A multi-degree-of-freedom random vibration test condition calculation method

Abstract

The application provides a multi-degree-of-freedom random vibration test condition calculation method, and belongs to the technical field of vibration environment test, and comprises the following steps: S1, determining a task scene and a life period event; S2, establishing a multi-degree-of-freedom random vibration time history sample; S3, statistically summarizing a multi-degree-of-freedom random vibration power spectral density matrix to obtain maximum expected SDMs of all events in the task scene; S4, calculating the maximum expected SDMs of all events to synthesize a random vibration environment and obtaining a final synthesized SDM; S5, normalizing the power spectral density matrix; S6, testing the test condition calculation result to verify that the test condition calculation result can envelope measured data. Compared with a traditional multi-degree-of-freedom test condition calculation method, the application avoids the problem of being too conservative, solves the problem of matrix non-positive definiteness through positive definiteness checking and corresponding modification in a key step, and improves the fine level of test condition preparation.

Description

Technical Field

[0001] This invention belongs to the field of vibration environment testing technology, specifically relating to a method for calculating multi-degree-of-freedom random vibration test conditions. Background Technology

[0002] Multi-degree-of-freedom random vibration environment testing aims to more realistically simulate the vibration environment of a product during its intended use. The test conditions are generally specified using an acceleration power spectral density matrix. The effectiveness of vibration environment testing largely depends on the vibration magnitude and duration specified in the test conditions. Due to limitations in laboratory vibration environment simulation capabilities, laboratory vibration environment testing struggles to accurately reproduce the vibration response of a product during its intended use. In dynamic environmental engineering, a key challenge is ensuring that test conditions cover the vibration response during the intended use process without being overly conservative. Overly conservative test conditions can severely constrain product development, leading to significant increases in development schedule and cost. Compared to traditional single-exciter, single-axis vibration environment simulation, multi-degree-of-freedom vibration testing technology can simultaneously provide a controllable vibration energy distribution to the test product along multiple axes. This distribution is independent of the test product's dynamic characteristics, allowing for the selection of relatively small test margins while still covering the vibration response during the intended use process. To achieve the desired multi-degree-of-freedom vibration environment test objectives, the process of developing the corresponding vibration test conditions (including the maximum expected vibration environment of the product's life cycle and its fatigue equivalent duration) is often much more complex than that of uniaxial vibration environment testing.

[0003] Due to the lack of mature methods for calculating multi-degree-of-freedom vibration test conditions, a common approach in engineering is to use the single-degree-of-freedom vibration test conditions as the autospectral density term of the multi-degree-of-freedom power spectral density matrix, setting all cross-spectral density terms to 0. This method generates a power spectral density matrix that is overly conservative for multi-degree-of-freedom vibration testing, potentially producing vibration responses in the test specimen that are far beyond the actual usage level, thus reducing the realism of the test simulation. Another common engineering approach is to obtain the test spectrum by linearizing the frequency domain envelope of measured data from single-exciter random vibration test condition formulation, using this as the autospectral term of the multi-exciter test conditions, and artificially defining the coherence coefficient and phase angle. However, this method may result in a non-positive definite reference spectral matrix, ultimately failing to achieve multi-axis random vibration testing.

[0004] In the existing technology, the traditional multi-degree-of-freedom test condition calculation method has the problem of being too conservative, the power spectral density matrix has the problem of being non-positive definite, and the multi-degree-of-freedom random vibration test conditions formulated cannot effectively assess the environmental adaptability of the test piece, and the level of refinement is insufficient, so improvements are needed. Summary of the Invention

[0005] This invention provides a method for calculating test conditions for multi-degree-of-freedom random vibration, aiming to solve the problems of overly conservative traditional multi-degree-of-freedom test condition calculation methods and the non-positive definiteness of the power spectral density matrix, thereby improving the precision of test condition formulation.

[0006] The problem.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A method for calculating the conditions of a multi-degree-of-freedom random vibration test includes the following steps:

[0009] S1. Determine the task scenario and lifecycle events;

[0010] All expected environmental exposure events during the product lifecycle are listed together with their corresponding durations to form the test scenario for the specimen; the duration of the vibration environment is derived from the environmental profile of the product lifecycle.

[0011] S2. Establish a multi-degree-of-freedom random vibration time history sample;

[0012] S3. Perform statistical induction on the power spectral density matrix of multi-degree-of-freedom random vibration to obtain the maximum expectation SDM of all events in the task scenario;

[0013] S4. Calculate the maximum expected value (SDM) for all events, synthesize the random vibration environment, and obtain the final synthesized SDM;

[0014] S5. Normalize the power spectral density matrix;

[0015] S6. Verify the calculated results of the experimental conditions to ensure that they can encompass the measured data.

