A method for comprehensively analyzing and judging the frame modal resonance based on dynamic stress, vibration and OMA

Abstract

The present invention relates to a method for comprehensively analyzing and judging the modal resonance of a frame based on dynamic stress, vibration, and OMA. Based on the time-frequency analysis of the dynamic stress of the subway vehicle bogie frame, the vibration acceleration analysis, and the OMA analysis, it comprehensively judges whether local modal resonance occurs in the subway bogie frame during operation.

Description

Technical Field

[0001] The present invention relates to a method for comprehensively analyzing and judging the modal resonance of a frame based on dynamic stress, vibration, and OMA, belonging to the technical field of railway vehicle bogies. Background Art

[0002] At present, there is a preliminary and simple understanding of the phenomenon of modal resonance in the operation of subway bogie frames at home and abroad, and it is also realized that the occurrence of modal resonance is harmful to the damage of the frame structure. However, there is no clear and effective method for judging and identifying modal resonance.

[0003] There are some current modal identification means, such as the Operational Modal Analysis (OMA) method for on-line modal testing, which can measure the modes that occur in the operation of subway vehicle bogie frames. However, for the modes that occur, it cannot be explained whether they are coupled with the excitation on the line to generate resonance. Therefore, it is urgent to study a new method for judging the modal resonance of the frame to accurately judge whether modal resonance occurs during the operation of the frame on the line. Summary of the Invention

[0004] The present invention provides a method for comprehensively analyzing and judging the modal resonance of a frame based on dynamic stress, vibration, and OMA, which combines the dynamic stress level, vibration acceleration, and OMA of the subway frame line, and comprehensively analyzes and judges whether modal resonance occurs during the operation of the frame on the line.

[0005] The technical solution adopted by the present invention to solve its technical problems is:

[0006] A method for comprehensively analyzing and judging the modal resonance of a frame based on dynamic stress, vibration, and OMA specifically includes the following steps:

[0007] Step S1: Install vibration accelerometers for measuring vibration acceleration on the axle boxes, large-mass equipment, and mounting seats of the bogie to be tested;

[0008] Step S2: Select the parts on the bogie to be tested where the stress and stress gradient values are large, and install dynamic stress patches for measuring dynamic stress;

[0009] Step S3: Combine the modal simulation results of the frame and relevant structural modal test experience, and select the positions with typical modal vibration modes on the bogie to be tested to install vibration accelerometers for OMA testing;

[0010] Step S4: Simulate the load of the vehicle where the bogie to be tested is located, select the corresponding operation time period of its load, and collect the data of the vibration accelerometers for measuring vibration acceleration, the dynamic stress patches for measuring dynamic stress, and the vibration accelerometers for OMA testing arranged in Steps S1 to S3 during the operation of the vehicle;

[0011] Step S5: Analyze the axle box vibration acceleration of the bogie to be tested, perform Fourier transform on the time domain signal of the axle box vibration acceleration to obtain the power spectral density - frequency signal;

[0012] Step S6: Analyze the stress test data of the bogie to be tested, use the Miner linear fatigue cumulative damage law and the S - N curve to calculate the equivalent stress amplitude of each measuring point, and perform time - frequency analysis on the stress data of the stress measuring points with large equivalent stress amplitudes;

[0013] Step S7: Analyze the OMA (on - line running mode) test data of the bogie to be tested, perform joint analysis using the enhanced frequency domain decomposition method, the stochastic subspace method, and the multi - reference - point infinite impulse response filtering algorithm, and extract modal parameters from the test data. The modal parameters include frequency, damping, and mode shape, which are the modal frequencies and modal mode shapes of each order of the bogie to be tested;

[0014] Step S8: The frequency corresponding to the energy peak of the axle box vibration acceleration of the bogie to be tested obtained in Step S5 is M1, the obvious main frequency M2 of the stress measuring point with a large equivalent stress amplitude obtained in Step S6, and the corresponding frequency M3 of the mode shape that generates large stress of the stress measuring point with a large equivalent stress amplitude obtained in Step S7;

