depict typical embodiments of the present invention and will not be considered as limiting its scope. In the drawings, for clarity, the same or corresponding components will be denoted by the same or similar reference numerals.

[0041] Figure 1 A schematic flow chart showing a method for identifying the micro-vibration vibration source of a reaction wheel according to an embodiment of the present invention;

[0042] Figure 2 A schematic comparison diagram before and after noise reduction of the micro-vibration signal according to an embodiment of the present invention; and

[0043] Figure 3 A schematic diagram showing the identification results of the structural mode and harmonic disturbance according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0044] In the following description, the present invention is described with reference to the embodiments. However, those skilled in the art will recognize that the embodiments can be implemented without one or more specific details or in combination with other alternative and / or additional methods, materials or components. In other cases, well-known structures, materials or operations are not shown or described in detail to avoid obscuring the inventive points of the present invention. Similarly, for the purpose of explanation, specific numbers, materials and configurations are set forth in order to provide a comprehensive understanding of the embodiments of the present invention. However, the present invention is not limited to these specific details. In addition, it should be understood that the embodiments shown in the drawings are illustrative representations and not necessarily drawn to scale.

[0045] In this specification, the reference to "one embodiment" or "the embodiment" means that the specific features, structures, or characteristics described in connection with the embodiment are included in at least one embodiment of the present invention. The phrase "in one embodiment" that appears throughout this specification does not necessarily all refer to the same embodiment.

[0046] It should be noted that the embodiments of the present invention describe the method steps in a specific order. However, this is only for the purpose of elaborating on the specific embodiment and does not limit the order of the steps. On the contrary, in different embodiments of the present invention, the order of the steps can be adjusted according to the actual requirements.

[0047] Existing reaction wheel vibration source identification methods ignore some important disturbance factors in theoretical analysis. Moreover, without fully obtaining the structural modal characteristics in advance, they extract and fit harmonic parameters, making it difficult to remove the multi-order resonance effects introduced by the subsystem structural modes. As a result, the accuracy of vibration source identification is low, and it is impossible to further evaluate the contribution of the reaction wheel vibration source components to the overall micro-vibration. To address this issue, the present method proposes a method for identifying the vibration source and calculating the contribution of the reaction wheel micro-vibration. It considers factors such as rotor imbalance, local defects and surface waviness of the bearing, and the elasticity of the rotor-bearing and the housing. By integrating the five-degree-of-freedom rotor-bearing model and operational modal analysis, it obtains the complete modal characteristic frequencies of the reaction wheel and combines them with the three-dimensional spectral waterfall diagram of the reaction wheel micro-vibration for identification and verification. In dynamic modeling, the support bearing is equivalent to a spring-damper system, and the radial translational frequency, axial translational frequency, and gyroscopic wobbling frequency of the rotor-bearing are solved through reasonable theoretical derivation of dynamic modeling. To prevent damage to the reaction wheel by the force measurement method, operational modal testing is used to obtain the modal characteristics of the housing subsystem, avoiding the loss of dynamic modes in a single finite element simulation. Based on the micro-vibration test, for the processing of weak signals of micro-vibration, the AI C-SVD algorithm is used for noise reduction preprocessing. Based on singular value decomposition and the Akaike information criterion, the separation of noise signals and the order determination of effective components are realized, and the weak characteristic information in the signal is adaptively retained. According to the variation law of harmonics with speed, the effective harmonic coefficients in the signal characteristics are extracted; based on the resonance response characteristics of the vibration source harmonics and the structural modes, the harmonic amplitude coefficients are fitted, avoiding the reduction in accuracy when fitting the multi-order resonance response amplitudes. Finally, based on the accurately identified harmonic characteristic components and the fitted harmonic amplitude coefficients, the contribution of each vibration source and its contribution during the structural transmission process are calculated. The proposed identification method considers more comprehensive disturbance factors, including rotor imbalance, local defects and surface waviness of the bearing, and the elasticity of the rotor-bearing and the housing. By integrating theoretical modeling and operational modal testing, the complete modal information of the system rotor-bearing and the housing is obtained. After removing the modal resonance interference, the identification error of the harmonic coefficients is reduced; and based on the multi-order resonance response characteristics, the fitting accuracy of high-order harmonics is improved, realizing the quantitative analysis of the contribution of the reaction wheel vibration source. Thus, the frequency characteristic distribution and transmission characteristics of the reaction wheel micro-vibration can be accurately obtained, which can be used as a basis for guiding the design of vibration isolation schemes and the formulation of strategies.