[0016] As a further optimization, the steps for establishing multi-degree-of-freedom random vibration time history samples are performed as follows:

[0017] S2.1 Record the position and orientation of the field measurement sensors in detail, determine the frequency bandwidth and sampling frequency, and collect all vibration measurement data of the specimen installation platform;

[0018] S2.2 Analyze the structure of the platform under test, establish a rectangular coordinate system with its geometric center or center of mass as the origin, and determine the coordinates (x, y, y) of each measuring point. i y i z i );

[0019] S2.3 Analyze the task scenarios and task ratios during the lifespan of the platform under test, determine the events included in the task scenarios, and divide the measured data into samples according to different events;

[0020] S2.4. Based on the rigid body modal assumption, and according to the position and orientation of each measured point in the vibration environment in the specified coordinate system, a measurement coordinate transformation matrix is ​​constructed. The vibration environment transformation equation is as follows: The measurement data samples corresponding to each environmental event are transformed into multi-degree-of-freedom motion time history data samples.

[0021]

[0022] a mea =[a1 a2 L a] m ] T , a0 = [a x0 a y0 a z0 α x α y α z ] T (1b)

[0023] In the formula, a i (i = 1, 2, ..., m) represents the linear vibration acceleration at m measured points, and the transformation matrix is... The dimension is m×6.

[0024] As a further optimization, statistical induction is performed on the power spectral density matrix of multi-degree-of-freedom random vibrations to obtain the maximum expected value (SDM) step for all events in the task scenario. The SDM step is performed as follows:

[0025] S3.1 Calculate the SDM for each data sample;

[0026] S3.2 Calculate the SDM of all measured samples of a certain event in the task scenario, organize the SDM of the event according to the logical structure; regularize the cross-spectral density term, that is, transform it into the form of coherence spectrum and phase spectrum;

[0027] S3.3. For the SDM sample corresponding to a certain event obtained in step S3.2, perform statistical induction according to the parameter induction method to obtain the maximum expected SDM of the event.

[0028] As a further optimization, the calculation method for the SDM in the statistical induction step of the multi-degree-of-freedom random vibration power spectral density matrix is ​​as follows:

[0029] S3.1.1 The multi-degree-of-freedom vibration acceleration response signal data sample is {y{t}}. Fourier analysis is performed on this set of measured data to obtain the multi-degree-of-freedom Fourier spectrum vector {Y(ω)}.

[0030] S3.1.2 Calculate its instantaneous power spectral density matrix:

[0031]

[0032] S3.1.3 The cumulative power spectral density matrix obtained after K averaging is as follows:

[0033]

[0034] S3.1.4 Perform positive definiteness checks and corrections on the power spectral density matrix;

[0035] The positive definiteness of the spectral density matrix is ​​checked using the Cholesky decomposition method. If the matrix does not meet the positive definiteness requirement at certain frequencies, the SDM is modified to force it to be transformed into a positive definite matrix.

[0036] As a further optimization, the statistical induction method for the power spectral density matrix of multi-degree-of-freedom random vibration is as follows:

[0037] S3.3.1 It is assumed that the acceleration autospectral density of the random vibration response at the same measurement point on the platform during different usage processes follows a log-normal distribution;

[0038] S3.3.2 When the sample size N i When ≥6, the autospectral density terms of each measured SDM are statistically enveloped according to the upper limit of the one-sided normal tolerance. The maximum expected random vibration environment is defined using the 95 / 50 limit to obtain the maximum expected autospectral density of each, which is then used as the autospectral density term of the maximum expected SDM of the event. The cross-spectral density terms of each measured SDM are statistically averaged and used as the cross-spectral density term of the maximum expected SDM of the event.

[0039] S3.3.3 When the sample size N i When the value is less than 6, the mean spectral density matrix is ​​obtained by statistically averaging the measured SDMs. Then, while keeping the cross-spectral density term of the mean spectral density matrix unchanged, the amplitude of the auto-spectral density term is increased by 3dB to derive the maximum expected SDM.

[0040] S.3.3.4 When there is only one sample, it is considered to represent the mean spectral density matrix of the random vibration environment.

[0041] As a further optimization, the maximum expected SDM of all events is calculated to synthesize a random vibration environment. The final synthesized SDM is obtained as follows:

[0042] S4.1. Take the weighted average of the maximum expected value SDM of each event obtained in step S3 to obtain the composite SDM of all events;

[0043] S4.2 Amplify the power spectrum term of the synthesized SDM so that the root mean square value of each degree of freedom is equal to the maximum root mean square value of the corresponding degree of freedom of all measured SDMs obtained in step S3.1.

[0044] S4.3. Use the fatigue equivalent acceleration relation to scale the time and calculate the equivalent test time;

[0045] S4.4 After the test time is selected, the fatigue equivalence relation is used again for each degree of freedom to recalculate the autopower spectrum of the synthesized SDM; the positive definiteness of the SDM is checked and corrected.

