Calculation Method for Fatigue Reliability of Tire Demounter Bearings Based on Heterogeneous Dimensional Interference Model

Abstract

The present invention discloses a method for calculating the fatigue reliability of a tire dismounting machine bearing based on a heterogeneous dimension interference model. By using finite element analysis software and combining with the heterogeneous interference model, the service life and reliability of the bearing of the new tire dismounting machine are predicted. The theoretical method has a solid engineering and mathematical foundation, and the prediction results are also relatively scientific.

Description

Technical Field

[0001] The present invention belongs to the field of tire demounting machines, and particularly relates to a method for calculating the fatigue reliability of bearings of a tire demounting machine based on a heterodimensional interference model. Background Art

[0002] With the increase in the number of mining machinery in China, the number of tires used also increases. The giant tire demounting machine is specifically used to unload mining tires weighing 6t. During tire processing and production, the tire demounting machine is required to unload the tire and perform a 90° flip. During the flipping process, due to the huge inertial force of the tire, the tire is prone to collide with the tire demounting device, causing system vibration, and the bearings in the tire demounting device will also bear complex and variable loads. The complex working conditions are likely to cause the bearings to fail and trigger safety accidents. Summary of the Invention

[0003] In order to solve the deficiencies in the prior art, the present invention aims to provide a method for calculating the fatigue reliability of bearings of a tire demounting machine based on a heterodimensional interference model, and make predictions on the fatigue reliability of the bearings by combining engineering mechanics and statistical mathematical models.

[0004] To achieve the above object, the present invention adopts the following technical solutions:

[0005] A method for calculating the fatigue reliability of bearings of a tire demounting machine based on a heterodimensional interference model, the prediction method comprising the following steps:

[0006] 1) According to the structure of the tire demounting machine, establish a three-dimensional model of the tire demounting machine, and import the three-dimensional model of the tire demounting machine into ADAMS for dynamic simulation analysis, simulate the operation status of the tire demounting machine, and obtain the dynamic load spectrum of the bearing at the bottom rocker arm of the tire demounting machine;

[0007] 2) Establish a three-dimensional model of the bearing at the bottom rocker arm of the tire demounting machine, import the three-dimensional model of the bearing at the bottom rocker arm of the tire demounting machine and the dynamic load spectrum obtained by ADAMS into ANSYS for transient dynamic analysis of the bearing at the bottom rocker arm of the tire demounting machine, and obtain the equivalent stress load spectrum of the bearing at the bottom rocker arm of the tire demounting machine;

[0008] According to the results of the transient dynamic analysis, it is obtained that the fatigue part of the bearing is the inner ring of the bearing. Extract the stress time history of the fatigue part of the bearing, perform rainflow counting on the above stress time history, convert the random variable amplitude stress into a series of load cycles, and count the amplitude and mean distribution of the load cycles;

[0009] Use Goodman theory to correct the mean stress of the above load cycles, convert the stress state to a load cycle with a stress ratio of -1 according to equal life, and use the corrected load cycle as the equivalent stress for the next fatigue reliability analysis;

[0010] Perform probability statistics on the amplitude of the load cycle, fit it with the Weibull distribution, obtain the distribution-related parameters, and get the equivalent load distribution probability density function;

[0011] 3) Use the maximum likelihood method combined with the fatigue test data of bearing steel to obtain the life distribution parameters of bearing steel under any stress;

[0012] 4) According to the heterogeneous dimension interference model, complete the bearing fatigue reliability calculation under different lives.

[0013] In step 1), the bearing dynamic load spectra at the bottom rocker arm include the vertical force load spectrum, the axial force load spectrum, and the lateral load spectrum.

[0014] Furthermore, the specific method of step 3) is as follows:

[0015] Adopt the group method to conduct rotating bending fatigue tests on a group of actual samples, and correct the S-N relationship of the material to the S-N relationship of the actual samples. The correction formula is as follows:

[0016]

[0017] In the formula, σ a corresponds to the stress in the material test, S a corresponds to the stress of the actual sample, ε is the size coefficient, β is the surface quality coefficient, C L is the loading method, K f is the fatigue notch factor;

[0018] Use the Basquin equation combined with the maximum likelihood method to estimate the S-N curve of the bearing. The Basquin equation is

[0019] S m N = C;

[0020] In the formula, m is the exponent, N is the fatigue life, and C is a constant;

[0021] Taking the logarithm on both sides gives;

[0022] lgN p = lgC p -mlgS;