[0048] The following further describes the solution of the present invention with reference to the accompanying drawings of the embodiments.

[0049] Figure 1 The flow diagram showing a method for identifying the vibration source of a reaction wheel micro-vibration according to an embodiment of the present invention is shown. As Figure 1 shown, a method for identifying the vibration source of a reaction wheel micro-vibration includes:

[0050] First, in step 101, obtain the micro-vibration signal. Test the micro-vibration signals of the reaction wheel under multiple rotational speed conditions. In an embodiment of the present invention, the micro-vibration signal includes the magnitudes of three-direction disturbing forces and torques. In an embodiment of the present invention, the six-component force measurement method is used to test the micro-vibration signal of the reaction wheel. Specifically, the reaction wheel is installed on a device such as a Kistler force measurement table, and the reaction wheel is controlled to operate within the maximum rotational speed range [0, Ω max , and the rotational speed conditions are divided according to the specified spacing Ω. After each condition runs stably, collect the micro-vibration signal, that is, obtain the magnitudes of the three-direction disturbing forces and torques (F x , F y , F z , M x , M y , M z ) at a constant rotational speed;

[0051] Next, in step 102, form a three-dimensional spectral waterfall diagram. Perform noise reduction processing on the micro-vibration signals under each rotational speed condition, convert them into frequency-domain signals, and form a three-dimensional spectral waterfall diagram of the micro-vibration varying with the rotational speed based on the amplitude-frequency responses under each rotational speed condition. In an embodiment of the present invention, the AI C-SVD algorithm is used to perform noise reduction processing on the micro-vibration signals under each rotational speed condition. Specifically, it includes:

[0052] Take the m×n-dimensional Hankel matrix as the attractor trajectory matrix of the micro-vibration signal s u = [s(1), s(2), …, s(N)], and determine the optimal number of rows and columns of the matrix according to the maximum singular value energy criterion: if rem(N, 2) = 0, then n = N / 2, m = (N / 2) + 1; if rem(N, 2) = 1, then n = m = (N + 1) / 2;

[0053] Perform singular value decomposition (SVD) on the Hankel matrix constructed by the micro-vibration signal to obtain the singular values σ = (σ1, σ2, …, σ i , …, σ q ) of the matrix;

[0054] For the micro-vibration signal with colored noise, perform singular value correction according to the following formula:

[0055]

[0056] Use the Akaike information criterion (AIC) to determine the order of the singular values. Calculate the AIC values of the singular values according to the following formula, and set the index k of the minimum AIC value as the effective order of the singular values:

[0057]

[0058] Wherein, N is the length of the micro-vibration signal data, q is the number of singular values, and the likelihood estimation order d = 1, 2, …, q - 1;

[0059] Perform the inverse operation of singular value decomposition using the first k-order effective components to obtain the construction matrix of the approximate signal:

[0060] And

[0061] Restore the time sequence of the construction matrix of the approximate signal according to the averaging method, then the signal after noise reduction:

[0062]

[0063] Wherein, i = (1, 2, …, N), l = max(1, i - n + 1), h = min(n, i);

[0064] In an embodiment of the present invention, the time-domain signal after noise reduction is converted into a frequency-domain signal by using the fast Fourier transform;

[0065] Next, in step 103, identify and verify the modal characteristics. Based on the theoretical values and test values of the modal frequency characteristics, master the variation laws of the rotor-bearing and housing modes, and the characteristic peaks (f peak , A peak ) of the three-dimensional spectrum, and identify and verify the modal characteristics in the three-dimensional spectrum waterfall diagram.

[0066] In an embodiment of the present invention, the theoretical values of the modal frequency characteristics include the radial translational frequency, the axial translational frequency, and the gyroscopic precession frequency, which are calculated according to the following steps:

[0067] Use the Lagrange dynamics equation to establish a five-degree-of-freedom rotor-bearing model of the reaction wheel, and deduce the structural modal frequency f rb of the rotor-bearing. Substitute the structural parameters of the rotor and bearing into the following formulas to solve the radial translational frequency f r , the axial translational frequency f a and the gyroscopic precession frequency f θ1,θ2 :

[0068]

[0069] In an embodiment of the present invention, the construction process of the five-degree-of-freedom rotor-bearing model of the reaction wheel and the above formulas is as follows:

[0070] Equivalent the bearing of the reaction wheel to a spring-damper system. In its five directions, that is, the generalized coordinates u = (x y z θ φ) T under three-way translation and rotation vibration around the radial direction, then the five freedoms