[0046] S4.5 Multiply the diagonal elements of the SDM obtained in step S4.4 by the dispersion factor to account for uncontrollable factors, while keeping coherence and phase unchanged, to obtain the final synthesized SDM.

[0047] As a further optimization, the maximum expected SDM for all events is calculated. In the step of synthesizing random vibration environment, when describing uncontrollable factors, the dispersion factor multiplied by the diagonal elements of the SDM is increased by 3dB.

[0048] As a further optimization, the method for calculating the equivalent test time using fatigue equivalent acceleration relations to scale the time includes the following steps:

[0049] S4.3.1, Estimation of the equivalent fatigue duration of multi-degree-of-freedom random vibration environment specifications based on the Miner cumulative damage model:

[0050]

[0051] or

[0052]

[0053] In the formula, G1(f), σ1 and t1 are the self-spectral density, root mean square acceleration and fatigue equivalent duration of the vibration environment specification, respectively.

[0054] G2(f), σ2, and t2 are the autospectral density, root mean square acceleration, and vibration duration of the actual vibration environment, respectively.

[0055] M represents the fatigue characteristic index of the product;

[0056] S4.3.2. Based on the synthesized SDM, for each degree of freedom of motion, calculate the fatigue equivalent time corresponding to the corresponding degree of freedom of each event using equation (4) or (5); then, add up the fatigue equivalent time of the corresponding degree of freedom of all events to obtain the fatigue equivalent time corresponding to the synthesized SDM.

[0057] S4.3.3. Take the weighted average of the fatigue equivalent duration calculated for each degree of freedom by the square of the root mean square acceleration value, and derive the fatigue equivalent duration corresponding to the equivalent spectral density matrix.

[0058] As a further optimization, the normalization process for the power spectral density matrix is ​​performed as follows:

[0059] S5.1. Smooth the autospectral density curve in the double logarithmic coordinate system using a set of straight line segments to obtain the smoothed autospectral density represented by a broken line.

[0060] S5.2. Smooth the coherent function curve in the linear coordinate system using a set of straight line segments to obtain a smoothed coherent function represented by a broken line.

[0061] S5.3 Check and correct the positive definiteness of the normalized power spectral density matrix.

[0062] As a further optimization, the calculation results of the experimental conditions were verified to ensure that they could encompass the measured data. The steps were as follows:

[0063] S6.1 Using the normalized power spectral density matrix exported in step S5 Estimate the autospectral density of acceleration at all measurement points for statistical analysis.

[0064]

[0065] In the formula, The transformation matrix is ​​an m×N dimensional coordinate matrix. The element in the i-th row and k-th column;

[0066] for The element in the k-th row and l-th column;

[0067] N represents the number of degrees of freedom of motion in a multi-degree-of-freedom random vibration environment.

[0068] m is the number of measurement points used for statistical analysis;

[0069] S6.2, Based on the acceleration self-spectral density The corresponding root mean square acceleration value is obtained by frequency domain integration.

[0070] S6.3. Within the frequency range of interest, and The maximum spectrum of the vibration acceleration data measured at the corresponding point and maximum root mean square acceleration value Compare and verify that it can encompass the measured data.

[0071] The beneficial technical effects achieved by this invention are:

[0072] Based on field measurement data of random vibration environments, multi-degree-of-freedom random vibration test conditions were derived using statistical analysis and the envelope method. The test condition formulation process considered the inherent randomness, variability, and testing errors in the vibration environment data, as well as the impact of the data sample size on the dispersion characteristics of the vibration environment. This approach enables the formulation of more realistic and effective multi-degree-of-freedom random vibration test conditions, improving the precision of test condition formulation and thus more effectively assessing the environmental adaptability of the test specimens.

[0073] Compared with traditional multi-degree-of-freedom experimental condition calculation methods, this invention avoids the problem of being overly conservative; compared with the power spectral density matrix, it solves the problem of non-positive definiteness; the technical solution described in this invention improves the level of precision in experimental condition formulation, solves the problems existing in the prior art, and has outstanding substantive features and significant progress. Attached Figure Description

[0074] Figure 1 This is a flowchart of one specific embodiment of the present invention;

[0075] Figure 2 This is a schematic diagram of the measuring point arrangement in one specific embodiment of the present invention;

[0076] Figure 3 This is a typical data sample transformation result of one specific embodiment of the present invention;

[0077] Figure 4 This is the maximum expected SDM of a flat road surface in one specific embodiment of the present invention;

[0078] Figure 5 This is a synthesized SDM according to one specific embodiment of the present invention;

[0079] Figure 6 This is a standardized SDM according to one specific embodiment of the present invention;

[0080] Figure 7 This is a verification of the experimental conditions calculation results of one specific embodiment of the present invention. Detailed Implementation

[0081] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection claimed by the present invention.

