CN110738000B - Method for determining high cycle fatigue life of bolt hole in complex stress state - Google Patents
Method for determining high cycle fatigue life of bolt hole in complex stress state Download PDFInfo
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Abstract
The application relates to a method for determining high cycle fatigue life of a bolt hole in a complex stress state, which comprises the following steps: acquiring the thickness of the structure and the diameter of the bolt hole, and determining an extrusion distribution coefficient according to the thickness and the diameter; establishing a finite element model of the structure, applying two different loads in the finite element model and the solid structure model of the structure to obtain the maximum stress of the bolt hole under the two loads and the nominal stress caused by the bypass load of the bolt hole, and determining a stress concentration coefficient according to the two loads and the maximum stress and the nominal stress under the corresponding loads; determining the plate width of the structure according to the extrusion stress concentration coefficient; determining stress severity coefficients according to local maximum stress under the stress load to be solved by the structure, nominal stress caused by bypass load, nail transmission load and the like; and finally obtaining the high-cycle fatigue life of the bolt hole under the complex stress state according to the stress severity coefficient.
Description
Technical Field
The application belongs to the technical field of mechanical fatigue life calculation, and particularly relates to a method for determining the high-cycle fatigue life of a bolt hole in a complex stress state.
Background
In the engineering use environment of the bolt hole subjected to shearing, a stress severity coefficient method is usually adopted to calculate the high-cycle fatigue life of the bolt hole.
As shown in fig. 1, the following is a brief explanation of the stress severity method:
FIG. 2 shows a typical connection element configuration detail, with the perforated structural sheet material being subjected to a load that is partially bypassed, referred to as bypass load P pl The other part being carried away by the fastener, referred to as the nail load P dc 。
Bypass load P pl The local maximum stress generated is σ 1 Local maximum stress σ 1 The formula is shown in formula 1, and K in formula 1 tg Theoretical stress concentration coefficient of the empty hole plate of net area, W isThe board is wide, and D is the bolt hole diameter, and t is the plate thickness:
nail load P dc Local drum stress sigma generated 2 Local maximum stress σ 2 See formula 2, K in formula 2 tb For the extrusion stress concentration coefficient, θ is the extrusion distribution coefficient:
by a bypass load P pl Load P transferred by nail dc Local maximum stress sigma generated max ＝σ 1 +σ 2 ，σ max The formula (2) is shown in formula 3, and the formula 3
Nominal stress due to bypass load:
nominal stress
Coefficient of severity of stress
α is the pore surface coefficient and β is the pore fill coefficient. According to formula 1 and formula 2, the specific calculation formula of the stress severity factor SSF is shown in formula 4:
the existing method calculates or checks the table by formula through determining the plate width W and the bolt hole diameter DTo obtain K in equation 1 tg 、K tb Determining theta, alpha and beta according to the types of different bolt holes by looking up a table, and then determining P through finite element analysis pl 、P dc Finally, the stress severity factor SSF is determined, and then the service life of the material is determined according to the load spectrum of the material by referring to the S-N curve. However, for complex multi-pin connection structures, it is often difficult to determine the board width W, and therefore K relative to the board width W cannot be determined tg 、K tb And P is often determined in finite element calculation of nail hole dense structure pl It is also very difficult.
Disclosure of Invention
The purpose of the present application is to provide a method for determining the high cycle fatigue life of a bolt hole under a complex stress state, so as to solve or alleviate at least one problem in the background art.
The technical scheme of the application is as follows: a method of determining high cycle fatigue life of a bolt hole under a complex stress condition, the method comprising:
acquiring the thickness of the structure and the diameter of the bolt hole, and determining an extrusion distribution coefficient according to the thickness and the diameter;
establishing a finite element model of the structure, applying two different loads in the finite element model and the solid structure model of the structure to obtain the maximum stress of the bolt hole under the two loads and the nominal stress caused by the bypass load of the bolt hole, and determining the theoretical stress concentration coefficient and the extrusion stress concentration coefficient of the empty hole plate with the net area according to the two loads and the maximum stress and the nominal stress under the corresponding loads;
determining the plate width of the structure according to the extrusion stress concentration coefficient;
determining a stress severity coefficient according to the plate width and thickness, the local maximum stress under the stress load to be solved by the structure, the nominal stress caused by the bypass load, the nail transmission load, the hole surface coefficient and the hole filling coefficient;
and finally obtaining the high-cycle fatigue life of the bolt hole under a complex stress state according to the stress severity coefficient.
