CN111090953B - Contact fatigue failure analysis method based on material damage theory and abrasion coupling - Google Patents
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Abstract
The invention discloses a contact fatigue failure analysis method based on material damage theory and abrasion coupling, which comprises the following steps: 1. extracting two-dimensional surface roughness along the tooth profile direction; 2. establishing a two-dimensional gear pair contact finite element model based on an ABAQUS platform, and introducing the two-dimensional surface roughness to the pinion tooth profile of the model; 3. defining gear material parameters and material constitutive relations by using a material constitutive relation self-defining subroutine UMAT of ABAQUS; 4. calculating the abrasion loss and updating the tooth profile node coordinates by using an Archard abrasion model; 5. fatigue damage was calculated using Brown-Miller multiaxial fatigue criteria, and the total damage was used to update the elastic modulus, hardening modulus, and yield strength in the material properties. The technical effects are as follows: and the gear contact fatigue failure is analyzed under the consideration of wear conditions, so that the recognition of the mechanism of the gear contact fatigue failure is improved, and the loss of production benefits caused by the gear contact fatigue failure is reduced.
Description
Technical Field
The invention belongs to a method for analyzing contact fatigue failure of mechanical parts, and particularly relates to a method for analyzing contact fatigue failure based on material damage theory and abrasion coupling.
Background
Contact fatigue failure is a typical failure form of mechanical parts, and has become a major factor limiting the equipment reliability, man-machine safety and economic benefits of gear drive machines. The problem of contact fatigue of gears has been studied extensively in many ways, such as operating factors, material factors. Existing studies remain on the impact of a single factor on fatigue failure, such as inclusions, roughness, residual stress, etc. Chinese patent document CN107885907a discloses in 2018, 4, 6 a method for assessing the risk of contact fatigue failure of a case hardened gear, comprising the steps of: 1. calculating contact parameters of the meshing position according to the geometric kinematics of the gear pair, and establishing a contact analysis model; 2. based on a gear pair contact analysis model, carrying out contact stress strain analysis to obtain equivalent shear stress of a complex multi-axis stress field; 3. estimating the local material strength of the gear teeth according to the hardness curve and the material parameters of the gear materials; 4. converting the residual stress into equivalent shear stress according to the residual stress curve of the gear material; 5. dividing the equivalent shear stress by the localized material strength of the gear gives the exposure value at any point of the critical contact area. The patent application obtains a technical means for evaluating the risk of contact fatigue failure of gears, but the technical means is limited to residual stress, and the contact fatigue failure under other factors is not considered, and the degradation of material properties is also considered. However, in practical engineering, fatigue failure is often not caused by a single factor, which results in lower accuracy of the results obtained by analysis using this method.
Disclosure of Invention
Aiming at the problems existing in the prior art, the technical problem to be solved by the invention is to provide a contact fatigue failure analysis method based on the coupling of material damage theory and wear, which can analyze the contact fatigue failure problem of a gear under the conditions of surface roughness and wear, improve the accuracy of analysis of the contact fatigue failure resistance of the gear, and reduce accidents and economic losses caused by the contact fatigue failure of the gear.
The technical problem to be solved by the invention is realized by the technical scheme, which comprises the following steps:
step 1, measuring the microscopic morphology of the gear surface by using an optical morphology measuring instrument and extracting the two-dimensional surface roughness along the tooth profile direction;
step 2, establishing a two-dimensional gear pair contact finite element model based on an ABAQUS platform, and introducing the extracted two-dimensional surface roughness to a pinion tooth profile in the two-dimensional gear pair contact finite element model by using a PYTHON program to obtain a pinion tooth profile containing the two-dimensional surface roughness, wherein the pinion tooth profile keeps a smooth appearance;
step 3, defining gear material parameters and material constitutive relations by using a material constitutive relation self-defining subroutine UMAT of ABAQUS, wherein the material constitutive relations reflect coupling of material elastoplastic response and material damage under the action of microscopic morphology;
step 4, using an ABAQUS grid movement subroutine UMESHMOTION to read the contact pressure, the sliding distance and the coordinates of contact points in the rolling contact process of the two-dimensional gear pair, and using an Archard abrasion model to calculate the abrasion loss and update the tooth profile node coordinates;
step 5, calculating a critical plane of each gear material point, and a shear strain amplitude, a positive strain amplitude and a positive stress average value on the critical plane based on a critical plane method; fatigue damage generated per load cycle was calculated using Brown-Miller multiaxial fatigue criteria, total damage was calculated from the fatigue damage per load cycle as the number of load cycles increased and the elastic modulus, hardening modulus, and yield strength in the material properties were updated using the total damage.
