CN113946998A - Tire unloader bearing fatigue reliability calculation method based on different dimension interference model - Google Patents

Tire unloader bearing fatigue reliability calculation method based on different dimension interference model Download PDF

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CN113946998A
CN113946998A CN202111235092.8A CN202111235092A CN113946998A CN 113946998 A CN113946998 A CN 113946998A CN 202111235092 A CN202111235092 A CN 202111235092A CN 113946998 A CN113946998 A CN 113946998A
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bearing
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fatigue
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tire unloader
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王乾廷
程龙
凌静秀
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Fujian University of Technology
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Abstract

The invention discloses a tire unloader bearing fatigue reliability calculation method based on a different dimension interference model, which predicts the service life and reliability of a novel tire unloader bearing by combining a heterogeneous interference model through finite element analysis software.

Description

Tire unloader bearing fatigue reliability calculation method based on different dimension interference model
Technical Field
The invention belongs to the field of tire unloading machines, and particularly relates to a tire unloading machine bearing fatigue reliability calculation method based on a different-dimension interference model.
Background
Along with the increase of the number of mining machines in China, the number of tires used by the mining machines is also increased. The giant tire unloader is specially used for unloading mining tires with the weight of 6t, the tires need to be unloaded by the tire unloader and turned over for 90 degrees during tire processing and production, and during the turning over process, due to the huge inertia force of the tires, the tires are easy to collide with the tire unloader, so that system vibration is caused, and a bearing in the tire unloader can bear complicated and variable loads. The complex working condition easily makes the bearing take place inefficacy, causes the incident.
Disclosure of Invention
In order to solve the defects in the prior art, the invention aims to provide a tire unloader bearing fatigue reliability calculation method based on a different dimension interference model, and the fatigue reliability of a bearing is predicted by combining engineering mechanics and a statistical mathematical model.
In order to achieve the purpose, the invention adopts the following technical scheme:
the tire unloader bearing fatigue reliability calculation method based on the different dimension interference model comprises the following steps:
1) establishing a three-dimensional model of the tire unloader according to the structure of the tire unloader, guiding the three-dimensional model of the tire unloader into ADAMS for dynamic simulation analysis, simulating the operation condition of the tire unloader, and obtaining a dynamic load spectrum of a bearing at the lowest rocker arm of the tire unloader;
2) establishing a three-dimensional model of a bearing at the lowest rocker arm of the tire unloader, and leading the three-dimensional model of the bearing at the lowest rocker arm of the tire unloader and a dynamic load spectrum obtained by ADAMS into ANSYS to perform transient dynamics analysis on the bearing at the lowest rocker arm of the tire unloader so as to obtain an equivalent stress load spectrum of the bearing at the lowest rocker arm of the tire unloader;
obtaining a bearing fatigue part as a bearing inner ring according to the transient dynamics analysis result, extracting a stress time history of the bearing fatigue part, performing rain flow counting on the stress time history, converting random variable amplitude stress into a series of load cycles, and counting the amplitude and mean distribution of the load cycles;
carrying out average stress correction on the load cycle by using a Goodman theory, converting the stress state into the load cycle with the stress ratio of-1 according to the equal service life, and carrying out next fatigue reliability analysis by using the corrected load cycle as equivalent stress;
carrying out probability statistics on the amplitude of the load cycle, fitting by using Weibull distribution, and solving distribution related parameters to obtain an equivalent load distribution probability density function;
3) the service life distribution parameters of the bearing steel under any stress are obtained by combining the maximum likelihood method with the fatigue test data of the bearing steel;
4) and according to the different dimension interference model, the fatigue reliability calculation of the bearing under different service lives is completed.
In the step 1), the dynamic load spectrums of the bearing at the lowest rocker arm comprise a vertical force load spectrum, an axial force load spectrum and a transverse load spectrum.
