CN108959692A - Average shearing stress calculation method under a kind of Multiaxial Non-proportional load - Google Patents
Average shearing stress calculation method under a kind of Multiaxial Non-proportional load Download PDFInfo
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Abstract
The invention discloses average shearing stress calculation methods under a kind of Multiaxial Non-proportional load, under Multiaxial Non-proportional load, shear stress direction vector and size in material plane are all as the time is continually changing, under a Multiaxial Non-proportional Cyclic Load, shear stress vector end will depict a trace in material plane.Therefore, under Multiaxial Non-proportional load, not only determine that the amplitude of shear stress is extremely difficult, but also determine that average shearing stress is also very difficult.The present invention is converted by coordinate, and projection obtainsShear stress time history in plane；It is described with discrete pointThe discribed trace in shear stress vector end in plane；Each discrete shear stress endpoint is passed through into coordinate origin in material plane respectively and orthogonal local coordinate system projects；The trace centre of figure of shear stress is determined according to the average value of projected length in two reference axis；Coordinates computed origin acquires material and exists to the distance of centre of figureAverage shearing stress in plane.
Description
Technical field
The invention belongs to air line technical field, refer specifically to calculate for average shearing stress under a kind of Multiaxial Non-proportional load
Method.
Background technique
With the development of aviation industry, novel aircrafts show that flying area is vast, flying speed mentions more and more
The features such as high, the flight service life extends, the requirement for safety and economy is also higher and higher.Studies have shown that fatigue rupture is
The failure of one of the main reason for structural failure, especially non-proportional loading.About 80% or more belongs in machine components failure
Fatigue rupture.Since fatigue rupture is gone to toward without apparent signs of deformation, the generation for leading to major accident is tended to.
Non-proportional loading problem in engineer application is often handled in the form of being reduced to single shaft fatigue at present, big in this way
Calculating step is simplified greatly, but also causes to have big difference between fatigue life prediction and true lifetime, it is pre- to reduce fatigue life
The reference value of survey.Therefore, fatigue life of the research structure part under Multi-axial Loading finds the more acurrate fatigue life more simplified
Prediction technique is still major subjects in current engineering.
In Multiaxial Fatigue Damage prediction, calculating stress amplitude and average shearing stress in material plane is to carry out the tired longevity
It is most basic in life analysis, while being also very crucial one of problem.In true non-proportional loading loading procedure, suffered by component
To load be often variable amplitude loading, even random load.As shown in Figure 1, being answered during a complex loading recycled
Force vector SnA closed curve Ψ ' is depicted, wherein stress vector SnDirect stress vector σ can be decomposed intonWith shear stress to
Measure τ.Direct stress σnOnly change its size, does not change direction, therefore its amplitude and mean value are all easier to determine.It is answered however, cutting
The size and Orientation of force vector τ is often to change over time, and the tip of τ depicts a closed curve Ψ, due to the song
The shape of line changes with the variation of external applied load, it is thus determined that the amplitude and mean value of shear stress are all a complicated problems.
Summary of the invention
It is directed to above-mentioned status, it is an object of the invention to by considering that each pair of point is average on the trace of shear stress vector end
The combined influence of stress value calculates average shearing stress, is allowed to more sensitive for loading sequence.
In order to achieve the above objectives, The technical solution adopted by the invention is as follows:
Average shearing stress calculation method under a kind of Multiaxial Non-proportional load of the invention, comprises the following steps that
(1) fatigue dangerous point O is defined, and is set to coordinate origin；Define rectangular coordinate system Oxyz；Define plane Δ；
Local coordinate system Ouv on the Δ of definition face；
(2) Multiaxial stress loading sequence is inputted；
(3) for given planeIt is converted by coordinate, the space vector of the stress on O point is projected into institute
In the face Δ of research, obtains shear stress vector of the material on the Δ of face under Multiaxial Non-proportional load and change over time course；
(4) with discrete point describe above-mentioned material on the Δ of face shear stress vector end in a Multiaxial Non-proportional cyclic loading
Under discribed trace；
(5) each discrete shear stress is passed through into coordinate origin in material plane and orthogonal local coordinate system respectively
Ouv is projected；
(6) centre of figure of shear stress trace is determined according to the average value of projected length in two reference axis；
(7) coordinates computed origin is to the distance of above-mentioned centre of figure, as material shear stress mean value on this plane.
