CN113591268B - Method and device for evaluating reliability of contact fatigue life of gear under variable amplitude load - Google Patents

Method and device for evaluating reliability of contact fatigue life of gear under variable amplitude load Download PDF

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CN113591268B
CN113591268B CN202110704007.1A CN202110704007A CN113591268B CN 113591268 B CN113591268 B CN 113591268B CN 202110704007 A CN202110704007 A CN 202110704007A CN 113591268 B CN113591268 B CN 113591268B
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gear
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contact fatigue
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stress
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CN113591268A (en
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邓海龙
于欢
刘其晨
郭扬
康贺铭
李永平
李明凯
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Inner Mongolia University of Technology
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Abstract

The invention relates to a gear contact fatigue life assessment technology, in particular to a gear contact fatigue life reliability assessment method and device under variable amplitude load, comprising the following steps: based on an empirical formula and a numerical model, determining an optimal maximum contact stress calculation method; constructing a gear contact fatigue initiation life assessment model under variable amplitude load by combining a nonlinear damage function; constructing a gear contact fatigue extension life assessment model under variable amplitude load; constructing a gear contact fatigue life-span assessment model according to the gear germination and expansion failure modes; based on the load and strength relation, three life state equations are established by combining the three life evaluation models, and the reliability index is solved, so that the reliability evaluation method based on the gear contact fatigue life model under variable amplitude load is highest in accuracy. The invention has the advantages that the reliability of the contact fatigue life of the gear under the variable amplitude load can be evaluated more stably and accurately, and the dependence on factors such as gear materials, structural dimensions, test amounts and the like is reduced.

Description

Method and device for evaluating reliability of contact fatigue life of gear under variable amplitude load
Technical Field
The invention relates to a gear contact fatigue life assessment technology, in particular to a gear contact fatigue life reliability assessment method and device under variable amplitude load.
Background
The existing gear transmission has the advantages of high transmission efficiency, accurate transmission ratio, large power range and the like, and the gear is an indispensable part in industrial products. Gears play a critical role in the safety, reliability and economy of machinery.
The transmission gear is forward to the goal of high transmission efficiency, stable transmission ratio, long life and high reliability. However, due to insufficient knowledge of the failure mechanism of gear contact fatigue, incomplete consideration of factors influencing the fatigue life of the gear contact and the poor reliability analysis method of the fatigue life of the gear contact, the current research on the fatigue life of the gear is still evaluated based on an empirical formula and a gear fatigue test.
Therefore, it is needed to establish a gear contact fatigue life evaluation equation and a contact fatigue life reliability evaluation method which can take into consideration the influences of residual stress, temperature and the like, reduce the dependence on factors such as gear materials, structural dimensions, process parameters, test amounts and the like in an empirical formula, and accurately evaluate the gear contact fatigue life.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method and a device for evaluating the reliability of the contact fatigue life of gears under variable amplitude load.
The aim of the invention is achieved by the following technical scheme: the method for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load comprises the following steps:
s101, calculating the maximum contact stress of the gear based on an empirical formula;
s102, establishing a two-dimensional meshing gear static model and a two-dimensional meshing gear dynamic model based on a numerical calculation theory and an equivalent boundary condition, and respectively obtaining the corresponding maximum contact stress of the gears;
s103, comparing the maximum contact stress obtained based on the two-dimensional meshing gear static model and the two-dimensional meshing gear dynamic model with the maximum contact stress obtained by an empirical formula respectively, and determining an optimal numerical calculation model;
s104, constructing a gear contact fatigue crack initiation life assessment model under variable amplitude load based on a nonlinear damage function;
s105, constructing a gear contact fatigue crack growth life assessment model under variable amplitude load based on a Paris formula, a crack growth angle, gear material hardness and crack tip stress intensity factor;
s106, constructing a gear contact fatigue life-span assessment model according to the gear sprouting and expansion failure mode under variable amplitude load;
s107, based on the load and strength relation, combining the gear contact fatigue crack initiation life assessment model, the gear contact fatigue crack propagation life assessment model and the gear contact fatigue total life assessment model under variable amplitude loading, and respectively establishing a gear contact fatigue life state equation mainly for initiation, a gear contact fatigue life state equation mainly for propagation and a gear contact fatigue total life state equation;
s108, solving the reliability index through a one-time second-order moment method, comparing the differences of the reliability indexes of the three state equations, and determining that the reliability evaluation method based on the gear contact fatigue life evaluation model under variable amplitude load has highest precision.