[0015] Step S9: Compare the values of M1, M2, and M3. If the following conditions are met, it is determined that the bogie to be tested undergoes modal resonance during on - line running. Specifically,

[0016]

[0017] As a further preference of the present invention, in Step S3, several vibration accelerometers for OMA testing are installed. The several vibration accelerometers for OMA testing cover all elastic mode shapes within 100 Hz of the bogie to be tested, and each order of mode shape is uniquely distinguishable;

[0018] Specifically, at the joints of the side beam, cross beam, end beam of the bogie to be tested and adjacent structures, the distance between adjacent accelerometers is 0.5 m;

[0019] As a further preference of the present invention, in Step S3, when performing OMA testing, the wheel - rail excitation source during vehicle operation is used to excite the bogie to be tested, and the vibration response of the bogie to be tested caused by the excitation is measured;

[0020] As a further preference of the present invention, the specific method for simulating the load of the vehicle where the bogie to be tested is located in Step S4 is to add sandbags to the vehicle where the bogie to be tested is located. When the vehicle load reaches C1 or C2, select the corresponding operation time period of the load, and collect the data of the strain gauges and accelerometers arranged in Steps S1 to S3 during on - line running;

[0021] Among them, the counterweight method when the vehicle load reaches C1 is as follows: one passenger per seat, with a passenger mass of 80 kg, 4 - 10 passengers per square meter in the corridor and porch, and a load of 300 kg per square meter in the luggage compartment;

[0022] The counterweight method when the vehicle load reaches C2 is as follows: one passenger per seat, with a passenger mass of 80 kg, 2 - 4 passengers per square meter in the corridor and porch, and a load of 300 kg per square meter in the luggage compartment;

[0023] As a further preference of the present invention, in step S5, the axle - box vibration acceleration time - domain signal of the bogie to be tested is a continuous - time non - periodic signal. In actual applications, what can be collected is the discrete sampling value x(n) of the continuous signal. Perform Fourier transform on it, Among them, n = 0, 1, …, N - 1, j is the imaginary unit, to obtain the power - spectral density - frequency signal;

[0024] As a further preference of the present invention, in step S6, when analyzing the stress test data of the bogie to be tested, the Miner linear fatigue cumulative damage rule and the S - N curve are used to calculate the equivalent stress amplitude σ aeq of each measuring point. Among them, according to the Miner linear fatigue cumulative damage rule, the formula for calculating the damage generated within the measured kilometer number L1 of testing a stress spectrum is

[0025]

[0026] Suppose the equivalent stress amplitude acts for a certain number of times, and the damage formula generated by the bogie to be tested is

[0027]

[0028] Suppose the safe operating mileage for generating damage is L kilometers, then

[0029]

[0030] Substitute formula (6.1) and formula (6.2) into formula (6.3), and obtain

[0031]

[0032] Finally, the equivalent stress amplitude is obtained;

[0033] Among them, L1 is the measured number of kilometers of a stress spectrum, which is generally the total mileage of dynamic stress testing; D1 is the damage generated by a stress spectrum within L1 kilometers; L is the safe operating mileage set to generate damage, that is, the total mileage of the bogie to be tested; N is the number of times the equivalent stress amplitude set in formula (6.2) acts, that is, the number of cycles corresponding to the fatigue limit; D is the damage generated by the bogie to be tested in formula (6.2); n i is the number of stress cycles corresponding to each stress level; m is the exponent of the S-N curve, taking 6.5 for cast steel materials and 3.5 for welded joints; σ -1ai is the amplitude of each stress level;

[0034] As a further preference of the present invention, for the stress time-domain data of the stress measurement points with large equivalent stress amplitudes obtained through the foregoing, the stress measurement points with large equivalent stress amplitudes are the dangerous position measurement points. Fourier transform is performed once every fixed period of time to obtain a curve of the dynamic stress frequency changing with time, and it is continuously displayed in a single graph to obtain its full-course main frequency;

