A multi-point random vibration analysis method for vehicle-mounted equipment

Abstract

The present invention relates to the field of rail transit simulation analysis, and more specifically, to a multi-point random vibration analysis method for vehicle-mounted equipment. The present invention includes the following steps: S1, analyzing the measured road spectrum data, and calculating the load correlation function matrix in combination with the relevant model; S2, combining the load correlation function matrix with the random load model to calculate the multi-point input load matrix; S3, performing Cholesky decomposition on the multi-point input load matrix to obtain a deterministic spectrum load matrix; S4, performing finite element frequency response analysis on the deterministic spectrum load matrix, and calculating the stress results of the deterministic spectrum load matrix; S5, performing Lie algebraic transformation on the stress results to obtain the power spectrum density function and root mean square function of the stress response; S6, based on the Miner linear cumulative damage criterion, performing fatigue damage analysis on the root mean square function of the stress response. The present invention uses a multi-point input load model based on the measured road spectrum to improve the analysis accuracy and better match the actual working conditions.

Description

Technical Field

[0001] The present invention relates to the field of rail transit simulation analysis, and more specifically to a multi-point random vibration analysis method for vehicle-mounted equipment. Background Art

[0002] Rail transit inverter equipment is usually suspended under the car body and will be subjected to complex and harsh vibration environment during service. Therefore, its vibration reliability and fatigue life have attracted much attention.

[0003] In the structural design process of converter equipment, it is usually necessary to verify the strength, stiffness and fatigue life through simulation analysis.

[0004] Figure 1 A schematic diagram of a typical rail transit AC device of the prior art is disclosed, such as Figure 1 A typical rail transit converter is shown in FIG. 1 , in which a cabinet 1 is connected to a vehicle body via a lifting lug 2 , so the main load on the cabinet is input from the vehicle body via the lifting lug 2 .

[0005] The national standard "GB / T21563-2010 Shock and vibration test for rail transit locomotive and vehicle equipment" stipulates that the vibration load of the on-board equipment is applied in the form of body force, that is, the input at each lifting lug is exactly the same.

[0006] However, in reality, due to the large spatial scale of the converter and the distance between the lifting ears being 1 to 4 m, the vibration input at different lifting ears has certain differences in frequency and amplitude, that is, there is a multi-point input effect.

[0007] The national standard fails to effectively consider the multi-point input effect by using physical loading, and therefore cannot fully and accurately simulate the actual on-site service environment.

[0008] Chinese invention patent CN201910547403.0 proposes a method for predicting the life of a high-speed rail gearbox structure: establish an SN curve model of the gearbox material; determine the allowable number of cycles of the gearbox structure under different equivalent stress conditions based on the established SN curve model of the gearbox material and the gearbox equivalent stress obtained by performing random vibration analysis on the gearbox structure; predict the fatigue life of the gearbox structure using the three-interval method and the linear cumulative damage law based on the determined allowable number of cycles of the gearbox structure under different equivalent stress conditions. The above invention patent can perform fatigue assessment on rail transit equipment, but it cannot accurately simulate the service environment of the equipment, and the accuracy of the simulation analysis is relatively low. Summary of the invention

[0009] The purpose of the present invention is to provide a multi-point random vibration analysis method for vehicle-mounted equipment to solve the problems that the prior art does not consider the multi-point input effect, cannot accurately simulate the real environment, and has low simulation accuracy.

[0010] In order to achieve the above object, the present invention provides a multi-point random vibration analysis method for vehicle-mounted equipment, comprising the following steps:

[0011] S1. Analyze the measured road spectrum data and calculate the load correlation function matrix in combination with the relevant model;

[0012] S2, combining the load correlation function matrix with the corresponding random load model to calculate a multi-point input load matrix;

[0013] S3, performing Cholesky decomposition on the multi-point input load matrix to obtain a deterministic spectrum load matrix;

[0014] S4. Perform finite element frequency response analysis on the deterministic spectrum load matrix and calculate the stress results of the deterministic spectrum load matrix.

[0015] S5. Stress results Perform Lie algebraic transformation to obtain the power spectrum density function and root mean square function of the stress response;

[0016] S6. Based on Miner's linear cumulative damage criterion, fatigue damage analysis is performed on the root mean square parameters of stress response.

