CN115713024B - Bearing load-temperature-stress equivalent method based on symbolic regression algorithm - Google Patents

Bearing load-temperature-stress equivalent method based on symbolic regression algorithm Download PDF

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CN115713024B
CN115713024B CN202310010494.0A CN202310010494A CN115713024B CN 115713024 B CN115713024 B CN 115713024B CN 202310010494 A CN202310010494 A CN 202310010494A CN 115713024 B CN115713024 B CN 115713024B
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contact line
bearing
load
temperature
radial load
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CN115713024A (en
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杨冰
王栓程
周书蔚
肖守讷
阳光武
朱涛
王明猛
陈东东
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Southwest Jiaotong University
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Abstract

The invention relates to the technical field of bearing performance detection, and provides a bearing load-temperature-stress equivalent method based on a symbolic regression algorithm. On the basis of a finite element analysis technology, the method combines a symbol regression algorithm to train data obtained through finite element analysis calculation, obtains equivalent association function expressions among the bearing radial load-axial load, the radial load-temperature and the radial load-axial load-temperature, establishes the equivalent relation between the bearing load-temperature and verifies the effectiveness of the equivalent association function expression, and thereby provides reliable simulation support for establishing a single bearing stand test bench.

Description

Bearing load-temperature-stress equivalent method based on symbolic regression algorithm
Technical Field
The invention relates to the technical field of bearing performance detection, in particular to an equivalent simulation detection method of bearing performance, and particularly relates to a bearing load-temperature-stress equivalent method based on a symbolic regression algorithm.
Background
The high-speed rail is used as an important mark of the modernization of transportation and embodies the level of national industrialization. The transmission system bearing is used as an important guarantee for the high-speed running of the railway vehicle, and the service performance of the transmission system bearing has important influence on the safety of the railway vehicle. When designing the reliability of the bearing of the high-speed railway transmission system, design researchers need to comprehensively consider the factors such as load, temperature, vibration, flow field and the like borne by the bearing, and generally adopt a control variable method to explore the relationship between each influencing factor and the reliability of the system. In order to verify whether a bearing meets a reliability design standard, a bench test of a high-speed rail transmission system is needed, and how to realize equivalent simulation of service conditions of multi-field coupling of bearing load, vibration, flow field, temperature and the like based on a transmission system multi-physical field coupling theory and method is one of main difficulties in realizing full-parameter simulation of the transmission system bearing by breaking through a bench simulation reproduction technology of key parameters of the service state of the transmission system.
In the existing bearing stand test, an axial load loading dynamic actuator is often required to be arranged in a test stand in order to research the influence of axial load on a bearing, and meanwhile, an environment box is often required to be arranged in order to realize the simulation of the temperature rise effect of the bearing so as to research the influence of temperature on the bearing, so that the structure of the test stand is very complex and a large amount of funds are required to be consumed. Therefore, how to establish a single bearing stand test bed by using limited resources is a problem which needs to be solved urgently at present.
Disclosure of Invention
The invention aims to provide a bearing load-temperature-stress equivalent method based on a symbolic regression algorithm to realize establishment of an equivalent relation between bearing load and temperature, so that reliable simulation support is provided for establishment of a single bearing stand test bed.
The purpose of the invention is realized by the following technical scheme:
in a first aspect, the invention provides a bearing load-temperature-stress equivalent method based on a symbolic regression algorithm, which comprises the following steps:
s1, establishing a bearing three-dimensional model, and establishing a bearing finite element model according to the bearing three-dimensional model;
step S2, establishing a bearing finite element sub-model according to the bearing finite element model, wherein the bearing finite element sub-model comprises a bearing outer ring, a bearing inner ring and a roller, and defines a contact line between the inner surface of the bearing outer ring and the roller as a contact line A, a contact line between the circumferential outer wall of the roller and the bearing outer ring as a contact line B, a contact line between the circumferential outer wall of the roller and the bearing inner ring as a contact line C, and a contact line between the outer surface of the bearing inner ring and the roller as a contact line D;
s3, designing a radial load-axial load two-factor five-horizontal orthogonal test scheme according to the actual service working condition of the bearing;
step S4, according to the radial load-axial load two-factor five-horizontal orthogonal test scheme, applying corresponding radial loads and axial loads in the radial load-axial load two-factor five-horizontal orthogonal test scheme to the roller in the bearing finite element sub-model in sequence, obtaining stress values of a certain point on each contact line in different radial load-axial load two-factor five-horizontal orthogonal test schemes through finite element analysis and calculation, and establishing a radial load-axial load stress value data set corresponding to each contact line;
and training any 80% of data in the data concentration of the radial load-axial load stress value corresponding to each contact line by adopting a symbolic regression algorithm to obtain a radial load-axial load equivalent correlation function expression corresponding to a certain point on each contact line.
In some possible embodiments, in step S4, a certain point on each contact line includes a fixed point and a maximum point, the fixed point is a position where a maximum stress value on the contact line is located when a radial load is applied only to the roller in the bearing finite element sub-model, and the maximum point is a position where a maximum stress value on each contact line is located when a radial load and an axial load are applied simultaneously to the roller in the bearing finite element sub-model;
when a certain point on each contact line is a fixed point, the corresponding equivalent correlation function expression of the radial load and the axial load is as follows:
Figure DEST_PATH_IMAGE001
in the formula:f A1 is the stress value at a fixed point on the contact line a,f B1 is the stress value of the fixed point on the contact line B,f C1 the stress value for a fixed point on the contact line C,f D1 is the stress value at a fixed point on the contact line D,xin order to be a radial load,yis an axial load;
when each contact lineWhen the certain point is a maximum value point, the corresponding radial load-axial load equivalent correlation function expression is as follows:
Figure 564009DEST_PATH_IMAGE002
in the formula:f A2 the stress value of the maximum point on the contact line a,f B2 the stress value of the maximum point on the contact line B,f C2 the stress value of the maximum point on the contact line C,f D2 the stress value of the maximum point on the contact line D,xin order to be a radial load,yis an axial load.
In some possible embodiments, in step S4, after obtaining the radial load-axial load equivalent correlation function expression corresponding to a certain point on each contact line, the remaining 20% of the data in the radial load-axial load stress value data set corresponding to each contact line is used as verification data to verify the accuracy of the radial load-axial load equivalent correlation function expression.
In a second aspect, the invention provides a bearing load-temperature-stress equivalent method based on a symbolic regression algorithm, which comprises the following steps:
s1, establishing a bearing three-dimensional model, and establishing a bearing finite element model according to the bearing three-dimensional model;
step S2, establishing a bearing finite element sub-model according to the bearing finite element model, wherein the bearing finite element sub-model comprises a bearing outer ring, a bearing inner ring and a roller, and defines a contact line between the inner surface of the bearing outer ring and the roller as a contact line A, a contact line between the circumferential outer wall of the roller and the bearing outer ring as a contact line B, a contact line between the circumferential outer wall of the roller and the bearing inner ring as a contact line C, and a contact line between the outer surface of the bearing inner ring and the roller as a contact line D;
s3, designing a radial load-temperature two-factor five-level orthogonal test scheme according to the actual service working condition of the bearing;
s4, according to the radial load-temperature two-factor five-level orthogonal test scheme, sequentially applying radial loads corresponding to the radial load-temperature two-factor five-level orthogonal test scheme to the roller in the bearing finite element submodel, setting a temperature field where the bearing finite element submodel is located, calculating stress values of a certain point on each contact line in the different radial load-temperature two-factor five-level orthogonal test schemes through finite element analysis, and establishing a radial load-temperature stress value data set corresponding to each contact line;
and training any 80% of data in the data set of the radial load-temperature stress value corresponding to each contact line by adopting a symbolic regression algorithm to obtain a radial load-temperature equivalent correlation function expression corresponding to a certain point on each contact line.