[0023] In the formula, the subscript p represents the survival rate. When the survival rate is 50%, the median of the logarithmic life is equal to the average value of the logarithmic life, that is:

[0024] μ(S) = lgN 50 = lgC - m 50 lgS;

[0025] In the formula, μ(S) is the mean value of the logarithmic life of the actual sample under different stresses;

[0026] The logarithmic life of bearing steel follows a normal distribution, and the relationship between the mean of logarithmic life and the standard deviation of logarithmic life under different survival rates is as follows:

[0027] μ(S) - lgN p = υ p σ(S);

[0028] In the formula, σ(S) is the standard deviation of the logarithmic life of the actual sample under different stresses, and υp is the standard normal deviation corresponding to the failure probability.

[0029] When the fatigue life N follows a lognormal distribution, its probability density function is:

[0030]

[0031] Substitute different stresses and the corresponding lives into the above probability density function and multiply to obtain the likelihood function:

[0032]

[0033] Take the logarithm of both sides of the above formula to obtain:

[0034] Based on the above formula, the life distribution parameters of bearing steel under any stress are obtained, and finally the logarithmic life mean of the actual sample and the logarithmic standard deviation parameter equation of the actual sample are obtained respectively.

[0035] Furthermore, the specific method of step 4) is as follows: According to the heterodimensional interference model, calculate the fatigue life under different reliabilities, and the model is as follows:

[0036]

[0037] In the formula, R is the fatigue reliability, h(S) is the probability density function of the equivalent load distribution, and f(n, S) is the probability density function of the life under different stresses.

[0038] The present invention adopts the above technical solutions and has the following beneficial effects:

[0039] The object of the present invention is a bearing of a giant tire unloading machine. Since the unloaded tire weighs 6 tons, the large tire unloading device is subjected to relatively complex forces and large impact forces during operation. As an important rotating support component on the tire unloading machine, the fatigue reliability of the bearing is an important part of the reliability of the whole machine system. However, at present, few people pay attention to the fatigue reliability of this kind of tire unloading machine bearing. The present invention fills the blank in this research field and provides theoretical support for the fatigue reliability of this new type of tire unloading machine bearing;

[0040] The numerical simulation method and prediction model used in the present invention have a solid foundation in engineering mechanics and mathematics. The prediction method is time-saving and labor-saving, and the prediction results are relatively reliable. The method used is applicable to the engineering field. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments;

[0042] Figure 1 is a schematic structural diagram of a tire changer;

[0043] Figure 2 is a three-dimensional model diagram of a tire changer;

[0044] Figure 3 is a schematic diagram of a virtual prototype of a tire changer;

[0045] Figure 4 is a schematic diagram of a vertical force load spectrum;

[0046] Figure 5 is a schematic diagram of an axial force load spectrum;

[0047] Figure 6 is a schematic diagram of a lateral load spectrum;

[0048] Figure 7 is a three-dimensional model diagram of the bearing at the bottommost rocker arm of the tire changer;

[0049] Figure 8 is a schematic diagram of the application of three-directional loads;

[0050] Figure 9 is a schematic diagram of the constraint and load application to the bearing at the bottommost rocker arm of the tire changer;

[0051] Figure 10 is the total deformation nephogram of the bearing at the bottommost rocker arm of the tire changer;

[0052] Figure 11 is the equivalent stress nephogram of the bearing at the bottommost rocker arm of the tire changer;

[0053] Figure 12 is the equivalent strain nephogram of the bearing at the bottommost rocker arm of the tire changer;

[0054] Figure 13 is the stress-time history diagram of the fatigue part of the bearing;

[0055] Figure 14 is the statistical result diagram of the rain flow counting of the stress-time history;

[0056] Figure 15 is the statistical result diagram of the stress amplitude frequency;

[0057] Figure 16 is the statistical result diagram of the stress mean frequency;

[0058] Figure 17 is the corrected equivalent load frequency statistical graph;

[0059] Figure 18 is the effect graph of Weibull distribution fitting amplitude;

[0060] Figure 19 is the schematic diagram of Weibull graphical method test;

[0061] Figure 20 is the comparison graph of median S-N curve and actual sample logarithmic life mean value;

[0062] Figure 21 is the comparison graph of standard deviation curve and actual sample logarithmic life standard deviation;

[0063] Figure 22 is the bearing fatigue reliability change curve graph. Specific implementation manner

[0064] Based on the multi-axial fatigue critical plane theory, the present invention combines the ANSYS and ADAMS numerical simulation platforms to predict the fatigue life of the bearings at the bottom rocker arm of the giant tire unloader. The specific structure of the tire unloader is as Figure 1 shown. The tire unloader has a total of 8 guide wheels and 16 pairs of rocker arms, and two deep groove ball bearings are installed at each rocker arm.

