CN106886638A - A kind of endless-track vehicle power transmission shaft loading spectrum preparation method based on Density Estimator - Google Patents

Abstract

The present invention relates to a kind of endless-track vehicle power transmission shaft loading spectrum preparation method based on Density Estimator, comprise the following steps：Step S1, the collection of endless-track vehicle torque load sample data and pretreatment；Step S2, pass sequentially through for the first time rain-flow counting, equal amplitude extreme value twice infer, second rain-flow counting, two-dimentional Density Estimator, multi-state synthesis and the two-dimentional loading spectrum of extrapolation generation.The present invention takes rain-flow counting twice, and first time rain-flow counting result is inferred for equal amplitude extreme value, and second rain-flow counting result is used for Density Estimator, can well be fitted equal amplitude distribution, can do rationally extrapolation to actual measurement rainflow matrix again.The loading spectrum developed using this method has highly similar probability density distribution to actual measurement rainflow matrix, while also achieving the reasonable extrapolation to surveying rainflow matrix, has reached Expected Results.

Description

A kind of endless-track vehicle power transmission shaft loading spectrum preparation method based on Density Estimator

Technical field

The present invention relates to vehicle reliability technical field, more particularly to a kind of endless-track vehicle transmission based on Density Estimator Axle load composes preparation method.

Background technology

Loading spectrum is the basic foundation for carrying out vehicle stand under load parts Design of Mechanical Structure and fatigue test, and acquisition meets reality The loading spectrum of border service condition then turns into the important prerequisite of vehicle component Anti fatigue Design.Due to load cycle comprising amplitude and Two dimensions of average, can reflect the two-parameter rain flow method of characteristic of material mechanics as general in loading spectrum compilation process now Method of counting.Logarithm equivalent life probability distribution based on typical mission, Yan Chuliang proposes the intermediate value with high confidence level Fatigue load spectrum compilation theory, improves aircaft configuration and determines longevity and the reliability lengthened the life.Existing document is respectively in military creeper truck Transmission device durability evaluation has done correlative study with fatigue life prediction aspect.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 is obtained more and more Research and apply, but it then less is concerned with the combination for compiling spectrum flow.

Analysis of fatigue and the conventional loading spectrum of experiment include two-dimentional loading spectrum, one-dimensional loading spectrum and eight grades of program spectrums.It is military The transmission device of endless-track vehicle, running gear, track and driver behavior are different from general vehicle, and these features travel it Load is complicated and changeable, and the fault rate that power train parts occur fatigue rupture is high, therefore develops confidence level power train higher and determine Reliability lifting of the longevity loading spectrum to vehicle is significant.

The content of the invention

In view of above-mentioned analysis, the present invention is intended to provide a kind of endless-track vehicle power transmission shaft loading spectrum based on Density Estimator Preparing method, is used to solve the reliability disadvantages of existing endless-track vehicle power 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 power transmission shaft loading spectrum preparation method based on Density Estimator, comprises the following steps：Step S1, Endless-track vehicle torque transmission shaft load sample data is gathered and pre-processed；

Step S2, pretreated torque load sample data is passed sequentially through first time rain-flow counting, equal amplitude extreme value Infer, second rain-flow counting, two-dimentional Density Estimator, multi-state synthesize and the two-dimentional loading spectrum of extrapolation generation.

Further, the step S2 comprises the following steps：

Step S201, pretreated torque load sample data is carried out into segmentation statistics by gear, determine each gear Torque range for rain-flow counting and group number；

Step S202, the torque range of the rain-flow counting obtained according to step S201 and packet are to each gear torque load sample Notebook data carries out first time rain-flow counting, obtains each gear rainflow matrix；

Step S203, equal amplitude extreme value is made according to each gear rainflow matrix infer, obtain the equal amplitude extreme value of each gear；

Maximum, average in all gear average maximum that step S204, selecting step S203 are calculated is minimum The minimum value in maximum and amplitude minimum in minimum value, amplitude maximum in value, by the average scope and width chosen Value scope is derived by torque range, as second torque range 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 torque range and packet count phase of the torque range and packet count of the two-dimentional Density Estimator and second rain-flow counting Together；

Step S206, multi-state synthesis and extrapolation obtain each operating mode extrapolation load frequency, with reference to step S205 obtain it is each The density estimation of the new rainflow matrix of gear obtains two-dimentional loading spectrum.

