A frequency domain synthesis method of sinusoidal superimposed random complex vibration load

Abstract

This invention discloses a frequency domain synthesis method for sinusoidal superimposed random composite vibration loads, belonging to the field of engineering vibration simulation technology. It solves the technical problem that finite element analysis software cannot directly handle sinusoidal + random time-domain-frequency domain hybrid composite excitations. This method employs a frequency domain substitution superposition strategy. First, it removes the narrowband frequency band corresponding to the sinusoidal sweep signal from the basic random vibration power spectral density (PSD). Then, it replaces the energy of this frequency band with a narrowband spectrum calculated according to the sinusoidal sweep parameters, ultimately synthesizing a continuous total PSD curve with correct energy composition. Simultaneously, through broadband spectrum interpolation generation, narrowband spectrum mathematical modeling, signal substitution superposition, and post-processing steps, it achieves the conversion of the composite vibration spectrum into standardized load data recognizable by the finite element solver. This invention can accurately reproduce the load input of the vibration test bench at the simulation end, establishing a comparable and controllable bridge between experiment and simulation, improving the confidence and predictive value of simulation results, and supporting simulation-driven product design and optimization.

Description

Technical Field

[0001] This invention relates to the field of engineering vibration simulation technology, and in particular to a frequency domain synthesis method for sinusoidal superposition random (SoR) composite vibration loads. This method is suitable for converting composite vibration spectra in test standards into standardized load inputs that can be recognized by finite element solvers, thereby enabling accurate reproduction of physical test loads at the simulation end. Background Technology

[0002] In engineering vibration environment testing, the sinusoidal superposition random composite vibration test method is widely used to simulate the complex dynamic loads under real service conditions of products. This method, by superimposing one or more sinusoidal sweep signals on a broadband random vibration background, can comprehensively simulate the complex vibration environment caused by the combined effects of periodic and random excitations, and is an important means of product reliability testing.

[0003] During the product simulation design phase, vibration response prediction is required through finite element analysis. However, the conventional load modules of mainstream commercial finite element analysis software (such as ANSYS, NASTRAN, Abaqus, etc.) are difficult to directly define such sinusoidal + random time-frequency hybrid excitations, presenting two major technical obstacles: First, there is a conflict in the load definition domain. Random vibration loads are usually defined in the form of power spectral density (PSD) in the frequency domain, while sinusoidal sweep loads are described in the form of amplitude-frequency relationship in the time domain. The two definition domains are not directly compatible. Second, there are limitations on solver input. Standard harmonic response or spectrum analysis modules only support a single type of load input and cannot natively handle the superposition calculation of random loads and sinusoidal loads.

[0004] The aforementioned technical barriers result in a fundamental difference between the input conditions for finite element simulation analysis and the load conditions for physical experiments, severely weakening the confidence and predictive value of simulation results and hindering the implementation of simulation-driven product design and optimization processes. Currently, there is no effective general method to achieve accurate conversion from sinusoidal superposition random composite vibration spectra to loads identifiable by finite element solvers. Therefore, there is an urgent need to develop a dedicated frequency domain synthesis method to establish a comparable and controllable bridge between physical experiments and simulation analysis. Summary of the Invention

[0005] This invention aims to provide a frequency domain synthesis method for sinusoidal superimposed random composite vibration loads, solving the problem that finite element analysis software cannot directly handle time-frequency domain hybrid excitations, achieving accurate conversion of composite vibration spectra to standardized load inputs, enabling the simulation end to accurately reproduce the load input of the test bench, and improving the accuracy of vibration response prediction.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A frequency domain synthesis method for sinusoidal superimposed random composite vibration loads employs a frequency domain substitution superposition strategy to synthesize a broadband random vibration spectrum and a narrowband sinusoidal sweep spectrum, yielding a total power spectral density curve that can be directly imported into finite element analysis software. The method includes the following steps:

[0008] S1. Input Parameter Acquisition and Verification: Receives discrete frequency-amplitude point pairs of broadband random vibration spectrum, narrowband parameters of sinusoidal sweep frequency, quality factor, and global adjustment parameters, and automatically verifies the validity and monotonicity of the input data; the narrowband parameters include the center frequency and corresponding amplitude, supporting direct input of a list or automatic generation of a dense sweep frequency list after inputting sparse point pairs; the global adjustment parameters include the bandwidth adjustment factor and the number of sampling points.

[0009] S2. Broadband random component generation: Based on the discrete frequency-amplitude point pairs from step 1), a continuous broadband random vibration power spectral density curve is generated using logarithmic linear interpolation or linear interpolation mode. During the interpolation process, all input inflection frequency points are forcibly included to ensure that the spectrum is undistorted at key points.