Specifically, the gear contact fatigue crack initiation life assessment model under the variable amplitude load is as follows:
Figure BDA0003131440210000021
wherein N is pre Sigma n is the fatigue initiation life of gear contact j For the already service life, N fj Is sigma (sigma) j Fatigue life, sigma, corresponding to stress level max For maximum stress, sigma rs N is the surface residual stress f max For maximum stress sigma max Fatigue life, sigma, of the corresponding j In order to be loaded with the stress,
Figure BDA0003131440210000022
is a correction coefficient.
Specifically, the gear contact fatigue crack growth life evaluation model under the variable amplitude load is as follows:
Figure BDA0003131440210000031
wherein N is p A, prolonging fatigue crack growth life of gear contact 0 Is the initial crack length; a, a c-i To correspond to crack propagation length at a certain amplitude; h b The overall hardness of the gear is that of the gear; h L Is the local hardness of the gear; c is the coefficient of crack growth rate; m is the index of crack growth rate, eta HV Is a hardness factor; τ max-i Is the maximum stress in the stress region; epsilon is the hole coefficient; k (K) t Is a hole shape factor; η is a matrix tissue correction coefficient; u (a) is the crack closure coefficient of effect.
Specifically, the gear contact fatigue life assessment model is as follows:
Figure BDA0003131440210000032
a gear contact fatigue life reliability assessment device under variable amplitude load, comprising:
a maximum contact stress calculation unit 301, configured to calculate a maximum contact stress on the gear contact surface according to the hertz contact theory;
the maximum contact stress calculation unit 302 is configured to respectively construct a two-dimensional static model and a two-dimensional dynamic model of the gear based on a numerical calculation theory and an equivalent boundary condition, and respectively obtain the maximum contact stress on the corresponding gear contact surface based on the two-dimensional static model and the two-dimensional dynamic model;
the optimal numerical calculation model selecting unit 303 is configured to compare the maximum contact stress obtained based on the two-dimensional static model and the two-dimensional dynamic model with the maximum contact stress obtained based on the empirical formula, and select an optimal numerical calculation model;
an external cause maximum contact stress variation determining unit 304, configured to compare maximum contact stresses obtained based on the two-dimensional static model and the two-dimensional dynamic model under different environmental conditions with maximum contact stresses obtained based on the two-dimensional static model and the two-dimensional dynamic model under initial environmental conditions, respectively, and determine an influence of each factor on the maximum contact stress;
the gear contact fatigue crack initiation life assessment model construction unit 305 is used for establishing a gear contact fatigue crack initiation life assessment model under variable amplitude load based on a nonlinear damage function;
the gear contact fatigue crack growth life assessment model construction unit 306 is used for constructing a gear contact fatigue crack growth life assessment model under variable amplitude load based on a Paris formula, a crack growth angle, gear material hardness and a crack tip stress intensity factor;
the gear contact fatigue life-span assessment model construction unit 307 is configured to construct a gear contact fatigue life-span assessment model based on the gear initiation+extension failure mode under the variable amplitude load.
Specifically, the method further comprises a life state equation I construction unit 308, configured to establish a gear contact fatigue life state equation I based on the gear contact fatigue crack initiation life assessment model under the variable amplitude load;
specifically, the method further comprises a life state equation II construction unit 309, configured to establish a gear contact fatigue life state equation II based on the gear contact fatigue crack growth life assessment model under the variable amplitude load;
specifically, the method further comprises a life state equation III construction unit 3010 for establishing a gear contact fatigue initiation and extension life state equation based on the gear contact fatigue life assessment model under the variable amplitude load.
Specifically, the reliability index calculation unit 3011 is further included for reliability index calculation based on the three life state equations.
Specifically, the device further comprises a reliability difference comparing unit 3012, configured to compare reliability indexes based on the three life state equations, compare the reliability index differences, and obtain an optimal life reliability evaluation method.
