CN109271711A - A kind of comentation hardening gear finite element modeling method considering uneven characteristic - Google Patents

A kind of comentation hardening gear finite element modeling method considering uneven characteristic Download PDF

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CN109271711A
CN109271711A CN201811112667.5A CN201811112667A CN109271711A CN 109271711 A CN109271711 A CN 109271711A CN 201811112667 A CN201811112667 A CN 201811112667A CN 109271711 A CN109271711 A CN 109271711A
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gear
finite element
residual stress
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hardness
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CN109271711B (en
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刘怀举
何海风
朱才朝
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Chongqing University
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    • 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
    • G06F30/00—Computer-aided design [CAD]
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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Abstract

The invention discloses a kind of comentation hardening gear finite element modeling method for considering uneven characteristic, it the following steps are included: 1, obtain the hardness gradient curve of comentation hardening gear；2, the initial residual stress under different depth is obtained；3, using Matlab numerical analysis software, the curvilinear equation of the gear profile is write, generates data point, imports Proe Software Create geometrical model, then geometrical model is imported into Abaqus finite element software；4, material is obtained with the yield limit curve of change in depth；5, by stress transmission method, the initial residual stress along gear-profile and facewidth direction measured is converted to the initial residual stress of the reference axis along finite element model；6, cutting and grid division are carried out to model, then imports the yield limit of gear and initial residual stress in the model of gear.The present invention solves the problems, such as the comentation hardening gear finite element modeling that foundation considers uneven characteristic, can improve the precision of finite element analysis.

Description

A kind of comentation hardening gear finite element modeling method considering uneven characteristic
Technical field
The invention belongs to gear technique fields, and in particular to a kind of comentation hardening gear finite element modeling method.
Background technique
With the continuous development of modern industry, mechanized equipment to the reliability requirements of the components of such as gear increasingly Height, so that comentation hardening has become most of transmission gear and has to the technique used, this is in heavy duty, high power density tooth It is especially apparent on wheel.On the one hand the hardness of gear surface and subsurface can be improved in comentation hardening, also can be on the other hand tooth Wheel introduces certain initial residual compression field, therefore can significantly improve the fatigue strength of gear, and then increase its service life. However, the model of gear established at present using finite element software, does not account for the gear caused by comentation hardening nearly all The uneven characteristic of material properties, this will make subsequent analysis biggish error occur.In fact, since gear structure is multiple It is miscellaneous, consider that the time of day comentation hardening gear finite element model of uneven characteristic becomes the one of the field so that establishing A technical problem.
Summary of the invention
The technical problem to be solved by the invention is to provide a kind of comentation hardening gear for considering uneven characteristic is limited Meta Model method, it is it can be considered that since the non-uniform hardness gradient of gear internal caused by comentation hardening and parameter remnants are answered The field of force establishes the gear finite element model closer to truth, improves the precision of finite element analysis.
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, using classical Thomas hardness gradient formula, obtain the hardness gradient curve of comentation hardening gear；
Step 2, using X-ray residual stress diffractometer to gear tooth along the initial residual stress of the facewidth and flank profil direction It measures, and gear surface is corroded using etch, and then obtain the initial residual stress under different depth；
Step 3, using Matlab numerical analysis software, write the curvilinear equation of the gear profile, generate data point, import Proe Software Create geometrical model, then geometrical model is imported into Abaqus finite element software, it prepares for building finite element model；
Step 4 obtains material by the relationship of material hardness and yield limit according to the hardness gradient curve that step 1 obtains With the yield limit curve of change in depth；
Step 5 passes through stress transmission method, and the initial residual stress along gear-profile and facewidth direction measured is converted to The initial residual stress of reference axis along finite element model；
Step 6, using secondary development software, cutting and grid division are carried out to model, then by the surrender pole of gear Limit and initial residual stress import in the model of gear, then according to the needs of finite element analysis, in constraint setup module release Model applies torque along the rotary freedom of z-axis or on the axis, and constrains the freedom degree in other directions, and final obtain considers not The comentation hardening gear finite element model of uniform properties.