Further, the specific method of the step 3) comprises the following steps:
performing a rotary bending fatigue test on a group of actual samples by using a grouping method, and correcting the S-N relation of the material into the S-N relation of the actual samples by using a correction formula as follows:
Figure BDA0003317417420000021
in the formula, σaCorresponding to the stress, S, of the test in the materialaCorresponding to the stress of the actual sample, epsilon is the size coefficient, beta is the surface quality coefficient, CLIn a loading mode, KfIs the fatigue notch coefficient;
estimating an S-N curve of the bearing by combining a Basquin equation with a maximum likelihood method
SmN＝C；
Wherein m is an index, N is a fatigue life, and C is a constant;
taking logarithm of two sides to obtain;
lgNp＝lgCp-mlgS；
where the subscript p denotes the survival rate, the median log life equals the mean log life when the survival rate is 50%:
μ(S)＝lgN50＝lgC-m50lgS；
in the formula, mu (S) is the mean value of the logarithmic life of actual samples under different stresses;
the bearing steel logarithmic life is distributed normally, and the logarithmic life mean value and the logarithmic life standard deviation under different survival rates are related as follows:
μ(S)-lgNp＝υpσ(S)；
wherein, sigma (S) is the standard deviation of logarithmic life of actual samples under different stresses, upsilonPIs a standard normal offset corresponding to the probability of corruption,
when the fatigue life N follows the lognormal distribution, the probability density function is as follows:
Figure BDA0003317417420000031
substituting different stresses and corresponding lives into the probability density function and multiplying to obtain a likelihood function:
Figure BDA0003317417420000032
taking logarithm of two sides of the above formula to obtain:
Figure BDA0003317417420000033
and obtaining the service life distribution parameters of the bearing steel under any stress based on the formula, and finally obtaining the logarithmic service life mean value of the actual sample piece and the logarithmic standard deviation parameter equation of the actual sample piece respectively.
Further, the specific method of the step 4) comprises the following steps: according to the different dimension interference model, the fatigue life under different reliabilities is calculated, and the model is as follows:
Figure BDA0003317417420000034
wherein R is fatigue reliability, h (S) is an equivalent load distribution probability density function, and f (n, S) is a life probability density function under different stresses.
By adopting the technical scheme, the invention has the following beneficial effects:
the invention aims at a giant tire unloader bearing, and because the unloaded tire weight reaches 6 tons, the large tire unloader is complex in stress and large in various impact forces in the working process. The bearing is used as an important rotary supporting component on the tire unloader, the fatigue reliability of the bearing is an important ring in the reliability of a whole tire unloader system, but the fatigue reliability of the bearing of the tire unloader is less concerned at present, the invention fills the blank of the research field, and makes theoretical support for the fatigue reliability of the bearing of the novel tire unloader;
the numerical simulation method and the prediction model applied by the invention have solid engineering mechanics and mathematical foundation, the prediction method is time-saving and labor-saving, the prediction result is relatively reliable, and the used method is suitable for the engineering field.
Drawings
The invention is described in further detail below with reference to the accompanying drawings and the detailed description;
FIG. 1 is a schematic structural view of a tire unloader;
FIG. 2 is a three-dimensional model diagram of the tire unloader;
FIG. 3 is a schematic diagram of a virtual prototype of a tire unloader;
FIG. 4 is a schematic diagram of a vertical force load spectrum;
FIG. 5 is a schematic of an axial force load spectrum;
FIG. 6 is a schematic of a transverse load spectrum;
FIG. 7 is a three-dimensional model view of a bearing at the lowermost rocker arm of the tire unloader;
FIG. 8 is a schematic view of a three-way load application;
FIG. 9 is a schematic view of the restraint and load application of the bearing at the lowermost rocker arm of the tire unloader;
FIG. 10 is a cloud of the total deformation of the bearing at the lowermost rocker arm of the tire unloader;
FIG. 11 is an equivalent stress cloud of a bearing at the lowermost rocker arm of the tire unloader;
FIG. 12 is an equivalent strain cloud of a bearing at the lowermost rocker arm of the tire unloader;
FIG. 13 is a time history of stress at a fatigue location of a bearing;
FIG. 14 is a graph of the statistics of stress time history rain flow counts;
FIG. 15 is a graph of stress magnitude frequency statistics;
FIG. 16 is a graph of stress mean frequency statistics;
FIG. 17 is a corrected equivalent load frequency histogram;
FIG. 18 is a graph of the effect of fitting amplitudes on a Weibull distribution;
FIG. 19 is a schematic representation of a Weibull plot test;
FIG. 20 is a graph comparing the median S-N curve to the log life mean of actual samples;
FIG. 21 is a graph of standard deviation curves versus log life standard deviation for actual samples;
FIG. 22 is a graph showing the fatigue reliability of a bearing.
Detailed Description
The method is based on the multiaxial fatigue critical surface theory, and combined with ANSYS and ADAMS numerical simulation platforms, the fatigue life of a bearing at the lowermost rocker arm of the giant tire unloader is predicted, and the tire unloader has the structure shown in figure 1. The tire unloader is provided with 8 guide rail wheels in total, 16 pairs of rocker arms, and two deep groove ball bearings are arranged at each rocker arm.