The invention has the following advantages: according to the invention, gear contact fatigue under variable amplitude load is taken as a research object, and based on an empirical formula, a two-dimensional meshing gear static model and a two-dimensional meshing gear dynamic model, the maximum contact stress of the corresponding gears is respectively obtained and compared, so that an optimal numerical calculation model is determined; aiming at the gear contact fatigue life prediction methods under different variable amplitude loads, on one hand, a gear contact fatigue crack initiation life assessment model under the variable amplitude loads is creatively established based on a nonlinear damage function; on the other hand, the existing Paris formula is corrected, and the influences of crack expansion angles, gear material hardness, crack tip stress intensity factors and the like are considered, so that a gear contact fatigue crack expansion life assessment model under variable amplitude load is constructed; finally, constructing a gear contact fatigue life assessment model based on the gear sprouting and expansion failure mode under the variable amplitude load; based on the load and strength relation, combining the three life evaluation models to respectively establish three life state equations; solving the three life state equations by a one-time second-order moment method, obtaining corresponding reliability indexes, comparing the differences of the reliability indexes of the three state equations, and determining that the reliability evaluation method based on the gear contact fatigue life model under variable amplitude load has highest accuracy. The method can evaluate the reliability of gear contact fatigue initiation and extension life under variable amplitude load more stably and accurately, reduce the dependence on factors such as gear materials, structural dimensions, test amounts and the like, provide constructive references for industrial production, and reduce accidents and malignant accidents.
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FIG. 1 is a flow chart of an evaluation method of the present invention;
FIG. 2 is a schematic diagram showing the definition of relevant parameters in the crack propagation process according to the embodiment of the invention;
FIG. 3 is a schematic diagram of a gear contact fatigue life reliability assessment device according to the present invention;
FIG. 4 is a schematic representation of the residual life factor definition under two-stage luffing load loading of the present invention;
FIG. 5 shows the results of three state-of-life equation comparisons obtained in accordance with the present invention.
Detailed Description
For the purpose of making the technical solution and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and examples. It should be understood that the particular embodiments described herein are illustrative only and are not intended to limit the invention, i.e., the embodiments described are merely some, but not all, of the embodiments of the invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by a person skilled in the art without making any inventive effort, are intended to be within the scope of the present invention.
It is noted that relational terms such as "first" and "second", and the like, are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or apparatus that comprises the element.
The present invention will be further described with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.
As shown in fig. 1-5;
the method for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load comprises the following steps:
s101: and calculating the maximum contact stress on the gear contact surface according to an empirical formula.
Gear maximum contact calculation based on Hertz contact theoryStress sigma Zmax The calculation model is as follows:
Figure BDA0003131440210000051
the above formula (1) is a theoretical formula, wherein F is the applied load, k 1 、k 2 Poisson ratio v to gears 1, 2 1 、v 2 Modulus of elasticity E 1 、E 2 Related constant, d 1 、d 2 The pitch radii of the gears 1, 2 are given, and α is the gear pressure angle.
S102: based on a numerical calculation theory and an equivalent boundary condition, respectively constructing a two-dimensional static model and a two-dimensional dynamic model, and respectively obtaining the maximum contact stress on the corresponding gear contact surface based on the two-dimensional static model and the two-dimensional dynamic model.
In the implementation, two modules of Standard and Explicit based on ABAQUS can be combined with equivalent boundary conditions and loads to respectively construct a two-dimensional static model and a two-dimensional dynamic model, and the maximum contact stress value and the appearance position on the gear contact surface corresponding to the two models are respectively obtained.
S103: and comparing the corresponding maximum contact stress obtained based on the two-dimensional static model and the two-dimensional dynamic model with the maximum contact stress obtained based on the empirical formula to determine an optimal numerical calculation model.
And comparing the maximum contact stress calculation results of the two models based on the S102 with the maximum contact stress calculated in the S101 to determine an optimal numerical calculation model. The comparative analysis shows that the calculation accuracy of the two-dimensional dynamic model is higher than that of the two-dimensional static model because the dynamic model takes the influence of dynamic impact load and the like into consideration.
S104: and constructing a gear contact fatigue crack initiation life assessment model under variable amplitude load.
In particular, the method is based on a nonlinear injury function D f Considering the effects of maximum stress, load loading order, surface residual stress, the nonlinear damage function under luffing load can be defined as:
Figure BDA0003131440210000061
in the formula (2), sigma max For maximum stress, sigma rs As a result of the residual stress of the surface,
Figure BDA0003131440210000062
for stress ratio->
Figure BDA0003131440210000063
Is a circulation ratio. Based on Corten-Dolan theory, the influence of maximum stress on damage is considered, and the nonlinear damage function D f Can be expressed as:
Figure BDA0003131440210000064
wherein N is f max For maximum stress sigma max Corresponding fatigue life. d is an index related to stress ratio and cycle ratio.
