A method for constructing a bench bearing test spectrum based on a combined torque and speed counting method

Abstract

The present invention discloses a method for constructing a bearing bench test spectrum based on a combined rotational speed and torque counting method, including: Step 1, obtaining and preprocessing the road operation data of the sample load spectrum; Step 2, performing combined rotational speed and torque counting on the preprocessed data; Step 3, constructing a damage model of the bearing; Step 4, extrapolating the original data; Step 5, compiling a multi-level program load spectrum. The present invention adopts a frequency extrapolation method combining a Gaussian kernel function with a K strengthening coefficient extrapolation to improve the authenticity of the data after the bearing load spectrum is extrapolated; according to the corresponding relationship between the rotational speed and the bearing fatigue life, the present invention proposes a load spectrum construction method based on combined rotational speed and torque counting, improving the accuracy of fatigue life analysis. At the same time, by constructing a multi-level spectrum image of the combined rotational speed and torque distribution, the analysis characteristics of the load spectrum are intuitively reflected.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability durability tests for automotive bearing parts, and relates to a method for constructing a bench spectrum based on combined counting of rotational speed and torque. Background Art

[0002] In automobiles, more than about 90% of the fractures can be attributed to fatigue failure of parts. Fatigue failure is a common and most harmful failure mode of automotive parts. Fatigue damage mostly occurs in the frame, leaf spring, helical spring, shaft and rod parts that bear alternating loads. Therefore, the importance of reliability durability analysis of vehicle part fatigue life cannot be underestimated in the process of vehicle forward development research.

[0003] In the process of analyzing vehicle reliability durability, as the top-level input of the entire process of durability forward research and development, if there is a statistical deviation between the load input result and the actual user load, it will greatly affect the subsequent design analysis, resulting in over-design or under-assessment problems. Therefore, load spectrum analysis is an important part of vehicle durability research and development. The conventional method for analyzing reliability durability requires obtaining the service life through the full-cycle load spectrum, but the data volume collected from the test road load spectrum cannot cover the load conditions throughout the life cycle. Therefore, it is necessary to use the test load samples to infer the extreme loads and their frequencies that may occur within the entire life cycle.

[0004] As a key method for obtaining the load distribution, the counting method is particularly important. For general non-rotating parts or shaft parts where the torque fluctuation is independent of their rotational motion, the rain flow counting method can be used. For parts such as bearings where the rotational speed affects the fluctuation frequency, the rotational rain flow counting method or the rotational torque histogram counting method needs to be used.

[0005] However, neither of the above two methods can well reflect the combined distribution law of rotational speed and torque, and cannot intuitively and efficiently reflect the influence of rotational speed and torque on the fatigue life of bearings. Therefore, in the process of selecting the load counting method in the present invention, attention is paid to the accuracy of combined consideration of rotational speed and torque. Therefore, the rotational speed-torque combined counting method is used to count the load of the bearing, and load extrapolation is carried out through the Gaussian kernel function combined with the K strengthening coefficient extrapolation, and a test spectrum construction method with great guiding significance for bearing reliability durability is constructed. Summary of the Invention

[0006] The object of the present invention is to provide a method for constructing a bench bearing test spectrum based on the combined torque and speed counting method. The present invention adopts a frequency extrapolation method that combines a Gaussian kernel function with a K strengthening coefficient extrapolation to improve the authenticity of the data after extrapolating the bearing load spectrum. And because the traditional analysis of the bearing force process inadequately considers factors such as bearing radial deformation, the present invention uses the method of piecewise interpolation after software simulation to calculate the bearing force to improve the accuracy of the force analysis result. Also, in view of the lack of analysis of the influence of speed on the construction result in the current bearing test spectrum construction process, and the speed directly determines the value of the fatigue life curve, therefore, according to the corresponding relationship between speed and bearing fatigue life, the present invention proposes a load spectrum construction method based on the combined counting of speed and torque, which improves the accuracy of fatigue life analysis. At the same time, by constructing a multi-level spectrum image of the combined speed-torque distribution, the analysis characteristics of the load spectrum are intuitively reflected.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A method for constructing a bearing bench test spectrum based on the combined speed and torque counting method, comprising:

[0009] Step 1: Obtain the road operation data of the sample load spectrum and, after preprocessing, take the preprocessed time-domain data;

[0010] Step 2: Perform combined speed and torque counting on the preprocessed time-domain data: Record the loading frequencies in each torque-speed interval of the preprocessed time-domain data by means of interval counting.