[0010] S3. Narrowband Sine Component Modeling: For the center frequency of each sinusoidal sweep signal, calculate its corresponding bandwidth and narrowband rectangular window height, and construct a mathematical model of the power spectral density of the narrowband sinusoidal component; where the bandwidth is calculated by the physical bandwidth parameter k, the rectangular window height is determined according to the energy equivalence principle combined with the bandwidth adjustment factor, and the frequency range of the narrowband rectangular window is [fc - k / 4, fc + k / 4], where fc is the center frequency;

[0011] S4. Signal replacement and superposition: Locate the upper and lower frequency boundaries of each narrow band, and cut the broadband frequency array into three segments: below the lowest narrow band, between each narrow band, and above the highest narrow band. Within each narrow band, linearly superimpose the sinusoidal narrow band spectrum with the original random background spectrum of that band, and then embed the superimposed narrow band spectrum into the corresponding position of the broadband frequency array. All segments are spliced ​​together in frequency order to obtain the synthesized total power spectral density curve.

[0012] S5. Result Output and Post-processing: Generate a standardized data file containing frequency and power spectral density, and output a spectrum visualization graph and parameter report. The parameter report includes the characteristic parameters of each narrowband, the narrowband frequency overlap detection results, and total energy statistics.

[0013] Furthermore, the rectangular window height H mentioned in step S3 is calculated based on the fact that the square of the effective value of the sinusoidal signal is equal to its total energy within the bandwidth. After introducing a bandwidth adjustment factor, the theoretical height is corrected to ensure energy equivalence.

[0014] Furthermore, during the signal replacement and superposition process described in step S4, the first and last points of the narrowband spectrum array are forcibly set to zero to ensure a smooth transition between the narrowband spectrum and the broadband spectrum at the splicing point, avoiding non-physical abrupt changes.

[0015] Furthermore, in step S4, if there are multiple sinusoidal sweep frequency bands, and all the narrowband frequency bands do not overlap, the total energy of the synthesized total power spectral density is equal to the sum of the energy of the broadband random component and the energy of all narrowband sinusoidal components, thus satisfying the energy conservation.

[0016] Furthermore, the quality factor mentioned in step S1 supports a constant value or a frequency-related function form, and the broadband random component generation mentioned in step S2 supports local spectrum extraction for background spectrum calculation within a narrowband window.

[0017] Furthermore, the linear superposition in step S4 specifically involves: generating a basic broadband signal template covering the entire frequency range, cyclically processing each center frequency, generating a corresponding ideal narrowband signal and a background random spectrum within the narrowband window, linearly superimposing the amplitudes of the two, and replacing the corresponding narrowband portion in the spectrum of the basic template.

[0018] Furthermore, the standardized data file mentioned in step S5 is in CSV format, which can be directly imported into the table load definition module of the finite element analysis software, and the spectrum visualization graph is a spectrum diagram in logarithmic coordinates.

[0019] The principle and beneficial effects of this technical solution:

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] The frequency domain synthesis method for sinusoidal superposition of random composite vibration loads of the present invention has the following significant advantages over the prior art:

[0022] 1. Overcoming core technological barriers: It breaks through the problem that finite element analysis software cannot directly handle time-frequency domain hybrid excitation. By using a frequency domain replacement superposition strategy, it realizes the load synthesis of sinusoidal frequency sweep and random vibration, so that the simulation input conditions are consistent with the physical test load conditions, which greatly improves the confidence and predictive value of the simulation results.

[0023] 2. Strong physical equivalence: The synthesis strategy of this invention is physically equivalent to the signal superposition method of the vibration table control system. Moreover, the linear superposition of the sinusoidal narrowband spectrum and the background random spectrum is adopted in the narrowband frequency band, which accurately restores the actual situation of two excitation sources acting simultaneously in the physical experiment and avoids the simulation error caused by simple replacement.

[0024] 3. High engineering applicability: It supports diverse parameter input methods, adapts to the requirements of sinusoidal superposition random composite vibration spectrum of different test standards, and the interpolation mode, frequency sweep law, etc. can be flexibly configured. Moreover, the output CSV format file can be directly imported into mainstream finite element analysis software without additional format conversion, thus reducing the threshold for engineering applications.

[0025] 4. Excellent synthesis accuracy and robustness: By forcibly including input turning frequency points, setting the beginning and end points of narrowband to zero, and frequency overlap detection, the spectral fidelity and splicing smoothness of the synthesized spectrum are guaranteed, and the algorithm satisfies energy conservation, so the accuracy of the synthesis result is controllable; at the same time, it has a complete parameter verification and anomaly handling mechanism, and strong robustness.

[0026] 5. High computational efficiency: The algorithm uses vectorized operations and Boolean indexes to split and concatenate the frequency array, with a time complexity of O(n), which can efficiently process a large number of frequency points; and the basic broadband signal is generated only once and reused in multiple narrowband processing, further improving computational efficiency. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the algorithm framework for a frequency domain synthesis method of sinusoidal superimposed random composite vibration loads.

[0028] Figure 2 This is a sequence diagram of an algorithm for frequency domain synthesis of sinusoidal superimposed random composite vibration loads;

[0029] Figure 3 The graph shows the relationship between acceleration and frequency for the sinusoidal vibration component.

[0030] Figure 4 The graph shows the relationship between the acceleration power spectral density and frequency of the random vibration component.

