CN110738000A - High cycle fatigue life determination method for bolt holes in complex stress states - Google Patents
High cycle fatigue life determination method for bolt holes in complex stress states Download PDFInfo
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Abstract
The application relates to a method for determining high cycle fatigue life of a bolt hole in complex stress states, which comprises the steps of obtaining the thickness and the diameter of the structure and the diameter of the bolt hole, 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 a solid structure model of the structure to obtain the maximum stress of the bolt hole under two loads and the nominal stress caused by bypass load of the bolt hole, determining a stress concentration coefficient according to the maximum stress and the nominal stress under the two loads and 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 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 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 high cycle fatigue life determination method for bolt holes in complex stress states.
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 link construction detail, with the perforated structural sheet material being subjected to a load that is partially bypassed, referred to as the bypass load PplAnother portion is transmitted by the fastener, called the nail load Pdc。
By-pass load PplThe local maximum stress generated is σ1Local maximum stress σ1The formula is shown in formula 1, and K in formula 1tgFor the theoretical stress concentration coefficient of the empty hole plate of net area, W is the plate width, D is the bolt hole diameter, t is the plate thickness:
nail load PdcLocal drum stress sigma generated2Local maximum stress σ2The formula (2) is shown in the formula (2), and K is shown in the formula (2)tbFor the extrusion stress concentration coefficient, θ is the extrusion distribution coefficient:
by a bypass load PplLoad P transferred by naildcLocal maximum stress sigma generatedmax＝σ1+σ2，σmaxThe formula (2) is shown in formula 3, and the formula 3Nominal stress due to bypass load:
nominal stress
Coefficient of severity of stressα for pore surface coefficient, β for pore fillingAnd (4) charging 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 firstly determines the plate width W and the bolt hole diameter D to calculate or look up a table through a formula to obtain K in the formula 1tg、KtbDetermining theta, α and β by looking up a table according to the types of different bolt holes, and then determining P by finite element analysispl、PdcFinally, 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 width W of the plate, and therefore K relative to the width W of the plate cannot be determinedtg、KtbAnd P is often determined in finite element calculation of nail hole dense structureplIt is also very difficult.
Disclosure of Invention
The purpose of the application is to provide methods for determining the high cycle fatigue life of bolt holes under complex stress conditions, so as to solve or reduce at least problems in the background art.
The technical scheme is that the method for determining the high cycle fatigue life of the bolt hole in complex stress states 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 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 the complex stress state according to the stress severity coefficient.
In the method embodiment of the present application, the determining an extrusion profile factor as a function of the thickness and diameter is obtained by the following equation:
when the bolt is stressed in the form of single shear,
θ＝1.0085+0.6536η+0.3653η2-0.0119η3-0.0068η4；
when the bolt is stressed in the form of double shear,
θ＝1.0015+0.1573η+0.0360η2-0.0025η3；
where θ is the squeeze distribution coefficient and η is the ratio of thickness t to diameter D.
In the method embodiment 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 the method embodiment of the present application, the theoretical stress concentration coefficients and the compressive stress concentration coefficients of the net area void cell plate are determined from the maximum stress and the nominal stress at two loads and corresponding loads, following the relationship:
in the formula, KtgTheoretical stress concentration coefficient, K, of a clear area of a perforated platetbIs the extrusion stress concentration coefficient;
σmax1local maximum stress, P, for the th load applicationdc1For the nail transfer load caused by th load application, σpl(non)1At timesNominal stress due to load imposed by-pass load;
σmax2local maximum stress, P, for the second load applicationdc2For nail-transfer loads induced by the second load application, σpl(non)2Nominal stress due to the bypass load applied for the second load.
In a method embodiment 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 the method embodiment of the present application, the determining the stress severity coefficient is determined by the following equation:
where SSF is the stress severity coefficient, α is the pore surface coefficient, β is the pore fill coefficient, σ is the pore fill coefficientmaxIs the local maximum stress.
In an embodiment of method of the present application, the obtaining the high cycle fatigue life of the bolt hole under the complex stress condition 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
To more clearly illustrate the solution provided by the present application, reference will now be made briefly to the accompanying drawings, which are, by way of illustration, merely embodiments of the present 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 applicationtbGraph with D/W ratio.
FIG. 5 is a schematic illustration of a structure to determine bolt hole life according to an embodiment of the present application .
Fig. 6 is a schematic view of the structure of fig. 5 under load.
FIG. 7 shows the structure of FIG. 5 for determining KtgAnd KtbSchematic 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 method aims to solve the problems that the plate width of a structure cannot be determined and the stress concentration coefficient is difficult to determine in the prior art, and provides methods capable of accurately determining the fatigue life of the bolt hole under a complex stress statetgAnd KtbAnd 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, η is t/D;
θ＝1.0085+0.6536η+0.3653η2-0.0119η3-0.0068η4； (5)
θ＝1.0015+0.1573η+0.0360η2-0.0025η3； (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 , namely the nominal stress of the bypass load caused by the bypass load).
