CN110807281B - Gear PSN curve drawing method considering material inclusion and residual stress - Google Patents
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- 239000000463 material Substances 0.000 title claims abstract description 49
- 238000000034 method Methods 0.000 title claims abstract description 13
- 238000009826 distribution Methods 0.000 claims abstract description 50
- 238000005070 sampling Methods 0.000 claims abstract description 13
- 238000000342 Monte Carlo simulation Methods 0.000 claims abstract description 11
- 238000002474 experimental method Methods 0.000 claims abstract description 7
- 238000005096 rolling process Methods 0.000 claims abstract description 7
- 238000007619 statistical method Methods 0.000 claims abstract description 5
- 238000004364 calculation method Methods 0.000 claims description 9
- 238000005259 measurement Methods 0.000 claims description 4
- 238000012360 testing method Methods 0.000 abstract description 9
- 238000010586 diagram Methods 0.000 description 9
- 239000013078 crystal Substances 0.000 description 6
- 238000004458 analytical method Methods 0.000 description 4
- 238000012614 Monte-Carlo sampling Methods 0.000 description 3
- 229910000831 Steel Inorganic materials 0.000 description 3
- 238000013461 design Methods 0.000 description 3
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- 239000010959 steel Substances 0.000 description 3
- 239000000654 additive Substances 0.000 description 2
- 230000000996 additive effect Effects 0.000 description 2
- PNEYBMLMFCGWSK-UHFFFAOYSA-N aluminium oxide Inorganic materials [O-2].[O-2].[O-2].[Al+3].[Al+3] PNEYBMLMFCGWSK-UHFFFAOYSA-N 0.000 description 2
- 238000009827 uniform distribution Methods 0.000 description 2
- 238000000767 Anderson–Darling test Methods 0.000 description 1
- 244000309464 bull Species 0.000 description 1
- 238000005255 carburizing Methods 0.000 description 1
- 239000011248 coating agent Substances 0.000 description 1
- 238000000576 coating method Methods 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 239000006185 dispersion Substances 0.000 description 1
- 238000009661 fatigue test Methods 0.000 description 1
- 238000000227 grinding Methods 0.000 description 1
- 238000010791 quenching Methods 0.000 description 1
- 230000000171 quenching effect Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000005309 stochastic process Methods 0.000 description 1
- 238000010998 test method Methods 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
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Abstract
The invention discloses a gear PSN curve drawing method considering material inclusion and residual stress, which comprises the following steps: 1. establishing a two-dimensional plane strain finite element model; 2. obtaining the distribution condition of residual stress along the depth direction through experiments; sampling by a Monte Carlo method to obtain a characteristic sample containing inclusions and residual stress characteristics of the secondary surface of the gear material; 3. introducing the characteristic sample into a two-dimensional plane strain finite element model, and then calculating by using ABAQUS to obtain a model sample stress-strain field in the rolling process under the same load; 4. calculating a predicted fatigue life of the model sample; 5. and (3) repeating the step (3) and the step (4) to obtain model samples under corresponding loads by adopting at least 4 different loads, and carrying out statistical analysis on the predicted life results of the samples to obtain a PSN curve. According to the method, no test is needed, and the PSN curve of the gear material under different failure rates can be analyzed at a small cost.
Description
Technical Field
The invention belongs to a method for predicting contact fatigue life of mechanical parts, and particularly relates to a gear PSN curve drawing taking material inclusion and residual stress into consideration.
Background
The contact fatigue failure problem is an important factor limiting the performance of mechanical parts, and becomes a key problem to be solved or improved in the development of the mechanical industry. The problem of fatigue failure has been widely studied. In order to reveal fatigue failure rules, researchers perform extensive fatigue experiments, but the fatigue experiments are time-consuming and labor-consuming, and cannot obtain sufficient samples.
The SN curve is a basic fatigue performance curve of the material, and the PSN curve is an SN curve corresponding to different failure rates P plotted in consideration of dispersion of fatigue life. The SN curve or PSN curve of the part is obtained, and more, macroscopic performance states are obtained through experiments, and specific factors causing fatigue failure, such as residual stress, inclusions, roughness, hardening layers and the like, are not sufficiently known.
