CN109271713B - Gear contact fatigue analysis method considering crystal microstructure mechanics - Google Patents
Gear contact fatigue analysis method considering crystal microstructure mechanics Download PDFInfo
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Abstract
The invention discloses a gear contact fatigue analysis method considering crystal microstructure mechanics, which comprises the following steps: 1. establishing a two-dimensional plane strain finite element model by using ABAQUS platform through using the geometric parameters of the gear pair at the node; 2. observing grain size images of different depth positions of the gear material by using a microscope; 3. using MATLAB software to generate a crystal microstructure distribution diagram of the crystal microstructure size along the depth gradient distribution, and simultaneously adding the crystal microstructure distribution into the two-dimensional plane strain finite element model in the step 1; 4. and calculating the fatigue damage under a certain load condition by using a Fatemi-Socie multiaxial fatigue criterion to obtain the fatigue damage value of any point of the key contact area. The invention has the technical effects that: the problem of contact fatigue failure of the gear under the condition of considering the mechanics of the crystal microstructure can be solved, and the loss of production benefits caused by the contact fatigue failure of the gear is reduced.
Description
Technical Field
The invention belongs to an analysis method of contact fatigue failure of mechanical parts, and particularly relates to a gear pair contact fatigue analysis method considering crystal microstructure mechanics.
Background
Contact fatigue failure is a typical failure mode of mechanical parts, and the problem of contact fatigue failure has been a major factor limiting the equipment reliability, ergonomic safety, and economic efficiency of gear drive machines. The contact fatigue problem of gears has been widely studied in many aspects, such as condition factors and material factors. However, the existing research still remains on a macroscopic level, and the microstructure of the micro crystal which is generally regarded as important is less understood, so that the analysis of the contact fatigue of the gear in the engineering practice still has great difficulty.
Disclosure of Invention
The invention aims to solve the technical problem of providing a gear contact fatigue analysis method considering crystal microstructure mechanics, which can analyze the problem of contact fatigue failure of a gear under the condition of considering the crystal microstructure mechanics, is beneficial to establishing the relation between the micro crystal microstructure and the gear contact fatigue failure, and the obtained analysis result has a guiding function on the contact fatigue failure resistance design of the gear in the engineering practice, thereby reducing accidents and economic losses caused by the gear contact fatigue failure.
The technical problem to be solved by the invention is realized by the technical scheme, which comprises the following steps:
step 1, establishing a two-dimensional plane strain finite element model by using ABAQUS platform through using the geometric parameters of a gear pair at a node;
step 2, observing a grain size image of the gear material by using a microscope, and determining the sizes of the crystal microstructures at different depth positions;
step 3, using MATLAB software to generate a crystal microstructure distribution diagram of the crystal microstructure size distributed along the depth gradient, and adding the crystal microstructure distribution into a two-dimensional plane strain finite element model;
and 4, calculating the fatigue damage under a certain load condition by using a Fatemi-Socie multi-axis fatigue criterion to obtain a fatigue damage value of any point of a key contact area, and judging the contact fatigue failure position of the gear according to the maximum fatigue damage value.
The invention has the technical effects that:
the problem of contact fatigue failure of the gear is analyzed under the condition of considering the mechanics of the crystal microstructure, theoretical support is provided for the contact fatigue resistant manufacture of the gear, and accidents and economic losses caused by the contact fatigue failure of the gear in the engineering practice are reduced.
