WO2023087890A1 - 一种基于动应力、振动和oma综合分析判断构架模态共振方法 - Google Patents

一种基于动应力、振动和oma综合分析判断构架模态共振方法 Download PDF

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WO2023087890A1
WO2023087890A1 PCT/CN2022/119847 CN2022119847W WO2023087890A1 WO 2023087890 A1 WO2023087890 A1 WO 2023087890A1 CN 2022119847 W CN2022119847 W CN 2022119847W WO 2023087890 A1 WO2023087890 A1 WO 2023087890A1
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stress
tested
bogie
oma
vibration
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PCT/CN2022/119847
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French (fr)
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金鑫
贾小平
徐步震
朱程
杨陈
戎芳明
李雨晗
李龙涛
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中车南京浦镇车辆有限公司
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/04—Ageing analysis or optimisation against ageing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

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  • the invention relates to a method for judging frame modal resonance based on comprehensive analysis of dynamic stress, vibration and OMA, and belongs to the technical field of rail vehicle bogies.
  • OMA line operation modal test method
  • the invention provides a method for judging the modal resonance of a frame based on comprehensive analysis of dynamic stress, vibration and OMA, which combines the dynamic stress level, vibration acceleration and OMA of the subway frame line to comprehensively analyze and judge whether the modal resonance occurs in the frame during line operation.
  • a method for judging frame modal resonance based on dynamic stress, vibration and OMA comprehensive analysis specifically comprising the following steps:
  • Step S1 Install a vibration accelerometer for vibration acceleration testing on the axle box, large-mass equipment and mounting base of the bogie to be tested;
  • Step S2 Select the parts on the bogie to be tested with large stress and stress gradient values, and install dynamic stress patches for dynamic stress testing;
  • Step S3 Combining the frame modal simulation results and relevant structural modal test experience, select a position with a typical mode shape on the bogie to be tested to install a vibration accelerometer for OMA testing;
  • Step S4 Carry out load simulation on the vehicle where the bogie to be tested is located, select its load corresponding to the operating time period, and collect the vibration accelerometers arranged in steps S1 to S3 for the vibration acceleration test and the dynamic stress test during the operation of the vehicle.
  • Step S5 analyzing the axlebox vibration acceleration of the bogie to be tested, performing Fourier transform on the axlebox vibration acceleration time-domain signal to obtain the power spectral density-frequency signal;
  • 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 point with a large equivalent stress amplitude analyze;
  • Step S7 Analyze the OMA (line operating mode) test data of the bogie to be tested, use the enhanced frequency domain decomposition method, the random subspace method and the multi-reference point infinite length impulse response filtering algorithm for joint analysis, and extract from the test data
  • Modal parameters the modal parameters include frequency, damping and mode shape, which are the modal frequencies and mode shapes of each order of the bogie to be tested;
  • Step S8 In step S5, the frequency corresponding to the energy peak value of the axlebox vibration acceleration of the bogie to be tested is obtained as M1; in step S6, the obvious main frequency M2 of the stress measuring point with a large equivalent stress amplitude is obtained; in step S7, etc. The corresponding frequency M3 of the modal mode shape of the large stress generated by the stress measuring point with a large effect stress amplitude;
  • Step S9 Compare the values of M1, M2 and M3. If the following conditions are met, it is judged that the bogie to be tested has modal resonance during line operation, specifically:
  • the installed vibration accelerometers for OMA testing include several, and several vibration accelerometers for OMA testing cover all elastic mode shapes within 100Hz of the bogie to be tested, and Each mode mode shape is uniquely distinguished;
  • the distance between adjacent accelerometers is 0.5m
  • step S3 when performing the OMA test, the wheel-rail excitation source in the vehicle running process 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;
  • step S4 the specific method of performing load simulation on the vehicle where the bogie to be tested is to add sandbags to the vehicle where the bogie to be tested is located, and the vehicle load reaches C1 or C2 , and the corresponding operating time of the load is selected Section, collect the data of strain gauges and accelerometers placed in steps S1 to S3 during line operation;
  • the counterweight method for the vehicle load to reach C 1 is: one passenger per seat, the passenger mass is 80kg, there are 4-10 passengers per square meter in corridors and porches, and the luggage room load per square meter is 300kg;
  • the counterweight method for the vehicle load to reach C 2 is: one passenger per seat, the passenger mass is 80kg, there are 2-4 passengers per square meter in corridors and porch, and the luggage room load per square meter is 300kg;
  • step S5 the axlebox vibration acceleration time-domain signal of the bogie to be tested is a continuous time aperiodic signal, and what can be collected in actual applications is the discrete sampling value x(n) of the continuous signal , and perform Fourier transform on it,
  • step S6 analyze the stress test data of the bogie to be tested and use Miner's linear fatigue cumulative damage rule and SN curve to calculate the equivalent stress range ⁇ aeq of each measuring point, wherein, by Miner's linear fatigue cumulative damage rule , the formula for calculating the damage generated within the measured kilometers L 1 of a stress spectrum is
  • L1 is the actual measured kilometers of a stress spectrum, which is generally the total mileage of the dynamic stress test; D1 is the damage caused by a stress spectrum within 1 km of L; L is the set safe operating mileage for damage, 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, which is the number of cycles corresponding to the fatigue limit; D is the damage; n i is the number of stress cycles corresponding to each level of stress; m is the index of the SN curve, 6.5 for cast steel materials and 3.5 for welded joints; ⁇ -1ai is the amplitude of each level of stress level;
  • the stress measuring point with a large equivalent stress amplitude is the dangerous position measuring point, and every fixed Carry out a Fourier transform for a period of time to obtain the curve of dynamic stress frequency changing with time, and display it continuously in a graph to obtain its main frequency;
