CN109271713A - Consider the Gear Contact fatigue analysis method of crystal microstructure mechanics - Google Patents
Consider the Gear Contact fatigue analysis method of crystal microstructure mechanics Download PDFInfo
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Abstract
The invention discloses a kind of Gear Contact fatigue analysis methods for considering crystal microstructure mechanics, comprising the following steps: two-dimensional plain strain finite element model is established using ABAQUS platform in 1, the geometric parameter by using gear pair at node;2, the grain size image of gear material different depth position is observed using microscope;3, the crystal microstructure distribution map being distributed using MATLAB Software Create crystal microstructure size along concentration gradient, while crystal microstructure distribution being added in the two-dimensional plain strain finite element model of step 1;4, the fatigue damage under a certain load-up condition is calculated using Fatemi-Socie non-proportional loading criterion, obtains the fatigue damage value at any point of critical contact areas.The solution have the advantages that: Gear Contact Fatigue Failures under conditions of considering crystal microstructure mechanics are able to solve, the loss of the productivity effect as caused by Gear Contact fatigue failure is reduced.
Description
Technical field
The invention belongs to the analysis methods of component of machine contact fatigue failure, and in particular to a kind of consideration crystal microstructure
The gear pair contact fatigue analysis method of mechanics.
Background technique
Contact fatigue failure is a kind of typical failure form of component of machine, and contact fatigue Problem of Failure has become limit
Gear processed drives mechanical equipment Reliability, the principal element of man-machine safety and economic benefit.The contact fatigue problem of gear is
Through widely being studied at many aspects, such as operating condition factor, material factor.But existing research remains in macroscopic aspect,
For generally believing that it is less that important microcosmic crystal microstructure understands, the Gear Contact analysis of fatigue of engineering in practice is resulted in still
So there is very big difficulty.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of Gear Contact fatigues for considering crystal microstructure mechanics point
Analysis method, it can analyze contact fatigue Problem of Failure of gear under conditions of considering crystal microstructure mechanics, help to establish
Microcosmic crystal microstructure is contacted with Gear Contact fatigue failure, analysis result obtained engineering in practice, to gear
Anti- contact fatigue failure Design has directive function, reduces accident and economic loss caused by Gear Contact fatigue failure.
The technical problem to be solved by the present invention is in this way technical solution realize, it the following steps are included:
Step 1, the geometric parameter by using gear pair at node establish two dimensional plane strain using ABAQUS platform
Finite element model;
Step 2, the grain size image that gear material is observed using microscope determine crystal microstructure in different depth position
The size set;
Step 3 is distributed using MATLAB Software Create crystal microstructure size along the crystal microstructure that concentration gradient is distributed
Figure, while crystal microstructure distribution being added in two-dimensional plain strain finite element model;
Step 4 calculates the fatigue damage under a certain load-up condition using Fatemi-Socie non-proportional loading criterion, obtains pass
Fatigue damage value at any point of key contacts region judges Gear Contact fatigue failure position by maximum fatigue damage value.
The solution have the advantages that:
The contact fatigue Problem of Failure that gear is analyzed under conditions of considering crystal microstructure mechanics is the anti-contact of gear
Fatigue manufacture provides theory support, reduces engineering in practice by Gear Contact fatigue failure bring accident and economic loss.
Detailed description of the invention
Detailed description of the invention of the invention is as follows:
Fig. 1 is the rough schematic view that gear engages contact condition;
Fig. 2 is the gear material grain size image in embodiment under the different depth of microscopic;
Fig. 3 is the crystal microstructure distribution map generated in embodiment;
Fig. 4 is the two-dimensional plain strain finite element model for being added to crystal microstructure;
Fig. 5 is two-dimensional plain strain finite element model boundary condition and load schematic diagram in embodiment;
Fig. 6 is the kinematic scheme of certain megawatt wind power gear case in embodiment;
Fig. 7 is the contact fatigue impairment value distribution map of the gear material in embodiment.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples:
The present invention the following steps are included:
The contact condition of step 1, gear at node can simplify as two-dimensional plain strain finite element model, simplified process
As shown in Figure 1, left side (a) is that node location contacts gear schematic diagram, right side (b) is that equivalent obtained rigid semicircle and flexibility are flat
The two-dimensional plain strain finite element model in face.It is computable flat to the two dimension according to Hertzian contact theory and gear actual condition
Face strains the parameter of finite element model, the calculating process are as follows:
R=r1r2/(r1+r2) (1)
In formula (1) and (2), r1, r2For the radius of curvature of two Gear Contact positions, r is two-dimensional plain strain finite element model
Composite curve radius, E1, E2For the elasticity modulus of two gears, E is the Equivalent Elasticity mould of two-dimensional plain strain finite element model
Amount, υ1, υ2For the Poisson's ratio of two gears."AGMA information sheet 908-B89,1989."Geometry
factors for determining the pitting resistance and bending strength of spur,
Helical and herringbone gear teeth " " (U.S.'s standards for gears 1989 " judgement spur gear, helical gear,
The pitting corrosion resistant performance of the double helical spurgear gear teeth and the geometry impact factor of bending strength ") at the 5-7 pages describe r1, r2, meter
Calculation method.