Drawings
The drawings of the invention are illustrated as follows:
FIG. 1 is a simplified schematic illustration of a gear mesh contact condition;
FIG. 2 is a grain size image of the gear material at different depths as observed by a microscope in the example;
FIG. 3 is a distribution diagram of the crystal microstructure produced in the examples;
FIG. 4 is a two-dimensional plane strain finite element model with the addition of a crystal microstructure;
FIG. 5 is a schematic diagram of boundary conditions and loading of a two-dimensional plane strain finite element model in an embodiment;
FIG. 6 is a diagram of a transmission system of a megawatt wind-power gearbox in an embodiment;
FIG. 7 is a graph showing a distribution of contact fatigue damage values of the gear material in the example.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
the invention comprises the following steps:
step 1, the contact state of the gear at the node can be simplified into a two-dimensional plane strain finite element model, the simplified process is shown in fig. 1, the left side (a) is a schematic diagram of the node position contact gear, and the right side (b) is the two-dimensional plane strain finite element model of the rigid semicircle and the flexible plane obtained through equivalence. According to the Hertz contact theory and the actual working condition of the gear, the parameters of the two-dimensional plane strain finite element model can be calculated, and the calculation process is as follows:
r＝r 1 r 2 /(r 1 +r 2 ) (1)
in the formulae (1) and (2), r 1 ，r 2 Is the curvature radius of the contact position of two gears, r is the comprehensive curvature radius of the two-dimensional plane strain finite element model, E 1 ，E 2 Is the elastic modulus of two gears, E is the equivalent elastic modulus of a two-dimensional plane strain finite element model, upsilon 1 ，υ 2 Is the poisson ratio of two gears. "AGMA information sheet 908-B89,1989," geometrical factors for determining the pitting resistance and bending strength of spur, helical, herringbone gear teeth "(U.S. Gear Standard," geometric factors for determining pitting resistance and bending strength of spur, helical, herringbone gear teeth "in 1989) is described on pages 5-7 1 ，r 2 The method of (1).
And 2, observing a grain size image of the gear material by using a microscope, and determining the sizes of the crystal microstructures at different depth positions. The grain size images observed by the microscope at different depth positions are shown in fig. 2, and six depth positions are respectively selected for observation.
And 3, generating a crystal microstructure distribution diagram of the crystal microstructure size along the depth gradient by using a MATLAB software Multi Parametric Toolbox (MPT). In the step, firstly, the coordinates of the central point of the crystal microstructure are determined according to the average diameters of the crystal microstructures at different depth positions obtained in the step 2, and the coordinates are input into MATLAB software; secondly, inputting the boundary of the rectangular crystal microstructure in MATLAB software, wherein the size of the boundary is determined according to research needs; and finally, automatically calculating by a multi-parameter tool box to obtain a crystal microstructure distribution diagram. The distribution of the generated crystal microstructure is shown in fig. 3, and the vertical direction of fig. 3 represents the depth direction. Adding the crystal microstructure distribution to the two-dimensional plane strain finite element model in step 1, wherein the added two-dimensional plane strain finite element model is shown in fig. 4, wherein the coordinate system is set as x representing the rolling direction, and y represents the direction opposite to the depth direction.
FIG. 5 shows the loading pattern and boundary conditions of a two-dimensional plane strain finite element model with a fixed bottom edge. A2 mm x 3mm rectangle was selected in the model as the key material region, and the crystal microstructure was added. The rigid half circle was moved in the calculation from x = -4mm to x =4mm, whereby the rolling contact of the gear was simulated.
Step 4, calculating gear contact Fatigue damage according to a Fatemi-scie multiaxial Fatigue criterion proposed in the article "a critical plane to multi-axial Fatigue large including out-of-phase loading", fatigue & Fracture & structural, 11 (1988) 149-165 "(" a critical plane method for studying multiaxial Fatigue damage including non-proportional load state ", fatigue and Fracture of Engineering Materials and Structures, volume 11, 1988, pages 149-165), by a.
D FS,max ＝max(D FS,i ) (4)
In the formula D FS,i Represents the fatigue damage value of the i-th slip plane, D FS,max The fatigue damage value representing the crystal microstructure is the maximum value of the fatigue damage values of all slip planes of the crystal microstructure,
is the plastic shear strain amplitude on the slip plane, i represents the ith slip plane. The gear steel is a typical BCC structure, each crystal microstructure comprises 6 {110} slip planes, each slip plane has two slip directions, k' represents a material constant, sigma y Represents the yield strength, σ n The normal stress of the slip surface is represented, and the normal stress is calculated by the following method:
in the formula sigma p (t) represents the stress state at any point on the slip plane, σ xx Is positive stress in the x direction, σ yy Positive stress in the y direction, σ zz Is positive stress in the z direction, τ xy Is the x-y plane shear stress, tau xz Is the shear stress in the x-z plane, τ yz Is the y-z plane shear stress, n x ,n y ,n z Is the cosine of the direction of the plane of the slip plane.
Examples
Fig. 6 is a schematic diagram of a transmission system of a megawatt wind turbine gearbox served by the gear sample, the sample is from an intermediate gear pair, and when the gear sample is actually applied in engineering, the probability of failure of the transmission stage of the gear sample is obviously higher than that of other gears.
