CN115391960B - Spindle composite fatigue life analysis method considering dispersion coefficient and multi-axis load - Google Patents

Spindle composite fatigue life analysis method considering dispersion coefficient and multi-axis load Download PDF

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CN115391960B
CN115391960B CN202211322296.XA CN202211322296A CN115391960B CN 115391960 B CN115391960 B CN 115391960B CN 202211322296 A CN202211322296 A CN 202211322296A CN 115391960 B CN115391960 B CN 115391960B
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CN115391960A (en
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王学民
饶云松
黄维娜
李晓明
古远兴
沈莲
卢绪平
李乐
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AECC Sichuan Gas Turbine Research Institute
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/04—Ageing analysis or optimisation against ageing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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Abstract

The invention provides a spindle composite fatigue life analysis method considering dispersion coefficients and multi-axis loads, which comprises the following steps of: step one, carrying out finite element calculation on a low-pressure turbine shaft; step two, obtaining equivalent steady state stress sigma 'of six components in the main cycle' eq And equivalent steady state stress sigma 'of six components under primary and secondary cycle compounding' eq And calculating the equivalent steady-state stress; thirdly, taking values of the dispersion coefficient by adopting a setting method, and obtaining the equivalent steady-state stress sigma of the shaft test piece under the primary and secondary circulation compounding s,eq And performing fatigue life damage analysis. Based on a fatigue analysis model of a local equivalent steady state stress method of finite element results, and according to a matching principle among a shaft key position fatigue life calculation formula, material performance data, an accumulated damage life calculation analysis formula and judgment criteria, the rapid analysis of the high-low cycle composite fatigue life damage of the low-pressure turbine shaft is realized.

Description

Spindle composite fatigue life analysis method considering dispersion coefficient and multi-axis load
Technical Field
The specification relates to the technical field of aero-engines, in particular to a spindle composite fatigue life analysis method considering dispersion coefficients and multi-axis loads.
Background
The low-pressure turbine shaft of the aircraft engine is an important part for connecting a gas compressor and a turbine part and transmitting power, the load borne in flight is very complex, the load comprises steady-state load torque, axial force, high-cycle load vibration torque and bending moment, and the main shaft working in a high-temperature area of the engine also bears thermal load, axisymmetrical radial load and the like. Due to the structural requirement of the engine, the low-pressure turbine shaft is designed with complex geometric shapes such as holes, grooves, splines, steps and the like, and due to stress concentration, local stress is often very high under high and low cyclic loads in flight, and once cracks and even shaft fracture occur, serious consequences are caused to the engine. Therefore, the high-low cycle composite fatigue life damage analysis of the low-pressure turbine shaft has important significance on the safety and the stability of the shaft.
At the present stage, the low-pressure turbine shaft of the engine is usually subjected to a test method, namely a fatigue test for a given number of cycles is directly carried out on the shaft, and the approved service life of the shaft is determined. Although the method has reliable results, the test cost is high (at least 3 shafts are needed), and the method is not suitable for predicting the fatigue life of the low-pressure turbine shaft of the engine in the design or modification stage.
In addition, the prior art adopts the 'stress standard method of the Scei engine' to evaluate the composite fatigue life by shearing stress, neglects the influence of high-cycle bending load, and assumes that the stress caused by axial force is uniformly distributed along the cross section of the shaft. In fact, the stress concentration zones, bending moments and axial forces, of the low-pressure turboshaft disk-shaft connection section often cause localized high stress zones. This method has major limitations.
Meanwhile, a large number of fatigue test results show that the dispersity of the composite material changes along with the service life, the dispersity of a long service life area is large, and the dispersity of a short service life area is small; the dispersancy is also related to fatigue test load properties, with less dispersancy for low cycle fatigue loads and greater dispersancy for high cycle fatigue loads.
Disclosure of Invention
In view of this, the embodiments of the present disclosure provide a method for analyzing a composite fatigue life of a main shaft in consideration of a dispersion coefficient and a multi-axis load, so as to accurately reflect load and fatigue characteristics borne by a low-pressure turbine shaft.
The scheme of the invention is as follows: a spindle composite fatigue life analysis method considering dispersion coefficients and multi-axis loads comprises the following steps:
step one, carrying out finite element calculation on a low-pressure turbine shaft;
step two, obtaining equivalent steady state stress sigma 'of six components in the main cycle' eq And equivalent steady state stress sigma 'of six components under primary and secondary cycle compounding' eq And calculating equivalent steady-state stress;
thirdly, taking values of the dispersion coefficient by adopting a setting method to obtain the equivalent steady-state stress sigma of the shaft test piece under the primary and secondary circulation compounding s,eq And performing fatigue life damage analysis.
Further, the first step specifically comprises: and establishing a finite element model of the lower shaft under the corresponding load according to the low-cycle steady-state load and the high-cycle load borne by the low-pressure turbine shaft, and obtaining a strength calculation result.
Further, step two includes step 2.1: using the Goodman diagram corrected by the number of main cycles, from 0 to
Figure 396285DEST_PATH_IMAGE001
Is converted into equivalent steady state stress
Figure 893126DEST_PATH_IMAGE002
In which
Figure 543550DEST_PATH_IMAGE003
Low cycle load of main cycleLoad stress component, K t Is the theoretical stress concentration coefficient.
Further, step 2.1 specifically comprises: by the formula
Figure 202064DEST_PATH_IMAGE004
Calculating the conversion of the main cyclic stress into the equivalent steady state stress
Figure 69264DEST_PATH_IMAGE005
In which K is t Is theoretical stress concentration coefficient, K f,n Effective stress concentration coefficient for N cycles (N = lgN),
Figure 369795DEST_PATH_IMAGE006
Is the lowest tensile strength of the material at the working temperature,
Figure 140305DEST_PATH_IMAGE007
Symmetric bending fatigue strength for N cycles (N = lgN),
Figure 969721DEST_PATH_IMAGE003
Is the main cycle low cycle load stress component.
