CN106886638B - A kind of endless-track vehicle transmission shaft loading spectrum preparation method based on Density Estimator - Google Patents
A kind of endless-track vehicle transmission shaft loading spectrum preparation method based on Density Estimator Download PDFInfo
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- CN106886638B CN106886638B CN201710054130.7A CN201710054130A CN106886638B CN 106886638 B CN106886638 B CN 106886638B CN 201710054130 A CN201710054130 A CN 201710054130A CN 106886638 B CN106886638 B CN 106886638B
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Abstract
The endless-track vehicle transmission shaft loading spectrum preparation method based on Density Estimator that the present invention relates to a kind of includes the following steps: step S1, the acquisition of endless-track vehicle torque load sample data and pretreatment；Step S2, passing sequentially through first time, rain-flow counting, the deduction of equal amplitude extreme value, second of rain-flow counting, two-dimentional Density Estimator, multi-state synthesize and the two-dimentional loading spectrum of extrapolation generation twice.The present invention takes rain-flow counting twice, and first time rain-flow counting result is inferred for equal amplitude extreme value, and second of rain-flow counting result is used for Density Estimator, can be fitted equal amplitude distribution well and do reasonable extrapolation to actual measurement rainflow matrix.The loading spectrum compiled using this method and actual measurement rainflow matrix have the similar probability density distribution of height, while also achieving the reasonable extrapolation to actual measurement rainflow matrix, have reached desired effect.
Description
Technical field
The present invention relates to vehicle reliability technical field more particularly to a kind of endless-track vehicle transmissions based on Density Estimator
Axle load composes preparation method.
Background technique
Loading spectrum is the basic foundation for carrying out vehicle loaded components Design of Mechanical Structure and fatigue test, and acquisition meets reality
The loading spectrum of border service condition then becomes the important prerequisite of vehicle component Anti fatigue Design.Due to load cycle include amplitude and
Two dimensions of mean value can reflect that the two-parameter rain flow method of characteristic of material mechanics becomes general in loading spectrum compilation process now
Method of counting.Logarithm equivalent life probability distribution based on typical mission, Yan Chuliang propose the intermediate value with high confidence level
Fatigue load spectrum compilation theory improves the reliability that aircaft configuration determines the longevity He lengthens the life.Existing document is respectively in military creeper truck
Correlative study has been done in terms of transmission device durability evaluation and fatigue life prediction.Probability Distribution Fitting is being done to rainflow matrix
When, compared with traditional parameters method, the fitting effect of nonparametric method has more advantage, and wherein kernel density estimation method obtains more and more
Research and application, but it then less is concerned with the combination for compiling spectrum process.
Analysis of fatigue and the common loading spectrum of test include two-dimentional loading spectrum, one-dimensional loading spectrum and eight grades of program spectrums.It is military
Transmission device, running gear, track and the driver behavior of endless-track vehicle are different from general vehicle, these features make its traveling
Load is complicated and changeable, and the high failure rate of fatigue rupture occurs for power train components, therefore it is fixed to compile the higher power train of confidence level
Longevity loading spectrum is of great significance to the reliability promotion of vehicle.
Summary of the invention
In view of above-mentioned analysis, the present invention is intended to provide a kind of endless-track vehicle transmission shaft loading spectrum based on Density Estimator
Preparing method, to solve the reliability disadvantages of existing endless-track vehicle transmission shaft loading spectrum establishment.
The purpose of the present invention is mainly achieved through the following technical solutions:
A kind of endless-track vehicle transmission shaft loading spectrum preparation method based on Density Estimator, include the following steps: step S1,
The acquisition of endless-track vehicle torque transmission shaft load sample data and pretreatment；
Step S2, pretreated torque load sample data is passed sequentially through into first time rain-flow counting, equal amplitude extreme value
Deduction, second of rain-flow counting, two-dimentional Density Estimator, multi-state synthesis and extrapolation generate two-dimentional loading spectrum.
Further, the step S2 includes the following steps:
Step S201, pretreated torque load sample data is split statistics by gear, determines each gear
The torque range and group number of rain-flow counting；
Step S202, according to the torque range of the obtained rain-flow counting of step S201 and grouping to each gear torque load sample
Notebook data carries out first time rain-flow counting, obtains each gear rainflow matrix；
Step S203, make equal amplitude extreme value according to each gear rainflow matrix to infer, obtain the equal amplitude extreme value of each gear；
Step S204, the maximum value in all gear mean value maximum that selecting step S203 is calculated, mean value are minimum
Minimum value in value, the maximum value in amplitude maximum and the minimum value in amplitude minimum, by the mean value range and width chosen
Value range is derived by torque range, as the torque range of second of rain-flow counting, then selected packet count, generate new rain stream
Matrix；
Step S205, using the two-dimentional Density Estimator based on Gaussian kernel, the density for obtaining the new rainflow matrix of each gear is estimated
Meter；The two dimension torque range of Density Estimator and the torque range and packet count phase of packet count and second of rain-flow counting
Together；
Step S206, multi-state synthesis and extrapolation obtain each operating condition extrapolation load frequency, obtain in conjunction with step S205 each
The density estimation of the new rainflow matrix of gear obtains two-dimentional loading spectrum.
