CN107451359A - A kind of gear meshing characteristic finite element method for considering matrix cracking and influenceing - Google Patents
A kind of gear meshing characteristic finite element method for considering matrix cracking and influenceing Download PDFInfo
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Abstract
The present invention relates to a kind of gear meshing characteristic finite element method for considering matrix cracking and influenceing, comprise the following steps：Obtain the gear pair basic parameter of driving wheel and driven pulley and the Crack Parameters containing matrix cracking gear；Healthy gear three-dimensional finite element model is established according to gear pair basic parameter, gear FEM model of the cutting generation containing matrix cracking is carried out to gear matrix；Mesh refinement is carried out to crack surface, and according to the interaction between crack surface, plane-plane contact unit Conta174 and Targe170 are established on crack surface；According to the Crack Parameters, gear meshing characteristic is calculated, and calculates the difference established and whether contacted for result of calculation on crack surface.This method make it that Gear with Crack mesh stiffness and tooth root strain calculation result are more accurate, help that for the understanding containing non-penetrating matrix cracking gear meshing characteristic and the interphase interaction of crack surface, result of study certain reference can be provided for design of gears.
Description
Technical field
The invention belongs to mechanical kinetics technical field, and in particular to a kind of gear meshing characteristic for considering matrix cracking has
Finite element analysis method.
Background technology
Gear is a kind of important mechanical transmission component, but due to foozle, insufficient lubrication, overload, stress concentration
Etc. reason, crackle occurs on gear.Crackle can not only extend along the gear teeth, can equally be extended along gear matrix.Existing skill
Substantial amounts of research has been carried out to Gear with Crack meshing characteristic using analytic method, finite element method in art.But it there are following
Deficiency：(1), analytic method mainly for tooth root crackle studied, due to the complexity of non-penetrating matrix cracking, parsing side
Method can not effectively calculate damage of the matrix cracking for gear matrix；(2), same, finite element method is split mainly for tooth root
Line is studied, and the concern for non-penetrating matrix cracking is seldom, does not consider the influence of the interphase interaction of crack surface, this
Error will be produced and do not meet reality；(3) strain of healthy gear, is only have studied in the prior art, ignores matrix cracking pair
In the influence of gear strain, calculate inaccurate.
The content of the invention
(1) technical problems to be solved
In order to solve the above mentioned problem of prior art, it is special that the present invention provides a kind of gear engagement for considering that matrix cracking influences
Property finite element method, by ANSYS softwares establish containing non-penetrating matrix cracking gear FEM model, to containing non-
Penetrate matrix cracking gear meshing characteristic to be studied, simultaneously, it is also contemplated that the interaction between crack surface, build on crack surface
Vertical contact, improves and calculates accuracy, be allowed to more conform to reality.
(2) technical scheme
In order to achieve the above object, the main technical schemes that the present invention uses include：
A kind of gear meshing characteristic finite element method for considering matrix cracking and influenceing, comprises the following steps：
S1, the gear pair basic parameter for obtaining driving wheel and driven pulley and the Crack Parameters containing matrix cracking gear；
S2, the gear three-dimensional finite element model containing the non-penetrating matrix cracking of parabola is established, comprised the following steps：
S201, according to the gear pair basic parameter, utilize the APDL language programmed functions of ANSYS softwares, use
Solid185 unit simulation gear entities, establish healthy gear three-dimensional finite element model；
S202, on the basis of the healthy gear three-dimensional finite element model, to gear matrix carry out cut generation contain
There is the gear FEM model of matrix cracking；
S203, the crack surface progress mesh refinement to the gear FEM model containing matrix cracking, and according to
Interaction between crack surface, surface-to-surface contact elements Conta174 and Targe170 are established on the crack surface；
S3, according to the Crack Parameters, calculate gear meshing characteristic, and calculate to establish on crack surface and whether contact for counting
Calculate the difference of result；Wherein, the Crack Parameters include crack depth, crack width, and the gear meshing characteristic includes engagement
Rigidity, strain.
As a kind of preferred scheme of method as described above, the gear pair basic parameter includes the number of teeth, modulus of elasticity, pool
Loose ratio, internal bore radius, base radius, modulus, the facewidth, pressure angle, addendum coefficient, tip clearance coefficient, coefficient of friction；The crackle
Parameter includes crack initiation site angle, crack width, crack depth, direction of crack propagation angle.