Further, the step S203 includes that obtaining equal amplitude by each gear rainflow matrix is independently distributed, using logarithm just State is distributed 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 each gear amplitude is determined by fitting parameter Probability density function f_X(x), each gear average probability density function f_Y(y)；

By each gear amplitude probability density functional integration formulaObtain each gear load The maximum x of amplitude_max, each gear amplitude minimum takes the minimum amplitude of respective notch rainflow matrix；It is close by load average probability Degree functional integration formulaTry to achieve the maximum y of each gear load average_max, it is general by load average Rate density function integral formulaTry to achieve the minimum of each gear average.

Further, selection logarithm normal distribution or Weibull distribution in AD average values it is less distribution as amplitude fitting Distribution, selection normal distribution, Three-paramerter Lognormal Distribution or the less distribution plan of AD average values in three-parameter Weibull distribution Close distribution of mean value.

Further, the step S205, including following sub-step：

Step S2051, two-dimentional Density Estimator grid is divided with the torque range and packet count of second rain-flow counting；

Step S2052, using improvement Sheather-Jones plug-in types band width selection method (ISJ methods) obtain Gaussian kernel Optimal diagonal bandwidthWith

Specifically, according to lower two formula, the optimal diagonal bandwidth of Gaussian kernel is calculatedWith

Wherein,

N⁺It is 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, first variable of x and y is amplitude, and the second variable is average；

Dimensional Gaussian Density Estimator is calculated by the Gaussian kernel of the diagonal bandwidth matrices of band

Step S2054, the equal amplitude range amendment dimensional Gaussian Density Estimator with each gear, and by density and normalizing Change, obtain the density estimation of the new rainflow matrix of each gear.

Further, the step S206 is specifically included：

Step S2061, each gear is calculated according to torque load sample data under i-th load cycle of operating mode in unit The frequency occurred under journey

M is respective notch operating mode species sum, and the test miles of each operating mode of respective notch is respectively l₁,l₂,...,l_m, by Each operating loading circulation frequency of respective notch respectively n that test statistics are obtained₁,n₂,...,n_m；

Step S2062, the load cycle extrapolation frequency N for calculating the i-th operating mode appearance of each gear_i=f_ip_iL

L is the design service life mileage of respective notch vehicle, and the distance travelled of each operating mode accounts for the hundred of service life mileage Divide ratio respectively p₁,p₂,...,p_m, the distance travelled under i-th operating mode of respective notch is p_iL；

Step S2063, according to formulaObtain each gear multi-state two dimension loading spectrum；

In formula, N_iIt is i-th operating mode extrapolation load frequency of respective notch,It is i-th operating mode rain in early spring stream of respective notch The dimensional Gaussian Density Estimator of matrix；

Step S2064, by each gear multi-state two dimension load spectral synthesis obtain two-dimentional loading spectrum.

Further, the step 1 includes following sub-step：

Step S101, by resistance strain gage be arranged in left side decelerator input shaft on wireless telemetering obtain torque signal, N circle endless-track vehicle real train tests are carried out, Real-time Collection often encloses the power transmission shaft load data of endless-track vehicle, forms n independent random Sample data；Also synchro measure gear signal；

Step S102, the high-frequency noise in rain stream filtering removal sample data is carried out to sample data.

Further, the step 1 also includes sample size Confidence test step, and confidence level inspection is carried out to sample size Test, when sample size is by inspection, continue next step；As do not passed through, then increase test number (TN), until by inspection；

Described Confidence test step includes：

The pseudo- damage D of the torque load sample data that n circle experiments are obtained is calculated using TecWare softwares, then by public affairs FormulaEquivalent life is calculated, and then obtains logarithm equivalent life lgT, the logarithm equivalent life lgT that n circle experiments are obtained It is expressed as x₁,x₂,...,x_n, 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 formula_γFor The t distribution quantile corresponding with γ.

Further, also including step S3；Step S3, mean stress amendment is done using Goodman equations average is not zero Load cycle change into the load cycle that average is zero by Fatigue Damage Equivalence method, so as to two-dimentional loading spectrum is converted into one Dimension loading spectrum.

