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CN119129281B - Cylindrical roller bearing fatigue life analysis method based on multi-factor coupling - Google Patents

Cylindrical roller bearing fatigue life analysis method based on multi-factor coupling Download PDF

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CN119129281B
CN119129281B CN202411533802.9A CN202411533802A CN119129281B CN 119129281 B CN119129281 B CN 119129281B CN 202411533802 A CN202411533802 A CN 202411533802A CN 119129281 B CN119129281 B CN 119129281B
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fatigue life
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rolling element
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CN119129281A (en
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赵昭
谢辉
牛蔺楷
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Taiyuan University of Technology
C&U Co Ltd
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C&U Co Ltd
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Abstract

一种基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，S1，建立轴承热‑流‑固耦合动力学模型；S2，建立接触次表面应力计算模型；S3，基于I‑H理论计算轴承的疲劳寿命。本发明的有益效果是：区别于现有技术中单一因素去计算轴承的疲劳寿命，本发明基于轴承实际工况，考虑实际工况下润滑、热和套圈柔性变形对轴承寿命的影响，使得本发明所得出的疲劳寿命更贴合实际工况，为设计生产端提供了充足的理论支持。

A method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling, S1, establishing a thermal-fluid-solid coupling dynamic model of the bearing; S2, establishing a contact subsurface stress calculation model; S3, calculating the fatigue life of the bearing based on the I-H theory. The beneficial effects of the present invention are: different from the prior art that uses a single factor to calculate the fatigue life of the bearing, the present invention is based on the actual working conditions of the bearing, and considers the effects of lubrication, heat and flexible deformation of the ring on the bearing life under actual working conditions, so that the fatigue life obtained by the present invention is more in line with the actual working conditions, providing sufficient theoretical support for the design and production end.

Description

Cylindrical roller bearing fatigue life analysis method based on multi-factor coupling
Technical Field
The invention relates to a bearing fatigue life analysis method, in particular to a cylindrical roller bearing fatigue life analysis method based on multi-factor coupling.
Background
The fatigue life analysis of the cylindrical thin-wall roller bearing in the modern high-end equipment generally comprises rolling bodies, outer rings, inner rings and other parts, and generally works under high-speed, heavy-load and high-Wen Keke working conditions such as aerospace, wind power generation, industrial gearboxes and the like, and particularly in the fields, the coupling effects of lubrication, heat and flexible deformation of the thin-wall ferrule under complex and severe working conditions must be considered.
Currently, there are many basic theories for analyzing bearing fatigue life. In the bearing fatigue life analysis theory, the L-P fatigue life analysis method provides important development for bearing fatigue life analysis and is widely applied. However, the L-P theory has certain limitations, such as the inability to cope with the problem of infinite long life. Considering the limitations of the L-P theory, researchers have proposed an I-H theoretical model based on the L-P theory that can take into account stress limit values. Based on the I-H theory, a plurality of documents are provided for researching an analysis method of the fatigue life of the bearing, for example, a plurality of scholars research the influence rule of friction effect on the bearing life, and the scholars also provide a fatigue life analysis method based on the damage accumulation theory.
However, under complex and severe working conditions, the rheological property of the lubricating oil in the bearing, heat generation and deformation of the bearing and flexible deformation of the thin-wall ferrule of the bearing are mutually coupled, and all the current analysis methods cannot analyze the influence of the analysis methods on the fatigue life of the bearing based on the coupling property of the lubricating-heat-flexible deformation. In order to more reasonably analyze the fatigue life of a bearing, a bearing fatigue life analysis method capable of comprehensively considering complex coupling relations among lubrication, heat and flexible deformation is needed.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for analyzing the fatigue life of a cylindrical roller bearing by considering lubrication-heat-flexible deformation coupling.
In order to achieve the aim, the technical scheme of the invention is that a cylindrical roller bearing fatigue life analysis method based on multi-factor coupling,
S1, establishing a bearing heat-flow-solid coupling dynamic model, which comprises the following specific steps:
s101, establishing a ferrule flexible body model;
s102, establishing a bearing lubrication model considering nonlinear viscoelastic characteristics;
s103, establishing a bearing thermal network model taking the temperature of lubricating oil into consideration;
s104, establishing a bearing dynamics model based on interaction relations among the elements of the bearing;
S105, realizing the coupling of the four models in S101-S104 by a parameter coupling mode, and establishing a bearing heat-flow-solid coupling dynamics model;
s2, establishing a contact subsurface stress calculation model;
S3, calculating the fatigue life of the bearing based on the I-H theory.
Further, in the step S101, the ferrule flexible body model is built by using a curved beam unit based on a finite element method.
Further, in the step S102, the constitutive model of the nonlinear viscoelastic fluid property is expressed as follows:
Where τ is the shear stress and, (U s is the sliding speed between the rolling element and the ferrule, h is the central oil film thickness), G is the shear modulus, τ 0 is the yield shear stress, η is the lubricating oil viscosity,
The calculation formula of the center oil film thickness h is as follows:
h=Ry3.05U0.69g0.56W-0.1
where U is a dimensionless speed parameter, u=η 0u/(EeqRy);
W is a dimensionless load, w=q/(E eqRy l);
g is a dimensionless material parameter, g=λe eq (in the above expression, Q is a contact load, η 0 is a reference viscosity, u is a rolling speed, E eq is an equivalent elastic modulus, l is a rolling body length, λ is a viscosity-pressure coefficient of lubricating oil, and R y is a rolling direction equivalent radius).
Further, in the step S102, in view of the influence of the pressure p and the temperature T on the shear modulus G, the yield shear stress τ 0, and the lubricating oil viscosity η, the correction calculation formulas of the shear modulus G, the yield shear stress τ 0, and the lubricating oil viscosity η are as follows:
In the above formula eta 0, Reference viscosity, reference shear modulus and reference yield shear stress, respectively, alpha i、βj、γk、αG、βG、ατ and beta τ are specific constants, T and T 0 are current temperature and reference temperature, respectively, and p is current pressure.