[0082] like Figure 1 As shown, a specific embodiment of a method for calculating multi-degree-of-freedom random vibration test conditions includes the following steps:

[0083] S1. Determine the task scenario and lifecycle events.

[0084] All anticipated environmental exposure events throughout the product lifecycle are listed along with their corresponding durations to form the test scenario for the specimen. The duration of the vibration environment can be derived from the environmental profile throughout the product lifecycle.

[0085] S2. Establish a multi-degree-of-freedom random vibration time history sample.

[0086] S2.1 Record the position and orientation of the field measurement sensors in detail, determine the frequency bandwidth and sampling frequency, and collect all vibration measurement data of the specimen installation platform;

[0087] S2.2 Analyze the structure of the platform under test, establish a rectangular coordinate system with its geometric center or center of mass as the origin, and determine the coordinates (x, y, y) of each measuring point. i y i z i );

[0088] S2.3 Analyze the task scenarios and task ratios during the lifespan of the platform under test, determine the events included in the task scenarios, and divide the measured data into samples according to different events;

[0089] S2.4. Based on the rigid body modal assumption, and according to the position and orientation of each measured point in the vibration environment in the specified coordinate system, a measurement coordinate transformation matrix is ​​constructed. The vibration environment transformation equation is as follows: The measurement data samples corresponding to each environmental event are transformed into multi-degree-of-freedom motion time history data samples.

[0090]

[0091] a mea =[a1 a2 L a] m ] T , a0 = [a x0 a y0 a z0 α x α y α z ] T (1b)

[0092] In the formula, a mea For the linear vibration acceleration at m measured points, the transformation matrix is... The dimension is m×6.

[0093] S3. Statistically summarize the power spectral density matrix of multi-degree-of-freedom random vibrations to obtain the maximum expected value (SDM) of all events in the task scenario.

[0094] S3.1 Calculate the power spectral density matrix (SDM) for each data sample. This matrix has dimensions n×n×m, where n is the number of degrees of freedom and m is the number of spectral lines. The SDM is calculated as follows:

[0095] S3.1.1 Assuming the multi-degree-of-freedom vibration acceleration response signal data sample is {y{t}}, perform Fourier analysis on this set of measured data to obtain the multi-degree-of-freedom Fourier spectrum vector {Y(ω)};

[0096] S3.1.2 Calculate its instantaneous power spectral density matrix:

[0097]

[0098] S3.1.3 The cumulative power spectral density matrix obtained after K averaging is as follows:

[0099]

[0100] S3.1.4 Perform positive definiteness checks and corrections on the power spectral density matrix.

[0101] The positive definiteness of the spectral density matrix (SDM) is checked using the Cholesky decomposition method. If the matrix does not meet the positive definiteness requirement at certain frequencies, a slight modification to the SDM is needed to force it to become a positive definite matrix. This process can be achieved by keeping the self-power spectrum unchanged, multiplying the cross-power spectrum terms by 0.98, and then repeatedly checking until the matrix meets the positive definiteness requirement.

[0102] S3.2 Calculate the SDM of all measurement samples for a certain event in the task scenario, and organize the SDM of a certain event according to a certain logical structure, such as [SDM_i_1,SDM_i_2,....,SDM_i_N] i ], where i is the event number, N i Let be the i-th sample. Regularize the cross-spectral density term, i.e., transform it into the form of coherence spectrum and phase spectrum.

[0103] S3.3, For the N corresponding to a certain event obtained in step S3.2 i For each SDM sample, statistical induction is performed using parametric induction methods to obtain the maximum expected SDM of the event. The specific steps include:

[0104] S3.3.1 Assume that the acceleration autospectral density of the random vibration response at the same measurement point on the platform during different usage processes follows a log-normal distribution.

[0105] S3.3.2, When the sample size N i When ≥6, the autospectral density terms of each measured SDM are statistically enveloped according to the upper limit of the one-sided normal tolerance. The maximum expected random vibration environment is defined using the 95 / 50 limit to obtain the maximum expected autospectral density of each, which is then used as the autospectral density term of the maximum expected SDM of the event. The cross-spectral density terms of each measured SDM are statistically averaged and used as the cross-spectral density term of the maximum expected SDM of the event.

[0106] S3.3.3 When the sample size 1 < N i When the value is less than 6, the mean spectral density matrix is ​​obtained by statistically averaging the measured SDMs. Then, while keeping the cross-spectral density term of the mean spectral density matrix unchanged, the amplitude of the auto-spectral density term is increased by 3 dB to derive the maximum expected SDM.

[0107] S3.3.4, when N i =1, meaning that when there is only one sample, it is considered to represent the mean spectral density matrix of the random vibration environment.

[0108] Perform a positive definiteness check and correction on the obtained maximum expected SDM according to the method in step S3.1.4.