The invention has the technical effects that:
the contact fatigue failure problem of the gear is analyzed under the condition of considering the surface roughness and the abrasion, the change of a stress strain field at the near surface caused by the evolution of the surface morphology is considered, the degradation of the material property is also considered, the understanding of the contact fatigue failure mechanism of the gear is enhanced, the accuracy of the analysis of the contact fatigue failure resistance performance of the gear is improved, and the accidents and economic losses caused by the contact fatigue failure of the gear in the actual engineering are reduced.
Drawings
The drawings of the present invention are described as follows:
FIG. 1 is a technical roadmap of the invention;
the surface topography along the tooth profile direction selected in fig. 2;
FIG. 3 contains a two-dimensional gear contact finite element model of surface roughness;
FIG. 4 is a schematic diagram of a multiaxial critical plane;
FIG. 5 shear strain amplitude, positive strain amplitude and positive stress amplitude results
Fig. 6 is a graph showing the fatigue damage results when the gears fail in the examples.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
as shown in fig. 1, the present invention includes the steps of:
and step 1, measuring the microscopic morphology of the gear surface by using an optical morphology measuring instrument and extracting the two-dimensional surface roughness along the tooth profile direction.
And observing the microscopic appearance of the surface of the gear by using an optical measuring instrument, respectively observing a plurality of position points along the tooth width direction near the gear pitch line, measuring the surface appearance at the gear node, and selecting the surface appearance along the tooth profile direction to obtain the two-dimensional surface roughness. As shown in fig. 2, the upper two graphs are the three-dimensional surface micro-topography of the gear measured by the optical topography measuring instrument, and the lower graph is the two-dimensional surface roughness in the selected tooth profile direction.
And 2, establishing a two-dimensional gear pair contact finite element model based on an ABAQUS platform. Establishing a large gear part and a small gear part, wherein the tooth surface near the pinion node is provided with partial bulges, the bulge length is equal to the measured two-dimensional surface roughness length, using a PYTHON program to introduce the extracted two-dimensional surface roughness data points to the tooth profile near the pinion node to obtain the pinion tooth profile with the two-dimensional surface roughness, cutting off redundant bulge parts, keeping the gear profile of the large gear smooth, and as shown in figure 3, taking a left image as a gear pair contact model, taking the large gear as a driving wheel to apply rolling, and taking the small gear as a driven wheel to apply torque; the upper right plot enlarges the pinion intermediate teeth containing a two-dimensional surface roughness; and selecting a portion of the area near the pinion node using an ALE adaptive mesh to calculate wear, defining contact between the pinion flanks and meshing, the enlarged ALE adaptive mesh area meshing being shown in the lower right of fig. 3.
And 3, defining gear material parameters and gear material constitutive relations by using a material constitutive relation self-defining subroutine UMAT of ABAQUS. According to the constitutive relation described in the literature "A non-linear continuous Fatigue damage model", lemaitre J and Chaboche JL, fatigue & Fracture Of Engineering Materials & Structures,11 (1988), 1-17 ("nonlinear continuous Fatigue damage model", lemaitre J and Chaboche JL, fatigue fracture of engineering materials and Structures, vol. 11, 1988, pages 1-17), the coupling of material elastoplastic response and material damage is reflected.
The yield conditions of the structure are as follows:
J 2 -Q＝0
wherein Q represents the initial radius of the yielding surface, which is equal to the initial yield limit of the gear material, J 2 Representing Von Mises equivalent stress in the follow-up reinforcement model, the value of which is equal to:
where α represents the back stress tensor at the center of the yield surface, s represents the bias stress tensor, and D represents the damage amount.
