CN113312822B - Method for predicting multi-axial fatigue life of bearing of tire unloader - Google Patents

Method for predicting multi-axial fatigue life of bearing of tire unloader Download PDF

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CN113312822B
CN113312822B CN202110636711.8A CN202110636711A CN113312822B CN 113312822 B CN113312822 B CN 113312822B CN 202110636711 A CN202110636711 A CN 202110636711A CN 113312822 B CN113312822 B CN 113312822B
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凌静秀
程龙
王乾廷
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Fujian University of Technology
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Abstract

The invention discloses a method for predicting the multi-axial fatigue life of a bearing of a tire unloader, which predicts the fatigue life of the bearing of the tire unloader by using a multi-axial fatigue critical surface theory, only considers the influence of normal stress on the service life compared with the traditional L-P bearing service life prediction theory, considers the influence of shearing, pulling and pressing multi-axial random variable amplitude stress, better accords with the actual condition of the bearing, and has more scientific prediction model and theory.

Description

Method for predicting multi-axial fatigue life of bearing of tire unloader
Technical Field
The invention belongs to the field of tire unloaders, and particularly relates to a method for predicting the multi-axial fatigue life of a bearing of a tire unloader.
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 method for predicting the multi-axial fatigue life of a bearing of a tire unloader, and provide related theoretical support for the mechanical characteristics and the use safety of the bearing.
In order to achieve the purpose, the invention adopts the following technical scheme:
a prediction method for multi-axial fatigue life of a tire unloader bearing, the prediction method comprising the steps of:
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 (here, a dangerous part bearing) at the rocker arm at the lowest part of the tire unloader;
2) establishing a three-dimensional model of a bearing at the lowest rocker arm of the tire unloader;
3) leading a three-dimensional model of a bearing at the lowest rocker arm of the tire unloader and a dynamic load spectrum obtained by ADAMS into ANSYS to carry out transient dynamic 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;
4) according to transient dynamics analysis, finding out a node with the maximum equivalent stress in ANSYS and obtaining the stress and strain time history of the node with the maximum equivalent stress;
5) searching a maximum shear strain surface of the maximum positive strain according to the stress and strain of the node with the maximum equivalent stress in combination with elastic mechanics, taking the surface as a critical surface, calculating normal positive strain, shear strain and positive stress on the critical surface, and recording the change history of the normal positive strain, the shear strain and the positive stress along with time;
6) carrying out cycle counting on three parameters of normal positive strain, shear strain and positive stress;
7) and combining the Wang-Brown model to predict the service life.
Further, in the step 1), the dynamic load spectrums of the bearing at the lowest rocker arm all comprise a vertical force load spectrum, an axial force load spectrum and a transverse load spectrum.
Further, the method for performing transient kinetic analysis in step 3) is as follows: the method comprises the steps of setting a material of a bearing at the lowest rocker arm of the tire unloader, constraining the bearing at the lowest rocker arm of the tire unloader and applying a load, setting an outer ring to be completely fixed, constraining the bottom surface of the inner ring to be completely constrained, constraining the rotation of a ball around the revolution direction by a cylindrical coordinate system to simulate the action of a constraint frame on the bearing, enabling the ball to be in friction contact with the inner ring and the outer ring, setting contact rigidity by adopting an augmented Lagrange algorithm, carrying out grid division to obtain the bearing at the rocker arm, and obtaining an equivalent stress load spectrum of the bearing at the lowest rocker arm of the tire unloader.