[0011] Step 3: Construct a damage model of the bearing: Conduct a bearing force analysis, calculate the equivalent dynamic load according to the analysis result, and then, in combination with the aISO correction coefficient considering the speed parameter, obtain a bearing life calculation formula with the bearing torque and speed as independent variables. Then, in combination with the combined counting result, construct a damage model of the bearing;

[0012] Step 4: Extrapolate the preprocessed data: According to the result of the bearing damage model and in combination with the target damage for bearing extrapolation, the K strengthening coefficient can be obtained. Then, the probability density function is obtained through kernel density estimation. After extrapolating the counting result obtained in Step 2 by combining the Gaussian kernel function with the K strengthening coefficient, a frequency matrix of speed and torque after extrapolation is obtained;

[0013] Step 5: Compile a multi-level program load spectrum: Divide the torque and speed into eight levels according to a certain ratio respectively. Use the Palmgren-Miner rule in combination with the S-N curve of the material for the frequency matrix of torque and speed after extrapolation in Step 4, and adopt the upward equivalent method to convert the frequencies in the 128*128-level small intervals into frequencies in the 8*8-level large intervals according to the equal damage conversion principle, so as to obtain an 8*8-level bench test spectrum of the bearing for speed and torque.

[0014] Optionally, the preprocessing in Step 1 includes outlier removal, over-threshold processing, and data resampling;

[0015] Outlier removal includes: performing a Fourier transform on the original data to obtain the original spectrum, filtering through Butterworth filtering, and screening out the torque data at each amplitude according to the frequency magnitude, which are divided into the main wave, the secondary wave, and the tertiary wave; removing the tertiary wave of the amplitude data segment less than ±1 Nm, and completing the preliminary filtering of invalid waves;

[0016] Over-threshold processing means that after outlier removal, the missing data is filled by means of piecewise interpolation;

[0017] Data resampling includes: resampling by interpolation at a specified frequency according to time, extracting non-repeating times, and performing interpolation at a fixed and unified sampling frequency to obtain the preprocessed time-domain data.

[0018] Optionally, in the process of Step 2 of rotational speed and torque joint counting, first divide the preprocessed time-domain data into small interval data with a size of 128*128 according to the rotational speed and torque target intervals, integrate the rotational speed n(t) in the i-th rotational speed and torque small interval over time t, and the corresponding time for each small interval is The number of torque segments in the small interval is m, and the integration result is recorded as the frequency Ni in this interval, and the frequencies of each interval are saved as a matrix;

[0019]

[0020] Optionally, in the process of Step 3 of constructing the bearing damage model, the calculation process of the bearing damage D is as follows:

[0021]

[0022] N Loading frequencies of each level of data, L nm The corresponding bearing life of each level is known.

[0023] Optionally, from Step 2, the loading frequencies corresponding to the rotational speed and torque of each level of the bearing before extrapolation can be obtained;

[0024] Bearing life before extrapolation:

[0025]

[0026] Among them, Cr is the basic dynamic load rating; m is the bearing life index, m = 3 for ball bearings, and m = 10 / 3 for roller bearings; a1 is the reliability correction factor; P is the equivalent dynamic load; a ISO The correction factor is a function of the rotational speed:

[0027]

[0028] aISO The specific calculation formula can be obtained by referring to the table according to the selected bearings; the contamination coefficient e of the automotive reducer bearings is selected as 0.8 - 0.9; the load fatigue limit C u can be obtained according to the bearing model on the supplier's official website; the lubrication condition of the bearing is expressed by the viscosity ratio κ, that is, the ratio of the actual kinematic viscosity to the reference kinematic viscosity:

[0029]

[0030] v is the actual kinematic viscosity, and the reference kinematic viscosity v1 depends on the bearing speed and the pitch diameter D pw , and is calculated according to the following formula:

[0031] When n < 1000 r / min,

[0032] v1 = 45000 * n -0.83 * D pw -0.5 ;

[0033] When n > 1000 r / min,

[0034] v1 = 4500 * n -0.5 * D pw -0.5 ;

[0035] P is the equivalent dynamic load, which can be calculated according to the force analysis of the bearing

[0036] P = X * A a + Y * A r ;

[0037] where A r is the radial force on the bearing, and A a is the axial force on the bearing. By setting several groups of bearing input torques T, after obtaining the fragment results of the bearing forces through software Romax finite element simulation calculation, interpolating the simulation results to obtain the fitting curve of the bearing forces with respect to the input torque T, and then substituting the test torque into the fitting curve to find the corresponding force results, the A r and A a can be obtained; X and Y are the distribution coefficients, and the equivalent dynamic loads at each torque level are obtained by combining the torque - force matrix.

[0038] Optionally, in step three:

[0039] The bearing life calculation formula at each torque speed is:

[0040]

[0041] f(T, n) represents that the bearing life at each torque speed can be simplified as a function of torque and speed.

[0042] Based on the finally calculated bearing lives at all levels and the load frequencies at all levels, the extrapolated front bearing damage matrix at the 128*128 level can be obtained:

[0043]

[0044] Based on the bearing damage matrix of this original data, the next step of load spectrum extrapolation can be carried out.