The total strain tensor epsilon can be expressed as:
ε＝ε e +ε p
wherein ε e Represent the elastic strain tensor, epsilon p Representing the plastic strain tensor.
The stress tensor sigma may be defined by the elastic strain tensor epsilon e Calculated from the damage amount D, the formula is:
σ＝(1-D)Cε e
wherein C represents a fourth-order elastic tensor.
The plastic strain rate can be expressed as:
in the method, in the process of the invention,representing the plastic ratio coefficient, +.>Indicating the plastic flow direction.
The plastic scaling factor can be expressed as:
the linear motor hardening model proposed by Prager in the literature "The theory of plasticity: a survey of recent achievements", prager W., proc Inst Mech Eng,169 (1955), 41-57 ("plasticity theory: recent review of results of research", prager W, england society of mechanical Engineers, volume 169, 1955, pages 41-57) determines that the back stress is:
in the method, in the process of the invention,representing back stress, M represents linear motion hardening modulus, the value of which can be determined from the stress-strain curve; e represents the elastic modulus. And programming in a subroutine UMAT according to the constitutive relation of the material.
And 4, using an ABAQUS grid movement subroutine UMESHMOTION to read the contact pressure, the sliding distance and the coordinates of the contact point in the gear rolling contact process.
The abrasion loss is calculated by the Archard abrasion model described in the literature "Contact and rubbing of flat surfaces", archard, journal of Applied Physics,24 (1953), 981-988 ("planar contact and friction", archard, journal of applied physics, volume 24, 1953, pages 981-988).
The equation for Archard wear is:
Δh＝kpΔs
where Δh represents the wear amount increment, p is the surface pressure, Δs is the slip distance increment, and k is the wear coefficient related to the properties of the material itself.
And updating the surface node coordinates based on the calculated wear amount to generate a new surface morphology.
And 5, calculating a critical plane of each gear material point based on a critical plane method, and calculating a shear strain amplitude, a positive strain amplitude and a positive stress average value on the critical plane. Firstly, reading the principal stress, the shearing stress, the principal strain and the shearing strain of a material point in a finite element; the stress strain at each angle for each material point was then calculated according to the formula described in book "Theory of Elasticity", mcGrawHill Book Company,1970 ("elastic mechanics", S.P.Timoshenko, J.N.Goodier, H.N.Abramson mcgraw hill book, 1970) as follows:
wherein θ is the critical plane angle, σ x ，σ z And τ xz Respectively represent two principal stresses and one shear stress, ε x ，ε z And gamma is equal to xz Representing two principal strains and one shear strain, sigma, respectively θ Representing the normal stress, ε, on a critical plane at an angle θ to the rolling direction θ Representing positive strain in a critical plane at an angle θ to the rolling direction, γ θ Representing the shear strain in a critical plane at an angle θ to the rolling direction.
The maximum shear strain gamma will occur in one cycle max The angle of (2) is denoted as the critical plane, and a schematic diagram of the critical plane is shown in fig. 4. And calculates the shear strain amplitude delta gamma at the critical plane max Positive strain amplitude delta epsilon n Mean value sigma of positive stress m The calculation formula is as follows:
wherein, gamma max 、ε max And sigma (sigma) max Respectively the maximum shear strain, the maximum positive strain and the maximum positive stress on the critical surface in the cyclic loading process, and gamma min 、ε min And sigma (sigma) min The minimum shear strain, the minimum positive strain and the minimum positive stress on the critical surface in the cyclic loading process are respectively shown.