[0109] Repeat steps S3.2 to S3.3 to obtain the maximum expected value (SDM) of all events in the task scenario.

[0110] S4. Calculate the maximum expected SDM for all events, synthesize the random vibration environment, and obtain the final synthesized SDM.

[0111] S4.1. Take a weighted average of the maximum expected value (SDM) of each event obtained in step S3 to obtain the composite SDM of all events. The weighted average coefficient is determined based on the proportion of task time.

[0112] S4.2 Amplify the power spectrum term of the synthesized SDM so that the root mean square value of each degree of freedom is equal to the maximum root mean square value of the corresponding degree of freedom of all measured SDMs obtained in step S3.1.

[0113] S4.3. Time scaling is performed using the fatigue equivalent acceleration relation to calculate the equivalent test time. Specific steps include:

[0114] S4.3.1, Estimation of the equivalent fatigue duration of multi-degree-of-freedom random vibration environment specifications based on the Miner cumulative damage model:

[0115]

[0116] or

[0117]

[0118] In the formula, G1(f), σ1 and t1 are the self-spectral density, root mean square acceleration and fatigue equivalent duration of the vibration environment specification, respectively.

[0119] G2(f), σ2, and t2 are the autospectral density, root mean square acceleration, and vibration duration of the actual vibration environment, respectively.

[0120] M is the fatigue characteristic index of the product, and in this specific embodiment, M = 7 is selected.

[0121] S4.3.2. Based on the synthesized SDM, for each degree of freedom, calculate the fatigue equivalent time corresponding to the corresponding degree of freedom for each event using equation (4) or (5). Then, add up the fatigue equivalent times for the corresponding degrees of freedom of all events to obtain the fatigue equivalent time corresponding to the synthesized SDM.

[0122] S4.3.3 In general, the fatigue equivalent duration obtained for each degree of freedom is different, and a uniform fatigue equivalent duration needs to be selected. In this specific embodiment, the fatigue equivalent duration calculated for each degree of freedom is weighted and averaged according to the square of the root mean square acceleration value to derive the fatigue equivalent duration corresponding to the equivalent spectral density matrix.

[0123] S4.4 Once the test time is selected, the fatigue equivalence relation is applied again for each degree of freedom to recalculate the autopower spectral density of the synthesized SDM. The positive definiteness of the SDM is then checked and corrected.

[0124] S4.5 Multiply the diagonal elements of the SDM obtained in step S4.4 by a certain dispersion factor. In this specific embodiment, 3dB is added to account for uncontrollable factors, while keeping coherence and phase unchanged, to obtain the final synthesized SDM. The time obtained in step S4.3 is the experimental time.

[0125] S5. Normalize the power spectral density matrix.

[0126] S5.1. Smooth the autospectral density curve in the double logarithmic coordinate system using a set of straight line segments to obtain the smoothed autospectral density represented by a broken line.

[0127] S5.2. Use a set of straight line segments to smooth the coherent function curve in the linear coordinate system to obtain a smoothed coherent function represented by a broken line.

[0128] S5.3 Check and correct the positive definiteness of the normalized power spectral density matrix.

[0129] S6. Verify the calculated results of the experimental conditions to ensure that they can encompass the measured data.

[0130] S6.1 Using the normalized power spectral density matrix exported in step S5 To estimate the acceleration autospectral density at all measurement points used for statistical analysis.

[0131]

[0132] In the formula, The transformation matrix is ​​an m×N dimensional coordinate matrix. The element in the i-th row and k-th column;

[0133] for The element in the k-th row and l-th column;

[0134] N represents the number of degrees of freedom of motion in a multi-degree-of-freedom random vibration environment.

[0135] m represents the number of measurement points used for statistical analysis.

[0136] S6.2, Based on the acceleration self-spectral density The corresponding root mean square acceleration value is obtained by frequency domain integration.

[0137] S6.3. Within the frequency range of interest, and The maximum spectrum of the vibration acceleration data measured at the corresponding point and maximum root mean square acceleration value Compare and verify that it can encompass the measured data.

[0138] The following example, using a set of experimental data, further illustrates the scheme in this specific embodiment. Data is collected through a transportation test to demonstrate the method for determining the experimental conditions of the multi-degree-of-freedom random vibration power spectral density matrix. It should be noted that the data in this example is only for better illustration and understanding of the technical solution and should not be construed as limiting the scope of the rights to be protected by this invention.

[0139] This example studies a wheeled vehicle equipped with an equipment storage rack, measuring the six-degree-of-freedom vibration environment at that location. One triaxial accelerometer is positioned at each of the four corners of the equipment storage rack's connection surface to the vehicle chassis. Twelve measurement channels are used to calculate the six-degree-of-freedom vibration environment. The sensor positions and coordinate system definitions are as follows: Figure 2 As shown.