Taking into account the effect of the load loading order, the index d can be given by equation (4):
Figure BDA0003131440210000065
then equation (3) can be converted into:
Figure BDA0003131440210000066
further, in consideration of the influence of the surface residual stress, the equation (5) may be expressed as:
Figure BDA0003131440210000071
introducing correction factors
Figure BDA0003131440210000072
For nonlinear injury function D f Make corrections (I)>
Figure BDA0003131440210000073
The values can be obtained by fitting experimental data, and equation (6) can be further converted into:
Figure BDA0003131440210000074
defining a Residual Life Factor (RLF) α as:
Figure BDA0003131440210000075
wherein N is R To effect a residual life after N cycles at sigma stress level, N f Fatigue life corresponding to sigma stress level. As shown in FIG. 4, for two-stage loading, if N is the fatigue life f1 Is of the initial stress level sigma 1 Applying n 1 Cycle, i.e. sigma 1 Equivalent number of cycles at stress level n 11 Then relative alpha 11 Expressed as:
Figure BDA0003131440210000076
since the damage has the following relationship with the Residual Life Factor (RLF) α:
D＝1-α F(σ,p) (10)
combining equation (9) and equation (10) yields:
Figure BDA0003131440210000077
wherein F is 1 (sigma, p) and F 2 (σ, p) is σ 1 Sum sigma 2 Two correlation functions of stress levels. Thus, sigma 2 Residual life N at stress level R12 As followsThe illustration is:
N R12 ＝α 12 N f2 (12)
if sigma 2 Stress level application n 2 Of a period, i.e. n 2 <N R12 Then the corresponding RLF can be obtained:
α 22 ＝α 12 -n 2 /N f2 (13)
thus, for multi-level loading, α ij The value of (2) can be obtained by:
Figure BDA0003131440210000081
substituting formula (7) into formula (14) to obtain:
Figure BDA0003131440210000082
in two-stage loading, corresponding to sigma 1 Sum sigma 2 Equation (σ) for the level lesion point 1 ,n 1 ) Sum (sigma) 2 ,n 2 ) Expressed as:
logσ 1 ＝Alogn 1 +logσ s (16)
logσ 2 ＝Alogn 2 +logσ s (17)
wherein sigma s For yield strength, substituting α for n in combination with equation (11) yields:
Figure BDA0003131440210000083
thus, in combination with the cycle times previously applied, a fatigue life prediction model under variable amplitude load can be constructed:
Figure BDA0003131440210000084
namely:
Figure BDA0003131440210000091
s105: and constructing a gear contact fatigue crack extension life assessment model under variable amplitude load based on the Paris formula, the crack extension angle, the gear material hardness and the crack tip stress intensity factor.
Based on a type II crack tip stress intensity factor calculation formula:
Figure BDA0003131440210000092
wherein τ c Is shear stress; a is the half crack length; ζ is the crack propagation increment; τ eqv Equivalent shear stress. The calculation mode of each parameter is as follows:
τ eqv ＝η HV ·τ max_corr (22)
Figure BDA0003131440210000093
Figure BDA0003131440210000094
δ K ＝(K t -1)·η+1 (25)
ψ＝e -4.3ε (26)
wherein eta HV Is a hardness factor; τ max_corr To correct the maximum shear stress; τ max Is the maximum stress in the stress region; ψ is the number of holes that can change the bearing surface; epsilon is the hole coefficient; k (K) t Is a hole shape factor; delta K Correcting the coefficient for the notch effect; η is a matrix tissue correction coefficient; HV (z) is the hardness at depth z, and the core hardness HV c Surface hardness HV s Equivalent depth z eff And (5) correlation.
Taking into account the crack closure effect, introducing a crack closure effect coefficient U (a)
Figure BDA0003131440210000101
Formula (21) is rewritten as:
Figure BDA0003131440210000102
based on the Paris formula, taking into account the gear hardness effects, the gear contact fatigue crack growth life assessment model can be expressed as:
Figure BDA0003131440210000103
wherein a is 0 Is the initial crack length; h b The overall hardness of the gear is that of the gear; h L Is the local hardness of the gear; c is the coefficient of crack growth rate; m is an index of crack growth rate.
Integrating the formula (29) to obtain a gear contact fatigue crack growth life assessment model under variable amplitude load:
Figure BDA0003131440210000104
s106: and constructing a gear contact fatigue life-span assessment model according to the gear sprouting and expansion failure mode under the variable amplitude load.