[0017] In one embodiment, the expression of the load correlation function matrix is ​​as follows:

[0018] R(ΔL)=exp(-αΔL / L0);

[0019] Among them, ΔL is the distance between any two input points, L0 is the feature distance, and α is a constant.

[0020] In one embodiment, the step S2 further comprises:

[0021] The power spectrum density function S0 of the acceleration load corresponding to the converter is selected as the random load model;

[0022] Combined with the load correlation function matrix R between different input points, the cross-power spectrum density function matrix S of the load at the input point is calculated UU ;

[0023] The cross power spectral density function matrix S UU As a multi-point input load matrix, the expression is as follows, S UU =RS0.

[0024] In one embodiment, the step S3 further comprises:

[0025] The cross power spectral density function matrix S UU Perform Cholesky decomposition to obtain the deterministic spectrum load matrix D, which is expressed as follows:

[0026] S UU =DD T ;

[0027] Where D is the deterministic spectrum loading matrix.

[0028] In one embodiment, the step S4 further comprises:

[0029] The deterministic spectrum load matrix D is used as the load condition and input into the finite element software. The frequency response analysis module is used to perform frequency response analysis and calculate the stress results of the deterministic load matrix.

[0030] In one embodiment, in step S5, the stress response satisfies the Gaussian distribution, and the power spectral density function S of the stress response is σσ , calculated by the following changes:

[0031]

[0032] in, is the stress result for the deterministic spectral load matrix.

[0033] In one embodiment, in step S5, the root mean square function of the stress response, including the first-order stress response result 1σ, is obtained by the following calculation:

[0034]

[0035] Where ω is the frequency of the power spectral density function, S σσ is the power spectral density function.

[0036] In one embodiment, in step S6, the accumulated fatigue B of the structure is obtained through fatigue damage analysis, and the expression is as follows:

[0037]

[0038] Among them, n 1σ、 n 2σ and n 3σ They represent the fatigue cycle numbers of the stress levels of the first-level stress response result 1σ, the second-level stress response result 2σ, and the third-level stress response result 3σ respectively;

[0039] N 1σ、 N 2σ and N3σ are the allowable number of cycles for the corresponding stress levels.

[0040] In one embodiment, in step S6:

[0041] The first-order stress response result 1σ corresponds to 0.6831f0t;

[0042] The secondary stress response result 2σ corresponds to 0.271f0t;

[0043] The third-level stress response result 3σ corresponds to 0.0433f0t;

[0044] Among them, f0 is the statistical frequency, t is the statistical time;

[0045] N 1σ、 N 2σ and N 3σ Obtained from the SN curve corresponding to the material.

[0046] In one embodiment, in step S6, the statistical frequency f0 is obtained by the following formula:

[0047]

[0048]

[0049] in, and σ x are the root mean square of velocity and displacement, respectively.

[0050] The present invention provides a multi-point random vibration analysis method for on-board equipment, which fully considers the multi-point input effect of the load, thereby improving the analysis accuracy. The multi-point input model based on the measured road spectrum is more targeted and makes the simulation more compatible with the actual working conditions. As a general method, in addition to being used for rail transit inverters, it can also be further extended to other structures on the train that are suspended by lugs. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The above and other features, properties and advantages of the present invention will become more apparent through the following description in conjunction with the accompanying drawings and embodiments, in which the same reference numerals always represent the same features, wherein:

[0052] Figure 1 A schematic diagram of a typical rail transit AC device of the prior art is disclosed;

[0053] Figure 2 A flow chart of a method for analyzing multi-point random vibration of a converter according to an embodiment of the present invention is disclosed;

[0054] Figure 3A typical power spectrum density function diagram of the prior art is revealed;

[0055] Figure 4 The SN curve diagram of a typical aluminum alloy in the prior art is disclosed.

[0056] The meanings of the reference numerals in the figures are as follows:

[0057] 1 cabinet;

[0058] 2 Lifting ears. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the invention and are not used to limit the invention.

[0060] The multi-point input effect is usually characterized by the acceleration load correlation function at different input points.

[0061] At present, there are few studies on the correlation functions of on-board equipment loads in the rail transit field, and there is no mature and available correlation function model.

[0062] In the following embodiments, the vehicle-mounted device is a converter for further explanation.