In some possible embodiments, in step S4, the certain point on each contact line includes a fixed point and a maximum point, the fixed point is a position where a maximum stress value on the contact line is located when a radial load is applied only to the roller in the bearing finite element sub-model, and the maximum point is a position where a maximum stress value on each contact line is located when a radial load and an axial load are applied simultaneously to the roller in the bearing finite element sub-model;
when a certain point on each contact line is a fixed point, the corresponding radial load-temperature equivalent correlation function expression is as follows:
Figure DEST_PATH_IMAGE003
in the formula:f A1 is the stress value at a fixed point on the contact line a,f B1 is the stress value of the fixed point on the contact line B,f C1 the stress value for a fixed point on the contact line C,f D1 is the stress value of the fixed point on the contact line D,xin order to be a radial load,zis the temperature;
when a certain point on each contact line is a maximum value point, the corresponding radial load-temperature equivalent correlation function expression is as follows:
Figure 664689DEST_PATH_IMAGE004
in the formula:f A2 is the maximum point on the contact line AThe value of the stress of (a) is,f B2 the stress value of the maximum point on the contact line B,f C2 the stress value of the maximum point on the contact line C,f D2 the stress value of the maximum point on the contact line D,xin order to be a radial load,zis the temperature.
In some possible embodiments, in step S4, after obtaining the radial load-temperature equivalent correlation function expression corresponding to a certain point on each contact line, the remaining 20% of the data in the radial load-temperature stress value data set corresponding to each contact line is used as verification data to verify the accuracy of the radial load-temperature equivalent correlation function expression.
In a third aspect, the invention provides a bearing load-temperature-stress equivalent method based on a symbolic regression algorithm, which comprises the following steps:
s1, establishing a bearing three-dimensional model, and establishing a bearing finite element model according to the bearing three-dimensional model;
step S2, establishing a bearing finite element submodel according to the bearing finite element model, wherein the bearing finite element submodel comprises a bearing outer ring, a bearing inner ring and a roller, and defines a contact line between the inner surface of the bearing outer ring and the roller as a contact line A, a contact line between the circumferential outer wall of the roller and the bearing outer ring as a contact line B, a contact line between the circumferential outer wall of the roller and the bearing inner ring as a contact line C, and a contact line between the outer surface of the bearing inner ring and the roller as a contact line D;
s3, designing a radial load-axial load-temperature three-factor five-horizontal orthogonal test scheme according to the actual service working condition of the bearing;
step S4, according to the radial load-axial load-temperature three-factor five-level orthogonal test scheme, applying corresponding radial loads and axial loads in the radial load-axial load-temperature three-factor five-level orthogonal test scheme to the roller in the bearing finite element sub-model in sequence, setting a temperature field where the bearing finite element sub-model is located, calculating and obtaining stress values of a certain point on each contact line in different radial load-axial load-temperature three-factor five-level orthogonal test schemes through finite element analysis, and establishing a radial load-axial load-temperature stress value data set corresponding to each contact line;
and training any 80% of data in the data concentration of the radial load-axial load-temperature stress value corresponding to each contact line by adopting a symbolic regression algorithm to obtain a radial load-axial load-temperature equivalent correlation function expression corresponding to a certain point on each contact line.
In some possible embodiments, in step S4, a certain point on each contact line includes a fixed point and a maximum point, the fixed point is a position where a maximum stress value on the contact line is located when a radial load is applied only to the roller in the bearing finite element sub-model, and the maximum point is a position where a maximum stress value on each contact line is located when a radial load and an axial load are applied simultaneously to the roller in the bearing finite element sub-model;
when a certain point on each contact line is a fixed point, the corresponding radial load-axial load-temperature equivalent correlation function expression is as follows:
Figure 470971DEST_PATH_IMAGE005
Figure 773164DEST_PATH_IMAGE006
in the formula:f A1 is the stress value at a fixed point on the contact line a,f B1 is the stress value of the fixed point on the contact line B,f C1 the stress value for a fixed point on the contact line C,f D1 is the stress value of the fixed point on the contact line D,xin order to be a radial load,zis the temperature;
when a certain point on each contact line is a maximum value point, the corresponding radial load-axial load-temperature equivalent correlation function expression is as follows:
Figure 639489DEST_PATH_IMAGE007
in the formula:f A2 the stress value of the maximum point on the contact line a,f B2 is the stress value of the maximum point on the contact line B,f C2 the stress value of the maximum point on the contact line C,f D2 the stress value of the maximum point on the contact line D,xin order to be a radial load,zis the temperature.
In some possible embodiments, in step S4, after obtaining the radial load-axial load-temperature equivalent correlation function expression corresponding to a certain point on each contact line, the remaining 20% of the data in the radial load-axial load-temperature stress value data set corresponding to each contact line is used as verification data to verify the accuracy of the radial load-axial load-temperature equivalent correlation function expression.
The technical scheme of the embodiment of the invention at least has the following advantages and beneficial effects:
on the basis of a finite element analysis technology, the method combines a symbol regression algorithm to train data obtained through finite element analysis calculation, obtains equivalent association function expressions among the bearing radial load-axial load, the radial load-temperature and the radial load-axial load-temperature, establishes the equivalent relation between the bearing load-temperature and verifies the effectiveness of the equivalent association function expression, and thereby provides reliable simulation support for establishing a single bearing stand test bench.
Drawings
FIG. 1 is a schematic structural diagram of a three-dimensional model of a bearing provided by the present invention;
FIG. 2 is a schematic structural diagram of a finite element model of a bearing provided by the present invention;
FIG. 3 is a structural schematic of a bearing finite element submodel provided by the present invention;
FIG. 4 is a schematic diagram of the location of each contact line in the bearing finite element submodel provided by the present invention;
fig. 5 is a curved surface diagram of an equivalent correlation function of fixed points on each contact line when the radial load and the axial load are equivalent, which is provided in embodiment 1 of the present invention;
fig. 6 is an equivalent correlation function surface diagram of the maximum point on each contact line when the radial load-axial load is equivalent, according to embodiment 1 of the present invention;
FIG. 7 is a curved surface diagram of equivalent correlation functions of fixed points on contact lines when radial load-temperature are equivalent, according to example 2 of the present invention;
fig. 8 is a curved surface diagram of an equivalent correlation function of maximum points on each contact line during radial load-temperature equivalence according to embodiment 2 of the present invention;
fig. 9 is a diagram of factors and index trends of fixed points and maximum points on each contact line under each working condition according to embodiment 3 of the present invention;
FIG. 10 is a curved surface diagram of an equivalent correlation function of fixed points on contact lines in radial load-axial load-temperature equivalence, which is provided by embodiment 3 of the present invention;
fig. 11 is a curved surface diagram of an equivalent correlation function of the maximum point on each contact line during the radial load-axial load-temperature equivalence provided in embodiment 3 of the present invention.