[0035] As a further preference of the present invention, in step S7, when analyzing the OMA test data of the bogie to be tested, the specific steps of the multi-reference point infinite impulse response filtering algorithm are as follows. Given the impulse response function h(k), with n-order modes, the frequency response function of the structure is

[0036]

[0037] where z = e jωΔt , Δt is the sampling interval, l is the number of waveform points or length, N = 2n, j is the imaginary unit, and ω is;

[0038] Derive the coefficients of the characteristic equation from formula (7.1) to obtain the eigenvalues of the characteristic equation, thereby obtaining the modal frequency, damping, and extracting the modal shape;

[0039] As a further preference of the present invention, in step S7, when analyzing the OMA test data of the bogie to be tested, the specific steps of the stochastic subspace method are as follows. For a linear system with n degrees of freedom, its discrete state space equation is:

[0040] {x k+1} = [A]{x k} + {w k} (7.2)

[0041] {y k} = [C]{x k} + {v k} (7.3)

[0042] where, {x k} is the n-dimensional state vector, {yk} is an N - dimensional output vector, where N is the number of response points; {w k} and {v k} are the input and output white noises with a mean of 0 respectively; [A] and [C] represent the n×n - order state matrix and the N×n - order output matrix respectively. By solving for [A] and [C], the modal parameters can be identified;

[0043] As a further preference of the present invention, in step S7, when analyzing the OMA test data of the bogie to be tested, the specific steps of the enhanced frequency - domain decomposition method are as follows. Let x(t) be the unknown and unmeasurable excitation, and y(t) be the measured response data. Then the power - spectrum matrix of the response is of order m×m, where m is the number of measurement points:

[0044]

[0045] Among them, the power - spectrum matrix of the response is of order m×m, where m is the number of measurement points; G xx (jω) is the power - spectrum matrix of x(t), that is, of order r×r, where r is the number of excitation points; H(jω) is the m×r - order frequency - response function matrix; the superscripts "-" and " T " of the matrix represent complex conjugate and transpose respectively; when K is fixed, d k is a constant, and λ k is the K - order pole;

[0046] When ω = ω i , G yy (jω) is estimated by formula (7.4), and then its singular - value decomposition is performed to decompose the power spectrum into the power spectra of single - degree - of - freedom systems corresponding to multiple orders of modes;

[0047] When the K - order mode is the main mode, there is only one term in formula (7.4), and the mode shape is

[0048]

[0049] Among them, the frequency and damping can be obtained from the logarithmic decrement of the single - degree - of - freedom correlation function corresponding to the mode shape.

[0050] Through the above technical solutions, compared with the prior art, the present invention has the following beneficial effects:

[0051] Based on dynamic stress, vibration, and OMA, the present invention comprehensively analyzes the modes that occur in the subway vehicle bogie during line operation, and can accurately determine whether the modes that occur are resonances caused by coupling with the excitations on the line. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The present invention will be further described below in conjunction with the drawings and embodiments.

[0053] Figure 1It is the power spectral density - frequency signal diagram obtained in the preferred embodiment provided by the present invention when analyzing the axle box vibration acceleration of the bogie to be tested;

[0054] Figure 2 It is the curve diagram showing the variation of dynamic stress frequency with time obtained in the preferred embodiment provided by the present invention when analyzing the stress test data of the bogie to be tested;

[0055] Figures 3 - 4 It is the modal schematic diagram at different angles obtained in the preferred embodiment provided by the present invention when analyzing the OMA test data of the bogie to be tested. Detailed implementation manners

[0056] Now, the present invention will be further described in detail with reference to the accompanying drawings. In the description of the present application, it should be understood that the orientation or positional relationships indicated by terms such as "left side", "right side", "upper part", "lower part", etc. are based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. "First", "second", etc. do not represent the importance of components, so they cannot be understood as limitations on the present invention. The specific dimensions adopted in this embodiment are only for illustrating the technical solution by way of example, and do not limit the protection scope of the present invention.