Further, also including step S4；Step S4, one-dimensional loading spectrum is simplified generation eight grades of programs spectrum：

One-dimensional loading spectrum is simplified to by eight grades of block loading spectrums using unequal interval method, will one-dimensional loading spectrum amplitude most Big value is multiplied by unequal interval proportionality coefficient and obtains 8 grades of amplitudes；

Make low load to eight grades of block loading spectrums to cast out；Low load casts out threshold value and takes the 8th grade 0.8 times 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 checked with minimum testing time criterion The confidence level of data, shows that this test data meets 80% confidence level, and relative error limit is no more than ± 5%, can subsequently lead to Cross the confidence level for increasing test number (TN) to improve load data；

2) made using the irregular actual measurement equal amplitude Two dimensional Distribution of rainflow matrix of dimensional Gaussian Density Estimator fitting herein Optimal diagonal bandwidth is tried to achieve with improvement Sheather-Jones methods.The volume of rain-flow counting twice is taken to compose flow, first time rain Flow accounting infers that second rain-flow counting is used for Density Estimator, solves rain-flow counting and cuclear density for equal amplitude extreme value The distortion effect produced when estimating that packet selection is inconsistent.From the contrast that actual measurement rainflow matrix is composed with design load, use The loading spectrum that this method is developed has highly similar probability density distribution to actual measurement rainflow matrix, while also achieving to reality The reasonable extrapolation of rainflow matrix is surveyed, Expected Results has been reached；

3) selection threshold value is the 8th grade 0.8 times of load value when the low load in one-dimensional loading spectrum is cast out so that low load is cast out It is front and rear, the frequency and reduce 99.33%, to damage and only reduce 0.29%, it is reasonable that low load casts out threshold value selection, is keeping damaging and base The loading frequency of loading spectrum is greatly reduced in the case that this is constant.

Other features and advantages of the present invention will be illustrated in the following description, also, the partial change from specification Obtain it is clear that or being understood by implementing the present invention.The purpose of the present invention and other advantages can be by the explanations write Specifically noted structure is realized and obtained in book, claims and accompanying drawing.

Brief description of the drawings

Accompanying drawing is only used for showing the purpose of specific embodiment, and is not considered as limitation of the present invention, in whole accompanying drawing In, identical reference symbol represents identical part.

Fig. 1 is embodiment of the present invention loading spectrum Planning procedure figure；

Fig. 2 is embodiment of the present invention torque sensor position schematic diagram；

Fig. 3 is embodiment of the present invention test load rainflow matrix block diagram；

Fig. 4 is embodiment of the present invention test load rainflow matrix contour map；

Fig. 5 is embodiment of the present invention two dimension loading spectrum block diagram；

Fig. 6 is embodiment of the present invention two dimension loading spectrum contour map；

Fig. 7 is that embodiment of the present invention rainflow matrix composes logarithm accumulation frequency curve map with one-dimensional loading

Fig. 8 is that the low load of the embodiment of the present invention casts out preceding one-dimensional loading spectrum logarithm accumulation frequency curve map；

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 map；

Figure 10 is eight grades of program spectrum schematic diagrames of the embodiment of the present invention；

Figure 11 is the low accumulated damage curve for carrying and casting out preceding one-dimensional loading spectrum；

Figure 12 is the low accumulated damage curve for carrying and casting out rear one-dimensional loading spectrum.

Specific embodiment

The preferred embodiments of the present invention are specifically described below in conjunction with the accompanying drawings, wherein, accompanying drawing constitutes the application part, and It is used to explain principle of the invention together with embodiments of the present invention.

As shown in figure 1, the present embodiment loading spectrum preparation method, comprises the following steps：

Step S1, the collection of endless-track vehicle torque load sample data and pretreatment；

Specifically include following sub-step：

Step S101, n circle endless-track vehicle real train tests are carried out, Real-time Collection often encloses the power transmission shaft charge number of endless-track vehicle 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 decelerator, Selection resistance strain gage obtains torque signal as torque sensor by adhering resistance strain sheets and wireless telemetering.Meanwhile, also Synchro measure gear signal；It is the transport condition of monitoring vehicle, can also synchro measure engine speed and rotating speed of transmission shaft letter Number.

The annular fluctuating dirt road of real train test selection, completes 12 circles and tests by three veteran drivers, the crawler belt Gear distribution and gearshift frequency of the car on the road surface are determined according to surface conditions and driving habit by driver, often enclosed completely The load data of experiment is considered as an independent sample.Selected road surface is the special road surface of creeper truck performance test, its fluctuating journey Degree and road conditions can reflect the feature of fluctuating dirt road, and creeper truck is also contains under the random driving situation of driver The various operating modes such as step, acceleration, braking, straight trip, turning, therefore the torque load data for obtaining are tested as with press proof using every circle This.