Preferably, the step (1) further comprises: tired dangerous point O being taken as coordinate origin, and defines natural coordinates
It is Oxyz；If face to be asked is Δ, the positional relationship of face Δ and natural system of coordinates Oxyz byθ is indicated:Normal for face Δ exists
The angle of projection and x-axis in x-y plane, θ are the normal of face Δ and the angle of z-axis；And define the local coordinate system on the Δ of face
Ouv。
Preferably, the step (2) further comprises: the form of stress loading course matrix is indicated:
Wherein, σxx(t) be acting surface perpendicular to x-axis, direction along x-axis direct stress；σxyIt (t) is acting surface perpendicular to x
Axis, direction along y-axis shear stress；σxz(t) be acting surface perpendicular to x-axis, direction along z-axis shear stress；σyxIt (t) is work
With face perpendicular to y-axis, direction along x-axis shear stress；σyy(t) be acting surface perpendicular to y-axis, direction along y-axis direct stress；
σyz(t) be acting surface perpendicular to y-axis, direction along z-axis shear stress；σzxIt (t) is acting surface perpendicular to z-axis, direction is along x
The shear stress of axis；σzy(t) be acting surface perpendicular to z-axis, direction along y-axis shear stress；σzzIt (t) is acting surface perpendicular to z
Axis, direction along z-axis direct stress.
Preferably, the step (3) further comprises: object is acted on by non-proportional loading load, and face to be asked is face Δ, will
Natural system of coordinates x, y, z are projected on the local coordinate system u, v on the Δ of face, then face Δ and natural system of coordinates x, and the position of y, z are closed
The angle that system passes through its unit normal direction vector n and x, z-axisIt determines；Assuming that the unit normal direction vector n and x of face Δ, y, z-axis
Direction cosines distinguish nx, ny, nz, with θ,It indicates are as follows:
Stress on the Δ of face is expressed as:
Wherein, SnxFor the stress on the Δ of face along the x-axis direction；SnyFor the stress on the Δ of face along the y-axis direction；SnzFor on the Δ of face
Stress along the z-axis direction；
Stress S on the Δ facenIt is indicated with tensor form are as follows:
Sn=σ (t) n
Vector SnIt is decomposed into the direct stress σ perpendicular to face Δn, i.e. SnProjection on n:
σn=(nSn) n=(n σ (t) n) n
And the shear stress vector τ in the Δ of face:
τ=Sn-σn=σ (t) n- (n σ (t) n) n.
Preferably, the step (4) further comprises: the trace at material face Δ shear stress vector end is Ψ, by one
The point of serial variance is constituted, wherein shear stress τj=τ (tj), 0≤tj≤ T, tjIndicate time point, T is a cycle period, j
=1,2 ... k, k numerical value is bigger, and the shape of polygon is just closer to true curve Ψ, the coordinate of these discrete points is defined as:
(τu(tj), τv(tj))。
Preferably, the step (5) further comprises: by local coordinate of the discrete point on the Δ of face described in step (4)
It is to be projected on Ouv, the value of projection is the coordinate (τ of the pointu(tj), τv(tj)), the u on local coordinate system Ouv, the direction of v axis
Vector is defined as:
Then projection τ of the shear stress in u Yu the direction vu(tj), τv(tj) be respectively as follows:
τu(tj)=u τ=u [σ (tj)·n-(n·σ(tj) n) n]=u σ (tj)·n
τv(tj)=v τ=v [σ (tj)·n-(n·σ(tj) n) n]=v σ (tj)·n。
Preferably, the step (6) further comprises: define shear stress trace centre of figure be trace Ψ on it is all from
Scatterplot is respectively in u, the average value of v direction projection, that is, the coordinate of shear stress central point are as follows:
Preferably, the step (7) further comprises: defining average shearing stress size is from point O to the vector of center C
Value, it may be assumed that
Beneficial effects of the present invention:
Calculation method of the invention is suitable for the determination that metal material carries out average shearing stress under Multiaxial Non-proportional load,
For the previous methods problem insensitive for shear stress vector end trace shape, shear stress vector end trace is considered in detail
Upper influence of each node for whole amplitude, the fatigue life point under structure design and military service load to carry out aeronautic structure
Analysis provides base support.