Further, according to step S102, a friction traction curve is obtained, which specifically includes the following steps:
s1021, the constitutive model of the nonlinear viscoelastic fluid characteristic adopts a Runge-Kutta method to obtain the shearing stress tau of the contact surface of the rolling body and the ferrule;
s1022, integrating the shearing stress tau on the contact area to obtain the friction traction force;
S1023, comparing the friction traction with the contact load Q to obtain a friction traction coefficient;
S1024, friction traction curves under different T and U s are obtained by changing the values of the temperature T and the sliding speed U s.
Further, in the step S1024, a BP neural network is used to perform function fitting on the friction traction curve so as to directly use the friction traction curve in the dynamics model.
Further, in the step S103, a calculation formula for obtaining the thermal deformation of each element of the bearing based on the temperature T of each element of the bearing is as follows:
ut＝ΓL(T-Tα)
in the above formula, Γ is the thermal expansion coefficient, T α is the ambient temperature, and L is the characteristic length of each element of the bearing.
Further, in the step S103, a temperature node is set in each element of the bearing, and the following calculation formula is listed based on the law of conservation of energy:
node 1 (T 1-T10)/R1cv10+(T1-T2)/R2cc1 =0)
Node 2 (T 2-T1)/R1cc2+(T2-T3)/R3cc2 =0)
Node 3:(T3-T2)/R2cc3+(T3-T4)/R4cc3+(T3-T0)/R0cv3＝Q1
Node 4 (T 4-T5)/R5cc4+(T4-T3)/R4cc3 =0)
Node 5:(T5-T4)/R5cc4+(T5-T6)/R6cc5+(T5-T0)/R0cv5＝Q2
Node 6 (T 6-T5)/R6cc5+(T6-T7)/R7cc6 =0)
Node 7:(T7-T6)/R7cc6+(T7-T8)/R8cc7+(T7-T0)/R7cv0＝Q3
Node 8 (T 8-T7)/R8cc7+(T8-T9)/R9cc8 =0)
Node 9 (T 9-T8)/R9cc8+(T9-T10)/R10cv9 =0)
In the above, T 1 is an outer ring temperature node, T 2 is an outer raceway temperature node, T 3 is an outer raceway lubricant temperature node, T 4 is a rolling element-outer raceway outer side node, T 5 is a rolling element temperature node, T 6 is a rolling element-inner raceway inner side node, T 7 is an inner raceway lubricant temperature node, T 8 is an inner raceway temperature node, T 9 is an inner ring temperature node, T 10 is an air temperature node, T 0 is a lubricant temperature node, Q 1、Q2、Q3 is a friction heat generation rate at a rolling element-outer raceway contact position, a friction heat generation rate between a rolling element and lubricating oil in a bearing cavity, and a friction heat generation rate at a rolling element-inner raceway contact position, R is a thermal resistance value (in the subscript, cv represents heat convection, cc represents heat conduction, and Arabic represents a temperature node).
Further, in the step S104, a GUPTA bearing model is used to build a dynamic model of the bearing.
Further, the step S105 establishes a bearing heat-fluid-solid coupling dynamics model according to the following steps:
s1051, initializing the temperature, the position and the speed of each element of the bearing;
S1052, calculating the current friction traction coefficient based on the bearing lubrication model in the step S102;
S1053, calculating the geometric approach amount and the contact load and the friction heat generation rate between the elements of the bearing based on the GUPTA dynamic model in the step S104;
S1054, substituting the friction heat generation rate obtained in the step S1053 into the bearing thermal network model in the step S103 to update the temperature of each element of the bearing, and obtaining the thermal deformation of each element of the bearing;
S1055, updating the geometric dimensions of each element of the bearing based on the elastic deformation of each element of the bearing calculated by the ferrule flexible body model in S101 and the thermal deformation of each element of the bearing obtained in the step S1054;
s1056, substituting the updated temperature obtained in the step S1054 into the bearing lubrication model in the step S102 to update the viscosity and traction coefficient of the lubricating oil;
s1057, substituting the updated geometric dimensions and traction coefficients in the steps S1055 and S1056 into GUPTA to update the position and speed of the bearing element;
S1058, iterating the steps of S1051-S1057 above until the termination condition is met, and then exiting, wherein the termination condition can be the reaching of the calculation time.
Further, in the step S2, the subsurface stress of the contact area is calculated by using a discrete convolution (Discrete Convolution, DC) and a fast fourier transform (Fast Fourier Transformation, FFT) method.
Further, the step S2 obtains the subsurface stress of the contact area according to the following steps:
S201, calculating a contact half-width b, and dispersing the whole contact area into N x、Ny and N z points along the length direction (x direction), the contact half-width direction (y direction) and the depth direction (z direction) of the rolling element;
S202, calculating an influence coefficient sequence { D } N (a symbol { } N represents a sequence with the length of N), and expanding the sequence { D } N into a sequence { D } 2N (a symbol { } 2N represents a sequence with the length of 2N) through zero padding and surrounding processing;
S203, performing fast Fourier transform on the sequence { D } 2N in the step S202 to obtain
S204, calculating a pressure sequence { P } N, and expanding { P } N into { P } 2N by a zero filling method;
S205, adopting Fourier transformation to the sequence { P } 2N in the S204 step to obtain a sequence
S206, the sequence in the step S203And in step S205Multiplying between the units to obtain the frequency
S207, for the frequency sequence in S206Adopting inverse Fourier transform to obtain a sequence { V } 2N;
S208, extracting the nth (n E [0, N-1 ]) element from the sequence { V } 2N obtained in the step S206, and obtaining the stress distribution.