In the embodiment, when the evaluation is performed, the gear contact fatigue full life evaluation model can be obtained according to the gear contact fatigue crack initiation life evaluation model under the variable amplitude load of the formula (20) and the gear contact fatigue crack propagation life evaluation model of the formula (30):
Figure BDA0003131440210000105
based on the gear contact fatigue life assessment model, gear contact fatigue life assessment under variable amplitude load can be performed.
S107: and establishing a gear life state equation under variable amplitude load based on the strength and load combined with the gear failure criterion.
The failure state of a component can be expressed as based on load and strength:
R(t)-S(t)≤0 (32)
introducing M such that:
M＝R-S (33)
m is called a state equation, when M >0, the strength is greater than the load, and the component is not in a failure state; when M <0, the strength is less than the load, and the component is in a failure state; when m=0, the strength is equal to the load, the member is at the limit of meeting the safe state, and the strength is smaller than the load at the next moment due to the trend of the strength and the load with time, and the member enters the failure state. Thus, m=0 is called the limit state equation.
S108: and establishing a minimized problem equation based on the failure criterion and establishing a reliability index solving method of the multivariable nonlinear state equation by a first-order second-order moment method.
And a reliability index beta is introduced, wherein the reliability index beta is the maximum point of the failure probability of the gear under the y space formed by a plurality of influencing factors of the service life of the gear. The reliability index problem when the failure probability is maximized can be equated with the minimum distance problem from the origin to m=0 in the y-space.
Figure BDA0003131440210000111
The minimization problem of equation (19) is constrained by the condition m=0, introducing a lagrangian multiplier λ, obtaining the minimization equation of the limiting state equation:
Figure BDA0003131440210000112
the first order moment method is to solve the functional function by performing first order Taylor expansion on the functional function and neglecting the high order moment. Therefore, under the condition that the distribution of the random variables is not clear, a new mathematical model can be constructed by the method, and the reliability analysis method of the component under a certain working condition can be further solved.
The reliability index calculation formula can be obtained based on the first-order matrix formula and the second-order matrix formula:
Figure BDA0003131440210000113
s109: and respectively establishing a gear contact fatigue life state equation mainly based on initiation, a gear contact fatigue life state equation mainly based on propagation and a gear contact fatigue crack initiation and propagation life state equation based on the gear contact fatigue crack initiation life assessment model, the gear contact fatigue crack propagation life assessment model and the gear contact fatigue full life assessment model under the variable amplitude load by combining the failure criteria, and solving.
Based on formulas (20), (30) and (31), three gear contact fatigue life state equations are respectively established:
M i ＝N pre -v 0 ·T (37)
M pI ＝N p -v 0 ·T (38)
M zI ＝N-v 0 ·T (39)
wherein v is 0 Is the gear speed.
And solving the reliability index under each state equation through a formula (36).
S1010: and solving the reliability indexes based on the three state equations, and comparing the reliability index differences.
Based on the reliability index solutions of the three state equations, the reliability index differences of the three life state equations and the gear contact fatigue failure probability trend are compared, and the reliability assessment method based on the gear contact fatigue life model under variable amplitude load is highest in accuracy.
By utilizing the method, the reliability of the contact fatigue life of the gear under the variable amplitude load can be evaluated more stably and accurately, and the dependence on the gear material, the structural size and the test amount is reduced.
Based on the same inventive concept as the gear contact fatigue crack initiation and extension life reliability evaluation method under variable amplitude load, the application provides a gear contact fatigue crack initiation and extension life reliability evaluation device under variable amplitude load, as described in the following examples. Because the principle of solving the problem of the gear contact fatigue life reliability evaluation device is similar to that of the gear contact fatigue life reliability evaluation method, the implementation of the gear contact fatigue life reliability evaluation device can be referred to the implementation of the gear contact fatigue life reliability evaluation method, and the repetition is omitted.