As a kind of preferred scheme of method as described above, the step S201 comprises the following steps：S20101：According to institute
State the modulus of elasticity of the gear in gear pair basic parameter, Poisson's ratio, internal bore radius, base radius, modulus, pressure angle,
Addendum coefficient, tip clearance coefficient, coefficient of friction, using the flank profil of the single gear of ANSYS Software Creates, the flank profil includes gradually opening
Line and easement curve；
S20102, swivel replication is carried out to the single gear teeth, generate healthy gear two-dimensional finite element model；
S20103, the gear two-dimensional finite element model to generation stretch along gear centre axis, and its tensile elongation is
The size of the facewidth numerical value, generate healthy gear three-dimensional finite element model；
S20104, mesh refinement is carried out to the flank of tooth near path of contact.
As a kind of preferred scheme of method as described above, the step S202 comprises the following steps：
S20201, in the healthy gear three-dimensional finite element model, according to the original position of matrix cracking, Crack Extension
Direction, select cracked gear body portion；
S20202, ordered using " VSBL " in ANSYS, by selected gear body portion according to the crack initiation site,
Direction of crack propagation is divided into two parts entity；
S20203, coordinate system is established on the divisional plane of two parts entity, generated according to crackle parabolic curve equation
Non-penetrating matrix cracking, the crackle parabolic curve equation are：
Wherein, q (x) be optional position x at crack depth, q0For initial crack depth, LcFor crack width, L is that gear is wide
Degree.
Carrying out mesh refinement to crack surface as a kind of preferred scheme of method as described above, in the step S203 includes
Three boundary curves for forming crack surface are subjected to equidistant partition first with " LESIZE " order, recycle " VMESH " order pair
Crack surface is refined.
As a kind of preferred scheme of method as described above, the step S3 includes：
S301, according to matrix cracking depth, calculate the gear meshing characteristic, comprise the following steps：
S30101, enter row constraint, the constraint to gear in the gear three-dimensional finite element model that step S2 is established
Mode includes making master and slave wheel inner ring node and respective geometric center be coupled, Complete Bind driven pulley central point, constraint
Driving wheel central point is allowed to can only be around central axis；Apply mode of loading and be included in the application torque of driving wheel geometric center, obtain
To the angular displacement of driving wheel；According to the calculation formula of mesh stiffness, obtain when establishing contact on crack surface and not establishing contact,
Gear Meshing Stiffness under the conditions of different matrix crack depth, wherein, the calculation formula of the mesh stiffness is：
Wherein, K represents mesh stiffness, and T represents the torque being applied on driving wheel, and Δ θ represents the angular displacement of driving wheel, rb
For driving wheel base radius；
According to being connect on line face during contactless unit on rigidity-crack surface of Stiffness amount=healthy gear without foundation
The rigidity of Gear with Crack when touching, builds when having osculating element on crack surface on rigidity-crack surface of Stiffness amount=healthy gear
The rigidity of Gear with Crack during vertical contact, calculate to obtain and contact is established on crack surface and is not established in the case of contact, under mesh stiffness
The percentage error of drop amount, the percentage error of the mesh stiffness slippage=[(on crack surface during contactless unit under rigidity
Stiffness amount when having osculating element on drop amount-crack surface) Stiffness amount during contactless unit on/crack surface] × 100%；
Meanwhile using the post-processing function of ANSYS softwares, obtain the contact pressure on crack surface under the conditions of different crack depths
Power is distributed；
S30102, according to different matrix crack depth, calculate the strain of tooth root：The crackle gear teeth are selected close to tooth root position
One point Q, in each position of engagement of gear, using the post-processing function of ANSYS softwares, extracts the Q as strain extraction point
The strain of point；According to nothing connects on Q points strain slippage=healthy gear Q points strain-crack surface during contactless unit on crack surface
The strain of unit Gear with Crack Q points is touched, Q point strain slippages=healthy gear Q points strain-are split when having osculating element on crack surface
There is the strain of osculating element Gear with Crack Q points on line face, obtain the percentage error of strain, the percentage error of Q points strain=
[(Q point strains slippage when having osculating element on Q points strain slippage-crack surface during contactless unit on crack surface)/crackle
Q points strain slippage during contactless unit on face] × 100%；S302, according to matrix cracking width, calculate the gear engagement
Characteristic, including：
S30201, according to matrix cracking width, calculate the Gear Meshing Stiffness：The constrained procedure of the gear with it is described
Apply mode of loading with the S30101, Gear Meshing Stiffness formula is the same as the S30101 under the conditions of different matrix crack width；
Meanwhile using the post-processing function of ANSYS softwares, obtain the displacement cloud of Gear with Crack under the conditions of different crack widths
Contact distribution on figure and crack surface；
S30202, according to matrix cracking width, calculate the Gear Root strain：Computational methods are the same as the step
S30102。
(3) beneficial effect
The beneficial effects of the invention are as follows：The gear meshing characteristic finite element fraction provided by the invention for considering matrix cracking and influenceing
Analysis method, the gear three-dimensional finite element model for the non-penetrating matrix cracking containing parabola established using ANSYS softwares, effectively consider
Matrix cracking is for gear matrix damage；In practical work process, crackle can not only extend along gear tooth, and can be to gear
Matrix extends, because analytic method can not effectively consider that matrix cracking for gear matrix damage, is established by ANSYS softwares and contained
The gear three-dimensional finite element model of matrix cracking solves the problem.