According to the obtained shear strain amplitude delta gamma on the critical surface max Positive strain amplitude delta epsilon n Mean value sigma of positive stress m Fatigue damage was calculated using Brown-Miller multiaxial fatigue criteria. According toDocuments "A theory for Fatigue under multiaxial stress-strain conditions", K.J.Miller, M.W.Brown, proc Inst Mech Eng,187 (1973) 745-755 ("Fatigue theory under multiaxial stress-strain", K.J.Miller, M.W.Brown, institute of mechanical engineers, volume 187, 1973, pages 745-755) and "A path-independent parameter for Fatigue under proportional and non-proportional loading", C.H.Wang, M.W.Brown, fatigue&Fracture Of Engineering Materials&The formula for the calculation of the Brown-Miller multiaxial fatigue damage proposed in Structure, 16 (1993) 1285-1298 ("Path independent fatigue parameters under proportional and non-proportional loads", C.H.Wang, M.W.Brown, fatigue fracture of engineering materials and Structures, volume 16, 1993, pages 1285-1298) is as follows:
wherein E is the modulus of elasticity, S is a material parameter determined by torsion and stretching experiments, and the values of material parameters a and B are a=1.3+0.7s, and b=1.5+0.5s, respectively. Sigma'. f And epsilon' f Respectively representing the fatigue strength parameter and the fatigue ductility parameter of the material, b and c respectively representing the fatigue strength index and the fatigue ductility index of the material, 2N f The fatigue life of the material point calculated from the stress-strain field at this time is shown.
According to the isopinear injury theory Minter theory, the single injury rate is:
in the formula, D represents damage amount, and N represents loading times.
Due to the high cycle fatigue life of gears, solution of the damage coupled constitutive equation over all loading cycles is not possible. To solve this calculation problem, it is assumed that the stress field and the strain field remain unchanged for a finite period Δn. The damage amount D is updated as follows:
in the formula, i represents the current loading time, j represents the number of units, and delta N represents the loading times represented by one cyclic loading.
Degradation of mechanical properties of the material total damage is calculated from fatigue damage per load cycle and used to update the elastic modulus, hardening modulus and yield strength in the material properties:
wherein E is the elastic modulus, M is the hardening modulus, sigma Y Is the yield limit. The gear fails when the damage amount D is accumulated to 1.
Examples
The main parameters of the gear pair are as follows:
and step 1, measuring the microscopic morphology of the surface of the gear by using an optical morphology measuring instrument, and adjusting the surface morphology of a lens position scanning sampling area to obtain the three-dimensional microscopic morphology of the surface of the gear, wherein the three-dimensional microscopic morphology of the gear is shown in the upper two diagrams of fig. 2. And selecting the surface morphology in the tooth profile direction by using scanning microscope image processing software gwydsion to obtain the two-dimensional surface roughness and extracting the two-dimensional surface roughness in the tooth profile direction, as shown in the graph in fig. 2. The sampling length was 1.37mm, the dot pitch was 2.745 μm, and the roughness root mean square value was 0.283. Mu.m.
And 2, establishing a two-dimensional gear pair contact finite element model based on an ABAQUS platform. A large gear part and a small gear part are established, the large gear is a driving wheel with the radius of 64.135mm, and the small gear is a driven wheel with the radius of 37.465mm. The tooth surface near the pinion node has a partial protrusion with a length equal to the measured two-dimensional surface roughness length, and the extracted two-dimensional surface roughness data is processed using the PYTHON programPoints are led into the tooth profile near the pinion node, so that the pinion tooth profile with two-dimensional surface roughness is obtained, redundant convex parts are cut off, and the gear tooth profile of the large gear keeps smooth appearance, as shown in figure 3. The left graph is a gear pair contact model, the large gear is a driving wheel which applies rolling, the rolling angle is 0.14, the small gear is a driven wheel which applies torque, and the torque size is 1.2 multiplied by 10 5 Nmm; the upper right plot enlarges the pinion intermediate teeth containing a two-dimensional surface roughness; and selecting a region with the size of 0.5mm multiplied by 0.5mm near the pinion node, using an ALE self-adaptive grid, adopting a grid movement subroutine UMESHMOTION of user-defined calling ABAQUS to calculate abrasion, defining contact between tooth surfaces of the pinion and dividing the grid, wherein the enlarged ALE self-adaptive grid region is divided into grids with the internal grid size of 0.2 mu m multiplied by 0.2 mu m as shown in the lower right part of figure 3.