Further, the second step also includes a step 2.2: by means of 10 7 Sub-cycle corrected Goodman diagram, in terms of equivalent steady state stress at the primary cycle σ' eq The equivalent steady-state stress σ 'of the primary and secondary cyclic loads in the composite was determined as the constant stress of the high-frequency load, using the stresses due to the vibration torque and the bending moment as the alternating amplitudes' eq 。
Further, step 2.2 specifically comprises:
by the formula
Figure 91261DEST_PATH_IMAGE008
Calculating equivalent steady state stress sigma 'under primary and secondary cyclic load combination' eq Where σ is H High cyclic load stress, K, for a sub-cycle f Is the effective stress concentration coefficient (fatigue notch coefficient), σ -1.7 Is 10 7 Symmetric bending fatigue strength under the secondary cycle;
equivalent steady state stresses are obtained for six local stress components:
Figure 929904DEST_PATH_IMAGE009
；
wherein the content of the first and second substances,
Figure 289341DEST_PATH_IMAGE010
is the equivalent steady-state stress in the x direction under a cylindrical coordinate system,
Figure 820816DEST_PATH_IMAGE011
Is the equivalent steady-state stress in the y direction under a cylindrical coordinate system,
Figure 898494DEST_PATH_IMAGE012
Is the equivalent steady-state stress in the z direction under a cylindrical coordinate system,
Figure 39363DEST_PATH_IMAGE013
Is the equivalent steady-state stress in the xy direction under a cylindrical coordinate system,
Figure 518886DEST_PATH_IMAGE014
Is the equivalent steady state stress in the yz direction under a cylindrical coordinate system,
Figure 221263DEST_PATH_IMAGE015
Is the equivalent steady state stress in the xz direction under a cylindrical coordinate system;
Figure 786236DEST_PATH_IMAGE016
is the main cyclic stress of the x direction under the cylindrical coordinate system,
Figure 966682DEST_PATH_IMAGE017
Is the main cyclic stress of the y direction under the cylindrical coordinate system,
Figure 566290DEST_PATH_IMAGE018
Is the main cyclic stress in the z direction under the cylindrical coordinate system,
Figure 173989DEST_PATH_IMAGE019
As a cylindrical coordinate systemMain cyclic stress in the lower xy direction,
Figure 226259DEST_PATH_IMAGE020
Is the main cyclic stress of yz direction under a cylindrical coordinate system,
Figure 944816DEST_PATH_IMAGE021
Is the main cyclic stress in the xz direction under a cylindrical coordinate system;
Figure 664510DEST_PATH_IMAGE022
torsional fatigue strength of N times of circulation,
Figure 941646DEST_PATH_IMAGE023
Is 10 7 Torsional fatigue strength of the secondary cycle,
Figure 746791DEST_PATH_IMAGE024
Is the torsional strength;
K t,x 、K t,y 、K t,z 、K t,xy 、K t,yz 、K t,xz the other theoretical stress concentration coefficients are respectively acted by the six stress components;
K f,x 、K f,y 、K f,z 、K f,xy 、K f,yz 、K f,xz the effective stress concentration coefficients of the six stress components under the action of the six stress components respectively;
K f,n,x 、K f,n,y 、K f,n,z 、K f,n,xy 、K f,n,yz 、K f,n,xz the effective stress concentration coefficients of the six stress components under the action of N cycles are respectively.
Further, the second step further comprises a step 2.3: calculating the equivalent steady state stress of the point subjected to N times of main cycles and 10 times of main cycles through six stress components 7 Equivalent steady state stress of sub-high cycle load
Figure 269039DEST_PATH_IMAGE025
；
Wherein the content of the first and second substances,
Figure 577661DEST_PATH_IMAGE026
is the equivalent steady state stress under the composite load of the primary and secondary cycles.
Further, step three includes step 3.1:
when the dispersion coefficient is the ultimate strength dispersion coefficient u, the value is 1.1;
when the dispersion coefficient is the fatigue limit strength dispersion coefficient f x By the formula
Figure 527162DEST_PATH_IMAGE027
And (6) obtaining.
Further, step three includes step 3.2:
by the formula
Figure 554024DEST_PATH_IMAGE028
Calculating and obtaining equivalent steady-state stress sigma of the shaft test piece under the primary and secondary circulation compounding s,eq Wherein, in the process,
Figure 879963DEST_PATH_IMAGE029
local stress under main cycle (low cycle) load,
Figure 43091DEST_PATH_IMAGE030
Local stress under sub-cycle (high cycle) load,
Figure 429073DEST_PATH_IMAGE031
Is the theoretical stress concentration coefficient under the main cycle (low cycle) load,
Figure 441766DEST_PATH_IMAGE032
Is the theoretical stress concentration coefficient under the sub-cycle (high cycle) load,
Figure 305817DEST_PATH_IMAGE033
Effective stress concentration coefficient (fatigue notch coefficient) of N times of cycles (N = lgN) under main cycle (low cycle) load,
Figure 589031DEST_PATH_IMAGE034
Effective stress concentration coefficient under the sub-cycle load,
Figure 145914DEST_PATH_IMAGE035
Is 10 x Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 881789DEST_PATH_IMAGE036
Is 10 5 The fatigue ultimate strength dispersion coefficient at the time of the secondary cycle, u is the ultimate strength dispersion coefficient,
Figure 815110DEST_PATH_IMAGE037
The tensile strength,
Figure 687251DEST_PATH_IMAGE038
Is 10 x Symmetric bending fatigue strength in the secondary cycle,
Figure 415035DEST_PATH_IMAGE039
Is 10 7 Symmetric bending fatigue strength under the secondary cycle;
by the formula
Figure 638206DEST_PATH_IMAGE040
Calculating and obtaining a fatigue reserve coefficient K 'of the shaft test piece, wherein f' R Is the ratio of the nominal equivalent stresses of the secondary cycle and the primary cycle (high and low cycles).