[0057] As described in the background art, some existing modal identification means cannot accurately determine whether each mode is coupled with the excitation on the line to generate resonance; because the present application aims to provide a brand - new method for judging the frame modal resonance, the principle of which is to comprehensively analyze the dynamic stress level, vibration acceleration and OMA of the subway frame line comprehensively. This judgment method has high accuracy and remarkable effect.

[0058] Specifically, it includes the following steps:

[0059] Step S1: Install vibration accelerometers for vibration acceleration testing on the axle box, large - mass equipment and mounting seat of the bogie to be tested; here, it is necessary to explain why it is necessary to identify the acceleration of the axle box. In the field of rail transit, for the axle box vibration acceleration test data, generally only the vibration transfer reference is made, that is, the vibration transfer ratio from the axle box vibration to the frame and even the car body; however, according to the industry consensus in the present application, it is considered that there are fixed - band excitations on the track, which may excite the natural frequency of a certain component of the bogie. Therefore, the main frequency identification of the axle box vibration acceleration is carried out.

[0060] Step S2: Select the parts on the bogie to be tested where both the stress and stress gradient values are large, and install dynamic stress patches for dynamic stress testing.

[0061] Step S3: Combine the frame modal simulation results and relevant structural modal test experiences, and select positions on the bogie to be tested with typical modal vibration modes to install vibration accelerometers for OMA testing;

[0062] Step S4: Simulate the load of the vehicle where the bogie to be tested is located, select the operation time period corresponding to its load, and collect the data of the vibration accelerometers arranged in Steps S1 to S3 for vibration acceleration testing, the dynamic stress patches for dynamic stress testing, and the vibration accelerometers for OMA testing during the vehicle operation;

[0063] Step S6: Analyze the axle box vibration acceleration of the bogie to be tested, perform Fourier transform on the time-domain signal of the axle box vibration acceleration to obtain the power spectral density - frequency signal;

[0064] Step S6: Analyze the stress test data of the bogie to be tested, use the Miner linear fatigue cumulative damage rule and the S - N curve to calculate the equivalent stress amplitude of each measuring point, and perform time - frequency analysis on the stress data of the stress measuring points with large equivalent stress amplitudes;

[0065] Step S7: Analyze the OMA test data of the bogie to be tested, perform joint analysis using the enhanced frequency domain decomposition method, the stochastic subspace method, and the multi - reference point infinite impulse response filtering algorithm, and extract modal parameters from the test data. The modal parameters include frequency, damping, and vibration mode, which are the modal frequencies and modal vibration modes of each order of the bogie to be tested;

[0066] Step S8: The frequency corresponding to the energy peak value of the axle box vibration acceleration of the bogie to be tested obtained in Step S5 is M1, the obvious main frequency M2 of the stress measuring points with large equivalent stress amplitudes obtained in Step S6, and the corresponding frequency M3 of the modal vibration mode that generates large stress of the stress measuring points with large equivalent stress amplitudes obtained in Step S7;

[0067] Step S9: Compare the values of M1, M2, and M3 numerically. If the following conditions are met, it is determined that the bogie to be tested undergoes modal resonance during line operation. Specifically,

[0068]

[0069] The above is only a general statement of the entire analysis and judgment method. The following is a specific elaboration one by one. In Step S3, the vibration accelerometers installed for OMA testing include several (the quantity should be sufficient). The several vibration accelerometers for OMA testing cover all elastic modal vibration modes within 100 Hz of the bogie to be tested, and each order of modal vibration mode is uniquely distinguishable. When performing OMA testing, the wheel - rail excitation source during vehicle operation is used to excite the bogie to be tested, and the vibration response of the bogie to be tested caused by the excitation is measured.

[0070] Specifically, at the joints of the side beams, cross beams, end beams of the bogie to be tested and adjacent structures, the distance between adjacent accelerometers is 0.5 m. That is to say, an accelerometer should be arranged every about 0.5 m. Accelerometers should also be arranged at positions such as the mounting seats of large-mass suspension devices to improve the measurement accuracy.