Detailed Description
The invention provides a bearing load-temperature-stress equivalent method based on a symbolic regression algorithm, which is used for establishing equivalent relations between a bearing radial load and an axial load, between the bearing radial load and the axial load and the temperature through a finite element analysis technology combined with the symbolic regression algorithm. It should be noted that the radial load in the present invention may be a vertical load, and the axial load may be a lateral load.
Example 1
The embodiment provides a bearing load-temperature-stress equivalent method based on a symbolic regression algorithm to establish an equivalent relation between a radial load and an axial load of a bearing, and the method comprises the following steps:
s1, establishing a bearing three-dimensional model, and establishing a bearing finite element model according to the bearing three-dimensional model.
As shown in fig. 1 and fig. 2, the three-dimensional bearing model in the present embodiment is built by using Solidworks 2018 according to the size of the CRH380 axle box bearing provided by LYC ltd, and on this basis, a finite element bearing model based on the three-dimensional bearing model is built by using Hyprmesh 2021 commercial software. Meanwhile, boundary conditions need to be added when a bearing finite element model is established, specifically, the boundary conditions between one roller of the bearing and the inner ring and the outer ring of the bearing are obtained through finite element calculation, wherein the outer surface of the outer ring of the bearing is fixed, the end surface of the inner ring of the bearing is axially constrained, the circumferential motion of all rollers of the bearing is simultaneously constrained, the inner surface of the inner ring of the bearing applies bearing forces with different loads, the temperature boundaries are applied to the surfaces of the rollers and the raceway, and convection heat exchange coefficients are applied to the other surfaces.
And S2, establishing a bearing finite element sub-model according to the bearing finite element model on the basis of the step S1, wherein the bearing finite element sub-model comprises a bearing outer ring, a bearing inner ring and a roller as shown in figure 3, and the bearing finite element sub-model is used as a finite element analysis calculation object, so that the period required by finite element analysis calculation can be effectively shortened, and the efficiency is improved. In order to facilitate the study of the stress variation at the contact portions among the bearing outer ring, the bearing inner ring, and the roller, and meanwhile, based on the fact that the contact portions among the three are in line contact, in the embodiment, the contact line between the inner surface of the bearing outer ring and the roller is defined as a contact line a, the contact line between the circumferential outer wall of the roller and the bearing outer ring is defined as a contact line B, the contact line between the circumferential outer wall of the roller and the bearing inner ring is defined as a contact line C, and the contact line between the outer surface of the bearing inner ring and the roller is defined as a contact line D, in combination with the content shown in fig. 4.
And S3, designing a radial load-axial load two-factor five-horizontal orthogonal test scheme by taking the radial load and the axial load as factors according to the actual service working condition of the bearing.
It is understood that the actual service condition of the bearing in this embodiment is also based on the actual service condition of the bearing provided by LYC limited, and the data setting range of the radial load and the axial load of the bearing is shown in table 1 below:
TABLE 1 data setting range table for radial load and axial load
Figure 509356DEST_PATH_IMAGE008
As can be seen from table 1, the radial load and the axial load in this embodiment have 5 levels, and at this time, a two-factor five-level orthogonal table with the radial load and the axial load as factors can be obtained according to the orthogonal test design method, as shown in table 2 below:
TABLE 2 radial load-axial load two-factor five-level orthogonal table
Figure 119329DEST_PATH_IMAGE009
It should be noted that the numbers in table 2 represent different two-factor five-horizontal-orthogonal radial load-axial load test schemes, that is, in this embodiment, 25 different two-factor five-horizontal-orthogonal radial load-axial load test schemes are designed to respectively represent 25 different working conditions of the bearing. Meanwhile, the factor 1 in table 2 represents the radial load, the factor 2 represents the axial load, and the factors 1 and 2 correspond to 1-5 levels respectively corresponding to 5 different levels in table 1.
And S4, according to the 25 radial load-axial load two-factor five-level orthogonal test schemes in the table 2, applying corresponding radial loads and axial loads in the radial load-axial load two-factor five-level orthogonal test schemes to the roller in the bearing finite element submodel in sequence, calculating stress values of a certain point on each contact line (namely the contact line A, the contact line B, the contact line C and the contact line D) in the different radial load-axial load two-factor five-level orthogonal test schemes through finite element analysis, and establishing a radial load-axial load stress value data set corresponding to each contact line.
That is to say, the radial load and the axial load corresponding to the two-factor five-level orthogonal test scheme with 25 radial load and axial load are sequentially applied to the roller in the bearing finite element submodel (for example, when the first two-factor five-level orthogonal test scheme with the radial load and the axial load is implemented, the radial load and the axial load applied to the roller are respectively 30kN and-15 kN), corresponding finite element analysis calculation is performed, so that 25 stress values corresponding to a certain point on each contact line under the loading condition of the two-factor five-level orthogonal test scheme with the radial load and the axial load can be obtained, and the 25 stress values corresponding to each contact line are collected together to establish a radial load-axial load stress value data set corresponding to each contact line.
It should be noted that the stress at a certain point on each contact line calculated by finite element analysis may be, but is not limited to, von.
After the radial load-axial load stress value data set corresponding to each contact line is obtained, any 80% of data in the radial load-axial load stress value data set corresponding to each contact line is trained by adopting a symbolic regression algorithm, so that a radial load-axial load equivalent correlation function expression corresponding to a certain point on each contact line is obtained.
It can be understood that, in step S4, a certain point on each contact line includes a fixed point and a maximum point, the fixed point is a position where a maximum stress value on the contact line is located when a radial load is applied only to the roller in the bearing finite element sub-model, and the maximum point is a position where a maximum stress value on each contact line is located when a radial load and an axial load are applied to the roller in the bearing finite element sub-model simultaneously.
On the basis, any 80% of data of the radial load-axial load stress value data concentration corresponding to each contact line is trained through a symbolic regression algorithm, and then the radial load-axial load equivalent correlation function expression corresponding to the fixed point or the maximum point on each contact line can be obtained.
Specifically, when a certain point on each contact line is a fixed point, the radial load-axial load equivalent correlation function expression corresponding to the fixed point on each contact line is as follows:
Figure 273098DEST_PATH_IMAGE010
in the formula:f A1 is the stress value at a fixed point on the contact line a,f B1 is the stress value at a fixed point on the contact line B,f C1 the stress value for a fixed point on the contact line C,f D1 is the stress value of the fixed point on the contact line D,xin order to be a radial load,yis an axial load.
When a certain point on each contact line is a maximum point, the expression of the equivalent correlation function of the radial load and the axial load corresponding to the maximum point on each contact line is as follows:
Figure 248008DEST_PATH_IMAGE011
in the formula:f A2 the stress value of the maximum point on the contact line a,f B2 is the stress value of the maximum point on the contact line B,f C2 the stress value of the maximum point on the contact line C,f D2 the stress value of the maximum point on the contact line D,xin order to be a radial load,yis an axial load.
In addition, in step S4, after obtaining the radial load-axial load equivalent correlation function expression corresponding to the fixed point or the maximum point on each contact line through the training of the symbolic regression algorithm, the remaining 20% of data in the radial load-axial load stress value data concentration corresponding to each contact line is also required to be used as verification data to verify the accuracy of the radial load-axial load equivalent correlation function expression.
