CN103616179A - Transmission gear fatigue life assessment method based on defect modeling - Google Patents

Abstract

The invention discloses a transmission gear fatigue life assessment method based on defect modeling. The method includes the following steps that (1), crack occurrence rules and reasonable crack forms are analyzed, and the method for introducing cracks into a gear model is researched; (2), material fatigue characteristic parameters are obtained through test data fitting or a numerical value estimation method; (3), a stress spectrum under the condition of working situations of a gear containing the cracks is calculated by using a finite element method, and the stress spectrum is corrected according to obtaining conditions of the material fatigue characteristic parameters; (4), fatigue life under the condition of working situations of a gear containing the cracks is calculated by using the reasonable fatigue damage accumulation theory. The fatigue life assessment method based on defect modeling is provided for the transmission gear, and an effective detection basis is provided for the remanufacturing process of a gear recycled part.

Description

A kind of transmission gear estimating method for fatigue life based on defect modeling

Technical field

The present invention relates to the estimating method for fatigue life with tooth root crackle transmission gear, specifically a kind of transmission gear estimating method for fatigue life based on defect modeling.

Background technology

Transmission gear is again in manufacture process, because gear surface profile is complicated, utilize existing surperficial recovery technique, can not meet its reparation demand, therefore gear is gear to be reclaimed to part reusability evaluate in the key of reproducing, by Non-Destructive Testing, filter out the recovery part that residual life is greater than a work period, carry out again manufacturing process and process.

In practice, the Dynamic Non-Destruction Measurement of manufacturing engineering can only obtain by detection distribution situation and the geometrical characteristic parameter of defect again, can not directly estimate the residual life that gear reclaims part, current main disposal route is exactly to detecting and exist the recovery part unification of defect to scrap processing through Non-Destructive Testing, evaluation criteria is too coarse, causes a large amount of wastes.

In order addressing the above problem, by needs, to adopt estimating method for fatigue life to reclaim part to gear and carry out Fatigue Life Assessment, mainly contain at present the fracture mechanics analysis method that traditional analysis of Fatigue-life method and the crack propagation life of take are research object.But traditional analysis of Fatigue-life does not all have to carry out under defect situation in supposition, can not the impact of reasonable consideration crackle on fatigue lifetime; And the crack propagation life theory of fracturing mechanics is also in the primary stage of development, do not reach the standard of engineering practice.

Summary of the invention

Object of the present invention aims to provide a kind of transmission gear analysis of Fatigue-life method based on defect modeling, make in the situation that introducing defect, the structural change that defect is brought changes the impact of stress into, can use fatigue analysis method to carry out analysis of Fatigue-life to transmission gear, for transmission gear is manufactured the standard of scrapping that provides meticulous again.

For achieving the above object, the technical solution adopted in the present invention is as follows:

A kind of transmission gear estimating method for fatigue life based on defect modeling of the present invention, the method comprises the steps:

(1) find the dangerouse cross-section of tooth root: according to 30 ° of tangent line theories, to cross a bit on gear teeth center line, make the tangent line of root fillet, two direct lines in point of contact are dangerouse cross-section;

(2) utilize parametric description crackle geometric properties, and be incorporated into dangerouse cross-section: adopt wide, dark, long three parametric description crackle geometric properties, then at tooth root dangerouse cross-section place, carry out three-dimensional cracks Geometric Modeling;

(3) obtain Fatigue Characteristics of Materials data S-N curve, have following two kinds of modes:

(3.1) have under test figure support, by approximating method, obtain rational S-N Curve under log-log coordinate:

lgN=a+blgσ（1）

$b=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg {\mathrm{\σ}}_i\lg N_i-\frac{1}{n}\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg {\mathrm{\σ}}_i\right)\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg N_i\right)}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(\lg {\mathrm{\σ}}_i\right)}^2-\frac{1}{n}{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg {\mathrm{\σ}}_i\right)}^2}---\left(2\right)$

$a=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg N_i-\frac{b}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg {\mathrm{\σ}}_i---\left(3\right)$

In above formula, a, b are real constant; N is data point number; σ _iit is the fatigue stress of i fatigue data; N _ifor at σ _ifatigue lifetime under stress level;

(3.2) under supporting without test figure, utilize power function formula the most frequently used in S-N curve estimation:

S ^mN=C （4）

In above formula, m and C are constants, are taken the logarithm and obtained in formula (4) both sides:

lgS=A+BlgN （5）

A=lgC/m （6）

B=-1/m； （7）

The S-N curve that this evaluation method estimation obtains is only 10 ³-10 ⁶in interval, use, its method of estimation is for estimating 10 respectively ³inferior and 10 ⁶fatigue stress when inferior, the straight line that connects this point-to-point transmission is exactly the S-N curve of estimation.

