CN111159827B - High-speed rail bearing probability fatigue reliability assessment method - Google Patents
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Abstract
The invention discloses a high-speed rail bearing probability fatigue reliability assessment method, which aims at L10The method comprises the steps of firstly quantifying the dispersibility of the material and the randomness of the load, and selecting random factor representative points based on a number theory point selection method; secondly, establishing a three-dimensional finite element simulation model of the high-speed rail bearing according to the selected representative points, further analyzing the contact stress of the bearing under the influence of random factors, and establishing a BP neural network agent model of the maximum contact stress; and then, the fatigue life of the bearing is analyzed by a finite element simulation method through load spectrum compilation and an S-N curve of a material, the accumulated damage of the bearing and the reliability smaller than the critical damage are further calculated according to the fatigue damage accumulation principle, and an effective method is provided for high-precision and high-efficiency evaluation of the failure physics and the fatigue life of the high-speed rail bearing.
Description
Technical Field
The invention belongs to the field of reliability of mechanical parts, and particularly relates to a high-speed rail bearing probability fatigue reliability assessment method.
Background
At present, China has become the world with the highest mileage, driving speed and traffic volume of high-speed railways. As a basic key part of a high-speed rail, the localization of a bearing is a key problem which needs to be solved by the high-speed rail technology in China. The bearing of the high-speed rail main transmission case bears high rotating speed, random load and strong impact in the operation process, and the physical failure is complex. L in international standard ISO rolling bearing rated dynamic load and rated service life10The lifetime is a test and calculation under a predetermined condition. The influence of random eccentric load, improper installation, material property dispersion and other factors on the L in the specific operation of the bearing10And correcting the life formula. The failure mechanism of the fatigue pitting corrosion of the high-speed rail rolling bearing is that under the continuous action of alternating contact stress, local surface metal of a rolling body or a raceway falls off, so that the bearing generates vibration and noise to fail. The bearing failure physics is described from the failure mechanism of the bearing based on the fatigue damage accumulation principle, and a data basis and a technical support can be provided for sample performance test and reliability evaluation in the bearing research and development process. However, the fatigue life is dispersed due to manufacturing errors, material property dispersion and load randomness, so that the error of estimating and predicting the bearing life according to a fixed value is large.
Disclosure of Invention
For L10The service life formula is complex to correct, load randomness and material dispersibility are not considered on the basis of a fatigue damage accumulation principle, and the invention provides a high-speed rail bearing probability fatigue reliability evaluation method.
The technical scheme of the invention is as follows: a high-speed rail bearing probability fatigue reliability assessment method comprises the following steps:
s1, quantifying the dispersibility and random working conditions of the high-speed rail bearing material, and determining a main failure mode and a failure mechanism;
s2, calculating random radial force and axial force borne by the bearing according to the uncertainty information of the high-speed rail bearing material and the random working condition quantized in the step S1, and selecting a random factor representative point;
s3, establishing a finite element model of the high-speed rail bearing according to the random factor representative points selected in the step S2, carrying out statics analysis, and analyzing the maximum contact stress at each random factor representative point.
And S4, establishing a neural network proxy model of the maximum contact stress under the random factors according to the maximum contact stress at each random factor representative point in the step S3.
And S5, compiling a load spectrum by adopting a rain flow counting method, and analyzing the fatigue life under each stress level by using a finite element simulation method according to the S-N curve of the material.
S6, establishing an S-N curve of the high-speed rail bearing according to the fatigue life of each stress level in the step S5, calculating the fatigue life and probability distribution under each working condition, and calculating the accumulated damage probability distribution and parameters thereof;
and S7, calculating the probability distribution and parameters of the critical accumulated damage, and further calculating the reliability of reaching the critical damage.
Further, step S2 selects a random factor representative point based on a number theory point selection method.
Further, the step S4 is to establish a BP neural network proxy model of the maximum contact stress of the bearing under random factors.
Further, in step S5, a load spectrum is specifically compiled by a rain flow counting method.