Further, the step S203 includes obtaining equal amplitude by each gear rainflow matrix and being independently distributed, just using logarithm
State distribution or Weibull Distribution amplitude distribution, using normal distribution, Three-paramerter Lognormal Distribution or three parameter Weibulls
Fitting of distribution distribution of mean value, obtains the fitting parameter that the equal amplitude of each gear is independently distributed, and determines each gear amplitude by fitting parameter
Probability density function fX(x), each gear mean value probability density function fY(y)；
By each gear amplitude probability density functional integration formulaObtain each gear load
The maximum x of amplitudemax, each gear amplitude minimum takes the minimum amplitude of respective notch rainflow matrix；It is close by load mean value probability
Spend functional integration formulaAcquire the maximum y of each gear load mean valuemax, general by load mean value
Rate density function integral formulaAcquire the minimum of each gear mean value.
Further, fitting of the lesser distribution of AD average value as amplitude in logarithm normal distribution or Weibull distribution is selected
It is distributed, the lesser distribution of AD average value is quasi- in selection normal distribution, Three-paramerter Lognormal Distribution or three-parameter Weibull distribution
Close distribution of mean value.
Further, the step S205, including following sub-step:
Step S2051, with the torque range and the two-dimentional Density Estimator grid of packet count division of second of rain-flow counting；
Step S2052, Gaussian kernel is obtained using improvement Sheather-Jones plug-in type band width selection method (ISJ method)
Optimal diagonal bandwidthWith
Specifically, according to lower two formula, the optimal diagonal bandwidth of Gaussian kernel is calculatedWith
Wherein,
N+Be positive natural number；
Step S2053, dimensional Gaussian Density Estimator is made to new rainflow matrix；
Specifically, the Gaussian kernel with diagonal bandwidth matrices is calculated
Wherein, x=[x1,x2]TWith y=[y1,y2]T, the first variable of x and y are amplitude, and the second variable is mean value；
Dimensional Gaussian Density Estimator is calculated by the Gaussian kernel with diagonal bandwidth matrices
Step S2054, dimensional Gaussian Density Estimator is corrected with the equal amplitude range of each gear, and by density and normalizing
Change, obtains the density estimation of the new rainflow matrix of each gear.
Further, the step S206 is specifically included:
Step S2061, the load cycle of i-th of operating condition under each gear is calculated in unit according to torque load sample data
The frequency occurred under journey
M is respective notch operating condition type sum, and the test miles of each operating condition of respective notch is respectively l1,l2,...,lm, by
Each operating loading circulation frequency of the respective notch that test statistics obtain is respectively n1,n2,...,nm；
Step S2062, the load cycle extrapolation frequency N that i-th of operating condition of each gear occurs is calculatedi=fipiL
L is the design service life mileage of respective notch vehicle, and the mileage travelled of each operating condition accounts for the hundred of service life mileage
Divide than being respectively p1,p2,...,pm, the mileage travelled under i-th of operating condition of respective notch is piL；
Step S2063, according to formulaObtain each gear multi-state two dimension loading spectrum；
In formula, NiIt extrapolates the load frequency for i-th operating condition of respective notch,For i-th of operating condition rain in early spring stream of respective notch
The dimensional Gaussian Density Estimator of matrix；
Step S2064, each gear multi-state two dimension load spectral synthesis is obtained into two-dimentional loading spectrum.
Further, the step 1 includes following sub-step:
Step S101, resistance strain gage is arranged in wireless telemetering on the input shaft of left side retarder and obtains torque signal,
It carries out n and encloses endless-track vehicle real train test, acquire the transmission shaft load data of every circle endless-track vehicle in real time, form n independent random
Sample data；Also synchro measure gear signal；
Step S102 carries out the high-frequency noise in rain stream filtering removal sample data to sample data.
Further, the step 1 further includes sample size Confidence test step, carries out confidence level inspection to sample size
It tests, when sample size is by examining, continuation is in next step；If do not passed through, then increase test number (TN), is examined until passing through；
The Confidence test step includes:
The pseudo- damage D that the torque load sample data that n circle test obtains is calculated using TecWare software, then by public affairs
FormulaEquivalent life is calculated, and then obtains logarithm equivalent life lgT, n is enclosed into the logarithm equivalent life lgT that test obtains
It is expressed as x1,x2,...,xn, calculate the average value of incrementWith standard deviation s；
By minimum testing time criterion formula
Judge whether experimental test frequency n meets the sample size requirements of given confidence level γ and relative error δ, t in formulaγFor
T corresponding with γ is distributed quantile.