And 3, defining gear material parameters and a mechanism by using a material mechanism self-defining subroutine UMAT of ABAQUS, wherein the mechanism reflects coupling of material elastoplastic response and material damage under the action of microscopic morphology. The FORTRAN language based subroutine UMAT gives this construct to each material point.
And 4, using an ABAQUS grid movement subroutine UMESHMOTION to read the surface contact pressure, the sliding distance of the surface contact point and the coordinates of the contact point at each moment in the gear rolling contact process. Calculating the wear amount and updating the surface node coordinates using an Archard wear model, the wear coefficient k=2×10 -11 MPa -1 。
And 5, searching a critical surface where the maximum shear stress of each material point in the rolling contact process is located, and calculating a shear strain amplitude, a positive strain amplitude and a positive stress average value on the critical surface. Its shear strain amplitude delta gamma max Positive strain amplitude delta epsilon n Mean value sigma of positive stress m The results are shown in fig. 5, and it can be seen from fig. 5: although the surface becomes gradually smooth under the action of abrasion, the strain generated under the same working condition is increased due to the attenuation of the material property, so that the maximum value of the shear strain amplitude, the positive strain amplitude and the positive stress mean value still appears at the near surface and is gradually increased.
According toThe calculated shear strain amplitude, positive strain amplitude and positive stress mean value are used for calculating fatigue damage by using Brown-Miller multiaxial fatigue criterion and acceleration algorithm, and the selected fatigue strength parameter sigma' f =2894mpa, fatigue ductility parameter ε' f =0.134, fatigue strength index b= -0.087, fatigue ductility index c= -0.58.
Gear pass 4.2×10 7 Failure after the secondary cyclic loading, the accumulated fatigue damage result in failure is shown in fig. 6, and failure points occur at the near surface of the pinion. The analytical results of the present method were confirmed to be reliable, in agreement with the test results in the literature "The effect of contact severity on micropitting: simulation and experiments", zhou Ye, zhu Caichao, tribology International,138 (2019) 463-472 ("influence of contact severity on microetching: simulation and experiment", zhou, zhu Cai, tribology International, volume 138, 2019, pages 463-472).
Claims (8)
1. The contact fatigue failure analysis method based on the material damage theory and abrasion coupling is characterized by comprising the following steps of:
step 1, measuring the microscopic morphology of the gear surface by using an optical morphology measuring instrument and extracting the two-dimensional surface roughness along the tooth profile direction;
step 2, establishing a two-dimensional gear pair contact finite element model based on an ABAQUS platform, and introducing the extracted two-dimensional surface roughness to a pinion tooth profile in the two-dimensional gear pair contact finite element model by using a PYTHON program to obtain a pinion tooth profile containing the two-dimensional surface roughness, wherein the pinion tooth profile keeps a smooth appearance; the large gear applies rolling, the small gear applies torque, contact between tooth surfaces of the large gear and the small gear is defined, grids are divided, ALE self-adaptive grids are used in the area near the small gear node, and a grid moving subroutine UMESHMOTION of ABAQUS is called to calculate abrasion;
step 3, defining gear material parameters and material constitutive relations by using a material constitutive relation self-defining subroutine UMAT of ABAQUS, wherein the material constitutive relations reflect coupling of material elastoplastic response and material damage under the action of microscopic morphology;
step 4, using an ABAQUS grid movement subroutine UMESHMOTION to read the contact pressure, the sliding distance and the coordinates of contact points in the rolling contact process of the two-dimensional gear pair, and using an Archard abrasion model to calculate the abrasion loss and update the tooth profile node coordinates;
step 5, calculating a critical plane of each gear material point, and a shear strain amplitude, a positive strain amplitude and a positive stress average value on the critical plane based on a critical plane method; fatigue damage generated per load cycle was calculated using Brown-Miller multiaxial fatigue criteria, total damage was calculated from the fatigue damage per load cycle as the number of load cycles increased and the elastic modulus, hardening modulus, and yield strength in the material properties were updated using the total damage.