Further, step three includes step 3.3:
when the fatigue storage coefficient K' of the shaft test piece is 1, lg (sigma) after logarithm of nominal equivalent stress is taken m,L ) A formula for calculating a relation with x (x = lgN) and obtaining a logarithmic value of fatigue life N (x = lgN) is as follows:
when x is less than or equal to 3:
Figure 109639DEST_PATH_IMAGE041
；
when 3 < x < 4:
Figure 600401DEST_PATH_IMAGE042
；
when x = 4:
Figure 499087DEST_PATH_IMAGE043
；
when 4 < x < 5:
Figure 943975DEST_PATH_IMAGE044
；
when x = 5:
Figure 953519DEST_PATH_IMAGE045
；
when x is more than 5 and less than or equal to 6:
Figure 65831DEST_PATH_IMAGE046
；
when x is more than or equal to 6:
Figure 135419DEST_PATH_IMAGE047
；
wherein, the first and the second end of the pipe are connected with each other,
Figure 333182DEST_PATH_IMAGE029
local stress under main cycle (low cycle) load,
Figure 880838DEST_PATH_IMAGE030
Local stress under sub-cycle (high cycle) load,
Figure 113236DEST_PATH_IMAGE031
Is the theoretical stress concentration coefficient under the main cycle (low cycle) load,
Figure 586680DEST_PATH_IMAGE032
Is the theoretical stress concentration coefficient under the sub-cycle (high cycle) load,
Figure 271740DEST_PATH_IMAGE033
Effective stress concentration coefficient (fatigue notch coefficient) for N cycles (N = lgN) under main cycle (low cycle) load,
Figure 888666DEST_PATH_IMAGE048
Effective stress concentration coefficient under main cyclic load,
Figure 709991DEST_PATH_IMAGE035
Is 10 x Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 386960DEST_PATH_IMAGE036
Is 10 5 The fatigue ultimate strength dispersion coefficient at the time of the secondary cycle, u is the ultimate strength dispersion coefficient,
Figure 559316DEST_PATH_IMAGE037
Is the tensile strength,
Figure 448774DEST_PATH_IMAGE038
Is 10 x Symmetric bending fatigue strength at the time of secondary cycle,
Figure 390185DEST_PATH_IMAGE039
Is 10 7 Symmetric bending fatigue strength under secondary cycle;
Figure 706897DEST_PATH_IMAGE049
；
Figure 366549DEST_PATH_IMAGE050
；
Figure 558233DEST_PATH_IMAGE051
；
Figure 354151DEST_PATH_IMAGE052
；
Figure 107343DEST_PATH_IMAGE053
；
wherein the content of the first and second substances,
Figure 988712DEST_PATH_IMAGE029
local stress under main cycle (low cycle) load,
Figure 485552DEST_PATH_IMAGE030
Local stress under sub-cycle (high cycle) load,
Figure 135976DEST_PATH_IMAGE031
Is the theoretical stress concentration coefficient under the main cycle (low cycle) load,
Figure 60070DEST_PATH_IMAGE032
Is the theoretical stress concentration coefficient under the sub-cycle (high cycle) load,
Figure 694314DEST_PATH_IMAGE033
Effective stress concentration coefficient (fatigue notch coefficient) of N times of cycles (N = lgN) under main cycle (low cycle) load,
Figure 729266DEST_PATH_IMAGE035
Is 10 x Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 998311DEST_PATH_IMAGE036
Is 10 5 The fatigue ultimate strength dispersion coefficient at the time of the secondary cycle, u is the ultimate strength dispersion coefficient,
Figure 93306DEST_PATH_IMAGE037
The tensile strength,
Figure 949266DEST_PATH_IMAGE038
Is 10 x Symmetric bending fatigue strength at the time of secondary cycle,
Figure 522330DEST_PATH_IMAGE039
Is 10 7 Symmetric bending fatigue strength under secondary cycle,
Figure 412926DEST_PATH_IMAGE054
Nominal equivalent stress at 0 cycles;
Figure 678822DEST_PATH_IMAGE055
；
wherein the content of the first and second substances,
Figure 22079DEST_PATH_IMAGE056
is the actual stress under the main cycle (low cycle) load,
Figure 664412DEST_PATH_IMAGE057
Nominal equivalent stress under main cycle (low cycle) load,
Figure 143935DEST_PATH_IMAGE058
Is 10 3 Nominal equivalent stress at the second cycle,
Figure 79268DEST_PATH_IMAGE059
Is 10 4 Nominal equivalent stress at the sub-cycle,
Figure 909821DEST_PATH_IMAGE060
Is 10 5 Nominal equivalent stress at the sub-cycle,
Figure 824687DEST_PATH_IMAGE061
Is 10 6 Nominal equivalent stress at sub-cycle.
Further, step three includes step 3.4:
calculating linear accumulated damage of a low-pressure turbine shaft under single primary and secondary cycle composite load
Figure 424296DEST_PATH_IMAGE062
Wherein n is low voltageThe actual cycle number of the main cycle experienced by the turbine shaft, and N is the life of the main cycle under the composite load spectrum;
calculating the overall linear accumulated damage of the low-pressure turbine shaft under the composite load of a plurality of primary and secondary cycles
Figure 31995DEST_PATH_IMAGE063
Wherein k is the number of primary and secondary cycle composite stress spectrums of the shaft dangerous section, n i Actual number of cycles of the main cycle, N, for a composite stress spectrum i Is the calculated main cycle life of the ith composite stress spectrum.
Compared with the prior art, the beneficial effects that can be achieved by the at least one technical scheme adopted by the embodiment of the specification at least comprise: based on a fatigue analysis model of a local equivalent steady state stress method of a finite element result, and according to a matching principle among a fatigue life calculation formula of a key position of a shaft, material performance data, a cumulative damage life calculation analysis formula and judgment criteria, the high-low cycle composite fatigue life damage rapid analysis of the low-pressure turbine shaft is realized.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic diagram of an embodiment of the present invention;
FIG. 2 is a modified Goodman diagram for N cycles;
FIG. 3 is 10 7 Modified goodmann plots of the minor cycles.
Detailed Description
The embodiments of the present application will be described in detail below with reference to the accompanying drawings.
The following description of the embodiments of the present application is provided by way of specific examples, and other advantages and effects of the present application will be readily apparent to those skilled in the art from the disclosure herein. It is to be understood that the embodiments described are only a few embodiments of the present application and not all embodiments. The application is capable of other and different embodiments and its several details are capable of modifications and various changes in detail without departing from the spirit of the application. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
As shown in fig. 1 to 3, an embodiment of the present invention provides a method for analyzing a composite fatigue life of a spindle in consideration of a dispersion coefficient and a multi-axis load, which specifically includes the following steps:
1. low pressure turbine shaft finite element calculation
And establishing a lower shaft finite element model under corresponding load according to the low-cycle steady-state load and the high-cycle load borne by the low-pressure turbine shaft to obtain a strength calculation result.