The solution have the advantages that:
It solves the technical problem that heterogeneous comentation hardening gear is difficult to set up finite element model, is carried out accurately to be subsequent Finite element analysis lays the foundation, and can improve the precision of finite element analysis.
Detailed description of the invention
Detailed description of the invention of the invention is as follows:
Fig. 1 is the gear hardness profile based on Thomas hardness gradient formula；
Fig. 2 is the gear initial residual stress curve graph obtained in embodiment using X-ray diffractometer measurement；
Fig. 3 is embodiment middle gear tooth curve figure；
Fig. 4 is gear residual stress conversion figure；
Fig. 5 is evolution diagram of the embodiment middle gear yield limit with depth；
Fig. 6 is embodiment middle gear illustraton of model and cutting schematic diagram；
Fig. 7 is the grid dividing figure of embodiment middle gear finite element model；
Fig. 8 is the gear initial residual stress cloud atlas 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:
Step 1, using classical Thomas hardness gradient formula, obtain the hardness gradient curve of comentation hardening gear.
“Flank carrying capacity and running behavior of hard-machined bevel Gears ", Thomas, J.Doctoral Thesis, TU Munich, 1998 (" the side carrying energy of harden-cutting bevel gear Power and runnability research ", Thomas, J., doctoral thesis, Technical University at Munich, 1998) describe Thomas hardness gradient The expression formula of formula is as follows:
In formula (1), d is the distance away from gear surface, HV(d)To be the material hardness at d away from case depth, ECD is There is effect case depth, effective hardness layer is defined as the depth bounds that hardness is not less than 550HV, dcoreRepresent core hardness from The shortest distance on surface, HVcoreFor core hardness, aa,ab,ba,bb,ca,cbSolution formula for coefficient, these coefficients is as follows:
ba=-2aa·dHV,max (4)
bb=-2ab·dcore (5)
ca=HVsurface (6)
cb=550-ab·ECD2-bb·ECD (7)
Wherein, HVsurfaceFor gear surface hardness, dHV,maxFor the depth where highest hardness, H ' (ECD) be with it is effective The related coefficient of hardened layer.And above-mentioned coefficient has following expression:
H ' (ECD)=2aa·ECD+ba (8)
A=-H ' (ECD) (10)
+ 2 (HV of B=2ECDH ' (ECD)core-550) (11)
C=-ECD2·H′(ECD)-2·ECD·(HVcore-550) (12)
Bringing the expression formula of coefficient into hardness gradient solution equation just can obtain corresponding gear hardness with change in depth Curve is as shown in Figure 1.As seen from Figure 1: the figure is as synthesized by several sections of curves, within effective case depth, curve It is the quadratic equation of opening upwards in effective hardness layer to hardened layer range for a quadratic equation curve that Open Side Down Curve, and more than after case depth, then become the straight line for being parallel to x-axis.
Step 2, the initial residual stress using X-ray diffractometer to gear tooth along the facewidth and flank profil direction are surveyed Amount, and gear surface is corroded using etch, and then obtain the initial residual stress under different depth, it sends out after tested Existing, the initial residual stress numerical values recited of both direction is closer to.In addition, " Evaluation of contact fatigue life of a wind turbine gear pair considering residual stress”.Liu,H.,et Al.Journal of Tribology, 2018:p.041102. (" consider the wind power gear pair contact fatigue life of residual stress Estimate " Liu Heli etc., tribology periodical, 2018) the 5-6 pages also describe initial residual stress of the gear in the two directions can To be considered identical.Therefore in the present invention, the residual stress of both direction is indicated with identical data.In embodiment In, the stain in initial residual stress data such as Fig. 2 measured by gear, it is contemplated that directly add the data measured has in gear Complex steps in meta-model are limited, while data fluctuations are also larger, therefore the present invention is applied using Matlab matched curve, it is residual Residue stress matched curve such as Fig. 2's shown in solid, the expression formula of the matched curve are as follows:
σr=13.65d4-118.82·d3+356.94·d2-349.41·d-83.86 (13)
In formula (13), d is the distance away from gear surface.