Further, the step S2 specifically includes the following sub-steps:
s21, calculating random radial force and axial force borne by the bearing according to the uncertainty information of the high-speed rail bearing material and the random working condition quantized in the step S1;
s22, obtaining a S-dimensional generated vector (N, h) by a grid Point (GLP) set in a standard independent space1,h2,...,hS) Further, a unit hypercube [ 01 ] is obtained from the formula (1)]SInner point set:
wherein N is the number of point sets to be constructed, hSIs Fibonacci sequence, and the Fibonacci sequence is defined by a recursive method as follows: h isj＝hj-1+hj-2,h0＝h11(n ═ 1, 2.., S), int (·) denotes taking the largest integer no less than or equal to that in parentheses;
s23, taking the limit of the normalized random variable as L, and carrying out scaling and translation transformation on the point set generated in the step S22 by using the formula (2) to obtain a square [ -L, L]SInner uniformly distributed point set:
θj,k＝2(xj,k-0.5)L,(k＝1,2,…,N,j＝1,2,…,S) (2)
and S24, transforming the sample points of the standard independent space to the sample points corresponding to the original space by utilizing Nataf inverse transformation, wherein the transformed sample points are input representative points.
Further, the step S3 specifically includes the following sub-steps:
s31, establishing a three-dimensional model of the high-speed rail bearing in three-dimensional drawing software;
s32, importing the high-speed rail bearing three-dimensional model established in the step S31 into ANSYS WORKBENCH;
s33, pre-processing the model imported in the step S32 such as network division, contact setting, constraint setting and the like;
s34, carrying out statics analysis on the model processed in the step S33 to obtain the maximum contact stress at each random factor representative point.
Further, the step S4 specifically includes the following sub-steps:
s41, setting the structural parameters of the neural network by taking the random factor representative points selected in the step S3 as input and the maximum contact stress at each representative point obtained in the step S34 as output;
and S42, training the neural network established in the step S41, and establishing a BP neural network agent model of the maximum contact stress under the action of random factors of the high-speed rail bearing.
Further, the step S5 specifically includes the following sub-steps:
s51, compiling a load spectrum by a rain flow counting method;
and S52, analyzing the fatigue life of the high-speed rail bearing under each stress level by using a finite element simulation method according to the load spectrum and the S-N curve of the material.
Further, the step S6 specifically includes the following sub-steps:
s61, according to the fatigue life of each stress level in the step S5, the fatigue life of each working condition is calculated according to the established S-N curve of the high-speed rail bearing, and the fatigue life distribution is evaluated.
S62, converting the probability distribution of the fatigue life into the probability distribution of the damage by adopting a one-to-one probability density conversion method according to the fatigue life and the distribution thereof calculated in S61:
fn(Nfi)dNfi＝fD(Di)dDi (3)
wherein f isn(. is a probability density function of fatigue life, fD(. is a probability density function of damage, NfiIs the fatigue life at the i-th stress level, DiDamage at the ith stress level.
And S63, calculating the cumulative damage distribution and the distribution parameters thereof according to the cumulative damage formula (4) and the damage distributions.
Wherein k represents the stress order, NfiDenotes the fatigue life at the i-th stress level, niRepresenting the actual number of cycles of the ith stress stage, DSExpressed as the accumulation of damage, r, at a certain number of cycles for each stress leveliIs the stress level correlation coefficient.
Further, the step S7 specifically includes the following sub-steps:
s71, calculating the critical damage and the distribution thereof according to the formula (5):
wherein N ismaxRepresenting the fatigue life value corresponding to the maximum first-order load in the applied load series, c and d are material constants, rmaxFor rate of lesion development, mmaxNumber of damaged nuclei for the material, DCRIs a critical fatigue damage.
S72, calculating the fatigue reliability by using a Monte Carlo simulation method according to the formula (6):
R＝P(ZD＝DCR-DS≥0) (6)
wherein D isSExpressed as the accumulation of damage at a certain number of cycles per stress level, DCRFor critical fatigue damage, P (-) is the probability that the bearing will not fail.
The invention has the beneficial effects that: for L10The method for evaluating the probability fatigue reliability of the high-speed rail bearing comprises the steps of firstly quantifying the dispersibility of materials and the randomness of loads, and selecting random factor representative points based on a number theory point selection method; secondly, establishing a three-dimensional finite element simulation model of the high-speed rail bearing according to the selected representative points, further analyzing the contact stress of the bearing under the influence of random factors, and establishing a BP neural network agent model of the maximum contact stress; and then, the fatigue life of the bearing is analyzed by a finite element simulation method through load spectrum compilation and an S-N curve of a material, the accumulated damage of the bearing and the reliability of reaching critical damage are further calculated according to the fatigue damage accumulation principle, and an effective method is provided for high-precision and high-efficiency failure physics depicting of the high-speed rail bearing and fatigue life assessment.