Step 2, the grain size image that gear material is observed using microscope determine crystal microstructure in different depth position
The size set.The grain size image that microscope is observed in different depth position as shown in Fig. 2, choose six depth positions respectively
It sets and is observed.
Step 3 generates crystal using MATLAB software (MPT) the multi-parameter tool box Multi Parametric Toolbox
The crystal microstructure distribution map that microstructure size is distributed along concentration gradient.In this step, first by being obtained not in step 2
Crystal microstructure average diameter with depth location determines crystal microstructure center point coordinate, and the seat is inputted in MATLAB software
Mark;Second, input the boundary of rectangular crystal micro-structure in MATLAB software, the size on the boundary according to research it needs to be determined that;
Crystal microstructure distribution map is obtained finally, calculating automatically by multi-parameter tool box.Crystal microstructure distribution map after generation is such as
Shown in Fig. 3, Fig. 3's vertically represents depth direction.Crystal microstructure distribution is added to the two dimensional plane strain finite element of step 1
In model, two-dimensional plain strain finite element model after addition as shown in figure 4, wherein Coordinate Setting is that x represents rotating direction,
Y represents the opposite direction of depth direction.
Fig. 5 show the loading method and boundary condition of two-dimensional plain strain finite element model, the perimeter strip of the model
Part is fixed for bottom edge.The rectangle of 2mm × 3mm is chosen in the model as critical material region, adds crystal microstructure.Rigidity
Semicircle is moved to x=4mm from x=-4mm in calculating, simulates being in rolling contact for gear with this.
Step 4, according to A.Fatemi and D.F.Socie in paper " A critical plane approach to
multiaxial fatigue damage including out-of-phase loading",Fatigue&Fracture of
(" research includes Nonproportional Loading state by Engineering Materials&Structures, 11 (1988) 149-165.
Multiaxial Fatigue Damage critical plane method ", the fatigue and fracture of engineering material and structure, volume 11,1988,149-
Page 165) in propose Fatemi-Socie non-proportional loading criterion calculate Gear Contact fatigue damage, the Fatemi-Socie multiaxis
Tired criterion are as follows:
DFS,max=max (DFS,i) (4)
D in formulaFS,iRepresent the fatigue damage value of i-th of slide surface, DFS,maxThe fatigue damage value of crystal microstructure is represented,
It is the maximum value of all slide surface fatigue damage values of crystal microstructure,It is the plasticity shearing strain amplitude on slide surface, i is represented
I-th of slide surface.Gear-used steels are typical BCC structures, include 6 { 110 } slide surfaces, each cunning in each crystal microstructure
There are two glide direction on shifting face, k ' represents material constant, σyRepresent yield strength, σnIndicate the mormal stress of slide surface, it should
The calculation method of direct stress are as follows:
σ in formulap(t) any tangent stress on slide surface, σ are indicatedxxFor the direction x direct stress, σyyIt is just answered for the direction y
Power, σzzFor the direction z direct stress, τxyFor x-y plane shearing stress, τxzFor x-z-plane shearing stress, τyzFor y-z plane shearing stress, nx,
ny,nzThe direction cosines of plane where slide surface.
Embodiment
It is illustrated in figure 6 the transmission system schematic diagram for the MW class wind turbine gear-box that the gear sample is on active service,
The sample is from intergrade gear pair, and in practical implementation, the probability of the gear stage failure where the sample gear is bright
It is aobvious to be higher than other gears.
The major parameter of gear pair is as follows:
Step 1, according to formula (1)~(2), by r1=49mm, r2=248mm finds out comprehensive bent in two dimensional touch model
Rate radius is r=40.91mm, by E1,2=2.10 × 1011It is E=1.15 × 10 that Pa, which can find out equivalent elastic modulus,11Pa.According to
The above parameter establishes the two-dimensional plain strain finite element model such as Fig. 1 (b) signal.In this embodiment, two dimensional plane strain has
The size for limiting the flexible flat of meta-model is defined as 20mm × 10mm, and the model after foundation is as shown in Figure 5.
Step 2, the grain size image that gear material is observed using microscope determine crystal microstructure in different depth position
The size set.Sample gear material is 18CrNiMo7-6 steel, is handled through over carburizing, quenching and grinding.Microscope is not
Grain size image with depth location observation is as shown in Figure 2.It chooses six depth locations respectively to be observed, this six observation bits
Set is surface region respectively, at depth 0.4mm, at depth 0.8mm, at depth 1.2mm, at depth 1.6mm and depth 2.0mm
Place.As seen from the figure, the crystal microstructure diameter at surface is averagely about 15um, and depth is the crystal microstructure diameter at 2.0mm
It is averagely about 55um.