[0045] Optionally, in the process of extrapolating the original data in Step Four:

[0046] The overall load spectrum extrapolation adopts the method of combining the Gaussian kernel function with the K-strengthening coefficient extrapolation;

[0047] For the load extreme value extrapolation in the direct extrapolation process of the K-strengthening coefficient, the load function method is selected. The damage-frequency distribution of the original data is combined with various distributions for fitting and comparison. The distribution function with the smallest goodness of fit under the 90th percentile confidence level for each working condition is selected. Through the distribution goodness-of-fit test method, it is checked whether the initially selected fitting distribution model is accurate. The Anderson-Darling test statistic determines the goodness of fit:

[0048]

[0049] This test method compares AD 2 with the critical value of the corresponding distribution cluster. At the significance level α, the null hypothesis H0 is accepted or rejected; F n (x) represents the probability density distribution function of the experimental data, and F(x) represents the probability density distribution function of the distribution to be compared; among them, the smaller the AD value, the better the fitting effect of the distribution;

[0050] Furthermore, the probability density function corresponding to the data distribution is determined, and the inferred extreme value is obtained;

[0051] Based on the inferred extreme value and the required extrapolated target reliability, the total damage D of the target life can be determined 目标 , and the calculation of the K-strengthening extrapolation coefficient is obtained based on the following formula:

[0052]

[0053] The total damage D of the current test data 试验 is obtained from the damage model in Step Three.

[0054] Optionally, in Step Four described above, the process of combining the Gaussian kernel function with the K-strengthening coefficient extrapolation is as follows:

[0055] Assume that the random variable x follows an unknown probability density function Using the samples x1,..., x drawn from it nEstimate the distribution of the function Define a smooth function K(*) as the kernel function, and h as the smoothing parameter (bandwidth); the bandwidth h = b - a, that is, assume the length of the interval. Assume the number of samples falling into the interval [a, b] is k, then the relationship between the kernel function K(*) and the number of samples is:

[0056]

[0057] Then the probability density function obtained according to the kernel density estimation principle is:

[0058]

[0059] The selected Gaussian kernel function is:

[0060]

[0061] Its corresponding two-dimensional kernel density estimation is:

[0062]

[0063] Here, an adaptive bandwidth form is selected:

[0064] Introduce an adaptive factor λ i ;

[0065]

[0066] In the formula, λ i is the adaptive factor; is the probability density value at the point u i ;

[0067] g is calculated from

[0068]

[0069] ;

[0070] The final adaptive kernel density estimation is:

[0071]

[0072] N is the number of sample data;

[0073] After combining the extrapolation of the K strengthening coefficient and the extrapolation of the Gaussian kernel function, a set of frequency data at each level of rotational speed and torque after extrapolation that is extended in both frequency and rotational speed-torque is obtained:

[0074]

[0075] Optionally, during the process of compiling the multi-level program load spectrum in Step Five, since the data source of the frequency matrix for the combined speed-torque counting comes from two variables, speed and torque;

[0076] According to the principle of equivalent damage, the user's full-life cycle load spectrum under the extrapolated road conditions is reconstructed into a program loading spectrum as the loading input basis for durability or reliability tests; for the 128*128 level of extrapolated bearing damage obtained in Step Four, using the principle of equal damage conversion, it is converted into a relatively concise 8*8 level spectrum, and the proportionality coefficients of the 8-level spectrum are graded according to 1, 0.95, 0.85, 0.725, 0.575, 0.425, 0.275, and 0.125; the principle is:

[0077]

[0078] That is, the damage of each level in the 8*8 level spectrum is equal to the sum of the damage in the 128*128 level spectrum it includes. In the formula, N eq is the frequency corresponding to a set of torque and speed in the 8*8 level spectrum, and L eq is the bearing fatigue life corresponding to a set of speed and torque in the 8*8 level spectrum; in the formula, N i is the frequency corresponding to a set of speed and torque in the 128*128 level spectrum, and L i is the bearing fatigue life corresponding to a set of speed and torque in the 128*128 level spectrum; l is the number of small intervals of the 128-level spectrum included in the interval corresponding to one level in the eight-level spectrum.

[0079] The beneficial effects of the present invention are:

[0080] (1) During the process of extrapolating the load frequency, compared with the traditional extrapolation method, the present invention adopts an extrapolation method combining the Gaussian kernel function and the K strengthening coefficient. The extrapolation process fully considers the distribution characteristics of the original load, combines the advantages of the Gaussian kernel function in expanding the distribution interval and the K strengthening coefficient in linearly extrapolating the data frequency, and realizes that the extrapolated load spectrum not only meets the required number of cycles of the test, but also the load boundary is reasonably expanded. The load cycles that exist but are not collected in the extrapolated load spectrum are retained, improving the accuracy of load extrapolation.

[0081] (2) During the process of bearing force analysis, based on the traditional bearing force analysis calculation, the present invention combines the finite element software simulation results for piecewise interpolation calculation, considering the influence of factors such as the radial deformation of the bearing and the deflection deformation of the transmission shaft on the bearing force during the bearing force analysis process. The data obtained through finite element simulation improves the fitting degree of the force analysis result and the actual bearing force, and the fitting interpolation of the simulation results not only expands the limited simulation results to the full torque cycle but also saves the test time.