Detailed description of the invention
Fig. 1 is decomposition situation schematic diagram of the stress in material plane；
Fig. 2 is the schematic diagram of the method for the present invention；
Fig. 3 a is true stress exploded view；
Fig. 3 b is that stress vector is projected to floor map to be asked；
Fig. 4 is to describe shear stress vector end trace schematic diagram with discrete point；
Fig. 5 isThe lower shear stress curve in θ=84 ° and shear stress center schematic diagram.
Specific embodiment
For the ease of the understanding of those skilled in the art, the present invention is made further below with reference to embodiment and attached drawing
Bright, the content that embodiment refers to not is limitation of the invention.
Referring to shown in Fig. 2, average shearing stress calculation method under a kind of Multiaxial Non-proportional load of the invention, including step is such as
Under:
(1) fatigue dangerous point O is defined, and is set to coordinate origin；Define rectangular coordinate system Oxyz；Define plane Δ；
Local coordinate system Ouv on the Δ of definition face；
Referring to shown in Fig. 3 a, object is acted on by non-proportional loading load, tired dangerous point O is taken as coordinate origin, and fixed
Adopted natural system of coordinates Oxyz；If face to be asked is Δ, the positional relationship of face Δ and natural system of coordinates Oxyz byθ is indicated:For face
The angle of the projection on the x-y plane of the normal of Δ and x-axis, θ are the normal of face Δ and the angle of z-axis；And it defines on the Δ of face
Local coordinate system Ouv.
(2) Multiaxial stress loading sequence is inputted；
The form of stress loading course matrix is indicated:
Wherein, σxx(t) be acting surface perpendicular to x-axis, direction along x-axis direct stress；σyxIt (t) is acting surface perpendicular to x
Axis, direction along y-axis shear stress；σxz(t) be acting surface perpendicular to x-axis, direction along z-axis shear stress；σyxIt (t) is work
With face perpendicular to y-axis, direction along x-axis shear stress；σyy(t) be acting surface perpendicular to y-axis, direction along y-axis direct stress；
σyz(t) be acting surface perpendicular to y-axis, direction along z-axis shear stress；σzxIt (t) is acting surface perpendicular to z-axis, direction is along x
The shear stress of axis；σzy(t) be acting surface perpendicular to z-axis, direction along y-axis shear stress；σzzIt (t) is acting surface perpendicular to z
Axis, direction along z-axis direct stress.
(3) for given planeIt is converted by coordinate, the space vector of the stress on O point is projected into institute
In the face Δ of research, obtains shear stress vector of the material on the Δ of face under Multiaxial Non-proportional load and change over time course；
Referring to shown in Fig. 3 b, object is acted on by non-proportional loading load, and face to be asked is face Δ, by natural system of coordinates x, y, z
It is projected on local coordinate system u, v on the Δ of face, then face Δ and natural system of coordinates x, the positional relationship of y, z pass through its unit normal direction
The angle of vector n and x, z-axisIt determines；Assuming that the unit normal direction vector n and x of face Δ, y, the direction cosines difference of z-axis
nx, ny, nz, useIt indicates are as follows:
Stress on the Δ of face is expressed as:
Wherein, SnxFor the stress on the Δ of face along the x-axis direction；SnyFor the stress on the Δ of face along the y-axis direction；SnzFor on the Δ of face
Stress along the z-axis direction；
Stress S on the Δ facenIt is indicated with tensor form are as follows:
Sn=σ (t) n
Vector SnIt is decomposed into the direct stress σ perpendicular to face Δn, i.e. SnProjection on n:
σn=(nSn) n=(n σ (t) n) n
And the shear stress vector τ in the Δ of face:
τ=Sn-σn=σ (t) n- (n σ (t) n) n.
