CN114357614A - Bogie fatigue life online estimation method based on axle box vibration - Google Patents
Bogie fatigue life online estimation method based on axle box vibration Download PDFInfo
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- CN114357614A CN114357614A CN202111587981.0A CN202111587981A CN114357614A CN 114357614 A CN114357614 A CN 114357614A CN 202111587981 A CN202111587981 A CN 202111587981A CN 114357614 A CN114357614 A CN 114357614A
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Abstract
The invention discloses an axle box vibration-based bogie fatigue life online estimation method, which is characterized in that a transfer function method is utilized, axle box vibration acceleration PSD is used as input, dynamic stress PSD of a bogie attention area is used as output, and a frequency domain fatigue damage calculation method is combined to realize the estimation of fatigue damage of the attention area. The axle box acceleration sensor is used as a general configuration of a new generation of railway vehicle, the vibration input of a bogie system is basically definite, online fatigue damage estimation can be carried out on a bogie frame, and a basis is provided for fatigue life management of key parts of the railway vehicle.
Description
Technical Field
The invention belongs to the field of railway vehicle structure health monitoring, and particularly relates to an axle box vibration-based bogie fatigue life online estimation method.
Background
A new generation of intelligent high-speed rail is provided with a temperature and vibration composite sensor at the positions of an axle box, a gear box and the like, how to use a small amount of sensors to master more vehicle running states becomes a preoccupation in vehicle health monitoring research.
The current method for evaluating the fatigue life of the bogie is mainly realized by arranging sensors in a concerned area, and a large number of sensors are required to be arranged on the bogie because the concerned area of a bogie system is more. The stock of the railway vehicle is huge, on one hand, the economical efficiency of excessive sensors is not high, on the other hand, the excessive sensors are not beneficial to improving the reliability of the fatigue damage monitoring of the bogie, and the phenomena of 'misjudgment' and 'missed judgment' cannot be processed. Based on the method, the fatigue damage assessment of the bogie is realized based on a small number of sensors, the cost of bogie structure health monitoring is reduced, and the reliability of fatigue damage assessment is improved.
Disclosure of Invention
The invention aims to provide an axle box vibration-based bogie fatigue life online estimation method, which obtains a stress PSD of a concerned position according to axle box vibration acceleration PSD in combination with a transfer function and realizes fatigue damage evaluation by using a fatigue damage calculation method of a frequency domain method.
In order to achieve the purpose, the invention adopts the following technical scheme:
the bogie fatigue life online estimation method based on axle box vibration comprises the following steps:
(1) constructing a transfer function between axle box vibration and bogie dynamic stress
Firstly, the transfer function is calibrated in a laboratory stage, and the input is acquired: the axle box vibration acceleration signal, and output: dynamic stress at critical locations of the bogie; and (3) calculating the mutual power density of the input and the output and the self-power spectral density of the input, and combining the formula (1) to realize the calibration of the transfer function H (f). In the actual measurement stage of the line, the input power spectral density S is calculated according to the axle box vibration signalij(f) When i ≠ j, Sij(f) For the cross-power spectral density between the ith and jth vibration signals, S when i equals jij(f) Representing the self-power spectral density of the ith vibration signal, dividing the input power spectral density Sij(f) Combined transfer function Hj(f) Substituting equation (2) to calculate the output power spectral density Sy(f)；
(2) Fatigue damage estimation based on frequency domain method
Firstly, calculating input power spectral density S according to the vibration signalij(f) (ii) a Calculating output power spectral density according to the input power spectral density and the transfer function constructed in the step (1)
Secondly, according to the output power spectral density Sy(f) The estimation of the fatigue damage of the concerned area is realized by combining with the frequency domain fatigue damage calculation method, and the damage in unit time
Wherein v ispFor peak crossing frequency, C and k are both material constants, and p(s) is the rain flow amplitude probability density function.
Further, the mean value of the transfer function constructed in step (1) may be modified by multiplying the transfer function by the mean error of the transfer function.
Further, the input power spectral density Sij(f) And an output power spectral density Sy(f) All are calculated by fast fourier transform.