[0082] (3) According to the bearing life calculation formula, it can be known that the rotational speed parameter affects the reference kinematic viscosity and then affects the viscosity ratio, resulting in a change in the value of coefficient a during the calculation of life. However, in most current bearing test bench spectra loading processes, the influence of rotational speed is not considered. Therefore, the rotational speed-torque combined counting method adopted in the present invention can greatly improve the accuracy and authenticity of the bearing life analysis results. ISO Coefficient size changes, but in most current bearing test bench spectra loading processes, the influence of rotational speed is not considered. Therefore, the rotational speed-torque combined counting method adopted in the present invention can greatly improve the accuracy and authenticity of the bearing life analysis results. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] The drawings are used to provide a further understanding of the present invention and form a part of the specification. Together with the following specific embodiments, they are used to explain the present invention, but do not constitute a limitation to the present invention. In the drawings:

[0084] Figure 1 is a flowchart of the multi-stage bench spectrum construction method based on the rotational speed-torque combined counting method of the present invention;

[0085] Figure 2 is a schematic diagram of the multi-stage bench spectrum construction of the present invention. Each Ni and the corresponding torque and rotational speed are recorded and saved as a frequency matrix;

[0086] Figure 3 is the finally obtained 8×8 stage test spectrum for bearing rotational speed and torque, i.e., the required bearing bench test spectrum (in the figure, the torque is divided into 16 levels for easy analysis of the image). SPECIFIC EMBODIMENTS

[0087] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0088] The first part:

[0089] Describe the complete steps of the method of the present invention.

[0090] Combined with Figure 1 , the multi-stage bench spectrum construction method based on the rotational speed-torque combined counting method proposed by the present invention specifically includes the following steps:

[0091] Step 1: Obtain and preprocess the sample load spectrum road operation data: The original data directly collected by the sensor may have phenomena such as mutations, noises, and spikes due to the influence of the driving environment, interference signals, and buildings. Operations such as outlier rejection need to be performed to preprocess the original data.

[0092] The outliers are removed based on the Dalai criterion. Considering that there are a large number of small torque fluctuation signals in the torque load, a large number of small-amplitude and high-frequency load cycles will be formed. Such loads basically do not cause fatigue damage but will greatly increase the calculation amount and form data redundancy, that is, high-frequency noise. Therefore, such loads need to be removed. By performing Fourier transform on the original data, the original spectrum can be obtained. Through Butterworth filtering, the torque data at each amplitude can be screened out according to the frequency size, and divided into the main wave, secondary wave, and tertiary wave. Removing the tertiary wave with small amplitude and high frequency (amplitude data segment less than ±1 Nm) can complete the preliminary filtering of invalid waves.

[0093] The over-threshold processing means that after removing the abnormal data outside the required torque and speed range, the missing data is filled by the method of piecewise interpolation.

[0094] The reason for data resampling is that the sampling frequencies of each signal are inconsistent, and the data points of each signal cannot be made to correspond one by one in time. Therefore, in order to be able to perform the joint distribution statistics of each signal, all data is resampled to unify the sampling frequency. Resampling is performed by interpolation at the specified frequency of 10 Hz, the non-repeating time is extracted, and interpolation is performed at a fixed and unified sampling frequency.

[0095] Step 2: Perform joint counting of rotational speed and torque on the original data: Count the data at each torque and rotational speed by dividing the preprocessed time-domain data into intervals (generally, the torque and rotational speed are each divided into 128 levels), and integrate the rotational speed in time for each torque-rotational speed small interval:

[0096]

[0097] Record the frequency N in each torque-rotational speed interval i . Record and save each Ni and the corresponding torque and rotational speed as a frequency matrix. The result is as Figure 2 shown.

[0098] Step 3: Build a damage model: Calculate the damage process at each rotational speed and torque of the bearing. According to the fact that the damage of each level of bearing is equal to the loading frequency N of each level divided by the corresponding bearing life L of each level nm It can be known that:

[0099]

[0100] According to Step 2, the loading frequencies corresponding to each rotational speed and torque of the bearing before extrapolation can be obtained.

[0101] The life of the bearing before extrapolation can be known from "GB_T 6391-2010 Rolling bearings - Dynamic load ratings and rating life":

[0102]

[0103] where Cr is the basic dynamic load rating, which can be directly obtained by querying according to the bearing model; m is the bearing life index, m = 3 for ball bearings and m = 10 / 3 for roller bearings; a1 is the reliability correction factor; P is the equivalent dynamic load; a ISO The correction factor is a function of the rotational speed and is also related to the bearing contamination factor, the load fatigue limit, and the lubrication conditions:

[0104]

[0105] a ISO The specific calculation formula of a can be obtained by referring to the table according to the selected bearing. According to the reference materials: the contamination factor ec of the automotive reducer bearing is generally selected as 0.8 - 0.9; the load fatigue limit Cu can be obtained from the supplier's official website according to the bearing model; the lubrication condition of the bearing is represented by the viscosity ratio κ, that is, the ratio of the actual kinematic viscosity to the reference kinematic viscosity:

[0106]

[0107] The actual kinematic viscosity v is related to the lubricant characteristics, rotational speed, and operating temperature during the bearing operation. The lubricant characteristics refer to the viscosity grade of the lubricant, and there are special standards in ISO. The actual viscosity of the lubricant can be obtained by referring to the table or calculation according to the viscosity grade and operating temperature of the lubricant.