(4) with discrete point describe above-mentioned material on the Δ of face shear stress vector end in a Multiaxial Non-proportional cyclic loading
Under discribed trace；
Referring to shown in Fig. 4, the trace at material face Δ shear stress vector end is Ψ, by the point institute structure of series of discrete
At wherein shear stress τ j=τ (tj), 0≤tj≤ T, tjIndicate time point, T is a cycle period, and j=1,2 ... k, k numerical value gets over
Greatly, the shape of polygon is just closer to true curve Ψ, the coordinate of these discrete points is defined as: (τu(tj), τv(tj))。
(5) each discrete shear stress is passed through into coordinate origin in material plane and orthogonal local coordinate system respectively
Ouv is projected；
Discrete point described in step (4) is projected on the local coordinate system Ouv on the Δ of face, the value of projection is the point
Coordinate (τu(tj), τv(tj)), the u on local coordinate system Ouv, the direction vector of v axis is defined as:
Then projection τ of the shear stress in u Yu the direction vu(tj), τv(tj) be respectively as follows:
τu(tj)=u τ=u [σ (tj)·n-(n·σ(tj) n) n]=u σ (tj)·n
τv(tj)=v τ=v [σ (tj)·n-(n·σ(tj) n) n]=v σ (tj)·n。
(6) centre of figure of shear stress trace is determined according to the average value of projected length in two reference axis；
The centre of figure for defining shear stress trace is that respectively in u, v direction projection is averaged all discrete points on trace Ψ
Value, that is, the coordinate of shear stress central point are as follows:
(7) coordinates computed origin is to the distance of above-mentioned centre of figure, as material shear stress mean value on this plane；
Defining average shearing stress size is from point O to the vector value of center C, it may be assumed that
This example is loaded using tension and torsion, and loading spectrum is shown in Table 1 following (other stress values: σyy, σzz, σxz, σyzIt is
0MPa):
Table 1
S1: fatigue dangerous point O is defined, and is set to coordinate origin；
S2: the loading spectrum of input table 1；
S3: it takesθ=84 °；
S4: the Shear stress time history on material Δ face is obtained by coordinate transform；
S5: discrete, discrete results and shear stress center schematic diagram such as Fig. 5 institute are carried out to shear stress vector end trace on Δ face
Show；
S6: calculating the centre of figure of shear stress trace, and coordinate is (0.41, -3.53)；
S7: average shearing stress value is calculated
There are many concrete application approach of the present invention, the above is only a preferred embodiment of the present invention, it is noted that for
For those skilled in the art, without departing from the principle of the present invention, it can also make several improvements, this
A little improve also should be regarded as protection scope of the present invention.
Claims (8)
1. average shearing stress calculation method under a kind of Multiaxial Non-proportional load, which is characterized in that comprise the following steps that
(1) fatigue dangerous point O is defined, and is set to coordinate origin；Define rectangular coordinate system Oxyz；Define plane Δ；Definition
Local coordinate system Ouv on the Δ of face；
(2) Multiaxial stress loading sequence is inputted；
(3) for given planeIt is converted by coordinate, the space vector of the stress on O point is projected to and is studied
Face Δ in, obtain shear stress vector of the material on the Δ of face under Multiaxial Non-proportional load and change over time course；
(4) above-mentioned material shear stress vector end institute under a Multiaxial Non-proportional cyclic loading on the Δ of face is described with discrete point
The trace of description；
(5) each discrete shear stress is passed through into coordinate origin in material plane and orthogonal local coordinate system Ouv respectively
It is projected；
(6) centre of figure of shear stress trace is determined according to the average value of projected length in two reference axis；
(7) coordinates computed origin is to the distance of above-mentioned centre of figure, as material shear stress mean value on this plane.
2. average shearing stress calculation method under Multiaxial Non-proportional load according to claim 1, which is characterized in that the step
Suddenly (1) further comprises: tired dangerous point O being taken as coordinate origin, and defines natural system of coordinates Oxyz；If face to be asked is Δ,
The positional relationship of face Δ and natural system of coordinates Oxyz byθ is indicated:For the normal projection and x-axis on the x-y plane of face Δ
Angle, θ be face Δ normal and z-axis angle；And define the local coordinate system Ouv on the Δ of face.