Step S102, the high-frequency noise in rain stream filtering removal sample data is carried out to sample data.

Severe experimental condition can cause certain interference to test system, while torque signal has transient characteristic, test Signal inevitably introduces the composition unfavorable to torsional analysis.The undesirable constituents of this experiment raw payload data is mainly height Frequency noise, high-frequency noise shows as the load cycle of the frequency very amplitude very little, and its fatigue life to power transmission shaft is hardly Influence is produced, 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, it is to avoid the effective load cycle of removal, filters removal, i.e., by casting out rain stream by high-frequency noise by 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 inspection, continue next step；As not Pass through, then increase test number (TN), until by inspection.

Specifically, the pseudo- damage of the torque load sample data that n circle real train tests are obtained is calculated using TecWare softwares D, then by formulaEquivalent life is calculated, and then obtains logarithm equivalent life lgT, the logarithm that n circle experiments are obtained Equivalent life lgT is expressed as x₁,x₂,...,x_n, 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 formula_γFor The t distribution quantile corresponding with γ.

In actual use, also can 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 experiment is obeyed with 95% confidence level Normal distribution.

The load sample logarithm equivalent life of table 1 is calculated

Confidence level γ=80% is taken, relative error limit δ=5% tries to achieve minimum testing time n=8.1, and it is 9 to round, i.e., The minimum testing time done experiment on the annular fluctuating dirt road of typical road surface is 9 times, and calculating process is as shown in table 2.Because actual The test number of turns is 12>9, thus according to statistical theory it could be assumed that：When the average log equivalent life tested using this as During the estimator of Parent Mean, 80% confidence level is met, relative error is no more than ± 5%.

The minimum testing time of table 2 is calculated

Step S2, pass sequentially through first time rain-flow counting, equal amplitude extreme value infer, second rain-flow counting, two-dimensional nucleus it is close Degree is estimated, multi-state synthesizes and the two-dimentional loading spectrum of extrapolation generation.

Step S2 includes following sub-step：

Step S201, pretreated torque load sample data is carried out into segmentation statistics by gear, determine each gear Scope for rain-flow counting and group number.

The main count parameter of rain-flow counting is load range and load series (being grouped), and load range will include the shelves The all actual measurement torque signals in position, load series is the size of two-dimentional rainflow matrix, if load series is taken as n, the rain stream for obtaining Matrix is n × n rank matrixes, and load series determines the precision of rainflow matrix, and general maximum takes 512.

This test torque load sample data presses gear segmentation statistics as shown in table 3,

The torque load sample data of table 3 is counted by gear

Step S202, the rain-flow counting scope obtained according to step S201 and packet carry out the to torque load sample data Rain-flow counting, obtains each gear rainflow matrix；

Specifically, using 4 rain-flow countings, each gear rainflow matrix Rain Flow Matrix (RFM) are obtained.

All gear rainflow matrixes that real train test torque data statistics is obtained are merged, load cycle frequency column is drawn Figure and contour map are as shown in Figure 3-4.

Step S203, equal amplitude extreme value is made according to each gear rainflow matrix infer, obtain the equal amplitude extreme value of each gear.

Specifically, obtain equal amplitude by each gear rainflow matrix to be independently distributed, using logarithm normal distribution or Weibull point Cloth is fitted amplitude distribution, and distribution of mean value is fitted 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 parameter_X(x)、 Each gear average probability density function f_Y(y)。

By each gear amplitude probability density functional integration formulaObtain each gear load The maximum x of amplitude_max, each gear amplitude minimum takes the minimum amplitude of rainflow matrix；Accumulated by load average probability density function Divide formulaTry to achieve the maximum y of each gear load average_max, by load average probability density letter Number integral formulaTry to achieve the minimum of each gear average.

This experiment 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) values as the goodness of fit, AD values are probability graph midpoints with a distance from fitting a straight line The weighted sum of squares of size, the smaller explanation fitting of distribution of its value must be better.The less distribution of selection AD average values is used 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 average Distribution selection normal distribution.