(4) acquisition and the correction of crack tip stress spectrum: the stress that obtains tooth root crack tip under working condition by Finite Element Method is composed, and revises according to the stress condition of Fatigue Characteristics of Materials data acquisition:

(S _a/S _a(R=-1))+(S _m/S _u)=1 （8）

S in above formula _afor the stress amplitude under actual stress type; S _mfor the mean stress under actual stress type; S _{a (R=-1)}stress amplitude while representing stress ratio R=-1 under Fatigue Characteristics of Materials data acquisition condition; S _ufor material limits intensity; Take a work period is unit of account, and the period of work period is distributed to each stress according to actual condition, calculates practical stress spectrum.

(5), according to S-N Curve and stress spectrum, in conjunction with Theory of The Cumulative Fatigue Damage, calculate band defect gear fatigue life:

The amount of damage of each load cycle is expressed as

$D=\frac{1}{N}---\left(9\right)$

In above formula, D is an amount of damage that load cycle causes; N represents under current stress (S), total fatigue lifetime of material or parts; In variable amplitude loading situation, take a work period is unit of account, calculated population amount of damage:

$D=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{1}{N_i}---\left(10\right)$

N _ibeing illustrated in stress level is S _itime material or parts fatigue lifetime;

By calculating the amount of damage D obtaining, carry out computing reciprocal, obtain

it is exactly issue of operable work week of member, namely fatigue lifetime.

In step (2), crack opening angle adopts breadth depth ratio to express, and when from crack-tip depth distance, take crack depth as radius, and crackle is rotated, and the crack model obtaining is simulates actual crack more really.

In step (4), the crack tip maximum equivalent of obtaining is revised, to obtain and the S-N curve acquisition condition loading spectrum that matches; S-N curve is to obtain the in the situation that of stress ratio R=-1.

The present invention compared with prior art has the following advantages and effect:

(1) with material fatigue life assessment, replace structure fatigue life assessment, improve analysis of fatigue efficiency.

Actual crack is described with geometric parameter, and introduce tooth root dangerouse cross-section as structure breach, the local maximum equivalent of crack tip and the fatigue properties data S-N curve of material are matched, convert structure fatigue life assessment to material fatigue life assessment, greatly reduce the gear fatigue life complicated degree of analysis with defect, improved Fatigue Life Assessment efficiency.

(2), by crackle geometric parameter and want fatigue lifetime to be mapped, realized and manufactured again efficiently reusability judgement.

By setting a series of Crack Parameters, calculate, set up and take a work period as MIN shreshold crack evaluation criteria, when gear recovery part is carried out to Non-Destructive Testing, according to testing result contrast extreme crackle evaluation criteria, can realize and manufacture again efficiently reusability judgement.

(3) can popularized type strong

The parts of the similar transmission gear of processing in manufacturing engineering again, can introduce parameterized defect at dangerouse cross-section by similarity method, then by above-mentioned fatigue analysis method, are set up and are manufactured coherent detection standard again.

Accompanying drawing explanation

Fig. 1 is the overview flow chart that the present invention is based on the transmission gear analysis of Fatigue-life method of defect modeling.

Fig. 2 is definite schematic diagram of tooth root dangerouse cross-section.

Fig. 3 is the illustraton of model that tooth root Crack Parametersization is described.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.

As shown in Figure 1, the present invention is based on the transmission gear analysis of Fatigue-life method of defect modeling, by analyzing the geometric properties of crackle, after being represented, its parametrization is incorporated into tooth root dangerouse cross-section, the analysis of Fatigue-life method of utilization based on local stress carried out Fatigue Life Assessment, below concrete operation step:

(1) analyze the dangerouse cross-section that tooth root crackle the most easily occurs

Tooth root dangerouse cross-section of the present invention is that basis 30 ° of tangent lines are as shown in Figure 2 theoretical next definite, crosses a bit on gear teeth center line, makes the tangent line of root fillet, and two direct lines in point of contact are exactly dangerouse cross-section.

(2) crackle adopts parametric description and is incorporated into dangerouse cross-section

The course of cracks forming more complicated, and affected by working condition etc., its spread scenarios is fixing rule not also, can fine description crackle geometric properties by wide (K), dark (D), long (L) three parameters, as shown in Figure 3.The different breadth depth ratio of crackle has mainly been described crack opening angle, and aspect crack length, situation about progressively narrowing for simulating crack edge, when from crack-tip depth distance, take crack depth as radius, crackle is rotated, and the crack model obtaining can be simulated actual crack comparatively really.Its introducing method generally carries out three-dimensional cracks Geometric Modeling at tooth root dangerouse cross-section place, and asks difference operation to be incorporated into tooth root dangerouse cross-section place by boolean.