It further, further include step S3；Step S3, it does mean stress amendment using Goodman equation mean value is not zero
Load cycle be converted to the load cycle that mean value is zero by Fatigue Damage Equivalence method, so that two-dimentional loading spectrum is converted into one
Tie up loading spectrum.
It further, further include step S4；Step S4, one-dimensional loading is composed to simplify and generates eight grades of program spectrums:
One-dimensional loading spectrum is simplified to by eight grades of blocky loading spectrums using unequal interval method, i.e., most by the amplitude of one-dimensional loading spectrum
Big value obtains 8 grades of amplitudes multiplied by unequal interval proportionality coefficient；
Make low load to eight grades of blocky loading spectrums to cast out；Low load casts out 0.8 times that threshold value takes the 8th grade of amplitude；
Using upper equivalent method, the symmetrical loading that the symmetrical loading circulation in gamut is converted to 8 order of magnitude is followed
Ring obtains eight grades of program spectrums.
The present invention has the beneficial effect that:
1) with the quantitative description equivalent life reciprocal of fatigue damage, actual measurement load sample is examined with minimum testing time criterion
The confidence level of data shows that this test data meets 80% confidence level, and relative error limit is subsequent to lead to no more than ± 5%
Cross the confidence level for increasing test number (TN) to improve load data；
2) the irregular equal amplitude Two dimensional Distribution of actual measurement rainflow matrix is fitted using dimensional Gaussian Density Estimator herein, made
Optimal diagonal bandwidth is acquired with improvement Sheather-Jones method.The volume of rain-flow counting twice is taken to compose process, first time rain
Flow accounting infers that second of rain-flow counting is used for Density Estimator for equal amplitude extreme value, solves rain-flow counting and cuclear density
The distortion effect that estimation grouping selection generates when inconsistent.From the comparison that actual measurement rainflow matrix is composed with design load, use
The loading spectrum that this method compiles has the similar probability density distribution of height with actual measurement rainflow matrix, while also achieving to reality
The reasonable extrapolation for surveying rainflow matrix, has reached desired effect；
3) selecting threshold value when the low load of one-dimensional loading spectrum is cast out is 0.8 times of the 8th grade of load value, so that low load is cast out
Front and back, the frequency and reduce 99.33%, damage and only reduce 0.29%, it is low load cast out threshold value selection rationally, keep damage and base
The load frequency of loading spectrum is greatly reduced in the case that this is constant.
Other features and advantages of the present invention will illustrate in the following description, also, partial become from specification
It obtains it is clear that understand through the implementation of the invention.The objectives and other advantages of the invention can be by written explanation
Specifically noted structure is achieved and obtained in book, claims and attached drawing.
Detailed description of the invention
Attached drawing is only used for showing the purpose of specific embodiment, and is not to be construed as limiting the invention, in entire attached drawing
In, identical reference symbol indicates identical component.
Fig. 1 is loading spectrum of embodiment of the present invention Planning procedure figure；
Fig. 2 is torque sensor of embodiment of the present invention position schematic diagram；
Fig. 3 is test load of embodiment of the present invention rainflow matrix histogram；
Fig. 4 is test load of embodiment of the present invention rainflow matrix contour map；
Fig. 5 is two dimension of embodiment of the present invention loading spectrum histogram；
Fig. 6 is two dimension of embodiment of the present invention loading spectrum contour map；
Fig. 7 is that rainflow matrix of the embodiment of the present invention and one-dimensional loading compose logarithm and accumulate frequency curve graph
Fig. 8 is that one-dimensional loading spectrum logarithm accumulates frequency curve graph before the low load of the embodiment of the present invention is cast out；
Fig. 9 is that the low load of the embodiment of the present invention casts out rear one-dimensional loading spectrum logarithm accumulation frequency curve graph；
Figure 10 is that eight grades of programs of the embodiment of the present invention compose schematic diagram；
Figure 11 is the accumulated damage curve of one-dimensional loading spectrum before low load is cast out；
Figure 12 is the low accumulated damage curve for carrying and casting out rear one-dimensional loading spectrum.
Specific embodiment
Specifically describing the preferred embodiment of the present invention with reference to the accompanying drawing, wherein attached drawing constitutes the application a part, and
Together with embodiments of the present invention for illustrating the principle of the present invention.
As shown in Figure 1, the present embodiment loading spectrum preparation method, includes the following steps:
Step S1, the acquisition of endless-track vehicle torque load sample data and pretreatment；
Specifically include following sub-step:
Step S101, it carries out n and encloses endless-track vehicle real train test, acquire the transmission shaft charge number of every circle endless-track vehicle in real time
According to n independent random sample data of formation.