FEM model of the present invention considers the interaction between crack surface, and surface-to-surface contact elements are established on crack surface
Interaction between Conta174 and Targe170 simulating cracks face so that Gear with Crack mesh stiffness and tooth root strain gauge
It is more accurate to calculate result, osculating element is established on crack surface, more conforms to reality.Because gear engagement position constantly changes,
Crack surface can contact with each other or separate each other, not account for the interaction between crack surface in previous research, between crack surface
Do not constrain, this phenomenon does not meet reality clearly, and result of calculation can be made to produce error.Surface-to-surface is established on crack surface to connect
Tactile unit can effectively reduce error, closing to reality.Meanwhile error produced by contact is established on crack surface and is not established is carried out
Quantify, analyze influence of the osculating element for result of calculation on crack surface, contribute to people for containing non-penetrating matrix cracking
The understanding of the interphase interaction of gear meshing characteristic and crack surface.The inventive method analyzes matrix cracking parameter for strain
Influence, help to deepen overall understanding of the people for the gear containing matrix cracking, side provided for the analysis of fatigue of Gear with Crack
Help.
The present invention have studied matrix cracking for tooth by establishing the three-dimensional finite element model containing non-penetrating matrix cracking
The influence of meshing characteristic is taken turns, result of study can provide certain reference for design of gears, such as：Larger position is being strained, is being adopted
Measure is taken to reduce strain size and strain concentration phenomenon.Meanwhile crackle is weighed according to the rigidity and strain variation of Gear with Crack
The degree of injury of gear, help is provided for Gear Fault Diagnosis.
Brief description of the drawings
Fig. 1 is the finite element method that the analysis gear matrix cracking in the specific embodiment of the invention influences on meshing characteristic
Flow chart；
Fig. 2 is the FEM model containing matrix cracking gear in the specific embodiment of the invention；
Fig. 3 is the non-penetrating matrix cracking schematic diagram of parabola in the specific embodiment of the invention；
Fig. 4 is healthy Gear Meshing Stiffness and crack depth q in the specific embodiment of the invention0=5mm, 15mm,
Contact and the mesh stiffness of Gear with Crack under not set up the condition are established during 25mm, on crack surface；
Fig. 5 is the various crack depth conditions corresponding to the A moment in mesh stiffness Fig. 4 in the specific embodiment of the invention
Under displacement cloud atlas and crack surface on contact distribution；
Healthy gear and crack depth q in Fig. 6 specific embodiment of the invention0=5mm, 15mm, 25mm crackle
Gear establishes contact and the strain of root portion position Q points under not set up the condition on crack surface；
Fig. 7 is healthy Gear Meshing Stiffness and crack width L in the specific embodiment of the inventionc=5mm, 15mm,
Contact and the mesh stiffness of Gear with Crack under not set up the condition are established during 25mm, on crack surface；
Under the conditions of Fig. 8 is the various crack width corresponding to the A moment in mesh stiffness Fig. 7 in the specific embodiment of the invention
Contact distribution；
Fig. 9 is healthy gear and the crack width L in the specific embodiment of the inventionc=5mm, 15mm, 25mm's splits
Line gear establishes contact and the strain of root portion position Q points under not set up the condition on crack surface.
Embodiment
In order to preferably explain the present invention, in order to understand, below in conjunction with the accompanying drawings, by embodiment, to this hair
It is bright to be described in detail.
