阅读说明：本技术 变幅载荷下齿轮接触疲劳寿命可靠性评估方法及装置 (Method and device for evaluating reliability of contact fatigue life of gear under variable amplitude load ) 是由 邓海龙 于欢 刘其晨 郭扬 康贺铭 李永平 李明凯 于 2021-06-24 设计创作，主要内容包括：本发明涉及齿轮接触疲劳全寿命评估技术,具体公开了变幅载荷下齿轮接触疲劳寿命可靠性评估方法及装置,包括：基于经验公式和数值模型计算,确定最佳最大接触应力计算方法；结合非线性损伤函数构建变幅载荷下齿轮接触疲劳萌生寿命评估模型；构建变幅载荷下齿轮接触疲劳扩展寿命评估模型；根据齿轮萌生+扩展失效模式构建齿轮接触疲劳全寿命评估模型；基于载荷及强度关系,结合所述三种寿命评估模型建立三种寿命状态方程,求解其可靠性指数,可知基于变幅载荷下齿轮接触疲劳全寿命模型的可靠性评估方法精度最高。本发明的优点是可以比较稳定与准确地评估变幅载荷下齿轮接触疲劳寿命可靠性,减少对齿轮材料、结构尺寸、试验量等因素的依赖性。(The invention relates to a gear contact fatigue full-life assessment technology, and particularly discloses a method and a device for assessing the reliability of the gear contact fatigue life under variable amplitude load, wherein the method comprises the following steps: determining an optimal maximum contact stress calculation method based on an empirical formula and numerical model calculation; combining a nonlinear damage function to construct a gear contact fatigue initiation life evaluation model under variable amplitude load; constructing a gear contact fatigue extension life evaluation model under variable amplitude load; constructing a gear contact fatigue full-life evaluation model according to a gear germination and extension failure mode; based on the load and strength relationship, three life state equations are established by combining the three life evaluation models, the reliability index is solved, and the reliability evaluation method based on the gear contact fatigue full-life model under the variable amplitude load is known to have the highest precision. The method 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 quantity and the like is reduced.)

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: the method 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 equivalent boundary conditions, and respectively obtaining 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 evaluation model under variable amplitude load based on the nonlinear damage function;

s105, constructing a gear contact fatigue crack propagation life evaluation model under the variable amplitude load based on the Paris formula, the crack propagation angle, the gear material hardness and the crack tip stress intensity factor;

s106, constructing a gear contact fatigue full-life evaluation model according to the gear germination and expansion failure mode under the variable amplitude load;

s107, respectively establishing a gear contact fatigue life state equation mainly based on the initiation, a gear contact fatigue life state equation mainly based on the propagation and a gear contact fatigue life state equation based on the load and strength relation by combining the gear contact fatigue crack initiation life evaluation model, the gear contact fatigue crack propagation life evaluation model and the gear contact fatigue life full-life evaluation model under the variable amplitude loading;

and S108, solving the reliability index through a first-order second-order moment method, comparing the difference of the reliability indexes of the three state equations, and determining that the reliability evaluation method based on the gear contact fatigue full-life evaluation model under the variable amplitude load has the highest precision.

2. The method for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load according to claim 1, wherein: in the step S104, the gear contact fatigue crack initiation life evaluation model under variable amplitude loading is as follows:

wherein N is_preSigma n for the onset of gear contact fatigue life_jTo have a useful life, N_fjIs σ_jFatigue life, σ, corresponding to stress level_maxIs the maximum stress, σ_rsIs surface residual stress, N_{f max}Is the maximum stress sigma_maxCorresponding fatigue life, σ_jIn order to load the stress, the stress is loaded,is a correction factor.

3. The method for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load as recited in claim 2, wherein: the gear contact fatigue crack propagation life evaluation model under the variable amplitude load in the step S105 is as follows:

wherein N is_pFor gear contact fatigue crack propagation life, a₀Is the initial crack length; a is_c-iCorresponding to the crack propagation length under a certain amplitude; h_bThe overall hardness of the gear is set; h_LThe local hardness of the gear is obtained; c is the coefficient of crack propagation rate; m is an index of crack propagation velocity, η_HVIs a hardness factor; tau is_max-iIs the maximum stress in the stress region; epsilon is the hole coefficient; k_tIs the hole shape factor; eta is the matrix structure correction coefficient, and U (a) is the crack closure effect coefficient.