[0071] The Lagrange dynamic equations of the degree-of-freedom rotor-bearing system are as follows:

[0072]

[0073] Among them, the Lagrange function \(L = T - V\), where \(T\) and \(V\) are the kinetic energy and potential energy of the system in generalized coordinates respectively, \(\delta W\) is the virtual work, and \(\delta u\) is the virtual displacement;

[0074] Considering the inevitable factors such as rotor dynamic and static imbalance, bearing local defects, and surface waviness, the periodic vibration generated by the structural components is assumed to be a series of discrete harmonics proportional to the square of the rotational speed. Then, the harmonic excitation \(H\) of each degree of freedom u can be expressed as:

[0075]

[0076] Among them, \(\Omega\) is the reaction wheel rotational speed, \(n\) u is the number of harmonics under each degree of freedom, \(C\) ui is the harmonic amplitude coefficient, \(h\) ui is the harmonic coefficient, and \(\varphi\) ui is the harmonic phase angle;

[0077] Based on the small deformation displacement of the spring-damper, the kinetic energy, potential energy, and virtual work parameters of the rotor-bearing system are calculated and substituted into the Lagrange dynamic equations to derive the five-degree-of-freedom rotor-bearing dynamic differential equations:

[0078]

[0079] Among them, \(M\), \(K\), and \(C\) are the mass, stiffness, and damping matrices of the five-degree-of-freedom rotor-bearing respectively, and \(H\) u is the harmonic excitation matrix generated by rotor imbalance, bearing local defects, and surface waviness; and

[0080] Neglecting the structural damping \(C\) and excitation \(H\) of the rotor-bearing u , numerical derivation is performed on the dynamic differential equations to obtain the modal frequency expression of the rotor-bearing system. Among them, the radial translational frequency \(f\) r , the axial translational frequency \(f\) a and the gyroscopic precession frequency \(f\) θ1,θ2 are successively:

[0081]

[0082] Among them, are the radial stiffness and axial stiffness of the rotor support bearings respectively, \(k\) θ is the bearing angular stiffness; the actual total mass \(m\) of the reaction wheel rotor is \(m = m_0 + m\) s + 2m d, m0 is the mass of the rotor excluding imbalance, m s is the equivalent mass of the static imbalance of the rotor, and md is the equivalent mass of the dynamic imbalance; I r , I z are the radial and axial moments of inertia of the rotor respectively.

[0083] In an embodiment of the present invention, the measured values of the modal frequency characteristics mainly include the dynamic modal frequency of the housing system, which is obtained according to the following steps:

[0084] Fix the reaction wheel to be measured on a platform such as a marble platform, and evenly arrange a plurality of acceleration sensors on the surface of the structural housing;

[0085] Control the driving reaction wheel to run to the maximum speed Ω max , and collect the response signals of the sensors after stabilization; and

[0086] Obtain the dynamic modal frequency f of the housing system through operational modal analysis h ;

[0087] Finally, in step 104, locate the vibration source. Locate the vibration source based on the characteristic peak, modal characteristics, and vibration frequency characteristics of the rotor-bearing. Remove the modal frequency in the characteristic peak, and determine the effective harmonic coefficient h through frequency normalization and parameter setting ui , combine the vibration frequency characteristics of the rotor-bearing to locate the vibration source, identify rotor imbalance and bearing geometric defects, such as harmonic components h caused by local flaws and surface waviness, etc ur and h ub . In an embodiment of the present invention, the process of extracting and identifying the harmonic coefficient of the micro-vibration of the reaction wheel is as follows:

[0088] Combine the identified rotor-bearing and housing modal frequencies [f rb , f h to discriminate the characteristic peak (f peak , A peak ). If f peak is not the system modal frequency, retain it and perform

[0089] normalization processing:

[0090] f nor = 60f peak / Ω;

[0091] Traverse the normalized frequency characteristics at all speeds, set the tolerance coefficient ε and the peak ratio P k for screening, and extract the normalized frequencies within the frequency band of interest of the micro-vibration, which are the effective harmonic coefficients h ui ; and

[0092] Combined with the vibration characteristics of the rotor-bearing ui Locate and identify the vibration sources of each harmonic component, and determine the harmonic disturbance components caused by rotor imbalance and bearing defects.