[0108] The reference kinematic viscosity v1 depends on the bearing rotational speed and the pitch diameter D pw and is calculated according to the following formula:

[0109] When n < 1000 r / min,

[0110] v1 = 45000 * n -0.83 * D pw -0.5 ;

[0111] When n > 1000 r / min,

[0112] v1 = 4500 * n -0.5 * D pw -0.5 ;

[0113] P is the equivalent dynamic load, which can be calculated according to the force analysis of the bearing

[0114] P = X * A a + Y * A r ;

[0115] where A r is the radial force on the bearing, A aLet \(F_a\) be the axial force on the bearing. By setting several groups of bearing input torques \(T\), after obtaining the fragmentary results of the bearing forces through finite element simulation calculation using the software Romax, interpolating the simulation results to obtain the fitting curve of the bearing force with respect to the input torque \(T\), and then substituting the test torque into the fitting curve to find the corresponding force results, the force corresponding to each level of torque \(A\) can be obtained. r And \(A\) a ; \(X\) and \(Y\) are distribution coefficients. Referring to the national standard GB_T 6391 - 2010, the equivalent dynamic load at each level of torque can be obtained by combining the torque - force matrix.

[0116] Finally, the bearing life calculation formula at each torque and speed can be simplified as:

[0117]

[0118] According to the bearing life at each level calculated finally and the load frequency at each level, the extrapolated front - bearing damage matrix at the 128 * 128 level can be obtained:

[0119]

[0120] Based on this bearing damage matrix of the original data, the next step of load spectrum extrapolation can be carried out.

[0121] Step 4. Extrapolate the original data: Use the method of combining the Gaussian kernel function with the \(K\) strengthening coefficient extrapolation for load spectrum extrapolation.

[0122] Step 4.1: \(K\) strengthening coefficient extrapolation:

[0123] Since the extrapolation of the \(K\) strengthening coefficient needs to be obtained based on the damage before and after extrapolation, as follows:

[0124]

[0125] That is, the extrapolation multiple = total damage of the target life / total damage of the current test data.

[0126] For the acquisition of the target damage \(D\) 目标 , it needs to be obtained through load extreme value extrapolation:

[0127] For load extreme value extrapolation, the load function method is selected. The damage - frequency distribution of the original data is combined with various distributions for fitting and comparison. The distribution function with the smallest goodness - of - fit under the 90 - percentile confidence level for each working condition is selected. The accuracy of the initially selected fitting distribution model can be tested through the distribution goodness - of - fit test method, and the Anderson - Darling test statistic is used to determine the goodness - of - fit:

[0128]

[0129] This test method determines the goodness - of - fit by comparing \(AD\) 2Based on the magnitudes of the corresponding distribution cluster critical values, at the significance level α, accept or reject the null hypothesis H0, where F n (x) represents the probability density distribution function of the experimental data, and F(x) represents the probability density distribution function of the distribution to be compared; the smaller the AD value, the better the fitting effect of the distribution.

[0130] Here, the damage per unit mileage of the user is used as the intensity index, and this index should be able to represent the original load damage intensity per unit mileage of 90% percentile users. Fit the Weibull distribution probability curve through the input of the original damage per unit mileage, and take the value corresponding to P = 0.9 in the probability curve as the damage target value d per unit mileage of 90% percentile users 90 . Then, combined with the target life mileage L 目标 , calculate the overall damage target D of the vehicle's full life cycle 目标 = d 90 * L 目标 .

[0131] According to Step 3, D can be calculated 试验 .

[0132] Substitute the overall damage target D of the vehicle's full life cycle 目标 and the test damage D 试验 to obtain the K strengthening coefficient.

[0133] Step 4.2: The extrapolation process of the Gaussian kernel function:

[0134] Assume that the distribution of the corresponding values x of each rotational speed and torque follows an unknown probability density function Use the samples x1,..., x n extracted from it to estimate the distribution of the function . Define a smooth function K(*) as the kernel function, and h as the smooth parameter (bandwidth). The bandwidth h = b - a, which is the length of the assumed interval. Assume that the number of samples falling into the interval [a, b] is k, then the relationship between the kernel function K(*) and the number of samples is:

[0135]

[0136] Then, according to the principle of kernel density estimation, the probability density function is:

[0137]

[0138] The selected Gaussian kernel function is:

[0139]

[0140] Its corresponding two-dimensional kernel density estimation is:

[0141]

[0142] For another factor affecting the probability density function under the principle of kernel density estimation, namely the bandwidth, there is an optimal bandwidth selection. The larger the bandwidth coefficient, the smoother the estimated density function curve will be, but it may lead to underfitting, that is, masking some characteristics of the original sample data; the smaller the bandwidth coefficient, it may lead to overfitting of the estimated density function curve and an increase in variance.