Embodiment 1
A kind of gear meshing characteristic finite element method for considering matrix cracking and influenceing, as shown in figure 1, including following step
Suddenly：
Step 1：Obtain the gear pair basic parameter of driving wheel and driven pulley and the crackle ginseng containing matrix cracking gear
Number；Obtain gear pair basic parameter in the present embodiment and Crack Parameters containing matrix cracking gear are as shown in table 1：
The gear pair basic parameter of table 1 and the Crack Parameters containing matrix cracking gear
In the present embodiment, crack initiation site angle ψ and crack width LcKeep constant, crack depth q0In 5mm~25mm
Change, crack width LcChange between 5mm~25mm；
Step 2：The gear FEM model containing matrix cracking is established, crackle form is that the non-penetrating matrix of parabola splits
Line；
Step 2.1：The healthy gear FEM model containing 5 gear teeth is established using the APDL functions of ANSYS softwares.Bag
Include following steps：First：Modulus of elasticity, Poisson's ratio, internal bore radius, the basic circle half of gear in gear pair basic parameter
Footpath, modulus, pressure angle, addendum coefficient, tip clearance coefficient, coefficient of friction, it is bent using the flank profil of the single gear of ANSYS Software Creates
Line, tooth curve include involute and easement curve two parts；Second：The single gear teeth are carried out with swivel replication, generation health
Gear two-dimensional finite element model；3rd：The gear two-dimensional finite element model of generation is stretched along gear centre axis, it draws
Elongation is the facewidth numerical values recited, thus generates healthy gear three-dimensional finite element model；4th：To the flank of tooth near path of contact
Carry out mesh refinement.
Step 2.2：On the basis of the healthy model of gear, the gear FEM model containing matrix cracking is generated.Tool
Body comprises the following steps：First：In the healthy gear three-dimensional finite element model, according to the original position of matrix cracking, split
Line propagation direction, select cracked gear body portion；Second：(cut using " VSBL " order in ANSYS with working face
Cut body), selected gear body portion is divided into two parts entity according to crack initiation site, direction of crack propagation；3rd：Two
Coordinate system is established on the divisional plane of part entity, non-penetrating matrix cracking is generated according to crackle parabolic curve equation, wherein, crackle
Parabolic curve equation is：
Wherein, q (x) be optional position x at crack depth, q0For initial crack depth, LcFor crack width, L is that gear is wide
Degree.
The FEM model of the matrix cracking gear of foundation is as shown in Fig. 2 wherein O1For the centre point of driven wheel gear, O2
For from the centre point of main wheel gear, A1 is expressed as the crackle gear teeth, Fig. 2 b) be Fig. 2 a) enlarged drawing at A, Fig. 2 c) be Fig. 2 b)
Enlarged drawing A3 at A2 represents matrix cracking.The non-penetrating matrix cracking signal of parabola is as shown in figure 3, wherein scheme (b) for figure
(a) sectional view at B-B, P in1It is expressed as starting point, P2Terminal is expressed as, 1 is expressed as path, and A4 is expressed as crack surface, LcIt is expressed as
Crack width, q0It is expressed as crack depth.
Step 2.3：Establish contact.Further mesh refinement is carried out to crack surface according to solving precision and efficiency first,
" LESIZE " order (carrying out equidistant partition to line) is used to carry out three boundary curves for forming crack surface according to 1mm intervals
Equidistant partition.Then " VMESH " order (being used for mesh generation) is used to refine crack surface.Finally, it is crack surface is independent
Choose and in view of the possible contact occurred and Relative sliding between crack surface, on the crack surface of tessellated mesh
Establish surface-to-surface contact elements Conta174 and Targe170；Conta174 attributes are set by " KEYOPT ", i.e. adjust automatically is split
Gap between line face.
Step 3：The influence of crack depth, width for gear meshing characteristic is analyzed, and compares and contact is established on crack surface
Whether the influence for result of calculation；
Step 3.1：Analyze influence of the matrix cracking depth for gear meshing characteristic.