Then, by the lognormal probability density function f of load amplitude_XX (), the deduction for obtaining load amplitude maximum is public FormulaThe maximum x of each gear load amplitude is obtained by the formula_max, each gear amplitude is minimum Value takes the minimum amplitude of rainflow matrix；Similarly, each gear load is tried to achieve by load average Density Function of Normal Distribution integral formula The maximum and average minimum of average.

The present embodiment takes recommended value p=10^-6。

Step S204, second rain-flow counting is carried out, generate new rainflow matrix；

Specifically, maximum, average minimum in all gear average maximum that selecting step S203 is calculated In minimum value, the minimum value in maximum and amplitude minimum in amplitude maximum, by the average scope and amplitude chosen Scope is derived by torque range, as second parameter 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.

During application kernel density estimation method, can be as rain-flow counting, to equal amplitude two dimensional surface grid division, i.e., Equal amplitude packet.If the equal amplitude packet of rain-flow counting and Density Estimator occurs inconsistent, it is easy to cause what is estimated Distribution distortion.

Specifically, including following sub-step：

Step S2051, two-dimentional Density Estimator grid is divided with the torque range and packet count of second rain-flow counting；

Step S2052, using improvement Sheather-Jones plug-in types band width selection method (ISJ methods) obtain Gaussian kernel Optimal diagonal bandwidthWith

Specifically, according to lower two formula, the optimal diagonal bandwidth of Gaussian kernel is calculatedWith

Wherein,

N⁺It is 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, first variable of x and y is amplitude, and the second variable is average.

Dimensional Gaussian Density Estimator is calculated by the Gaussian kernel of the diagonal bandwidth matrices of band

Step S2054, the dimensional Gaussian Density Estimator with 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, each gear is calculated according to sample data under i-th load cycle of operating mode occur under unit mileage Frequency

M is respective notch operating mode species sum, and the test miles of each operating mode of respective notch is respectively l₁,l₂,...,l_m, by Each operating loading circulation frequency of respective notch respectively n that test statistics are obtained₁,n₂,...,n_m；

Step S2062, the load cycle extrapolation frequency N for calculating the i-th operating mode appearance of each gear_i=f_ip_iL

L is the design service life mileage of respective notch vehicle, and the distance travelled of each operating mode accounts for the hundred of service life mileage Divide ratio respectively p₁,p₂,...,p_m, the distance travelled under i-th operating mode of respective notch is p_iL；

Step S2063, according to formulaObtain each gear multi-state two dimension loading spectrum；

In formula, N_iIt is i-th operating mode extrapolation load frequency of respective notch,It is i-th operating mode rain in early spring stream of respective notch The dimensional Gaussian Density Estimator of matrix；

Step S2064, by each gear multi-state two dimension load spectral synthesis obtain two-dimentional loading spectrum.

Each operating loading frequency extrapolation of table 6

The D prism map and contour map of the two-dimentional loading spectrum for comprehensively obtaining are as seen in figs. 5-6.Contrast 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 proposed and can highly be fitted Survey equal amplitude distribution.

Step S3, two-dimentional loading spectrum is converted into one-dimensional loading spectrum.

Specifically, it is converted into one-dimensional loading by two-dimentional loading spectrum to compose, the load cycle that average must be not zero is damaged by fatigue Hinder equivalent method and change into the load cycle that average is zero, most common method is to do mean stress using Goodman equations to repair Just.All it is zero by the average of the load cycle after mean stress amendment, only amplitude is different, so as to two-dimentional loading spectrum be turned It is changed to one-dimensional loading spectrum.

It is the extrapolation effect of the one-dimensional loading spectrum to rainflow matrix of observation the present embodiment loading spectrum establishment, now will actual measurement rain stream Matrix is directly multiplied by extrapolation multipleThen one-dimensional amplitude is converted to mean stress amendment, is made Logarithm accumulation frequency curve is as shown in Figure 7, it can be seen that the one-dimensional loading spectrum that this method is developed has with actual measurement rainflow matrix While likelihood probability Density Distribution, additionally it is possible to which the rainflow ranges to not measuring are extrapolated, outside logarithm accumulation frequency curve Pushed section point slope compared with part is surveyed becomes suddenly big, it is meant that the rainflow ranges probability of occurrence of extrapolation is significantly less, and the frequency is tired out Product is relatively slow, is consistent with the situation of realization, realizes the reasonable extrapolation of rainflow matrix.

Step S4, one-dimensional loading spectrum is simplified generation eight grades of programs spectrum.