[0065] The specific operation steps are as follows:

[0066] The first part: Establish a three-dimensional model of the tire unloader, as Figure 2 shown, and import the three-dimensional model of the tire unloader into ADAMS, add relevant constraint forces and establish a virtual prototype of the tire unloader system as Figure 3 shown. First, perform a dynamic simulation analysis on the whole tire unloader to simulate the operation status of the tire unloader, and obtain the dynamic load spectra (vertical force load spectrum, axial force load spectrum and lateral load spectrum) at the bearings at the bottom rocker arm of the tire unloader (the bearings at this place are the bearings at the dangerous part, and the bearing model is 61918). The dynamic load spectra are as Figure 4 , 5 , and 6 shown.

[0067] The second part: Establish a three-dimensional model of the bearings at the rocker arm according to the actual bearing parameters, and omit unimportant components such as the cage, as Figure 7 shown.

[0068] Import the bearing model and the dynamic load spectra into ANSYS for transient dynamics analysis. The three-directional loads before 1 s are basically 0 N. To reduce the calculation amount, only perform transient dynamics analysis on the bearings between 1 s and 2 s. The load application is as Figure 8As shown, the material is set as GCr15 bearing steel. The bearing is constrained and loaded according to the actual working conditions as Figure 9 shown. During the process of the tire changer clamping the tire and turning it by 90°, as a supporting component, the bearing will not rotate. Therefore, it is set that the outer ring is completely fixed, the bottom surface of the inner ring is fully constrained, and the rotation of the ball around the revolution direction is constrained in the cylindrical coordinate system to simulate the effect of the cage on it. There is a frictional contact between the ball and the inner and outer rings. The friction scale factor is set to 0.02, the augmented Lagrangian algorithm is used, and the contact stiffness is set to 1. Mesh division is carried out, and there are a total of 72135 elements. The shortest simulation time step is set to 0.005 s, and the equivalent stress load spectrum and deformation results of the bearing are obtained as Figures 10 to 12 shown.

[0069] According to the transient dynamics analysis results, the fatigue part of the bearing is the inner ring of the bearing. The stress time history of the fatigue part of the bearing is extracted, the rain-flow counting is carried out on the above stress time history, the random variable amplitude stress is converted into a series of load cycles, and the amplitude and mean value distributions of the load cycles are statistically analyzed. The statistical results are as follows Figures 14 - 16 shown;

[0070] The Goodman theory is used to correct the mean stress of the above load cycles, the stress state is converted to the load cycle with a stress ratio of -1 according to the equal life, and the corrected load cycle is used as the equivalent stress for the next fatigue reliability analysis. The correction results are as Figure 17 shown;

[0071] The probability statistics of the amplitude of the load cycle are carried out, and it is fitted with the Weibull distribution to obtain the relevant distribution parameters; at the same time, the probability paper test is carried out on the distribution to obtain the fitting effect and test results, as Figure 18 , Figure 19 shown;

[0072] Take the confidence interval of 95% for the A-T hypothesis test. Through the test, it can be considered that the probability density function conforms to the Weibull distribution.

[0073] The Weibull related parameters are solved by the maximum likelihood method, and the relevant solution parameters are shown in the following table.

[0074] Table 1 Equivalent load distribution parameters

[0075]

[0076] The probability density function of the equivalent load distribution is:

[0077]

[0078] Part Three: The rotating bending fatigue test is carried out on a group of actual samples by the group method, and the test data are shown in the following table.

[0079] Table 2 Fatigue test data

[0080]

[0081]

[0082] Due to the differences in the actual working conditions, dimensions, and shapes of the bearings from those of the actual specimens used in the tests, as well as the form of the applied load, it is necessary to correct the S-N relationship of the material to that of the actual specimens. The correction formula is as follows:

[0083]

[0084] In the formula, σ a corresponds to the stress in the material during the test, S a corresponds to the stress of the actual specimen, ε is the size factor, and its value is taken as 0.856 by referring to the "Mechanical Design Handbook". β is the surface quality factor and is taken as 1. C L is the loading method. For steel in tension and compression, it is taken as 0.85. The fatigue notch factor K f is related to the stress concentration factor. The stress concentration of the bearing is generally related to the roughness. Here, it can be considered that the roughness of the bearing is the same as that of the specimen, and its value is taken as 1. The correction results are shown in the following table.