Further, the specific method for determining the critical plane in step 5) is as follows:
according to the stress and strain of the maximum node of the equivalent stress obtained by transient dynamics analysis, combining elastic mechanics, rotation stress and strain coordinates to any plane, the stress and strain on any plane are obtained, and the conversion formula is shown as the following formulas (1), (2) and (3), wherein theta, phi, and delta,
Figure GDA0003578593430000021
The value ranges of the two angles are [0 degrees, 180 degrees ], theta, and theta, and theta, and theta, and theta, and theta, and theta, and beta, and beta, and beta, beta,
Figure GDA0003578593430000022
Taking a search step length to search a critical surface, and obtaining the rest strain and stress components in the same way;
ε'＝(M)Tε(M) (1)；
σ'＝(M)Tσ(M) (2)；
in the formula, epsilon and sigma are strain tensors and stress tensors in an original coordinate system, and epsilon 'and sigma' are strain tensors and stress tensors in a new rotated coordinate system;
wherein the transformation matrix M is:
Figure GDA0003578593430000023
finding out a maximum shear strain surface with the maximum normal positive strain at the moment as a critical surface;
carrying out weighted average on two adjacent critical surfaces, wherein the calculation formula of the weight W (t) is shown as a formula (4),
Figure GDA0003578593430000024
in the formula, τ-1G is the shear modulus, D (t) is the degree of damage at this time, γmaxThe damage degree is obtained by the maximum shear strain for the maximum shear strain, and the calculation formulas are shown in formulas (5) and (6).
Figure GDA0003578593430000031
D(t)＝1/Nk (6)；
In formula (II), sigma'fIs the fatigue strength coefficient, σbIs the tensile strength of the bearing steel, and b and c are respectively a fatigue strength index and a fatigue ductility index epsilon'fIs fatigue ductility coefficient, NkFatigue life is considered; the weighted critical surface orientation calculation formula is shown in formulas (7), (8) and (9),
Figure GDA0003578593430000032
Figure GDA0003578593430000033
Figure GDA0003578593430000034
in the formula, θ (t),
Figure GDA0003578593430000035
And determining the final critical surface for the critical surfaces at different moments by carrying out weighted average on the two critical surfaces at different moments.
Further, the specific method of step 7) is as follows: the Wang-Brown model is of formula (10):
Figure GDA0003578593430000036
wherein the content of the first and second substances,
Figure GDA0003578593430000037
in order to maximize the amplitude of the shear strain,
Figure GDA0003578593430000038
is the maximum normal positive strain range, σ, in a shear strain cyclen,meanIs the average positive stress in a shear strain cycle, upsilon is Poisson's ratio, NfIs a life value, E is an elastic modulus, σ'fAnd b is the fatigue strength coefficient and index, ε'fAnd c is the fatigue ductility coefficient and index, the multiaxial parameter S is determined by the tensile and torsional fatigue limit, the multiaxial parameter S is of the formula (11):
Figure GDA0003578593430000039
in the formula, τ-1、σ-1Respectively a torsion limit and a tensile limit;
the shear strain cycle obtained by cycle counting and the maximum positive strain range are synthesized into an equivalent strain
Figure GDA0003578593430000041
At the same time, the corresponding average normal stress is substituted to calculate NfAnd calculating the damage D under the parameterf＝1/NfAnd (3) sequentially substituting the parameters of all the cycles into the formula (10), calculating the damage of each time, finally performing linear accumulation on the damage of each time according to a linear Miner formula, calculating the damage degree of one period, and converting the damage degree into the time length to obtain the fatigue life of the bearing at the lowest rocker arm.
By adopting the technical scheme, the invention has the following beneficial effects:
1. the invention predicts the bearing on the tire unloader, the life of the bearing of the tire unloader is rarely studied at present, the invention combines the numerical simulation method and the multiaxial life fatigue theory to study the novel tire unloader, and a more scientific method is provided for the prediction of the bearing life of the novel tire unloader;
2. compared with the traditional L-P bearing service life prediction theory that only the influence of normal stress on the service life is considered, the invention considers the influence of shearing, pulling and pressing multi-axis random variable amplitude stress, better accords with the actual condition of the bearing, and has more scientific prediction model and theory.