Further, the calculation formula of the influence coefficient in the step S202 is as follows:
,x+＝xm-xξ+Δ1/2,x-＝xm-xξ-Δ1/2,y+＝yn-yη+Δ2/2,y-＝yn-yη-Δ2/2,ξ and η in the above formula are local coordinates of discrete units, m, n, k are element numbers of the units in x, y, z directions, q, r=x, y or z, respectively (i.e. qr is a combination of two of x, y, z).
Further, for elastic half-space contact, the calculation formula of the function T Nqr used by the stress field is as follows:
TNyy(x,y,z)＝TNxx(y,x,z)
In the above-mentioned method, the step of, When z=0, the number of times,(Sign () is a sign function).
Further, the step S3 is to calculate the fatigue life of the bearing according to the following steps:
S301, calculating the service lives of the rolling body-rotating ferrule raceway contact position and the rolling body-static ferrule raceway contact position based on L-P;
s302, obtaining the I-H life of the contact positions of each rolling body, the rotary ferrule and the static ferrule according to the data obtained in the step S301;
And S303, obtaining the fatigue life of the bearing according to the data obtained in the step S302.
Further, in the step S301, for the rotating cage, the calculation formula of the L-P life at the contact point of the rolling element and the raceway is as follows:
For a stationary cage, the L-P life at the rolling element-raceway contact is calculated as follows:
In the above formula, q μj and q vj are contact loads of the rotating ferrule and the stationary ferrule (subscripts μ and v represent the rotating ferrule and the stationary ferrule, respectively, j represents the j-th rolling element), q cμj and q cvj are rated dynamic loads of the rotating ferrule and the stationary ferrule, and the calculation formulas of q cμj and q cvj are as follows:
In the above-mentioned method, the step of, D is the diameter of the rolling element, D m is the pitch diameter of the bearing, α is the contact angle, l is the length of the rolling element, and Z is the number of rolling elements.
Further, according to the formula in the step S301, the I-H lives L IHμj and L IHvj of the j-th rolling element in the step S302 where the rolling element contacts the rotating ferrule and the stationary ferrule are obtained, respectively, and the calculation formula is as follows:
In the above expression, σ VMμj,max and σ VMvj,max are the maximum Von-Mises stress at the contact points of the jth rolling element with the rotating ferrule and the stationary ferrule, respectively, and σ VM,lim is the limit value of Von-Mises stress. While AndAre fixed values which vary only in response to changes in bearing type.
Further, the calculation formula in the step S303 is as follows:
The fatigue life of the whole bearing is obtained by superposing the I-H life of the contact positions of each rolling body obtained in the step S302 and the rotating ring and the static ring respectively.
The method has the beneficial effects that the method is different from the single factor in the prior art for calculating the fatigue life of the bearing, is based on the actual working condition of the bearing, and considers the influence of lubrication, heat and flexible deformation of the ferrule on the service life of the bearing under the actual working condition, so that the fatigue life obtained by the method is more fit with the actual working condition, and provides sufficient theoretical support for designing a production end;
Secondly, the lubrication, the heat and the flexible deformation of the ferrule are coupled through parameters, so that the operation difficulty can be reduced, the calculation force cost required by the operation is reduced in a mode of reducing the operation difficulty, and the operation efficiency is improved; and the influence of multiple factors on the service life of the bearing is comprehensively considered, and the interaction among the multiple factors is also considered as correction of each independent factor, so that the fatigue life data obtained by the method is further close to the actual working condition.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of the overall composition of a dynamic model of thermal-fluid-solid coupling of a bearing according to an embodiment of the present invention;
FIG. 3 is a friction drag curve based on step S102 according to an embodiment of the present invention;
FIG. 4 is a BP neural network model for fitting a friction traction curve according to an embodiment of the present invention;
FIG. 5 shows rolling element-inner ring (rotating collar) contact loads at different temperatures in an embodiment of the present invention;
FIG. 6 shows rolling element-outer ring (stationary race) contact loads at different temperatures in an embodiment of the invention;
fig. 7 shows the bearing life at a temperature of t=300K in an embodiment of the invention;
Fig. 8 shows the bearing life at a temperature of t=310K in an embodiment of the invention.
Detailed Description
In the embodiment of the invention, the cylindrical roller bearing is selected as the bearing, the inner ring of the cylindrical roller bearing is a rotary ferrule, and the outer ring of the cylindrical roller bearing is a static ferrule. The following describes the calculation of the fatigue life of the cylindrical roller bearing according to the analysis method in the present embodiment.
S1, establishing a bearing thermal-fluid-solid coupling dynamic model, wherein the fixing steps are as follows:
s101, establishing a ferrule flexible body model based on a finite element method;
The flexible ferrule is modeled using a two-dimensional curved beam unit.
S102, establishing a bearing lubrication model capable of considering nonlinear viscoelastic characteristics;
the constitutive model of the nonlinear viscoelastic fluid employed can be expressed as:
Where τ is the shear stress and, (U s is the sliding speed between the rolling element and the ferrule, h is the central oil film thickness), G is the shear modulus, τ 0 is the yield shear stress, η is the lubricating oil viscosity,
The calculation formula of the center oil film thickness h is as follows:
h=Ry3.05U0.69g0.56W-0.1
where U is a dimensionless speed parameter, u=η 0u/(EeqRy);
W is a dimensionless load, w=q/(E eqRy l);
g is a dimensionless material parameter, g=λe eq (in the above expression, Q is a contact load, η 0 is a reference viscosity, u is a rolling speed, E eq is an equivalent elastic modulus, l is a rolling body length, λ is a viscosity-pressure coefficient of lubricating oil, and R y is a rolling direction equivalent radius). Here, the influence of pressure and temperature on fluid parameters is obvious, so that the shear modulus G, the yield shear stress τ 0 and the lubricating oil viscosity η need to be corrected according to the pressure p and the temperature T, and the calculation formula is as follows:
In the above formula eta 0, Reference viscosity, reference shear modulus and reference yield shear stress, respectively, alpha i、βj、γk、αG、βG、ατ and beta τ are specific constants, T and T 0 are current temperature and reference temperature, respectively, and p is current pressure.