Specifically, torque signal is obtained as shown in Fig. 2, torque sensor is arranged on the input shaft of left side retarder,
It selects resistance strain gage as torque sensor, obtains torque signal by adhering resistance strain sheets and wireless telemetering.Meanwhile also
Synchro measure gear signal；It, can also synchro measure engine speed and rotating speed of transmission shaft letter for the driving status for monitoring vehicle
Number.
Real train test selects annular fluctuating dirt road, completes the test of 12 circles, the crawler belt by three veteran drivers
Gear of the vehicle on the road surface distributes and shift frequency is determined by driver according to surface conditions and driving habit completely, every circle
The load data of test is considered as an independent sample.Selected road surface is the dedicated road surface of creeper truck performance test, fluctuating journey
Degree and road conditions are able to reflect the feature of fluctuating dirt road, and also contain creeper truck under the random driving situation of driver and rise
The various operating conditions such as step, acceleration, braking, straight trip, turning, therefore obtained torque load data are tested as with press proof using every circle
This.
Step S102 carries out the high-frequency noise in rain stream filtering removal sample data to sample data.
Severe experimental condition can cause test macro centainly to interfere, while torque signal has transient characteristic, test
Signal inevitably introduces the ingredient unfavorable to torsional analysis.The undesirable constituents of this test raw payload data is mainly height
Frequency noise, high-frequency noise show as the load cycle of the frequency very amplitude very little, hardly to fatigue life of transmission shaft
It has an impact, but is a no small burden to loading spectrum establishment and fatigue loading.Tired damage is caused farthest to retain
The torque signal of wound avoids removing effective load cycle, by high-frequency noise by the filtering removal of rain stream, i.e., by casting out rain stream
The load cycle of minimum amplitude rank reaches above-mentioned purpose in matrix.
Step S103, Confidence test is carried out to sample size, when sample size is by examining, continuation is in next step；As not
Pass through, then increase test number (TN), is examined until passing through.
Specifically, the pseudo- of torque load sample data that n circle real train test obtains is calculated using TecWare software to damage
D, then by formulaEquivalent life is calculated, and then obtains logarithm equivalent life lgT, n is enclosed into the logarithm that test obtains
Equivalent life lgT is expressed as x1,x2,...,xn, calculate the average value of incrementWith standard deviation s.
By minimum testing time criterion formula
Judge whether experimental test frequency n meets the sample size requirements of given confidence level γ and relative error δ, t in formulaγFor
T corresponding with γ is distributed quantile.
It in actual use, can also be directly by the coefficient of variationFind required minimum testing time.
The present embodiment 12 encloses test data, as shown in table 1.The logarithm equivalent life of this test is obeyed with 95% confidence level
Normal distribution.
1 load sample logarithm equivalent life of table calculates
Confidence level γ=80% is taken, relative error limit δ=5% acquires minimum testing time n=8.1, and being rounded is 9, i.e.,
The minimum testing time done experiment on typical road surface annular fluctuating dirt road is 9 times, and calculating process is as shown in table 2.Because practical
Test circle number be 12 > 9, so according to statistical theory it may be concluded that when using this test average log equivalent life as
When the estimator of Parent Mean, meet 80% confidence level, relative error is no more than ± 5%.
The minimum testing time of table 2 calculates
Step S2, it is close that first time rain-flow counting, the deduction of equal amplitude extreme value, second of rain-flow counting, two-dimensional nucleus are passed sequentially through
Degree estimation, multi-state synthesis and extrapolation generate two-dimentional loading spectrum.
Step S2 includes following sub-step:
Step S201, pretreated torque load sample data is split statistics by gear, determines each gear
The range and group number of rain-flow counting.
The main count parameter of rain-flow counting is load range and load series (being grouped), and load range will include the shelves
All actual measurement torque signals in position, load series is the size of two-dimentional rainflow matrix, if load series is taken as n, obtained rain stream
Matrix is n × n rank matrix, and load series determines that the precision of rainflow matrix, general maximum take 512.
This test torque load sample data is as shown in table 3 by gear segmentation statistics,
3 torque load sample data of table is counted by gear
Step S202, the is carried out to torque load sample data according to the obtained rain-flow counting range of step S201 and grouping
Rain-flow counting obtains each gear rainflow matrix；
Specifically, using 4 rain-flow countings, each gear rainflow matrix Rain Flow Matrix (RFM) is obtained.
All gear rainflow matrixes that real train test torque data is counted merge, and draw load cycle frequency column
Figure and contour map are as shown in Figure 3-4.
Step S203, make equal amplitude extreme value according to each gear rainflow matrix to infer, obtain the equal amplitude extreme value of each gear.