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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 a 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 schematic diagram of the normal stress time history (MPa) of node X plane 29;
FIG. 14 is a schematic diagram of the normal stress time history (MPa) of node X plane 29;
FIG. 15 is a schematic view of node number 29, plane X, positive strain (mm/mm);
FIG. 16 is a schematic view of XY-plane shear strain time history (rad/rad) at node number 29;
FIG. 17 shows [ epsilon ] at different bit planes'z、γ′yz、γ′zxCalculating a result graph of the strain value;
FIG. 18 shows the maximum shear stress threshold plane search (two lines 1 and 2 are θ,
Figure GDA0003578593430000051
Value);
FIG. 19 is a schematic diagram of the time course of three parameters (normal positive strain, shear strain, positive stress) of the critical plane;
FIG. 20 is a schematic of a three parameter cycle count;
FIG. 21 is a graph of the results of a three parameter cycle count.
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, the first part is: 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 a third part: 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.
The fourth part: looking at the node with the maximum equivalent stress number of 29 nodes in ANSYS, the stress and strain time histories of the node with the maximum equivalent stress (dangerous node) are obtained, and the partial stress and strain component time histories are shown in FIGS. 13-16.
The fifth part is that: according to the stress strain of the maximum node of the equivalent stress obtained by transient dynamics analysis, combining elastic mechanics, rotation stress and strain coordinates to any plane, the stress and the strain on any plane are obtained, and the conversion formula is shown as the following formulas (1), (2) and (3), wherein theta, phi, and phi,
Figure GDA0003578593430000061
The value ranges of the two angles are both (0 DEG, 180 DEG), and the calculation precision and the calculation amount, theta, and theta, and theta, are all taken into consideration,
Figure GDA0003578593430000062
And taking 10 degrees as a search step length to search the critical plane. The remaining strain and stress components are obtained in the same manner. The following calculations are all accomplished by MATLAB programming. Each time instant searches 18 x 18 planes. The results of the different plane strain calculations are shown in fig. 17.
ε'＝(M)Tε(M) (1)；
σ'＝(M)Tσ(M) (2)；
In the formula, epsilon and sigma are strain tensors and stress tensors in an original coordinate system, and epsilon 'and sigma' are strain tensors and stress tensors in a new coordinate system after rotation.
Wherein the transformation matrix M is:
Figure GDA0003578593430000063
the plane of maximum shear strain with the maximum normal positive strain at this time is found as the critical plane. The search results are shown in fig. 18.
The maximum shear strain surface at each moment is basically concentrated on theta being 100 degrees,
Figure GDA0003578593430000064
θ＝80°、
Figure GDA0003578593430000065
Figure GDA0003578593430000066
It is believed that the stress ratio changes at a certain time of the bearing, and the critical plane changes at this time. And carrying out weighted average on the two adjacent critical surfaces, wherein the weight W (t) is calculated according to the formula (4).
Figure GDA0003578593430000067
In the formula, τ-1For shear fatigue limit, it is generally 0.357. sigmabHere 213MPa, G is the shear modulus, 230GPa is obtained by table look-up, D (t) is the damage degree at this moment, gammamaxThe damage degree is obtained by the maximum shear strain for the maximum shear strain, and the calculation formulas are shown in formulas (5) and (6).
Figure GDA0003578593430000071
D(t)＝1/Nk (6)；
In the formula, sigma'fThe value for the fatigue strength coefficient is 1.5. sigmab，σbThe tensile strength of the bearing steel is 1080MPa according to a table look-up. b. c is fatigue strength index and fatigue ductility index, and the steel structure is generally-0.087 and-0.58 respectively. Epsilon'fCoefficient of fatigue ductility asb/E>0.003'f＝0.59(1.375-125σb[ E ]) by calculating ε'f＝0.432。NkThe fatigue life is considered. The weighted critical plane orientation calculation formula is shown in formulas (7) to (9).
Figure GDA0003578593430000072
Figure GDA0003578593430000073
Figure GDA0003578593430000074
In the formula, θ (t),
Figure GDA0003578593430000075
Critical surfaces at different moments are weighted and averaged, and the mean critical surface is 87.62 degrees,
Figure GDA0003578593430000076
Taking theta as 90 DEG,
Figure GDA0003578593430000077
As the final critical plane, normal positive strain, shear strain, and positive stress on the critical plane were calculated, and the time-dependent changes in the three parameters (normal positive strain, shear strain, and positive stress) were recorded, and the calculation results are shown in fig. 19.