The Chinese patent document CN 109271713A discloses a gear contact fatigue analysis method considering crystal microstructure mechanics in 2019, 1 and 25 days, comprising the following steps of 1, establishing a two-dimensional plane strain finite element model by using a ABAQUS platform through using geometric parameters of a gear pair at a node; step 2, observing grain size images of the gear material by using a microscope, and determining the sizes of the crystal microstructures at different depth positions; step 3, generating a crystal microstructure distribution diagram of crystal microstructure size distributed along a depth gradient by using MATLAB software, and adding the crystal microstructure distribution diagram into a two-dimensional plane strain finite element model; and 4, calculating fatigue damage under a certain load condition by using a Fatemi-society multiaxial fatigue criterion, obtaining a fatigue damage value at any point of a key contact area, and judging the contact fatigue failure position of the gear through the maximum fatigue damage value. This patent is able to determine the location of contact fatigue failure of gears under conditions that take into account the mechanics of the crystal microstructure, but it fails to address the problem of material inclusions and residual stresses affecting the contact fatigue life of gears.
Disclosure of Invention
Aiming at the problems existing in the prior art, the technical problem to be solved by the invention is to provide the gear PSN curve drawing method taking the inclusion and residual stress of the material into consideration, which can analyze the contact fatigue life of the gear material under the conditions of random inclusion and residual stress at a small cost without a test, and obtain the PSN curves under different failure rates.
The technical problem to be solved by the invention is realized by the technical scheme that the invention comprises the following steps:
step 1, establishing a two-dimensional plane strain finite element model by using geometric parameters of a gear pair and an ABAQUS platform;
step 2, obtaining the distribution condition of residual stress along the depth direction through experiments; sampling by a Monte Carlo method to obtain characteristic samples containing inclusions and residual stress characteristics on the secondary surface of the gear material, wherein the residual stress amplitude value in each characteristic sample normally fluctuates; the sizes and the positions of the inclusions are randomly generated on the material, and the coordinates of the sizes and the positions of the inclusions are uniformly distributed;
step 3, the characteristic sample obtained in the step 2 is imported into the two-dimensional plane strain finite element model in the step 1, and then ABAQUS calculation is used to obtain a model sample stress strain field in the rolling process under the same load;
step 4, calculating the predicted fatigue life of the model sample under the load condition in the step 3 and the minimum life depth position of the predicted fatigue life by using a Brown-Miller multiaxial fatigue criterion;
and 5, adopting at least 4 different loads, repeating the step 3 and the step 4 to obtain model samples under the corresponding loads, carrying out statistical analysis on the predicted life results of all the model samples, and analyzing the distribution rule of the predicted fatigue life to obtain SN curves of the gears under different failure rates, thus obtaining PSN curves.
The invention has the technical effects that: the method for analyzing the contact fatigue failure of the gear material under the conditions of random inclusion and residual stress can obtain PSN curves under different failure rates, and the obtained analysis result can be applied to the contact fatigue failure resistance of gears in engineering practice.
Drawings
The drawings of the present invention are described as follows:
FIG. 1 is a simplified schematic diagram of a gear mesh contact state;
FIG. 2 is a graph showing the distribution of residual stress and fitting curve obtained by actual measurement in the example;
FIG. 3 is a graph of inclusion distribution of 4 feature samples sampled by the Monte Carlo method;
FIG. 4 is a plot of residual stress profiles for 4 feature samples sampled by the Monte Carlo method;
FIG. 5 is a drive train diagram of a 2 megawatt wind gearbox in an embodiment;
FIG. 6 is a graph of the magnitude of orthogonal shear stress for a model sample in an embodiment;
FIG. 7 is a lifetime distribution diagram of a model sample in an embodiment;
FIG. 8 is a graph showing predicted fatigue life profiles under 4 loads for the example;
FIG. 9 is a plot of goodness-of-fit test results for lifetime at a normal load of 1450N/mm for the examples;
fig. 10 is a graph of gear PSN fitted with a three-parameter weibull distribution.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
the invention comprises the following steps:
and step 1, establishing a two-dimensional plane strain finite element model by using the geometric parameters of the gear pair and using an ABAQUS platform.