Generally, a stress concentration area of the low-pressure turbine shaft, such as a shaft neck, a radial hole on the shaft, an axial hole extending out of a disc, a radius, a boss, a gear edge and the like, is selected, and six stress component values of the maximum equivalent stress point at the positions are extracted (under a cylindrical coordinate, six stress components of any point on the shaft are
Figure 84264DEST_PATH_IMAGE064
) The stress component at this location under high and low cyclic loads is therefore made up of two parts (subscripts L and H indicate the stress-producing load as low and high cyclic loads, respectively):
Figure 68401DEST_PATH_IMAGE065
…（1）
wherein the content of the first and second substances,
Figure 522516DEST_PATH_IMAGE066
is the composite stress of the x direction under the cylindrical coordinate system,
Figure 566695DEST_PATH_IMAGE067
Is the composite stress of the y direction under the cylindrical coordinate system,
Figure 371840DEST_PATH_IMAGE068
Is the composite stress of the z direction under the cylindrical coordinate system,
Figure 392624DEST_PATH_IMAGE069
Is the composite stress of xy direction under the cylindrical coordinate system,
Figure 638928DEST_PATH_IMAGE070
Is the composite stress of yz direction under a cylindrical coordinate system,
Figure 588430DEST_PATH_IMAGE071
Is the composite stress in the xz direction under the cylindrical coordinate system,
Figure 615292DEST_PATH_IMAGE016
Is the main cycle (low cycle) stress of the x direction under the cylindrical coordinate system,
Figure 941231DEST_PATH_IMAGE017
Is the main cyclic (low cycle) stress of the y direction under a cylindrical coordinate system,
Figure 104359DEST_PATH_IMAGE018
Is the main cyclic (low cycle) stress of the z direction under a cylindrical coordinate system,
Figure 224762DEST_PATH_IMAGE019
Is the main cyclic (low cycle) stress of xy direction under a cylindrical coordinate system,
Figure 503034DEST_PATH_IMAGE020
Is the main cycle (low cycle) stress of yz direction under a cylindrical coordinate system,
Figure 367085DEST_PATH_IMAGE021
Is the main cycle (low cycle) stress of xz direction under a cylindrical coordinate system,
Figure 384719DEST_PATH_IMAGE072
Is the sub-cycle (high-cycle) stress of the x direction under a cylindrical coordinate system,
Figure 941603DEST_PATH_IMAGE073
Is the sub-cycle (high cycle) stress of the y direction under a cylindrical coordinate system,
Figure 943057DEST_PATH_IMAGE074
Is the sub-cycle (high cycle) stress of the z direction under the cylindrical coordinate system,
Figure 345219DEST_PATH_IMAGE075
Is the sub-cycle (high-cycle) stress of xy direction under a cylindrical coordinate system,
Figure 482939DEST_PATH_IMAGE076
Is the sub-cycle (high-cycle) stress of yz direction under a cylindrical coordinate system,
Figure 210724DEST_PATH_IMAGE077
The stress is the sub-cycle (high-cycle) stress in the xz direction in the cylindrical coordinate system.
2. Equivalent steady state stress calculation
2.1 equivalent Steady State stress at Main cycle (N Low cycles) # eq
Zero to stress using a N cycle modified Goodman diagram (see FIG. 2) ((v))
Figure 433895DEST_PATH_IMAGE078
) Is converted into equivalent steady state stress
Figure 403863DEST_PATH_IMAGE079
(MPa) calculated according to formula (2):
Figure 396089DEST_PATH_IMAGE080
………………………（2）
wherein:
K t : theoretical stress concentration coefficient；
K f : effective stress concentration coefficient (fatigue notch coefficient);
K f,n : effective stress concentration coefficient at N cycles (N = lgN);
Figure 29196DEST_PATH_IMAGE081
: a main cycle (low cycle) load stress component;
Figure 5242DEST_PATH_IMAGE082
: the lowest value of the tensile strength and the shear strength (MPa) of the material at the working temperature is selected;
Figure 14787DEST_PATH_IMAGE083
: the symmetric bending fatigue strength and the torsional fatigue strength in N cycles (N = lgN) are calculated by the following formula (3):
Figure 861520DEST_PATH_IMAGE084
（3）
Figure 196686DEST_PATH_IMAGE085
：10 3 the symmetric bending fatigue strength and the torsional fatigue strength of the secondary cycle are recommended to be 0.9 when no relevant material data exists
Figure 863291DEST_PATH_IMAGE086
、0.9
Figure 676526DEST_PATH_IMAGE087
，MPa；
Figure 407460DEST_PATH_IMAGE088
: size corrected 10 at operating temperature 6 Flexural fatigue strength, torsional fatigue strength (MPa) of a sub-symmetric cycleThe calculation formula is as follows (4):
Figure 382369DEST_PATH_IMAGE089
……………（4）
Figure 67428DEST_PATH_IMAGE090
: smooth material at operating temperature 10 7 The bending fatigue strength (MPa) of the secondary symmetric cycle is taken as the lowest value
D: the outer diameter (mm) of the cross section where the shaft calculation point is located;
d: diameter (mm) of a test bar for fatigue test.
2.2 equivalent steady stress σ' eq under combination of major and minor cycles (high and low cycles)
By means of 10 7 Subsycle corrected Goodman diagram (see FIG. 3) as equivalent steady state stress σ 'at N primary cycles' eq As the constant stress of the high-frequency load, the equivalent steady-state stress sigma 'under the composite of the main and secondary cyclic (high and low cycle) loads is obtained by using the stress generated by the vibration torque and the bending moment as the alternating amplitude' eq (MPa), calculated according to equation (5):
Figure 418775DEST_PATH_IMAGE091
（5）
wherein the content of the first and second substances,
Figure 240101DEST_PATH_IMAGE092
for the sub-cycle (high cycle) load stress,
Figure 385911DEST_PATH_IMAGE093
Is an effective stress concentration coefficient (fatigue notch coefficient),
Figure 292687DEST_PATH_IMAGE039
Is 10 7 Symmetric bending fatigue strength under the second cycle.
Thus, subjected to N main cycles (low cycles),10 7 The equivalent steady-state stress of 6 local stress components of the on-axis check point under the load of the second cycle (high cycle) is respectively as follows:
Figure 713304DEST_PATH_IMAGE094
（9）
in the formula:
Figure 389136DEST_PATH_IMAGE010
is the equivalent steady-state stress in the x direction under a cylindrical coordinate system,
Figure 469962DEST_PATH_IMAGE011
Is the equivalent steady-state stress in the y direction under a cylindrical coordinate system,
Figure 864035DEST_PATH_IMAGE012
Is the equivalent steady state stress in the z direction under a cylindrical coordinate system,
Figure 291605DEST_PATH_IMAGE013
Is the equivalent steady-state stress in the xy direction under a cylindrical coordinate system,
Figure 87523DEST_PATH_IMAGE014
Is the equivalent steady-state stress in the yz direction under a cylindrical coordinate system,
Figure 840715DEST_PATH_IMAGE015
Is the equivalent steady state stress in the xz direction under a cylindrical coordinate system;
Figure 456504DEST_PATH_IMAGE016
is the main cyclic stress of the x direction under a cylindrical coordinate system,
Figure 687765DEST_PATH_IMAGE011
Is the main cyclic stress in the y direction under a cylindrical coordinate system,
Figure 102304DEST_PATH_IMAGE012
Is the main cyclic stress in the z direction under the cylindrical coordinate system,
Figure 26398DEST_PATH_IMAGE013
Is the main cyclic stress in the xy direction under the cylindrical coordinate system,
Figure 395062DEST_PATH_IMAGE014
Is the main cyclic stress of yz direction under a cylindrical coordinate system,
Figure 430014DEST_PATH_IMAGE015
Is the main cyclic stress in the xz direction under the cylindrical coordinate system;
Figure 934945DEST_PATH_IMAGE022
torsional fatigue strength for N cycles (N = lgN),
Figure 29940DEST_PATH_IMAGE023
Is 10 7 Torsional fatigue strength of the secondary cycle,
Figure 354742DEST_PATH_IMAGE024
Is the torsional strength;
K t,x 、K t,y 、K t,z 、K t,xy 、K t,yz 、K t,xz -6 stress components are respectively under the respective effect of the respective theoretical stress concentration coefficients.