According to step S102, a friction traction curve can be obtained, which comprises the following specific steps:
S1021, carrying out numerical integration on the constitutive model of the nonlinear viscoelastic fluid characteristic by adopting a Runge-Kutta method, and obtaining shearing stress tau of the contact surface of the rolling body and the ferrule after integration;
s1022, integrating the shearing stress tau on the contact area to obtain the friction traction force;
S1023, comparing the friction traction with the contact load Q to obtain a friction traction coefficient;
s1024, obtaining friction traction curves under different T and U s by changing the temperature T and the sliding speed U s;
s1025, the friction traction curve can be directly used in the dynamics model after the BP neural network is adopted to carry out function fitting on the friction traction curve.
S103, establishing a bearing thermal network model capable of considering the temperature of the lubricating oil, calculating the internal temperature distribution of the bearing and the thermal deformation of each element of the bearing,
The internal temperature calculation process of the bearing is that temperature nodes are arranged at each key part of the rolling bearing, and if the air temperature and the internal temperature of the bearing cavity are known, 9 heat balance equations can be listed according to the law of conservation of energy (the heat flowing in and out of each node is equal), namely, node 1 is (T 1-T10)/R1cv10+(T1-T2)/R2cc1 =0)
Node 2 (T 2-T1)/R1cc2+(T2-T3)/R3cc2 =0)
Node 3:(T3-T2)/R2cc3+(T3-T4)/R4cc3+(T3-T0)/R0cv3＝Q1 node 4 (T 4-T5)/R5cc4+(T4-T3)/R4cc3 =0)
Node 5:(T5-T4)/R5cc4+(T5-T6)/R6cc5+(T5-T0)/R0cv5＝Q2 node 6 (T 6-T5)/R6cc5+(T6-T7)/R7cc6 =0)
Node 7:(T7-T6)/R7cc6+(T7-T8)/R8cc7+(T7-T0)/R7cv0＝Q3 node 8 (T 8-T7)/R8cc7+(T8-T9)/R9cc8 =0)
Node 9 (T 9-T8)/R9cc8+(T9-T10)/R10cv9 =0)
In the above, T 1 is an outer ring temperature node, T 2 is an outer raceway temperature node, T 3 is an outer raceway lubricant temperature node, T 4 is a rolling element-outer raceway outer side node, T 5 is a rolling element temperature node, T 6 is a rolling element-inner raceway inner side node, T 7 is an inner raceway lubricant temperature node, T 8 is an inner raceway temperature node, T 9 is an inner ring temperature node, T 10 is an air temperature node, T 0 is a lubricant temperature node, Q 1、Q2、Q3 is a friction heat generation rate at a rolling element-outer raceway contact position, a friction heat generation rate between a rolling element and lubricating oil in a bearing cavity, and a friction heat generation rate at a rolling element-inner raceway contact position, R is a thermal resistance value (in the subscript, cv represents heat convection, cc represents heat conduction, and Arabic represents a temperature node).
After the temperature T of each element of the bearing is calculated, the thermal deformation of the bearing element is calculated by the following formula:
ut＝ΓL(T-Tα)
in the above formula, Γ is the thermal expansion coefficient, T α is the ambient temperature, and L is the characteristic length of each element of the bearing.
S104, establishing a dynamic model of the cylindrical roller bearing by considering the interaction relation among the elements of the bearing.
And establishing a dynamic model of the cylindrical roller bearing based on the GUPTA bearing model.
S105, realizing the coupling of the models in the four steps S101-S104 by a parameter coupling mode, establishing a thermal-flow-solid coupling dynamic model of the cylindrical roller bearing, and respectively calculating the contact loads between the rotating ferrule and the static ferrule and the rolling body, wherein the specific steps are as follows:
s1051, initializing the temperature, the position and the speed of each element of the bearing;
S1052, calculating the current friction traction coefficient based on the bearing lubrication model in the step S102;
S1053, calculating the geometric approach amount and the contact load and the friction heat generation rate between the elements of the bearing based on the GUPTA dynamic model in the step S104;
S1054, substituting the friction heat generation rate obtained in the step S1053 into the bearing thermal network model in the step S103 to update the temperature of each element of the bearing, and obtaining the thermal deformation of each element of the bearing;
S1055, updating the geometric dimensions of each element of the bearing based on the elastic deformation of each element of the bearing calculated by the ferrule flexible body model in S101 and the thermal deformation of each element of the bearing obtained in the step S1054;
s1056, substituting the updated temperature obtained in the step S1054 into the bearing lubrication model in the step S102 to update the viscosity and traction coefficient of the lubricating oil;
s1057, substituting the updated geometric dimensions and traction coefficients in the steps S1055 and S1056 into GUPTA to update the position and speed of the bearing element;
S1058, iterating the steps S1051 to S1057 above until the termination condition is satisfied (the calculation time is reached).
And the establishment of the bearing thermal-fluid-solid coupling dynamic model is completed through the steps.
S2, establishing a contact subsurface stress calculation model, and calculating the contact subsurface stress according to the contact load obtained by calculation in the S1, wherein the specific steps are as follows:
S201, calculating a contact half-width b, and dispersing the whole contact area into N x、Ny and N z points along the length direction (x direction), the contact half-width direction (y direction) and the depth direction (z direction) of the rolling element;
S202, calculating an influence coefficient sequence { D } N (a symbol { } N represents a sequence with the length of N), and expanding the sequence { D } N into a sequence { D } 2N (a symbol { } 2N represents a sequence with the length of 2N) through zero padding and surrounding processing;
S203, performing fast Fourier transform on the sequence { D } 2N in the step S202 to obtain
S204, calculating a pressure sequence { P } N, and expanding { P } N into { P } 2N by a zero filling method;
S205, adopting Fourier transformation to the sequence { P } 2N in the S204 step to obtain a sequence
S206, the sequence in the step S203And in step S205Multiplying between the units to obtain the frequency
S207, for the frequency sequence in S206Adopting inverse Fourier transform to obtain a sequence { V } 2N;
S208, extracting the n (n E [0, N-1 ]) element sequence number from the sequence { V } 2N obtained in the step S206, and obtaining the stress distribution.