In this embodiment, the complexity and the mean square error value of the training model obtained by training the radial load-axial load stress value data set corresponding to each contact line through the symbolic regression algorithm are shown in table 3, and the lower corner marks FP and MP in the table represent a fixed point and a maximum point on the contact line respectively. Meanwhile, both 80% of training data and 20% of verification data are plotted in the equivalent correlation function surface graph, and the plotting results are shown in fig. 5 and fig. 6, where fig. 5 is a radial load-axial load equivalent correlation function surface graph when a certain point on each contact line is a fixed point, and fig. 6 is a radial load-axial load equivalent correlation function surface graph when a certain point on each contact line is a maximum point.
TABLE 3 table of equivalent correlation function expression complexity and mean square error values
Figure 729805DEST_PATH_IMAGE012
As can be seen from Table 3, B in Table 3 MP And C MP The corresponding mean square error value is larger than that of other points because the stress values of the maximum point on the contact line B and the maximum point on the contact line C are larger than those of the contact lines under other working conditions, the maximum stress values on the contact line B and the contact line C are respectively 600 MPa and 1000 MPa, and the mean square error value is defined by taking the mean value of the sum of squares of errors between the simulated value and the training value. With C MP Corresponding mean squared error values, C MP It is known that the average error between the simulation result of the maximum point on the contact line C and the training result of the symbolic regression algorithm is √ 822.649=28.682 MPa, which is only 2.868% of the maximum stress value on the contact line C (the maximum stress value on the contact line C is 1000 MPa), and the error range is within the acceptable range of engineering practice. Therefore, the equivalent correlation function expression obtained by adopting the symbolic regression algorithm fitting can approximately describe the equivalent relation between the radial load and the axial load.
As can be seen from fig. 5 and 6, the equivalent correlation function curved surface obtained by the symbolic regression algorithm is smooth, and the scatter of the training data and the verification data has good correlation with the equivalent correlation function curved surface. In the figure, the stress value of the fixed point on each contact line has no obvious change along with the increase of the axial load, and the change of the stress value of the maximum point on each contact line approximately linearly increases. Based on the fact that the shape of the bearing roller in the embodiment is a conical surface, the roller slightly slides in the axial direction after the axial load is added, and the stress value changes in a linear gradient mode.
After the equivalent correlation function expression is obtained, in order to achieve the purpose of equivalent axial load to radial load, the equivalent basis is that the stress values are equal in magnitude, and the equivalent correlation function expression before and after equivalence is controlledfThe value is not changed, changedxValue oryThe equivalent purpose can be achieved by the value. In the practical application process, the stress value of a certain point on each contact line can be obtained by only determining the magnitude of the radial load and the magnitude of the axial load and substituting the magnitude into the equivalent correlation function expression, and if the axial load is expected to be equivalent to the radial load, only the axial load (namely the axial load) is neededyA value) is considered to be 0,fthe value is not changed, by adjustingxThe values are equivalent.
Example 2
The embodiment provides a bearing load-temperature-stress equivalent method based on a symbolic regression algorithm to establish an equivalent relation between the radial load and the temperature of a bearing, and the method comprises the following steps:
s1, establishing a bearing three-dimensional model, and establishing a bearing finite element model according to the bearing three-dimensional model.
As shown in fig. 1 and fig. 2, the three-dimensional bearing model in the present embodiment is built by using Solidworks 2018 according to the CRH380 axle box bearing size provided by LYC ltd, and on the basis, a finite element bearing model based on the three-dimensional bearing model is built by using hypromesh 2021 commercial software. Meanwhile, boundary conditions need to be added when a bearing finite element model is established, specifically, the boundary conditions between one roller of the bearing and the inner ring and the outer ring of the bearing are obtained through finite element calculation, wherein the outer surface of the outer ring of the bearing is fixed, the end surface of the inner ring of the bearing is axially constrained, the circumferential motion of all rollers of the bearing is simultaneously constrained, the inner surface of the inner ring of the bearing applies bearing forces with different loads, the surfaces of the rollers and the raceway apply temperature boundaries, and convection heat exchange coefficients are applied to the other surfaces.
And S2, establishing a bearing finite element sub-model according to the bearing finite element model on the basis of the step S1, wherein the bearing finite element sub-model comprises a bearing outer ring, a bearing inner ring and a roller as shown in figure 3, and the bearing finite element sub-model is used as a finite element analysis calculation object, so that the period required by finite element analysis calculation can be effectively shortened, and the efficiency is improved. In order to facilitate the study of the stress variation at the contact portions among the bearing outer ring, the bearing inner ring, and the roller, and meanwhile, based on the fact that the contact portions among the three are in line contact, in the embodiment, the contact line between the inner surface of the bearing outer ring and the roller is defined as a contact line a, the contact line between the circumferential outer wall of the roller and the bearing outer ring is defined as a contact line B, the contact line between the circumferential outer wall of the roller and the bearing inner ring is defined as a contact line C, and the contact line between the outer surface of the bearing inner ring and the roller is defined as a contact line D, in combination with the content shown in fig. 4.
And S3, designing a radial load-temperature two-factor five-level orthogonal test scheme by taking the radial load and the temperature as factors according to the actual service working condition of the bearing.
It is understood that the actual service condition of the bearing in this embodiment is also based on the actual service condition of the bearing provided by LYC limited, and the data setting ranges of the radial load and the axial load of the bearing are shown in table 4 below:
TABLE 4 data setting range table of radial load and temperature
Figure 268102DEST_PATH_IMAGE013
As can be seen from table 4, the radial load and the temperature in this embodiment have 5 levels, and then a two-factor five-level orthogonal table with the radial load and the temperature as factors can be obtained according to the orthogonal test design method, as shown in table 5 below:
TABLE 5 radial load-temp. two-factor five-level orthogonal table
Figure 151745DEST_PATH_IMAGE014
It should be noted that the numbers in table 5 represent different radial load-temperature two-factor five-level orthogonal test schemes, that is, in this embodiment, 25 different radial load-temperature two-factor five-level orthogonal test schemes are designed to represent 25 different operating conditions of the bearing, respectively. Meanwhile, the factor 1 in table 5 represents the radial load, the factor 3 represents the temperature, and the factors 1 and 3 correspond to 1-5 levels in table 4, respectively.
And S4, according to the radial load-temperature two-factor five-level orthogonal test scheme in the table 5, sequentially applying corresponding radial loads in each radial load-temperature two-factor five-level orthogonal test scheme to the roller in the bearing finite element sub-model, setting a temperature field where the bearing finite element sub-model is located, calculating and obtaining the stress value of a certain point on each contact line (namely the contact line A, the contact line B, the contact line C and the contact line D) in different radial load-temperature two-factor five-level orthogonal test schemes through finite element analysis, and establishing a radial load-temperature stress value data set corresponding to each contact line.
That is to say, the radial loads corresponding to the two-factor five-level orthogonal test schemes of 25 radial loads and temperatures are sequentially applied to the roller in the bearing finite element submodel, the temperature field where the bearing finite element submodel is located is set to be the corresponding temperature (for example, when the first two-factor five-level orthogonal test scheme of radial loads and temperatures is implemented, the radial load applied to the roller is 30kN, and the temperature field where the bearing finite element submodel is located is 40 ℃), corresponding finite element analysis and calculation are performed, so that 25 stress values corresponding to a certain point on each contact line under the loading condition of the two-factor five-level orthogonal test schemes of 25 radial loads and temperatures can be obtained, and the radial load-temperature stress value data set corresponding to each contact line can be established by summarizing the 25 stress values corresponding to each contact line.