In one embodiment of the method of the present application, the determining of the extrusion distribution coefficient based on the thickness and the diameter is obtained by the following formula:
when the bolt is stressed in the form of single shear,
θ＝1.0085+0.6536η+0.3653η 2 -0.0119η 3 -0.0068η 4 ；
when the bolt is stressed in the form of double shear,
θ＝1.0015+0.1573η+0.0360η 2 -0.0025η 3 ；
in the formula, θ is the extrusion distribution coefficient, and η is the ratio of the thickness t to the diameter D.
In one embodiment of the method of the present application, the two different loads applied in the finite element model and the solid structure model of the structure are linearly uncorrelated.
In one embodiment of the method of the present application, the theoretical stress concentration coefficient and the compressive stress concentration coefficient of the empty hole plate of the net area are determined according to the maximum stress and the nominal stress under two loads and corresponding loads, and the following relations are followed:
in the formula, K tg Theoretical stress concentration coefficient, K, of a clear area of a perforated plate tb Is the extrusion stress concentration coefficient;
σ max1 local maximum stress, P, for the first load application dc1 For nail-transfer loads induced by first-time load application, σ pl(non)1 Nominal stress due to the bypass load applied for the first load;
σ max2 local maximum stress, P, for the second load application dc2 For nail-transfer loads induced by the second load application, σ pl(non)2 Nominal stress due to the bypass load applied for the second load.
In one embodiment of the method of the present application, determining a sheet width of the structure from the compressive stress concentration factor comprises:
obtaining a curve of the extrusion stress concentration coefficient and the width-thickness ratio;
determining the plate thickness ratio according to the extrusion stress concentration coefficient and the curve;
and determining the plate width according to the plate thickness ratio.
In one embodiment of the method of the present application, the determining the stress severity coefficient is determined by the following formula:
wherein SSF is the stress severity coefficient, α is the pore surface coefficient, β is the pore fill coefficient, σ is the pore fill coefficient max Is the local maximum stress.
In an embodiment of the method, the obtaining the high cycle fatigue life of the bolt hole under the complex stress state according to the stress severity coefficient includes:
obtaining an S-N curve of the structure;
and checking an S-N curve according to the stress severity coefficient and an overload spectrum born by the structure to determine the service life of the bolt hole.
According to the method, the finite element model modeling analysis result of the structure is effectively utilized, and the existing method is improved, so that the condition that the stress concentration coefficient of the bolt hole of the structure is determined inaccurately is avoided.
According to the method, the nail-passing load can be accurately obtained, the nominal stress caused by the bypass load is directly obtained through finite element calculation, the bypass load is prevented from being determined, the condition that the bypass load is inaccurate is calculated, the problem that the structural plate width with complex stress condition cannot be determined is solved by determining the stress severity coefficient and reversely pushing the plate width, the nominal stress can be more accurately obtained, and the fatigue life of the calculated bolt hole is more accurate.
Drawings
In order to more clearly illustrate the technical solutions provided by the present application, the following briefly introduces the accompanying drawings. It is to be understood that the drawings described below are merely exemplary of some embodiments of the application.
Fig. 1 is a flow chart of a method in the prior art.
Fig. 2 is a force diagram of a typical prior art connector structure.
Fig. 3 is a flow chart of a method of the present application.
FIG. 4 shows the compressive stress concentration coefficient K of the present application tb And D/W ratio.
FIG. 5 is a schematic diagram of a bolt hole life to be determined according to an embodiment of the present application.
Fig. 6 is a schematic view of the structure of fig. 5 under load.
FIG. 7 is a diagram of the structure shown in FIG. 5 for determining K tg And K tb Schematic diagram of the loading method.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application.
The purpose of the application is to solve the problems that the plate width of the structure cannot be determined and further the stress concentration coefficient is difficult to determine in the prior art, and provide a method for determining the fatigue life of the bolt hole in a complex stress state accurately. The method of the application determines the stress concentration coefficient K first tg And K tb And then determining the plate width W to solve the stress severity factor SSF, and determining the nominal stress caused by the bypass load by the method, so that the determination of the service life of the bolt hole is more accurate.
In order to achieve the above purpose, the method for determining the high cycle fatigue life of the bolt hole under the complex stress state of the application comprises the following steps, as shown in fig. 3:
s1, firstly, obtaining the thickness t of the structure to be calculated and the diameter D of the bolt hole, and then determining the extrusion distribution coefficient theta according to the ratio of the thickness t to the diameter D of the bolt hole.