[0140] ST1. Determine the task scenario and lifecycle events.

[0141] The task scenarios and task ratios of the tested platform are analyzed to determine the events and measurement times corresponding to the task scenarios, and the measured data are sampled according to different events. In this example, the transportation vibration task scenario includes 5 road condition events, and the total transportation distance is assumed to be 6000 kilometers.

[0142] Table 1 Task Scenario Event Table

[0143] flat road 65 76.9 5000 gravel road 30 28.7 860 cobblestone road 30 2.7 80 Fish-scale potholes 10 4.0 40 washboard road 6 6.7 40

[0144] ST2. Establish multi-degree-of-freedom random vibration time history samples

[0145] Calculate the matrix using the rigid body coordinate transformation method.

[0146]

[0147] Using the rigid body coordinate transformation equation (1), the measurement data sample corresponding to each road condition event is transformed into a six-degree-of-freedom motion time history data sample. The transformation results of typical data samples are shown in [reference needed]. Figure 3 As shown. Figure 3 The numbers from top to bottom are X, Y, Z, and θ. x θ y θ z The acceleration time-domain waveforms have a total of 6 degrees of freedom. The unit for linear acceleration is g, and the unit for angular acceleration is rad / s². 2 .

[0148] ST3. Statistical induction is performed on the power spectral density matrix of the multi-degree-of-freedom random vibration to obtain the maximum expected value (SDM) of the road condition event.

[0149] Following the method in step S3 of the above specific embodiment, each time history sample is transformed into a power spectral density matrix in the frequency domain. Each SDM needs to be verified using the Cholesky decomposition property to ensure that they are all positive definite. At the same time, the cross-spectral term is transformed into the form of coherence spectrum and phase spectrum.

[0150] The samples corresponding to each road condition event are statistically summarized. For the same road condition specimen, the self-spectral density is derived from the statistical envelope of the self-spectral density set of measured vibration environment data at the same degree of freedom, and the cross-spectral density is derived from the statistical average of the cross-spectral density sets of measured vibration environment data at different degrees of freedom, thus obtaining the maximum expected value (SDM) for that road condition event.

[0151] Figure 4 The maximum expected SDM is obtained by treating the flat road surface. The layout is based on the Hermitian features of the SDM, where the lower triangular part represents the phase between each degree of freedom, the upper triangular part represents the square root of the constant coherence, and the diagonal term is the autospectral density of the six degrees of freedom.

[0152] ST4. Calculate the maximum expected value (SDM) for all events to synthesize the random vibration environment and obtain the final synthesized SDM.

[0153] The weighted average SDM of all events is obtained by taking the weighted average of the maximum expected values ​​(SDM) of each event. The weighting coefficients are determined based on the proportion of task time. The weighted average SDM is checked at each spectral line to confirm whether it meets the positive definiteness criterion. Subsequently, the diagonal term of the weighted average ASD is amplified so that the root mean square value of the autospectral data of each degree of freedom is equal to the maximum root mean square value of the measured data of all events, as shown in Table 2.

[0154] Table 2 shows the root mean square value corresponding to the weighted average SDM and the maximum root mean square value in the measured data of all road condition events.

[0155]

[0156] Miller's law, calculated using fatigue equivalent time, was used to scale and sum the time corresponding to each road condition event, resulting in the test time for each degree of freedom at its maximum value, as shown in Table 3.

[0157] Table 3 shows the equivalent time obtained after converting each degree of freedom to the root mean square (MMS) value.

[0158] Equivalent time (h) 9.5 11.4 4.2 13.7 38.2 29.3

[0159] The equivalent test time for each degree of freedom is different, so a uniform test time needs to be selected, and all ASDs need to be scaled again according to this time. In this specific embodiment, a test time of 3 hours is selected, and the root mean square values ​​after scaling according to this test time are shown in Table 4.

[0160] Table 4. Equivalent root mean square values ​​of each degree of freedom when the test duration is 3 hours.

[0161] Equivalent root mean square value 0.072 0.121 0.140 1.832 1.262 0.836

[0162] Finally, uncontrollable factors were addressed by increasing the autospectral density term of each degree of freedom by +3 dB. The final synthesized SDM is as follows: Figure 5 As shown.

[0163] ST5. Normalize the power spectral density matrix.

[0164] The power spectral density matrix is ​​normalized according to step S5 in the above specific embodiment. Generally, the total number of line segments does not exceed 7, and the slope of the line segments is typically selected as 0 dB / Oct, ±3 dB / Oct, or ±6 dB / Oct. A positive definiteness check is then performed on the normalized power spectral density matrix. The normalized SDM is shown below. Figure 6 As shown.

[0165] ST6. Verify the calculated results of the experimental conditions to ensure they encompass the measured data.