[0071] The specific method for simulating the load on the vehicle where the bogie to be tested is located in step S4 is to add sandbags to the vehicle where the bogie to be tested is located until the vehicle load reaches C1 or C2. Select the corresponding operation time period of the load, and collect the data of the strain gauges and accelerometers arranged in steps S1 to S3 during the line operation.

[0072] Among them, the weight distribution method when the vehicle load reaches C1 is as follows: there is one passenger per seat, the passenger mass is 80 kg, there are 4 - 10 passengers per square meter in the corridors and vestibules, and the load per square meter in the luggage compartment is 300 kg.

[0073] The weight distribution method when the vehicle load reaches C2 is as follows: there is one passenger per seat, the passenger mass is 80 kg, there are 2 - 4 passengers per square meter in the corridors and vestibules, and the load per square meter in the luggage compartment is 300 kg.

[0074] In step S5, the time-domain signal of the axle box vibration acceleration of the bogie to be tested is a continuous-time non-periodic signal. In actual applications, the discrete sampling values x(n) of the continuous signal can be collected. Perform Fourier transform on it. Among them, n = 0, 1, …, N - 1, j is the imaginary unit, and the power spectral density - frequency signal as shown is obtained. Figure 1 as shown

[0075] In step S6, the Miner linear fatigue cumulative damage rule and the S - N curve are used to analyze the stress test data of the bogie to be tested to calculate the equivalent stress amplitude σ of each measuring point. aeq Among them, according to the Miner linear fatigue cumulative damage rule, the formula for calculating the damage generated within the measured kilometer number L1 of a stress spectrum test is

[0076]

[0077] Suppose the equivalent stress amplitude acts for several times, and the damage formula generated by the bogie to be tested is

[0078]

[0079] Suppose the safe operating mileage for generating damage is L kilometers, then

[0080]

[0081] Substitute Equation (6.1) and Equation (6.2) into Equation (6.3) to obtain

[0082]

[0083] Finally, the equivalent stress amplitude is obtained;

[0084] Among them, L1 is the measured number of kilometers of a stress spectrum, which is generally the total mileage of dynamic stress testing; D1 is the damage generated by a stress spectrum within L1 kilometers; L is the safe operating mileage number set to generate damage, that is, the total mileage of the bogie to be tested; N is the number of times the equivalent stress amplitude set in Equation (6.2) acts, that is, the number of cycles corresponding to the fatigue limit. Here, 2 million times are taken (generally 2 million times for welded joints and 10 million times for base metals); D is the damage generated by the bogie to be tested in Equation (6.2); n i is the stress cycle number corresponding to each stress level; m is the exponent of the S-N curve, taking 6.5 for cast steel materials and 3.5 for welded joints; σ -1ai is the amplitude of each stress level. Through the stress time-domain data of the stress measurement points with large equivalent stress amplitudes obtained above, the stress measurement points with large equivalent stress amplitudes are the dangerous position measurement points. Fourier transform is performed every fixed period of time to obtain the curve of the dynamic stress frequency changing with time, and it is continuously displayed in a single graph, as Figure 2 shown to obtain its full-course dominant frequency. It should be emphasized here that the reason for performing multiple Fourier transforms is that for dynamic stress testing, the conventional practice in the industry is to arrange strain gauges on the structure, extract the structural strain, convert it into stress, and evaluate whether the fatigue strength of the structure meets the requirements. This patent believes that the fatigue failure of the structure may not necessarily be due to the large stress of the structure itself, but may also be due to the fact that the natural frequency of the structure is excited by the track excitation during vehicle operation, resulting in modal resonance, which amplifies the structural stress to a certain extent and increases the number of fatigue cycles.

[0085] In step S7, when analyzing the OMA test data of the bogie to be tested, the specific steps of the multi-reference point infinite impulse response filtering algorithm (PolyIIR) are as follows. Given the impulse response function h(k), with n orders of modes, the frequency response function of the structure is

[0086]

[0087] where z = e jωΔt , Δt is the sampling interval, l is the number of waveform points or length, N = 2n, j is the imaginary unit, and ω is;

[0088] Derive the coefficients of the characteristic equation from Equation (7.1) to obtain the eigenvalues of the characteristic equation, thereby obtaining the modal frequency, damping, and extracting the modal shape.