It should be noted that the stress at a certain point on each contact line calculated by finite element analysis may be, but is not limited to, von.
After the radial load-temperature stress value data set corresponding to each contact line is obtained, any 80% of data in the radial load-temperature stress value data set corresponding to each contact line is trained by adopting a symbolic regression algorithm, so that a radial load-temperature equivalent correlation function expression corresponding to a certain point on each contact line is obtained.
It can be understood that, in step S4, a certain point on each contact line includes a fixed point and a maximum point, the fixed point is a position where a maximum stress value on the contact line is located when a radial load is applied only to the roller in the bearing finite element sub-model, and the maximum point is a position where a maximum stress value on each contact line is located when a radial load and an axial load are applied to the roller in the bearing finite element sub-model simultaneously.
On the basis, any 80% of data of the radial load-temperature stress value data concentration corresponding to each contact line is trained through a symbolic regression algorithm, and then the radial load-temperature equivalent correlation function expression corresponding to the fixed point or the maximum point on each contact line can be obtained.
Specifically, when a certain point on each contact line is a fixed point, the radial load-temperature equivalent correlation function corresponding to the fixed point on each contact line is expressed as follows:
Figure 500817DEST_PATH_IMAGE015
in the formula:f A1 is the stress value at a fixed point on the contact line a,f B1 is the stress value of the fixed point on the contact line B,f C1 the stress value for a fixed point on the contact line C,f D1 is the stress value of the fixed point on the contact line D,xin order to be a radial load,zis the temperature.
When a certain point on each contact line is a maximum point, the expression of the radial load-temperature equivalent correlation function corresponding to the maximum point on each contact line is as follows:
Figure 204331DEST_PATH_IMAGE016
in the formula:f A2 the stress value of the maximum point on the contact line a,f B2 the stress value of the maximum point on the contact line B,f C2 the stress value of the maximum point on the contact line C,f D2 the stress value of the maximum point on the contact line D,xin order to be a radial load,zis the temperature.
In addition, in step S4, after obtaining the radial load-temperature equivalent correlation function expression corresponding to the fixed point or the maximum point on each contact line through the training of the symbolic regression algorithm, the remaining 20% of data in the radial load-temperature stress value data set corresponding to each contact line is also required to be used as verification data to verify the accuracy of the radial load-temperature equivalent correlation function expression.
In this embodiment, the complexity and the mean square error value of the training model obtained by training the radial load-temperature stress value data set corresponding to each contact line through the symbolic regression algorithm are shown in table 6, and the lower corner marks FP and MP in the table represent the fixed point and the maximum point on the contact line, respectively. Meanwhile, the 80% training data and the 20% verification data are both drawn in the equivalent correlation function surface graph, and the obtained equivalent correlation function surface graph is shown in fig. 7 and 8, where fig. 7 is a radial load-temperature equivalent correlation function surface graph when a certain point on each contact line is a fixed point, and fig. 8 is a radial load-temperature equivalent correlation function surface graph when a certain point on each contact line is a maximum point.
TABLE 6 table of equivalent correlation function expression complexity and mean square error values
Figure 280740DEST_PATH_IMAGE017
As can be seen from fig. 7 and 8, the equivalent correlation function curved surface obtained by the symbolic regression algorithm is smooth, the scattered points of the training data and the verification data have good correlation with the equivalent correlation function curved surface, and the equivalent correlation function curved surface is a non-uniform and smooth curved surface. By analyzing with reference to table 6, compared with table 3 in embodiment 1, the mean square error value in the radial load-temperature equivalent correlation function expression in this embodiment is increased as a whole, and it can be inferred that the temperature has a more significant influence on the stress value result at a certain point on each contact line.
Example 3
The embodiment provides a bearing load-temperature-stress equivalent method based on a symbolic regression algorithm to establish an equivalent relation between radial load-axial load-temperature of a bearing, and the method comprises the following steps:
s1, establishing a bearing three-dimensional model, and establishing a bearing finite element model according to the bearing three-dimensional model.
As shown in fig. 1 and fig. 2, the three-dimensional bearing model in the present embodiment is built by using Solidworks 2018 according to the CRH380 axle box bearing size provided by LYC ltd, and on the basis, a finite element bearing model based on the three-dimensional bearing model is built by using hypromesh 2021 commercial software. Meanwhile, boundary conditions need to be added when a bearing finite element model is established, specifically, the boundary conditions between one roller of the bearing and the inner ring and the outer ring of the bearing are obtained through finite element calculation, wherein the outer surface of the outer ring of the bearing is fixed, the end surface of the inner ring of the bearing is axially constrained, the circumferential motion of all rollers of the bearing is simultaneously constrained, the inner surface of the inner ring of the bearing applies bearing forces with different loads, the surfaces of the rollers and the raceway apply temperature boundaries, and convection heat exchange coefficients are applied to the other surfaces.
And S2, establishing a bearing finite element sub-model according to the bearing finite element model on the basis of the step S1, wherein the bearing finite element sub-model comprises a bearing outer ring, a bearing inner ring and a roller as shown in figure 3, and the bearing finite element sub-model is used as a finite element analysis calculation object, so that the period required by finite element analysis calculation can be effectively shortened, and the efficiency is improved. In order to facilitate the study of the stress variation at the contact portions among the bearing outer ring, the bearing inner ring, and the roller, and meanwhile, based on the fact that the contact portions among the three are in line contact, in the embodiment, the contact line between the inner surface of the bearing outer ring and the roller is defined as a contact line a, the contact line between the circumferential outer wall of the roller and the bearing outer ring is defined as a contact line B, the contact line between the circumferential outer wall of the roller and the bearing inner ring is defined as a contact line C, and the contact line between the outer surface of the bearing inner ring and the roller is defined as a contact line D, in combination with the content shown in fig. 4.
And S3, designing a radial load-axial load-temperature three-factor five-horizontal orthogonal test scheme by taking the radial load, the axial load and the temperature as factors according to the actual service working condition of the bearing.
It is understood that the actual service condition of the bearing in this embodiment is also based on the actual service condition of the bearing provided by LYC limited, and the data setting ranges of the radial load, the axial load and the temperature of the bearing are shown in table 7 below:
TABLE 7 data setting range table for radial load, axial load and temperature
Figure 284469DEST_PATH_IMAGE018
As can be seen from table 7, the radial load, the axial load and the temperature in this embodiment have 5 levels, and then a three-factor five-level orthogonal table with the radial load, the axial load and the temperature as factors can be obtained according to the orthogonal test design method, as shown in table 8 below:
TABLE 8 radial load-axial load-temperature three-factor five-horizontal orthogonal table
Figure 804443DEST_PATH_IMAGE019
It should be noted that the numbers in table 8 represent different radial load-axial load-temperature three-factor five-level orthogonal test schemes, that is, 25 different radial load-axial load-temperature three-factor five-level orthogonal test schemes are designed in this embodiment to represent 25 different operating conditions of the bearing, respectively. Meanwhile, the factor 1 in table 8 represents the radial load, the factor 2 represents the axial load, the factor 3 represents the temperature, and the factors 1 to 5 corresponding to the factor 1, the factor 2, and the factor 3 correspond to 5 different levels in table 7, respectively.