  • step S7 the OMA test data of the bogie to be tested is analyzed, and the concrete steps of the multi-reference point infinite-length impulse response filtering algorithm adopted are: the known impulse response function h(k) has an n-order mode state, the frequency response function of the structure is
  • the coefficients of the characteristic equation are derived from the formula (7.1), and the characteristic value of the characteristic equation is obtained, thereby obtaining the modal frequency and damping, and extracting the mode shape;
  • the concrete step of the stochastic subspace method that adopts is, the linear system that degree of freedom is n, its discrete filling space equation is:
  • ⁇ x k ⁇ is an n-dimensional state vector
  • ⁇ y k ⁇ is an N-dimensional output vector
  • N is the number of response points
  • ⁇ w k ⁇ and ⁇ v k ⁇ are input and output white noise with a mean value of 0, respectively
  • [A ] and [C] represent the n ⁇ n order state matrix and the N ⁇ n order output matrix respectively, and the modal parameters can be identified after solving [A] and [C];
  • the specific steps of the enhanced frequency domain decomposition method that adopts are, let x(t) be the excitation that can not be measured unknown, y(t) is the measured response data, then the power spectrum array of the response is m ⁇ m order, and m is the number of measuring points:
  • the response power spectrum array is m ⁇ m order, m is the number of measuring points;
  • G xx (j ⁇ ) is the power spectrum array of x(t), that is, r ⁇ r order, r is the number of excitation points;
  • H(j ⁇ ) is m ⁇ r-order frequency response function matrix; the superscript "-" and "T" distribution of the matrix indicate complex conjugate and transpose; when K is constant, d k is a constant, and ⁇ k is a K-order pole;
  • G yy (j ⁇ ) is estimated by formula (7.4), and then its singular value decomposition is performed to decompose the power spectrum into a single-degree-of-freedom system power spectrum corresponding to multi-order modes;
  • the frequency and damping can be obtained from the logarithmic attenuation of the single degree of freedom correlation function corresponding to the mode shape.
  • the present invention has the following beneficial effects:
  • the present invention comprehensively analyzes the mode of the bogie frame of the subway vehicle during line operation, and can accurately judge whether the mode is the resonance generated by coupling with the excitation on the line.
  • Fig. 1 is the power spectral density-frequency signal figure that the present invention provides preferred embodiment when analyzing the axlebox vibration acceleration of bogie to be tested;
  • Fig. 2 is the graph that the present invention provides preferred embodiment when analyzing the stress test data of bogie to be tested, the dynamic stress frequency that obtains changes with time;
  • Fig. 3-Fig. 4 are schematic diagrams of different angles obtained when analyzing the OMA test data of the bogie to be tested according to the preferred embodiment of the present invention.
  • Step S1 Install a vibration accelerometer for vibration acceleration test on the axle box, large-mass equipment and mounting base of the bogie to be tested; here we need to explain why the acceleration identification of the axle box is required.
  • the vibration acceleration test data of the box is generally only used as a reference for vibration transmission, that is, the vibration transmission rate from the vibration of the axle box to the frame and even the car body; however, according to the consensus in the industry, this application believes that there is an excitation of a fixed frequency band on the track, which may stimulate the vibration of a certain part of the bogie. Natural frequency, so the main frequency identification is carried out for the vibration acceleration of the axle box.
  • Step S2 Select the parts on the bogie to be tested with large stress and stress gradient values, and install dynamic stress patches for dynamic stress testing;
  • Step S3 Combining the frame modal simulation results and relevant structural modal test experience, select a position with a typical mode shape on the bogie to be tested to install a vibration accelerometer for OMA testing;
  • Step S4 Carry out load simulation on the vehicle where the bogie to be tested is located, select its load corresponding to the operating time period, and collect the vibration accelerometers arranged in steps S1 to S3 for the vibration acceleration test and the dynamic stress test during the operation of the vehicle.
  • Step S5 analyzing the axlebox vibration acceleration of the bogie to be tested, performing Fourier transform on the axlebox vibration acceleration time-domain signal to obtain the power spectral density-frequency signal;
  • Step S6 Analyze the stress test data of the bogie to be tested, use Miner’s linear fatigue cumulative damage rule and 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 point with a large equivalent stress amplitude analyze;
  • Step S7 Analyze the OMA test data of the bogie to be tested, use the enhanced frequency domain decomposition method, the random subspace method and the multi-reference point infinite-length impulse response filtering algorithm for joint analysis, and extract the modal parameters from the test data, the
  • the modal parameters include frequency, damping and mode shape, that is, the modal frequencies and mode shapes of each order of the bogie to be tested;
  • Step S8 In step S5, the frequency corresponding to the energy peak value of the axlebox vibration acceleration of the bogie to be tested is obtained as M1; in step S6, the obvious main frequency M2 of the stress measuring point with a large equivalent stress amplitude is obtained; in step S7, etc. The corresponding frequency M3 of the modal mode shape of the large stress generated by the stress measuring point with a large effect stress amplitude;
  • Step S9 Compare the values of M1, M2 and M3. If the following conditions are met, it is judged that the bogie to be tested has modal resonance during line operation, specifically:
  • step S3 the installed vibration accelerometers for OMA testing include several (quantity should be sufficient), and several for OMA
  • the vibration accelerometer tested covers all elastic mode shapes within 100Hz of the bogie to be tested, and each mode shape is uniquely distinguished; when performing OMA testing, the wheel-rail excitation source during vehicle operation is used to excite the steering wheel to be tested. The vibration response of the bogie to be tested caused by the excitation is measured.