3. average shearing stress calculation method under Multiaxial Non-proportional load according to claim 2, which is characterized in that the step
Suddenly (2) further comprise: the form of stress loading course matrix is indicated:
Wherein, σxx(t) be acting surface perpendicular to x-axis, direction along x-axis direct stress；σxyIt (t) is acting surface perpendicular to x-axis, side
To the shear stress along y-axis；σxz(t) be acting surface perpendicular to x-axis, direction along z-axis shear stress；σyx(t) it hangs down for acting surface
Directly in y-axis, direction along x-axis shear stress；σyy(t) be acting surface perpendicular to y-axis, direction along y-axis direct stress；σyz(t)
Be acting surface perpendicular to y-axis, direction along z-axis shear stress；σzxIt (t) is acting surface perpendicular to z-axis, direction is cut along x-axis
Stress；σzy(t) be acting surface perpendicular to z-axis, direction along y-axis shear stress；σzzIt (t) is acting surface perpendicular to z-axis, direction
Along the direct stress of z-axis.
4. average shearing stress calculation method under Multiaxial Non-proportional load according to claim 3, which is characterized in that the step
Suddenly (3) further comprise: object is acted on by non-proportional loading load, and face to be asked is face Δ, and by natural system of coordinates x, y, z are to face Δ
On local coordinate system u, v on project, then face Δ and natural system of coordinates x, the positional relationship of y, z pass through its unit normal direction vector n
With the angle of x, z-axisIt determines；Assuming that the unit normal direction vector n and x of face Δ, the direction cosines of y, z-axis distinguish nx, ny,
nz, with θ,It indicates are as follows:
Stress on the Δ of face is expressed as:
Wherein, SnxFor the stress on the Δ of face along the x-axis direction；SnyFor the stress on the Δ of face along the y-axis direction；SnzFor on the Δ of face along z-axis
The stress in direction；
Stress S on the Δ facenIt is indicated with tensor form are as follows:
Sn=σ (t) n
Vector SnIt is decomposed into the direct stress σ perpendicular to face Δn, i.e. SnProjection on n:
σn=(nSn) n=(n σ (t) n) n
And the shear stress vector τ in the Δ of face:
τ=Sn-σn=σ (t) n- (n σ (t) n) n.
5. average shearing stress calculation method under Multiaxial Non-proportional load according to claim 4, which is characterized in that the step
Suddenly (4) further comprise: the trace at material face Δ shear stress vector end is Ψ, is made of the point of series of discrete,
Middle shear stress τj=τ (tj), 0≤tj≤ T, tjIndicate time point, T is a cycle period, and j=1,2 ... k, k numerical value is bigger, more
The shape of side shape is just closer to true curve Ψ, the coordinate of these discrete points is defined as: (τu(tj), τv(tj))。
6. average shearing stress calculation method under Multiaxial Non-proportional load according to claim 5, which is characterized in that the step
Suddenly (5) further comprise: discrete point described in step (4) being projected on local coordinate system Ouv on the Δ of face, the value of projection is
For the coordinate (τ of the pointu(tj), τv(tj)), the u on local coordinate system Ouv, the direction vector of v axis is defined as:
Then projection τ of the shear stress in u Yu the direction vu(tj), τv(tj) be respectively as follows:
τu(tj)=u τ=u [σ (tj)·n-(n·σ(tj) n) n]=u σ (tj)·n
τv(tj)=v τ=v [σ (tj)·n-(n·σ(tj) n) n]=v σ (tj)·n。
7. average shearing stress calculation method under Multiaxial Non-proportional load according to claim 6, which is characterized in that the step
Suddenly (6) further comprise: defining the centre of figure of shear stress trace is all discrete points on trace Ψ respectively in u, v direction projection
Average value, that is, the coordinate of shear stress central point are as follows:
8. average shearing stress calculation method under Multiaxial Non-proportional load according to claim 7, which is characterized in that the step
Suddenly (7) further comprise: defining average shearing stress size is from point O to the vector value of center C, it may be assumed that
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|---|---|---|---|---|
| CN110705137A (en) * | 2019-08-22 | 2020-01-17 | 中车青岛四方机车车辆股份有限公司 | Stress amplitude and mean value determining method and device |
| CN110705137B (en) * | 2019-08-22 | 2023-04-21 | 中车青岛四方机车车辆股份有限公司 | Method and device for determining stress amplitude and mean value |
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| CN108959692B (en) | 2022-07-12 |
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