And S4, according to the radial load-axial load-temperature three-factor five-level orthogonal test scheme in the table 8, sequentially applying the corresponding radial load and axial load in each radial load-axial load-temperature three-factor five-level orthogonal test scheme to the roller in the bearing finite element submodel, setting a temperature field where the bearing finite element submodel is located, calculating and obtaining the stress value of a certain point on each contact line (namely the contact line A, the contact line B, the contact line C and the contact line D) in different radial load-axial load-temperature three-factor five-level orthogonal test schemes through finite element analysis, and establishing a radial load-axial load-temperature stress value data set corresponding to each contact line.
That is, the radial load and the axial load corresponding to the 25 radial load-axial load-temperature three-factor five-level orthogonal test schemes are sequentially applied to the roller in the bearing finite element submodel, the temperature field where the bearing finite element submodel is located is set to be the corresponding temperature (for example, when the first radial load-axial load-temperature three-factor five-level orthogonal test scheme is implemented, the radial load and the axial load applied to the roller are respectively 30kN and-15 kN, and the temperature field where the bearing finite element submodel is 40 ℃), and corresponding finite element analysis and calculation are performed, so that 25 stress values corresponding to a certain point on each contact line under the loading condition of the 25 radial load-axial load-temperature three-factor five-level orthogonal test schemes can be obtained, and 25 stress values corresponding to each contact line are collected together, so that a radial load-axial load-temperature stress value data set corresponding to each contact line can be established.
It should be noted that the stress at a certain point on each contact line calculated by finite element analysis may be, but is not limited to, von.
After the radial load-axial load-temperature stress value data set corresponding to each contact line is obtained, any 80% of data in the radial load-axial load-temperature stress value data set corresponding to each contact line is trained by adopting a symbolic regression algorithm, so that a radial load-axial load-temperature equivalent correlation function expression corresponding to a certain point on each contact line is obtained.
It can be understood that, in step S4, a certain point on each contact line includes a fixed point and a maximum point, the fixed point is a position where a maximum stress value on the contact line is located when a radial load is applied only to the roller in the bearing finite element sub-model, and the maximum point is a position where a maximum stress value on each contact line is located when a radial load and an axial load are applied to the roller in the bearing finite element sub-model simultaneously.
On the basis, any 80% of data of the data concentration of the radial load-axial load-temperature stress value corresponding to each contact line is trained through a symbolic regression algorithm, and then the radial load-axial load-temperature equivalent correlation function expression corresponding to the fixed point or the maximum point on each contact line can be obtained.
Specifically, when a certain point on each contact line is a fixed point, the radial load-axial load-temperature equivalent correlation function expression corresponding to the fixed point on each contact line is as follows:
Figure 260832DEST_PATH_IMAGE020
in the formula:f A1 for fixing contact line AThe stress value of the fixed point is determined,f B1 is the stress value at a fixed point on the contact line B,f C1 the stress value for a fixed point on the contact line C,f D1 is the stress value at a fixed point on the contact line D,xin order to be a radial load,zis the temperature;
when a certain point on each contact line is a maximum point, the expression of the equivalent correlation function of the radial load, the axial load and the temperature corresponding to the maximum point on each contact line is as follows:
Figure 940599DEST_PATH_IMAGE021
in the formula:f A2 the stress value of the maximum point on the contact line a,f B2 the stress value of the maximum point on the contact line B,f C2 the stress value of the maximum point on the contact line C,f D2 the stress value of the maximum point on the contact line D,xin order to be a radial load,zis the temperature.
In addition, in step S4, after obtaining the radial load-axial load-temperature equivalent correlation function expression corresponding to the fixed point or the maximum point on each contact line through the training of the symbolic regression algorithm, the remaining 20% of data in the radial load-axial load-temperature stress value data concentration corresponding to each contact line is also required to be used as verification data to verify the accuracy of the radial load-temperature equivalent correlation function expression.
On the other hand, the present embodiment further discusses the primary and secondary relationships of the three influencing factors, namely, the radial load, the axial load and the temperature, on the simulation test results.
Specifically, a factor-index trend graph of the fixed point and the maximum point on each contact line under each working condition is plotted and obtained by adopting an intuitive analysis method with the factor level as an abscissa and the average deviation amount of the test index as an ordinate as shown in fig. 9, wherein (a) in fig. 9 is the factor-index trend graph of the fixed point on each contact line under each working condition as shown in the figure, and (b) in fig. 9 is the factor-index trend graph of the maximum point on each contact line under each working condition as shown in the figure, the abscissa a1-a5 represents 5 horizontal values of the radial load, the abscissa b1-b5 represents 5 horizontal values of the axial load, and the abscissa c1-c5 represents 5 horizontal values of the temperature.
As can be seen from fig. 9, the average deviation amount of the temperature is large, so for the three influencing factors of the radial load, the axial load and the temperature, the influence of the temperature on the simulation test result is large, and the primary and secondary relationships of the radial load and the axial load are determined by range analysis, and the range analysis result is shown in table 9. For the purpose of analysis, the range data in table 9 retain 0 significant digits, where a represents the radial load, b represents the axial load, and c represents the temperature.
TABLE 9 results of range analysis
Figure 408621DEST_PATH_IMAGE022
As can be seen from table 9, at the contact line C or the contact line D, the primary and secondary relationships of the influencing factors are temperature, axial load and radial load, and at the contact line a and the contact line B, the primary and secondary relationships of the influencing factors at the fixed point and the maximum point are not uniform. Although the axial load is ahead of the radial load in the primary and secondary relations of the influence factors, the radial load and the axial load are nearly at the same level in the table.
Meanwhile, in order to accurately estimate the importance degree of the influence of each influence factor on the simulation test result, analysis of variance is performed on the data in table 9, the calculated F value is listed in table 10, and the F distribution table is consulted to perform significance test. The results are shown in Table 10:
TABLE 10 summary of F-value calculation results
Figure 958551DEST_PATH_IMAGE023
As can be seen from the data in Table 10, since F 0.01 (4, 12) =5.412 are all larger than the fixed point on each contact lineThe F value of the contact line parameter is not judged according to the significance of the data discrimination factors a, b and c, a symbolic regression algorithm is adopted, the main influence characteristics are evaluated and screened by combining a random forest model, and the result shows that the axial load is insensitive to the stress result, so that an equivalent associated curved surface is drawn by adopting radial load-temperature-stress value data, the complexity and the mean square error value of a training model obtained by training a radial load-axial load-temperature stress value data set corresponding to each contact line through the symbolic regression algorithm are shown in a table 11, and lower corner marks FP and MP in the table respectively represent a fixed point and a maximum point on the contact line.
TABLE 11 equivalent correlation function expression complexity and mean square error values
Figure 823608DEST_PATH_IMAGE024
The data for the maximum point on each contact line in table 10 is analyzed for the maximum point on contact line A due to F 0.01 (4,12)=5.412＜F A =10.432，F 0.01 (4,12)=5.412＜F B =10.54，F 0.01 (4,12)=5.412＜F C =12.27, so changes in the levels of factors a, b, c all have a highly significant effect on the simulation test results. The difference between the F values corresponding to the radial load and the axial load in the table is small, the results obtained by combining random forest characteristic screening show that the axial load is insensitive to the stress value result again, a model obtained by training a symbolic regression algorithm is tested, 80% of training data and 20% of verification data are drawn in an equivalent correlation function curve diagram, and the drawing results are shown in fig. 10 and 11, wherein fig. 10 is a radial load-axial load-temperature equivalent correlation function curve diagram when a certain point on each contact line is a fixed point, fig. 11 is a radial load-axial load-temperature equivalent correlation function curve diagram when a certain point on each contact line is a maximum value point, in the diagram, the training points and the verification points are uniformly distributed in the equivalent correlation function curve based on the symbolic regression algorithm, the scattering points of the training data and the verification data have good correlation with the equivalent correlation function curve, and the stress value on each contact line approximately linearly changes along with the increase of the axial load and the temperatureAnd (4) melting.