The contact state of the gears at the nodes can be simplified into a two-dimensional plane strain finite element model, the simplification process is shown in fig. 1, the left side (a) is a schematic diagram of the node position contact gears, the right side (b) is a two-dimensional plane strain finite element model of two circles obtained equivalently, the two-dimensional plane strain finite element model is simply a two-dimensional circle contact model, and the radiuses of the two circles contacted in the model are respectively the radiuses of curvature of the two gears at the nodes. The calculation method of the curvature radius r comprises the following steps:
wherein r is the curvature radius of the two-dimensional plane strain finite element equivalent model, namely the involute curvature radius at the gear pitch line, and r k Is the pitch radius of the gear, r b Is the base radius.
Step 2, obtaining the distribution condition of residual stress along the depth direction through experiments; and sampling by a Monte Carlo method to obtain a characteristic sample containing inclusions and residual stress characteristics of the subsurface of the gear material.
Obtaining gears in depth direction using X-ray diffractometerThe residual stress distribution rule is fitted by a curve, wherein the residual stress can be decomposed into 3 directional components: sigma (sigma) 11 、σ 22 Sum sigma 33 . Residual stress component sigma 22 The value of (2) is small and can be regarded as 0, and in the example, the distribution of residual stress and the fitted curve obtained by actual measurement are shown in FIG. 2.
The inclusions are considered to be alumina inclusions, which are quite common nonmetallic inclusions in steel materials, typically spherical in shape, and are usually processed to be circular in a two-dimensional finite element model. And detecting the distribution condition of the inclusions in the gear material to be researched, and obtaining the density and size distribution of the inclusions. For example: density of about 30/mm 2 The number of inclusions distributed in the analyzed region of 2mm×1mm was 60. Since inclusions between 0 and 5 μm in size do not affect fatigue strength and undersize affects meshing in finite element modeling, only inclusion area sizes of 25 μm are considered here 2 ～100μm 2 Is evenly distributed between the two.
Fig. 3 is a schematic diagram of distribution of inclusions in 4 feature samples obtained by sampling the monte carlo method, wherein the size of the inclusions and the positions of the inclusions in each feature sample are randomly generated on a material, and the coordinates of the sizes of the inclusions and the positions of the inclusions are subjected to uniform distribution.
FIG. 4 shows the residual stress component σ of 4 feature samples obtained by Monte Carlo sampling 11 Along the depth profile, the residual stress amplitude in each feature sample normally fluctuates, σ 33 Similar to the above.
And step 3, importing the characteristic sample obtained in the step 2 into the two-dimensional plane strain finite element model in the step 1, and obtaining a model sample stress strain field of the rolling process under the same load by using ABAQUS calculation.
The inclusion distribution of fig. 3 and the residual stress distribution of fig. 4 are introduced into a two-dimensional plane strain finite element model, and the specific operation process is as follows: using Python script to assist modeling, and giving residual stress values in layers on the basis of an original model to introduce residual stress characteristics; the inclusion-corresponding region is given its corresponding material properties to introduce inclusion features.
The stress-strain history in the whole rolling process is calculated by ABAQUS finite element analysis software, fig. 6 is an orthogonal shear stress amplitude diagram of a model sample stress-strain field obtained by calculation, and as can be found from fig. 6: the presence of inclusions causes stress concentrations.
And 4, calculating the predicted fatigue life of the model sample under the load condition in the step 3 and the minimum life depth position of the model sample by using a Brown-Miller multiaxial fatigue criterion.
Gear contact fatigue damage was calculated according to the Brown-Miller multiaxial fatigue criteria set forth in M.W. Brown and K.Miller "A theory for fatigue failure under multiaxial stress-strain conditions," Proceedings of the Institution of Mechanical engineers, vol.187, pp.745-755,1973. ("fatigue failure theory under multiaxial stress-strain conditions", conference of mechanical engineers, volume 187, 1973, pages 745-755) and J.Morrow in "Fatigue design handbook," Advances in engineering, vol.4, pp.21-29,1968. ("fatigue design handbook", engineering front, volume 4, 1968, pages 745-755), the Brown-Miller multiaxial fatigue criteria being:
Δγ in formula (2) max Is the maximum shear strain amplitude, delta epsilon n Sigma, the average strain amplitude at the critical plane f ' is the fatigue strength coefficient of the material, ε f ' is the fatigue ductility coefficient of the material, sigma m Is the average stress, N f For the number of stress cycles, b is the material fatigue strength index and c is the material ductility index.