  • the distance between adjacent accelerometers is 0.5m, that is to say, an accelerometer needs to be arranged at an interval of about 0.5m.
  • an accelerometer needs to be arranged at the mounting seat of the large-mass suspension equipment to improve the measurement accuracy.
  • step S4 the specific method of carrying out load simulation on the vehicle where the bogie to be tested is to add sandbags to the vehicle where the bogie to be tested is located, and when the load of the vehicle reaches C 1 or C 2 , select its load corresponding to the operating time period, and during the operation of the line Gather the data of the strain gauges and accelerometers placed in steps S1 to S3;
  • the counterweight method for the vehicle load to reach C 1 is: one passenger per seat, the passenger mass is 80kg, there are 4-10 passengers per square meter in corridors and porches, and the luggage room load per square meter is 300kg;
  • the counterweight method for the vehicle load to reach C 2 is: one passenger per seat, the passenger mass is 80kg, there are 2-4 passengers per square meter in corridors and porch, and the luggage room load per square meter is 300kg.
  • step S6 the stress test data of the bogie to be tested is analyzed using Miner’s linear fatigue cumulative damage rule and the SN curve to calculate the equivalent stress amplitude ⁇ aeq of each measuring point, wherein, the Miner’s linear fatigue cumulative damage rule is used to calculate and test a stress spectrum
  • the damage formula generated within the measured kilometers L1 is
  • L1 is the actual measured kilometers of a stress spectrum, which is generally the total mileage of the dynamic stress test; D1 is the damage caused by a stress spectrum within 1 km of L; L is the set safe operating mileage for damage, That is the total mileage of the bogie to be tested; N is the number of times the equivalent stress amplitude set in the formula (6.2) acts, that is, the number of cycles corresponding to the fatigue limit, here is 2 million times (welded joints generally take 2 million times , the base material is 10 million times); D is the damage caused by the bogie to be tested in the formula (6.2); n i is the number of stress cycles corresponding to the stress level of each level; m is the index of the SN curve, and the cast steel material is 6.5, Welded joints take 3.5; ⁇ -1ai is the amplitude of stress levels at all levels.
  • the stress measuring point with a large equivalent stress amplitude is the dangerous position measuring point, and the Fourier transform is performed every fixed period of time. Transform to obtain the curve of dynamic stress frequency changing with time, and display it continuously in a graph, as shown in Figure 2 to obtain the main frequency of the whole process.
  • multiple Fourier transforms are required, because for dynamic stress testing, the industry's conventional practice is to arrange strain gauges on the structure, extract structural strain, convert it into stress, and evaluate whether the fatigue strength of the structure meets the requirements. Require.
  • step S7 the OMA test data of the bogie to be tested is analyzed, and the specific steps of the multi-reference point infinite impulse response filtering algorithm (PolyIIR) are as follows: the impulse response function h(k) is known, there are n-order modes, and the structure The frequency response function is
  • the coefficients of the characteristic equation are derived from the formula (7.1), and the eigenvalues of the characteristic equation are obtained, thereby obtaining the modal frequency and damping, and extracting the mode shape.
  • ⁇ x k ⁇ is an n-dimensional state vector
  • ⁇ y k ⁇ is an N-dimensional output vector
  • N is the number of response points
  • ⁇ w k ⁇ and ⁇ v k ⁇ are input and output white noise with a mean value of 0, respectively
  • [A ] and [C] denote the n ⁇ n order state matrix and the N ⁇ n order output matrix respectively, and the modal parameters can be identified after solving [A] and [C].
  • EFDD Enhanced Frequency Domain Decomposition
  • the response power spectrum array is m ⁇ m order, m is the number of measuring points;
  • G xx (j ⁇ ) is the power spectrum array of x(t), that is, r ⁇ r order, r is the number of excitation points;
  • H(j ⁇ ) is m ⁇ r-order frequency response function matrix; the superscript "-" and "T" distribution of the matrix indicate complex conjugate and transpose; when K is constant, d k is a constant, and ⁇ k is a K-order pole;
  • G yy (j ⁇ ) is estimated by formula (7.4), and then its singular value decomposition is performed to decompose the power spectrum into a single-degree-of-freedom system power spectrum corresponding to multi-order modes;
  • the frequency and damping can be obtained from the logarithmic attenuation of the single-degree-of-freedom correlation function corresponding to the mode shape, as shown in Figure 3- Figure 4.
  • the vibration acceleration test, dynamic stress test, and OMA test used in the specific implementation of this application are all routinely used test methods, but the processing of test data collection is different from conventional operations, so it can be judged more accurately Whether the modal resonance of the frame occurs during line operation is suitable for widespread promotion on subway vehicles.
  • connection in this application may be a direct connection between components or an indirect connection between components through other components.