Further, the rain flow amplitude probability density function p(s) is calculated by using a suitable distribution model, such as Dirlik method and Zhao Baker method.
The Dirlik method is performed by combining an exponential distribution and two rayleigh distributions, whose p(s) is expressed as:
wherein G is1、G2、G3R and Q are parameters,
G3＝1-G1-G2；
z is the normalized amplitude value of the signal,
xmwhich represents the mean frequency of the mean,
the Zhao Baker method linearly combines a weibull distribution and a rayleigh distribution, and p(s) is expressed as:
w is a weight coefficient, and W is a weight coefficient,
alpha and beta are weibull parameters, alpha-8-7 r,
Γ (·) is a gamma function,
further, the window size using the Dirlik method was 4s, and the window size using the Zhao Baker method was 0.5 s.
The invention has the following beneficial effects:
(1) the transfer function obtained through the cross-power spectral density and the self-power spectral density can be used for establishing a transfer relation between the dynamic stress PSD of the key position and the axle box acceleration PSD in a frequency domain, and the transfer function can be well attached to an actually measured value in the aspects of dynamic stress PSD, RMS (root mean square) value and irregularity factor prediction under the condition of considering nonlinearity. The total prediction error of the dynamic stress is less than 25 percent, and is acceptable in engineering application.
(2) The Dirlik method and the ZHao Baker method can well estimate the dynamic stress amplitude distribution, particularly the narrow-band process, the two distribution models have higher prediction accuracy on the signal distribution of the combination of the large stress amplitude distribution and the small stress amplitude distribution, the smaller window size can better represent the non-stationary characteristic of the dynamic stress, and the prediction accuracy is highest when the window lengths of the Dirlik method and the ZHao Baker method are respectively 4s and 0.5 s.
In conclusion, the invention provides an alternative method for monitoring the structural health, and the structural fatigue damage can be estimated on line based on the acceleration of the axle box.
Drawings
Fig. 1 is a schematic diagram of measured data, (a) is a left axle box three-way vibration acceleration measured signal, (b) is a right axle box three-way vibration acceleration measured signal, and (c) is an antenna beam measured dynamic stress.
Fig. 2 is a schematic representation of the cross-power spectral density between an axis vibration signal and an antenna beam strain signal.
FIG. 3 is a self-power spectral density of an axle box vibration signal.
Fig. 4 is a schematic diagram of the transfer function between the antenna beam and the pedestal signals, where the black bold line represents the average transfer function.
FIG. 5 is a graph comparing the predicted dynamic stress PSD and the measured dynamic stress PSD using the average transfer function.
FIG. 6 is a comparison of the irregularity factor and RMS of the predicted and measured values, and the corresponding error map.
Fig. 7 shows the transfer function mean error.
Fig. 8 is a comparison graph of the antenna beam dynamic stress PSD predicted by the transfer function after correction and the actually measured dynamic stress PSD.
FIG. 9 is a comparison graph of simulated and measured values for RMS and irregularity factors using a modified transfer function, along with error.
Fig. 10 is a comparison graph of the actually measured stress amplitude probability density function obtained by the rain flow counting method and the simulated stress amplitude probability density function calculated by the frequency domain method.
Fig. 11 is a schematic diagram of stress amplitude probability density function calculated based on time-domain rain flow counting and frequency-domain power spectral density meters with different window lengths, wherein (a) is time-domain rain flow counting and dirik method, and (b) is time-domain rain flow counting and Zhao Baker method.
Fig. 12 is a time-domain rain flow counting, Dirlik method and Zhao Baker method calculated fatigue damage comparison graph.