(3) estimation of Fatigue Characteristics of Materials data S-N curve, utilizes numerical estimation method estimation Fatigue Characteristics of Materials data S-N curve, can reduce the dependence to test, raises the efficiency, and reduces and consumes, and obtain manner mainly contains following two kinds:

(3.1) have under test figure support, by fitting process, obtain S-N Curve; (3.2) under supporting without test figure, numerical method is obtained S-N Curve.

(3.1) have under test figure support, by approximating method, obtain rational S-N Curve under log-log coordinate:

lgN=a+blgσ （1）

$b=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg {\mathrm{\σ}}_i\lg N_i-\frac{1}{n}\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg {\mathrm{\σ}}_i\right)\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg N_i\right)}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(\lg {\mathrm{\σ}}_i\right)}^2-\frac{1}{n}{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg {\mathrm{\σ}}_i\right)}^2}---\left(2\right)$

$a=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg N_i-\frac{b}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\lg {\mathrm{\σ}}_i---\left(3\right)$

In above formula, a, b are real constant; N is data point number; σ _iit is the fatigue stress of i fatigue data; N _ifor at σ _ifatigue lifetime under stress level.

(3.2) under supporting without test figure, utilize under log-log coordinate the mathematical relation of S-N curve:

S ^mN=C （4）

In above formula, m and C are constants, the parameter relevant with material, load mode and stress ratio specifically, and according to the difference of material, stress types and load mode, its numerical value is all different.General evaluation method is to take cycle index as 10 ³inferior and 10 ⁶inferior is unique point, utilizes experimental formula estimation:

$S_{10}^x=k{S}_u---\left(5\right)$

represent that cycle index is 10 ^xlimiting fatigue stress when inferior, S _ufor the ultimate strength of material, k is the constant coefficient under the different cycle indexes of being correlated with material, loading, and the stressed of gear tooth is mainly rotoflector type, works as N=10 ³time:

$S_{10}^3=0.9S_u---\left(6\right)$

Work as N=10 ⁶time:

$\left\{\begin{array}{cc}{S}_{10}^6=0.5S_u& S_u<1400\mathrm{MPa}\\ S_{10}^6=700\mathrm{MPa}& S_u\&GreaterEqual;1400\mathrm{MPa}\end{array}---\left(7\right)\right.$

According to cycle index, be 10 ³inferior and 10 ⁶the S obtaining when inferior and N, can calculate parameter m and C under current gear material condition.

Taken the logarithm and obtained in formula (4) both sides:

lgS=A+BlgN （8）

A=lgC/m （9）

B=-1/m； （10）

By in the numerical value substitution formula (9) of the m solving and C and formula (10), solve the numerical value of A and B, and in substitution formula (8), obtain the S-N curve under log-log coordinate, the S-N curve of this evaluation method estimation is generally only 10 ³-10 ⁶in interval, use.

(4) acquisition and the correction of crack tip stress spectrum

When gear is worked under multi-state, different load can cause different stress spectrums in cracks, generally by finite element analysis, can obtain effectively correct tooth root crack tip stress composes, according to working gear feature, can know, gear teeth root is only subject to pulling force or pressure-acting, and its minimum stress is 0, so stress ratio R=0, and S-N curve is to obtain the in the situation that of stress ratio R=-1, in order to overcome the impact of mean stress on fatigue lifetime, need to revise gear actual stress:

(S _a/S _a(R=-1))+(S _m/S _u)=1 （11）

S in above formula _afor the stress amplitude under actual stress type; S _mfor the mean stress under actual stress type; S _{a (R=-1)}stress amplitude while representing stress ratio R=-1; S _ufor material limits intensity.

Take a work period is unit of account, and the period of work period is distributed to each stress according to actual condition, calculates practical stress spectrum.

(5), according to S-N Curve and stress spectrum, in conjunction with Theory of The Cumulative Fatigue Damage, calculate band defect gear fatigue life.

Each fatigue stress can cause fatigue damage to material, when fatigue damage accumulation reaches critical value, fatigure failure just occurs, and the amount of damage of each stress stress is expressed as

$D=\frac{1}{N}---\left(12\right)$

In above formula, D is an amount of damage that load cycle causes; N represents under current stress (S), total fatigue lifetime of material or parts.

In variable amplitude loading situation, take a work period is unit of account, calculated population amount of damage:

$D=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{N_i}---\left(13\right)$

N _ibeing illustrated in stress level is S _itime material or parts fatigue lifetime.