Step 3.1.1：Calculate when establishing contact on crack surface and not establishing contact, under the conditions of different matrix crack depth
Gear Meshing Stiffness.After gear FEM model establishes completion, when carrying out finite element solving, make master and slave wheel inner ring node
It is coupled with respective geometric center, Complete Bind driven pulley central point, constraint driving wheel (gear where crackle) center
Point is allowed to apply clockwise direction 500Nm torque around central axis in driving wheel geometric center, obtain driving wheel
Angular displacement, corresponding mesh stiffness value is obtained according to mesh stiffness solution formula.Crack Parameters are：Crack depth q0=5mm,
15mm, 25mm, crack initiation site angle ψ=35 °, crack width Lc=25mm, direction of crack propagation angle υ=45 °.According to engagement
The calculation formula of rigidity is：
Wherein, K represents mesh stiffness, and T represents the torque being applied on driving wheel, Δ θ
Represent the angular displacement of driving wheel, rbFor driving wheel base radius.When osculating element is not established on crack surface, solution procedure and
Mesh stiffness calculation formula is identical with mesh stiffness is solved when having osculating element on crack surface.The mesh cycle of gear is divided into
20 parts, actual corresponding 21 different positions of engagement, in each position of engagement, obtained according to above-mentioned mesh stiffness method for solving
The rigidity value of the different positions of engagement.Because the meshing condition in each position of engagement is different, after loading, angular displacement is not
Together, so the rigidity in each position of engagement is different.Using mesh cycle as abscissa, the engagement for being engaged position is firm
Angle value is ordinate, draws mesh stiffness curve.There is osculating element on crack surface and be not in contact with mesh stiffness under the conditions of unit
Curve such as Fig. 4, wherein establishing contact on (I) crack surfaceRepresent q0=5mm,Represent q0=15mm,Table
Show q0=25mm, without establishing contact on (II) crack surfaceRepresent q0=5mm,Represent q0=15mm,Represent q0=25mm ,-represent healthy, the mesh stiffness slippage such as tables in Fig. 4 corresponding to 5 engagement moment such as A to E
Shown in 2, in table 2, contactless list on rigidity-crack surface of Stiffness amount=healthy gear during contactless unit on crack surface
The rigidity of Gear with Crack when first, have when having osculating element on crack surface on rigidity-crack surface of Stiffness amount=healthy gear
The rigidity of Gear with Crack during osculating element, the percentage error of mesh stiffness=[(Stiffness amount when establishing contact-do not contact
When Stiffness amount)/contactless unit when Stiffness amount] × 100%.
Using the post-processing function of ANSYS softwares, the displacement cloud of Gear with Crack under the conditions of different crack depths is respectively obtained
Contact distribution on figure and crack surface, in order to for error producing cause is explained further, as shown in Figure 5.Wherein, scheme
(a), (b), (c) are respectively crack depth q when being contacted on crack surface without foundation in 50Corresponding to=5mm, 15mm, 25mm
Displacement cloud atlas；As can be seen from the figure crack surface is mutually invaded and not conformed to the actual conditions.(d), (e), (f) are respectively in Fig. 5
When contact is established on crack surface, crack depth q0Displacement cloud atlas corresponding to=5mm, 15mm, 25mm；As can be seen from the figure split
Line face is not invade mutually and have Relative sliding and with being actually consistent.(g), (h), (i) are respectively to be established on crack surface in Fig. 5
After contact, crack depth q0Contact distribution on=5mm, 15mm, 25mm crack surface.
It can find out from Fig. 4 and table 2：(1) no matter contact whether is established on crack surface, with the increase of crack depth,
Gear Meshing Stiffness gradually decreases；(2) when the crackle gear teeth do not enter into engagement (see region 1), percentage error is gradually less.
But (see region 2) after the crackle gear teeth enter and engaged, percentage error tends to 0, i.e., osculating element is for time-varying on crack surface
Mesh stiffness does not influence；Reason is as shown in Figure 5：(1) with the increase of crack depth, real contact area and whole on crack surface
Individual crack surface area ratio is gradually smaller；(2) with the increase of crack depth, contact is gradually smaller on crack surface.So
Actual contact portion role is gradually smaller on crack surface, and percentage error is gradually smaller.
The percentage error of mesh stiffness under the conditions of the different crack depths of table 2
Step 3.1.2：The influence that analysis matrix cracking depth strains for Gear Root.Due to Gear Root position tension
Stretch or extrude most serious, and to study influence of the crackle for strain, so the point Q of tooth root position one makees on the left of the selection crackle gear teeth
For strain extraction point (the crackle gear teeth are close to tooth root position), the position of Q points is as shown in figure 3, Q points are apart from the distance of gear face
27mm.In each position of engagement of gear, the post-processing function of ANSYS softwares, the strain of extraction Q points are utilized.With mesh cycle
For abscissa, the strain of correspondence position Q points is ordinate, draws the curve that the strain of Q points changes with mesh cycle.Nothing on crack surface
Q points strain extracting mode and answer Q points strain extracting mode identical when having osculating element on crack surface during osculating element.