[0063] Figure 2 A flow chart of a method for analyzing multi-point random vibration of a converter according to an embodiment of the present invention is disclosed. Figure 2 As shown, in view of the problem that the load condition in the current converter simulation analysis does not consider the multi-point input effect, the converter multi-point random vibration analysis method proposed in the present invention includes the following steps:

[0064] S1. Analyze the measured road spectrum data and calculate the load correlation function matrix in combination with the relevant model;

[0065] S2, combining the load correlation function matrix with the corresponding random load model to calculate a multi-point input load matrix;

[0066] S3, performing Cholesky decomposition on the multi-point input load matrix to obtain a deterministic spectrum load matrix;

[0067] S4. Perform finite element frequency response analysis on the deterministic spectrum load matrix and calculate the stress results of the deterministic spectrum load matrix.

[0068] S5. Stress results Perform Lie algebraic transformation to obtain the power spectrum density function and root mean square function of the stress response;

[0069] S6. Based on Miner's linear cumulative damage criterion, fatigue damage analysis is performed on the root mean square parameters of stress response.

[0070] The present invention proposes a multi-point random vibration analysis method for a converter of a rail transit converter device, which is a new type of simulation working condition loading method:

[0071] Based on the measured road spectrum data, the acceleration time history curves measured at different lifting lugs of the converter equipment were analyzed for correlation, and the load correlation function matrix model at different lifting lugs was summarized.

[0072] The load-related function matrix model is integrated with the random load model given in the existing specifications for subsequent random vibration analysis and fatigue assessment;

[0073] Ultimately, the simulation analysis conditions are more consistent with the actual service status of the equipment on site, improving the accuracy and precision of the simulation analysis.

[0074] The following takes the vibration input point as the lifting lug as an example to explain each step in detail.

[0075] S1. Analyze the measured road spectrum data and obtain the load correlation function by combining the relevant model.

[0076] Optionally, the related model is a triangular model, a normal function model, etc.

[0077] In this embodiment, according to the physical mechanism of random load correlation in engineering, the correlation between the loads on each lug is inversely related to the distance between the lugs, and the expression of the load correlation function matrix is ​​as follows:

[0078]

[0079] Among them, ΔL is the distance between any two hanging ears, L0 is the characteristic distance, and α is a constant.

[0080] The measured vibration spectrum data at different lifting lugs are selected and imported into the simulation software for correlation analysis combined with the relevant model to fit L0 and α in formula (1) to determine the load correlation function.

[0081] In this embodiment, the simulation software is MATLAB.

[0082] by Figure 1 Taking the converter cabinet shown in the figure as an example, according to formula (1), the load correlation function matrix R between different lifting ears is calculated.

[0083] Figure 1 The converter shown has four lifting eyes.

[0084] The load-related function matrix R corresponding to the converter cabinet is of order 4×4, where the element R ij represents the correlation between the i-th and j-th lugs, i∈{1,2,3,4}, j∈{1,2,3,4}.

[0085] The distance between the two is ΔL ij Substitute into formula (1) and calculate the elements R of the load correlation function matrix one by one ij , thus obtaining the load correlation function matrix R.

[0086] S2. Combine the load correlation function matrix with the corresponding random load model to calculate the multi-point input load matrix.

[0087] The load correlation function is substituted into the random load model obtained from the specification, and the correlation terms between different lifting ears are further calculated to obtain the multi-point input load matrix.

[0088] According to GB / T21563-2010 Shock and vibration test for rail transit rolling stock equipment, the acceleration load power spectrum density function S0 corresponding to the converter is selected as the random load model.

[0089] Figure 3 A typical power spectrum density function diagram of the prior art is revealed, where the horizontal axis is frequency, the vertical axis is acceleration power spectrum density ASD, f1 is the minimum frequency, and f2 is the maximum frequency.

[0090] When the weight m is m<500kg, f1=5Hz, f2=150Hz, and the unit of m is kg.

[0091] When the weight m is 500kg<m<1250kg, f1=(1250 / m)×2Hz, f2=(1250 / m)×60Hz, and the unit of m is kg.

[0092] When the weight m is m>1250kg, f1=2Hz, f2=60Hz, and the unit of m is kg.

[0093] like Figure 3 The acceleration load power spectrum density function S0 shown in the figure is multiplied by the load correlation function matrix R between different input points to obtain the cross power spectrum density function matrix S of the load at the lug. UU , the expression is as follows:

[0094] S UU =RS0 (2)

[0095] S3. Perform Cholesky decomposition on the load matrix to obtain a deterministic spectrum load matrix, thus converting the stationary random vibration analysis into a deterministic frequency response analysis.