4. The method for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load according to claim 3, wherein: the gear contact fatigue full-life evaluation model in step S106 is:

5. the utility model provides a gear contact fatigue life reliability evaluation device under variable amplitude load which characterized in that: the method comprises 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 equivalent boundary conditions, 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;

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 calculation of an empirical formula respectively and selecting an optimal numerical calculation model;

the external cause-induced 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 condition respectively, and determining the influence of each factor on the maximum contact stress;

the gear contact fatigue crack initiation life evaluation model building unit is used for building a gear contact fatigue crack initiation life evaluation model under the variable amplitude load based on the nonlinear damage function;

the gear contact fatigue crack propagation life evaluation model building unit is used for building a gear contact fatigue crack propagation life evaluation model under the variable amplitude load based on a Paris formula, a crack propagation angle, gear material hardness and a crack tip stress intensity factor;

and the gear contact fatigue full-life evaluation model building unit is used for building a gear contact fatigue full-life evaluation model based on the gear germination and expansion failure modes under the variable amplitude load.

6. The device for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load as claimed in claim 5, wherein: the gear contact fatigue crack initiation life evaluation system further comprises a life state equation I building unit which is used for building a gear contact fatigue life state equation I based on the gear contact fatigue crack initiation life evaluation model under the variable amplitude load.

7. The device for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load as claimed in claim 6, wherein: the gear contact fatigue crack propagation life evaluation device further comprises a life state equation II building unit, wherein the life state equation II building unit is used for building a gear contact fatigue life state equation II based on the gear contact fatigue crack propagation life evaluation model under the variable amplitude load.

8. The device for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load as claimed in claim 7, wherein: the gear contact fatigue life-expanding evaluation system further comprises a life state equation III building unit, wherein the life state equation III building unit is used for building a gear contact fatigue initiation and life-expanding state equation based on the gear contact fatigue full-life evaluation model under the variable amplitude load.

9. The device for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load as claimed in claim 8, wherein: the system also comprises a reliability index calculation unit which is used for calculating the reliability index based on the three life state equations.

10. The device for evaluating the reliability of the contact fatigue life of the gear under the variable amplitude load as claimed in claim 9, wherein: the system also comprises a reliability difference comparison unit which is used for comparing reliability indexes based on the three life state equations, comparing the reliability index difference and obtaining the optimal life reliability evaluation method.

Technical Field

The invention relates to a gear contact fatigue full-life assessment technology, in particular to a method and a device for assessing the reliability of the gear contact fatigue life 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. The gears play a crucial role in mechanical safety, reliability and economy.

Transmission gears are being developed with the goal of high transmission efficiency, stable transmission ratio, long life, and high reliability. However, due to the reasons that the mechanism of the contact fatigue failure of the gear is not well known, the factors influencing the contact fatigue life of the gear are not considered comprehensively, and the reliability analysis method of the contact fatigue life of the gear is not sound, the current research on the life of the gear is still evaluated based on an empirical formula and a gear fatigue test.

Therefore, it is necessary to establish an evaluation equation and a reliability evaluation method for contact fatigue life of a gear, which can consider the influence of residual stress, temperature and the like, reduce the dependence on the gear material, the structure size, the process parameters, the test quantity and other factors in the empirical formula, and accurately evaluate the contact fatigue life of the gear.

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 a gear under a variable amplitude load.

The purpose of the invention is realized 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 equivalent boundary conditions, and respectively obtaining 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 evaluation model under variable amplitude load based on the nonlinear damage function;

s105, constructing a gear contact fatigue crack propagation life evaluation model under the variable amplitude load based on the Paris formula, the crack propagation angle, the gear material hardness and the crack tip stress intensity factor;

s106, constructing a gear contact fatigue full-life evaluation model according to the gear germination and expansion failure mode under the variable amplitude load;

s107, respectively establishing a gear contact fatigue life state equation mainly based on the initiation, a gear contact fatigue life state equation mainly based on the propagation and a gear contact fatigue life state equation based on the load and strength relation by combining the gear contact fatigue crack initiation life evaluation model, the gear contact fatigue crack propagation life evaluation model and the gear contact fatigue life full-life evaluation model under the variable amplitude loading;

and S108, solving the reliability index through a first-order second-order moment method, comparing the difference of the reliability indexes of the three state equations, and determining that the reliability evaluation method based on the gear contact fatigue full-life evaluation model under the variable amplitude load has the highest precision.