Specifically, it obtains equal amplitude by each gear rainflow matrix to be independently distributed, using logarithm normal distribution or Weibull point
Cloth is fitted amplitude distribution, is fitted distribution of mean value using normal distribution, Three-paramerter Lognormal Distribution or three-parameter Weibull distribution,
The fitting parameter that the equal amplitude of each gear is independently distributed is obtained, each gear amplitude probability density function f is obtained by fitting parameterX(x)、
Each gear mean value probability density function fY(y)。
By each gear amplitude probability density functional integration formulaObtain each gear load
The maximum x of amplitudemax, each gear amplitude minimum takes the minimum amplitude of rainflow matrix；By load mean value probability density function product
Divide formulaAcquire the maximum y of each gear load mean valuemax, by load mean value probability density letter
Number integral formulaAcquire the minimum of each gear mean value.
This test fitting result such as table 4-5.
Each gear amplitude distribution fitting result of table 4
Each gear distribution of mean value fitting result of table 5
Using Anderson-Darling (AD) value as the goodness of fit, AD value is probability graph midpoint with a distance from fitting a straight line
The weighted sum of squares of size, value is smaller to illustrate that fitting of distribution must be better.Select the lesser distribution of AD average value as equal amplitude
Fitting distribution, as shown in table 4,5, the fitting of this test load amplitude distribution selection logarithm normal distribution, the fitting of mean value
Distribution selection normal distribution.
Then, by the lognormal probability density function f of load amplitudeX(x), the deduction for obtaining load amplitude maximum is public
FormulaThe maximum x of each gear load amplitude is obtained by the formulamax, each gear amplitude is minimum
Value takes the minimum amplitude of rainflow matrix；Similarly, each gear load is acquired by load mean value Density Function of Normal Distribution integral formula
The maximum and mean value minimum of mean value.
The present embodiment takes recommended value p=10-6。
Step S204, second of rain-flow counting is carried out, new rainflow matrix is generated；
Specifically, selecting step S203 is calculated the maximum value in all gear mean value maximum, mean value minimum
In minimum value, the maximum value in amplitude maximum and the minimum value in amplitude minimum, by the mean value range and amplitude chosen
Range is derived by torque range, as the parameter of second of rain-flow counting, then selected packet count, generate new rainflow matrix.
Step S205, using the two-dimentional Density Estimator based on Gaussian kernel, the density for obtaining the new rainflow matrix of each gear is estimated
Meter.
It, can be as rain-flow counting, to equal amplitude two-dimensional surface grid division, i.e., during application kernel density estimation method
Equal amplitude grouping.If the grouping of the equal amplitude of rain-flow counting and Density Estimator occurs inconsistent, it is easy to cause to estimate
Distribution distortion.
Specifically, including following sub-step:
Step S2051, with the torque range and the two-dimentional Density Estimator grid of packet count division of second of rain-flow counting；
Step S2052, Gaussian kernel is obtained using improvement Sheather-Jones plug-in type band width selection method (ISJ method)
Optimal diagonal bandwidthWith
Specifically, according to lower two formula, the optimal diagonal bandwidth of Gaussian kernel is calculatedWith
Wherein,
N+Be positive natural number；
Step S2053, dimensional Gaussian Density Estimator is made to new rainflow matrix；
Specifically, the Gaussian kernel with diagonal bandwidth matrices is calculated
Wherein, x=[x1,x2]TWith y=[y1,y2]T, the first variable of x and y are amplitude, and the second variable is mean value.
Dimensional Gaussian Density Estimator is calculated by the Gaussian kernel with diagonal bandwidth matrices
Step S2054, with the dimensional Gaussian Density Estimator of the equal amplitude range amendment respective notch of each gear, and will be close
Degree and normalization, obtain the density estimation of the new rainflow matrix of each gear；
Step S206, multi-state synthesis and extrapolation obtain two-dimentional loading spectrum；
Including following sub-step:
Step S2061, the load cycle that i-th of operating condition under each gear is calculated according to sample data occurs under unit mileage
Frequency
M is respective notch operating condition type sum, and the test miles of each operating condition of respective notch is respectively l1,l2,...,lm, by
Each operating loading circulation frequency of the respective notch that test statistics obtain is respectively n1,n2,...,nm；
Step S2062, the load cycle extrapolation frequency N that i-th of operating condition of each gear occurs is calculatedi=fipiL
L is the design service life mileage of respective notch vehicle, and the mileage travelled of each operating condition accounts for the hundred of service life mileage
Divide than being respectively p1,p2,...,pm, the mileage travelled under i-th of operating condition of respective notch is piL；
Step S2063, according to formulaObtain each gear multi-state two dimension loading spectrum；
In formula, NiIt extrapolates the load frequency for i-th operating condition of respective notch,For i-th of operating condition rain in early spring stream of respective notch
The dimensional Gaussian Density Estimator of matrix；
Step S2064, each gear multi-state two dimension load spectral synthesis is obtained into two-dimentional loading spectrum.