Fig. 3 is a schematic structural diagram of a gear contact fatigue crack initiation and propagation life reliability evaluation device based on amplitude-variable load according to an embodiment of the present invention, as shown in fig. 3, a gear contact fatigue full life reliability evaluation device includes:
a maximum contact stress calculation unit 301, configured to calculate a maximum contact stress on the gear contact surface according to the hertz contact theory;
the maximum contact stress calculation unit 302 is configured to respectively construct a two-dimensional static model and a two-dimensional dynamic model of the gear based on a numerical calculation theory and an equivalent boundary condition, and respectively obtain the maximum contact stress on the corresponding gear contact surface based on the two-dimensional static model and the two-dimensional dynamic model;
the optimal numerical calculation model selecting unit 303 is configured to compare the maximum contact stress obtained based on the two-dimensional static model and the two-dimensional dynamic model with the maximum contact stress obtained based on the empirical formula, and select an optimal numerical calculation model;
an external cause maximum contact stress variation determining unit 304, configured to compare maximum contact stresses obtained based on the two-dimensional static model and the two-dimensional dynamic model under different environmental conditions with maximum contact stresses obtained based on the two-dimensional static model and the two-dimensional dynamic model under initial environmental conditions, respectively, and determine an influence of each factor on the maximum contact stress;
the gear contact fatigue crack initiation life assessment model construction unit 305 is used for establishing a gear contact fatigue crack initiation life assessment model under variable amplitude load based on a nonlinear damage function;
the gear contact fatigue crack growth life assessment model construction unit 306 is used for constructing a gear contact fatigue crack growth life assessment model under variable amplitude load based on a Paris formula, a crack growth angle, gear material hardness and a crack tip stress intensity factor;
the gear contact fatigue life-span assessment model construction unit 307 is configured to construct a gear contact fatigue life-span assessment model based on the gear initiation+extension failure mode under the variable amplitude load;
a life state equation I construction unit 308, configured to establish a gear contact fatigue life state equation I based on the gear contact fatigue crack initiation life assessment model under the variable amplitude load;
a life state equation II construction unit 309, configured to establish a gear contact fatigue life state equation II based on the gear contact fatigue crack growth life assessment model under the variable amplitude load;
the life state equation III construction unit 3010 is used for establishing a gear contact fatigue initiation and extension life state equation based on the gear contact fatigue full life assessment model under the variable amplitude load;
a reliability index calculation unit 3011 for calculating reliability indexes based on the three life state equations;
and a reliability difference comparing unit 3012, configured to compare reliability indexes based on the three life state equations, compare reliability index differences, and obtain a most reliable life prediction model.
By utilizing the method, the reliability of the contact fatigue life of the gear under the variable amplitude load can be evaluated more stably and accurately, and the dependence on the gear material, the structural size and the test amount is reduced.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining hardware and software aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions, which can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart illustrations and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way. Many possible variations and modifications of the disclosed technology can be made by anyone skilled in the art, or equivalent embodiments with equivalent variations can be made, without departing from the scope of the disclosed technology. Therefore, any modification, equivalent variation and modification of the above embodiments according to the technology of the present invention fall within the protection scope of the present invention.

Claims (8)

1. The method for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load is characterized by comprising the following steps of: comprising the following steps:
s101, calculating the maximum contact stress of the gear based on an empirical formula;
s102, establishing a two-dimensional meshing gear static model and a two-dimensional meshing gear dynamic model based on a numerical calculation theory and an equivalent boundary condition, and respectively obtaining the corresponding maximum contact stress of the gears;
s103, comparing the maximum contact stress obtained based on the two-dimensional meshing gear static model and the two-dimensional meshing gear dynamic model with the maximum contact stress obtained by an empirical formula respectively, and determining an optimal numerical calculation model;
s104, constructing a gear contact fatigue crack initiation life assessment model under variable amplitude load based on a nonlinear damage function;
s105, constructing a gear contact fatigue crack growth life assessment model under variable amplitude load based on a Paris formula, a crack growth angle, gear material hardness and crack tip stress intensity factor;
s106, constructing a gear contact fatigue life-span assessment model according to the gear sprouting and expansion failure mode under variable amplitude load;
s107, based on the load and strength relation, combining the gear contact fatigue crack initiation life assessment model, the gear contact fatigue crack propagation life assessment model and the gear contact fatigue total life assessment model under variable amplitude load, and respectively establishing a gear contact fatigue life state equation mainly based on initiation, a gear contact fatigue life state equation mainly based on propagation and a gear contact fatigue total life state equation;
s108, solving the reliability index through a one-time second-order moment method, comparing the differences of the reliability indexes of the three state equations, and determining that the reliability evaluation method based on the gear contact fatigue life evaluation model under variable amplitude load has the highest precision;
in step S104, the gear contact fatigue crack initiation life assessment model under the variable amplitude load is as follows:
Figure FDA0004243274110000021
wherein N is pre Sigma n is the fatigue initiation life of gear contact j For the already service life, N fj Is sigma (sigma) j Fatigue life, sigma, corresponding to stress level max For maximum stress, sigma rs N is the surface residual stress fmax For maximum stress sigma max Fatigue life, sigma, of the corresponding j In order to be loaded with the stress,
Figure FDA0004243274110000022
to correct the coefficient, sigma s Is the yield strength;
the gear contact fatigue crack growth life evaluation model under the variable amplitude load in the step S105 is as follows:
Figure FDA0004243274110000023
wherein N is p A, prolonging fatigue crack growth life of gear contact 0 Is the initial crack length; a, a c-i To correspond to crack propagation length at a certain amplitude; h b The overall hardness of the gear is that of the gear; h L Is the local hardness of the gear; c is the coefficient of crack growth rate; m is the index of crack growth rate, eta HV Is a hardness factor; τ max-i Is the maximum stress in the stress region; epsilon is the hole coefficient; k (K) t Is a hole shape factor; η is a matrix structure correction coefficient, U (a) is a crack closure effect coefficient, a is a half crack length, and d is an index related to stress ratio and cycle ratio.