The Brown-Miller criterion is a strain-based multiaxial fatigue criterion, with a maximum shear strain amplitude Δγ for each material point max The plane in which each material point is located is considered as a critical plane on which the failure is first considered. According to the stress-strain value at any point in the stress-strain field of the model sample calculated in the step 3, each material can be found through calculation of the stress-strain dataPoint maximum shear strain amplitude Δγ max A critical plane is located, and delta gamma on the critical plane is finally obtained max 、Δε n 、σ m . It was imported into equation (2) using MATLAB or Fe-Safe software due to σ f ’、ε f ' b, c are known material parameters, then for each material point of the stress strain field, the equation has only one unknown N f The predicted fatigue life N of all material points can be obtained f 。
And 5, adopting at least 4 different loads, repeating the step 3 and the step 4 to obtain model samples under the corresponding loads, carrying out statistical analysis on the predicted life results of all the model samples, and analyzing the distribution rule of the predicted fatigue life to obtain SN curves of the gears under different failure rates, thus obtaining PSN curves.
The novel small sample method described in the literature "P-S-N curve test scheme design and verification [ D ]", cui Jintao, university of northeast, 2011: and (5) counting by using the predicted life results under more than 4 different loads to obtain the P-S-N curves under different failure rates.
Examples
The gear is selected as the gear of the gear box of the 2 megawatt wind driven generator serving as shown in fig. 5. The gear is a pinion gear of a gear pair of a middle stage, the probability of fatigue failure of the gear pair is obviously larger than that of other gears, and the right side of fig. 5 is the condition when the gear pair is in fatigue failure. The gear material is 18CrNiMo7-6 steel, and is subjected to carburizing, quenching and grinding treatment.
The material parameters of the material are as follows:
the main parameters of the gear pair are as follows:
step 1, according to the formula (1) and main parameters of the gear pair, the two-dimensional circular contact model can be obtainedThe radius of curvature of (2) is: pinion r 1 =50mm, bull gear r 2 =250.3 mm, and a two-dimensional circular contact model was established according to the radius of curvature.
And 2, obtaining residual stress distribution of the gear along the depth direction by using an X-ray diffractometer, wherein the result is shown in the following table:
residual stress component sigma 11 Sum sigma 33 The result of the polynomial fit with depth x is:
σ 11 (x)＝-9.319x 3 +78.73x 2 -162.7x-124.5
σ 33 (x)＝-20.36x 3 +132.6x 2 -232.5x-35.05
residual stress component sigma 22 The value of (2) is small and can be regarded as 0. Sigma (sigma) 11 Sum sigma 33 After fitting with the curves, see the two curves shown in fig. 2.
The inclusions considered are alumina inclusions, which are very common nonmetallic inclusions in steel materials, typically spherical in shape and generally processed to be round in a two-dimensional finite element model, according to the studies in the paper "Micromechanical study of the effect of inclusions on fatigue failure in a roller bearing," International Journal of Structural Integrity, vol.6, pp.124-141,2015 ("micromechanics study of the effect of inclusions on rolling bearing fatigue failure", journal of international structural integrity, volume 6, 2015, pages 124-141 "), et cetera. And detecting the distribution condition of the inclusions in the gear material to obtain the density and size distribution of the inclusions. Density of about 30/mm 2 The number of inclusions distributed in the analyzed region of 2mm×1mm was 60. The inclusion size is between 0 and 10 μm, while considering that the inclusion of a minute size does not affect fatigue strength and that the undersize affects mesh division in finite element modeling, the inclusion area size is considered to be 25 μm here 2 ～100μm 2 Is evenly distributed between the two. FIG. 3 is a schematic view ofAnd (3) a schematic diagram of 4 inclusion characteristic samples obtained by Monte Carlo sampling, wherein the inclusion size and the position of each characteristic sample are randomly generated on the material, and the inclusion size and the inclusion position coordinates follow uniform distribution.
FIG. 4 shows the residual stress component σ of 4 residual stress feature samples obtained by Monte Carlo sampling 11 Along the depth profile, the residual stress amplitude in each feature sample normally fluctuates, σ 33 Conditions and sigma of (2) 11 Similarly.
In generating the curve of fig. 4, the residual stress curve of fig. 2 is scaled by a normal distribution based on the curve of fig. 2 to obtain 4 samples of fig. 4.