Detailed Description
The method for estimating the fatigue life of the bogie based on the axle box vibration comprises the following steps:
(1) constructing a transfer function between axle box vibration and bogie dynamic stress
Firstly, the transfer function is calibrated in a laboratory stage, and the input is acquired: the axle box vibration acceleration signal, and output: dynamic stress at critical locations of the bogie; and (3) calculating the mutual power density of the input and the output and the self-power spectral density of the input, and combining the formula (1) to realize the calibration of the transfer function H (f). In the actual measurement stage of the line, the input power spectral density S is calculated according to the axle box vibration signalij(f) When i ≠ j, Sij(f) For the cross-power spectral density between the ith and jth vibration signals, S when i equals jij(f) Representing the self-power spectral density of the ith vibration signal, dividing the input power spectral density Sij(f) Combined transfer function Hj(f) Substituting equation (2) to calculate the output power spectral density Sy(f)；
(2) Fatigue damage estimation based on frequency domain method
Firstly, calculating input power spectral density S according to the vibration signalij(f) (ii) a Calculating output power spectral density according to the input power spectral density and the transfer function constructed in the step (1)
Secondly, according to the output power spectral density Sy(f) The estimation of the fatigue damage of the concerned area is realized by combining with the frequency domain fatigue damage calculation method, and the damage in unit time
Wherein v ispFor peak crossing frequency, C and k are both material constants, and p(s) is the rain flow amplitude probability density function.
The statistical properties of the signal are often expressed in terms of the spectral moment and spectral width coefficient of the signal, the ith order spectral moment miComprises the following steps:
the irregularity factor r is:
the value range of the signal is 0-1, the larger the value of r is, the signal is represented as a narrow-band random process, and the spectral width coefficient
Peak crossing frequency vpAnd zero line forward crossing frequency v0Can be expressed as:
the reliability of this embodiment was tested, and since the antenna beam was far from the rear wheel pair, the vibration of the antenna beam was highly correlated with the vibration of the front wheel pair. Three-way vibration acceleration sensors are mounted on the left axle box and the right axle box, and the three-way vibration acceleration sensors collect three-way vibration signals (including transverse, longitudinal and vertical directions) to be used as input excitation of the antenna beam. And mounting the uniaxial strain gauge at the middle position of the antenna beam, and measuring the dynamic stress at the position as output. A 6 input single output system was established.
The test is carried out on 16 stations in total, and the measured data from the stations 2-3 are shown in figure 1.
Fig. 2 shows cross-power spectral densities of the pedestal vibration signal and the antenna beam stress signal, which describe the correlation of the two signals in the frequency domain.
FIG. 3 shows the input self-power spectral density
The transfer function of each time segment can be calculated based on the cross-power spectral density of the input and output signals and the self-power spectral density of the input signals, and the average transfer function is further calculated. As shown in fig. 4.
Fig. 5 shows the measured stress PSD and the simulated stress PSD in the selected four time periods without considering the correction of the transfer function, and it can be found that there is a large difference between the predicted value and the simulated value in some time periods.
The method provided by the embodiment is verified to be accurate by comparing the root mean square value and the irregular factor of the dynamic stress which is predicted and actually measured. As shown in fig. 6, the overall error of the prediction of RMS and irregularity factors is less than 35% relative to the measured values.
FIG. 7 further illustrates the average error distribution in the frequency domain of the transfer function determined by dividing the measured PSD by the predicted PSD for each segment. The prediction is often underestimated for a frequency amplitude of 60Hz and overestimated for a dominant frequency amplitude of 75 Hz. Therefore, by multiplying the transfer function by the average error of the transfer function and further modifying the transfer function, comparing fig. 6(c) and fig. 9(c), it can be found that the prediction error of the irregular factor of the predicted output power spectrum is significantly reduced, and the overall prediction error of the irregular factor is less than 20%, thereby better improving the accuracy of the present embodiment.
FIG. 8 shows the predicted stress PSD over the test segment using the modified transfer function. The prediction accuracy is higher compared with fig. 5.
As shown in fig. 9, the predicted rms and the irregularity factors are comparable to the measured values, and the overall error is still at an acceptable level. This shows that the modified transfer function better characterizes the transfer relationship between antenna beam stress and pedestal box acceleration.
By using the dynamic stress power spectral density obtained above, the rain flow stress amplitude probability density function can be calculated by combining dirik and Zhao Baker methods, as shown in fig. 10.
FIG. 11 shows a stress magnitude density function calculated based on time domain rain flow counts and frequency domain normal power spectral density. In the figure, a histogram is a probability density function calculated based on the time-domain rain flow counting result, and a solid line represents S obtained by predictiony(f) The calculated stress amplitude probability density function is an average probability density function obtained by adding the probability density functions of each time segment and dividing the sum by the total number of the time segments.