Specifically, the evaluation model of the contact fatigue crack initiation life of the gear under the variable amplitude load is as follows:

wherein N is_preSigma n for the onset of gear contact fatigue life_jTo have a useful life, N_fjIs σ_jFatigue life, σ, corresponding to stress level_maxIs the maximum stress, σ_rsIs surface residual stress, N_{f max}Is the maximum stress sigma_maxCorresponding fatigue life, σ_jIn order to load the stress, the stress is loaded,is a correction factor.

Specifically, the evaluation model of the contact fatigue crack propagation life of the gear under the variable amplitude load comprises the following steps:

wherein N is_pFor gear contact fatigue crack propagation life, a₀Is the initial crack length; a is_c-iCorresponding to the crack propagation length under a certain amplitude; h_bThe overall hardness of the gear is set; h_LThe local hardness of the gear is obtained; c is the coefficient of crack propagation rate; m is an index of crack propagation velocity, η_HVIs a hardness factor; tau is_max-iIs the maximum stress in the stress region; epsilon is the hole coefficient; k_tIs the hole shape factor; eta is a matrix structure correction coefficient; u (a) is the crack closure effect coefficient.

Specifically, the gear contact fatigue full-life evaluation model is as follows:

a gear contact fatigue life reliability evaluation device under variable amplitude load comprises:

a maximum contact stress calculation unit 301, configured to calculate a maximum contact stress on the gear contact surface according to the hertzian 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 maximum contact stresses on corresponding gear contact surfaces based on the two-dimensional static model and the two-dimensional dynamic model;

an optimal numerical calculation model selecting unit 303, 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 calculated based on an empirical formula, respectively, and select an optimal numerical calculation model;

a maximum contact stress variation determining unit 304 caused by an external cause, 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 an initial environmental condition, respectively, and determine an influence of each factor on the maximum contact stresses;

the gear contact fatigue crack initiation life evaluation model establishing unit 305 is used for establishing a gear contact fatigue crack initiation life evaluation model under a variable amplitude load based on a nonlinear damage function;

the gear contact fatigue crack propagation life evaluation model construction unit 306 is used for constructing a gear contact fatigue crack propagation life evaluation model under the variable amplitude load based on a Paris formula, a crack propagation angle, gear material hardness and a crack tip stress intensity factor;

and the gear contact fatigue full-life evaluation model constructing unit 307 is used for constructing a gear contact fatigue full-life evaluation model based on the gear germination and extension failure modes under the variable amplitude load.

Specifically, the gear contact fatigue crack initiation life evaluation method further comprises a life state equation I building unit 308, which is used for building a gear contact fatigue life state equation I based on the gear contact fatigue crack initiation life evaluation model under the variable amplitude load;

specifically, the system further comprises a life state equation II building unit 309, which is used for building a gear contact fatigue life state equation II based on the gear contact fatigue crack propagation life evaluation model under the variable amplitude load;

specifically, the gear contact fatigue life-expanding state equation establishing unit 3010 is further included, and is configured to establish a gear contact fatigue initiation + life-expanding state equation based on the gear contact fatigue full-life evaluation model under the variable amplitude load.

Specifically, the system further comprises a reliability index calculation unit 3011, configured to calculate a reliability index based on the three life state equations.

Specifically, the system further comprises a reliability difference comparison 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: the method takes the contact fatigue of the gear under the variable amplitude load as a research object, and respectively obtains the corresponding maximum contact stress of the gear and compares the maximum contact stress based on an empirical formula, a two-dimensional meshing gear static model and a two-dimensional meshing gear dynamic model, thereby determining an optimal numerical calculation model; aiming at the gear contact fatigue life prediction methods under different amplitude variation loads, on one hand, a gear contact fatigue crack initiation life evaluation model under the amplitude variation load is creatively established based on a nonlinear damage function; on the other hand, the existing Paris formula is corrected, the influences of crack propagation angle, gear material hardness, crack tip stress intensity factor and the like are considered, and a gear contact fatigue crack propagation life evaluation model under variable amplitude load is constructed; finally, a gear contact fatigue full-life evaluation model is established based on the gear germination and expansion failure modes under the variable amplitude load; based on the load and strength relation, respectively establishing three life state equations by combining the three life evaluation models; solving the three life state equations by a first-order second-order moment method to obtain corresponding reliability indexes, and comparing the difference of the reliability indexes of the three state equations to determine that the reliability evaluation method based on the gear contact fatigue full-life model under the variable amplitude load has the highest precision. The method can stably and accurately evaluate the contact fatigue initiation and the service life extension reliability of the gear under the variable amplitude load, reduces the dependence on the gear material, the structure size, the test quantity and other factors, provides a constructive reference for industrial production, and reduces the occurrence of accidents and malignant accidents.