[0096] The Cholesky decomposition is a decomposition of a symmetric positive definite matrix into the product of a lower triangular matrix and its transpose.

[0097] The cross power spectral density function matrix S UU Perform Cholesky decomposition to obtain the deterministic spectrum load matrix D, which is expressed as follows:

[0098] S UU =DD T (3)

[0099] Where D is the deterministic spectrum loading matrix.

[0100] Furthermore, Cholesky decomposition can be directly calculated quickly using numerical computing software.

[0101] Optionally, the numerical calculation software is MATLAB software.

[0102] S4. Perform finite element frequency response analysis on the deterministic spectrum load matrix and calculate the stress results of the deterministic spectrum load matrix.

[0103] D is used as the load condition and input into the finite element software. The frequency response analysis module of the finite element solver in the finite element software is used for analysis to calculate the stress results under the deterministic load matrix.

[0104] Optionally, the finite element software is ANSYS software.

[0105] S5. According to the Stainberg Lie algebra theory, the stress results under the deterministic load matrix are The power spectrum density function (PSD) and root mean square function (RMS) of the stress response are obtained by transformation.

[0106] S51, power spectrum density function S of stress response σσ Calculated by the following steps:

[0107] In this embodiment, the stress response conforms to the Gaussian distribution, and the power spectrum density function S of the stress response is σσ The following transformation calculation is performed:

[0108]

[0109] in, is the stress result under the deterministic spectrum load matrix.

[0110] S52. The root mean square function of the stress response is calculated by the following steps:

[0111] According to the integral relationship between the power spectrum density function and the RMS function, the RMS function of the converter includes the first-order stress response result 1σ, which is calculated as follows:

[0112]

[0113] Where ω is the frequency of the power spectral density function, S σσ is the power spectral density function.

[0114] S6. Based on Miner's linear cumulative damage criterion, fatigue damage analysis is performed on the root mean square function of stress response.

[0115] Miner's linear cumulative damage criterion is: in fatigue tests, the damage caused to the specimen under the repeated action of a given stress level is linearly cumulative with the number of cycles. When the damage accumulates to a certain critical value, the specimen is destroyed.

[0116] In this embodiment, the fatigue damage analysis is performed by combining Steinberg Lie algebra theory and Miner linear cumulative damage criterion, and the cumulative fatigue B of the structure can be expressed as:

[0117]

[0118] Among them, n 1σ、 n 2σ and n 3σ They represent the fatigue cycle numbers of the stress levels of the first-level stress response result 1σ (0.6831f0t), the second-level stress response result 2σ (0.271f0t) and the third-level stress response result 3σ (0.0433f0t);

[0119] f0 is the statistical frequency and t is the statistical time.

[0120] N 1σ、 N 2σ and N 3σ They are the allowable number of cycles for the corresponding stress levels, which can be obtained from the SN curve of the material.

[0121] Figure 4 The SN curve diagram of a typical aluminum alloy in the prior art is disclosed, such as Figure 4 As shown in the figure, the SN curve is a curve with the fatigue strength of the standard specimen of the material as the vertical coordinate and the logarithm of the fatigue life lgN as the horizontal coordinate. It represents the relationship between the fatigue strength and fatigue life of the standard specimen under certain cycle characteristics, also known as the stress-life curve.

[0122] Furthermore, the expression of the statistical frequency f0 is as follows:

[0123]

[0124] in, and σ x are the root mean square of velocity and displacement, respectively.

[0125] The multi-point random vibration analysis method for on-board equipment provided by the present invention fully considers the multi-point input effect of the load, thereby improving the analysis accuracy. The multi-point input model used is based on the measured road spectrum, which is more targeted and makes the simulation more compatible with the actual working conditions. As a general method, in addition to being used for rail transit inverters, it can also be further extended to other structures on the train that are suspended by lugs.

[0126] Although the above methods are illustrated and described as a series of actions for simplicity of explanation, it should be understood and appreciated that these methods are not limited by the order of the actions, because according to one or more embodiments, some actions may occur in a different order and / or concurrently with other actions from those illustrated and described herein or not illustrated and described herein but understandable to those skilled in the art.