[0093] In an embodiment of the present invention, the contribution of each vibration source may be further determined, including:

[0094] First, in step 105, the amplitude coefficient is obtained. The harmonic amplitude is fitted to obtain the amplitude coefficient of the harmonic excitation and the amplitude coefficient after the resonance with the rotor-bearing. Specifically, in one embodiment of the present invention, it includes:

[0095] Extract harmonic amplitude A ui , use the quadratic function to fit the harmonic amplitude and obtain the amplitude coefficient C of the harmonic excitation ui_in In one embodiment of the present invention, the effective harmonic coefficient h ui And the harmonic amplitude A of each harmonic component extracted from the three-dimensional spectrum ui In one embodiment of the present invention, the harmonic excitation generated by the rotor-bearing operation is proportional to the square of the rotation speed, and the amplitude coefficient C of the harmonic excitation is obtained by fitting the following quadratic function: ui_in :

[0096] A ui =C ui_in Ω 2 ;as well as

[0097] Ignoring the resonance effect of the shell structure mode, the resonance function is used to fit the harmonic amplitude to obtain the response amplitude coefficient C of the harmonic excitation after the rotor-bearing transmission effect. ui_rb and the amplification factor β k Since the harmonic excitation will produce resonance amplification under the transmission of the rotor-bearing and housing system due to the influence of the structural mode, the amplification effect of the housing mode on the source harmonic can be ignored. The resonant frequency f of the excitation harmonic and the rotor-bearing structural mode can be determined based on the amplitude response characteristics. nk and speed Ω nk , introduce the amplification factor β k and damping ratio ξ k , the following resonance function fitting is used to obtain the harmonic response amplitude coefficient C of the excitation harmonic and the rotor-bearing modal action: ui_rb :

[0098] A ui =∑β k C ui_rb Ω 2 ,

[0099] Among them, the amplification factor β k The expression is as follows:

[0100] and

[0101] Next, in step 106, the contribution amount is determined. The contribution amounts of each vibration source and under the action of structural transmission are calculated according to the frequency amplitude. In an embodiment of the present invention, with the square of the frequency-domain amplitude as the vibration energy reference, the transmission contribution amount r of the housing system to the overall micro-vibration is calculated according to the following formula h :

[0102]

[0103] Then the transmission contribution size r of the rotor-bearing mode to the overall micro-vibration rb is:

[0104]

[0105] Combining the harmonic components generated by rotor imbalance and bearing geometric defects and their amplitude coefficients, the contribution amounts r r and r b of the rotor and bearing structures to the micro-vibration are calculated respectively according to the following formula

[0106]

[0107] where C r_in is the harmonic excitation amplitude coefficient under the fitting of the rotor imbalance harmonic component h ur , and C b_in is the harmonic excitation amplitude coefficient under the fitting of the bearing geometric defect harmonic component h ub .

[0108] Taking a certain satellite as an example, the micro-vibration source identification and contribution calculation of the reaction wheel are carried out by using the identification method

[0109] First, a five-degree-of-freedom rotor-bearing model of the reaction wheel is established by using the Lagrange dynamics equation, the modal frequency formula of the rotor-bearing is deduced, the rotor and bearing structure parameters are brought into the modal frequency expression, and the radial translation and axial translation modal frequencies are numerically solved to be 112.5 Hz and 157 Hz, and the starting frequency fθ of the gyroscopic swing is 76.1 Hz

[0110] Next, the reaction wheel to be measured is fixed on the marble platform, and a plurality of acceleration sensors are uniformly arranged on the surface of the structural housing. The driving reaction wheel is controlled to run to the highest speed of 2500 r / min, and the response signals of the sensors are collected after stabilization. The dynamic modal frequencies of the housing system are obtained through operational modal analysis, which are [231.3 Hz, 365.6 Hz, 377.6 Hz, 554.5 Hz, 951.6 Hz] respectively

[0111] Next, use the six-component force measurement method to test the micro-vibration signal of the reaction wheel. Install the reaction wheel on the Kistler force measurement bench, control the operation of the reaction wheel within the maximum rotational speed range of [0, 2500 r / min], divide the rotational speed working conditions at intervals of 50 r / min, and collect measurements after each working condition runs stably to obtain the three-direction disturbing forces and moment magnitudes (Fx, Fy, Fz, Mx, My, Mz) at a constant rotational speed;

[0112] Next, perform noise reduction preprocessing on the micro-vibration signals under each rotational speed working condition based on the AIC-SVD algorithm, and use the fast Fourier transform to convert the noise-reduced time-domain signal into a frequency-domain signal. The comparison before and after noise reduction is as Figure 2 shown. Summarize the amplitude-frequency responses under all rotational speed working conditions and draw a three-dimensional spectral waterfall diagram of the micro-vibration of the reaction wheel changing with rotational speed; and