A sixth part: on the basis of obtaining a final critical surface, recording time histories of three parameters of normal positive strain, shear strain and positive stress on the critical surface, performing rain flow counting on the shear strain of a main parameter, wherein the principle of the three-parameter rain flow counting is shown in fig. 20, a 2-3-2 'is a shear strain cycle, in a range with an abscissa as 2-2', in the normal positive strain history, taking a peak point and a valley point 3 'as middle points, respectively calculating longitudinal distances between the middle point and two points in front and at the back, comparing the two values, taking the larger value as the normal positive strain history, in the normal stress history, in the range with the abscissa as 2-2', recording the maximum and minimum positive stresses, and simultaneously recording the average of the two values. The counting results are shown in fig. 21, and 32 cycles are counted.
A seventh part: and (3) combining the Wang-Brown model to predict the service life, wherein the model is shown as a formula (10).
Figure GDA0003578593430000081
In the formula (I), the compound is shown in the specification,
Figure GDA0003578593430000082
in order to maximize the amplitude of the shear strain,
Figure GDA0003578593430000083
is the maximum normal positive strain range, σ, in a shear strain cyclen，meanIs the average normal stress over one shear strain cycle. Upsilon is the poisson ratio. A table look-up shows that the Poisson ratio of the bearing steel is 0.3. The multiaxial parameter S may be determined from the tensile and torsional fatigue limits, as shown in equation (11). E is the modulus of elasticity and has a value of 210 GPa. N is a radical offIs a life value.
Figure GDA0003578593430000084
In the formula, τ-1、σ-1Respectively the torsion limit and the tensile limit. Sigma-1Typically 0.357 σbHere, the value is 386 MPa. Tau is-1231MPa, a ratio of the torsional limit to the tensile limit of 0.6, and S equal to 0.37.
Combining the shear strain cycle obtained by the cycle counting and the maximum positive strain range into an equivalent strain
Figure GDA0003578593430000085
At the same time, the corresponding average normal stress is substituted to calculate NfAnd calculating the damage D under the parameterf＝1/NfThe 32 cycle parameters are substituted into the formula in turn to obtain the damage of each time, and finally the damage of each time is linearly accumulated according to Miner formula to obtain the damage degree D of 4.59 multiplied by 10 in one period-6The circulation time is 2177928 times, each time is 2s, and the time length is 1209.96 h.
While the invention has been described in connection with the above embodiments, which are intended to be illustrative and not limiting, it will be understood by those of ordinary skill in the art 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 (3)

1. A prediction method for multi-axial fatigue life of a bearing of a tire unloader 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;
3) leading a three-dimensional model of a bearing at the lowest rocker arm of the tire unloader and a dynamic load spectrum obtained by ADAMS into ANSYS to carry out transient dynamic 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;
4) according to transient dynamics analysis, finding out a node with the maximum equivalent stress in ANSYS and obtaining the stress and strain time history of the node with the maximum equivalent stress;
5) searching a maximum shear strain surface of the maximum positive strain according to the stress and strain of the node with the maximum equivalent stress in combination with elastic mechanics, taking the surface as a critical surface, calculating normal positive strain, shear strain and positive stress on the critical surface, and recording the change history of the normal positive strain, the shear strain and the positive stress along with time;
6) carrying out cycle counting on three parameters of normal positive strain, shear strain and positive stress;
7) combining the Wang-Brown model to predict the service life;
the specific method for determining the critical surface in the step 5) is as follows:
according to the stress and strain of the maximum node of the equivalent stress obtained by transient dynamics analysis, combining elastic mechanics, rotation stress and strain coordinates to any plane, the stress and strain on any plane are obtained, and the conversion formula is shown as the following formulas (1), (2) and (3), wherein theta, phi, and delta,
Figure FDA0003578593420000011