[0031] Figure 5 The Z-axis power spectral density-frequency logarithmic coordinate plot;

[0032] Figure 6 A three-level simulation model for the powertrain system;

[0033] Figure 7 The figure shows the comparison results of simulation and actual measurement of the powertrain system. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. Here, the illustrative embodiments and descriptions of this invention are used to explain the invention, but are not intended to limit the invention.

[0035] It should also be noted that, in order to avoid obscuring the invention with unnecessary details, only the processing steps closely related to the solution according to the invention are shown in the accompanying drawings, while other details that are not closely related to the invention are omitted.

[0036] It should be emphasized here that the step markers mentioned below are not a limitation on the order of the steps, but should be understood as meaning that the steps can be executed in the order mentioned in the embodiments, or in a different order than in the embodiments, or several steps can be executed simultaneously.

[0037] Example 1

[0038] Please see Figure 1 A frequency domain synthesis method for sinusoidal superimposed random composite vibration loads specifically includes the following steps:

[0039] Step 1: Input Parameter Acquisition and Validation

[0040] It receives various parameters input by the user and performs data validity checks, specifically including four types of parameters:

[0041] 1) Broadband parameters: Discrete frequency-amplitude point pairs of broadband random vibration spectrum of arbitrary length. The program automatically verifies the validity of the data (no null values, outliers) and its monotonicity (frequency monotonically increasing).

[0042] 2) Narrowband parameters: The center frequency and corresponding amplitude of the sinusoidal sweep. Two input methods are supported: one is to directly input the list of center frequencies and the corresponding amplitude list, and the other is to input sparse (center frequency, amplitude) point pairs. The system will automatically generate a dense sweep list based on the set number of sweep points and logarithmic / linear rules to simulate the continuous sweep process.

[0043] 3) Global parameters: including bandwidth adjustment factor (used to correct the height of the narrowband rectangular window) and number of sampling points n (used to determine the resolution of the frequency array).

[0044] For practical applications of sinusoidal superposition random composite vibration tests, users only need to select the frequency sweep point distribution law (linear average or logarithmic average) and the number of sampling points n in the narrowband interpolation table to complete the input of core parameters.

[0045] Step 2: Broadband Random Component Generation

[0046] Based on the discrete frequency-amplitude point pairs of the broadband random vibration spectrum input in step 1, a continuous broadband random vibration power spectral density curve is generated, with the specific rules as follows:

[0047] 1) Supports two interpolation modes: logarithmic-linear interpolation is the default mode, which performs linear interpolation in logarithmic frequency coordinates, consistent with the engineering reality that vibration energy changes linearly on the logarithmic frequency axis; linear interpolation is performed in standard linear frequency coordinates.

[0048] 2) A forced inclusion mechanism is provided during the interpolation process to ensure that all user-inputted inflection frequency points are included in the final frequency vector, thus avoiding distortion of the spectrum at key points due to interpolation;

[0049] 3) Supports local spectrum generation function, which can extract background random spectrum within a specified frequency range according to the parameters of the narrowband window, in preparation for subsequent superposition of narrowband and wideband.

[0050] Step 3: Narrowband Sine Component Modeling

[0051] For the center frequency f of each sinusoidal sweep signal c A power spectral density model for narrowband sinusoidal components is constructed through mathematical modeling. The sinusoidal sweep signal is idealized as a rectangular window function in the frequency domain, and the bandwidth and height of the rectangular window are calculated as follows:

[0052] 1) Bandwidth calculation

[0053] To better align with engineering practice, a physical parameter k is introduced to characterize the bandwidth characteristics. The final width of the narrowband rectangular window is k / 2, corresponding to a frequency range of [f...]. c - k / 4, f c + k / 4].

[0054] 2) Calculation of rectangular window height

[0055] According to the principle of energy equivalence, the total energy of a sinusoidal signal within its bandwidth is equal to the square of its effective value. Let the height of the rectangular window be H. The theoretical value of H is derived through the energy equivalence formula. Then, a user-adjustable bandwidth factor is introduced to correct the theoretical bandwidth, resulting in the final formula for calculating the height of the rectangular window, ensuring that the energy of the narrowband sinusoidal component is consistent with the actual sinusoidal sweep signal.

[0056] For the center frequency is The amplitude is A (unit: m / s) 2 A sinusoidal frequency sweep signal, during the actual frequency sweep process, at a certain instant, has its energy concentrated in the sinusoidal frequency sweep signal. Within a narrow band centered on this point. In the frequency domain, this can be idealized as a rectangular window function. The bandwidth of this window... and height H (unit: It is determined by the following formula:

[0057] 1. Quality factor and bandwidth calculation:

[0058]

[0059] Where Q is the quality factor, and BW 3dB This represents a -3dB bandwidth. The program uses a more physical parameter k to characterize the bandwidth properties.

[0060]

[0061] For a center frequency of f c The rectangular frame has a width of k / 2, meaning the frequency range is [f c - k / 4, f c + k / 4].