Drawings
Fig. 1 is a schematic flow chart of a high-speed rail bearing probability fatigue reliability evaluation method according to an embodiment of the invention.
Fig. 2 is a schematic view of a high-speed rail bearing according to an embodiment of the present invention, in which (a) is a three-dimensional model diagram of the high-speed rail bearing, and (b) is a maximum contact stress cloud diagram of the high-speed rail bearing.
FIG. 3 is a diagram of a neural network architecture for maximum contact stress in accordance with an embodiment of the present invention.
FIG. 4 is an S-N curve of GCr15 bearing steel according to an embodiment of the present invention.
Fig. 5 is a fatigue life probability distribution diagram of the high-speed rail bearing according to the embodiment of the invention during acceleration.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In order to improve the fatigue damage accumulation evaluation accuracy, the dispersion of material performance and the randomness of load need to be considered. In the absence of enough data to describe the dispersibility of the material, the elastic modulus of the material is described by intervals, the random working condition of the bearing is described by random variables, and how to select a test design point under the mixing uncertainty is a key problem. The scheme provides a high-speed rail bearing probability fatigue life assessment method under mixed uncertainty. The method has the advantages that the problem of test design point selection of multidimensional mixed uncertainty factors can be solved through number theory point selection; and a proxy model of the random factor representative point and the contact stress is established based on the BP neural network, so that the efficiency of probability fatigue life evaluation can be improved. The method can be an effective way for accurately depicting the high-speed rail bearing failure physics and improving the bearing performance evaluation precision, and the specific flow is shown in figure 1 and comprises the following steps:
s1, quantifying the dispersibility and random working conditions of the high-speed rail bearing material, and determining a main failure mode and a failure mechanism;
s2, calculating random radial force and axial force borne by the bearing according to the uncertainty information of the high-speed rail bearing material and the random working condition quantized in the step S1, and selecting random factor representative points based on a number theory point selection method;
s3, establishing a finite element model of the high-speed rail bearing according to the random factor representative points selected in the step S2, carrying out statics analysis, and analyzing the maximum contact stress at each random factor representative point.
S4, establishing a BP neural network proxy model of the maximum contact stress under the random factors according to the maximum contact stress at each random factor representative point in the step S3.
And S5, compiling a load spectrum by adopting a rain flow counting method, and analyzing the fatigue life under each stress level by using a finite element simulation method according to the S-N curve of the material.
S6, establishing an S-N curve of the bearing according to the fatigue life of each stress level in the step S5, and calculating the fatigue life and probability distribution under each working condition, and the accumulated damage probability distribution and parameters thereof;
and S7, calculating the probability distribution and parameters of the critical accumulated damage, and further calculating the reliability of reaching the critical damage.
In step S1, the embodiment of the present invention takes a high-speed rail bearing as an example, quantifies randomness and random conditions of the performance of the high-speed rail bearing material, and determines a main failure mode and a failure mechanism. The method specifically comprises the following steps:
s11, the uncertainty of the material performance of the high-speed rail bearing is described by interval variables, and the elastic modulus of each component material of the bearing is shown in Table 1;
s12, determining three random working conditions of the high-speed rail bearing in the invention: acceleration, uniform speed and deceleration. Respectively corresponding to high-speed rail outbound, operation and inbound;
s13, determining the main failure mode of the high-speed rail bearing as fatigue pitting;
s14, the failure mechanism of fatigue pitting corrosion is that under the action of load, contact stress is generated between the rolling body and the inner and outer raceways. When the bearing rotates, the contact stress is changed circularly, and after the bearing works for a plurality of times, the local surface metal of the rolling body or the raceway falls off, so that the bearing generates vibration and noise to lose efficacy.