2. The contact fatigue failure analysis method according to claim 1, wherein: in step 1, observing the microscopic appearance of the surface of the gear by using an optical measuring instrument, respectively taking a plurality of position points along the tooth width direction near the gear pitch line for observation, measuring the surface appearance at the gear node, and selecting the surface appearance along the tooth profile direction to obtain the two-dimensional surface roughness.
3. The contact fatigue failure analysis method according to claim 2, characterized in that: in step 3, the gear material parameters and the material constitutive relations are as follows:
the yield conditions are:
J 2 -Q＝0
wherein Q represents the initial radius of the yield surface, J 2 Representing Von Mises equivalent stress in the follow-up reinforcement model, the value of which is equal to:
wherein α represents a back stress tensor of the center of the yield surface, s represents a bias stress tensor, and D represents a damage amount;
the total strain tensor ε is:
ε＝ε e +ε p
wherein ε e Represent the elastic strain tensor, epsilon p Representing a plastic strain tensor;
the stress tensor sigma is:
σ＝(1-D)Cε e
wherein C represents a fourth-order elastic tensor;
the plastic strain rate is:
in the method, in the process of the invention,representing the plastic ratio coefficient, +.>Indicating the plastic flow direction;
the plastic ratio coefficient is:
the back stress is as follows:
in the method, in the process of the invention,the back stress is represented by M, the linear motion hardening modulus is represented by M, and the elastic modulus is represented by E.
4. A contact fatigue failure analysis method according to claim 3, wherein: in step 4, the Archard wear model is:
Δh＝kpΔs
wherein Vh represents an abrasion loss increment, the unit is mm, ρ is surface pressure, and the unit is MPa; Δs is the slip distance increment in mm; k is the wear coefficient in MPa -1 。
5. The contact fatigue failure analysis method according to claim 4, wherein: in step 5, the shear strain amplitude Δγ in the critical plane max Positive strain amplitude delta epsilon n Mean value sigma of positive stress m The calculation formula is as follows:
wherein, gamma max 、ε max And sigma (sigma) max Respectively the maximum shear strain, the maximum positive strain and the maximum positive stress on the critical surface in the cyclic loading process, and gamma min 、ε min And sigma (sigma) min The minimum shear strain, the minimum positive strain and the minimum positive stress on the critical surface in the cyclic loading process are respectively shown.
6. The contact fatigue failure analysis method according to claim 5, wherein: in step 5, the Brown-Miller multiaxial fatigue damage calculation formula is as follows:
wherein, E is elastic modulus, S is a material parameter determined by torsion and stretching experiments, and the values of the material parameters A and B are respectively A=1.3+0.7S and B=1.5+0.5S; sigma'. f And epsilon' f Respectively representing the fatigue strength parameter and the fatigue ductility parameter of the material, b and c respectively representing the fatigue strength index and the fatigue ductility index of the material, 2N f The fatigue life of the material point calculated from the stress-strain field at this time is shown.
7. The contact fatigue failure analysis method according to claim 6, wherein: in step 5, the single damage rate is:
wherein D represents damage amount, and N represents loading times;
the update formula of the damage amount D is as follows:
in the formula, i represents the current loading time, j represents the number of units, and delta N represents the loading times represented by one cyclic loading.
8. The contact fatigue failure analysis method according to claim 7, wherein: in step 5, the elastic modulus, the hardening modulus and the yield strength in the material properties are updated using the total damage as follows:
wherein E is the elastic modulus, M is the hardening modulus, sigma Y Is the yield limit; the gear fails when the damage amount D is accumulated to 1.
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| CN111999054B (en) * | 2020-08-17 | 2021-10-22 | 湖南大学 | Cylindrical straight tooth abrasion simulation method considering actual tooth surface elastic-plastic contact |
| CN112287554B (en) * | 2020-10-31 | 2022-10-28 | 重庆望江工业有限公司 | Method for predicting contact fatigue damage of gear surface |
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| CN114611364A (en) * | 2022-03-22 | 2022-06-10 | 南京航空航天大学 | Fretting fatigue life prediction method considering surface hardness and plastic strain |
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