The calculation formula of the influence coefficient in step S202 is as follows:
,x+＝xm-xξ+Δ1/2,x-＝xm-xξ-Δ1/2,y+＝yn-yη+Δ2/2,y-＝yn-yη-Δ2/2,ξ and η in the above formula are local coordinates of discrete units, m, n, k are element numbers of the units in x, y, z directions, q, r=x, y or z, respectively (i.e. qr is a combination of two of x, y, z). For elastic half-space contact, the function T Nqr used for stress field is calculated as follows:
TNyy(x,y,z)＝TNxx}y,x,z)
In the above-mentioned method, the step of, When z=0, the number of times,(Sign () is a sign function).
The contact subsurface stress calculation model is completed through the steps.
S3, calculating the fatigue life of the bearing based on the I-H theory, wherein the specific steps are as follows:
S301, calculating the service lives of the rolling body-rotating ferrule raceway contact position and the rolling body-static ferrule raceway contact position based on L-P;
for a rotating cage, the calculation formula for the L-P life at the rolling element-raceway contact is as follows:
For a stationary cage, the L-P life at the rolling element-raceway contact is calculated as follows:
In the above formula, q μj and q vj are contact loads of the rotating ferrule and the stationary ferrule (subscripts μ and v represent the rotating ferrule and the stationary ferrule, respectively, j represents the j-th rolling element), q cμj and q cvj are rated dynamic loads of the rotating ferrule and the stationary ferrule, and the calculation formulas of q cμj and q cvj are as follows:
In the above-mentioned method, the step of, D is the diameter of the rolling element, D m is the pitch diameter of the bearing, α is the contact angle, l is the length of the rolling element, and Z is the number of rolling elements.
S302, according to the data obtained in the step S301, the I-H life L IHμj and L IHvj of the contact positions of the jth rolling element and the rotary ferrule and the static ferrule are obtained, and the calculation formula is as follows:
In the above expression, σ VMμj,max and σ VMvj,max are the maximum Von-Mises stress at the contact points of the jth rolling element with the rotating ferrule and the stationary ferrule, respectively, and σ VM,lim is the limit value of Von-Mises stress. While AndAre fixed values which vary only in accordance with the variation of the bearing type, in this embodiment, that is, the coefficients of the cylindrical roller bearing are as follows:
S303, obtaining the fatigue life of the bearing according to the data obtained in the step S302, wherein the calculation is shown as follows:
The fatigue life of the whole bearing is obtained by superposing the I-H life of the contact positions of each rolling body obtained in the step S302 and the rotating ring and the static ring respectively.
And the fatigue life calculation of the bearing is completed through the steps.
The above embodiment is only one of the preferred embodiments of the present invention, and common changes and substitutions made by those skilled in the art within the scope of the technical solution of the present invention are included in the scope of the present invention.

Claims (16)

1.一种基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：1. A method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling, characterized in that: S1，建立轴承热-流-固耦合动力学模型，具体步骤如下：S1, establish the bearing thermal-fluid-solid coupling dynamics model. The specific steps are as follows: S101，建立套圈柔性体模型；S101, establishing a ferrule flexible body model; S102，建立考虑非线性粘弹特性的轴承润滑模型；S102, establishing a bearing lubrication model considering nonlinear viscoelastic characteristics; S103，建立考虑润滑油温度的轴承热网络模型；S103, establishing a bearing thermal network model taking into account lubricating oil temperature; S104，基于轴承各元件之间的相互作用关系，采用GUPTA轴承模型建立轴承的动力学模型；S104, based on the interaction relationship between the various components of the bearing, a dynamic model of the bearing is established using a GUPTA bearing model; S105，通过参数耦合方式实现S101-S104中四个模型的耦合，建立轴承热-流-固耦合动力学模型；S105, coupling the four models in S101-S104 is realized by parameter coupling, and a thermal-fluid-solid coupling dynamic model of the bearing is established; 所述步骤S105按照以下步骤建立轴承热-流-固耦合动力学模型：The step S105 establishes a bearing thermal-fluid-solid coupling dynamics model according to the following steps: S1051，初始化轴承各元件温度、位置和速度；S1051, initializing the temperature, position and speed of each bearing component; S1052，基于S102步骤中的轴承润滑模型计算当前摩擦牵引系数；S1052, calculating the current friction traction coefficient based on the bearing lubrication model in step S102; S1053，基于S104步骤中的GUPTA动力学模型计算轴承各元件之间的几何趋近量和接触载荷以及摩擦生热率；S1053, calculating the geometric approach and contact load between the bearing components and the friction heat generation rate based on the GUPTA dynamic model in step S104; S1054，将S1053步骤中得出的摩擦生热率代入S103步骤中的轴承热网络模型更新轴承各元件的温度，并得出轴承各元件的热变形；S1054, substituting the friction heat generation rate obtained in step S1053 into the bearing thermal network model