The above results indicate that temperature is the most important influence factor affecting the stress value at a certain point on each contact line, the order of the temperature term in the equivalent correlation function expression obtained by the symbolic regression algorithm is relatively higher than that of other influence factor terms, and the orders of the influence factor terms in the equivalent correlation function expressions corresponding to different concerned parts (i.e. a fixed point and a maximum value point) are different. As can be seen from table 3 in example 1, table 6 in example 2, and table 11 in example 3, the mean square error value of the contact line C is larger than that of the other points due to the larger maximum stress value extracted at the position, such as 2000 MPa for the maximum stress value at the fixed point on the contact line C in fig. 10 and 2000 MPa for the maximum stress value at the fixed point on the contact line D in fig. 10 (D) MP =300 MPa) is about 7 times the stress value of the latter, so C MP The calculated mean square error value is larger.
In summary, the bearing load-temperature-stress equivalent method based on the symbolic regression algorithm provided by the invention obtains an equivalent associated function expression of a certain point on each contact line in a bearing by combining the finite element analysis with the symbolic regression algorithm, so that an equivalent relation between the bearing load and the temperature is established.
From the engineering analysis, the increase of the stress value of a certain point on any contact line in the bearing can influence the reliability analysis result of the bearing. The simulation test results in the invention show that the stress value of the contact line position of the bearing inner ring and the roller (namely the contact line C and the contact line D) is generally higher than that of other contact lines no matter the fixed point or the maximum point, and the contact line position is a key focus position. The above results indicate that the temperature has a great influence on the stress value of the contact line position inside the bearing, and the lubricating grease can reduce the friction between the roller and the raceway to a certain extent, reduce the temperature between the contact surfaces of the bearing, and reduce the rotating speed of the bearing to achieve the same effect. In the bearing rack test, an infrared thermometer is arranged on the upper part of a bearing box body in a punching mode to monitor the temperature inside a bearing, monitoring data of a normal running state and monitoring data of abnormal temperature rise are led into finite element software to be analyzed, a symbol regression algorithm is also adopted to carry out data processing, a bearing health state data set and an abnormal temperature rise data set can be established, an equivalent correlation function expression can be used for data screening and triggering limiting of a bearing temperature alarm device, and a basis is provided for monitoring and evaluating the bearing health state. For insensitivity of the axial load, considering that the load range of the axial load is lower than that of the radial load, the axial load can be equivalent to the radial load by referring to an equivalent correlation function expression of a fixed point at a position of a contact line (namely a contact line a and a contact line B) between a roller and a bearing outer ring in the radial load-axial load equivalent result in embodiment 1, and an equivalent effect can be verified by arranging a strain gauge on the bearing outer ring to perform a calibration test, which is significant for constructing a bearing service environment rack equivalent model based on service life consistency and simplifying a bearing rack design scheme.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A bearing load-temperature-stress equivalent method based on a symbolic regression algorithm is characterized by comprising the following steps:
s1, establishing a bearing three-dimensional model, and establishing a bearing finite element model according to the bearing three-dimensional model;
s2, establishing a bearing finite element sub-model according to the bearing finite element model, wherein the bearing finite element sub-model comprises a bearing outer ring, a bearing inner ring and a roller, and defines a contact line between the inner surface of the bearing outer ring and the roller as a contact line A, a contact line between the circumferential outer wall of the roller and the bearing outer ring as a contact line B, a contact line between the circumferential outer wall of the roller and the bearing inner ring as a contact line C, and a contact line between the outer surface of the bearing inner ring and the roller as a contact line D;
s3, designing a radial load-axial load two-factor five-horizontal orthogonal test scheme according to the actual service working condition of the bearing;
s4, according to the radial load-axial load two-factor five-horizontal orthogonal test scheme, sequentially applying corresponding radial loads and axial loads in the radial load-axial load two-factor five-horizontal orthogonal test scheme to the roller in the bearing finite element sub-model, obtaining stress values of a certain point on each contact line in different radial load-axial load two-factor five-horizontal orthogonal test schemes through finite element analysis and calculation, and establishing a radial load-axial load stress value data set corresponding to each contact line;
training any 80% of data of the radial load-axial load stress value data concentration corresponding to each contact line by adopting a symbolic regression algorithm to obtain a radial load-axial load equivalent correlation function expression corresponding to a certain point on each contact line;
in step S4, a certain point on each contact line includes a fixed point and a maximum point, the fixed point is a position where a maximum stress value on the contact line is located when a radial load is applied only to the roller in the bearing finite element sub-model, and the maximum point is a position where a maximum stress value on each contact line is located when a radial load and an axial load are simultaneously applied to the roller in the bearing finite element sub-model;
in step S4, after obtaining the radial load-axial load equivalent correlation function expression corresponding to a certain point on each contact line, the remaining 20% of data in the radial load-axial load stress value data concentration corresponding to each contact line is used as verification data to verify the accuracy of the radial load-axial load equivalent correlation function expression.
2. The symbolic regression algorithm-based bearing load-temperature-stress equivalence method according to claim 1, wherein when a certain point on each contact line is a fixed point, the corresponding radial load-axial load equivalence correlation function expression is as follows:
f A1 ＝-7.025×10 -4 ·x 2 +1.109·x-5.894×10 -5 ·xy+6.918；
f B1 ＝5.377×10 -3 ·x 2 -2.441×10 -5 ·xy+0.7071·x+62.81；
f C1 ＝1.536·x+7.008×10 -2 ·y+31.24；
f D1 ＝2.269×10 -5 ·x 3 +2.837×10 -6 ·x 2 y+1.013·x-9.406×10 -3 ·y-0.5417；
in the formula:f A1 is the stress value at a fixed point on the contact line a,f B1 is the stress value of the fixed point on the contact line B,f C1 the stress value for a fixed point on the contact line C,f D1 the stress value of a fixed point on the contact line D is shown, x is a radial load, and y is an axial load;
when a certain point on each contact line is a maximum value point, the corresponding radial load-axial load equivalent correlation function expression is as follows:
f A2 ＝-0.2056·y 2 -1.7027566×10 -2 ·xy+2.587·x+3.118·y+39.97；
f B2 ＝0.3614·y 2 -24.46·y+8.155·x+8.927；
f C2 ＝0.2755·y 2 -9.839×10 -2 ·xy+4.729·x-7.459·y；
f Ｄ2 ＝6.199×10 -2 ·y 2 -2.829·y+1.964·x-9.405；
in the formula:f A2 the stress value of the maximum point on the contact line a,f B2 is the most on the contact line BThe stress value of the large-value point,f C2 the stress value of the maximum point on the contact line C,f D2 the stress value of the maximum point on the contact line D is shown, x is the radial load, and y is the axial load.