K f,x 、K f,y 、K f,z 、K f,xy 、K f,yz 、K f,xz -6 stress components are respectively applied to respective effective stress concentration coefficients.
K f,n,x 、K f,n,y 、K f,n,z 、K f,n,xy 、K f,n,yz 、K f,n,xz -the effective stress concentration coefficients for the respective 6 stress components under N cycles (x = lgN) are calculated as follows:
Figure 193385DEST_PATH_IMAGE095
……（10）
2.3 equivalent steady state stress calculation
According to a fourth intensity theory, the equivalent steady-state stress of six stress components of the assessment point is calculated to obtain the point subjected to N times of main cycles (low cycles) and 10 times of main cycles (low cycles) 7 The equivalent steady state stress for the next (high cycle) cycle load is calculated as:
Figure 340374DEST_PATH_IMAGE096
（11）
in the formula:
Figure 606270DEST_PATH_IMAGE026
is the equivalent steady state stress under the composite load of the main cycle and the secondary cycle (high cycle and low cycle).
3. Fatigue life damage analysis
3.1 value of dispersion coefficient
The dispersion coefficient includes an ultimate strength dispersion coefficient u and a fatigue ultimate strength dispersion coefficient f x 。
The ultimate strength dispersion coefficient u is independent of the frequency of action, and is generally 1.1 for forgings.
Fatigue limit strength dispersion coefficient f x (subscript x = lgN, N is cycle number) Depending on the processing technology, the service cycle life and the like of the component, the low-pressure turbine shaft is generally processed by a forging at present, so f x The relationship between x (x = lgN) and x (x = lgN) can be expressed as follows:
Figure 949527DEST_PATH_IMAGE097
（12）
3.2 equivalent steady state stress sigma s, eq under the primary and secondary circulation (high and low cycle) composition of the shaft test piece
The formula (11) is corrected (by sigma) by adopting 3.1 sections of dispersion coefficient values b U replaces sigma b ，σ -1,x /f x Instead of sigma -1,x ，σ -1,6 /f 5 In place of sigma -1,6 ) Meanwhile, the stress concentration coefficients of the high/low circumference stress components are respectively taken as the stress concentration coefficients of the high/low circumference equivalent stress, and the primary and secondary stress of the shaft test piece can be obtainedEquivalent steady state stress sigma under cycle (high and low cycle) compounding s,eq (MPa) see formula (13), and similarly, parameter f 'is introduced' R The fatigue reserve coefficient K of the shaft test piece can be deduced ' The calculation formula is as follows (14).
Figure 326282DEST_PATH_IMAGE098
（13）
Figure 71384DEST_PATH_IMAGE099
（14）
In the formula:
Figure 242602DEST_PATH_IMAGE029
local stress under main cycle (low cycle) load,
Figure 541996DEST_PATH_IMAGE030
Local stress under sub-cycle (high cycle) load,
Figure 722442DEST_PATH_IMAGE031
Is the theoretical stress concentration coefficient under the main cycle (low cycle) load,
Figure 820586DEST_PATH_IMAGE032
Is the theoretical stress concentration coefficient under the sub-cycle (high cycle) load,
Figure 428285DEST_PATH_IMAGE033
Effective stress concentration coefficient (fatigue notch coefficient) for N cycles (N = lgN) under main cycle (low cycle) load,
Figure 480554DEST_PATH_IMAGE034
Is the effective stress concentration coefficient under the secondary cycle load,
Figure 464691DEST_PATH_IMAGE035
Is 10 x Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 918806DEST_PATH_IMAGE036
Is 10 5 The fatigue ultimate strength dispersion coefficient at the time of the secondary cycle, u is the ultimate strength dispersion coefficient,
Figure 697406DEST_PATH_IMAGE037
The tensile strength,
Figure 971392DEST_PATH_IMAGE038
Is 10 x Symmetric bending fatigue strength at the time of secondary cycle,
Figure 228061DEST_PATH_IMAGE039
Is 10 7 Symmetric bending fatigue strength under secondary cycle;
f' R is the ratio of the nominal equivalent stresses of the secondary cycle and the primary cycle (high and low cycles). The calculation formula is as follows:
Figure 35218DEST_PATH_IMAGE100
（15）
wherein the content of the first and second substances,
Figure 984720DEST_PATH_IMAGE057
nominal equivalent stress under main cycle (low cycle) load,
Figure 11581DEST_PATH_IMAGE101
Nominal equivalent stress under sub-cycle (high cycle) load,
Figure 337521DEST_PATH_IMAGE029
Local stress under main cycle (low cycle) load,
Figure 766228DEST_PATH_IMAGE030
In the form of partial stress under subcycle (high cycle) load
Figure 152210DEST_PATH_IMAGE031
Is the theoretical stress concentration coefficient under the main cycle (low cycle) load,
Figure 400789DEST_PATH_IMAGE032
Is the theoretical stress concentration coefficient under sub-cycle (high cycle) loading.