[0127] As shown in this application and claims, unless the context clearly indicates an exception, the words "a", "an", "an" and / or "the" do not refer to the singular and may also include the plural. Generally speaking, the terms "include" and "comprise" only indicate the inclusion of the steps and elements that have been clearly identified, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements.

[0128] The above embodiments are provided for persons familiar with the art to implement or use the present invention. Personnel familiar with the art can make various modifications or changes to the above embodiments without departing from the inventive concept of the present invention. Therefore, the protection scope of the present invention is not limited to the above embodiments, but should be the maximum scope of the innovative features mentioned in the claims.

Claims

1. A multi-point random vibration analysis method for vehicle-mounted equipment, characterized in that: The following steps are involved: S1. Analyze the measured road spectrum data and calculate the load correlation function matrix in combination with the relevant model; S2, combining the load correlation function matrix with the corresponding random load model to calculate a multi-point input load matrix; S3, performing Cholesky decomposition on the multi-point input load matrix to obtain a deterministic spectrum load matrix; S4. Perform finite element frequency response analysis on the deterministic spectrum load matrix and calculate the stress results of the deterministic spectrum load matrix. S5. Stress results Performing Lie algebraic transformation to obtain the power spectrum density function of the stress response, and obtaining the root mean square function of the stress response according to the integral relationship between the power spectrum density function and the root mean square function; S6. Based on Miner's linear cumulative damage criterion, fatigue damage analysis is performed on the root mean square function of stress response; The step S2 further comprises: The power spectrum density function S0 of the acceleration load corresponding to the converter is selected as the random load model; Combined with the load correlation function matrix R between different input points, multiplication is performed to obtain the cross-power spectrum density function matrix S of the load at the input point. UU ; The cross power spectral density function matrix S UU As a multi-point input load matrix, the expression is as follows, S UU =RS0.

2. The multi-point random vibration analysis method for vehicle-mounted equipment according to claim 1, characterized in that: The expression of the load correlation function matrix is ​​as follows: R(ΔL)=exp(-αΔL / L0); Among them, ΔL is the distance between any two input points, L0 is the feature distance, and α is a constant.

3. The multi-point random vibration analysis method for vehicle-mounted equipment according to claim 1, characterized in that: The step S3 further comprises: The cross power spectral density function matrix S UU Perform Cholesky decomposition to obtain the deterministic spectrum load matrix D, which is expressed as follows: S UU =DD T ; Where D is the deterministic spectrum loading matrix.

4. The multi-point random vibration analysis method for vehicle-mounted equipment according to claim 1, characterized in that: The step S4 further comprises: The deterministic spectrum load matrix D is used as the load condition and input into the finite element software. The frequency response analysis module is used to perform frequency response analysis and calculate the stress results of the deterministic load matrix.

5. The multi-point random vibration analysis method for vehicle-mounted equipment according to claim 1, characterized in that: In step S5, the stress response satisfies the Gaussian distribution, and the power spectral density function S of the stress response is σσ , calculated by the following changes: in, is the stress result for the deterministic spectral load matrix.

6. The multi-point random vibration analysis method for vehicle-mounted equipment according to claim 1, characterized in that: In step S6, the accumulated fatigue B of the structure is obtained through fatigue damage analysis, and the expression is as follows: Among them, n 1σ 、n 2σ and n 3σ They represent the fatigue cycle numbers of the stress levels of the first-level stress response result 1σ, the second-level stress response result 2σ, and the third-level stress response result 3σ respectively; N 1σ 、N 2σ and N 3σ are the allowable number of cycles for the corresponding stress levels.

7. The multi-point random vibration analysis method for vehicle-mounted equipment according to claim 6, characterized in that: In step S6: The first-order stress response result 1σ corresponds to 0.6831f0t; The secondary stress response result 2σ corresponds to 0.271f0t; The third-level stress response result 3σ corresponds to 0.0433f0t; Among them, f0 is the statistical frequency, t is the statistical time; N 1σ 、N 2σ and N 3σ Obtained from the SN curve corresponding to the material.

8. The multi-point random vibration analysis method for vehicle-mounted equipment according to claim 7, characterized in that: In step S6, the statistical frequency f0 is obtained by the following formula: in, and σ x are the root mean square of velocity and displacement, respectively.

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