TABLE 1 uncertainty description of high-speed rail bearing materials
| Component part | Material density/kg m-3 | Modulus of elasticity/GPa | Poisson ratio | Material |
| Inner ring | 7830 | [215 224] | 0.3 | GCr15 |
| Outer ring | 7830 | [215 224] | 0.3 | GCr15 |
| Roller | 7830 | [215 224] | 0.3 | GCr15 |
| Holding rack | 1370 | [6 10] | 0.3 | GRPA66 |
In step S2, according to the quantitative information of uncertainty of the high-speed rail bearing material and the random working condition determined in step S1, calculating the random radial force and the random axial force borne by the bearing, and selecting a random factor representative point based on a number theory point selection method specifically includes the following sub-steps:
s21, calculating according to the random working conditions determined in the step S1 to obtain the distribution of random radial force and axial force born by the bearing as shown in a table 2;
TABLE 2 radial and axial forces (KN) to which the bearing is subjected under different operating conditions
Method for quantifying modulus of elasticity of inner ring, outer ring and roller and cage of cage by interval variable for uncertainty of high-speed rail bearing material in steps S22 and S21Modulus of elasticity; the axial and radial forces experienced by the bearing are described by randomly distributed variables. Therefore, in the standard independent space, 4-dimensional generated vectors (N, h) are obtained by means of a grid Point (GLP) set1,h2,h3,h4) Further, a unit hypercube [ 01 ] is obtained from the formula (7)]SInner point set:
wherein, N is the number of point sets to be constructed, N is 30, hSIs Fibonacci sequence, and the Fibonacci sequence is defined by a recursive method as follows: h isj＝hj-1+hj-2,h0＝h11(n ═ 1, 2.., S), int (·) denotes taking the largest integer equal to or less than that in parentheses.
S23, taking the limit of the normalized random variable as L, where L is 2 in the present invention, and performing scaling and translation transformation on the point set generated in step S22 using equation (8) to obtain a square [ -L, L]SInner uniformly distributed point set:
θj,k＝2(xj,k-0.5)L,(k＝1,2,…,N,j＝1,2,…,S) (8)
and S24, transforming the sample points of the standard independent space to the sample points corresponding to the original space by utilizing Nataf inverse transformation, wherein the transformed sample points are input representative points.
In step S3, a finite element model of the high-speed rail bearing is built according to the random factor representative points selected in step S2, and a statics analysis is performed to analyze the maximum contact stress at each random factor representative point. The method specifically comprises the following steps:
s31, establishing a three-dimensional model of the high-speed rail bearing in three-dimensional drawing software, as shown in figure 2 (a);
s32, importing the high-speed rail bearing three-dimensional model established in the step S31 into ANSYS WORKBENCH;
s33, pre-processing the model imported in the step S32 such as network division, contact setting, constraint setting and the like;
s34, the model processed in step S33 is subjected to statics analysis, and the maximum contact stress at each random factor representative point is obtained, as shown in fig. 2 (b).
In step S4, a BP neural network proxy model of the maximum contact stress under random factors is established according to the maximum contact stress at each random factor representative point in step S3.
S41, setting the structural parameters of the neural network by taking the random factor representative points selected in the step S3 as input and the maximum contact stress at each representative point obtained in the step S34 as output, as shown in FIG. 3;
and S42, training the neural network established in the step S41, and establishing a BP neural network agent model of the maximum contact stress under the action of random factors.
In step S5, a load spectrum is constructed by rain flow counting, and fatigue life at each stress level is analyzed by finite element simulation based on the S-N curve of the material (as shown in FIG. 4). The method specifically comprises the following steps:
s51, compiling a load spectrum by a rain flow counting method;
and S52, analyzing the fatigue life of the high-speed rail bearing under each stress level by using a finite element simulation method according to the load spectrum and the S-N curve of the material.
In step S6, an S-N curve of the bearing is created based on the fatigue life at each stress level in step S5, and the fatigue life and probability distribution (fig. 5 is the fatigue life probability distribution at the time of acceleration of the high-speed rail bearing) under each condition are calculated and the cumulative damage probability distribution and parameters thereof are calculated. The method specifically comprises the following steps:
s61, according to the fatigue life of each stress level in the step S5, the fatigue life of each working condition is calculated according to the established S-N curve of the high-speed rail bearing, and the fatigue life distribution is evaluated.