Specifically, one-dimensional loading spectrum is simplified to by eight grades of block loading spectrums using unequal interval method, will one-dimensional loading spectrum Amplitude maximum be multiplied by unequal interval proportionality coefficient and obtain 8 grades of amplitudes.

Make low load to eight grades of block loading spectrums to cast out.Low load casts out threshold value and takes eight grades of the 8th grade 0.8 times of amplitude of spectrums.Fig. 8 institutes It is shown as before low load casts out, the frequency and be 1.43E+08, Fig. 9 is shown after low load casts out, 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.Will amplitude between 1 grade and 2 grades symmetrical loading circulation, using equivalent damage , into the symmetrical loading circulation that amplitude is 1 grade, then the rest may be inferred for method migration.

Equivalent damage conversion formula is

In formula, N_eqIt is the equivalent cycle frequency, S_iIt is former load amplitude,_mIt is the power exponent of SN curves (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 carrying Acceleration is played in lotus spectrum fatigue test.

After obtaining loading spectrum using the present embodiment preparation method, with reference to material of transmission shaft parameter, you can use nominal stress The fatigue life of method estimation one-dimensional loading spectrum.The material of power transmission shaft is 20Cr2Ni4A in this experiment, and material parameter is by reference book In check in, it is considered to influence the principal element of fatigue strength for effective stress concentration factor, be calculated by basic Miner rules The fatigue damage amount of service life mileage one-dimensional loading spectrum, computing formula is as follows

In formula, S_iIt is the amplitude of one-dimensional loading spectrum, n_iIt is correspondence amplitude S_iThe load frequency, S_EIt is correspondence infinite life N_E= 10⁷Fatigue limit,_mIt is double-log SN slope of a curves.

It is low carry cast out preceding one-dimensional loading spectrum accumulated damage curve as shown in figure 11, damage and be 0.0101, be it is low carry house Go rear one-dimensional loading spectrum accumulated damage curve as shown in figure 12, damage and be 0.0100.Contrast it is low load cast out before and after, the frequency and 99.33% is reduced, 0.29% is damaged and reduce, it can be seen that the low load of this paper casts out threshold value selection rationally, is keeping damaging Hinder and greatly reduced in the case of being basically unchanged the loading frequency of loading spectrum.

In sum, a kind of preparation method of endless-track vehicle power transmission shaft loading spectrum, the method be the embodiment of the invention provides

1) with the quantitative description equivalent life reciprocal of fatigue damage, actual measurement load sample is checked with minimum testing time criterion The confidence level of data, shows that this test data meets 80% confidence level, and relative error limit is no more than ± 5%, can subsequently lead to Cross the confidence level for increasing test number (TN) to improve load data.

2) using the irregular actual measurement equal amplitude Two dimensional Distribution of rainflow matrix of dimensional Gaussian Density Estimator fitting, using changing Good Sheather-Jones methods try to achieve optimal diagonal bandwidth.It is inconsistent with Density Estimator packet selection to solve rain-flow counting When the distortion effect that produces, propose that a kind of new volume for taking rain-flow counting twice composes flow, first time rain-flow counting is used for equal Amplitude extreme value infers that second rain-flow counting is used for Density Estimator.In contrast from actual measurement rainflow matrix with design load spectrum See, the loading spectrum for developing has highly similar probability density distribution to actual measurement rainflow matrix, while also achieving to actual measurement The reasonable extrapolation of rainflow matrix, has reached Expected Results.

3) selection threshold value is the 8th grade 0.8 times of load value when the low load in one-dimensional loading spectrum is cast out so that low load is cast out It is front and rear, the frequency and reduce 99.33%, to damage and only reduce 0.29%, illustrate the low load of this paper, to cast out threshold value selection reasonable, in guarantor Hold the loading frequency damaged and loading spectrum is greatly reduced in the case of being basically unchanged.

It will be understood by those skilled in the art that all or part of flow of above-described embodiment method is realized, can be by meter Calculation machine program is completed to instruct the hardware of correlation, and described program can be stored in computer-readable recording medium.Wherein, institute It is disk, CD, read-only memory or random access memory etc. to state computer-readable recording medium.

The above, the only present invention preferably specific embodiment, but protection scope of the present invention is not limited thereto, Any one skilled in the art the invention discloses technical scope in, the change or replacement that can be readily occurred in, Should all be included within the scope of the present invention.