2. The method for evaluating the reliability of the fatigue life of a gear in contact with a variable amplitude load according to claim 1, wherein: the gear contact fatigue life assessment model in step S106 is as follows:
Figure FDA0004243274110000031
3. a gear contact fatigue life reliability evaluation device under luffing load applied to the gear contact fatigue life reliability evaluation method under luffing load as defined in claim 1 or 2, characterized in that: comprising the following steps:
the maximum contact stress calculation unit is used for calculating the maximum contact stress on the gear contact surface according to the Hertz contact theory;
the maximum contact stress calculation unit is used for respectively constructing a two-dimensional static model and a two-dimensional dynamic model of the gear based on a numerical calculation theory and an equivalent boundary condition, and respectively obtaining the maximum contact stress on a corresponding gear contact surface based on the two-dimensional static model and the two-dimensional dynamic model;
the optimal numerical calculation model selecting unit is used for comparing the maximum contact stress obtained based on the two-dimensional static model and the two-dimensional dynamic model with the maximum contact stress obtained based on the empirical formula calculation respectively, and selecting the optimal numerical calculation model;
the external cause maximum contact stress change determining unit is used for comparing the maximum contact stress obtained based on the two-dimensional static model and the two-dimensional dynamic model under different environmental conditions with the maximum contact stress obtained based on the two-dimensional static model and the two-dimensional dynamic model under the initial environmental conditions respectively, and determining the influence of each factor on the maximum contact stress;
the gear contact fatigue crack initiation life assessment model construction unit is used for establishing a gear contact fatigue crack initiation life assessment model under variable amplitude load based on a nonlinear damage function;
the gear contact fatigue crack extension life assessment model construction unit is used for constructing a gear contact fatigue crack extension life assessment model under variable amplitude load based on a Paris formula, a crack extension angle, gear material hardness and a crack tip stress intensity factor;
the gear contact fatigue life-span assessment model building unit is used for building a gear contact fatigue life-span assessment model based on the gear germination and expansion failure mode under the variable amplitude load.
4. A gear contact fatigue life reliability assessment device under variable amplitude load as claimed in claim 3, wherein: the gear contact fatigue life equation I is built based on the gear contact fatigue crack initiation life assessment model under the variable amplitude load.
5. The device for evaluating reliability of contact fatigue life of gears under variable amplitude load as set forth in claim 4, wherein: the gear contact fatigue life state equation II is built based on the gear contact fatigue crack propagation life assessment model under the variable amplitude load.
6. The device for evaluating reliability of contact fatigue life of gears under variable amplitude load according to claim 5, wherein: the system further comprises a life state equation III construction unit which is used for establishing a gear contact fatigue initiation and extension life state equation based on the gear contact fatigue full life assessment model under the variable amplitude load.
7. The device for evaluating reliability of contact fatigue life of gears under variable amplitude load as set forth in claim 6, wherein: the system further comprises a reliability index calculation unit which is used for calculating the reliability index based on the three life state equations.
8. The device for evaluating reliability of contact fatigue life of gears under variable amplitude load as set forth in claim 7, wherein: the system further comprises a reliability difference comparison unit which is used for comparing reliability indexes based on the three life state equations, comparing the reliability index differences and obtaining an optimal life reliability assessment method.
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