It should be noted that being, matched curve herein is only one embodiment, because of different processing and heat treatment process Under gear residual stress distribution be all different, need just obtain by re-measuring.
Step 3, using Matlab numerical analysis software, write the curvilinear equation of the gear profile, generate data point, and handle These data, which import in Proe software, generates geometrical model, and then the geometrical model of generation is imported Abaqus finite element software, It prepares for building finite element model.
The key step that geometrical model generates includes: the contour curve equation for 1) deriving gear, and according to the equation, Program is write in Matlab, generates data point set, is formed by gear profile curve after data point connection as shown in figure 3, but needing Notice that the curve is one embodiment；2) data of previous step are imported into Proe software, a flank profil is generated, by the flank profil Array is carried out according to the number of teeth, obtains gear geometrical model；3) geometrical model is imported into Abaqus software.
Step 4 obtains material by the relationship of material hardness and yield limit according to the hardness gradient curve that step 1 obtains With the yield limit curve of change in depth.
“ISO 6336-5 Calculation of load capacity of spur and helical gears- 2003 (" International Standards Organization 6336-5-2003 straight-tooth of Part 5:Strength and quality of materials " The 5th part calculating of wheel and helical gear bearing capacity: the intensity and quality of material " 2003) describes gear yield limit and hard The relationship of degree is as follows:
σy(d)=σy(core)+(σy(surface)-σy(core))/(HVsurface-HVcore)*(HV(d)-HVcore) (14)
In formula (14), σy(d)And HV(d)It is the yield limit and hardness at d, σ with being respectively away from case depthy(core)For The yield limit of core, σy(surface)For the yield limit on surface.
Step 5 passes through stress transmission method, and the initial residual stress along gear-profile and facewidth direction measured is converted to The initial residual stress of reference axis along finite element model.
Books " Chen Tianfu edits the Chongqing the mechanics of materials [M]: publishing house of University Of Chongqing 2006.2 " are in chapter 9 stress shape The calculation formula for deriving the stress of different directions is described in detail in state analysis and strength theory, and the stress analysis based on the book is public Formula derives the Stress calculation formula of each change in coordinate axis direction in standard cartesian coordinate system.
In finite element model, the facewidth direction of gear is defined for the z-axis in cartesian coordinate system, as shown in figure 4, only examining The gear is considered in the initial residual stress in the facewidth and flank profil direction, and the residual stress in other directions thinks to be not present, therefore Following stress transmission formula can be obtained:
σz,r=σT,r (15)
Wherein, σ, τ respectively represent direct stress and shearing stress component, x, y, and z represents three in standard cartesian coordinate system Reference axis, T, D, R represent the facewidth of gear, depth and rotating direction, and subscript r indicates initial residual stress, and α represents flank profil and appoints The angle of the normal orientation of any and the direction x.
Step 6, using secondary development software, cutting and grid division are carried out to model, then by the surrender pole of gear Limit and initial residual stress import in the model of gear, then according to the needs of finite element analysis, in constraint setup module release Model applies torque along the rotary freedom of z-axis or on the axis, and constrains the freedom degree in other directions, and final obtain considers not The comentation hardening gear finite element model of uniform properties.
In finite element software, yield limit and initial residual stress are applied according to region, therefore, body Existing comentation hardening gear has the anisotropic property of hardness gradient and residual stress field, can not just apply again to entire model identical Data, it is necessary to which model is carried out reasonable cutting, to add different material properties to different regions.When cutting The region divided is thinner, and added yield limit and initial residual stress are more accurate, and model all the more meets virtual condition, therefore answers By the enough fine of model cutting, and reusing manually method at this time just seems unrealistic, therefore uses secondary development software Gear geometrical model is carried out cutting and grid division in Abaqus by Python, and is completed addition residual stress and surrendered pole The operation such as limit, to obtain the comentation hardening gear finite element model for considering uneven characteristic.