[0062] 2. Calculation of rectangular window height:

[0063] According to the principle of energy equivalence, a sinusoidal signal has a bandwidth of The total energy within the window is equal to the square of its effective value. Let the height of the rectangular window be H, then:

[0064]

[0065] Therefore, we can conclude that: Introducing a user-adjustable bandwidth factor. After adjusting the theoretical bandwidth, the final height calculation formula is as follows:

[0066]

[0067] For the composite vibration test involved in this project, the width of the rectangular frame is [missing information]. , The height of the rectangle is

[0068] Step 4: Signal replacement and overlay

[0069] This step is the core frequency domain synthesis step, which realizes the substitution and superposition of broadband random components and multiple narrowband sinusoidal components, ensuring the continuity of the synthesized spectrum and satisfying energy conservation. The specific process is as follows:

[0070] 1) Let the basic broadband random spectrum be... The i-th narrowband sine spectrum is Its frequency support set is Furthermore, all narrowband frequency bands do not overlap with each other, that is... The total power spectral density of the synthesis for:

[0071]

[0072] 2) Locate the upper and lower frequency boundaries of each narrowband sine spectrum and divide the wideband frequency array into three parts: the frequency band below the lowest narrowband, the frequency band between each narrowband, and the frequency band above the highest narrowband;

[0073] 3) For each narrowband frequency band, perform a linear superposition operation: generate an ideal narrowband signal at that frequency point, and at the same time extract the background random spectrum within the narrowband window. Linearly superimpose the amplitude of the narrowband signal with the amplitude of the background random spectrum. This operation accurately reflects the actual situation of two excitation sources acting simultaneously in physical experiments.

[0074] 4) The superimposed narrowband spectrum is "embedded" into the corresponding narrowband position of the broadband frequency array, and the first and last points of the narrowband spectrum array are forced to be zero to ensure a smooth transition at the splicing point and avoid non-physical abrupt changes.

[0075] 5) The cut broadband frequency band and the mosaicked narrowband frequency band are spliced ​​together in ascending frequency order to obtain the synthesized total power spectral density curve S. total And S total The total energy is equal to the sum of the energy of the broadband random component and the energy of all narrowband sinusoidal components, satisfying the law of conservation of energy.

[0076] In actual implementation, a basic broadband signal covering the entire frequency range is first generated as a template, and each center frequency is processed cyclically to complete narrowband superposition and template replacement, finally obtaining the total synthesized spectrum; at the same time, the synthesized spectrum when each center frequency acts independently can be output to meet diverse simulation analysis needs.

[0077] Step 5: Result Output and Post-processing

[0078] The synthesized total power spectral density curve is converted into a format recognizable by the finite element solver, and visualization and parameter analysis are performed. Specific outputs include:

[0079] 1) Standardized data file: Generates a CSV format file containing two columns, "Frequency" and "PSD", which can be directly imported into the table load definition module of finite element analysis software such as ANSYS, NASTRAN, and Abaqus;

[0080] 2) Graphical visualization: Automatically generates spectrum plots in logarithmic coordinates, clearly showing the broadband baseline, narrowband peak and their relative positional relationship, making it easy for users to intuitively verify the spectrum;

[0081] 3) Parameter Report: Automatically calculates and outputs detailed parameter statistics, including the center frequency of each narrowband, input amplitude, calculated rectangle height, and upper and lower frequency boundaries; automatically detects and reports frequency overlap between narrowbands, providing early warnings of problems where algorithm assumptions are not met; and also provides global statistics such as coverage bandwidth and total energy.

[0082] Example 2

[0083] Modular program design and technical implementation of a frequency domain synthesis method for sinusoidal superposition of random composite vibration loads

[0084] I. Input Module

[0085] 1. Broadband parameter input: Accepts frequency-amplitude lists of arbitrary length, automatically verifies data validity and monotonicity.

[0086] 2. Narrowband parameter input: Two methods are provided:

[0087] a) List format: Directly input the center frequency list f_center_list and the corresponding amplitude list A_list.

[0088] b) Interpolation table: Input sparse (f_center, A) point pairs, and the program will automatically generate a dense sweep list based on the set number of sweep points and logarithmic / linear rules to simulate the continuous sweep process.

[0089] 3. Q value definition: Q_func is a function object that takes frequency as input, and supports constant Q (such as Q=30) or frequency-related Q value.

[0090] 4. Global Parameter: Bandwidth Adjustment Factor Number of sampling points n.

[0091] For the composite vibration test involved in this project, the user only needs to select the distribution law of the frequency sweep points of the narrowband interpolation table (linear average or logarithmic average) and the number of sampling points n.

[0092] II. Core Computing Module

[0093] 1. The `generate_broadband_signal` function:

[0094] Function: Generates a broadband spectral continuous curve based on discrete points.

[0095] Technical details: Internally, numpy.interp is used for efficient interpolation; local spectrum generation is supported through the window_center and window_width parameters for background spectrum extraction within a narrow window.

[0096] 2. The `generate_narrowband_signal` function:

[0097] Function: Generates a narrowband rectangular spectrum based on the center frequency, amplitude, Q, and β.