[0143] Here, an adaptive bandwidth form is adopted for selection:

[0144] Introduce an adaptive factor λ i ;

[0145]

[0146] In the formula, λ i is the adaptive factor; is the probability density value at point u i ; g is calculated from

[0147]

[0148] obtained.

[0149] Finally, the adaptive kernel density estimation is:

[0150]

[0151] N is the number of sample data. Substitute the torque and speed used in the estimation into the above x and y, and the adaptive kernel density estimation result can be obtained.

[0152] For the kernel density estimation after introducing the adaptive factor, the bandwidth can change with the data, being smaller in dense data areas and larger in sparse data areas. The probability density obtained by comparing with the traditional fixed bandwidth is closer to the actual distribution.

[0153] By combining the extrapolation of the K strengthening coefficient and the extrapolation of the Gaussian kernel function, a set of frequency data at each level of speed and torque after extrapolation that is extended in both frequency and speed-torque can be obtained:

[0154]

[0155] Step 5: Compile a multi-level program load spectrum. Divide the torque and rotational speed into eight levels according to a certain ratio respectively. For the frequency matrix of the extrapolated torque and rotational speed in Step 4, by using the Palmgren-Miner rule and combining the damage equivalence principle, adopt the upward equivalence method to convert the frequencies in the 128*128-level small intervals into frequencies in the 8*8-level large intervals. The proportionality coefficients of the 8 levels are classified as 1, 0.95, 0.85, 0.725, 0.575, 0.425, 0.275, and 0.125. The principle is as follows:

[0156]

[0157] That is, the damage of each level in the 8*8-level spectrum is equal to the sum of the damages in the 128*128-level spectrum it includes. In the formula, N eq is the frequency corresponding to a set of torque and rotational speed in the 8*8-level spectrum, and L eq is the bearing fatigue life corresponding to a set of rotational speed and torque in the 8*8-level spectrum; in the formula, N i is the frequency corresponding to a set of rotational speed and torque in the 128*128-level spectrum, and L i is the bearing fatigue life corresponding to a set of rotational speed and torque in the 128*128-level spectrum; l is the number of 128-level small intervals included in the interval corresponding to one level in the eight-level spectrum.

[0158] The finally obtained 8*8-level test spectrum of bearing rotational speed and torque is the required bearing bench test spectrum. As Figure 3 shown (in the figure, the torque is divided into 16 levels for easy analysis of the image).

[0159] The second part:

[0160] Analyze the feasibility of the present invention from a theoretical perspective:

[0161] (1) During the process of extrapolating the load frequency, compared with the traditional extrapolation method, the present invention adopts an extrapolation method combining the Gaussian kernel function and the K strengthening coefficient. The extrapolation process fully considers the distribution characteristics of the original load, combines the advantages of the Gaussian kernel function in expanding the distribution interval and the K strengthening coefficient in linearly extrapolating the data frequency, and realizes that the extrapolated load spectrum not only meets the required number of cycles of the test, but also the load boundary is reasonably expanded. The load cycles that exist but are not collected in the extrapolated load spectrum are retained, improving the accuracy of load extrapolation.

[0162] (2) During the bearing force analysis process, based on the traditional bearing force analysis and calculation, the present invention performs piecewise interpolation calculation in combination with the simulation results of finite element software, considering factors such as the radial deformation of the bearing and the deflection deformation of the transmission shaft on the bearing force during the bearing force analysis process. The data obtained through finite element simulation improves the fitting degree of the force analysis result with the actual bearing force, and fitting and interpolating the simulation results not only extends the limited simulation results to the full torque cycle but also saves the test time.

[0163] (3) According to the bearing life calculation formula, it can be seen that the rotational speed parameter affects the reference kinematic viscosity and then affects the viscosity ratio, causing the change in the magnitude of the a coefficient when calculating the life. However, the influence of rotational speed is not considered in the loading process of most current bearing test bench spectra. Therefore, the rotational speed-torque joint counting method adopted in the present invention can greatly improve the accuracy and authenticity of the bearing life analysis result. ISO In the embodiment of the present invention, in step 1, the rotational speed-torque characteristic parameter data collected by the sensor is preprocessed; based on this, in steps 2-5, the frequencies of torque and rotational speed under each working condition are jointly counted according to different vehicle driving conditions, and then the rotational speed and torque distribution under the expected life are extrapolated through the Gaussian kernel function combined with the K strengthening coefficient. The two parameters of torque and rotational speed that affect the reliability and durability of the reducer bearing are represented together in space, and then through the Palmgren-Miner rule combined with the equivalent damage conversion method, the upward equivalent method is used to convert it into a test bench test spectrum. In this way, after accurately and reasonably extrapolating the test load spectrum obtained, the accuracy of life analysis is greatly improved; at the same time, the three-dimensional load spectrum image is also convenient for more intuitive and efficient analysis of reliability and durability.