Embodiment
The present embodiment is a modulus for 11mm, the spur gear that the number of teeth is 24, and major parameter is as shown in table 1:
1. gear major parameter of table
Step 1, the gear material be 18CrNimo7-6, the surface hardness of gear is 670HV, and core hardness is 420HV, effective case depth 2.2mm, case depth 3.8mm.According to formula (2-12), it is bent that hardening can be solved The coefficient of line is respectively as follows: aa=-24.79；ba=0；ca=670；ab=12.06；bb=-162.15；cb=848.36.Thus, The hardness curve formula of the embodiment are as follows:
Step 2 tests gear initial residual stress, and carries out curve fitting to the result of test, the song of fitting Line formula is shown in formula (13).
Step 3, according to the parameter of the present embodiment gear, establish the tooth profile curve equation of the spur gear, it is raw using Matlab At tooth curve such as Fig. 3, due to the gear be spur gear, facewidth direction have identical Cross Section Morphology, That is, having described the topographical information of the gear enough using two dimensional model.It is established based on this principle, the present embodiment Gear geometrical model such as Fig. 6 (a).It is to establish carburized gears finite element in Abaqus software that the geometrical model is imported by Proe Model is prepared.
Step 4, in embodiment, it is contemplated that 30 coupon of the gear material forging Φ (heat treatment: quenching of certain gear-box factory 850 DEG C of ± 10 DEG C of oil are cold, 180 DEG C ± 20 DEG C of tempering) yield strength is 850MPa, tensile strength 1080MPa, and 10 coupon of Φ (heat treatment: forging normalizing+tempering) yield strength 1055MPa (it is required that > 900MPa), tensile strength 1270MPa (> 1080MPa). Therefore the center portion yield strength for defining the gear material is 800MPa, and surface layer yield strength is 1300MPa.Then according to formula (14), the expression formula of yield strength is obtained are as follows:
σy(d)=800+ (1300-800)/(670-420) * (HV(d)-420) (20)
Thus to obtain the yield limit distribution such as Fig. 5 of embodiment gear.
Although step 5, in a certain depth of gear, initial residual stress the size in facewidth direction and flank profil direction all It is the same, but in cartesian coordinate system, due to the complexity of gear shape, so that in each change in coordinate axis direction, any point Each residual stress component is different from, and the addition of residual stress must be in change in coordinate axis direction, therefore, according to analysis pair before Residual stress is converted, referring to formula (15-18).
Step 6, consider gear analysis when, generally only loading end is analyzed, thus cutting be concentrated mainly on it is a certain Side.Using Python secondary development software to embodiment gear carry out cutting, due to each gear teeth of gear be it is identical, because This only shows the cutting figure of one of gear teeth in the present embodiment.In view of the hardened layer of the present embodiment is 3.8mm, being more than should The material of depth hardness having the same, while also existing without residual stress, so the present embodiment is within away from surface 4mm Material carries out cutting, while each section is 0.05mm.Monodentate illustraton of model is shown in Fig. 6 (b), and the part of cutting is Fig. 6 (c).It cuts After point, model is programmed for by Python and carries out grid dividing, grid dividing is shown in Fig. 7, in main cutting area, grid seed Density is 0.0025mm.After this, apply different yield limit and residual stress for different regions.Finally, according to The needs of finite element analysis apply torque along the rotary freedom of z-axis or on the axis in constraint setup module releasing theory, and The freedom degree in other directions is constrained, it is final to obtain the comentation hardening gear finite element model for considering uneven characteristic.