3.3 Fatigue life
Fatigue reserve coefficient K of shaft test piece ' When the value is 1, lg (sigma) after logarithm of nominal equivalent stress is obtained m ) The relationship with x (x = lgN) is as follows:
when x is less than or equal to 3:
Figure 264839DEST_PATH_IMAGE102
；
when 3 < x < 4:
Figure 813632DEST_PATH_IMAGE042
；
when x = 4:
Figure 603472DEST_PATH_IMAGE043
；
when 4 < x < 5:
Figure 339346DEST_PATH_IMAGE044
；
when x = 5:
Figure 7088DEST_PATH_IMAGE103
；
when x is more than 5 and less than or equal to 6:
Figure 144808DEST_PATH_IMAGE104
；
when x is more than or equal to 6:
Figure 872593DEST_PATH_IMAGE105
；(16)
wherein the content of the first and second substances,
Figure 95764DEST_PATH_IMAGE057
nominal equivalent stress under main cycle (low cycle) load,
Figure 567197DEST_PATH_IMAGE048
Effective stress concentration coefficient (fatigue notch coefficient) under main cycle (low cycle) load,
Figure 825003DEST_PATH_IMAGE034
Effective stress concentration coefficient (fatigue notch coefficient) under the sub-cycle (high-cycle) load,
Figure 458109DEST_PATH_IMAGE033
Effective stress concentration coefficient (fatigue notch coefficient) of N times of cycles (N = lgN) under main cycle (low cycle) load,
Figure 667111DEST_PATH_IMAGE048
Is the effective stress concentration coefficient under the main cyclic load,
Figure 676656DEST_PATH_IMAGE035
Is 10 x Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 788968DEST_PATH_IMAGE106
Is 10 4 Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 858555DEST_PATH_IMAGE036
Is 10 5 Fatigue ultimate strength Dispersion coefficient at Secondary cycle, f' R Is the ratio of the nominal equivalent stresses of the minor cycle and the major cycle (high and low cycles), u is the ultimate strength dispersion coefficient,
Figure 56319DEST_PATH_IMAGE037
The tensile strength,
Figure 869554DEST_PATH_IMAGE038
Is 10 x The symmetric bending fatigue strength of the secondary cycle,
Figure 570794DEST_PATH_IMAGE039
Is 10 7 Symmetric bending fatigue strength under secondary cycle,
Figure 811282DEST_PATH_IMAGE107
Is 10 6 Symmetric bending fatigue strength under the second cycle.
According to lg (sigma) m,L ) And x (x = lgN), and the turning point (when x =3, σ) in the relational expression is taken m,L =σ 3 (ii) a x =4, σ m,L =σ 4 (ii) a x =5, σ m,L =σ 5 (ii) a x =6, σ m,L =σ 6 ) And complements the approximation hypothesis: x =0, σ max,L =σ 0 =σ b And u is the ratio of the sum of the total weight of the components. Instant messenger
Figure 496341DEST_PATH_IMAGE049
；
Figure 113267DEST_PATH_IMAGE108
；
Figure 433128DEST_PATH_IMAGE109
；
Figure 110097DEST_PATH_IMAGE110
；
Figure 16873DEST_PATH_IMAGE111
。(17)
Wherein, the first and the second end of the pipe are connected with each other,
Figure 171911DEST_PATH_IMAGE057
nominal equivalent stress under main cycle (low cycle) load,
Figure 847743DEST_PATH_IMAGE048
Effective stress concentration coefficient (fatigue notch coefficient) under main cycle (low cycle) load,
Figure 695613DEST_PATH_IMAGE034
Effective stress concentration coefficient (fatigue notch coefficient) under the sub-cycle (high-cycle) load,
Figure 89685DEST_PATH_IMAGE033
Effective stress concentration coefficient (fatigue notch coefficient) of N times of cycles (N = lgN) under main cycle (low cycle) load,
Figure 48414DEST_PATH_IMAGE035
Is 10 x Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 844332DEST_PATH_IMAGE106
Is 10 4 Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 331945DEST_PATH_IMAGE036
Is 10 5 Fatigue ultimate strength Dispersion coefficient at Secondary cycle, f' R Is the ratio of the nominal equivalent stresses of the minor cycle and the major cycle (high and low cycles), u is the ultimate strength dispersion coefficient,
Figure 711849DEST_PATH_IMAGE037
The tensile strength,
Figure 208689DEST_PATH_IMAGE038
Is 10 x The symmetric bending fatigue strength of the secondary cycle,
Figure 859113DEST_PATH_IMAGE039
Is 10 7 Symmetric bending fatigue strength under the second cycle,
Figure 48786DEST_PATH_IMAGE107
Is 10 6 Symmetric bending fatigue strength under sub-cycle、
Figure 151871DEST_PATH_IMAGE054
Is the nominal equivalent stress at 0 cycles.
Assuming that linear interpolation is performed between the turning points, a calculation formula of the fatigue life N after logarithm (x = lgN) is obtained can be derived as shown in the following formula.
Figure 452403DEST_PATH_IMAGE112
（18）
Wherein the content of the first and second substances,
Figure 222912DEST_PATH_IMAGE056
actual stress under a main cycle (low cycle) load,
Figure 317907DEST_PATH_IMAGE057
Nominal equivalent stress under main cycle (low cycle) load,
Figure 908289DEST_PATH_IMAGE058
Is 10 3 Nominal equivalent stress at the second cycle,
Figure 511046DEST_PATH_IMAGE059
Is 10 4 Nominal equivalent stress at the second cycle,
Figure 136063DEST_PATH_IMAGE060
Is 10 5 Nominal equivalent stress at the second cycle,
Figure 401959DEST_PATH_IMAGE061
Is 10 6 Nominal equivalent stress at sub-cycle.
3.4 Cumulative damage
Assuming that the major-minor cycle (high-low cycle) composite stress spectrum of the shaft danger section is as follows: under the composite load of primary and secondary cycles (high and low cycles), ("0-sigma") m,L -0') main (low-cycle) cyclic stressing n cycles, nominal alternating stress amplitude of the sub-cycles (high-cycle) "±σ m,H Action 10 7 And (5) circulating above. The linear cumulative damage (D) under the load spectrum is calculated and evaluated according to equation (19).
Figure 479636DEST_PATH_IMAGE062
…………………………………（19）
Wherein N is the actual cycle number of the main cycle which the low-pressure turbine shaft passes through, and N is the service life of the main cycle under the composite load spectrum.
Assuming that the number of main and sub-cycle (high and low cycles) composite stress spectra of the axial risk section is k, the actual cycle number of the main cycle (low cycle) of the ith composite stress spectrum is n i . The main cycle (low cycle) life N of the ith composite stress spectrum can be respectively calculated according to the formula (18) i . The total linear cumulative damage (D) of the k composite stress spectra is calculated and evaluated according to equation (20).
Figure 856391DEST_PATH_IMAGE063
…………………………………………（20）
The embodiment of the invention has the following beneficial effects:
based on the finite element calculation result, all load (including bending moment load and the like) types born by the shaft can be considered, and the local stress of all key sections can be obtained simultaneously;
introducing an ultimate strength dispersion coefficient u and a fatigue ultimate strength dispersion coefficient f x The influence of material performance dispersity is considered, and the method can be used for designing the strength of the initial low-pressure turbine shaft and ensuring the reliability of structural design;
a fatigue life rapid calculation formula is established, and the fatigue life rapid calculation formula can be used for evaluating the accumulated damage of a plurality of continuous load spectrums based on a linear accumulated damage theory;
the method has the advantages that the material data value taking requirement is clear, the calculation process can be intelligentized through programming, and the design efficiency of the composite fatigue of the shaft is high.