The 4 fitted curves in fig. 4 are 4 curves obtained by sampling in normal distribution by the monte carlo method. The monte carlo method is a probabilistic sampling method. The probability sampling is performed by the Monte Carlo method (the probability of residual stress is normal distribution, and the probability of inclusion is random distribution). Obtaining a scaling ratio according to the probability of normal distribution of residual stress in each sampling, and multiplying the scaling ratio by the residual stress curve obtained by measurement to obtain a residual stress curve of the sample; each inclusion sampling may result in a set of random inclusion location coordinates and size distribution.
And 3, importing the material characteristics obtained in the step 2 into the two-dimensional plane strain finite element model in the step 1, and calculating to obtain a model sample stress strain field in the rolling process under the same load by using ABAQUS finite element analysis software.
At least 20 characteristic samples under the same load form a group of model samples, each group of model samples has the same number of the characteristic samples, the orthogonal shear stress amplitude distribution in the stress-strain field of one model sample is calculated and obtained as shown in figure 6, wherein F n For normal load, P H Is the corresponding hertz contact pressure.
And 4, calculating the predicted contact fatigue life of the gear under the condition of considering the random characteristics of the materials according to the calculation result of the finite element model obtained in the step 3 and the formula (2).
In step 3, the stress strain value at any point in the stress-strain field of the model sample is obtained through finite element calculation, and the equation (2) is introduced, so that for each material point in the stress-strain field, the equation has only one unknown quantity N f The predicted fatigue life N of all material points can be obtained f The predicted fatigue life calculation results for the model sample of fig. 6 are shown in fig. 7.
In FIG. 6, there are tens of thousands of nodes, i.e., material points, each of which can obtain N f Corresponding to the life cloud in FIG. 7, each node corresponds to a life N f When the life cloud chart in fig. 7 is counted to obtain the life distribution chart in fig. 8, the life and the depth of the point with the minimum life in each model sample are taken, and the minimum life depth position of the model sample is determined.
As can be seen from fig. 7: the fatigue life is predicted to have dispersibility due to the presence of inclusions, and a low life region exists in the surrounding area of the inclusions. The predicted fatigue life of the model sample was 10 8.567 The minimum lifetime is located between two inclusions at a depth of 0.452mm.
Step 5, repeating step 3 and step 4 when the normal load is 1050N/mm, 1450N/mm, 1750N/mm, 2050N/mm respectively, to obtain 4 groups of model samples (each sample is similar to a fatigue test), wherein the number of each group of model samples is about 30, and the life distribution of all model samples is shown in FIG. 8.
In fig. 8, the ordinate is the predicted fatigue life, and the abscissa is the depth of the minimum fatigue life from the surface. As can be seen from fig. 8: the life distribution shows dispersibility due to the introduction of the characteristics of inclusion, residual stress and the like of the material. As the load increases, the predicted fatigue life decreases and the depth at which the minimum fatigue life is significantly increased, i.e., under large loads, fatigue cracks are more prone to initiate at deeper locations.
Statistical analysis of the life distribution law, data were entered into Minitab software, which was tested for goodness of fit using the Anderson-Darling test (i.e., AD test) as proposed in t.w. Anderson and d.a. Darling at "Asymptotic theory of certain" goodness of fit "criteria based on stochastic processes," The annals of mathematical statistics, vol.23, pp.193-212,1952 ("asymptotic theory based on some 'goodness of fit' criteria for random processes"), statistical annual-differentiation, volume 23, 1952, pages 193-212. The AD test is a commonly used goodness-of-fit test method that can be used to evaluate whether the data is subject to a known distribution, and the test results in a P value that is greater, indicating that the data is more likely to be subject to the selected distribution. FIG. 9 shows the test results at a normal load of 1450N/mm, wherein 4 of the graphs correspond to the test results of the normal distribution, the lognormal distribution, the two-parameter Weibull distribution, and the three-parameter Weibull distribution, respectively.
The P values for the corresponding 4 common distributions at 4 loads are as follows:
from the table, the lifetime distribution most accords with the three-parameter weibull distribution, and then the two-parameter weibull distribution, the normal distribution and the lognormal distribution are sequentially carried out.