The main parameters of the gear pair are as follows:
step 1, according to the formulas (1) to (2), the formula r 1 ＝49mm，r 2 (ii) determining the comprehensive radius of curvature of the two-dimensional contact model as r =40.91mm by E =248mm 1,2 ＝2.10×10 11 Pa is the equivalent modulus of elasticity E =1.15 × 10 11 Pa. Based on the above parameters, a two-dimensional plane strain finite element model as illustrated in fig. 1 (b) was established. In this example, the dimensions of the compliant plane of the two-dimensional plane strain finite element model are defined as 20mm x 10mm, and the model is constructed as shown in FIG. 5.
And 2, observing a grain size image of the gear material by using a microscope, and determining the sizes of the crystal microstructures at different depth positions. The sample gear is made of 18CrNiMo7-6 steel and is subjected to carburizing, quenching and grinding treatment. The grain size images observed by the microscope at different depth positions are shown in fig. 2. And respectively selecting six depth positions for observation, wherein the six observation positions are respectively a surface area, a position with the depth of 0.4mm, a position with the depth of 0.8mm, a position with the depth of 1.2mm, a position with the depth of 1.6mm and a position with the depth of 2.0 mm. As can be seen, the diameter of the crystal microstructure at the surface is about 15um on average, and the diameter of the crystal microstructure at the depth of 2.0mm is about 55um on average.
And 3, generating a crystal microstructure distribution diagram of the crystal microstructure size distributed along the depth gradient by using MATLAB software, wherein the average diameter of the crystal microstructure is determined according to the observation value in the step 2, so that the generated crystal microstructure model is close to the real condition, and the generated crystal microstructure distribution diagram is shown in FIG. 3. Adding the distribution of the crystal microstructure into the two-dimensional plane strain finite element model in the step 1, wherein the added two-dimensional plane strain finite element model is shown in fig. 4.
And 4, calculating the contact fatigue damage of the gear in the mechanical state considering the crystal microstructure according to the calculation result of the two-dimensional plane strain finite element model in the step 3 and the formula (3) -formula (6). The calculation results are shown in fig. 7, and it can be seen that, in the mechanical state of the crystal microstructure, the damage of the gear material below the surface has dispersibility, and the maximum damage value is 3.6 × 10 -3 The maximum lesion site occurs at a depth of about 1 mm.
The damage of the crystal microstructure under the Contact surface observed by the experiment in the documents "n.k.arakere, n.branch, g.levensque, v.svendsen, and n.h.forster," Rolling Contact Fatigue Life and spread performance Characteristics of AISI M50, "2014." (n.k.arakere, n.branch, g.levensque, v.svendsen, and n.h.forster, "Rolling Contact Fatigue Life and flaking Characteristics of AISI M50," 2014) is consistent with the result distribution trend of the present invention, thereby verifying the reliability of the present invention.
Claims (2)
1. The gear contact fatigue analysis method considering the crystal microstructure mechanics is characterized by comprising the following steps of:
step 1, establishing a two-dimensional plane strain finite element model by using ABAQUS platform through using the geometric parameters of a gear pair at a node;
step 2, observing a grain size image of the gear material by using a microscope, and determining the sizes of the crystal microstructures at different depth positions;
step 3, using MATLAB software to generate a crystal microstructure distribution diagram of the crystal microstructure size distributed along the depth gradient, and adding the crystal microstructure distribution into a two-dimensional plane strain finite element model;
step 4, calculating fatigue damage under a certain load condition by using a Fatemi-Socie multiaxial fatigue criterion to obtain a fatigue damage value of any point of a key contact area, and judging a contact fatigue failure position of the gear according to the maximum fatigue damage value;
the Fatemi-Socie multiaxial fatigue criterion is as follows:
D FS,max ＝max(D FS,i )
in the formula D FS,i Represents the fatigue damage value of the i-th slip plane, D FS,max The fatigue damage value representing the crystal microstructure is the maximum value of the fatigue damage values of all slip planes of the crystal microstructure,
is the plastic shear strain amplitude on the slip plane, i represents the ith slip plane; the gear steel is a typical BCC structure, each crystal microstructure comprises 6 {110} slip planes, each slip plane has two slip directions, k' represents a material constant, sigma y Represents the yield strength, σ n The normal stress of the slip surface is represented, and the normal stress is calculated by the following method:
in the formula sigma p (t) represents the stress state at any point on the slip plane, σ xx Is positive stress in the x direction, σ yy Positive stress in the y direction, σ zz Is positive stress in the z direction, τ xy Is the x-y plane shear stress, tau xz Is the shear stress in the x-z plane, τ yz Is the y-z plane shear stress, n x ,n y ,n z Is the cosine of the direction of the plane of the slip plane, σ n Indicating the normal stress of the slip plane.