By calculating the amount of damage D obtaining, carry out computing reciprocal, obtain

it is exactly issue of operable work week of member, namely fatigue lifetime.

Finally illustrate that a kind of transmission gear analysis of Fatigue-life method based on defect modeling of the present invention is not limited to above-described embodiment, can also make various modifications, conversion and distortion.Therefore instructions and accompanying drawing should be considered to illustrative, rather than circumscribed.Every technical scheme according to the present invention is modified, modification or equivalent variations, and does not depart from thought and the scope of technical solution of the present invention, and it all should be encompassed in the middle of claim scope of the present invention.

Claims (3)

1. the transmission gear estimating method for fatigue life based on defect modeling, is characterized in that, the method comprises the steps:

(1) find the dangerouse cross-section of tooth root: according to 30 ° of tangent line theories, to cross a bit on gear teeth center line, make the tangent line of root fillet, two direct lines in point of contact are dangerouse cross-section;

(2) utilize parametric description crackle geometric properties, and be incorporated into dangerouse cross-section: adopt wide, dark, long three parametric description crackle geometric properties, then at tooth root dangerouse cross-section place, carry out three-dimensional cracks Geometric Modeling;

(3) obtain Fatigue Characteristics of Materials data S-N curve, have following two kinds of modes:

(3.1) have under test figure support, by approximating method, obtain rational S-N Curve under log-log coordinate:

lgN=a+blgσ （1）

$b=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\lg {\mathrm{\&sigma;}}_i\lg N_i-\frac{1}{n}\left(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\lg {\mathrm{\&sigma;}}_i\right)\left(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\lg N_i\right)}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\left(\lg {\mathrm{\&sigma;}}_i\right)}^2-\frac{1}{n}{\left(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\lg {\mathrm{\&sigma;}}_i\right)}^2}---\left(2\right)$

$a=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\lg N_i-\frac{b}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\lg {\mathrm{\&sigma;}}_i---\left(3\right)$

In above formula, a, b are real constant; N is data point number; σ _iit is the fatigue stress of i fatigue data; N _ifor at σ _ifatigue lifetime under stress level;

(3.2) under supporting without test figure, utilize power function formula the most frequently used in S-N curve estimation:

S ^mN=C （4）

In above formula, m and C are constants, are taken the logarithm and obtained in formula (4) both sides:

lgS=A+BlgN （5）

A=lgC/m （6）

B=-1/m； （7）

The S-N curve that this evaluation method estimation obtains is only 10 ³-10 ⁶in interval, use, its method of estimation is for estimating 10 respectively ³inferior and 10 ⁶fatigue stress when inferior, the straight line that connects this point-to-point transmission is exactly the S-N curve of estimation.

(4) acquisition and the correction of crack tip stress spectrum: the stress that obtains tooth root crack tip under working condition by Finite Element Method is composed, and revises according to the stress condition of Fatigue Characteristics of Materials data acquisition:

(S _a/S _a(R=-1))+(S _m/S _u)=1 （8）

S in above formula _afor the stress amplitude under actual stress type; S _mfor the mean stress under actual stress type; S _{a (R=-1)}stress amplitude while representing stress ratio R=-1 under Fatigue Characteristics of Materials data acquisition condition; S _ufor material limits intensity; Take a work period is unit of account, and the period of work period is distributed to each stress according to actual condition, calculates practical stress spectrum.

(5), according to S-N Curve and stress spectrum, in conjunction with Theory of The Cumulative Fatigue Damage, calculate band defect gear fatigue life:

The amount of damage of each load cycle is expressed as

$D=\frac{1}{N}---\left(9\right)$

In above formula, D is an amount of damage that load cycle causes; N represents under current stress (S), total fatigue lifetime of material or parts; In variable amplitude loading situation, take a work period is unit of account, calculated population amount of damage:

$D=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{N_i}---\left(10\right)$

N _ibeing illustrated in stress level is S _itime material or parts fatigue lifetime;

By calculating the amount of damage D obtaining, carry out computing reciprocal, obtain it is exactly issue of operable work week of member, namely fatigue lifetime.

2. the transmission gear estimating method for fatigue life based on defect modeling according to claim 1, it is characterized in that, in step (2), crack opening angle adopts breadth depth ratio to express, when from crack-tip depth distance, take crack depth as radius, crackle is rotated, the crack model obtaining is simulates actual crack more really.

3. the transmission gear estimating method for fatigue life based on defect modeling according to claim 1, is characterized in that, in step (4), the crack tip maximum equivalent of obtaining is revised, to obtain and the S-N curve acquisition condition loading spectrum that matches; S-N curve is to obtain the in the situation that of stress ratio R=-1.

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