The extrapolation of each operating loading frequency of table 6
The D prism map and contour map of comprehensive obtained two-dimentional loading spectrum are as seen in figs. 5-6.Comparison actual measurement rain stream square
System of battle formations 3-4 can be seen that the two-dimentional loading spectrum Planning procedure based on Density Estimator that the present embodiment is proposed and can highly be fitted
Survey equal amplitude distribution.
Step S3, two-dimentional loading spectrum is converted into one-dimensional loading spectrum.
Specifically, one-dimensional loading spectrum is converted by two-dimentional loading spectrum, the load cycle that mean value is not zero must be damaged by fatigue
Hurt equivalent method and be converted to the load cycle that mean value is zero, most common method is to do mean stress using Goodman equation to repair
Just.The mean value of load cycle after correcting by mean stress is all zero, and only amplitude is different, so that two-dimentional loading spectrum be turned
It is changed to one-dimensional loading spectrum.
For extrapolation effect of the one-dimensional loading spectrum to rainflow matrix for observing the establishment of the present embodiment loading spectrum, rain stream will be now surveyed
Matrix is directly multiplied by extrapolation multipleThen one-dimensional amplitude is converted to mean stress amendment, made
It is as shown in Figure 7 that logarithm accumulates frequency curve, it can be seen that the one-dimensional loading spectrum that this method compiles has with actual measurement rainflow matrix
While likelihood probability Density Distribution, additionally it is possible to extrapolate to the rainflow ranges not measured, logarithm accumulates the outer of frequency curve
Pushed section point slope compared with surveying part becomes larger suddenly, it is meant that the rainflow ranges probability of occurrence of extrapolation is substantially less, and the frequency is tired
Product is slower, is consistent with situation is realized, realizes the reasonable extrapolation of rainflow matrix.
Step S4, one-dimensional loading is composed to simplify and generates eight grades of program spectrums.
Specifically, one-dimensional loading spectrum is simplified to by eight grades of blocky loading spectrums using unequal interval method, i.e., composed one-dimensional loading
Amplitude maximum obtain 8 grades of amplitudes multiplied by unequal interval proportionality coefficient.
Make low load to eight grades of blocky loading spectrums to cast out.Low load casts out 0.8 times that threshold value takes the 8th grade of amplitude of eight grades of spectrums.Fig. 8 institute
Be shown as it is low load cast out before, the frequency and be 1.43E+08, Fig. 9 show it is low load cast out after, the frequency and be 9.67E+05.
Using upper equivalent method, the symmetrical loading that the symmetrical loading circulation in gamut is converted to 8 order of magnitude is followed
Ring obtains eight grades of program block spectrums, as shown in Figure 10.Symmetrical loading circulation i.e. by amplitude between 1 grade and 2 grades, using equivalent damage
Method migration is recycled at the symmetrical loading that amplitude is 1 grade, and then the rest may be inferred.
Equivalent damage conversion formula is
In formula, NeqFor the equivalent cycle frequency, SiFor former load amplitude,mFor the power exponent of SN curve (stress- life).
Above-mentioned transformation rule can be converted into small magnitude high frequency time load cycle the load cycle of amplitude low frequency time, to load
Acceleration is played in lotus spectrum fatigue test.
After obtaining loading spectrum using the present embodiment preparation method, in conjunction with material of transmission shaft parameter, that is, nominal stress can be used
Method estimates the fatigue life of one-dimensional loading spectrum.The material of transmission shaft is 20Cr2Ni4A in this test, and material parameter is by reference book
In check in, consider influence fatigue strength principal element be effective stress concentration factor, be calculated by basic Miner rule
The fatigue damage amount of service life mileage one-dimensional loading spectrum, calculation formula are as follows
In formula, SiFor the amplitude of one-dimensional loading spectrum, niFor corresponding amplitude SiThe load frequency, SEFor corresponding infinite life NE=
107Fatigue limit,mFor double-log SN slope of a curve.
It is low load cast out before one-dimensional loading spectrum accumulated damage curve it is as shown in figure 11, damage and be 0.0101, be low loads house
Go the accumulated damage curve of rear one-dimensional loading spectrum as shown in figure 12, damage and be 0.0100.Compare it is low load cast out front and back, the frequency and
99.33% is reduced, damage and reduction 0.29% are keeping damaging it can be seen that the low load of this paper casts out threshold value selection rationally
Hurt and greatly reduce in the case where being basically unchanged the load frequency of loading spectrum.