The value ranges of the two angles are [0 degrees, 180 degrees ], theta, and theta, and theta, and theta, and theta, and theta, and theta, and beta, and beta, and beta, beta,
Figure FDA0003578593420000012
Taking a search step length to search a critical surface, and obtaining the rest strain and stress components in the same way;
ε'＝(M)Tε(M) (1)；
σ'＝(M)Tσ(M) (2)；
in the formula, epsilon and sigma are strain tensors and stress tensors in an original coordinate system, and epsilon 'and sigma' are strain tensors and stress tensors in a new rotated coordinate system;
wherein the transformation matrix M is:
Figure FDA0003578593420000021
finding out a maximum shear strain surface with the maximum normal positive strain at the moment as a critical surface;
carrying out weighted average on two adjacent critical surfaces, wherein the calculation formula of the weight W (t) is shown as a formula (4),
Figure FDA0003578593420000022
in the formula, τ-1G is the shear modulus, D (t) is the degree of damage at this time, γmaxThe maximum shear strain is obtained by the damage degree through the maximum shear strain, the calculation formula is shown as the formulas (5) and (6),
Figure FDA0003578593420000023
D(t)＝1/Nk (6)；
in formula (II), sigma'fIs the fatigue strength coefficient, σbIs the tensile strength of the bearing steel, and b and c are respectively a fatigue strength index and a fatigue ductility index epsilon'fIs fatigue ductility coefficient, NkFatigue life is considered; the weighted critical surface orientation calculation formula is shown in formulas (7), (8) and (9),
Figure FDA0003578593420000024
Figure FDA0003578593420000025
Figure FDA0003578593420000026
in the formula, θ (t),
Figure FDA0003578593420000027
For critical planes at different times, pass pairCarrying out weighted average on two critical surfaces at different moments to determine a final critical surface;
the specific method of step 7) is as follows: the Wang-Brown model is of formula (10):
Figure FDA0003578593420000028
Figure FDA0003578593420000031
wherein the content of the first and second substances,
Figure FDA0003578593420000032
in order to maximize the amplitude of the shear strain,
Figure FDA0003578593420000033
is the maximum normal positive strain range, σ, in a shear strain cyclen,meanMean positive stress in one shear strain cycle, v is Poisson's ratio, NfIs a life value, E is an elastic modulus, σ'fAnd b is the fatigue strength coefficient and index, ε'fAnd c is the fatigue ductility coefficient and index, the multiaxial parameter S is determined by the tensile and torsional fatigue limit, the multiaxial parameter S is of the formula (11):
Figure FDA0003578593420000034
in the formula, τ-1、σ-1Respectively, a torsion limit and a tensile limit;
the shear strain cycle obtained by cycle counting and the maximum positive strain range are synthesized into an equivalent strain
Figure FDA0003578593420000035
At the same time, the corresponding average normal stress is substituted to calculate NfAnd calculating the damage D under the parameterf＝1/NfThe parameters of all the cycles are sequentially substituted into the formula (10), and the parameters are obtained for each cycleAnd finally, linearly accumulating the damage of each time according to a linear Miner formula to obtain the damage degree of one period, and converting the damage degree into the duration to obtain the fatigue life of the bearing at the lowest rocker arm.
2. The method for predicting the multi-axial fatigue life of the bearing of the tire unloader as recited in 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 predicting the multi-axial fatigue life of the bearing of the tire unloader as recited in claim 1, wherein: the method for performing transient dynamics analysis in step 3) is as follows: the method comprises the steps of setting a material of a bearing at the lowest rocker arm of the tire unloader, constraining the bearing at the lowest rocker arm of the tire unloader and applying a load, setting an outer ring to be completely fixed, constraining the bottom surface of the inner ring to be completely constrained, constraining the rotation of a ball around the revolution direction by a cylindrical coordinate system to simulate the action of a constraint frame on the bearing, enabling the ball to be in friction contact with the inner ring and the outer ring, setting contact rigidity by adopting an augmented Lagrange algorithm, carrying out grid division to obtain the bearing at the rocker arm, and obtaining an equivalent stress load spectrum of the bearing at the lowest rocker arm of the tire unloader.
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