Drawings

FIG. 1 is a flow chart of an evaluation method of the present invention;

FIG. 2 is a diagram illustrating the definition of relevant parameters during crack propagation according to an embodiment of the present invention;

FIG. 3 is a schematic structural diagram of a gear contact fatigue life-cycle reliability evaluation apparatus according to the present invention;

FIG. 4 is a schematic diagram illustrating the residual life factor definition under two-step variable amplitude load loading in accordance with the present invention;

FIG. 5 shows comparison results of three life state equations obtained by the embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of 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 present invention, 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 derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.

It is noted that relational terms such as "first" and "second," and the like, may be 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. Also, 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 an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

The invention will be further described with reference to the accompanying drawings, but the scope of the invention is not limited to the following.

As shown in FIGS. 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: the maximum contact stress on the gear contact surface is calculated according to an empirical formula.

Calculating maximum contact stress sigma of gear based on Hertz contact theory_ZmaxThe calculation model is as follows:

the above formula (1) is a theoretical formula, where F is the applied load, k₁、k₂Is the Poisson ratio v to the gears 1, 2₁、v₂And modulus of elasticity E₁、E₂Constant of correlation, d₁、d₂Is the pitch circle radius of the gears 1, 2 and alpha is the gear pressure angle.

S102: and respectively constructing a two-dimensional static model and a two-dimensional dynamic model based on a numerical calculation theory and equivalent boundary conditions, 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 specific implementation, a two-dimensional static model and a two-dimensional dynamic model can be respectively constructed based on the Standard and the Explicit of ABAQUS in combination with equivalent boundary conditions and loads, and the maximum contact stress value and the occurrence 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 by calculation based on an 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, and determining an optimal numerical calculation model. The comparison 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 considers the influence of dynamic impact load and the like.

S104: and (3) constructing a gear contact fatigue crack initiation life evaluation model under the variable amplitude load.

In specific implementation, the method is based on a nonlinear damage function D_fConsidering the effects of maximum stress, load loading order, and surface residual stress, the nonlinear damage function under variable amplitude load can be defined as:

in the formula (2), σ_maxIs the maximum stress, σ_rsIn order to obtain the residual stress on the surface,in order to be a stress ratio,is the recycle ratio. Based on Corten-Dolan theory, the influence of maximum stress on damage is considered, and a nonlinear damage function D is obtained_fCan be expressed as:

wherein N is_{f max}Is the maximum stress sigma_maxCorresponding fatigue life. d is the sum of the stressCyclic ratio related index.

Considering the effect of the load loading sequence, the index d can be given by equation (4):

equation (3) can be converted to:

further, considering the influence of the surface residual stress, equation (5) can be expressed as:

introducing correction factorsFor nonlinear damage function D_fThe correction is carried out so that the correction is carried out,the values can be fitted through experimental data and equation (6) can be further converted to:

the Residual Life Factor (RLF) α is defined as:

wherein N is_RFor residual life after N cycles at stress level σ, N_fThe fatigue life corresponding to the stress level σ. As shown in FIG. 4, for two-stage loading, if N is the fatigue life_f1Initial stress level σ of₁Application ofn₁The cycle being a₁Number of equivalent cycles n at stress level₁₁Then relative to alpha₁₁Expressed as:

the following relationship exists for damage and Residual Life Factor (RLF) α:

D＝1-α^F(σ,p) (10)

combining equation (9) and equation (10) yields:

wherein F₁(sigma, p) and F₂(σ, p) is σ₁And σ₂Two correlation functions of stress level. Thus, σ₂Residual life N at stress level_R12As follows:

N_R12＝α₁₂N_f2 (12)

if σ is₂Stress level application n₂One period, i.e. n₂<N_R12Then the corresponding RLF is obtained:

α₂₂＝α₁₂-n₂/N_f2 (13)

thus, for multi-level loading, α_ijThe value of (d) can be obtained by:

substituting equation (7) into equation (14) yields:

in two-stage loading, corresponding to σ₁And σ₂Equation for the order damage Point (σ)₁,n₁) And (σ)₂,n₂) Expressed as:

logσ₁＝Alogn₁+logσ_s (16)

logσ₂＝Alogn₂+logσ_s (17)

wherein sigma_sFor yield strength, the combination formula (11) is obtained by substituting α for n:

therefore, in combination with the cycle cycles previously applied, a model for predicting fatigue life under variable amplitude load can be constructed:

namely:

s105: and constructing a gear contact fatigue crack propagation life evaluation model under the variable amplitude load based on the Paris formula, the crack propagation angle, the gear material hardness and the crack tip stress intensity factor.

Based on a calculation formula of the stress intensity factor of the II type crack tip:

wherein, tau_cIs a shear stress; a is the half crack length; ζ is the crack propagation increment; tau is_eqvEquivalent shear stress. The parameters were calculated as follows:

τ_eqv＝η_HV·τ_{max_corr} (22)

δ_K＝(K_t-1)·η+1 (25)

ψ＝e^-4.3ε (26)

wherein eta_HVIs a hardness factor; tau is_{max_corr}To correct for maximum shear stress; tau is_maxIs the maximum stress in the stress region; psi is the bearing surface changes due to the influence of the holes; epsilon is the hole coefficient; k_tIs the hole shape factor; delta_KCorrecting the coefficient for the notch effect; eta is a matrix structure correction coefficient; HV (z) is hardness at depth z and core hardness HV_cSurface hardness HV_sAnd an equivalent depth z_effAnd (4) correlating.

Taking into account the crack closure effect, introducing a crack closure effect coefficient U (a)

Rewrite equation (21) to:

based on the Paris formula, considering the influence of gear hardness, the gear contact fatigue crack propagation life evaluation model can be expressed as:

wherein a is₀Is the initial crack length; h_bThe overall hardness of the gear is set; h_LThe local hardness of the gear is obtained; c is the coefficient of crack propagation rate; m is an index of crack propagation rate.

And (3) integrating the formula (29) to obtain a gear contact fatigue crack propagation life evaluation model under the variable amplitude load:

s106: and constructing a gear contact fatigue full-life evaluation model according to the gear germination and expansion failure mode under the variable amplitude load.

In an embodiment, during evaluation, the gear contact fatigue crack initiation 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):

based on the gear contact fatigue full-life evaluation model, gear contact fatigue full-life evaluation under variable amplitude load can be carried out.

S107: and establishing a gear life state equation under the variable amplitude load based on the strength and load combined with the gear failure criterion.

Based on the load and strength, the failure state of a component can be expressed as:

R(t)-S(t)≤0 (32)

introducing M such that:

M＝R-S (33)

when M is greater than 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 is equal to 0, the strength is equal to the load, the component is in the limit of meeting the safety state, and the strength and the load have the tendency of changing along with time, so that the strength is smaller than the load at the next moment, and the component enters a failure state. Therefore, the extreme state equation is called as M-0.

S108: and establishing a minimization problem equation based on the failure criterion and establishing a reliability index solving method of a multivariable nonlinear state equation by a first-order second-order moment method.

And in addition, a reliability index beta is introduced, which means the maximum point of the failure probability of the gear in a y space formed by a plurality of influence factors on the service life of the gear. The problem of finding the reliability index when the probability of failure is the maximum can be equivalent to finding the problem of the minimum distance from the origin to M ═ 0 in the y space.

The minimization problem constraint condition M of the equation (19) is 0, a lagrange multiplier λ is introduced, and a minimization equation of the extreme state equation is obtained:

the first-order second-order moment method is used for solving the function by performing first-order Taylor expansion on the function and neglecting a slightly higher order moment. Therefore, by the method, a new mathematical model can be constructed to further solve the reliability analysis method of the component under a certain working condition under the condition that the distribution of the random variables is not clear.