[0089] The specific steps of the adopted Stochastic Subspace Identification (SSI) method are as follows. For a linear system with n degrees of freedom, its discrete loading space equation is:

[0090] {x k+1} = [A]{x k} + {w k} (7.2)

[0091] {y k} = [C]{x k} + {v k} (7.3)

[0092] where {x k} is an n-dimensional state vector, {y k} is an N-dimensional output vector, and N is the number of response points; {w k} and {v k} are the input and output white noises with a mean of 0, respectively; [A] and [C] represent the n×n state matrix and the N×n output matrix, respectively. By solving for [A] and [C], the modal parameters can be identified.

[0093] The specific steps of the adopted Enhanced Frequency Domain Decomposition (EFDD) method are as follows. Let x(t) be the unknown and unmeasurable excitation, and y(t) be the measured response data. Then the power spectral matrix of the response is of order m×m, where m is the number of measurement points:

[0094]

[0095] where the power spectral matrix of the response is of order m×m, and m is the number of measurement points; G xx (jω) is the power spectral matrix of x(t), which is of order r×r, and r is the number of excitation points; H(jω) is the frequency response function matrix of order m×r; the superscripts "-" and " T " of the matrix represent complex conjugate and transpose, respectively; when K is fixed, d k is a constant, and λ k is the Kth-order pole;

[0096] When ω = ω i , G yy (jω) is estimated from Equation (7.4), and then its singular value decomposition is performed to decompose the power spectrum into the power spectra of single-degree-of-freedom systems corresponding to multiple modes;

[0097] When the Kth mode is the dominant mode, Equation (7.4) has only one term, and the mode shape is

[0098]

[0099] Among them, the frequency and damping can be obtained from the logarithmic decrement of the single-degree-of-freedom correlation function corresponding to the vibration mode, specifically as Figures 3 - 4 shown.

[0100] In summary, it can be seen that the vibration acceleration test, dynamic stress test, and OMA test used in the specific implementation process of this application are all commonly used test methods. However, the processing of the test acquisition data is different from the conventional operation. Therefore, it can be more accurately judged whether the frame undergoes modal resonance during the line operation, and it is suitable for wide promotion on subway vehicles.

[0101] Those skilled in the art of this technology can understand that unless otherwise defined, all terms (including technical terms and scientific terms) used here have the same meaning as the general understanding of those of ordinary skill in the art to which this application belongs. It should also be understood that terms defined in general dictionaries should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless defined as here.

[0102] The meaning of "and / or" described in this application refers to the situation where each exists alone or both exist simultaneously.

[0103] The meaning of "connection" described in this application can be a direct connection between components or an indirect connection between components through other components.

[0104] Taking the above ideal embodiments of the present invention as inspiration, through the above description, relevant staff can completely make various changes and modifications without departing from the technical idea of this invention. The technical scope of this invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for comprehensively analyzing and judging the modal resonance of a frame based on dynamic stress, vibration, and OMA, characterized in that: Specifically, it includes the following steps: Step S1: Install vibration accelerometers for vibration acceleration testing on the axle boxes, large-mass equipment, and mounting seats of the bogie to be tested; Step S2: Select the parts on the bogie to be tested where the stress and stress gradient values are large, and install dynamic stress patches for dynamic stress testing; Step S3: Combining the frame modal simulation results and relevant structural modal testing experience, select the positions on the bogie to be tested with typical modal vibration modes and install vibration accelerometers for OMA testing; Step S4: Simulate the load of the vehicle where the bogie to be tested is located, select the operation time period corresponding to its load, and collect the data of the vibration accelerometers for vibration acceleration testing, dynamic stress patches for dynamic stress testing, and vibration accelerometers for OMA testing arranged in Steps S1 to S3 during the vehicle operation; Step S5: Analyze the axle box vibration acceleration of the bogie to be tested, perform Fourier transform on the time-domain signal of the axle box vibration acceleration to obtain the power spectral density - frequency signal; Step S6: Analyze the stress test data of the bogie to be tested, calculate the equivalent stress amplitude of each measuring point using the Miner linear fatigue cumulative damage rule and the S - N curve, and perform time-frequency analysis on the stress data of the stress measuring points with large equivalent stress amplitudes; Step S7: Analyze the OMA test data of the bogie to be tested, perform joint analysis using the enhanced frequency domain decomposition method, random subspace method, and multi-reference point infinite impulse response filtering algorithm, and extract modal parameters from the test data. The modal parameters include frequency, damping, and vibration mode, which are the modal frequencies and modal vibration modes of each order of the bogie to be tested; Step S8: The frequency corresponding to the energy peak value of the axle box vibration acceleration of the bogie to be tested obtained in Step S5 is M1, the obvious main frequency M2 of the stress measuring points with large equivalent stress amplitudes obtained in Step S6, and the corresponding frequency M3 of the modal vibration mode that generates large stress of the stress measuring points with large equivalent stress amplitudes obtained in Step S7; Step S9: Compare the values of M1, M2, and M3. If the following conditions are met, it is determined that the bogie to be tested has modal resonance during line operation. Specifically:

2. The method for judging the modal resonance of a frame based on the comprehensive analysis of dynamic stress, vibration and OMA according to claim 1, characterized in that: In Step S3, several vibration accelerometers for OMA testing are installed. The several vibration accelerometers for OMA testing cover all elastic modal vibration modes within 100 Hz of the bogie to be tested, and each modal vibration mode is uniquely distinguishable; Specifically, at the joints of the side beams, cross beams, end beams, and adjacent structures of the bogie to be tested, the distance between adjacent accelerometers is 0.5 m.

3. The method for judging the modal resonance of the frame based on the comprehensive analysis of dynamic stress, vibration and OMA according to claim 2, characterized in that: In Step S3, during OMA testing, the wheel-rail excitation source during vehicle operation is used to excite the bogie to be tested, and the vibration response of the bogie to be tested caused by the excitation is measured.

4. The method for judging the frame modal resonance based on the comprehensive analysis of dynamic stress, vibration and OMA according to claim 1, wherein: The specific method for simulating the load of the vehicle where the bogie to be tested is located in Step S4 is to add sandbags to the vehicle where the bogie to be tested is located. When the vehicle load reaches C1 or C2, select the operation time period corresponding to its load, and collect the data of the strain gauges and accelerometers arranged in Steps S1 to S3 during line operation; Among them, the counterweight method when the vehicle load reaches C1 is as follows: one passenger per seat, with a passenger mass of 80 kg, 4 - 10 passengers per square meter in the corridor and porch, and a load of 300 kg per square meter in the luggage compartment; The counterweight method when the vehicle load reaches C2 is as follows: one passenger per seat, with a passenger mass of 80 kg, 2 - 4 passengers per square meter in the corridor and porch, and a load of 300 kg per square meter in the luggage compartment.

5. The method for judging the frame modal resonance based on the comprehensive analysis of dynamic stress, vibration and OMA according to claim 1, characterized in that: In step S5, the time domain signal of the axle box vibration acceleration of the bogie to be tested is a continuous-time non-periodic signal. In actual applications, the discrete sampling values x(n) of the continuous signal can be collected. Perform Fourier transform on it, Among them, j is the imaginary unit, and the power spectral density - frequency signal is obtained.