The specific operation steps are as follows:
a first part: building a three-dimensional model of the tire unloader, as shown in fig. 2, introducing the three-dimensional model of the tire unloader into ADAMS, adding related constraint force and building a virtual prototype of a tire unloader system, as shown in fig. 3, firstly carrying out dynamic simulation analysis on the whole tire unloader, simulating the operation condition of the tire unloader, and obtaining dynamic load spectrums (a vertical force load spectrum, an axial force load spectrum and a transverse load spectrum) at a bearing (here, a bearing at a dangerous part, and the bearing model is 61918) at the lowest rocker arm of the tire unloader, wherein the dynamic load spectrums are shown in fig. 4, 5 and 6.
A second part: and establishing a three-dimensional model of the bearing at the rocker arm according to the actual bearing parameters, and omitting non-important parts such as a retainer and the like, as shown in FIG. 7.
And (3) introducing the bearing model and the dynamic load spectrum into ANSYS for transient dynamic analysis, wherein the three-way load before 1s is basically 0N, only the bearing between 1s and 2s is subjected to the transient dynamic analysis for reducing the calculation amount, the load is applied as shown in FIG. 8, and the material is GCr15 bearing steel. The bearing is restrained and loaded according to actual working conditions, and the restraint and the loading are shown in figure 9. In the process that the tire unloader clamps a tire and turns over 90 degrees, the bearing is used as a supporting part and cannot rotate, so that the outer ring is set to be completely fixed, the bottom surface of the inner ring is fully constrained, the rotation of the ball in the revolution direction is constrained by a cylindrical coordinate system to simulate the action of a constraint frame on the ball, the ball is in friction contact with the inner ring and the outer ring, the friction proportion factor is set to be 0.02, the algorithm adopts an augmented Lagrange algorithm, and the contact rigidity is set to be 1. The grid division was performed for a total of 72135 cells. The shortest simulation time step is set to be 0.005s, and the equivalent stress load spectrum and the deformation result of the bearing are obtained and are shown in FIGS. 10 to 12.
Obtaining a bearing fatigue part as a bearing inner ring according to the analysis result of transient dynamics, extracting a stress time history of the bearing fatigue part, performing rain flow counting on the stress time history, converting random variable amplitude stress into a series of load cycles, and counting the amplitude and mean distribution of the load cycles, wherein the counting result is shown in the following figures 14-16;
the average stress of the load cycle is corrected by using the Goodman theory, the stress state is converted into the load cycle with the stress ratio of-1 according to the equal service life, the corrected load cycle is used as the equivalent stress to carry out the next fatigue reliability analysis, and the correction result is shown in FIG. 17;
carrying out probability statistics on the amplitude of the load cycle, fitting by using Weibull distribution, and solving distribution related parameters; meanwhile, probability paper inspection is carried out on the distribution to obtain a fitting effect and an inspection result, which are respectively shown in fig. 18 and fig. 19;
and performing A-T hypothesis test with a confidence interval of 95%, wherein the probability density function can be considered to be in accordance with Weibull distribution through the test.
Solving the Weibull correlation parameters by using a maximum likelihood method, wherein the correlation solving parameters are shown in the following table.
TABLE 1 equivalent load distribution parameters
Figure BDA0003317417420000051
The equivalent load distribution probability density function is:
Figure BDA0003317417420000061
and a third part: the grouping method performed a rotary bending fatigue test on a group of actual samples, and the test data are shown in the following table.
TABLE 2 fatigue test data
Figure BDA0003317417420000062
Figure BDA0003317417420000071
Because the actual working condition, the size and the shape of the bearing are different from the shape and the loading load form of an actual sample used in the test, the S-N relation of the material needs to be corrected into the S-N relation of the actual sample, and the correction formula is as follows:
Figure BDA0003317417420000072
in the formula, σaCorresponding to the stress, S, of the test in the materialaCorresponding to the stress of the actual sample, epsilon is a size coefficient, the value is 0.856 by looking up a mechanical design manual, beta is a surface quality coefficient, and 1, C is takenLFor the loading mode, the steel material is drawn and pressed to 0.85. Coefficient of fatigue failure KfThe bearing stress concentration is generally related to the roughness in relation to the stress concentration coefficient, and here, the roughness of the bearing and the test piece can be considered to be consistent, and the value is 1. The results of the correction are shown in the following table.