The reliability index calculation formula can be obtained based on a first-order matrix formula and a second-order matrix formula:

s109: and respectively establishing an initiation-oriented gear contact fatigue life state equation, a propagation-oriented gear contact fatigue life state equation and a gear contact fatigue crack initiation and propagation life state equation by combining the failure criterion and solving the equations based on the gear contact fatigue crack initiation life evaluation model, the gear contact fatigue crack propagation life evaluation model and the gear contact fatigue full life evaluation model under the variable amplitude load.

Based on the formulas (20), (30) and (31), three gear contact fatigue life state equations are respectively established:

M_i＝N_pre-v₀·T (37)

M_pI＝N_p-v₀·T (38)

M_zI＝N-v₀·T (39)

wherein v is₀Is the gear speed.

And solving through a formula (36) to obtain the reliability index under each state equation.

S1010: and solving the reliability indexes of the three state equations based on the three state equations, and comparing the difference of the reliability indexes.

And solving the reliability indexes based on the three state equations, comparing the difference of the reliability indexes of the three life state equations with the probability trend of the contact fatigue failure of the gear, and determining that the reliability evaluation method based on the gear contact fatigue full-life model under the variable amplitude load has the highest precision.

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 structure size and the test quantity is reduced.

Based on the same inventive concept as the method for evaluating the contact fatigue crack initiation and the extended life reliability of the gear under the variable amplitude load, the application provides a device for evaluating the contact fatigue crack initiation and the extended life reliability of the gear under the variable amplitude load, as described in the following embodiments. The principle of solving the problems of the gear contact fatigue full-life reliability assessment device is similar to that of the gear contact fatigue full-life reliability assessment method, so the implementation of the gear contact fatigue full-life reliability assessment device can refer to the implementation of the gear contact fatigue full-life reliability assessment method, and repeated parts are not described again.

Fig. 3 is a schematic structural diagram of a gear contact fatigue crack initiation and extended life reliability assessment device based on a variable amplitude load in an embodiment of the present invention, and as shown in fig. 3, the gear contact fatigue full life reliability assessment device includes:

a maximum contact stress calculation unit 301, configured to calculate a maximum contact stress on the gear contact surface according to the hertzian 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 maximum contact stresses on corresponding gear contact surfaces based on the two-dimensional static model and the two-dimensional dynamic model;

an optimal numerical calculation model selecting unit 303, 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 calculated based on an empirical formula, respectively, and select an optimal numerical calculation model;

a maximum contact stress variation determining unit 304 caused by an external cause, 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 an initial environmental condition, respectively, and determine an influence of each factor on the maximum contact stresses;

the gear contact fatigue crack initiation life evaluation model establishing unit 305 is used for establishing a gear contact fatigue crack initiation life evaluation model under a variable amplitude load based on a nonlinear damage function;

the gear contact fatigue crack propagation life evaluation model construction unit 306 is used for constructing a gear contact fatigue crack propagation life evaluation model under the variable amplitude load based on a Paris formula, a crack propagation angle, gear material hardness and a crack tip stress intensity factor;

the gear contact fatigue full-life assessment model construction unit 307 is used for constructing a gear contact fatigue full-life assessment model based on the gear germination and extension failure mode under the variable amplitude load;

a life state equation I building unit 308, configured to build a gear contact fatigue life state equation I based on the gear contact fatigue crack initiation life evaluation model under the variable amplitude load;

a life state equation II building unit 309, configured to build a gear contact fatigue life state equation II based on the gear contact fatigue crack propagation life evaluation model under the variable amplitude load;

the life state equation III building unit 3010 is configured to build a gear contact fatigue initiation and life extension state equation based on the gear contact fatigue full-life evaluation model under the variable amplitude load;

a reliability index calculation unit 3011, configured to calculate a reliability index based on the three life state equations;

and the reliability difference comparison unit 3012 is configured to compare reliability indexes based on the three life state equations, compare the 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 structure size and the test quantity is reduced.

As will be appreciated by one skilled in the art, 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 flowcharts and/or block diagrams, and combinations of flows and/or blocks in the flowcharts 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 flow or flows of the flowcharts 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. Those skilled in the art can make numerous possible variations and modifications to the described embodiments, or modify equivalent embodiments, without departing from the scope of the invention. Therefore, any modification, equivalent change and modification made to the above embodiments according to the technology of the present invention are within the protection scope of the present invention, unless the content of the technical solution of the present invention is departed from.