The results of the fitting with the three-parameter weibull distribution at 4 loads are shown in fig. 10, fig. 10 being a plot of the PSN fitted at 4 loads, where N α For a stress-life curve with failure rate of α%, the black triangles are the predicted fatigue life results for the corresponding model samples at 1050N/mm, 1450N/mm, 1750N/mm, 2050N/mm 4 loads.
Lotsberg and G.Sigurdsson in 2006, "Hot spot stress SN curve for fatigue analysis of plated structures," Journal of Offshore Mechanics and Arctic Engineering, vol.128, pp.330-336,2006 "(" Hot Point stress SN Curve for fatigue analysis of coating Structure ", programming of marine mechanics and North engineering, vol.128, 2006, pages 330-336) and A.Zarganian et al in 2019," On the fatigue behavior of additive manufactured lattice structures, "Theoretical and Applied Fracture Mechanics, vol.100, pp.225-232,2019" ("fatigue behavior for additive manufactured lattice Structure", theory and applied fracture mechanics, vol.100, 2019, pages 225-232) have all used finite element simulations to obtain PSN curves similar to the present invention, indicating that the present invention is feasible.
Claims (1)
1. A gear PSN curve drawing method considering material inclusion and residual stress is characterized by comprising the following steps:
step 1, establishing a two-dimensional plane strain finite element model by using geometric parameters of a gear pair and an ABAQUS platform;
the curvature radius of the two gears at the node of the two-dimensional plane strain finite element model is as follows:
wherein r is the curvature radius of the two-dimensional plane strain finite element equivalent model, and r k Is the pitch radius of the gear, r b Is the radius of the base circle;
step 2, obtaining the distribution condition of residual stress along the depth direction through experiments; obtaining a residual stress distribution rule of the gear along the depth direction by using an X-ray diffractometer, and fitting by using a curve;
sampling by a Monte Carlo method to obtain characteristic samples containing inclusions and residual stress characteristics on the secondary surface of the gear material, wherein the residual stress amplitude value in each characteristic sample normally fluctuates; the sizes and the positions of the inclusions are randomly generated on the material, and the coordinates of the sizes and the positions of the inclusions are uniformly distributed;
sampling residual stress and inclusions according to a Monte Carlo method, obtaining a scaling ratio according to the probability of normal distribution of the residual stress in each sampling, and multiplying the scaling ratio by the residual stress curve obtained by measurement to obtain a residual stress curve of a sample; sampling the inclusions to obtain a group of random inclusion position coordinates and size distribution each time;
step 3, the characteristic sample obtained in the step 2 is imported into the two-dimensional plane strain finite element model in the step 1, and then ABAQUS calculation is used to obtain a model sample stress strain field in the rolling process under the same load;
step 4, calculating the predicted fatigue life of the model sample under the load condition in the step 3 and the minimum life depth position of the predicted fatigue life by using a Brown-Miller multiaxial fatigue criterion;
the predicted fatigue life is:
substituting the stress-strain value in the stress-strain field obtained by calculating the model sample into a formula:
in Deltagamma max Is the maximum shear strain amplitude, delta epsilon n Sigma, the average strain amplitude at the critical plane f Is the fatigue strength coefficient epsilon of the material f Is the fatigue ductility coefficient sigma of the material m Is the average stress, N f To predict fatigue life, b is the material fatigue strength index, c is the material ductility index;
obtaining predicted fatigue life N of material point f ；
And 5, adopting at least 4 different loads, repeating the step 3 and the step 4 to obtain model samples under the corresponding loads, carrying out statistical analysis on the predicted life results of all the model samples, and analyzing the distribution rule of the predicted fatigue life to obtain SN curves of the gears under different failure rates, thus obtaining PSN curves.
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| 7075-T651铝合金薄壁管件多轴低周疲劳行为及寿命预测;陈亚军;刘辰辰;褚玉龙;宋肖肖;;材料工程(第10期);第60-69页 * |
| Q890D高强钢中厚板焊接接头残余应力的有限元模拟;房元斌;张贵芝;张立平;孔祥意;占小红;;机械工程材料(第09期);第73-76页 * |
| 复合材料气瓶的多轴疲劳寿命预测研究;黄其忠;郑津洋;胡军;任明法;张靖;;玻璃钢/复合材料(第11期);第39-45页 * |
| 夹杂物尺寸与S135钻杆钢疲劳强度的相关性;刘飞;;机械工程材料(第12期);第26-29页 * |
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