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Abstract

一种基于动应力、振动和OMA综合分析判断构架模态共振方法，基于地铁车辆转向架构架动应力时频分析、振动加速度分析和OMA分析，综合判断地铁转向架构架在运用中是否发生局部模态共振。

Description

一种基于动应力、振动和OMA综合分析判断构架模态共振方法 技术领域
本发明涉及一种基于动应力、振动和OMA综合分析判断构架模态共振方法，属于轨道车辆转向架技术领域。
背景技术
目前国内外对于地铁转向架构架在线路运行中出现模态共振的现象有了初步的简单认知，也意识到发生模态共振对于构架结构损伤的危害性。但是并没有形成明确有效的模态共振的判断识别方法。
当前存在一些模态识别手段，例如线路运行模态测试方法(OMA)，可以测出地铁车辆转向架构架在线路运行中出现的模态。但是出现的模态，无法说明其是否与线路上的激励发生耦合从而产生共振。因此亟需研究一种新的判断构架模态共振的方法，以可以准确判断构架在线路运行过程中是否发生模态共振
发明内容
本发明提供一种基于动应力、振动和OMA综合分析判断构架模态共振方法，结合地铁构架线路动应力水平、振动加速度和OMA，综合分析判断构架在线路运行中是否发生模态共振。
本发明解决其技术问题所采用的技术方案是：
一种基于动应力、振动和OMA综合分析判断构架模态共振方法，具体包括以下步骤：
步骤S1：在待测试转向架的轴箱、大质量设备以及安装座上安装用于振动加速度测试的振动加速度计；
步骤S2：选取待测试转向架上应力以及应力梯度数值均大的部位，安装用于动应力测试的动应力贴片；
步骤S3：结合构架模态仿真结果及相关结构模态测试经验，选取待测试转向架上具有典型模态振型的位置安装用于OMA测试的振动加速度计；
步骤S4：对待测试转向架所在车辆进行载重模拟，选取其载重对应运营时间段，在车辆运行过程中采集步骤S1至步骤S3中布置的用于振动加速度测试的振动加速度计、用于动应力测试的动应力贴片以及用于OMA测试的振动加速度计的数据；
步骤S5：分析待测试转向架的轴箱振动加速度，对轴箱振动加速度时域信号进行傅里叶变换，得到功率谱密度-频率信号；
步骤S6：分析待测试转向架的应力测试数据，采用Miner线性疲劳累计损伤法则和S-N 曲线计算各测点的等效应力幅，对等效应力幅值大的应力测点的应力数据进行时频分析；
步骤S7：分析待测试转向架的OMA(线路运行模态)测试数据，采用增强型频域分解方法、随机子空间方法以及多参考点无限长脉冲响应滤波算法进行联合分析，由测试数据中提取模态参数，所述的模态参数包括频率、阻尼以及振型，即为待测试转向架各阶模态频率和模态振型；
步骤S8：步骤S5中获取待测试转向架的轴箱振动加速度的能量峰值对应的频率为M1，步骤S6中获取等效应力幅值大的应力测点的明显主频M2，步骤S7中获取等效应力幅值大的应力测点产生大应力的模态振型的对应频率M3；
步骤S9：将M1、M2以及M3进行数值比较，若满足如下条件，即判断待测试转向架在线路运行中发生模态共振，具体为
Figure PCTCN2022119847-appb-000001
作为本发明的进一步优选，步骤S3中，安装的用于OMA测试的振动加速度计包括若干个，若干个用于OMA测试的振动加速度计涵盖待测试转向架100Hz内所有弹性模态振型，且每阶模态振型均为唯一区分；
具体的，在待测试转向架的侧梁、横梁、端梁以及相邻结构的交接处，相邻加速度计之间的距离为0.5m；
作为本发明的进一步优选，步骤S3中，进行OMA测试时，采用车辆运行过程中的轮轨激励源激励待测试转向架，测量激励引起的待测试转向架振动响应；
作为本发明的进一步优选，步骤S4中对待测试转向架所在车辆进行载重模拟的具体方法为，对待测试转向架所在的车辆进行添加沙袋，车辆载重达到C 1或C 2，选取其载重对应运营时间段，在线路运行过程中采集步骤S1至步骤S3所布应变片和加速度计的数据；
其中，车辆载重达到C 1的配重方式为：每个座位一名乘客，乘客质量为80kg，在走廊和门廊中每平方米有4-10名乘客，每平方米行李间载重300kg；
车辆载重达到C 2的配重方式为：每个座位一名乘客，乘客质量为80kg，在走廊和门廊中每平方米有2-4名乘客，每平方米行李间载重300kg；
作为本发明的进一步优选，步骤S5中，待测试转向架的轴箱振动加速度时域信号是连续时间非周期性信号，实际的应用中能够采集到的是连续信号的离散采样值x(n)，对其进行傅 里叶变换，
Figure PCTCN2022119847-appb-000002
其中，
Figure PCTCN2022119847-appb-000003
n＝0,1,…，N-1，j为虚数单位，得到功率谱密度-频率信号；
作为本发明的进一步优选，步骤S6中分析待测试转向架的应力测试数据采用Miner线性疲劳累计损伤法则和S-N曲线计算各测点的等效应力幅σ aeq，其中，由Miner线性疲劳累计损伤法则，计算测试一个应力谱的实测公里数L 1内产生的损伤公式为
Figure PCTCN2022119847-appb-000004
设等效应力幅作用若干次，待测试转向架产生的损伤公式为
Figure PCTCN2022119847-appb-000005
设产生损伤的安全运行里程为L公里，则
Figure PCTCN2022119847-appb-000006