[0098] Technical details: The rectangular window is generated efficiently using the vectorized operation of numpy.where; the LR_set_zero option is provided to force the first and last points of the generated array to be set to zero, ensuring a smooth transition to zero values ​​at the boundary when splicing with other spectra, avoiding non-physical abrupt changes.

[0099] 3. The `combine_signals` function:

[0100] Function: Executes the core "replacement overlay" algorithm.

[0101] Technical details: The array is quickly partitioned using Boolean indexing and concatenated using numpy.concatenate. The algorithm has a time complexity of O(n), which is efficient for handling large-scale frequency points.

[0102] III. SweepFrequency Batch Processing

[0103] Design pattern: Use object-oriented class encapsulation to bind sweep parameters (center frequency list, amplitude list, etc.) to the generation method for easy management and expansion.

[0104] Workflow:

[0105] 1. Calculate or receive the Q value of all center frequency points during initialization.

[0106] 2. In the generate_all_results method, a basic broadband signal covering the entire frequency range is first generated as a template.

[0107] 3. Process each center frequency in a loop:

[0108] a) Generate an ideal narrowband signal at that frequency point.

[0109] b) Call generate_broadband_signal, using the same frequency window parameters as the narrowband, to generate the background random spectrum S_broad_narrow within the narrowband window.

[0110] c) Execute narrow_amp = narrow_amp + broad_amp_narrow. This step is crucial because it means that within the narrow band, the final spectral value is a linear superposition of the "sine rectangular spectrum" and the "original random background spectrum at that location," rather than a simple replacement. This more accurately reflects the actual situation where two excitation sources act simultaneously in a physical experiment.

[0111] d) Replace the corresponding part of the base template spectrum with the superimposed narrowband spectrum.

[0112] 4. Output results at two levels:

[0113] a) Synthetic spectrum when each center frequency acts independently;

[0114] b) The total composite spectrum of all narrowbands simultaneously superimposed onto the broadband.

[0115] IV. Output and Post-processing Module

[0116] 1. Data file output: Generates a CSV file containing two columns, "Frequency" and "PSD", which can be directly imported into the tabular load definition of software such as ANSYS.

[0117] 2. Graphical visualization: Automatically generates spectrum plots in logarithmic coordinates, clearly showing the broadband baseline, narrowband peak and their relative relationships.

[0118] 3. Parameter report generation:

[0119] a) Automatically calculate and list the center frequency, input amplitude, calculated rectangle height, and upper and lower frequency limits for each narrowband.

[0120] b) Automatically detect and report whether there is frequency overlap between narrowbands, and provide early warning of potential algorithm assumption failures.

[0121] c) Provide statistical information such as coverage bandwidth and total energy.

[0122] V. Overall Algorithm Architecture

[0123] Please see the appendix Figure 1 The diagram uses color coding to distinguish node types: start / end nodes are light blue, input / output nodes are light green, decision nodes are light yellow, data reading nodes are light pink, and processing nodes are light purple. The diagram clearly shows the complete process from parameter input, broadband / narrowband component generation, signal superposition to result output.

[0124] Specifically, the process begins with parameter input and verification. Then, it splits into two branches to complete the generation of broadband random components and the modeling of narrowband sinusoidal components, respectively. Next, it enters the core signal replacement and superposition step. After superposition, the result is verified. If the verification is successful, it enters the output and post-processing stage, outputting standardized documents, visualization graphics, and parameter reports, and the process ends. If the verification fails, it returns to the parameter input stage for correction.

[0125] VI. Data Flow and Control Flow

[0126] Please see Figure 2The diagram shows the algorithm sequence of this invention, illustrating the data flow and control flow characteristics of the method, including the data flow characteristics of unidirectional main flow, branch merging, and data reuse, as well as the control flow characteristics of sequential execution, loop iteration, and conditional branching.

[0127] After the data is input from the user, the main program calls the broadband generation module and the narrowband generation module to complete the component calculation, and then calls the superposition module to perform frequency domain replacement superposition. The superposition result is transmitted to the post-processing module to complete the format conversion, visualization and report generation, and finally the result is fed back to the user. At the same time, the program demonstrates the cyclic iteration process of frequency sweeping and the multiplexing mechanism of the basic broadband signal.

[0128] 1. Characteristics of data flow

[0129] a) Unidirectional main flow: Data mainly flows unidirectionally from user → main program → various modules → output module → user, which conforms to a typical data processing pipeline mode.

[0130] b) Branch merging: In the frequency sweeping cycle, each center frequency independently generates a narrowband signal, which is eventually merged into the total signal.

[0131] c) Data multiplexing: The basic broadband signal is generated only once and multiplexed in multiple center frequency processing to improve computational efficiency.

[0132] 2. Control flow characteristics

[0133] a) Sequential execution: The entire process is executed strictly in the order shown in the sequence diagram, with no parallel processing.

[0134] b) Iterative loop: The frequency sweep process uses a for loop to process the center frequency one by one.

[0135] c) Conditional branching: In narrowband generation and signal combining, there are conditional judgments based on frequency comparison.

[0136] d) Error handling: Not shown in the diagram, but the actual code includes parameter validation and exception handling mechanisms.