[0166] The normalized SDM derived in step ST5 is verified. The acceleration autospectral density of the measurement points used for statistical analysis is estimated according to formula (6). Figure 2 Taking the X-axis response at measuring point 1 as an example, the estimated probability density curve and the measured power spectral density curve are as follows: Figure 7 As shown, the estimated curve can encompass the measured data without being overly conservative.

[0167] The beneficial technical effects achieved by this invention are:

[0168] A method for calculating multi-degree-of-freedom random vibration test conditions is proposed, and the formulation process is given. When determining test conditions, the measured data are processed into a probability spectral density matrix form. The self-spectral density is derived from the statistical envelope of the self-spectral density set of measured vibration environment data at the same degree of freedom, and the cross-spectral density is derived from the statistical average of the cross-spectral density sets of measured vibration environment data at different degrees of freedom. The test time for each degree of freedom is determined according to the fatigue damage equivalence principle, thereby deriving a unified test duration.

[0169] This invention enables the calculation of an accurate power spectral density matrix, avoiding the overly conservative problems of traditional experimental condition calculation methods and improving the precision of experimental condition formulation. The positive definiteness check of the matrix ensures its feasibility. The technical solution described in this invention can be used in the formulation of multi-degree-of-freedom random vibration test conditions in various fields such as aerospace, aviation, and shipbuilding, effectively improving the realism of multi-degree-of-freedom random vibration test simulations and possessing significant engineering application value.

[0170] The multi-degree-of-freedom random vibration test condition calculation method described in this invention is based on field measurement data of a random vibration environment. It utilizes statistical analysis and the envelope method to derive multi-degree-of-freedom random vibration test conditions. The test condition formulation process considers the inherent randomness, variability, and testing errors in the vibration environment data, as well as the reflection of the vibration environment dispersion characteristics by the number of data samples. This enables the formulation of more realistic and effective multi-degree-of-freedom random vibration test conditions, improving the precision of test condition formulation and thus more effectively assessing the environmental adaptability of the test specimen.

Claims

1. A method for calculating the conditions of a multi-degree-of-freedom random vibration test, characterized in that, The steps include the following: S1. Determine the task scenario and lifecycle events; All expected environmental exposure events during the product lifecycle are listed together with their corresponding durations to form the test scenario; the duration of the vibration environment is derived from the environmental profile of the product lifecycle. S2. Establish a multi-degree-of-freedom random vibration time history sample; S3. Perform statistical induction on the multi-degree-of-freedom random vibration SDM to obtain the maximum expected SDM of all events in the task scenario, as follows: S3.1 Calculate the SDM for each data sample, where SDM refers to the power spectral density matrix; S3.2 Calculate the SDM of all measured samples for a certain event in the task scenario, and organize the SDM of the event according to the logical structure; regularize the cross-spectral density term, that is, transform it into the form of coherence spectrum and phase spectrum; S3.3 For the SDM samples corresponding to a certain event obtained in step S3.2, perform statistical induction according to the parameter induction method to obtain the maximum expected SDM of the event. The statistical induction method is as follows: S3.3.

1. Set the acceleration autospectral density of the random vibration response at the same measurement point on the platform during different usage processes to follow a log-normal distribution; S3.3.2, When the sample size When ≥6, the autospectral density terms of each measured SDM are statistically enveloped according to the upper limit of the one-sided normal tolerance. The maximum expected random vibration environment is defined using the 95 / 50 limit to obtain the maximum expected autospectral density of each, which is then used as the autospectral density term of the maximum expected SDM of the event. The cross-spectral density terms of each measured SDM are statistically averaged and used as the cross-spectral density term of the maximum expected SDM of the event. S3.3.3, When the sample size When the value is less than 6, the mean spectral density matrix is ​​obtained by statistically averaging the measured SDMs. Then, while keeping the cross-spectral density term of the mean spectral density matrix unchanged, the amplitude of the auto-spectral density term is increased by 3dB to derive the maximum expected SDM. S.3.3.4 When there is only one sample, it is considered to represent the mean spectral density matrix of the random vibration environment; S4. Calculate the maximum expected SDM for all events, synthesize the random vibration environment, and obtain the final synthesized SDM, as follows: S4.

1. Take the weighted average of the maximum expected value SDM of each event obtained in step S3 to obtain the composite SDM of all events; S4.2 Amplify the power spectrum term of the synthesized SDM so that the root mean square value of each degree of freedom is equal to the maximum root mean square value of the corresponding degree of freedom of all measured SDMs obtained in step S3.

1. S4.

3. Use the fatigue equivalent acceleration relation to scale the time and calculate the equivalent test time; S4.4 After the test time is selected, the fatigue equivalence relation is used again for each degree of freedom to recalculate the autopower spectrum of the synthesized SDM; the positive definiteness of the SDM is checked and corrected. S4.5 Multiply the diagonal elements of the SDM obtained in step S4.4 by the dispersion factor to account for uncontrollable factors, while keeping coherence and phase unchanged, to obtain the final synthesized SDM; S5. Normalize the power spectral density matrix as follows: S5.