[0164] The above is only the embodiment of the present invention and is not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

[0165] The above is only the embodiment of the present invention and is not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A method for constructing a bearing bench test spectrum based on a combined torque and speed counting method, characterized in that Including: Step 1: Obtain the road operation data of the sample load spectrum, preprocess it, and take the preprocessed time-domain data; Step 2: Conduct torque-speed joint counting on the preprocessed time-domain data: Record the loading frequencies in each torque-speed interval by counting in intervals for the preprocessed time-domain data; Step 3. Construct a bearing damage model: Conduct a bearing force analysis. After calculating the equivalent dynamic load based on the analysis results, consider the a ISO correction factor of the rotational speed parameter to obtain a bearing life calculation formula with the bearing torque and rotational speed as independent variables, and then combine the combined counting results to construct a bearing damage model; Step 4: Extrapolate the preprocessed data: According to the results of the bearing damage model and in combination with the target damage for bearing extrapolation, the K strengthening coefficient can be obtained. Then, the probability density function is obtained through kernel density estimation. After extrapolating the counting results obtained in Step 2 using the Gaussian kernel function in combination with the K strengthening coefficient, a frequency matrix regarding torque-speed after extrapolation is obtained; Step 5: Compile a multi-level program load spectrum: Divide the torque and speed into eight levels according to certain ratios respectively. Use the Palmgren-Miner rule in combination with the S-N curve of the material for the frequency matrix of torque-speed after extrapolation in Step 4, and adopt the upward equivalent method to convert the frequencies in the 128*128-level small intervals into frequencies in the 8*8-level large intervals according to the equal damage conversion principle, obtaining an 8*8-level bench test spectrum of the bearing for torque-speed.

2. The method for constructing a bearing bench test spectrum based on the combined torque and speed counting method according to claim 1, characterized in that, The preprocessing in Step 1 includes outlier removal, over-threshold processing, and data resampling; The outlier removal includes: Performing Fourier transform on the original data to obtain the original spectrum, screening out the torque data at each amplitude according to the frequency magnitude through Butterworth filtering, and dividing them into the main wave, secondary wave, and tertiary wave; Removing the tertiary wave of the amplitude data segment less than ±1 Nm, completing the preliminary filtering of invalid waves; The over-threshold processing means that after outlier removal, the missing data is filled by piecewise interpolation; The data resampling includes: Interpolating at a specified frequency according to time for resampling, extracting non-repeating times, and interpolating at a fixed unified sampling frequency to obtain the preprocessed time-domain data.

3. The method for constructing a bearing bench test spectrum based on the combined torque and speed counting method according to claim 1 or 2, characterized in that In the process of torque and speed joint counting in the second step, the preprocessed time-domain data is first divided into small interval data with a size of 128*128 according to the torque and speed target intervals, and the speed n(t) in the i-th torque and speed small interval is integrated over time t. The corresponding time for each small interval is The number of torque segments in the small interval is m, and the integration result is recorded as the frequency N in this interval i , and the frequencies of each interval are saved as a matrix; 4. The method for constructing a bearing bench test spectrum based on the combined torque and speed counting method according to claim 1 or 2, characterized in that During the process of constructing the bearing damage model in Step 3, the calculation process of the bearing damage D is as follows: N is the data loading frequency at each level, and L nm is the corresponding bearing life at each level.

5. The method for constructing a bearing bench test spectrum based on the combined torque and speed counting method according to claim 1 or 2, characterized in that From Step 2, the loading frequencies corresponding to each level of torque-speed of the bearing before extrapolation can be obtained; The bearing life before extrapolation: where Cr is the basic dynamic load rating; m is the bearing life exponent, m = 3 for ball bearings and m = 10 / 3 for roller bearings; a1 is the reliability correction factor; P is the equivalent dynamic load; a ISO The correction factor is a function of the rotational speed: a ISO The specific calculation formula can be obtained by referring to the table according to the selected bearings; the contamination coefficient e of the automotive reducer bearings c is selected as 0.8 - 0.9; the load fatigue limit C u can be obtained from the supplier's official website according to the bearing model; the lubrication condition of the bearing is expressed by the viscosity ratio κ, that is, the ratio of the actual kinematic viscosity to the reference kinematic viscosity: ν is the actual kinematic viscosity, and the reference kinematic viscosity ν1 depends on the bearing speed n and the pitch diameter D pw , and is calculated according to the following formula: When n < 1000 r / min, ν1 = 45000 * n -0.83 * D pw -0.5 ; When n > 1000 r / min, ν1 = 4500 * n -0.5 * D pw -0.5 ; P is the equivalent dynamic load, which can be calculated according to the force analysis of the bearing P = X * A a + Y * A r ; Where A r is the radial force on the bearing, and A a is the axial force on the bearing. By setting several groups of bearing input torques T, after obtaining the fragmentary results of the bearing forces through software Romax finite element simulation calculation, interpolating the simulation results to obtain the fitting curve of the bearing forces with respect to the input torque T, and then substituting the test torque into the fitting curve to find the corresponding force results, the corresponding A r and A a can be obtained; X and Y are distribution coefficients, and the equivalent dynamic load at each torque level is obtained by combining the torque-force matrix.