[0137] Example 3

[0138] The application background of this embodiment is as follows: To establish a high-fidelity vibration simulation model for a powertrain system, it is necessary to simulate the complex vibration environment of the product in actual service. The offline test is carried out using the sinusoidal superposition random composite vibration test method (following the "Vibration Test Method for Powertrain Systems" and the international standard ISO 19453-3). The composite vibration spectrum in the test standard is converted into a load input that can be recognized by the ANSYS finite element software through the frequency domain synthesis method of this invention. Finally, the simulation results are consistent with the trend of the measured data, with a maximum error of less than 15%, and the failure risk location in the powertrain vibration test is identified.

[0139] I. Setting Test Load Parameters

[0140] This embodiment conducts sinusoidal superposition random vibration tests on the powertrain system along the X, Y, and Z axes. The test duration for each axis is 42 hours. The sinusoidal vibration component uses a scan rate of 0.5 octaves per minute, and the random vibration component has an RMS acceleration value of 68.7 m / s². The random vibration loads on the three main axes are equivalent, using the same vibration spectrum. Specific load parameters are as follows:

[0141] 1. Sinusoidal vibration component:

[0142] Please refer to Table 1 and Figure 3 , Figure 3 The curve in the figure shows the sinusoidal vibration component of the sinusoidal random mixed vibration curve.

[0143] Table 1. Maximum acceleration and corresponding frequency values

[0144]

[0145] 2. Random vibration component:

[0146] Please refer to Table 2 and Figure 4 This demonstrates the relationship between power spectral density (PSD) and frequency.

[0147] Table 2 PSD and Frequency Values

[0148]

[0149] 3. Global parameters:

[0150] The bandwidth parameter k = 10Hz; the narrowband rectangle width k / 2 = 5Hz; the number of sampling points n = 69, ensuring that the resolution of the frequency array meets the simulation requirements.

[0151] II. Load Frequency Domain Synthesis Execution Steps Based on the Method of the Invention

[0152] Based on the above test load parameters, the frequency domain synthesis method of sinusoidal superposition random composite vibration load of the present invention is used to complete the entire process from parameter input to finite element load file output. The specific execution steps are as follows:

[0153] Step 1: Input Parameter Acquisition and Validation

[0154] Input the sinusoidal narrowband parameters from Table 1, the broadband random parameters from Table 2, the constant k=10Hz, n=69, and other parameters into the synthesis method to automatically complete the data validity verification:

[0155] 1. Verify that the frequency points (10, 300, 500, 2000Hz) of the broadband random parameters are monotonically increasing, with no outliers or empty values; the verification passes.

[0156] 2. Verify the integrity of the frequency-amplitude point pairs for each axis of the sinusoidal narrowband signal. The number of sweep points and the sweep frequency law parameters of the interpolation table input are set reasonably. Verification passed.

[0157] 3. Verify that the global parameters such as bandwidth parameter k and number of sampling points n are valid values ​​and there are no cases of exceeding limits. The verification is successful.

[0158] Step 2: Broadband Random Component Generation

[0159] Based on the four discrete frequency-PSD point pairs in Table 2, the linear interpolation mode of this invention is used to generate continuous broadband random vibration PSD curves in the range of 10Hz to 2000Hz. During the interpolation process, the forced inclusion of input points option is enabled to ensure that all four transition frequency points of 10, 300, 500, and 2000Hz are included in the final frequency vector, avoiding distortion of the spectrum at key points. At the same time, the local spectrum extraction function is enabled to prepare for the subsequent extraction of background random spectrum within the narrowband window.

[0160] Step 3: Narrowband Sine Component Modeling

[0161] For the sinusoidal sweep center frequencies (100, 200, 440, 180, 240, 260Hz) of the X, Y, and Z axes in Table 1, and the remaining 63 sweep center frequencies generated by interpolation, the mathematical modeling of the narrowband sinusoidal components is completed one by one, and the height of the rectangular window at the corresponding frequency is calculated. The specific calculation process takes 200Hz (amplitude 30m / s²) on the Z axis as an example:

[0162] 1. Bandwidth calculation: Given bandwidth parameter k = 10Hz; narrowband rectangular window width k / 2 = 5Hz, frequency range is [200−5 / 2, 200+5 / 2] = [197.5, 202.5]Hz;

[0163] 2. Calculation of rectangular window height: Given amplitude A = 30 m / s², β = 0.4, k = 10 Hz, according to the formula H = A 2 / (βk), we calculate H=900 / (0.4×10)=225(m / s) 2 ) 2 / Hz;

[0164] 3. The remaining center frequencies are modeled using the same formula as above. All narrow-band rectangular windows follow the energy equivalence principle to ensure that they are consistent with the energy of the actual sinusoidal sweep signal.

[0165] For the powertrain system composite vibration test in this embodiment, after correction by the bandwidth adjustment factor, the height of the rectangular window can be simplified to 0.25A. 2 This will further improve the efficiency of engineering calculations.