6. The method for judging the modal resonance of a frame based on the comprehensive analysis of dynamic stress, vibration and OMA according to claim 1, characterized in that: In step S6, when analyzing the stress test data of the bogie to be tested, the equivalent stress amplitude σ of each measuring point is calculated by using the Miner linear fatigue cumulative damage law and the S-N curve. aeq , where, according to the Miner linear fatigue cumulative damage law, the formula for calculating the damage generated within the measured kilometer number L1 of testing a stress spectrum is Assume that the equivalent stress amplitude acts for a certain number of times, and the damage formula generated by the bogie to be tested is Assume that the safe operating mileage for generating damage is L kilometers, then Substitute Formula (6.1) and Formula (6.2) into Formula (6.3) to obtain Finally, the equivalent stress amplitude is obtained; Among them, L1 is the measured kilometer number of a stress spectrum, which is generally the total mileage of dynamic stress testing; D1 is the damage generated by a stress spectrum within L1 kilometers; L is the safe operating mileage number for generating damage, that is, the total mileage of the bogie to be tested; N is the number of times of the equivalent stress amplitude action set in formula (6.2), that is, the number of cycles corresponding to the fatigue limit; D is the damage generated by the bogie to be tested in formula (6.2); n i is the number of stress cycles corresponding to each stress level; m is the exponent of the S-N curve, taking 6.5 for cast steel materials and 3.5 for welded joints; σ -1ai is the amplitude of each stress level.

7. The method for judging the modal resonance of the frame based on the comprehensive analysis of dynamic stress, vibration and OMA according to claim 6, wherein: Through the stress time - domain data of the stress measurement points with large equivalent stress amplitudes obtained above, the stress measurement points with large equivalent stress amplitudes are the dangerous position measurement points. Fourier transform is performed once every fixed period of time to obtain the curve of the dynamic stress frequency changing with time, and it is continuously displayed in a single graph to obtain its full - range main frequency.

8. The method for judging the modal resonance of the frame based on the comprehensive analysis of dynamic stress, vibration and OMA according to claim 1, characterized in that: In step S7, when analyzing the OMA test data of the bogie to be tested, the specific steps of the multi - reference - point infinite - impulse - response filtering algorithm are as follows: Given the impulse response function h(k), with n - order modes, the frequency response function of the structure is where \(z = e\) jωΔt , \(\Delta t\) is the sampling interval, \(l\) is the number of waveform points or the length, \(N = 2n\), \(j\) is the imaginary unit, and \(\omega\) is the angular frequency; Derive the coefficients of the characteristic equation from Formula (7.1) to obtain the eigenvalues of the characteristic equation, thereby obtaining the modal frequency, damping, and extracting the modal shape.

9. The method for judging the modal resonance of a frame based on the comprehensive analysis of dynamic stress, vibration and OMA according to claim 1, characterized in that: In step S7, when analyzing the OMA test data of the bogie to be tested, the specific steps of the stochastic subspace method are as follows: For a linear system with n degrees of freedom, its discrete state - space equation is: {x k+1} = [A]{x k} + {w k} (7.2) {y k} = [C]{x k} + {v k} (7.3) Among them, {x k} is an n-dimensional state vector, {y k} is an N-dimensional output vector, and N is the number of response points; {w k} and {v k} are input and output white noises with a mean of 0 respectively; [A] and [C] represent an n×n state matrix and an N×n output matrix respectively. By solving for [A] and [C], the modal parameter identification can be carried out.

10. The method for judging the frame modal resonance based on the comprehensive analysis of dynamic stress, vibration and OMA according to claim 1, wherein: In step S7, when analyzing the OMA test data of the bogie to be tested, the specific steps of the enhanced frequency - domain decomposition method are as follows: Assume that x(t) is the unknown and unmeasurable excitation, and y(t) is the measured response data, then the power spectral matrix of the response is: Among them, the power spectral matrix of the response is of order m×m, where m is the number of measurement points; G xx (jω) is the power spectral matrix of x(t), that is, of order r×r, where r is the number of excitation points; H(jω) is the frequency response function matrix of order m×r; the superscript "-" of the matrix T " indicates complex conjugate and transpose; when K is constant, d k is a constant, and λ k is the pole of order K; When ω = ω i , G yy (jω) is estimated by formula (7.4), and then its singular value decomposition is performed to decompose the power spectrum into the power spectra of single-degree-of-freedom systems corresponding to multiple orders of modes; When the K - order mode is the main mode, there is only one term in Formula (7.4), and the mode shape is Among them, the frequency and damping can be obtained from the logarithmic decay of the single - degree - of - freedom correlation function corresponding to the mode shape.

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