in step S103 to update the temperature of each bearing component, and obtain the thermal deformation of each bearing component; S1055，基于S101中的套圈柔性体模型计算得出的轴承各元件的弹性变形以及基于S1054步骤中得出的轴承各元件的热变形更新轴承各元件的几何尺寸；S1055, updating the geometric dimensions of each bearing component based on the elastic deformation of each bearing component calculated by the ring flexible body model in S101 and the thermal deformation of each bearing component calculated in step S1054; S1056，将S1054步骤中得出的更新后的温度代入S102步骤中的轴承润滑模型中更新润滑油的粘度以及牵引系数；S1056, substituting the updated temperature obtained in step S1054 into the bearing lubrication model in step S102 to update the viscosity and traction coefficient of the lubricating oil; S1057，将上述S1055和S1056步骤中更新的几何尺寸、牵引系数代入GUPTA模型中更新轴承元件的位置和速度；S1057, substituting the geometric dimensions and traction coefficients updated in the above steps S1055 and S1056 into the GUPTA model to update the position and speed of the bearing element; S1058，将以上S1051-S1057步骤反复迭代直至满足终止条件后退出；S1058, repeatedly iterate the above steps S1051-S1057 until the termination condition is met and then exit; S2，建立接触次表面应力计算模型；S2, establish a contact subsurface stress calculation model; S3，基于I-H理论计算轴承的疲劳寿命。S3, calculation of bearing fatigue life based on I-H theory. 2.根据权利要求1所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述步骤S101中，套圈柔性体模型是基于有限单元法采用曲梁单元建立。2. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 1 is characterized in that: in the step S101, the ring flexible body model is established based on the finite element method using a curved beam element. 3.根据权利要求1所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述步骤S102中，采用的非线性粘弹流体特性的本构模型表示如下：3. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 1, characterized in that: in the step S102, the constitutive model of the nonlinear viscoelastic fluid characteristics adopted is expressed as follows: 上式中τ为剪切应力，中Us为滚动体和套圈之间的滑动速度，h为中心油膜厚度，G为剪切模量，τ0为屈服剪应力，η为润滑油粘度， In the above formula, τ is the shear stress, Where Us is the sliding speed between the rolling element and the ring, h is the center oil film thickness, G is the shear modulus, τ0 is the yield shear stress, η is the viscosity of the lubricating oil, 其中，中心油膜厚度h的计算公式如下：The calculation formula of the center oil film thickness h is as follows: h＝Ry3.05U0.69g0.56W-0.1 h＝R y 3.05U 0.69 g 0.56 W -0.1 其中U为无量纲速度参数，U＝η0u/(EeqRy)；Where U is the dimensionless velocity parameter, U = η 0 u/(E eq R y ); W为无量纲载荷，W＝Q/(EeqRyl)；W is the dimensionless load, W = Q/(E eq R y l); g为无量纲材料参数，g＝λEeq g is a dimensionless material parameter, g = λE eq 以上表达式中，Q为接触载荷，η0为参考粘度，u为滚动速度，Eeq为等效弹性模量，l为滚动体长度，λ为润滑油的粘压系数，Ry为滚动方向等效半径。In the above expressions, Q is the contact load, η 0 is the reference viscosity, u is the rolling speed, E eq is the equivalent elastic modulus, l is the rolling element length, λ is the viscosity-pressure coefficient of the lubricating oil, and R y is the equivalent radius in the rolling direction. 4.根据权利要求3所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述步骤S102中，鉴于压力p和温度T对剪切模量G、屈服剪应力τ0和润滑油粘度η的影响，剪切模量G、屈服剪应力τ0和润滑油粘度η的修正计算公式如下：4. The method for analyzing fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 3, characterized in that: in the step S102, in view of the influence of pressure p and temperature T on shear modulus G, yield shear stress τ 0 and lubricating oil viscosity η, the modified calculation formulas of shear modulus G, yield shear stress τ 0 and lubricating oil viscosity η are as follows: 上式中η0、分别为参考粘度、参考剪切模量和参考屈服剪应力；αi、βj、γk、αG、βG、ατ和βτ为特定常数；T和T0分别为当前温度和参考温度；p为当前压力。In the above formula, η 0 , are the reference viscosity, reference shear modulus and reference yield shear stress respectively; α i , β j , γ k , α G , β G , α τ and β τ are specific constants; T and T 0 are the current temperature and reference temperature respectively; p is the current pressure. 5.根据权利要求4所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：根据S102步骤得出摩擦牵引曲线，其具体步骤如下：5. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 4 is characterized in that: the friction traction curve is obtained according to step S102, and the specific steps are as follows: S1021，非线性粘弹流体特性的本构模型采用Runge-Kutta法得出滚动体和套圈接触面的剪切应力τ；S1021, the constitutive model of nonlinear viscoelastic fluid characteristics uses the Runge-Kutta method to obtain the shear stress τ at the contact surface between the rolling element and the ring; S1022，将剪切应力τ在接触区域上进行积分得出摩擦牵引力；S1022, integrating the shear stress τ over the contact area to obtain the friction traction force; S1023，将摩擦牵引力和接触载荷Q作比得出摩擦牵引系数；S1023, comparing the friction traction force and the contact load Q to obtain a friction traction coefficient; S1024，通过改变温度T和滑动速度Us的值得出不同T和Us下的摩擦牵引曲线。S1024, by changing the values of temperature T and sliding speed U s, the friction traction curves under different T and U s are obtained. 6.根据权利要求5所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：在所述S1024步骤中，采用BP神经网络对摩擦牵引曲线进行函数拟合。6. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 5 is characterized in that: in the step S1024, a BP neural network is used to perform function fitting on the friction traction curve. 