S62, converting the probability distribution of the fatigue life into the probability distribution of the damage by adopting a one-to-one probability density conversion method according to the fatigue life and the distribution thereof calculated in S61:
fn(Nfi)dNfi＝fD(Di)dDi (9)
wherein f isn(. is a probability density function of fatigue life, fD(. is a probability density function of damage, NfiIs the fatigue life at the i-th stress level, DiDamage at the ith stress level.
S63, calculating the cumulative damage distribution and its distribution parameters from the cumulative damage formula (10) and the distribution of each damage.
Wherein k represents the stress order, NfiDenotes the fatigue life at the i-th stress level, niRepresenting the actual number of cycles of the ith stress stage, DSExpressed as the accumulation of damage, r, at a certain number of cycles for each stress leveliIs a stress correction factor.
In step S7, the critical cumulative damage probability distribution and parameters are calculated, and the reliability of reaching the critical damage is further calculated. The method specifically comprises the following steps:
s71, calculating the critical damage and the distribution thereof according to the formula (11):
wherein N ismaxRepresenting the fatigue life value corresponding to the maximum first-order load in the applied load series, c and d are material constants, rmaxFor rate of lesion development, mmaxNumber of damaged nuclei for the material, DCRIs a critical fatigue damage. It is proposed here to take
S72, calculating the fatigue reliability by using a Monte Carlo simulation method according to the formula (12):
R＝P(ZD＝DCR-DS≥0) (12)
wherein D isSExpressed as stress levelsAccumulation of damage under a certain number of cycles, DCRFor critical fatigue damage, p (-) is the probability that the bearing will not fail.
In summary, it can be seen that for L10The service life formula is modified complicatedly, and the probability fatigue reliability evaluation method for the high-speed rail bearing selects random factor representative points based on a number theory point selection method by quantifying the dispersibility of materials and the randomness of loads; secondly, establishing a three-dimensional finite element simulation model of the high-speed rail bearing according to the selected representative points, further analyzing the contact stress of the bearing under the influence of random factors, and establishing a BP neural network proxy model of the contact stress of the bearing under uncertain factors; and then analyzing the fatigue life of the bearing under each stress level by load spectrum compilation and finite element simulation methods, further calculating the accumulated damage of the bearing and the reliability of the accumulated damage smaller than the critical damage according to the fatigue damage accumulation principle, and providing an effective method for accurately depicting the failure physics and predicting the life.
Claims (9)
1. A high-speed rail bearing probability fatigue reliability assessment method comprises the following steps:
s1, quantifying the dispersibility and random working conditions of the high-speed rail bearing material, and determining a failure mode and a failure mechanism;
s2, calculating random radial force and axial force borne by the bearing according to the uncertainty information of the high-speed rail bearing material and the random working condition quantized in the step S1, and selecting a random factor representative point;
s3, establishing a finite element model of the high-speed rail bearing according to the random factor representative points selected in the step S2, carrying out statics analysis, and analyzing the maximum contact stress at each random factor representative point;
s4, establishing a BP neural network proxy model of the maximum contact stress under random factors according to the maximum contact stress at each random factor representative point in the step S3;
s5, compiling a load spectrum, and analyzing the fatigue life under each stress level by using a finite element simulation method according to an S-N curve of the material;
s6, establishing an S-N curve of the bearing according to the fatigue life of each stress level in the step S5, and calculating the fatigue life and probability distribution under each working condition, and the accumulated damage probability distribution and parameters thereof;
and S7, calculating the probability distribution and parameters of the critical accumulated damage, and further calculating the reliability of reaching the critical damage.
2. The method for evaluating the probability fatigue reliability of the high-speed rail bearing according to claim 1, wherein the step S2 is to select the random factor representative point based on a number theory point selection method.
3. The method for evaluating the probabilistic fatigue reliability of a high-speed rail bearing according to claim 1, wherein the step S5 is to compile a load spectrum by a rain flow counting method.