[0113] Next, summarize the modal frequency characteristics obtained from theoretical calculations and operational modal tests, and master the variation laws of the rotor-bearing and housing modes. Extract the characteristic peaks (f peak ,A peak ) of the three-dimensional spectrum, and identify and verify the modal characteristics in the three-dimensional spectral waterfall diagram;

[0114] Next, remove the modal frequencies in the characteristic peaks, normalize the frequencies, set the tolerance ε = 0.05 and the peak ratio P k ≥50% to screen the peaks, determine the effective harmonic coefficient h ui , and combine the vibration frequency characteristics of the rotor and bearing to locate the vibration source, and identify the harmonic components h ur and h ub caused by rotor imbalance and bearing geometric defects. The identification results of the structural modes and harmonic perturbations are as Figure 3 shown;

[0115] Next, extract the harmonic amplitude A ui , fit the harmonic amplitude with a quadratic function to obtain the amplitude coefficient C ui_in of the harmonic excitation; ignore the resonance influence of the housing structural mode, fit the harmonic amplitude with a resonance function to obtain the response amplitude coefficient C ui_rb of the harmonic excitation after transmission through the rotor-bearing and the amplification coefficient β k ; and

[0116] Finally, using the square of the frequency-domain amplitude as the reference for vibration energy, calculate the contribution magnitudes of each vibration source component and its structural transmission according to the foregoing method. The results are shown in Table 1:

[0117]

[0118] Table 1

[0119] It can be seen that the micro-vibration vibration sources of the reaction wheel include the fundamental frequency harmonics caused by rotor imbalance, the 0.6 times frequency harmonics generated by the bearing cage runout, and various high-order harmonics under the combined action of local defects, waviness of bearing components and rotor imbalance. The harmonic excitation contributions generated by the rotor and the bearing are relatively small, but the disturbance contributions after acting with the path are relatively large. Among them, the energy contribution of the rotor-bearing is concentrated in the radial torque, reaching 89.2% as a whole; the energy contributions of the housing except for the radial torque exceed 40%. Therefore, in addition to directly adding vibration isolators, it is possible to try to use magnetic levitation bearings or carbon fiber composite material housings with a larger modulus of elasticity to improve the structure and reduce the generation and transmission amplification effects of micro-vibrations during the operation of the structure.

[0120] The present invention further provides a system for identifying the micro-vibration vibration sources of a reaction wheel, which includes:

[0121] A first test platform, when testing the dynamic modal frequency of the reaction wheel housing system, the reaction wheel is fixed on the first test platform, and the first test platform can be, for example, a marble platform;

[0122] A test module, which includes an acceleration sensor, a sensing device or apparatus for measuring the magnitude of disturbing force and torque. When testing the dynamic modal frequency of the reaction wheel housing system, the acceleration sensors are uniformly arranged on the surface of the reaction wheel housing, and the sensing device or apparatus for measuring the magnitude of disturbing force and torque is used to obtain micro-vibration signals;

[0123] A second test platform, when obtaining micro-vibration signals, the reaction wheel is installed on the second test platform, and the second test platform can be, for example, a Kistler force measuring table, etc.;

[0124] A control module, which is used to control the reaction wheel to rotate at a specified speed to obtain the dynamic modal frequency and micro-vibration signals of the housing system; and

[0125] A calculation module, which is used to execute each calculation step in the identification method, including the calculation of the theoretical value of modal frequency characteristics, the acquisition of three-dimensional spectral waterfall diagrams, the determination of effective harmonic coefficients, the determination of harmonic components, the fitting of harmonic replication, the calculation of amplitude coefficients, and the calculation of the contribution amounts of each vibration source, etc.

[0126] Although the above-described embodiments of the present invention have been described, it should be understood that they are presented only as examples and not as limitations. It will be apparent to those skilled in the relevant art that various combinations, modifications and changes can be made to them without departing from the spirit and scope of the present invention. Therefore, the width and scope of the present invention disclosed herein should not be limited by the above-disclosed exemplary embodiments, but should be defined only by the appended claims and their equivalents.