将公式(6.1)、公式(6.2)代入公式(6.3)，得出
Figure PCTCN2022119847-appb-000007
最终得到等效应力幅；
其中，L 1为一个应力谱的实测公里数，一般情况下是动应力测试的总里程；D 1为L 1公里内一个应力谱产生的损伤；L为设定产生损伤的安全运行里程数，即为待测试转向架总里程；N为公式(6.2)中设定的等效应力幅作用的次数，即为疲劳极限所对应的循环数；D为公式(6.2)中待测试转向架产生的损伤；n i为各级应力水平对应的应力循环次数；m为S-N曲线的指数，铸钢材料取6.5，焊接接头取3.5；σ -1ai为各级应力水平的幅值；
作为本发明的进一步优选，通过前述获得的等效应力幅值大的应力测点的应力时域数据，所述等效应力幅值大的应力测点即为危险位置测点，每隔固定的一段时间进行一次傅里叶变换，得到动应力频率随时间变换的曲线，并连续得显示在一张图中，获取其全程主频；
作为本发明的进一步优选，步骤S7中分析待测试转向架的OMA测试数据，采用的多参考点无限长脉冲响应滤波算法的具体步骤为，已知脉冲响应函数h(k)，有n阶模态，结构的频 响函数为
Figure PCTCN2022119847-appb-000008
其中，z＝e jωΔt，Δt为采样间隔，l为波形点数或长度，N＝2n，j为虚数单位，ω为；
由公式(7.1)推导特征方程系数，得到特征方程的特征值，从而得到模态频率、阻尼，提取模态振型；
作为本发明的进一步优选，步骤S7中分析待测试转向架的OMA测试数据，采用的随机子空间方法的具体步骤为，自由度为n的线性系统，其离散装填空间方程为：
{x k+1}＝[A]{x k}+{w k}      (7.2)
{y k}＝[C]{x k}+{v k}      (7.3)
其中，{x k}是n维状态向量，{y k}是N维输出向量，N为响应点数；{w k}和{v k}分别是均值为0的输入和输出白噪声；[A]和[C]分别表示n×n阶状态矩阵和N×n阶输出矩阵，求解得出[A]和[C]即可进行模态参数的识别；
作为本发明的进一步优选，步骤S7中分析待测试转向架的OMA测试数据，采用的增强型频域分解方法的具体步骤为，设x(t)是未知的不能测量的激励，y(t)是测量的响应数据，则响应的功率谱阵即m×m阶，m为测点数量为：
Figure PCTCN2022119847-appb-000009
其中，响应的功率谱阵为m×m阶，m为测点数量；G xx(jω)为x(t)的功率谱阵，即r×r阶，r为激励点数；H(jω)为m×r阶频响函数矩阵；矩阵的上角标“-”“T”分布表示复共轭和转置；当K一定时，d k是常数，λ k为K阶极点；
当ω＝ω i时，由公式(7.4)预估G yy(jω)，然后对其进行奇异值分解，将功率谱分解为对应多阶模态的单自由度系统功率谱；
当K阶模态为主要模态时，公式(7.4)仅有一项，则振型为
Figure PCTCN2022119847-appb-000010
其中，频率和阻尼从振型对应的单自由度相关函数的对数衰减可得。
通过以上技术方案，相对于现有技术，本发明具有以下有益效果：
本发明基于动应力、振动和OMA，对地铁车辆转向架构架在线路运行中出现的模态进行综合分析，可以准确判断出现的模态是否是与线路上的激励发生耦合产生的共振。
附图说明
下面结合附图和实施例对本发明进一步说明。
图1是本发明提供优选实施例的在分析待测试转向架的轴箱振动加速度时得到的功率谱密度-频率信号图；
图2是本发明提供优选实施例的在分析待测试转向架的应力测试数据时得到的动应力频率随时间变换的曲线图；
图3-图4是本发明提供优选实施例在分析待测试转向架的OMA测试数据时得到的不同角度的模态示意图。
具体实施方式
现在结合附图对本发明作进一步详细的说明。本申请的描述中，需要理解的是，术语“左侧”、“右侧”、“上部”、“下部”等指示的方位或位置关系为基于附图所示的方位或位置关系，仅是为了便于描述本发明和简化描述，而不是指示或暗示所指的装置或元件必须具有特定的方位、以特定的方位构造和操作，“第一”、“第二”等并不表示零部件的重要程度，因此不能理解为对本发明的限制。本实施例中采用的具体尺寸只是为了举例说明技术方案，并不限制本发明的保护范围。
如背景技术中阐述的，目前存在的一些模态识别手段，并不能准确的判断各个模态是否与线路上的激励发生耦合从而产生共振；因为本申请旨在提供一种全新的用于判断构架模态共振的方法，其原理是将地铁构架线路的动应力水平、振动加速度以及OMA综合进行全面分析，此判断方法精确度高且效果显著。
具体包括以下步骤：
步骤S1：在待测试转向架的轴箱、大质量设备以及安装座上安装用于振动加速度测试的振动加速度计；这里需要阐述一下为何需要对轴箱进行加速度识别，在轨道交通领域，对于轴箱振动加速度测试数据，一般仅做振动传递参考，即轴箱振动至构架乃至车体的振动传递率；但是本申请根据业内共识，认为轨道存在固定频带的激励，可能会激发转向架某部件的固有频率，因此针对轴箱振动加速度进行主频识别。
步骤S2：选取待测试转向架上应力以及应力梯度数值均大的部位，安装用于动应力测试的动应力贴片；
步骤S3：结合构架模态仿真结果及相关结构模态测试经验，选取待测试转向架上具有典型模态振型的位置安装用于OMA测试的振动加速度计；
步骤S4：对待测试转向架所在车辆进行载重模拟，选取其载重对应运营时间段，在车辆运行过程中采集步骤S1至步骤S3中布置的用于振动加速度测试的振动加速度计、用于动应力测试的动应力贴片以及用于OMA测试的振动加速度计的数据；