4. The method for evaluating the probability fatigue reliability of the high-speed rail bearing according to claim 2, wherein the step S2 specifically comprises the following sub-steps:
s21, calculating random radial force and axial force borne by the bearing according to the uncertainty information of the high-speed rail bearing material and the random working condition quantized in the step S1;
s22, obtaining a S-dimensional generated vector (N, h) by a grid Point (GLP) set in a standard independent space1,h2,...,hS) Further, a unit hypercube [ 01 ] is obtained from the formula (1)]SInner point set:
wherein N is the number of point sets to be constructed, hSIs Fibonacci sequence, and the Fibonacci sequence is defined by a recursive method as follows: h isj＝hj-1+hj-2,h0＝h11, where j 1,2, S, int (·) denotes taking the largest integer less than or equal to the parenthesis;
s23, taking the limit of the normalized random variable as L, and scaling the point set generated in the step S22 by using the formula (2)Translation transformation to obtain square [ -L, L [ -L [ ]]SInner uniformly distributed point set:
θj,k＝2(xj,k-0.5)L,k＝1,2,…,N,j＝1,2,…,S (2)
and S24, transforming the sample points of the standard independent space to the sample points corresponding to the original space by utilizing Nataf inverse transformation, wherein the transformed sample points are input representative points.
5. The method for evaluating the probability fatigue reliability of the high-speed rail bearing according to claim 4, wherein the step S3 specifically comprises the following sub-steps:
s31, establishing a three-dimensional model of the high-speed rail bearing in three-dimensional drawing software;
s32, importing the high-speed rail bearing three-dimensional model established in the step S31 into ANSYS WORKBENCH;
s33, pre-processing the model imported in the step S32 by network division, contact setting and constraint setting;
s34, carrying out statics analysis on the model processed in the step S33 to obtain the maximum contact stress at each random factor representative point.
6. The method for evaluating the probability fatigue reliability of the high-speed rail bearing according to claim 5, wherein the step S4 specifically comprises the following sub-steps:
s41, setting the structural parameters of the neural network by taking the random factor representative points selected in the step S3 as input and the maximum contact stress at each representative point obtained in the step S34 as output;
and S42, training the neural network established in the step S41, and establishing a BP neural network agent model of the maximum contact stress under the action of random factors.
7. The method for evaluating the probability fatigue reliability of the high-speed rail bearing according to claim 6, wherein the step S5 specifically comprises the following sub-steps:
s51, compiling a load spectrum by a rain flow counting method;
and S52, analyzing the fatigue life of the high-speed rail bearing at each stress level according to the load spectrum and the S-N curve of the material.
8. The method for assessing the probability fatigue reliability of the high-speed rail bearing according to claim 7, wherein the step S6 specifically comprises the following sub-steps:
s61, according to the fatigue life of each stress level in the step S5, the fatigue life of each working condition is calculated according to the S-N curve of the high-speed rail bearing, and the fatigue life distribution is evaluated;
s62, converting the probability distribution of the fatigue life into the probability distribution of the damage by adopting a one-to-one probability density conversion method according to the fatigue life and the distribution thereof calculated in S61:
fn(Nfi)dNfi＝fD(Di)dDi (3)
wherein f isn(. is a probability density function of fatigue life, fD(. is a probability density function of damage, NfiIs the fatigue life at the i-th stress level, DiDamage at the ith stress level;
s63, calculating the cumulative damage distribution and the distribution parameters thereof according to the cumulative damage formula (4) and the damage distributions;
wherein k represents the stress order, NfiDenotes the fatigue life at the i-th stress level, niRepresenting the actual number of cycles of the ith stress stage, DSExpressed as the accumulation of damage, r, at a certain number of cycles for each stress leveliIs the stress level correlation coefficient.
9. The method for assessing the probability fatigue reliability of the high-speed rail bearing according to claim 8, wherein the step S7 specifically comprises the following substeps:
s71, calculating the critical damage and the distribution thereof according to the formula (5):
wherein N ismaxRepresenting the fatigue life value corresponding to the maximum first-order load in the applied load series, c and d are material constants, rmaxFor rate of lesion development, mmaxNumber of damaged nuclei for the material, DCRCritical fatigue damage;
s72, calculating the fatigue reliability by using a Monte Carlo simulation method according to the formula (6):
R＝P(ZD＝DCR-DS≥0) (6)
wherein D isSExpressed as the accumulation of damage at a certain number of cycles per stress level, DCRFor critical fatigue damage, P (-) is the probability that the bearing will not fail.
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