2. The method for analyzing the contact fatigue of the gear considering the mechanics of the crystal microstructure according to claim 1, wherein in the step 1, the method for calculating the parameters of the two-dimensional plane strain finite element model comprises the following steps:
r＝r 1 r 2 /(r 1 +r 2 )
in the formula, r 1 ，r 2 Is the curvature radius of the contact position of two gears, r is the comprehensive curvature radius of the two-dimensional plane strain finite element model, E 1 ，E 2 Is the elastic modulus of two gears, E is the equivalent elastic modulus of a two-dimensional plane strain finite element model, upsilon 1 ，υ 2 Is the poisson ratio of two gears.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101576608A (en) * | 2008-05-05 | 2009-11-11 | 通用汽车环球科技运作公司 | Methods and systems to predict fatigue life in aluminum castings |
| JP2011108032A (en) * | 2009-11-18 | 2011-06-02 | Ihi Corp | Device and method for evaluating fatigue strength of polycrystalline metallic material |
| WO2013040315A1 (en) * | 2011-09-16 | 2013-03-21 | Sentient Corporation | Method and system for predicting surface contact fatigue life |
| CN106096073A (en) * | 2016-05-23 | 2016-11-09 | 北京航空航天大学 | A kind of metal fatigue crackle life-cycle predictor method analyzing model based on the non-probability interval of damage mechanics |
| CN106501105A (en) * | 2016-12-31 | 2017-03-15 | 北京工业大学 | A kind of consideration micro structure is mingled with the determination method with the friction stir welding fatigue weakness zone of crystal orientation |
-
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- 2018-09-25 CN CN201811118963.6A patent/CN109271713B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101576608A (en) * | 2008-05-05 | 2009-11-11 | 通用汽车环球科技运作公司 | Methods and systems to predict fatigue life in aluminum castings |
| JP2011108032A (en) * | 2009-11-18 | 2011-06-02 | Ihi Corp | Device and method for evaluating fatigue strength of polycrystalline metallic material |
| WO2013040315A1 (en) * | 2011-09-16 | 2013-03-21 | Sentient Corporation | Method and system for predicting surface contact fatigue life |
| CN106096073A (en) * | 2016-05-23 | 2016-11-09 | 北京航空航天大学 | A kind of metal fatigue crackle life-cycle predictor method analyzing model based on the non-probability interval of damage mechanics |
| CN106501105A (en) * | 2016-12-31 | 2017-03-15 | 北京工业大学 | A kind of consideration micro structure is mingled with the determination method with the friction stir welding fatigue weakness zone of crystal orientation |
Non-Patent Citations (7)
| Title |
|---|
| A critical plane approach to multiaxial fatigue damage including out‐of‐phase loading;Ali Fatemi;《Fatigue & Fracture of Engineering Materials & Structures》;19881231;第11卷;149-165 * |
| A fracture mechanics model of gear flanks fatigue;Glodez, S;《JOURNAL OF MECHANICAL ENGINEERING》;19970630;第43卷(第5-6期);203-218 * |
| Failure analysis of a petrochemical plant reducing gear;Griza, Sandro;《ENGINEERING FAILURE ANALYSIS》;20130430;第29卷;56-61 * |
| Microstructure-sensitive modeling of rolling contact fatigue;Erick S.Alley;《International Journal of Fatigue》;20100531;第32卷(第5期);841-850 * |
| 基于Voronoi有限元方法的滚动轴承疲劳寿命分析;张晶;《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》;20180115(第01期);C029-102 * |
| 机车牵引齿轮接触应力及疲劳失效微观分析;邵建敏;《现代制造工程》;20120731(第07期);36-39 * |
| 计算微观接触力学基本单元解的解析研究与应用;牛飞飞;《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》;20170315(第03期);C029-167 * |
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