Claims (10)

1. a kind of endless-track vehicle power transmission shaft loading spectrum preparation method based on Density Estimator, it is characterised in that including following step Suddenly：

Step S1, the collection of endless-track vehicle torque transmission shaft load sample data and pretreatment；

Step S2, pretreated torque load sample data is passed sequentially through first time rain-flow counting, equal amplitude extreme value infer, Second rain-flow counting, two-dimentional Density Estimator, multi-state synthesis and the two-dimentional loading spectrum of extrapolation generation.

2. loading spectrum preparation method according to claim 1, it is characterised in that：The step S2 comprises the following steps：

Step S201, pretreated torque load sample data is carried out into segmentation statistics by gear, determine each gear for the first time The torque range and group number of rain-flow counting；

Step S202, the torque range of the rain-flow counting obtained according to step S201 and packet are 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, equal amplitude extreme value is made according to each gear rainflow matrix infer, obtain the equal amplitude extreme value of each gear；

In maximum, average minimum in all gear average maximum that step S204, selecting step S203 are calculated Minimum value, amplitude maximum in maximum and amplitude minimum in minimum value, by the average scope and amplitude model chosen Enclose and be derived by torque range, as second torque range 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, obtain the density estimation of the new rainflow matrix of each gear；Institute State the torque range and packet count of two-dimentional Density Estimator identical with the torque range and packet count of second rain-flow counting；

Step S206, multi-state synthesis and extrapolation obtain each operating mode extrapolation load frequency, with reference to each gear that step S205 is obtained The density estimation of new rainflow matrix obtains two-dimentional loading spectrum.

3. loading spectrum preparation method according to claim 2, 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 fitting distribution of mean value, obtain the equal amplitude of each gear and independently divide The fitting parameter of cloth, each gear amplitude probability density function f is determined by fitting parameter_X(x), each gear average probability density function f_Y(y)；

By each gear amplitude probability density functional integration formulaObtain each gear load amplitude Maximum x_max, each gear amplitude minimum takes the minimum amplitude of respective notch rainflow matrix；By load average probability density letter Number integral formulaTry to achieve the maximum y of each gear load average_max, it is close by load average probability Degree functional integration formulaTry to achieve the minimum of each gear average.

4. loading spectrum preparation method according to claim 3, it is characterised in that：Selection logarithm normal distribution or Weibull point The less distribution of AD average values is distributed as the fitting of amplitude in cloth, selection normal distribution, Three-paramerter Lognormal Distribution or three The less fitting of distribution distribution of mean value of AD average values in parameters of Weibull.

5. loading spectrum preparation method according to claim 2, it is characterised in that：

The step S205, including following sub-step：

Step S2051, two-dimentional Density Estimator grid is divided with the torque range and packet count of second rain-flow counting；

Step S2052, using improvement Sheather-Jones plug-in types band width selection method (ISJ methods), to obtain Gaussian kernel optimal Diagonal bandwidthWith

Specifically, according to lower two formula, the optimal diagonal bandwidth of Gaussian kernel is calculatedWith

$t_{X_1}={\left(\frac{{\widehat{\mathrm{\ψ}}}_{0,2}^{3/4}}{4\mathrm{\π}N{\widehat{\mathrm{\ψ}}}_{2,0}^{3/4}({\widehat{\mathrm{\ψ}}}_{1,1}+\sqrt{{\widehat{\mathrm{\ψ}}}_{2,0}{\widehat{\mathrm{\ψ}}}_{0,2}})}\right)}^{1/3}$

$t_{X_2}={\left(\frac{{\widehat{\mathrm{\ψ}}}_{2,0}^{3/4}}{4\mathrm{\π}N{\widehat{\mathrm{\ψ}}}_{0,2}^{3/4}({\widehat{\mathrm{\ψ}}}_{1,1}+\sqrt{{\widehat{\mathrm{\ψ}}}_{2,0}{\widehat{\mathrm{\ψ}}}_{0,2}})}\right)}^{1/3}$

Wherein,

N⁺It is 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

$\mathrm{\φ}(x,y)=\frac{1}{2\mathrm{\π}\sqrt{t_{X_1}{t}_{X_2}}}{e}^{-\frac{{(x_1-y_1)}^2}{2t_{X_1}}-\frac{{(x_2-y_2)}^2}{2t_{X_2}}}$

Wherein, x=[x₁,x₂]^TWith y=[y₁,y₂]^T, first variable of x and y is amplitude, and the second variable is average；

Dimensional Gaussian Density Estimator is calculated by the Gaussian kernel of the diagonal bandwidth matrices of band

$\hat{f}\left(x\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}\mathrm{\φ}(x,y_i);$

Step S2054, the equal amplitude range amendment dimensional Gaussian Density Estimator with each gear, and by density and normalization, obtain To the density estimation of the new rainflow matrix of each gear.