[0166] Step 4: Signal replacement and overlay

[0167] This step is the core synthesis process. Based on a frequency domain substitution superposition strategy, it completes the linear superposition and splicing of the broadband random spectrum and all narrowband sine spectra. Specifically, it is executed as follows:

[0168] 1. Generate a basic broadband signal template covering the frequency range of 10Hz to 2000Hz, with 100 frequency points, as the basis for load synthesis;

[0169] 2. Iterate through each sweep frequency center frequency, locate its narrowband frequency upper and lower bounds, and extract the background random spectrum within the narrowband window using the local spectrum extraction function in step 2.

[0170] 3. Perform linear superposition operation: linearly superimpose the ideal narrowband spectrum amplitude with the background random spectrum amplitude to accurately reflect the actual situation of simultaneous action of sinusoidal and random excitation sources in physical experiments;

[0171] 4. Force the first and last points of the superimposed narrowband spectrum array to be set to zero to avoid non-physical abrupt changes when splicing with the broadband spectrum;

[0172] 5. The superimposed narrowband spectral bands were used to replace the corresponding parts in the basic broadband signal template. After testing, it was found that all narrowband frequency bands did not overlap, which met the algorithm assumptions.

[0173] 6. The cut broadband frequency band and the embedded narrowband frequency band are spliced ​​together in ascending order of frequency to obtain the sinusoidal superposition random total power spectral density curve of the X, Y and Z axes. The total energy is equal to the sum of the energy of the broadband random component and the energy of all narrowband sinusoidal components, which satisfies the law of conservation of energy.

[0174] Step 5: Result Output and Post-processing

[0175] After synthesis, three types of results are output to meet the simulation requirements of the powertrain system, directly connecting to the load input and simulation verification of the ANSYS finite element analysis software:

[0176] 1. Standardized CSV Load File: Generates a CSV format file containing two columns, "Frequency" and "PSD", and outputs the composite load files for the X, Y, and Z axes respectively. It can be directly imported into ANSYS's tabular load definition module without additional format conversion.

[0177] 2. Logarithmic coordinate spectrum visualization: Automatically generates a three-axis power spectral density-frequency logarithmic coordinate graph, clearly showing the baseline of the broadband random spectrum, the peak values ​​and relative positions of each narrowband sine spectrum, allowing engineers to intuitively verify the consistency between the spectrum and the test standard;

[0178] 3. Detailed parameter report: Outputs narrowband characteristic parameters for 69 sweep center frequencies, including center frequency, input acceleration amplitude, calculated rectangular window height, and upper and lower frequency boundaries; detects and reports that all narrowband frequency bands are non-overlapping, the algorithm assumptions are met, and there is no synthesis risk; outputs global statistical information such as coverage bandwidth (10Hz~2000Hz), total energy, and RMS acceleration value of the triaxial synthesized spectrum, verifying consistency with the experimental standard (RMS=68.7m / s²).

[0179] III. Engineering Application and Simulation Verification of Composite Loads

[0180] The triaxial CSV format load file synthesized by the method of this invention was imported into ANSYS finite element software and applied to the layered vibration simulation of a powertrain system (three layers: shell, controller assembly, and PCB board). The results were compared and verified with measured data from offline tests. The specific application and verification results are as follows:

[0181] 1. Simulation model adaptation: Please refer to Figure 6 The three-level simulation model of the powertrain system all uses the load file synthesized in this invention as input. The shell model has a mesh size of about 2 million elements, the controller component module model has about 250,000 elements, and the PCB board model has about 90,000 elements. The mesh generation adopts patch conformal tetrahedral mesh, and the key areas (mounting holes, connection interfaces, and measurement point positions) are locally densified.

[0182] 2. Boundary condition matching: Each level of the model sets equivalent boundary conditions according to the actual installation state of the experiment, and introduces equivalent mass blocks to compensate for the mass of omitted parts, ensuring that the total mass of each level of the simulation system is consistent with the state of the whole machine, and that the excitation transmission path conforms to the physical reality;

[0183] 3. Damping settings: Based on the PSD curves of the powertrain system component-level sinusoidal vibration test, the damping ratio is extracted using the half-power bandwidth method. The damping parameters are input into the finite element model through the MDAMP command stream to ensure that the simulated dynamic characteristics are consistent with the actual measurements.

[0184] 4. Simulation Result Verification: Compare the simulation results after inputting the synthetic load with the measured data from the offline whole-machine vibration test. Please refer to Table 3 and... Figure 7 The simulation results at key locations are highly consistent with the measured data, with a maximum error of less than 15%, meeting the simulation accuracy requirements.

[0185] Table 3. Accuracy Results of Simulation Tests

[0186]

[0187] 5. Failure Risk Identification: Based on high-precision simulation results, the location of potential failure risks in the powertrain system during vibration testing was successfully identified, providing accurate simulation basis for product structural optimization and reliability improvement.

[0188] The above application results show that the frequency domain synthesis method of sinusoidal superposition random composite vibration load of the present invention can accurately reproduce the composite vibration load of powertrain system physical test, solve the technical problem that finite element software cannot directly handle time-frequency domain hybrid composite excitation, establish a comparable and controllable bridge between test and simulation, and improve the confidence and predictive value of vibration simulation results.