Claims

1. A method for identifying the micro-vibration vibration source of a reaction wheel, characterized in that, Including the steps: Obtain the micro-vibration signals of the reaction wheel under multiple rotational speed conditions; Perform noise reduction processing on the micro-vibration signals under each rotational speed condition, convert them into frequency-domain signals, and form a three-dimensional spectral waterfall diagram of the micro-vibration varying with rotational speed based on the amplitude-frequency responses under each rotational speed condition; Extract the characteristic peaks based on the theoretical values and measured values of the modal frequency characteristics, and identify and verify the modal characteristics in the three-dimensional spectral waterfall diagram; And Locate the vibration source based on the characteristic peaks, modal characteristics, and vibration frequency characteristics of the rotor-bearing.

2. The recognition method according to claim 1, wherein The obtaining of the micro-vibration signal of the reaction wheel under any rotational speed condition includes the steps: Install the reaction wheel on the force-measuring platform; And Control its operation within the maximum rotational speed range of the reaction wheel, divide the rotational speed conditions at specified intervals, and collect the micro-vibration signals after each condition runs stably.

3. The recognition method according to claim 1, wherein The micro-vibration signal includes the magnitudes of three-direction disturbing forces and torques.

4. The recognition method according to claim 1, wherein Perform noise reduction processing on the micro-vibration signals under each rotational speed condition based on the AI C-SVD algorithm. The noise reduction processing includes the steps: Take the m×n-dimensional Hankel matrix as the attractor trajectory matrix of the micro-vibration signal, and determine the optimal number of rows and columns of the matrix according to the maximum singular value energy criterion; Perform singular value decomposition on the Hankel matrix constructed by the micro-vibration signal to obtain the singular values of the matrix; For the micro-vibration signal with colored noise, perform singular value correction, use the Akaike information criterion to order the singular values, calculate the AIC value of the singular values, and set the index k of the minimum AIC value as the effective order of the singular values; Perform the inverse operation of singular value decomposition using the first k-order effective components to obtain the construction matrix of the approximate signal; And Restore the time series of the construction matrix of the approximate signal according to the averaging method to obtain the noise-reduced signal.

5. The recognition method according to claim 1, wherein The calculation of the theoretical value of the modal frequency characteristic includes the steps: Establish a five-degree-of-freedom rotor-bearing model of the reaction wheel; and Calculate the structural modal frequencies of the rotor-bearing, where the structural modal frequencies include the radial translational frequency, the axial translational frequency, and the gyroscopic wobbling frequency.

6. The recognition method according to claim 1, characterized in that The measured value of the modal frequency characteristic is obtained according to the following steps: Fix the reaction wheel on the platform, and evenly arrange multiple acceleration sensors on its housing surface; Control the reaction wheel to run to the highest rotational speed, and collect the response signals of the acceleration sensors after stabilization; And Based on the response signals, obtain the dynamic modal frequencies of the housing through operational modal analysis.

7. The recognition method according to claim 1, characterized in that, Locating the vibration source based on the characteristic peaks, modal characteristics, and vibration frequency characteristics of the rotor-bearing includes the steps: Remove the modal frequencies in the characteristic peaks; Determine the effective harmonic coefficient through frequency normalization and parameter setting; and Combine the vibration frequency characteristics of the rotor and bearing to identify the harmonic components caused by rotor imbalance and bearing geometric defects to locate the vibration source.

8. The recognition method according to claim 1, wherein Determining the effective harmonic coefficient includes the steps: Combine the identified rotor-bearing and housing modal frequencies to discriminate the characteristic peaks. If the frequency of the characteristic peak is not the system modal frequency, retain it and perform normalization processing on it; And Traverse the normalized frequency features at all rotational speeds, set the tolerance coefficient and peak ratio for screening, and extract the normalized frequencies within the frequency band of concern for micro-vibrations, which are the effective harmonic coefficients.

9. The recognition method according to claim 1, characterized in that, It also includes determining the contribution magnitudes of each vibration source, including the steps of: Fitting the harmonic amplitudes to obtain the amplitude coefficients of the harmonic excitation and the amplitude coefficients after resonance with the rotor-bearing; and Calculating the contribution magnitudes of each vibration source and under the action of structural transmission according to the frequency amplitudes.

10. The recognition method according to claim 9, characterized in that, The acquisition of the amplitude coefficients includes the steps of: Based on the effective harmonic coefficients and the three-dimensional spectral waterfall diagram, extract the harmonic amplitudes of each harmonic component; Use a quadratic function fitting to obtain the amplitude coefficients of the harmonic excitation; And Use a resonance function fitting to obtain the harmonic response amplitude coefficients of the excitation harmonic and the rotor-bearing mode interaction.

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