6. The method for constructing a bearing bench test spectrum based on the combined torque and speed counting method according to claim 5, wherein In Step 3: The bearing life calculation formula at each torque-speed is: f(T,n) represents that the bearing life at each torque-speed can be simplified as a function of torque and speed; According to the finally calculated bearing life at each level and in combination with the load frequencies at each level, the bearing damage matrix before extrapolation at the 128*128 level can be obtained: Based on this bearing damage matrix of the original data, the next step of load spectrum extrapolation can be carried out.

7. The method for constructing a bearing bench test spectrum based on the combined torque and speed counting method according to claim 1 or 2, characterized in that During the extrapolation of the original data in Step 4: The overall load spectrum extrapolation adopts the method of extrapolation using the Gaussian kernel function in combination with the K strengthening coefficient; For the load extreme value extrapolation in the direct extrapolation process of the K strengthening coefficient, the load function method is selected. The damage-frequency distribution of the original data is combined with various distributions for fitting and comparison. The distribution function with the minimum goodness of fit under the 90th percentile confidence level for each working condition is selected. Through the distribution goodness-of-fit test method, it is checked whether the initially selected fitting distribution model is accurate. The Anderson-Darling test statistic determines the goodness of fit: This test method accepts or rejects the original hypothesis H0 at the significance level α by comparing the magnitude of AD 2 and the critical value of the corresponding distribution cluster; F n (x) represents the probability density distribution function of the experimental data, and F(x) represents the probability density distribution function of the distribution to be compared; the smaller the AD value, the better the fitting effect of the distribution; Furthermore, the probability density function corresponding to the data distribution is determined to obtain the inferred extreme value; The total damage D of the target life can be determined by extrapolating the target reliability according to the inferred extreme value in combination with the requirements. 目标 , the calculation of the K-strengthening extrapolation coefficient is obtained based on the following formula: Total damage D of current test data 试验 It can be obtained from the damage model in Step 3.

8. The method for constructing a bearing bench test spectrum based on the combined torque and speed counting method according to claim 1 or 2, characterized in that, In step four described above, the Gaussian kernel function combined with the K strengthening coefficient extrapolation process is as follows: Suppose the random variable x follows an unknown probability density function Using the samples x1,..., x drawn from it n For the function Estimate the distribution; define a smooth function K(*) as the kernel function, and h as the smoothing parameter - bandwidth; the bandwidth h = b - a, that is, assume the length of the interval, and assume the number of samples falling into the interval [a, b] is k. Then the relationship between the kernel function K(*) and the number of samples is: The probability density function obtained according to the principle of kernel density estimation is as follows: The selected Gaussian kernel function is: Its corresponding two-dimensional kernel density estimate is: Here, the form of adaptive bandwidth is adopted for selection: Introduce an adaptive factor λ i ; where λ i is the adaptive factor; is the probability density value at point u i ; g is obtained from calculation; The final adaptive kernel density estimate is: N is the number of sample data; After combining the K strengthening coefficient extrapolation and the Gaussian kernel function extrapolation, a set of frequency data at each torque speed after extrapolation with expansion in both frequency and torque speed is obtained:

9. The method for constructing a bearing bench test spectrum based on the combined torque and speed counting method according to claim 1 or 2, characterized in that In the process of compiling the multi-level program load spectrum in step five, since the data source of the frequency matrix corresponding to the speed-torque joint counting comes from two variables, speed and torque; According to the equivalent damage principle, the user's full life cycle load spectrum under the extrapolated road conditions is reconstructed into a program load spectrum as the loading input basis for durability or reliability tests; the 128*128 level bearing damage after extrapolation obtained in step four is converted into a relatively concise 8*8 level spectrum by the principle of equal damage conversion. The proportionality coefficients of the 8-level spectrum are graded according to 1, 0.95, 0.85, 0.725, 0.575, 0.425, 0.275, and 0.125; the principle is: That is, the damage of each level in the 8×8 level spectrum is equal to the sum of the damages in the 128×128 level spectrum it includes, where N eq is the frequency corresponding to a set of torque and speed in the 8×8 level spectrum, and L eq is the bearing fatigue life corresponding to a set of torque and speed in the 8×8 level spectrum; where N i,j is the frequency corresponding to a set of torque and speed in the 128*128 level spectrum, and L i,j is the bearing fatigue life corresponding to a set of torque and speed in the 128*128 level spectrum; l is the number of small intervals of the 128 level spectrum included in the interval corresponding to one level of the eight-level spectrum.

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