[0085] Table 3 Fatigue test data after correction

[0086]

[0087]

[0088] The fatigue life of general materials follows a lognormal distribution. Assuming that the life of bearing steel follows a lognormal distribution, the K-S hypothesis test is performed on the above data, and the hypothesis is correct through the test.

[0089] Using the Basquin equation combined with the maximum likelihood method to estimate the S-N curve of the bearing, the Basquin equation is

[0090] S m N = C (3);

[0091] In the formula, m is the exponent, N is the fatigue life, and C is a constant.

[0092] Taking the logarithm of both sides gives:

[0093] lgN p = lgC p -mlgS (4);

[0094] In the formula, the subscript p represents the survival rate. When the survival rate is 50%, the median of the logarithmic life is equal to the average value of the logarithmic life, that is,

[0095] μ(S) = lgN 50 = lgC - m 50 lgS(5);

[0096] Where μ(S) is the mean logarithmic life of the actual specimens under different stresses.

[0097] When S = 788 MPa, substituting the mean logarithmic life of the actual specimens with a stress of 788 MPa as the population mean into formulas (4) and (5), we can obtain

[0098] lgC = 2.90m 50 + 5.4061

[0099] μ(S) = 5.4061 - m 50 lgS + 2.90m 50 (6);

[0100] The logarithmic life of bearing steel follows a normal distribution, and the relationship between the mean logarithmic life and the standard deviation of logarithmic life at different survival rates is as follows:

[0101] μ(S) - lgN p = υ p σ(S) (7);

[0102] Where σ(S) is the standard deviation of the logarithmic life of the actual specimens under different stresses. υ p is the standard normal deviate corresponding to the failure probability and can be obtained by looking up the table.

[0103] Substituting formulas (4) and (5) into formula (7), we can obtain the following formula:

[0104]

[0105] Substituting the standard deviation of the logarithmic life of the actual specimens under a stress of 788 Mpa as the population standard deviation of logarithmic life into equation

[0106] (8), that is

[0107]

[0108] That is,

[0109] When the survival rate P = 84.1%, υ p = 1, after arrangement, we can obtain

[0110] σ(S) = 1.1344 + m 50 lgS + m 84.1 lgS (9);

[0111] When the fatigue life N follows a lognormal distribution, its probability density function is:

[0112]

[0113] Substitute different stresses and the corresponding lifetimes into the probability density function formula (10) and multiply them to obtain the likelihood function as formula (11).

[0114]

[0115] Take the logarithm of both sides of the above formula to obtain

[0116]

[0117] Convert formula (12) into formula (13), and find the minimum value of formula (13) to obtain the maximum value of the likelihood function formula (13).

[0118]

[0119] Find the minimum value of F to obtain the parameter m 50 , m 84.1 The maximum likelihood estimator of m 50 = 15.04, m 84.1 = 5.32,

[0120] Substitute the numerical values of the parameters m 50 , m 84.1 into formula (6) and formula (9) respectively to obtain the lifetime distribution parameters of bearing steel under any stress. The logarithmic lifetime mean value and logarithmic standard deviation parameter equations of the actual samples are shown in formulas (14) and (15).

[0121] σ(S) = 29.29 - 9.72lgS (14);

[0122] μ(S) = 48.97 - 15.04lgS (15);

[0123] Plot the S-N curve obtained by the maximum likelihood method, the logarithmic lifetime mean value of the samples, and the logarithmic standard deviation of the samples on the same graph for comparison. The logarithmic lifetime mean value and logarithmic lifetime standard deviation of the samples are shown in Table 4, and the comparison results are shown in Figure 20 , 21 . In a certain interval, the degree of coincidence is good, which proves that the parameter equations obtained by using the maximum likelihood method are relatively reasonable.

[0124] Table 4 Logarithmic Lifetime Mean Value and Standard Deviation of Actual Samples

[0125]

[0126]

[0127] Part IV: According to the heterogeneous dimension interference model, the fatigue life under different reliabilities is calculated. The model is shown in Equation (16). Substitute the above-calculated Equations (1) and (10) into the following Equation (16), and the final result is as Figure 22 shown.

[0128]

[0129] where R is the fatigue reliability, h(S) is the probability density function of the equivalent load distribution, and f(n,S) is the probability density function of the life under different stresses.