TABLE 3 corrected fatigue test data
Figure BDA0003317417420000073
Figure BDA0003317417420000081
Generally, the fatigue life of the material is subjected to the log-normal distribution, the bearing steel life is assumed to be subjected to the log-normal distribution, K-S hypothesis test is carried out on the data, and the hypothesis is correct through the test.
Estimating an S-N curve of the bearing by combining a Basquin equation with a maximum likelihood method
SmN＝C (3)；
In the formula, m is an index, N is a fatigue life, and C is a constant.
Taking logarithm of two sides to obtain:
lgNp＝lgCp-mlgS (4)；
where the subscript p denotes the survival rate, the median log life equals the mean log life when the survival rate is 50%, i.e.,
μ(S)＝lgN50＝lgC-m50 lgS (5)；
in the formula, μ (S) is the mean logarithmic life of actual samples under different stresses.
When S is 788MPa, the logarithmic life mean of the actual sample with a stress of 788MPa is substituted into the formulae (4), (5) as the parent mean,
lgC＝2.90m50+5.4061
μ(S)＝5.4061-m50lgS+2.90m50 (6)；
the bearing steel logarithmic life is distributed normally, and the logarithmic life mean value and the logarithmic life standard deviation under different survival rates are related as follows:
μ(S)-lgNp＝υpσ(S) (7)；
wherein, the sigma (S) is the standard deviation of the logarithmic life of the actual sample under different stresses. Upsilon isPIs a standard normal offset corresponding to the failure probability, and can be obtained by looking up a table.
Substituting equations (4), (5) into equation (7) yields the following equation:
Figure BDA0003317417420000091
substituting the standard deviation of the logarithmic life of the actual sample piece under the stress of 788Mpa into formula (8) as the standard deviation of the logarithmic life of the parent body, namely
Figure BDA0003317417420000092
That is to say that the first and second electrodes,
Figure BDA0003317417420000093
when the survival rate P is 84.1%, upsilon p1, the product can be obtained by finishing,
σ(S)＝1.1344+m50lgS+m84.1lgS (9)；
when the fatigue life N follows the lognormal distribution, the probability density function is as follows:
Figure BDA0003317417420000094
substituting different stresses and corresponding lives into a probability density function expression (10) and multiplying to obtain a likelihood function expression (11),
Figure BDA0003317417420000101
the logarithm of the two sides of the formula is obtained,
Figure BDA0003317417420000102
the maximum value of the likelihood function equation (13) can be obtained by converting equation (12) into equation (13) and obtaining the minimum value of equation (13),
Figure BDA0003317417420000103
finding the minimum value of F to obtain the parameter m50，m84.1M is the maximum likelihood estimator of50＝15.04，m84.1＝5.32，
Will be the parameter m50、m84.1Numerical values are respectively substituted into the formula (6) and the formula (9) to obtain service life distribution parameters of the bearing steel under any stress, and logarithmic service life mean values of actual samples and logarithmic standard deviation parameter equations of the actual samples are shown in the formulas (14) and (15).
σ(S)＝29.29-9.72lgS (14)；
μ(S)＝48.97-15.04lgS (15)；
And drawing an S-N curve obtained by a maximum likelihood method, the log life mean value of the sample and the log standard deviation of the sample in the same graph for comparison, wherein the log life mean value of the sample and the log life standard deviation of the sample are shown in a table 4, and comparison results are shown in fig. 20 and 21. Within a certain interval, the goodness of fit is better, and the parameter equation calculated by using the maximum likelihood method is proved to be more reasonable.
TABLE 4 logarithmic life mean and standard deviation of actual samples
Figure BDA0003317417420000104
Figure BDA0003317417420000111
The fourth part: fatigue life under different reliability was calculated from the different-dimension interference model, which is expressed by the formula (16), and the final result is shown in fig. 22 by substituting the above-calculated formulas (1) and (10) into the formula (16).
Figure BDA0003317417420000112
Wherein R is fatigue reliability, h (S) is an equivalent load distribution probability density function, and f (n, S) is a life probability density function under different stresses.
While the invention has been described in connection with the above embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, which are illustrative and not restrictive, and that those skilled in the art will understand that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the present invention, and they should be construed as being included in the following claims and description.