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 (3)

1. A spindle composite fatigue life analysis method considering dispersion coefficients and multi-axis loads is characterized by comprising the following steps:
step one, carrying out finite element calculation on a low-pressure turbine shaft;
step two, obtaining equivalent steady state stress sigma 'of six components in the main cycle' eq And equivalent steady state stress sigma 'of six components under primary and secondary cycle compounding' eq And calculating the equivalent steady-state stress;
thirdly, taking values of the dispersion coefficient by adopting a setting method to obtain the equivalent steady-state stress sigma of the shaft test piece under the primary and secondary circulation compounding s,eq And carrying out fatigue life damage analysis;
the first step specifically comprises the following steps: establishing a lower shaft finite element model under corresponding load according to the low-cycle steady-state load and the high-cycle load borne by the low-pressure turbine shaft, and obtaining a strength calculation result;
the second step comprises a step 2.1: using the Goodman diagram corrected by the number of main cycles, from 0 to
Figure 717835DEST_PATH_IMAGE001
Is converted into equivalent steady state stress
Figure 692744DEST_PATH_IMAGE002
Wherein
Figure 502437DEST_PATH_IMAGE003
Is the main cyclic load stress component, K t Is the theoretical stress concentration coefficient;
the step 2.1 specifically comprises the following steps: by the formula
Figure 853784DEST_PATH_IMAGE004
Calculating the conversion of the main cyclic stress into the equivalent steady state stress
Figure 799743DEST_PATH_IMAGE005
In which K is t Is theoretical stress concentration coefficient, K f,n Effective stress concentration coefficient under N times of circulation,
Figure 211133DEST_PATH_IMAGE006
Is the lowest tensile strength of the material at the working temperature,
Figure 242543DEST_PATH_IMAGE007
Symmetric bending fatigue strength for N cycles,
Figure 132002DEST_PATH_IMAGE008
Is the main cyclic load stress component;
step two also includes step 2.2: by means of 10 7 Sub-cycle corrected Goodman diagram, in terms of equivalent steady state stress at the primary cycle σ' eq The equivalent steady state stress sigma 'under the combination of the primary and secondary cyclic loads is obtained as the constant stress of the high frequency load by using the stress generated by the vibration torque and the bending moment as alternating amplitude' eq ；
The step 2.2 specifically comprises the following steps:
by the formula
Figure 696582DEST_PATH_IMAGE009
Obtaining the equivalent steady state stress sigma 'under the combination of the primary and secondary cyclic loads' eq Where σ is H High cyclic load stress, K for a secondary cycle f Is the effective stress concentration coefficient, sigma -1.7 Is 10 7 Symmetric bending fatigue strength under the secondary cycle;
equivalent steady state stress is obtained for six local stress components:
Figure 13294DEST_PATH_IMAGE010
；
wherein the content of the first and second substances,
Figure 532000DEST_PATH_IMAGE011
is the equivalent steady-state stress in the x direction under a cylindrical coordinate system,
Figure 225149DEST_PATH_IMAGE012
Is the equivalent steady-state stress in the y direction under a cylindrical coordinate system,
Figure 286646DEST_PATH_IMAGE013
Is the equivalent steady state stress in the z direction under a cylindrical coordinate system,
Figure 164472DEST_PATH_IMAGE014
Is the equivalent steady-state stress in the xy direction under a cylindrical coordinate system,
Figure 45841DEST_PATH_IMAGE015
Is the equivalent steady state stress in the yz direction under a cylindrical coordinate system,
Figure 401736DEST_PATH_IMAGE016
Is the equivalent steady-state stress in the xz direction under the cylindrical coordinate system;
Figure 52160DEST_PATH_IMAGE017
is the main cyclic stress of the x direction under a cylindrical coordinate system,
Figure 602352DEST_PATH_IMAGE018
Is the main cyclic stress in the y direction under a cylindrical coordinate system,
Figure 971016DEST_PATH_IMAGE019
Is the main cyclic stress in the z direction under the cylindrical coordinate system,
Figure 130602DEST_PATH_IMAGE020
Is the main cyclic stress in the xy direction under the cylindrical coordinate system,
Figure 635533DEST_PATH_IMAGE021
Is the main cyclic stress of yz direction under a cylindrical coordinate system,
Figure 855162DEST_PATH_IMAGE022
Is the main cyclic stress in the xz direction under the cylindrical coordinate system;
Figure 711122DEST_PATH_IMAGE023
torsional fatigue strength for N cycles,
Figure 674399DEST_PATH_IMAGE024
Is 10 7 Torsional fatigue strength of the secondary cycle,
Figure 299416DEST_PATH_IMAGE025
Is the torsional strength;
K t,x 、K t,y 、K t,z 、K t,xy 、K t,yz 、K t,xz the other theoretical stress concentration coefficients are respectively acted by the six stress components;
K f,x 、K f,y 、K f,z 、K f,xy 、K f,yz 、K f,xz the effective stress concentration coefficients of the six stress components under the action of the six stress components respectively;
K f,n,x 、K f,n,y 、K f,n,z 、K f,n,xy 、K f,n,yz 、K f,n,xz effective stress concentration coefficients of the six stress components under the action of N cycles respectively;
step two also includes step 2.3: the equivalent steady state stress of the point subjected to N times of main cycles and 10 times of main cycles is calculated through six stress components 7 Equivalent steady state stress of sub-high cycle load
Figure 922902DEST_PATH_IMAGE026
；
Wherein the content of the first and second substances,
Figure 266158DEST_PATH_IMAGE027
the equivalent steady state stress under the primary and secondary cycle composite load;
step three comprises step 3.1:
when the dispersion coefficient is the ultimate strength dispersion coefficient u, the value is 1.1;
when the dispersion coefficient is the fatigue limit strength dispersion coefficient f x By the formula
Figure 33126DEST_PATH_IMAGE028
Obtaining;
step three comprises step 3.2:
by the formula
Figure 512649DEST_PATH_IMAGE029
Calculating and obtaining equivalent steady-state stress sigma of the shaft test piece under the primary and secondary circulation compounding s,eq Wherein, in the step (A),
Figure 74080DEST_PATH_IMAGE030
local stress under main cyclic load,
Figure 639054DEST_PATH_IMAGE031
Local stress under the sub-cycle load,
Figure 678554DEST_PATH_IMAGE032
Is the theoretical stress concentration coefficient under the main cyclic load,
Figure 278162DEST_PATH_IMAGE033
Is the theoretical stress concentration coefficient under the sub-cycle load,
Figure 511960DEST_PATH_IMAGE034
Effective stress concentration coefficient of N times of circulation under main circulation load,
Figure 829809DEST_PATH_IMAGE035
Under the load of a secondary cycle ofEffective stress concentration coefficient,
Figure 548366DEST_PATH_IMAGE036
Is 10 x Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 127115DEST_PATH_IMAGE037
Is 10 5 The fatigue ultimate strength dispersion coefficient at the time of the secondary cycle, u is the ultimate strength dispersion coefficient,
Figure 905715DEST_PATH_IMAGE038
Is the tensile strength,
Figure 569915DEST_PATH_IMAGE039
Is 10 x Symmetric bending fatigue strength in the secondary cycle,
Figure 92163DEST_PATH_IMAGE040
Is 10 7 Symmetric bending fatigue strength under the secondary cycle;
by the formula
Figure 525418DEST_PATH_IMAGE041
Calculating and obtaining a fatigue reserve coefficient K 'of the shaft test piece, wherein f' R Is the ratio of the nominal equivalent stresses of the secondary cycle and the primary cycle.