步骤S5：分析待测试转向架的轴箱振动加速度，对轴箱振动加速度时域信号进行傅里叶变换，得到功率谱密度-频率信号；
步骤S6：分析待测试转向架的应力测试数据，采用Miner线性疲劳累计损伤法则和S-N曲线计算各测点的等效应力幅，对等效应力幅值大的应力测点的应力数据进行时频分析；
步骤S7：分析待测试转向架的OMA测试数据，采用增强型频域分解方法、随机子空间方法以及多参考点无限长脉冲响应滤波算法进行联合分析，由测试数据中提取模态参数，所述的模态参数包括频率、阻尼以及振型，即为待测试转向架各阶模态频率和模态振型；
步骤S8：步骤S5中获取待测试转向架的轴箱振动加速度的能量峰值对应的频率为M1，步骤S6中获取等效应力幅值大的应力测点的明显主频M2，步骤S7中获取等效应力幅值大的应力测点产生大应力的模态振型的对应频率M3；
步骤S9：将M1、M2以及M3进行数值比较，若满足如下条件，即判断待测试转向架在线路运行中发生模态共振，具体为
Figure PCTCN2022119847-appb-000011
上述仅是对整个分析判断方法做了大概陈述，下面对其进行逐一具体阐述，步骤S3中，安装的用于OMA测试的振动加速度计包括若干个(数量要足够)，若干个用于OMA测试的振动加速度计涵盖待测试转向架100Hz内所有弹性模态振型，且每阶模态振型均为唯一区分；进行OMA测试时，采用车辆运行过程中的轮轨激励源激励待测试转向架，测量激励引起的待测试转向架振动响应。
具体的，在待测试转向架的侧梁、横梁、端梁以及相邻结构的交接处，相邻加速度计之间的距离为0.5m，也就是说每间隔0.5m左右即需布置一个加速度计，在大质量悬挂设备安装座等位置也应该布置，以提高测量精度。
步骤S4中对待测试转向架所在车辆进行载重模拟的具体方法为，对待测试转向架所在的车辆进行添加沙袋，车辆载重达到C 1或C 2，选取其载重对应运营时间段，在线路运行过程中采集步骤S1至步骤S3所布应变片和加速度计的数据；
其中，车辆载重达到C 1的配重方式为：每个座位一名乘客，乘客质量为80kg，在走廊和门廊中每平方米有4-10名乘客，每平方米行李间载重300kg；
车辆载重达到C 2的配重方式为：每个座位一名乘客，乘客质量为80kg，在走廊和门廊中每平方米有2-4名乘客，每平方米行李间载重300kg。
步骤S5中，待测试转向架的轴箱振动加速度时域信号是连续时间非周期性信号，实际的应用中能够采集到的是连续信号的离散采样值x(n)，对其进行傅里叶变换，
Figure PCTCN2022119847-appb-000012
其中，
Figure PCTCN2022119847-appb-000013
n＝0,1,…，N-1，j为虚数单位，得到图1所示的功率谱密度-频率信号。
步骤S6中分析待测试转向架的应力测试数据采用Miner线性疲劳累计损伤法则和S-N曲线计算各测点的等效应力幅σ aeq，其中，由Miner线性疲劳累计损伤法则，计算测试一个应力谱的实测公里数L 1内产生的损伤公式为
Figure PCTCN2022119847-appb-000014
设等效应力幅作用若干次，待测试转向架产生的损伤公式为
Figure PCTCN2022119847-appb-000015
设产生损伤的安全运行里程为L公里，则
Figure PCTCN2022119847-appb-000016
将公式(6.1)、公式(6.2)代入公式(6.3)，得出
Figure PCTCN2022119847-appb-000017
最终得到等效应力幅；
其中，L 1为一个应力谱的实测公里数，一般情况下是动应力测试的总里程；D 1为L 1公里内一个应力谱产生的损伤；L为设定产生损伤的安全运行里程数，即为待测试转向架总里程；N为公式(6.2)中设定的等效应力幅作用的次数，即为疲劳极限所对应的循环数，这里取200万次(焊接接头一般取200万次，母材取1000万次)；D为公式(6.2)中待测试转向架产生的损伤；n i为各级应力水平对应的应力循环次数；m为S-N曲线的指数，铸钢材料取6.5，焊 接接头取3.5；σ -1ai为各级应力水平的幅值。通过前述获得的等效应力幅值大的应力测点的应力时域数据，所述等效应力幅值大的应力测点即为危险位置测点，每隔固定的一段时间进行一次傅里叶变换，得到动应力频率随时间变换的曲线，并连续得显示在一张图中，如图2所示获取其全程主频。这里需要着重阐述的是，为何需要进行多次傅里叶变换，是因为对于动应力测试，业内常规做法是在结构上布置应变片，提取结构应变，换算成应力，评估结构的疲劳强度是否满足要求。本专利认为，结构发生疲劳失效，不一定是因为结构本身应力大，也可能是由于结构固有频率在车辆运行过程中被轨道激励激发出来，产生模态共振，一定程度上放大了结构应力，增多了疲劳循环次数造成的。
步骤S7中分析待测试转向架的OMA测试数据，采用的多参考点无限长脉冲响应滤波算法(PolyIIR)的具体步骤为，已知脉冲响应函数h(k)，有n阶模态，结构的频响函数为
Figure PCTCN2022119847-appb-000018
其中，z＝e jωΔt，Δt为采样间隔，l为波形点数或长度，N＝2n，j为虚数单位，ω为；
由公式(7.1)推导特征方程系数，得到特征方程的特征值，从而得到模态频率、阻尼，提取模态振型。