FIG. 12 shows fatigue damage calculated by time-domain rain flow counting, Dirlik method and Zhao Baker method, total damage calculated by time-domain rain flow counting 2.84 × 10-4As a reference line, the fatigue damage calculated by the two methods is continuously reduced along with the continuous increase of the window size, and when the window size of Dirlik is 4s and the window size of the Zhao Baker method is 0.5s, the calculation result is closest to the time domain calculation result.
In summary, the transfer relationship between the bogie dynamic stress and the axle box acceleration can be established by a transfer function method, the stress PSD of the bogie frame attention area is calculated by the axle box vibration acceleration PSD, and the fatigue damage is calculated by the stress PSD. Currently, axle box acceleration sensors have been used as a common configuration for a new generation of rail vehicles, enabling online fatigue damage estimation of the bogie. Provides basis for the fatigue life management of key parts of the railway vehicle.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any modification and replacement based on the technical solution and inventive concept provided by the present invention should be covered within the scope of the present invention.
Claims (5)
1. The bogie fatigue life online estimation method based on axle box vibration is characterized by comprising the following steps of:
(1) constructing a transfer function between axle box vibration and bogie dynamic stress
Firstly, the transfer function is calibrated in a laboratory stage, and the input is acquired: the vibration acceleration signal of the axle box is sent,and outputting: dynamic stress at critical locations of the bogie; and (3) calculating the mutual power density of the input and the output and the self-power spectral density of the input, and combining the formula (1) to realize the calibration of the transfer function H (f). In the actual measurement stage of the line, the input power spectral density S is calculated according to the axle box vibration signalij(f) When i ≠ j, Sij(f) For the cross-power spectral density between the ith and jth vibration signals, S when i equals jij(f) Representing the self-power spectral density of the ith vibration signal, dividing the input power spectral density Sij(f) Combined transfer function Hj(f) Substituting equation (2) to calculate the output power spectral density Sy(f)；
(2) Fatigue damage estimation based on frequency domain method
Firstly, calculating input power spectral density S according to the vibration signalij(f) (ii) a Calculating output power spectral density according to the input power spectral density and the transfer function constructed in the step (1)
Secondly, according to the output power spectral density Sy(f) The estimation of the fatigue damage of the concerned area is realized by combining with the frequency domain fatigue damage calculation method, and the damage in unit time
Wherein v ispFor peak crossing frequency, C and k are both material constants, and p(s) is the rain flow amplitude probability density function.
2. The method for on-line estimation of axle box vibration-based bogie fatigue life according to claim 1, characterized in that: the mean value of the transfer function constructed in the step (1) can be corrected, and the mean error of the transfer function and the transfer function is multiplied for correction, so that the prediction precision of the output power spectral density is improved.
3. The method for on-line estimation of axle box vibration-based bogie fatigue life according to claim 1, characterized in that: the input position is selected on the axle box, the output position is a weak position concerned by the bogie, and a transfer function of the input and the output is constructed.
4. The method for on-line estimation of axle box vibration-based bogie fatigue life according to claim 1, characterized in that: the rain flow amplitude probability density function p(s) is calculated by selecting a Dirlik method and a Zhao Baker method distribution model.
5. The method for on-line estimation of axle box vibration-based bogie fatigue life according to claim 4, characterized in that: the window size using the Dirlik method is 4s, and the window size using the Zhao Baker method is 0.5s, with the highest prediction accuracy.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114791364A (en) * | 2022-06-23 | 2022-07-26 | 岚图汽车科技有限公司 | Multi-axial bench vibration durability test method and device |
| WO2024075768A1 (en) * | 2022-10-04 | 2024-04-11 | 日立建機株式会社 | Stress estimation device |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114791364A (en) * | 2022-06-23 | 2022-07-26 | 岚图汽车科技有限公司 | Multi-axial bench vibration durability test method and device |
| WO2024075768A1 (en) * | 2022-10-04 | 2024-04-11 | 日立建機株式会社 | Stress estimation device |
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