The method for determining the extrusion distribution coefficient theta in the process is different due to different stress forms of the bolt, when the stress form of the bolt is single shear, the value of the extrusion distribution coefficient theta can be determined according to a formula 5, when the stress form of the bolt is double shear, the value of the extrusion distribution coefficient theta can be determined according to a formula 6, and in the formula 5 and the formula 6, eta is t/D;
θ＝1.0085+0.6536η+0.3653η 2 -0.0119η 3 -0.0068η 4 ； (5)
θ＝1.0015+0.1573η+0.0360η 2 -0.0025η 3 ； (6)
s2, establishing a finite element model of the structure, applying two different loads at positions far away from the bolt holes in the analyzed finite element model, and applying the two different loads in the analyzed solid structure model (or the geometric structure model) respectively to obtain the maximum stress of the bolt holes under the two loads and the nominal stress caused by the bypass load of the bolt holes (the stress at the position 2D from the center of the bolt holes tends to be consistent, namely the nominal stress of the bypass load caused by the bypass load).
Wherein, the two loads applied in the process are linearly uncorrelated.
The local maximum stress sigma due to the first applied load can be obtained by two different load conditions in the above process max1 Nail-transferring load P dc1 Nominal stress sigma due to bypass load pl(non)1 And local maximum stress sigma due to the second applied load max2 Nail-transferring load P dc2 Nominal stress sigma due to bypass load pl(non)2 . There are equation 7 and equation 8 from equation 3. The theoretical stress concentration coefficient K can be obtained by combining formula 7 and formula 8 tg (equation 9) and the compressive stress concentration coefficient K tb (equation 10):
s13 finding the stress concentration coefficient K tb And the value of the plate width W can be further determined by combining the curve of the ratio of the aperture D to the plate width W or the ratio of the plate width W to the aperture D as shown in fig. 4;
s14 local maximum pressure σ under stress load to be solved by actual structure max Nominal stress sigma due to bypass load pl(non) Nail-transferring load P dc And the hole surface coefficient alpha, the hole filling coefficient beta and the plate width W and the thickness t determined in the process can be used for obtaining the stress severity coefficient SSF, namely the following formula
S15, finally, according to the determined stress severity coefficient, obtaining the high cycle fatigue life of the bolt hole according to other related steps of a nominal stress method, wherein the specific process is as follows:
firstly, acquiring an S-N curve of the structure;
and then, according to the stress severity coefficient and an overload spectrum born by the structure, checking an S-N curve to determine the service life of the bolt hole.
In order to make the content of the present application easier to understand, the present application will be further explained in a specific case.
Fig. 5 shows a structural diagram of the bolt hole life to be determined, which comprises an upper wall plate 1, a beam 2, a lower wall plate 3, a force bearing member 4, a typical bolt 5 and a bolt hole 6 required for determining the fatigue life. The beam 2 is bent, the load is transferred to another bearing component through the section bar, the service life of a bolt hole on the lower edge strip of the beam 2 needs to be determined, and the dispersion coefficient is 4.
First, as can be seen from an analysis, the beam bends, the lower edge strips are pulled when the beam bends, and the bolts transmit a smaller part of the load to the other load-bearing member because the lower edge strips are deformed in tension. The load on the lower wall plate 3 is gradually transferred to the lower edge strip of the beam and the profile by means of the bolts.
S1, the thickness and the bolt hole diameter can be measured by measuring the structure, and in this example, the bolt hole diameter D is 8mm, the thickness t is 8mm, and θ is 1.19 according to equation 6.
S2, according to the stress analysis, the stress near the bolt hole caused by the bending of the beam is the nominal stress caused by the bypass load, so two groups of different loads for bending the beam are loaded, as shown in figures 6 and 7, in the embodiment, two groups of loads for bending the beam are applied, and the sigma is respectively obtained maxl ＝41.6MPa，P dcl ＝23.53N，σ pl(non)1 ＝21.0MPa，σ max2 ＝61.6MPa，P dc2 ＝87.2N，σ pl(non)2 ＝30.5MPa。
K can be obtained from the equations 9 and 10 tg ＝1.96，K tb ＝1.195。
S3, when D/W is 0.164 and the sheet width W is 48.8mm, as shown in fig. 3.
S4, applying the real load condition to be calculated to obtain sigma max ＝81.6MPa，P dc ＝397.2N，σ pl(non) 39.5 MPa; the table look-up determines α to 1.0 and β to 0.9, and the equation 11 determines the stress severity factor SSF to l.94.