In conclusion the embodiment of the invention provides a kind of preparation method of endless-track vehicle transmission shaft loading spectrum, this method
1) with the quantitative description equivalent life reciprocal of fatigue damage, actual measurement load sample is examined with minimum testing time criterion
The confidence level of data shows that this test data meets 80% confidence level, and relative error limit is subsequent to lead to no more than ± 5%
Cross the confidence level for increasing test number (TN) to improve load data.
2) the irregular equal amplitude Two dimensional Distribution of actual measurement rainflow matrix is fitted using dimensional Gaussian Density Estimator, using changing
Good Sheather-Jones method acquires optimal diagonal bandwidth.It is inconsistent to solve rain-flow counting and Density Estimator grouping selection
When the distortion effect that generates, propose a kind of new volume spectrum process for taking rain-flow counting twice, first time rain-flow counting is for equal
Amplitude extreme value infers that second of rain-flow counting is used for Density Estimator.From the comparison that actual measurement rainflow matrix and design load are composed
It sees, the loading spectrum compiled has the similar probability density distribution of height with actual measurement rainflow matrix, while also achieving to actual measurement
The reasonable extrapolation of rainflow matrix, has reached desired effect.
3) selecting threshold value when the low load of one-dimensional loading spectrum is cast out is 0.8 times of the 8th grade of load value, so that low load is cast out
Front and back, the frequency and reduction 99.33%, damage and only reduction 0.29% illustrate that the low load of this paper casts out threshold value and selects rationally, protecting
It holds damage and greatly reduces the load frequency of loading spectrum in the case where being basically unchanged.
It will be understood by those skilled in the art that realizing all or part of the process of above-described embodiment method, meter can be passed through
Calculation machine program is completed to instruct relevant hardware, and the program can be stored in computer readable storage medium.Wherein, institute
Stating computer readable storage medium is disk, CD, read-only memory or random access memory etc..
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by anyone skilled in the art,
It should be covered by the protection scope of the present invention.
Claims (9)
1. a kind of endless-track vehicle transmission shaft loading spectrum preparation method based on Density Estimator, which is characterized in that including walking as follows
It is rapid:
Step S1, the acquisition of endless-track vehicle torque transmission shaft load sample data and pretreatment；
Step S2, by pretreated torque load sample data pass sequentially through first time rain-flow counting, equal amplitude extreme value infer,
Second of rain-flow counting, two-dimentional Density Estimator, multi-state synthesis and extrapolation generate two-dimentional loading spectrum；
The step S2 includes the following steps:
Step S201, pretreated torque load sample data is split statistics by gear, determines each gear for the first time
The torque range and group number of rain-flow counting；
Step S202, according to the torque range of the obtained rain-flow counting of step S201 and grouping to each gear torque load sample number
According to first time rain-flow counting is carried out, each gear rainflow matrix is obtained；
Step S203, make equal amplitude extreme value according to each gear rainflow matrix to infer, obtain the equal amplitude extreme value of each gear；
Step S204, the maximum value in all gear mean value maximum that selecting step S203 is calculated, in mean value minimum
Minimum value, the maximum value in amplitude maximum and the minimum value in amplitude minimum, by the mean value range and amplitude model chosen
It encloses and is derived by torque range, as the torque range of second of rain-flow counting, then selected packet count, generate new rain stream square
Battle array；
Step S205, using the two-dimentional Density Estimator based on Gaussian kernel, the density estimation of the new rainflow matrix of each gear is obtained；Institute
Torque range and the packet count for stating two-dimentional Density Estimator are identical as the torque range of second rain-flow counting and packet count；
Step S206, multi-state synthesis and extrapolation obtain each operating condition extrapolation load frequency, each gear obtained in conjunction with step S205
The density estimation of new rainflow matrix obtains two-dimentional loading spectrum.
2. loading spectrum preparation method according to claim 1, it is characterised in that: the step S203 includes, by each gear
Rainflow matrix obtains equal amplitude and is independently distributed, using logarithm normal distribution or Weibull Distribution amplitude distribution, using normal state
Distribution, Three-paramerter Lognormal Distribution or three-parameter Weibull distribution are fitted distribution of mean value, obtain the equal amplitude of each gear and independently divide
The fitting parameter of cloth determines each gear amplitude probability density function f by fitting parameterX(x), each gear mean value probability density function
fY(y)；
By each gear amplitude probability density functional integration formulaObtain each gear load amplitude
Maximum xmax, each gear amplitude minimum takes the minimum amplitude of respective notch rainflow matrix；By load mean value probability density letter
Number integral formulaAcquire the maximum y of each gear load mean valuemax, close by load mean value probability
Spend functional integration formulaAcquire the minimum of each gear mean value.
3. loading spectrum preparation method according to claim 2, it is characterised in that: selection logarithm normal distribution or Weibull point
The lesser distribution of AD average value is distributed as the fitting of amplitude in cloth, selects normal distribution, Three-paramerter Lognormal Distribution or three
The lesser fitting of distribution distribution of mean value of AD average value in parameters of Weibull.