Fig. 8 is the initial residual stress cloud atlas for being applied with residual stress, it can be found that the remnants in the direction y are answered in x Very big difference is distributed in power, this is because the angle of the normal direction of flank profil and x-axis each point be different from caused by.But It is according to obtained equivalent Mises residual stress cloud atlas it can be found that the residual stress curve identical that the figure has and is fitted Distribution, in addition, yield limit is bent although can not intuitively show the yield limit of model with cloud atlas in finite element model The addition of line and the adding method of residual stress are similar, it is contemplated that the residual stress of addition is verified effectively, therefore demonstrates The practicability and reliability of the method for the present invention.

Claims (5)

1. a kind of comentation hardening gear finite element modeling method for considering uneven characteristic, characterized in that the following steps are included:
Step 1, using classical Thomas hardness gradient formula, obtain the hardness gradient curve of comentation hardening gear；
Step 2, the initial residual stress using X-ray residual stress diffractometer to gear tooth along the facewidth and flank profil direction carry out Measurement, and gear surface is corroded using etch, and then obtain the initial residual stress under different depth；
Step 3, using Matlab numerical analysis software, write the curvilinear equation of the gear profile, generate data point, import Proe Software Create geometrical model, and geometrical model is imported into Abaqus finite element software, it prepares for building finite element model；
Step 4 obtains material with depth by the relationship of material hardness and yield limit according to the hardness gradient curve that step 1 obtains Spend the yield limit curve of variation；
Step 5 passes through stress transmission method, and the initial residual stress along gear-profile and facewidth direction measured, which is converted to edge, to be had Limit the initial residual stress of each reference axis in meta-model；
Step 6, using secondary development software, cutting and grid division are carried out to model, then by the yield limit of gear with And initial residual stress imports in the model of gear, then according to the needs of finite element analysis, in constraint setup module releasing theory Apply torque along the rotary freedom of z-axis or on the axis, and constrain the freedom degree in other directions, so that it is uneven to construct consideration The comentation hardening gear finite element model of characteristic.
2. the comentation hardening gear finite element modeling method according to claim 1 for considering uneven characteristic, characterized in that In step 1, classical hardness curve formula are as follows:
In formula, d is the distance away from gear surface, HV(d)To be the material hardness at d away from case depth, ECD is to have effect hardening Layer depth, effective hardness layer are defined as the depth bounds that hardness is not less than 550HV, dcoreIt is most short from surface to represent core hardness Distance, HVcoreFor core hardness, aa,ab,ba,bb,ca,cbFor coefficient.
3. the comentation hardening gear finite element modeling method according to claim 2 for considering uneven characteristic, characterized in that In step 4, the relationship of gear yield limit and hardness are as follows:
σy(d)=σy(core)+(σy(surface)-σy(core))/(HVsurface-HVcore)*(HV(d)-HVcore)
Wherein σy(d)To be the yield limit at d, σ away from case depthy(core)For the yield limit of core, σy(surface)For surface Yield limit.
4. the comentation hardening gear finite element modeling method according to claim 3 for considering uneven characteristic, characterized in that In steps of 5, according to established gear geometrical model, the z coordinate axis that gear tooth width direction is geometrical model is defined, according to flat The initial residual stress of gear-profile and facewidth direction is converted to and is answered in the remnants of three change in coordinate axis direction by face Stress Analysis Method Power, stress transmission formula are as follows:
Wherein, σ, τ respectively represent direct stress and shearing stress component, x, y, and z represents three coordinates in standard cartesian coordinate system Axis, T, R represent the facewidth and rotating direction of gear, and subscript r indicates initial residual stress, and α represents the normal direction side of flank profil any point To the angle with the direction x.
5. the comentation hardening gear finite element modeling method according to claim 4 for considering uneven characteristic, characterized in that In step 6, gear geometrical model is carried out in Abaqus by cutting and grid division using Python secondary development software, and Different yield limit and initial residual stress are assigned for each region, then according to the needs of finite element analysis, about Beam setup module releasing theory applies torque along the rotary freedom of z-axis or on the axis, and constrains the freedom degree in other directions, To construct the comentation hardening gear finite element model for considering uneven characteristic.
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