S5, according to the stress severity coefficients SSF and sigma non And the overload spectrum born by the structure, checking an S-N curve, obtaining that the service life of the bolt hole is 39122 times, and dividing by the dispersion coefficient 4 to obtain that the service life of the bolt hole is 9780.5 times.
The method is improved on the conventional high cycle fatigue life calculation method, is simple and convenient to operate, and enables the calculation result to be more accurate.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (4)
1. A method for determining the high-cycle fatigue life of a bolt hole in a complex stress state is characterized by comprising the following steps:
obtaining the thickness of the structure and the diameter of the bolt hole, obtaining the thickness and the diameter according to the following formula to determine the extrusion distribution coefficient,
when the bolt is stressed in a single shear mode:
θ＝1.0085+0.6536η+0.3653η 2 -0.0119η 3 -0.0068η 4 ；
when the bolt is stressed in a double shear mode:
θ＝1.0015+0.1573η+0.0360η 2 -0.0025η 3 ；
in the formula, theta is an extrusion distribution coefficient, and eta is a ratio of the thickness t to the diameter D;
establishing a finite element model of the structure, applying two different linearly uncorrelated loads in the finite element model and the solid structure model of the structure to obtain the maximum stress of the bolt holes under the two loads and the nominal stress caused by the bypass load of the bolt holes, and determining the theoretical stress concentration coefficient and the extrusion stress concentration coefficient of the empty hole plate with a net area according to the maximum stress and the nominal stress under the two loads and the corresponding loads, wherein the following relations are followed:
in the formula, K tg Theoretical stress concentration coefficient, K, of a clear area perforated hollow panel tb To compressive stressA concentration factor;
σ max1 local maximum stress, P, for the first load application dc1 For nail-transfer loads induced by first-time load application, σ pl(non)1 Nominal stress due to the bypass load applied for the first load;
σ max2 local maximum stress, P, for the second load application dc2 For nail-transfer loads induced by the second load application, σ pl(non)2 Nominal stress due to the bypass load applied for the second load;
determining the plate width of the structure according to the extrusion stress concentration coefficient;
determining a stress severity coefficient according to the local maximum stress under the stress load to be solved by the plate width, the thickness and the structure, nominal stress caused by bypass load, nail transmission load, a hole surface coefficient and a hole filling coefficient;
and finally obtaining the high-cycle fatigue life of the bolt hole under the complex stress state according to the stress severity coefficient.
2. The method for determining the high cycle fatigue life of a bolt hole under a complex stress state according to claim 1, wherein determining the plate width of the structure according to the compressive stress concentration coefficient comprises:
obtaining a curve of the extrusion stress concentration coefficient and the width-thickness ratio;
determining the plate thickness ratio according to the extrusion stress concentration coefficient and the curve;
and determining the plate width according to the plate thickness ratio.
3. The method for determining the high cycle fatigue life of a bolt hole under a complicated stress state according to claim 2, wherein the determined stress severity coefficient is determined by the following formula:
in the formula, SSF is severe in stressCoefficient, α is the pore surface coefficient, β is the pore filling coefficient, σ max Is the local maximum stress.
4. The method for determining the high cycle fatigue life of a bolt hole under a complex stress state according to claim 3, wherein the obtaining the high cycle fatigue life of the bolt hole under the complex stress state according to the stress severity coefficient comprises:
obtaining an S-N curve of the structure;
and checking an S-N curve according to the stress severity coefficient and an overload spectrum born by the structure to determine the service life of the bolt hole.
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| CN108108530A (en) * | 2017-12-01 | 2018-06-01 | 中国航空工业集团公司沈阳飞机设计研究所 | A kind of fatigue life calibration method suitable for structural connection |
| CN108169013A (en) * | 2017-12-01 | 2018-06-15 | 中国航空工业集团公司沈阳飞机设计研究所 | A kind of fatigue life calibration method suitable for Multi-fasteners joint test specimen |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108108530A (en) * | 2017-12-01 | 2018-06-01 | 中国航空工业集团公司沈阳飞机设计研究所 | A kind of fatigue life calibration method suitable for structural connection |
| CN108169013A (en) * | 2017-12-01 | 2018-06-15 | 中国航空工业集团公司沈阳飞机设计研究所 | A kind of fatigue life calibration method suitable for Multi-fasteners joint test specimen |
Non-Patent Citations (1)
| Title |
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| 疲劳寿命下连接件的优化设计;姜昊等;《国外电子测量技术》;20150115(第01期);全文 * |
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