[0189] Those skilled in the art will understand that the exemplary components, systems, and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software, or a combination of both. Whether implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention. When implemented in hardware, it can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this invention are programs or code segments used to perform the desired tasks. The programs or code segments can be stored in a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried in a carrier wave.

[0190] It should be clarified that the present invention is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present invention is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of the present invention.

[0191] In this invention, features described and / or illustrated for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or in place of features of other embodiments.

[0192] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, various modifications and variations of the embodiments of the present invention are possible. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A frequency domain synthesis method of sinusoidal superimposed random complex vibration loads, characterized in that, A frequency domain substitution and superposition strategy is used to synthesize a broadband random vibration spectrum and a narrowband sinusoidal sweep spectrum, resulting in a total power spectral density curve that can be directly imported into finite element analysis software. The specific steps include: S1. Input Parameter Acquisition and Verification: Receives discrete frequency-amplitude point pairs of broadband random vibration spectrum, narrowband parameters of sinusoidal sweep frequency, quality factor, and global adjustment parameters, and automatically verifies the validity and monotonicity of the input data; the narrowband parameters include the center frequency and corresponding amplitude, supporting direct input of a list or automatic generation of a dense sweep frequency list after inputting sparse point pairs; the global adjustment parameters include the bandwidth adjustment factor and the number of sampling points. S2. Broadband random component generation: Based on the discrete frequency-amplitude point pairs from step S1, a continuous broadband random vibration power spectral density curve is generated using logarithmic linear interpolation or linear interpolation mode. During the interpolation process, all input inflection frequency points are forcibly included to ensure that the spectrum is undistorted at key points. S3. Narrowband Sine Component Modeling: For the center frequency of each sinusoidal sweep signal, calculate its corresponding bandwidth and narrowband rectangular window height, and construct a mathematical model of the power spectral density of the narrowband sinusoidal component; where the bandwidth is calculated by the physical bandwidth parameter k, the rectangular window height is determined according to the energy equivalence principle combined with the bandwidth adjustment factor, and the frequency range of the narrowband rectangular window is [fc - k / 4, fc + k / 4], where fc is the center frequency; S4. Signal replacement and superposition: Locate the upper and lower frequency boundaries of each narrow band, and cut the broadband frequency array into three segments: below the lowest narrow band, between each narrow band, and above the highest narrow band. Within each narrow band, linearly superimpose the sinusoidal narrow band spectrum with the original random background spectrum of that band, and then embed the superimposed narrow band spectrum into the corresponding position of the broadband frequency array. All segments are spliced ​​together in frequency order to obtain the synthesized total power spectral density curve. S5. Result Output and Post-processing: Generate a standardized data file containing frequency and power spectral density, and output a spectrum visualization graph and parameter report. The parameter report includes the characteristic parameters of each narrowband, the narrowband frequency overlap detection results, and total energy statistics.

2. The frequency domain synthesis method of sinusoidal superimposed random complex vibration load according to claim 1, characterized in that, The rectangular window height H mentioned in step S3 is calculated based on the fact that the square of the effective value of the sinusoidal signal is equal to its total energy within the bandwidth. After introducing a bandwidth adjustment factor, the theoretical height is corrected to ensure energy equivalence.

3. The frequency domain synthesis method of sinusoidal superimposed random complex vibration load according to claim 1, characterized in that, In the signal replacement and superposition process described in step S4, the first and last points of the narrowband spectrum array are forcibly set to zero to ensure a smooth transition between the narrowband spectrum and the broadband spectrum at the splicing point and avoid non-physical abrupt changes.

4. The frequency domain synthesis method of sinusoidal superimposed random complex vibration load according to claim 1, characterized in that, If there are multiple sinusoidal sweep narrowbands in step S4, and all narrowband frequency bands do not overlap, the total energy of the synthesized total power spectral density is equal to the sum of the energy of the broadband random component and the energy of all narrowband sinusoidal components, thus satisfying the law of conservation of energy.

5. The frequency domain synthesis method of sinusoidal superimposed random complex vibration load according to claim 1, characterized in that, The quality factor mentioned in step S1 supports a constant value or a frequency-related function form, and the broadband random component generation mentioned in step S2 supports local spectrum extraction for background spectrum calculation within a narrowband window.

6. The frequency domain synthesis method of sinusoidal superimposed random complex vibration load according to claim 1, characterized in that, The linear superposition in step S4 specifically involves: generating a basic broadband signal template covering the entire frequency range, cyclically processing each center frequency, generating a corresponding ideal narrowband signal and a background random spectrum within the narrowband window, linearly superimposing the amplitudes of the two signals, and replacing the corresponding narrowband portion in the spectrum of the basic template.

7. The frequency domain synthesis method of sinusoidal superimposed random complex vibration load according to claim 1, characterized in that, The standardized data file mentioned in step S5 is in CSV format and can be directly imported into the table load definition module of the finite element analysis software. The spectrum visualization graph is a spectrum diagram in logarithmic coordinates.

Images