2. The method for analyzing the composite fatigue life of the main shaft in consideration of the dispersion coefficient and the multi-axial load according to claim 1, wherein the third step includes a step 3.3:
when the fatigue storage coefficient K' of the shaft test piece is 1, lg (sigma) after logarithm of nominal equivalent stress is taken m,L ) A formula for calculating a relation with x (x = lgN) and obtaining a logarithmic value of fatigue life N (x = lgN) is as follows:
when x is less than or equal to 3:
Figure 474920DEST_PATH_IMAGE042
；
when 3 < x < 4:
Figure 859371DEST_PATH_IMAGE043
；
when x = 4:
Figure 185310DEST_PATH_IMAGE044
；
when 4 < x < 5:
Figure 473072DEST_PATH_IMAGE045
；
when x = 5:
Figure 593475DEST_PATH_IMAGE046
；
when x is more than 5 and less than or equal to 6:
Figure 232267DEST_PATH_IMAGE047
；
when x is more than or equal to 6:
Figure 96318DEST_PATH_IMAGE048
；
wherein the content of the first and second substances,
Figure 238586DEST_PATH_IMAGE030
local stress under the main cyclic load,
Figure 795469DEST_PATH_IMAGE031
Is the local stress under the sub-cycle load,
Figure 157443DEST_PATH_IMAGE032
Is the theoretical stress concentration coefficient under the main cyclic load,
Figure 559605DEST_PATH_IMAGE033
Is the theoretical stress concentration coefficient under the sub-cycle load,
Figure 821959DEST_PATH_IMAGE034
Effective stress concentration coefficient of N times of circulation under main circulation load,
Figure 549744DEST_PATH_IMAGE049
Is the effective stress concentration coefficient under the main cyclic load,
Figure 631969DEST_PATH_IMAGE036
Is 10 x Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 103402DEST_PATH_IMAGE037
Is 10 5 The fatigue ultimate strength dispersion coefficient at the time of the secondary cycle, u is the ultimate strength dispersion coefficient,
Figure 485842DEST_PATH_IMAGE038
The tensile strength,
Figure 118948DEST_PATH_IMAGE039
Is 10 x Symmetric bending fatigue strength in the secondary cycle,
Figure 452584DEST_PATH_IMAGE040
Is 10 7 Symmetric bending fatigue strength under the secondary cycle;
Figure 462129DEST_PATH_IMAGE050
；
Figure 433496DEST_PATH_IMAGE051
；
Figure 768662DEST_PATH_IMAGE052
；
Figure 700846DEST_PATH_IMAGE053
；
Figure 638715DEST_PATH_IMAGE054
；
wherein, the first and the second end of the pipe are connected with each other,
Figure 871113DEST_PATH_IMAGE030
local stress under the main cyclic load,
Figure 970656DEST_PATH_IMAGE031
Local stress under the sub-cycle load,
Figure 655716DEST_PATH_IMAGE032
Is the theoretical stress concentration coefficient under the main cycle load,
Figure 633161DEST_PATH_IMAGE033
Is the theoretical stress concentration coefficient under the sub-cycle load,
Figure 454487DEST_PATH_IMAGE034
Effective stress concentration coefficient of N times of circulation under main circulation load,
Figure 724931DEST_PATH_IMAGE036
Is 10 x Fatigue limit strength dispersion coefficient at the time of secondary cycle,
Figure 631707DEST_PATH_IMAGE037
Is 10 5 The fatigue ultimate strength dispersion coefficient at the time of the second cycle, u being the ultimate strength dispersion coefficient、
Figure 911379DEST_PATH_IMAGE038
Is the tensile strength,
Figure 587211DEST_PATH_IMAGE039
Is 10 x Symmetric bending fatigue strength at the time of secondary cycle,
Figure 435081DEST_PATH_IMAGE040
Is 10 7 Symmetric bending fatigue strength under the second cycle,
Figure 953787DEST_PATH_IMAGE055
Nominal equivalent stress at 0 cycles;
Figure 646936DEST_PATH_IMAGE056
；
wherein, the first and the second end of the pipe are connected with each other,
Figure 823881DEST_PATH_IMAGE057
is the actual stress under the main cyclic load,
Figure 701707DEST_PATH_IMAGE058
Is the nominal equivalent stress under the main cyclic load,
Figure 583076DEST_PATH_IMAGE059
Is 10 3 Nominal equivalent stress at the second cycle,
Figure 79916DEST_PATH_IMAGE060
Is 10 4 Nominal equivalent stress at the second cycle,
Figure 854974DEST_PATH_IMAGE061
Is 10 5 Nominal equivalent stress at the second cycle,
Figure 638122DEST_PATH_IMAGE062
Is 10 6 Nominal equivalent stress at sub-cycle.
3. The method for analyzing the composite fatigue life of the main shaft considering the dispersion coefficient and the multi-axial load as claimed in claim 2, wherein the step three includes a step 3.4:
calculating linear accumulated damage of a low-pressure turbine shaft under single primary and secondary cycle composite load
Figure 272366DEST_PATH_IMAGE063
Wherein N is the actual cycle number of the main cycle experienced by the low-pressure turbine shaft, and N is the service life of the main cycle under the composite load spectrum;
calculating the overall linear accumulated damage of the low-pressure turbine shaft under the composite load of a plurality of primary and secondary cycles
Figure 307318DEST_PATH_IMAGE064
Wherein k is the number of primary and secondary cycle composite stress spectrums of the shaft dangerous section, n i Actual number of cycles of the main cycle, N, for a composite stress spectrum i Is the calculated main cycle life of the ith composite stress spectrum.
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