Claims (4)

1. The tire unloader bearing fatigue reliability calculation method based on the different dimension interference model is characterized by comprising the following steps: the prediction method comprises the following steps:
1) establishing a three-dimensional model of the tire unloader according to the structure of the tire unloader, guiding the three-dimensional model of the tire unloader into ADAMS for dynamic simulation analysis, simulating the operation condition of the tire unloader, and obtaining a dynamic load spectrum of a bearing at the lowest rocker arm of the tire unloader;
2) establishing a three-dimensional model of a bearing at the lowest rocker arm of the tire unloader, and leading the three-dimensional model of the bearing at the lowest rocker arm of the tire unloader and a dynamic load spectrum obtained by ADAMS into ANSYS to perform transient dynamics analysis on the bearing at the lowest rocker arm of the tire unloader so as to obtain an equivalent stress load spectrum of the bearing at the lowest rocker arm of the tire unloader;
obtaining a bearing fatigue part as a bearing inner ring according to the transient dynamics analysis result, extracting a stress time history of the bearing fatigue part, performing rain flow counting on the stress time history, converting random variable amplitude stress into a series of load cycles, and counting the amplitude and mean distribution of the load cycles;
carrying out average stress correction on the load cycle by using a Goodman theory, converting the stress state into the load cycle with the stress ratio of-1 according to the equal service life, and carrying out next fatigue reliability analysis by using the corrected load cycle as equivalent stress;
carrying out probability statistics on the amplitude of the load cycle, fitting by using Weibull distribution, and solving distribution related parameters to obtain an equivalent load distribution probability density function;
3) the service life distribution parameters of the bearing steel under any stress are obtained by combining the maximum likelihood method with the fatigue test data of the bearing steel;
4) and according to the different dimension interference model, the fatigue reliability calculation of the bearing under different service lives is completed.
2. The method for calculating the fatigue reliability of the bearing of the tire unloader based on the different-dimension interference model according to claim 1, wherein: in the step 1), the dynamic load spectrums of the bearing at the lowest rocker arm comprise a vertical force load spectrum, an axial force load spectrum and a transverse load spectrum.
3. The method for calculating the fatigue reliability of the bearing of the tire unloader based on the different-dimension interference model according to claim 1, wherein: the specific method of the step 3) comprises the following steps:
performing a rotary bending fatigue test on a group of actual samples by using a grouping method, and correcting the S-N relation of the material into the S-N relation of the actual samples by using a correction formula as follows:
Figure FDA0003317417410000011
in the formula, σaCorresponding to the stress, S, of the test in the materialaCorresponding to the stress of the actual sample, epsilon is the size coefficient, beta is the surface quality coefficient, CLIn a loading mode, KfIs the fatigue notch coefficient;
estimating an S-N curve of the bearing by combining a Basquin equation with a maximum likelihood method
SmN＝C；
Wherein m is an index, N is a fatigue life, and C is a constant;
taking logarithm of two sides to obtain;
lgNp＝lgCp-mlgS；
where the subscript p denotes the survival rate, the median log life equals the mean log life when the survival rate is 50%:
μ(S)＝lgN50＝lgC-m50lgS；
in the formula, mu (S) is the mean value of the logarithmic life of actual samples under different stresses;
the bearing steel logarithmic life is distributed normally, and the logarithmic life mean value and the logarithmic life standard deviation under different survival rates are related as follows:
μ(S)-lgNp＝υpσ(S)；
wherein, sigma (S) is the standard deviation of logarithmic life of actual samples under different stresses, upsilonPIs a standard normal offset corresponding to the probability of corruption,
when the fatigue life N follows the lognormal distribution, the probability density function is as follows:
Figure FDA0003317417410000021
substituting different stresses and corresponding lives into the probability density function and multiplying to obtain a likelihood function:
Figure FDA0003317417410000022
taking logarithm of two sides of the above formula to obtain:
Figure FDA0003317417410000023
and obtaining the service life distribution parameters of the bearing steel under any stress based on the formula, and finally obtaining the logarithmic service life mean value of the actual sample piece and the logarithmic standard deviation parameter equation of the actual sample piece respectively.
4. The method for calculating the fatigue reliability of the bearing of the tire unloader based on the different-dimension interference model according to claim 3, wherein: the specific method of the step 4) comprises the following steps: according to the different dimension interference model, the fatigue life under different reliabilities is calculated, and the model is as follows:
Figure FDA0003317417410000031
wherein R is fatigue reliability, h (S) is an equivalent load distribution probability density function, and f (n, S) is a life probability density function under different stresses.
CN202111235092.8A 2021-10-22 2021-10-22 Tire unloader bearing fatigue reliability calculation method based on different dimension interference model Pending CN113946998A (en)

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