采用的随机子空间方法(SSI)的具体步骤为，自由度为n的线性系统，其离散装填空间方程为：
{x k+1}＝[A]{x k}+{w k}      (7.2)
{y k}＝[C]{x k}+{v k}      (7.3)
其中，{x k}是n维状态向量，{y k}是N维输出向量，N为响应点数；{w k}和{v k}分别是均值为0的输入和输出白噪声；[A]和[C]分别表示n×n阶状态矩阵和N×n阶输出矩阵，求解得出[A]和[C]即可进行模态参数的识别。
采用的增强型频域分解方法(EFDD)的具体步骤为，设x(t)是未知的不能测量的激励，y(t)是测量的响应数据，则响应的功率谱阵即m×m阶，m为测点数量为：
Figure PCTCN2022119847-appb-000019
其中，响应的功率谱阵为m×m阶，m为测点数量；G xx(jω)为x(t)的功率谱阵，即r×r阶，r为激励点数；H(jω)为m×r阶频响函数矩阵；矩阵的上角标“-”“T”分布表示复共轭和转置；当K一定时，d k是常数，λ k为K阶极点；
当ω＝ω i时，由公式(7.4)预估G yy(jω)，然后对其进行奇异值分解，将功率谱分解为对应多阶模态的单自由度系统功率谱；
当K阶模态为主要模态时，公式(7.4)仅有一项，则振型为
Figure PCTCN2022119847-appb-000020
其中，频率和阻尼从振型对应的单自由度相关函数的对数衰减可得，具体如图3-图4所示。
综上可知，本申请具体实施过程中用到的振动加速度测试、动应力测试、OMA测试都是常规使用的测试手段，但是对于测试采集数据的处理与常规操作不同，因此可以较为准确的判断出构架在线路运行中是否发生模态共振，适合在地铁车辆上广泛推广。
本技术领域技术人员可以理解，除非另外定义，这里使用的所有术语(包括技术术语和科学术语)具有与本申请所属领域中的普通技术人员的一般理解相同的意义。还应该理解的是，诸如通用字典中定义的那些术语应该被理解为具有与现有技术的上下文中的意义一致的意义，并且除非像这里一样定义，不会用理想化或过于正式的含义来解释。
本申请中所述的“和/或”的含义指的是各自单独存在或两者同时存在的情况均包括在内。
本申请中所述的“连接”的含义可以是部件之间的直接连接也可以是部件间通过其它部件的间接连接。
以上述依据本发明的理想实施例为启示，通过上述的说明内容，相关工作人员完全可以在不偏离本项发明技术思想的范围内，进行多样的变更以及修改。本项发明的技术性范围并不局限于说明书上的内容，必须要根据权利要求范围来确定其技术性范围。

Claims (10)

  1. 一种基于动应力、振动和OMA综合分析判断构架模态共振方法，其特征在于：具体包括以下步骤：
    步骤S1：在待测试转向架的轴箱、大质量设备以及安装座上安装用于振动加速度测试的振动加速度计；
    步骤S2：选取待测试转向架上应力以及应力梯度数值均大的部位，安装用于动应力测试的动应力贴片；
    步骤S3：结合构架模态仿真结果及相关结构模态测试经验，选取待测试转向架上具有典型模态振型的位置安装用于OMA测试的振动加速度计；
    步骤S4：对待测试转向架所在车辆进行载重模拟，选取其载重对应运营时间段，在车辆运行过程中采集步骤S1至步骤S3中布置的用于振动加速度测试的振动加速度计、用于动应力测试的动应力贴片以及用于OMA测试的振动加速度计的数据；
    步骤S5：分析待测试转向架的轴箱振动加速度，对轴箱振动加速度时域信号进行傅里叶变换，得到功率谱密度-频率信号；
    步骤S6：分析待测试转向架的应力测试数据，采用Miner线性疲劳累计损伤法则和S-N曲线计算各测点的等效应力幅，对等效应力幅值大的应力测点的应力数据进行时频分析；
    步骤S7：分析待测试转向架的OMA测试数据，采用增强型频域分解方法、随机子空间方法以及多参考点无限长脉冲响应滤波算法进行联合分析，由测试数据中提取模态参数，所述的模态参数包括频率、阻尼以及振型，即为待测试转向架各阶模态频率和模态振型；
    步骤S8：步骤S5中获取待测试转向架的轴箱振动加速度的能量峰值对应的频率为M1，步骤S6中获取等效应力幅值大的应力测点的明显主频M2，步骤S7中获取等效应力幅值大的应力测点产生大应力的模态振型的对应频率M3；
    步骤S9：将M1、M2以及M3进行数值比较，若满足如下条件，即判断待测试转向架在线路运行中发生模态共振，具体为
    Figure PCTCN2022119847-appb-100001
  2. 根据权利要求1所述的基于动应力、振动和OMA综合分析判断构架模态共振方法，其特征在于：步骤S3中，安装的用于OMA测试的振动加速度计包括若干个，若干个用于OMA测试的振动加速度计涵盖待测试转向架100Hz内所有弹性模态振型，且每阶模态振型均为唯一区分；
    具体的，在待测试转向架的侧梁、横梁、端梁以及相邻结构的交接处，相邻加速度计之 间的距离为0.5m。
  3. 根据权利要求2所述的基于动应力、振动和OMA综合分析判断构架模态共振方法，其特征在于：步骤S3中，进行OMA测试时，采用车辆运行过程中的轮轨激励源激励待测试转向架，测量激励引起的待测试转向架振动响应。
  4. 根据权利要求1所述的基于动应力、振动和OMA综合分析判断构架模态共振方法，其特征在于：步骤S4中对待测试转向架所在车辆进行载重模拟的具体方法为，对待测试转向架所在的车辆进行添加沙袋，车辆载重达到C 1或C 2，选取其载重对应运营时间段，在线路运行过程中采集步骤S1至步骤S3所布应变片和加速度计的数据；