6. loading spectrum preparation method according to claim 5, it is characterised in that：The step S206 is specifically included：

Step S2061, each gear is calculated according to torque load sample data under i-th load cycle of operating mode under unit mileage The frequency of generation

$f_i=\frac{n_i}{l_i},i=1,2,...,m$

M is respective notch operating mode species sum, and the test miles of each operating mode of respective notch is respectively l₁,l₂,...,l_m, by testing Each operating loading circulation frequency of respective notch respectively n that statistics is obtained₁,n₂,...,n_m；

Step S2062, the load cycle extrapolation frequency N for calculating the i-th operating mode appearance of each gear_i=f_ip_iL

L is the design service life mileage of respective notch vehicle, and the distance travelled of each operating mode accounts for the percentage of service life mileage Respectively p₁,p₂,...,p_m, the distance travelled under i-th operating mode of respective notch is p_iL；

Step S2063, according to formulaObtain each gear multi-state two dimension loading spectrum；

In formula, N_iIt is i-th operating mode extrapolation load frequency of respective notch,It is the respective notch new rainflow matrix of i-th operating mode Dimensional Gaussian Density Estimator；

Step S2064, by each gear multi-state two dimension load spectral synthesis obtain two-dimentional loading spectrum.

7. loading spectrum preparation method according to claim 1, it is characterised in that：

The step 1 includes following sub-step：

Step S101, by resistance strain gage be arranged in left side decelerator input shaft on wireless telemetering obtain torque signal, carry out n Circle endless-track vehicle real train test, Real-time Collection often encloses the power transmission shaft load data of endless-track vehicle, forms n independent random sample number According to；Also synchro measure gear signal；

Step S102, the high-frequency noise in rain stream filtering removal sample data is carried out to sample data.

8. the loading spectrum preparation method according to claim 1 or 7, it is characterised in that：The step 1 also includes sample size Confidence test step, Confidence test is carried out to sample size, when sample size is by inspection, continues next step；As do not led to Cross, then increase test number (TN), until by inspection；

Described Confidence test step includes：

The pseudo- damage D of the torque load sample data that n circle experiments are obtained is calculated using TecWare softwares, then by formulaEquivalent life is calculated, and then obtains logarithm equivalent life lgT, the logarithm equivalent life lgT tables that n circle experiments are obtained It is shown as x₁,x₂,...,x_n, calculate the average value of incrementWith standard deviation s；

By minimum testing time criterion formula

$\mathrm{\δ}=\left|\frac{{\mathrm{st}}_{\mathrm{\γ}}}{\stackrel{\‾}{x}\sqrt{n}}\right|$

Judge whether experimental test frequency n meets the sample size requirements of given confidence level γ and relative error δ, t in formula_γIt is and γ Corresponding t distribution quantiles.

9. loading spectrum preparation method according to claim 1, it is characterised in that：Also include step S3；

Step S3, the load cycle that is not zero for average by mean stress amendment is done using Goodman equations by Fatigue Damage Equivalence Method changes into the load cycle that average is zero, so as to two-dimentional loading spectrum is converted into one-dimensional loading spectrum.

10. loading spectrum preparation method according to claim 9, it is characterised in that：Also include step S4；

Step S4, one-dimensional loading spectrum is simplified generation eight grades of programs spectrum：

One-dimensional loading spectrum is simplified to by eight grades of block loading spectrums using unequal interval method, will one-dimensional loading spectrum amplitude maximum It is multiplied by unequal interval proportionality coefficient and obtains 8 grades of amplitudes；

Make low load to eight grades of block loading spectrums to cast out；Low load casts out threshold value and takes the 8th grade 0.8 times of amplitude；

Using upper equivalent method, the symmetrical loading that the symmetrical loading circulation in gamut is converted to 8 order of magnitude is circulated To eight grades of program spectrums.