Step 3 is distributed using MATLAB Software Create crystal microstructure size along the crystal microstructure that concentration gradient is distributed
Figure, wherein the average diameter of crystal microstructure is determined according to the observation in step 2, guarantees the crystal microstructure model generated more
Close to truth, the crystal microstructure distribution map after generation is as shown in Figure 3.Crystal microstructure distribution is added to step 1
In two-dimensional plain strain finite element model, the two-dimensional plain strain finite element model after addition is as shown in Figure 4.
Step 4, according to the calculated result of step 3 two-dimensional plain strain finite element model, calculated according to formula (3)-formula (6)
Contact fatigue damage of the gear in the case where considering crystal microstructure mechanical state out.Its calculated result is as shown in Figure 7, it can be seen that
In the case where considering crystal microstructure mechanical state, gear material damages below surface has dispersibility, and maximum impairment value is 3.6
×10-3, maximum damage position is in the generation of depth about 1mm left-right position.
Document " N.K.Arakere, N.Branch, G.Levesque, V.Svendsen, and N.H.Forster, "
Rolling Contact Fatigue Life and Spall Propagation Characteristics of AISI
M50, " 2014. " (N.K.Arakere, N.Branch, G.Levesque, V.Svendsen, and N.H.Forster, " AISI
The rolling contact fatigue life and peeling feature of M50, " 2014 years) in the contact surface crystal below that is arrived by experimental observation
Damage of the micro-structure under rolling contact fatigue state is consistent with distribution of results trend of the invention, is demonstrated with this of the invention
Reliability.
Claims (3)
1. considering the Gear Contact fatigue analysis method of crystal microstructure mechanics, characterized in that the following steps are included:
It is limited to establish two dimensional plane strain using ABAQUS platform for step 1, the geometric parameter by using gear pair at node
Meta-model;
Step 2, the grain size image that gear material is observed using microscope, determine crystal microstructure in different depth position
Size;
Step 3, the crystal microstructure distribution map being distributed using MATLAB Software Create crystal microstructure size along concentration gradient, together
When by crystal microstructure distribution be added in two-dimensional plain strain finite element model;
Step 4 calculates the fatigue damage under a certain load-up condition using Fatemi-Socie non-proportional loading criterion, show that key connects
Fatigue damage value at touching region any point judges Gear Contact fatigue failure position by maximum fatigue damage value.
2. the Gear Contact fatigue analysis method according to claim 1 for considering crystal microstructure mechanics, characterized in that
In step 1, the calculation method of the parameter of the two-dimensional plain strain finite element model are as follows:
R=r1r2/(r1+r2)
In formula, r1, r2For the radius of curvature of two Gear Contact positions, r is the synthetic curvature half of two-dimensional plain strain finite element model
Diameter, E1, E2For the elasticity modulus of two gears, E is the equivalent elastic modulus of two-dimensional plain strain finite element model, υ1, υ2For two teeth
The Poisson's ratio of wheel.
3. the Gear Contact fatigue analysis method according to claim 2 for considering crystal microstructure mechanics, characterized in that
In step 4, the Fatemi-Socie non-proportional loading criterion are as follows:
DFS,max=max (DFS,i)
D in formulaFS,iRepresent the fatigue damage value of i-th of slide surface, DFS,maxThe fatigue damage value for representing crystal microstructure is crystal
The maximum value of all slide surface fatigue damage values of micro-structure,It is the plasticity shearing strain amplitude on slide surface, i is represented i-th
Slide surface, gear-used steels are typical BCC structures, include 6 { 110 } slide surfaces, each slide surface in each crystal microstructure
Glide direction there are two upper, k ' represent material constant, σyRepresent yield strength, σnIndicate the mormal stress of slide surface, this is just answered
The calculation method of power are as follows:
σ in formulap(t) any tangent stress on slide surface, σ are indicatedxxFor the direction x direct stress, σyyFor the direction y direct stress,
σzzFor the direction z direct stress, τxyFor x-y plane shearing stress, τxzFor x-z-plane shearing stress, τyzFor y-z plane shearing stress, nx,ny,
nzThe direction cosines of plane where slide surface.
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Cited By (2)
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CN110807281A (en) * | 2019-10-30 | 2020-02-18 | 重庆大学 | Gear PSN curve drawing method considering material inclusions and residual stress |
CN110926942A (en) * | 2019-11-19 | 2020-03-27 | 西安理工大学 | Numerical analysis method for rolling contact fatigue cracks of rails in ABAQUS |
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Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
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CN110807281A (en) * | 2019-10-30 | 2020-02-18 | 重庆大学 | Gear PSN curve drawing method considering material inclusions and residual stress |
CN110807281B (en) * | 2019-10-30 | 2024-01-26 | 重庆大学 | Gear PSN curve drawing method considering material inclusion and residual stress |
CN110926942A (en) * | 2019-11-19 | 2020-03-27 | 西安理工大学 | Numerical analysis method for rolling contact fatigue cracks of rails in ABAQUS |
CN110926942B (en) * | 2019-11-19 | 2022-01-07 | 西安理工大学 | Numerical analysis method for rolling contact fatigue cracks of rails in ABAQUS |
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