    其中，车辆载重达到C 1的配重方式为：每个座位一名乘客，乘客质量为80kg，在走廊和门廊中每平方米有4-10名乘客，每平方米行李间载重300kg；
    车辆载重达到C 2的配重方式为：每个座位一名乘客，乘客质量为80kg，在走廊和门廊中每平方米有2-4名乘客，每平方米行李间载重300kg。
  5. 根据权利要求1所述的基于动应力、振动和OMA综合分析判断构架模态共振方法，其特征在于：步骤S5中，待测试转向架的轴箱振动加速度时域信号是连续时间非周期性信号，
    实际的应用中能够采集到的是连续信号的离散采样值x(n)，对其进行傅里叶变换，
    Figure PCTCN2022119847-appb-100002
    其中，
    Figure PCTCN2022119847-appb-100003
    j为虚数单位，得到功率谱密度-频率信号。
  6. 根据权利要求1所述的基于动应力、振动和OMA综合分析判断构架模态共振方法，其特征在于：步骤S6中分析待测试转向架的应力测试数据采用Miner线性疲劳累计损伤法则和S-N曲线计算各测点的等效应力幅σ aeq，其中，由Miner线性疲劳累计损伤法则，计算测试一个应力谱的实测公里数L 1内产生的损伤公式为
    Figure PCTCN2022119847-appb-100004
    设等效应力幅作用若干次，待测试转向架产生的损伤公式为
    Figure PCTCN2022119847-appb-100005
    设产生损伤的安全运行里程为L公里，则
    Figure PCTCN2022119847-appb-100006
    将公式(6.1)、公式(6.2)代入公式(6.3)，得出
    Figure PCTCN2022119847-appb-100007
    最终得到等效应力幅；
    其中，L 1为一个应力谱的实测公里数，一般情况下是动应力测试的总里程；D 1为L 1公里内一个应力谱产生的损伤；L为设定产生损伤的安全运行里程数，即为待测试转向架总里程；N为公式(6.2)中设定的等效应力幅作用的次数，即为疲劳极限所对应的循环数；D为公式(6.2)中待测试转向架产生的损伤；n i为各级应力水平对应的应力循环次数；m为S-N曲线的指数，铸钢材料取6.5，焊接接头取3.5；σ -1ai为各级应力水平的幅值。
  7. 根据权利要求6所述的基于动应力、振动和OMA综合分析判断构架模态共振方法，其特征在于：通过前述获得的等效应力幅值大的应力测点的应力时域数据，所述等效应力幅值大的应力测点即为危险位置测点，每隔固定的一段时间进行一次傅里叶变换，得到动应力频率随时间变换的曲线，并连续得显示在一张图中，获取其全程主频。
  8. 根据权利要求1所述的基于动应力、振动和OMA综合分析判断构架模态共振方法，其特征在于：步骤S7中分析待测试转向架的OMA测试数据，采用的多参考点无限长脉冲响应滤波算法的具体步骤为，已知脉冲响应函数h(k)，有n阶模态，结构的频响函数为
    Figure PCTCN2022119847-appb-100008
    其中，z＝e jωΔt，Δt为采样间隔，l为波形点数或长度，N＝2n，j为虚数单位，ω为；
    由公式(7.1)推导特征方程系数，得到特征方程的特征值，从而得到模态频率、阻尼，提取模态振型。
  9. 根据权利要求1所述的基于动应力、振动和OMA综合分析判断构架模态共振方法，其特征在于：步骤S7中分析待测试转向架的OMA测试数据，采用的随机子空间方法的具体步骤为，自由度为n的线性系统，其离散装填空间方程为：
    {x k+1}＝[A]{x k}+{w k}  (7.2)
    {y k}＝[C]{x k}+{v k}  (7.3)
    其中，{x k}是n维状态向量，{y k}是N维输出向量，N为响应点数；{w k}和{v k}分别是均值为0的输入和输出白噪声；[A]和[C]分别表示n×n阶状态矩阵和N×n阶输出矩阵，求解得出[A]和[C]即可进行模态参数的识别。
  10. 根据权利要求1所述的基于动应力、振动和OMA综合分析判断构架模态共振方法，其特征在于：步骤S7中分析待测试转向架的OMA测试数据，采用的增强型频域分解方法的具体步骤为，设x(t)是未知的不能测量的激励，y(t)是测量的响应数据，则响应的功率谱阵即m×m阶，m为测点数量为：
    Figure PCTCN2022119847-appb-100009
    其中，响应的功率谱阵为m×m阶，m为测点数量；G xx(jω)为x(t)的功率谱阵，即r×r阶，r为激励点数；H(jω)为m×r阶频响函数矩阵；矩阵的上角标“-”“T”分布表示复共轭和转置；当K一定时，d k是常数，λ k为K阶极点；
    当ω＝ω i时，由公式(7.4)预估G yy(jω)，然后对其进行奇异值分解，将功率谱分解为对应多阶模态的单自由度系统功率谱；
    当K阶模态为主要模态时，公式(7.4)仅有一项，则振型为
    Figure PCTCN2022119847-appb-100010
    其中，频率和阻尼从振型对应的单自由度相关函数的对数衰减可得。
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