[0130] The above describes the implementation of the present invention in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific implementation manners. The above specific implementation manners are illustrative rather than restrictive of the present invention. Those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered by the scope of the claims and the specification of the present invention.

Claims

1. A method for calculating the fatigue reliability of a tire-changing machine bearing based on a heterodimensional interference model, characterized in that: The calculation method includes the following steps: 1) According to the structure of the tire-changing machine, establish a three-dimensional model of the tire-changing machine, and import the three-dimensional model of the tire-changing machine into ADAMS for dynamic simulation analysis to simulate the operation status of the tire-changing machine, and obtain the dynamic load spectrum of the bearing at the bottom rocker arm of the tire-changing machine; 2) Establish a three-dimensional model of the bearing at the bottom rocker arm of the tire-changing machine, and import the three-dimensional model of the bearing at the bottom rocker arm of the tire-changing machine and the dynamic load spectrum obtained by ADAMS into ANSYS for transient dynamic analysis of the bearing at the bottom rocker arm of the tire-changing machine, and obtain the equivalent stress load spectrum of the bearing at the bottom rocker arm of the tire-changing machine; According to the results of the transient dynamic analysis, the fatigue part of the bearing is the inner ring of the bearing. Extract the stress time history of the bearing fatigue part, perform rain flow counting on the above stress time history, convert the random variable amplitude stress into a series of load cycles, and statistically analyze the amplitude and mean distribution of the load cycles; Use Goodman theory to correct the mean stress of the above load cycles, convert the stress state to a load cycle with a stress ratio of -1 according to equal life, and use the corrected load cycle as the equivalent stress for the next fatigue reliability analysis; Perform probability statistics on the amplitude of the load cycle, fit it with Weibull distribution, find the relevant distribution parameters, and obtain the probability density function of the equivalent load distribution; 3) Use the maximum likelihood method combined with the fatigue test data of bearing steel to obtain the life distribution parameters of bearing steel under any stress; The specific method of step 3) is: Use the group method to conduct a rotating bending fatigue test on a group of actual samples, and correct the S-N relationship of the material to the S-N relationship of the actual samples. The correction formula is as follows: where, σ a corresponds to the stress in the material during the test, S a corresponds to the stress of the actual sample, ε is the size factor, β is the surface quality factor, C L is the loading method, K f is the fatigue notch factor; Use the Basquin equation combined with the maximum likelihood method to estimate the S-N curve of the bearing. The Basquin equation is S m N = C; In the formula, m is the exponent, N is the fatigue life, and C is a constant; Taking the logarithm on both sides, we can get; lgN p = lgC p - m lgS; In the formula, the subscript p represents the survival rate. When the survival rate is 50%, the median of the logarithmic life is equal to the average value of the logarithmic life, that is: μ(S) = lgN 50 = lgC - m 50 lgS; In the formula, μ(S) is the mean value of the logarithmic life of the actual samples under different stresses; The logarithmic life of bearing steel follows a normal distribution, and there is the following relationship between the mean value of the logarithmic life and the standard deviation of the logarithmic life under different survival rates: μ(S)-lgN p = υ p σ(S); where σ(S) is the standard deviation of the logarithmic life of the actual sample under different stresses, and υ p is the standard normal deviate corresponding to the failure probability When the fatigue life N follows a lognormal distribution, its probability density function is: Substitute different stresses and the corresponding lives into the above probability density function and multiply to obtain the likelihood function: Taking the logarithm on both sides of the above formula, we can get: Based on the above formula, the life distribution parameters of bearing steel under any stress are obtained. Finally, the parametric equations of the logarithmic life mean and the logarithmic standard deviation of the actual sample are obtained respectively; 4) According to the heterodimensional interference model, complete the calculation of the bearing fatigue reliability under different lives.

2. The method for calculating the fatigue reliability of a tire-changing machine bearing based on a heterodimensional interference model according to claim 1, characterized in that: In step 1), the dynamic load spectrum of the bearing at the bottom rocker arm includes a vertical force load spectrum, an axial force load spectrum, and a lateral load spectrum.

3. The method for calculating the fatigue reliability of a tire-changing machine bearing based on a heterodimensional interference model according to claim 1, characterized in that: The specific method of step 4): According to the heterodimensional interference model, calculate the fatigue life under different reliabilities. The model is as follows: Where R is the fatigue reliability, h(S) is the probability density function of the equivalent load distribution, and f(n,S) is the probability density function of the life at different stresses.

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