7.根据权利要求1所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述步骤S103中，基于轴承各元件的温度T得出轴承各元件的热变形的计算公式如下：7. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 1, characterized in that: in the step S103, the calculation formula for the thermal deformation of each bearing component is obtained based on the temperature T of each bearing component as follows: ut＝ΓL(T-Tα) ut =ΓL(TT α ) 上式中，Γ为热膨胀系数，Tα为环境温度，L为轴承各元件的特征长度。In the above formula, Γ is the thermal expansion coefficient, T α is the ambient temperature, and L is the characteristic length of each bearing element. 8.根据权利要求7所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述步骤S103中，在轴承各元件设置温度节点，基于能量守恒定律列出如下计算公式：8. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 7, characterized in that: in the step S103, temperature nodes are set in each bearing component, and the following calculation formula is listed based on the law of conservation of energy: 节点1:(T1-T10)/R1cv10+(T1-T2)/R2cc1＝0Node 1: (T 1 -T 10 )/R 1cv10 + (T 1 -T 2 )/R 2cc1 = 0 节点2:(T2-T1)/R1cc2+(T2-T3)/R3cc2＝0Node 2: (T 2 -T 1 )/R 1cc2 + (T 2 -T 3 )/R 3cc2 = 0 节点3:(T3-T2)/R2cc3+(T3-T4)/R4cc3+(T3-T0)/R0cv3＝Q1 Node 3: (T 3 -T 2 )/R 2cc3 + (T 3 -T 4 )/R 4cc3 + (T 3 -T 0 )/R 0cv3 = Q 1 节点4:(T4-T5)/R5cc4+(T4-T3)/R4cc3＝0Node 4: (T 4 -T 5 )/R 5cc4 + (T 4 -T 3 )/R 4cc3 = 0 节点5:(T5-T4)/R5cc4+(T5-T6)/R6cc5+(T5-T0)/R0cv5＝Q2 Node 5: (T 5 -T 4 )/R 5cc4 + (T 5 -T 6 )/R 6cc5 + (T 5 -T 0 )/R 0cv5 = Q 2 节点6:(T6-T5)/R6cc5+(T6-T7)/R7cc6＝0Node 6: (T 6 -T 5 )/R 6cc5 + (T 6 -T 7 )/R 7cc6 = 0 节点7:(T7-T6)/R7cc6+(T7-T8)/R8cc7+(T7-T0)/R7cv0＝Q3 Node 7: (T 7 -T 6 )/R 7cc6 + (T 7 -T 8 )/R 8cc7 + (T 7 -T 0 )/R 7cv0 = Q 3 节点8:(T8-T7)/R8cc7+(T8-T9)/R9cc8＝0Node 8: (T 8 -T 7 )/R 8cc7 + (T 8 -T 9 )/R 9cc8 = 0 节点9:(T9-T8)/R9cc8+(T9-T10)/R10cv9＝0Node 9: (T 9 -T 8 )/R 9cc8 + (T 9 -T 10 )/R 10cv9 = 0 上式中T1为外圈温度节点，T2为外滚道温度节点，T3为外滚道润滑剂温度节点，T4为滚动体-外滚道外侧节点，T5为滚动体温度节点，T6为滚动体-内滚道内侧节点，T7为内滚道润滑剂温度节点，T8为内滚道温度节点，T9为内圈温度节点，T10为空气温度节点，T0为润滑剂温度节点；Q1、Q2、Q3分别为滚动体-外滚道接触处的摩擦生热率、滚动体和轴承腔体内润滑油之间的摩擦生热率、滚动体-内滚道接触处的摩擦生热率；R为热阻值，上述热阻值的下标中，cv表示热对流，cc表示热传导，阿拉伯数字表示温度节点。In the above formula, T1 is the outer ring temperature node, T2 is the outer raceway temperature node, T3 is the outer raceway lubricant temperature node, T4 is the rolling element-outer raceway outer side node, T5 is the rolling element temperature node, T6 is the rolling element-inner raceway inner side node, T7 is the inner raceway lubricant temperature node, T8 is the inner raceway temperature node, T9 is the inner ring temperature node, T10 is the air temperature node, and T0 is the lubricant temperature node; Q1 , Q2 , and Q3 are the friction heat generation rate at the rolling element-outer raceway contact, the friction heat generation rate between the rolling element and the lubricating oil in the bearing cavity, and the friction heat generation rate at the rolling element-inner raceway contact, respectively; R is the thermal resistance value. In the subscripts of the above thermal resistance values, cv represents heat convection, cc represents heat conduction, and Arabic numerals represent temperature nodes. 9.根据权利要求1所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述S2步骤中，采用离散卷积和快速傅里叶变换的方法计算接触区域的次表面应力。9. The method for analyzing the fatigue life of a cylindrical roller bearing based on multi-factor coupling according to claim 1, characterized in that: in the step S2, a discrete convolution and fast Fourier transform method is used to calculate the sub-surface stress of the contact area. 10.根据权利要求9所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述S2步骤按照以下步骤得出接触区域次表面应力：10. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 9, characterized in that: the step S2 obtains the sub-surface stress of the contact area according to the following steps: S201，计算接触半宽b，并沿着滚动体长度方向即x方向、接触半宽方向即y方向以及深度方向即z方向将整个接触区域离散为Nx、Ny和Nz个点；S201, calculating the contact half-width b, and discretizing the entire contact area into N x , N y and N z points along the rolling element length direction, i.e., the x direction, the contact half-width direction, i.e., the y direction, and the depth direction, i.e., the z direction; S202，计算影响系数序列{D}N，符号{ }N表示长度为N的序列，并通过补零和环绕处理，将序列{D}N扩展为{D}2N，符号{ }2N表示长度为2N的序列；S202, calculating the influence coefficient sequence {D} N , where the symbol { } N represents a sequence with a length of N, and expanding the sequence {D} N to { D } 2N , where the symbol { } 2N represents a sequence with a length of 2N, by zero padding and wrapping; S203，对S202步骤中的序列{D}2N进行快速傅里叶变换，得到 S203, performing fast Fourier transform on the sequence { D } 2N in step S202, and obtaining S204，计算压力序列{P}N；并通过补零的方法，将{P}N扩展为 S204, calculating the pressure sequence {P} N ; and expanding {P} N to S205，对S204步骤中的序列{P}2N采用傅里叶变换，得到序列 S205, applying Fourier transform to the sequence { P } 2N in step S204 to obtain the sequence S206，将S203步骤中的序列和S205步骤中的在各个单元之间进行相乘，得到频率 S206, the sequence in step S203 and step S205 Multiply each unit to get the frequency S207，对S206步骤中的频率序列采用逆傅里叶变换，得到序列{V}2N；S207, the frequency sequence in step S206 Using inverse Fourier transform, we get the sequence {V} 2N ; S208，从S206步骤中得出的序列{V}2N中提取第n(n∈[0,N-1])个元素序号，得出应力分布。