Wherein, the two loads applied in the process are linearly independent.
The local maximum stress sigma generated by the th applied load can be obtained by two different load conditions in the processmax1Nail-transferring load Pdc1Nominal stress sigma due to bypass loadpl(non)1And local maximum stress sigma due to the second applied loadmax2Nail-transferring load Pdc2Nominal stress sigma due to bypass loadpl(non)2. There are formula 7 and formula 8 from formula 3. The theoretical stress concentration coefficient K can be obtained by combining formula 7 and formula 8tg(equation 9) and the compressive stress concentration coefficient Ktb(equation 10):
s13 finding the stress concentration coefficient KtbAnd combining the aperture D and the plate width W or the ratio curve of the plate width W and the aperture D as shown in FIG. 4, the value of the plate width W can be further determined ;
s14 local maximum pressure σ under stress load to be solved by actual structuremaxNominal stress sigma due to bypass loadpl(non)Nail-transferring load PdcAnd the hole surface coefficient α, the hole filling coefficient β, and the plate width W and the thickness t determined in the process, the stress severity coefficient SSF can be obtained, 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 the overload spectrum born by the structure, checking an S-N curve to determine the service life of the bolt hole.
To facilitate an understanding of the present disclosure, the present disclosure will be further illustrated in by specific cases of .
Fig. 5 shows a schematic 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 to determine the fatigue life, wherein the beam 2 is bent, the load is transferred to another force bearing member through a section bar, the life of the bolt hole on the lower edge strip of the beam 2 is required to be determined, and the dispersion coefficient is 4.
First, it can be seen by analysis that the beam bends, the lower bead is in tension when the beam bends, the bolts transmit a small portion of the load to the other load bearing members as the lower bead is in tension and the load on the lower wall plate 3 is gradually transmitted to the lower bead of the beam and the profile by 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 that two different groups of loads for bending the beam are loaded, as shown in FIGS. 6 and 7, in the embodiment, two groups of loads for bending the beam are applied, and the two groups of loads respectively obtain sigmamaxl＝41.6MPa，Pdcl＝23.53N，σpl(non)1＝21.0MPa，σmax2＝61.6MPa，Pdc2＝87.2N，σpl(non)2＝30.5MPa。
K can be obtained from the equations 9 and 10tg＝1.96，Ktb＝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 actual load condition to be calculated to obtain sigmamax＝81.6MPa，Pdc＝397.2N，σpl(non)The stress severity SSF is found to be l.94 by equation 11, while α is found to be 1.0, β is found to be 0.9 by table lookup.
S5, according to the stress severity coefficients SSF and sigmanonAnd 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 (7)
1, method for determining high cycle fatigue life of bolt hole under complex stress state, characterized in that, the method includes
Acquiring the thickness of the structure and the diameter of a 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 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 condition according to claim 1, wherein the determination of the extrusion distribution coefficient according to 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+0.3653η2-0.0119η3-0.0068η4；
when the bolt is stressed in the form of double shear,
θ＝1.0015+0.1573η+0.0360η2-0.0025η3；
where θ is the squeeze distribution coefficient and η is the ratio of thickness t to diameter D.
3. The method of claim 2, wherein the two different loads applied in the finite element model and the solid structure model of the structure are linearly uncorrelated.
4. The method for determining the high cycle fatigue life of the bolt hole under the complex stress state according to claim 3, wherein the theoretical stress concentration coefficient and the compressive stress concentration coefficient of the empty hole plate with 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, KtgTheoretical stress concentration coefficient, K, of a clear area of a perforated platetbIs the extrusion stress concentration coefficient;
σmax1local maximum stress, P, for the th load applicationdc1For the nail transfer load caused by th load application, σpl(non)1Nominal stress due to the bypass load applied for the th load;
σmax2local maximum stress, P, for the second load applicationdc2For nail-transfer loads induced by the second load application, σpl(non)2Nominal stress due to the bypass load applied for the second load.
5. The method of claim 4, wherein determining the plate width of the structure based on 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.
6. The method for determining the high cycle fatigue life of a bolt hole under a complex stress condition according to claim 5, wherein the determined stress severity coefficient is determined by the following formula:
where SSF is the stress severity coefficient, α is the pore surface coefficient, β is the pore fill coefficient, σ is the pore fill coefficientmaxIs the local maximum stress.
7. The method of claim 6, wherein obtaining the high cycle fatigue life of the bolt hole under the complex stress condition 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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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112926163A (en) * | 2021-04-07 | 2021-06-08 | 唐山学院 | Method and device for constructing bolt fatigue life prediction model based on Workbench and Matlab |
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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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| 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 |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112926163A (en) * | 2021-04-07 | 2021-06-08 | 唐山学院 | Method and device for constructing bolt fatigue life prediction model based on Workbench and Matlab |
| CN112926163B (en) * | 2021-04-07 | 2022-04-29 | 唐山学院 | Method and device for constructing bolt fatigue life prediction model based on Workbench and Matlab |
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