3. A bearing load-temperature-stress equivalent method based on a symbolic regression algorithm is characterized by comprising the following steps:
s1, establishing a bearing three-dimensional model, and establishing a bearing finite element model according to the bearing three-dimensional model;
s2, establishing a bearing finite element sub-model according to the bearing finite element model, wherein the bearing finite element sub-model comprises a bearing outer ring, a bearing inner ring and a roller, and defines a contact line between the inner surface of the bearing outer ring and the roller as a contact line A, a contact line between the circumferential outer wall of the roller and the bearing outer ring as a contact line B, a contact line between the circumferential outer wall of the roller and the bearing inner ring as a contact line C, and a contact line between the outer surface of the bearing inner ring and the roller as a contact line D;
s3, designing a radial load-temperature two-factor five-level orthogonal test scheme according to the actual service working condition of the bearing;
s4, according to the radial load-temperature two-factor five-level orthogonal test scheme, sequentially applying radial loads corresponding to the radial load-temperature two-factor five-level orthogonal test scheme to the roller in the bearing finite element submodel, setting a temperature field where the bearing finite element submodel is located, calculating stress values of a certain point on each contact line in different radial load-temperature two-factor five-level orthogonal test schemes through finite element analysis, and establishing a radial load-temperature stress value data set corresponding to each contact line;
training any 80% of data of the radial load-temperature stress value data concentration corresponding to each contact line by adopting a symbolic regression algorithm to obtain a radial load-temperature equivalent correlation function expression corresponding to a certain point on each contact line;
in step S4, a certain point on each contact line includes a fixed point and a maximum point, the fixed point is a position where a maximum stress value on the contact line is located when a radial load is applied only to the roller in the bearing finite element sub-model, and the maximum point is a position where a maximum stress value on each contact line is located when a radial load and an axial load are simultaneously applied to the roller in the bearing finite element sub-model;
in step S4, after obtaining the radial load-temperature equivalent correlation function expression corresponding to a certain point on each contact line, the remaining 20% of data in the radial load-temperature stress value data set corresponding to each contact line is used as verification data to verify the accuracy of the radial load-temperature equivalent correlation function expression.
4. The symbolic regression algorithm-based bearing load-temperature-stress equivalence method according to claim 3, wherein when a certain point on each contact line is a fixed point, the corresponding radial load-temperature equivalence correlation function is expressed as follows:
f A1 ＝1.265·x+2.246·z-0.01528·xz-89.63；
f B1 ＝-0.1623·x+1.492·z+0.02708·xz-8.942；
f C1 ＝1.193·x+1.994·z-55.38；
f D1 ＝0.4192·x+0.00775·z 2 +25.45；
in the formula:f A1 is the stress value at a fixed point on the contact line a,f B1 is the stress value of the fixed point on the contact line B,f C1 the stress value for a fixed point on the contact line C,f D1 the stress value of a fixed point on the contact line D is shown, x is the radial load, and z is the temperature;
when a certain point on each contact line is a maximum value point, the corresponding radial load-temperature equivalent correlation function expression is as follows:
f A2 ＝-0.4342·x+3.316·z+0.05027·xz-76.98；
f B2 ＝-4.536×10 -5 ·xz 2 +0.02401·z 2 +0.08346·x+71.5；
f C2 ＝5.739·x+17.96·z-486.0；
f Ｄ2 ＝0.4746·x+2.486·z+0.00524·xz-61.97；
in the formula:f A2 the stress value of the maximum point on the contact line a,f B2 the stress value of the maximum point on the contact line B,f C2 the stress value of the maximum point on the contact line C,f D2 the stress value of the maximum point on the contact line D is shown, x is the radial load, and z is the temperature.
5. A bearing load-temperature-stress equivalent method based on a symbolic regression algorithm is characterized by comprising the following steps:
s1, establishing a bearing three-dimensional model, and establishing a bearing finite element model according to the bearing three-dimensional model;
s2, establishing a bearing finite element sub-model according to the bearing finite element model, wherein the bearing finite element sub-model comprises a bearing outer ring, a bearing inner ring and a roller, and defines a contact line between the inner surface of the bearing outer ring and the roller as a contact line A, a contact line between the circumferential outer wall of the roller and the bearing outer ring as a contact line B, a contact line between the circumferential outer wall of the roller and the bearing inner ring as a contact line C, and a contact line between the outer surface of the bearing inner ring and the roller as a contact line D;
s3, designing a radial load-axial load-temperature three-factor five-horizontal orthogonal test scheme according to the actual service working condition of the bearing;
s4, according to the radial load-axial load-temperature three-factor five-horizontal orthogonal test scheme, sequentially applying corresponding radial loads and axial loads in the radial load-axial load-temperature three-factor five-horizontal orthogonal test scheme to a roller in a bearing finite element submodel, simultaneously setting a temperature field of the bearing finite element submodel, calculating and obtaining stress values of a certain point on each contact line in different radial load-axial load-temperature three-factor five-horizontal orthogonal test schemes through finite element analysis, and establishing a radial load-axial load-temperature stress value data set corresponding to each contact line;
training any 80% of data in the data concentration of the radial load-axial load-temperature stress value corresponding to each contact line by adopting a symbolic regression algorithm to obtain a radial load-axial load-temperature equivalent correlation function expression corresponding to a certain point on each contact line;
in step S4, a certain point on each contact line includes a fixed point and a maximum point, the fixed point is a position where a maximum stress value on the contact line is located when a radial load is applied only to the roller in the bearing finite element sub-model, and the maximum point is a position where a maximum stress value on each contact line is located when a radial load and an axial load are simultaneously applied to the roller in the bearing finite element sub-model;
in step S4, after obtaining the radial load-axial load-temperature equivalent correlation function expression corresponding to a certain point on each contact line, the remaining 20% of data in the radial load-axial load-temperature stress value data set corresponding to each contact line is used as verification data to verify the accuracy of the radial load-axial load-temperature equivalent correlation function expression.
6. The symbolic regression algorithm-based bearing load-temperature-stress equivalence method according to claim 5, wherein when a certain point on each contact line is a fixed point, the corresponding radial load-axial load-temperature equivalence correlation function expression is as follows:
f A1 ＝0.005465·z 2 -0.002224·xz+0.7544·z+0.1547；
f B1 ＝0.02725·xz-0.1736·x+1.508·z-9.605；
f C1 ＝1.205·x+2.0·z-56.61；
f D1 ＝0.4382·x+1.242·z-19.06；
in the formula:f A1 is the stress value at a fixed point on the contact line a,f B1 is the stress value of the fixed point on the contact line B,f C1 the stress value for a fixed point on the contact line C,f D1 the stress value of a fixed point on the contact line D is shown, x is the radial load, and z is the temperature;
when a certain point on each contact line is a maximum value point, the corresponding radial load-axial load-temperature equivalent correlation function expression is as follows:
f A2 ＝-8.189×10 -5 ·xz 2 +0.05326·xz+3.814·z-120.8；
f B2 ＝0.02593·z 2 -0.01335·xz+x+48.83；
f C2 ＝-0.09956·z 2 +34.0·z+5.629·x-1052.01；
f D2 ＝0.8832·x+2.745·z-82.02；
in the formula:f A2 the stress value of the maximum point on the contact line a,f B2 the stress value of the maximum point on the contact line B,f C2 the stress value of the maximum point on the contact line C,f D2 the stress value of the maximum point on the contact line D is shown, x is the radial load, and z is the temperature.
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