4. loading spectrum preparation method according to claim 1, it is characterised in that:
The step S205, including following sub-step:
Step S2051, with the torque range and the two-dimentional Density Estimator grid of packet count division of second of rain-flow counting；
Step S2052, the optimal diagonal bandwidth of Gaussian kernel is obtained using improvement Sheather-Jones plug-in type band width selection methodWith
Specifically, according to lower two formula, the optimal diagonal bandwidth of Gaussian kernel is calculatedWith
Wherein,
N is natural number；
Step S2053, dimensional Gaussian Density Estimator is made to new rainflow matrix；
Specifically, the Gaussian kernel with diagonal bandwidth matrices is calculated
Wherein, x=[x1,x2]TWith y=[y1,y2]T, the first variable of x and y are amplitude, and the second variable is mean value；
Dimensional Gaussian Density Estimator is calculated by the Gaussian kernel with diagonal bandwidth matrices
Step S2054, dimensional Gaussian Density Estimator is corrected with the equal amplitude range of each gear, and by density and normalization, obtained
To the density estimation of the new rainflow matrix of each gear.
5. loading spectrum preparation method according to claim 4, it is characterised in that: the step S206 is specifically included:
Step S2061, the load cycle of i-th of operating condition under each gear is calculated according to torque load sample data under unit mileage
The frequency of generation
M is respective notch operating condition type sum, and the test miles of each operating condition of respective notch is respectively l1,l2,...,lm, by testing
Counting each operating loading circulation frequency of obtained respective notch is respectively n1,n2,...,nm；
Step S2062, the load cycle extrapolation frequency N that i-th of operating condition of each gear occurs is calculatedi=fipiL
L is the design service life mileage of respective notch vehicle, and the mileage travelled of each operating condition accounts for the percentage of service life mileage
Respectively p1,p2,...,pm, the mileage travelled under i-th of operating condition of respective notch is piL；
Step S2063, according to formulaObtain each gear multi-state two dimension loading spectrum；
In formula, NiIt extrapolates the load frequency for i-th operating condition of respective notch,For the new rainflow matrix of i-th of operating condition of respective notch
Dimensional Gaussian Density Estimator；
Step S2064, each gear multi-state two dimension load spectral synthesis is obtained into two-dimentional loading spectrum.
6. loading spectrum preparation method according to claim 1, it is characterised in that:
The step S1 includes following sub-step:
Step S101, resistance strain gage is arranged in wireless telemetering on the input shaft of left side retarder and obtains torque signal, carries out n
Endless-track vehicle real train test is enclosed, the transmission shaft load data of every circle endless-track vehicle is acquired in real time, forms n independent random sample number
According to；Also synchro measure gear signal；
Step S102 carries out the high-frequency noise in rain stream filtering removal sample data to sample data.
7. loading spectrum preparation method according to claim 1 or 6, it is characterised in that: the step S1 further includes sample number
Confidence test step is measured, Confidence test is carried out to sample size, when sample size is by examining, continuation is in next step；As not
Pass through, then increase test number (TN), is examined until passing through；
The Confidence test step includes:
The pseudo- damage D that the torque load sample data that n circle test obtains is calculated using TecWare software, then by formulaEquivalent life is calculated, and then obtains logarithm equivalent life lgT, n is enclosed into the logarithm equivalent life lgT table that test obtains
It is shown as x1,x2,...,xn, calculate the average value of incrementWith standard deviation s；
By minimum testing time criterion formula
Judge whether experimental test frequency n meets the sample size requirements of given confidence level γ and relative error δ, t in formulaγFor with γ
Corresponding t is distributed quantile.
8. loading spectrum preparation method according to claim 1, it is characterised in that: further include step S3；
Step S3, mean stress is done using Goodman equation and corrects the load cycle that mean value is not zero by Fatigue Damage Equivalence
Method is converted to the load cycle that mean value is zero, so that two-dimentional loading spectrum is converted into one-dimensional loading spectrum.
9. loading spectrum preparation method according to claim 8, it is characterised in that: further include step S4；
Step S4, one-dimensional loading is composed to simplify and generates eight grades of program spectrums:
One-dimensional loading spectrum is simplified to by eight grades of blocky loading spectrums, i.e., the amplitude maximum composed one-dimensional loading using unequal interval method
8 grades of amplitudes are obtained multiplied by unequal interval proportionality coefficient；
Make low load to eight grades of blocky loading spectrums to cast out；Low load casts out 0.8 times that threshold value takes the 8th grade of amplitude；
Using upper equivalent method, the symmetrical loading that the symmetrical loading circulation in gamut is converted to 8 order of magnitude is recycled
It is composed to eight grades of programs.
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