1. Smooth the autospectral density curve in the double logarithmic coordinate system using a set of straight line segments to obtain the smoothed autospectral density represented by a broken line. S5.

2. Use a set of straight line segments to smooth the coherent function curve in the linear coordinate system to obtain a smoothed coherent function represented by a broken line. S5.3 Check and correct the positive definiteness of the normalized power spectral density matrix; S6. Verify the calculated results of the experimental conditions to ensure that they can encompass the measured data.

2. The method for calculating multi-degree-of-freedom random vibration test conditions according to claim 1, characterized in that, The steps for establishing multi-degree-of-freedom random vibration time history samples are performed as follows: S2.1 Record the position and orientation of the field measurement sensors in detail, determine the frequency bandwidth and sampling frequency, and collect all vibration measurement data of the specimen installation platform; S2.2 Analyze the structure of the platform under test, establish a rectangular coordinate system with its geometric center or center of mass as the origin, and determine the coordinates of each measuring point. , , ); S2.3 Analyze the task scenarios and task ratios during the lifespan of the platform under test, determine the events included in the task scenarios, and divide the measured data into samples according to different events; S2.

4. Based on the rigid body modal assumption, and according to the position and orientation of each measured point in the vibration environment in the specified coordinate system, a measurement coordinate transformation matrix is ​​constructed. The measurement data samples corresponding to each environmental event are transformed into multi-degree-of-freedom motion time history data samples. The vibration environment transformation equation is: （1a） In the formula, Let m be the linear vibration accelerations at m measured points, with subscripts i = 1, 2, ..., m, and the transformation matrix be... The dimension is .

3. The method for calculating multi-degree-of-freedom random vibration test conditions according to claim 1, characterized in that, In the step of statistically summarizing the power spectral density matrix of multi-degree-of-freedom random vibration, the SDM is calculated as follows: S3.1.1, Multi-degree-of-freedom vibration acceleration response signal data samples are Fourier analysis was performed on the measured data to obtain the multi-degree-of-freedom Fourier spectral vector. ; S3.1.2 Calculate its instantaneous power spectral density matrix: ………………………（2） S3.1.3 The cumulative power spectral density matrix obtained after K averaging is as follows: …………………………………（3） S3.1.4 Perform positive definiteness checks and corrections on the power spectral density matrix; The positive definiteness of the spectral density matrix is ​​checked using the Cholesky decomposition method. If the matrix does not meet the positive definiteness requirement at certain frequencies, the SDM is modified to force it to be transformed into a positive definite matrix.

4. The method for calculating multi-degree-of-freedom random vibration test conditions according to claim 1, characterized in that, The method for calculating the equivalent test time using fatigue equivalent acceleration relations includes the following steps: S4.3.1, Estimation of the equivalent fatigue duration of multi-degree-of-freedom random vibration environment specifications based on the Miner cumulative damage model: （4） or （5） In the formula, , and These are the self-spectral density, root mean square acceleration, and fatigue equivalent duration of the vibration environment specification, respectively. , and These represent the autospectral density, root mean square acceleration, and vibration duration of the actual vibration environment, respectively. The fatigue characteristic index of the product; S4.3.

2. Based on the synthesized SDM, for each degree of freedom of motion, calculate the fatigue equivalent time corresponding to the corresponding degree of freedom of each event using equation (4) or (5); Then, the fatigue equivalent time of the corresponding degrees of freedom of all events is added together to obtain the fatigue equivalent time of the synthesized SDM; S4.3.

3. Take the weighted average of the fatigue equivalent duration calculated for each degree of freedom by the square of the root mean square acceleration value, and derive the fatigue equivalent duration corresponding to the equivalent spectral density matrix.

5. The method for calculating multi-degree-of-freedom random vibration test conditions according to claim 1, characterized in that, The step of verifying the calculation results of the experimental conditions to confirm that they can encompass the measured data is performed as follows: S6.1 Using the normalized power spectral density matrix exported in step S5 Estimate the acceleration self-spectral density at all measurement points used for statistical analysis. : ， （6） In the formula, for 3D coordinate transformation matrix The element in the i-th row and k-th column; for The element in the k-th row and l-th column; N represents the number of degrees of freedom of motion in a multi-degree-of-freedom random vibration environment. m is the number of measurement points used for statistical analysis; S6.2, Based on the acceleration self-spectral density The corresponding root mean square acceleration value is obtained by frequency domain integration. ; S6.

3. Within the frequency range of interest, and The maximum spectrum of the vibration acceleration data measured at the corresponding point and maximum root mean square acceleration value Compare and verify that it can encompass the measured data.

Images