S208, extracting the nth (n∈[0,N-1]) element number from the sequence {V} 2N obtained in step S206, and obtaining the stress distribution. 11.根据权利要求10所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述S202步骤中的影响系数的计算公式如下：11. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 10, characterized in that: the calculation formula of the influence coefficient in step S202 is as follows: 上式中，x+＝xm-xξ+Δ1/2，x-＝xm-xξ-Δ1/2，y+＝yn-yη+Δ2/2，y-＝yn-yη-Δ2/2，ξ和η为离散单元的局部坐标，m，n，k分别为单元在x，y，z方向上的元素序号，q、r＝x、y或z，即qr是x、y、z的两两组合。 In the above formulas, x + =xm - xξ + Δ1 /2, x- =xm - xξ -Δ1/ 2 , y + = yn -yη+ Δ2 /2, y- = yn- yη -Δ2 / 2, ξ and η are the local coordinates of the discrete unit, m, n, k are the element numbers of the unit in the x, y, z directions respectively, q, r =x, y or z, that is, qr is a pairwise combination of x, y, z. 12.根据权利要求11所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：对于弹性半空间的接触，应力场所采用的函数TNqr的计算公式如下：12. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 11, characterized in that: for the contact in the elastic half-space, the calculation formula of the function T Nqr used in the stress field is as follows: TNyy(x,y,z)＝TNxx(y,x,z)T Nyy (x,y,z)＝T Nxx (y,x,z) 上式中，当z＝0时，，sign()为符号函数。In the above formula, When z = 0, , sign() is the sign function. 13.根据权利要求1所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述S3步骤按照以下步骤计算轴承的疲劳寿命：13. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 1, characterized in that: the step S3 calculates the fatigue life of the bearing according to the following steps: S301，基于L-P分别计算滚动体-旋转套圈滚道接触处和滚动体-静止套圈滚道接触处的L-P寿命；S301, based on L-P, respectively calculating the L-P life of the rolling element-rotating ring raceway contact and the rolling element-stationary ring raceway contact; S302，根据S301步骤中所得数据得出各个滚动体分别和旋转套圈以及静止套圈接触处的I-H寿命；S302, according to the data obtained in step S301, the I-H life of each rolling element at the contact point with the rotating ring and the stationary ring is obtained; S303，根据S302步骤中所得数据得出轴承的疲劳寿命。S303, obtaining the fatigue life of the bearing according to the data obtained in step S302. 14.根据权利要求13所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述S301步骤中，对于旋转套圈，滚动体-滚道接触处的L-P寿命的计算公式如下：14. The method for analyzing the fatigue life of a cylindrical roller bearing based on multi-factor coupling according to claim 13, characterized in that: in the step S301, for the rotating ring, the calculation formula for the L-P life at the rolling element-raceway contact is as follows: 对于静止套圈，滚动体-滚道接触处的L-P寿命的计算公式如下：For stationary rings, the L-P life at the rolling element-raceway contact is calculated as follows: 上式中，qμj和qvj为旋转套圈和静止套圈的接触载荷，下标μ和v分别表示旋转套圈和静止套圈，j表示第j个滚动体；qcμj和qcvj为旋转套圈和静止套圈的额定动载荷；其中，qcμj和qcvj的计算公式如下：In the above formula, q μj and q vj are the contact loads of the rotating ring and the stationary ring, the subscripts μ and v represent the rotating ring and the stationary ring respectively, and j represents the jth rolling element; q cμj and q cvj are the rated dynamic loads of the rotating ring and the stationary ring; among them, the calculation formulas of q cμj and q cvj are as follows: 上式中，D为滚动体直径，dm为轴承节径，α为接触角，l为滚动体长度，Z为滚动体个数。In the above formula, D is the rolling element diameter, dm is the bearing pitch diameter, α is the contact angle, l is the rolling element length, and Z is the number of rolling elements. 15.根据权利要求14所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：根据S301步骤中公式得出S302步骤中的第j个滚动体分别和旋转套圈以及静止套圈接触处的I-H寿命LIHμj和LIHvj，其计算公式如下：15. The method for analyzing the fatigue life of a cylindrical roller bearing based on multi-factor coupling according to claim 14, characterized in that: the IH life L IHμj and L IHvj at the contact point between the j-th rolling element and the rotating ring and the stationary ring in step S302 are obtained according to the formula in step S301, and the calculation formula is as follows: 上式中，σVMμj,max和σVMvj,max分别为第j个滚动体分别和旋转套圈以及静止套圈接触处的最大Von-Mises应力，σVM,lim为材料的Von-Mises应力的极限值。In the above formula, σ VMμj,max and σ VMvj,max are the maximum Von-Mises stresses at the contact points between the jth rolling element and the rotating ring and the stationary ring respectively, and σ VM,lim is the limit value of the Von-Mises stress of the material. 16.根据权利要求15所述的基于多因素耦合的圆柱滚子轴承疲劳寿命分析方法，其特征在于：所述S303步骤中的计算公式如下：16. The method for analyzing the fatigue life of cylindrical roller bearings based on multi-factor coupling according to claim 15, characterized in that: the calculation formula in step S303 is as follows: 上式用于将S302步骤中所得各个滚动体分别和旋转套圈以及静止套圈接触处的I-H寿命进行叠加得出轴承整体的疲劳寿命。The above formula is used to superimpose the I-H life of each rolling element obtained in step S302 at the contact point with the rotating ring and the stationary ring to obtain the fatigue life of the entire bearing.
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