Q point tooth root strain curves are as shown in fig. 6, wherein (I) under the conditions of having osculating element and contactless unit on crack surface
Contact is established on crack surfaceRepresent q0=5mm,Represent q0=15mm,Represent q0=25mm, (II) are split
Without foundation contact on line faceRepresent q0=5mm,Represent q0=15mm,Represent q0=25mm ,-
Represent healthy, the strain slippages in Fig. 6 corresponding to 3 engagement moment such as A to C are as shown in table 3, contactless unit on crack surface
When Q points strain slippage=healthy gear Q points strain-crack surface on contactless unit Gear with Crack Q points strain, have on crack surface
Being strained during osculating element has the strain of osculating element Gear with Crack Q points on slippage=healthy gear Q points strain-crack surface.Strain
Percentage error=[(strain strain when having an osculating element on slippage-crack surface on crack surface during contactless unit to decline
Amount) slippage is strained during contactless unit on/crack surface] × 100%.
Drawn from Fig. 6 and table 3 to draw a conclusion：(1) in region 1 and region 2, the change of the percentage error of Q points strain
Trend and the reason for produce the trend it is identical with step 3.1.1；(2) it is worth noting that in region 1, when on crackle crack surface
Contact is not established, i.e., when not considering the interaction between crack surface, the strain of Q points tends to 0；Consider the phase between crack surface
During interaction, Q points bear compressive strain.Because when on crackle crack surface without establish contact when, crack surface do not have it is restrained,
The matrix bearing capacitys of crack surface both sides decline it is a lot, so the strain of Q points is almost 0, but this do not meet it is actual.(3)
From fig. 6 it can be seen that Q points alternately bear compressive strain and stretching strain, and as the increase of crack depth, strain gradually subtract
It is small.
The percentage error that tooth root strains under the conditions of the different crack depths of table 3
Step 3.2：Analyze influence of the matrix cracking width for gear meshing characteristic.
Step 3.2.1：Influence of the different matrix crack width for Gear Meshing Stiffness is studied, is carrying out finite element solving
When, the way of restraint of gear, application mode of loading, mesh stiffness solution mode are identical with step 3.1.1.Crack Parameters are：Split
Line width Lc=5mm, 15mm, 25mm, crack initiation site angle ψ=35 °, crack depth q0=25mm, direction of crack propagation angle υ
=45 °.There is osculating element on crack surface and be not in contact with mesh stiffness curve under the conditions of unit as shown in fig. 7, wherein (I) crackle
Contact is established on faceRepresent q0=5mm,Represent q0=15mm,Represent q0=25mm, (II) crack surface
It is upper to be contacted without foundationRepresent q0=5mm,Represent q0=15mm,Represent q0=25mm ,-represent
Stiffness amount corresponding to 5 engagement moment such as health, A to E is as shown in table 4.It can find out in region from Fig. 7 and table 4
1, with the increase of crack width, mesh stiffness percentage error gradually increases, but is missed in region 2, mesh stiffness percentage
Differential nearly 0.(a), (b), (c) are crack width L respectively in Fig. 8cDuring=5mm, 15mm, 25mm, the contact on crack surface.
It can go out from Fig. 8, with the increase of row line width, contact gradually increases on crack surface, between illustrating on crackle broken face
Interaction it is increasing, so engagement percentage error gradually increase with the increase of crack width.
The percentage error of mesh stiffness under the conditions of 4 different crack widths of table
Step 3.2.2：The influence that research different matrix crack width strains for Gear Root, crack width Lc=5mm,
Under the conditions of 15mm, 25mm, the strain extracting mode of Q points is identical with step 3.1.2, and Q point strain curves are as shown in figure 9, wherein (I)
Contact is established on crack surfaceRepresent q0=5mm,Represent q0=15mm,Represent q0=25mm, (II) are split
Without foundation contact on line faceRepresent q0=5mm,Represent q0=15mm,Represent q0=25mm ,-
Health is represented, the tooth root strain slippage corresponding to engagement moment A, B, C is as shown in table 5.It can find out from Fig. 9 and table 5,
Region 1, with the increase of crack width, strain is gradually reduced.But percent strain error with the increase of crack width and
Gradually increase.In region 2, percent strain error is close to 0.
The percentage error that tooth root strains under the conditions of 5 different crack widths of table
Step 4：Analyze mesh stiffness and strain curve.It can be seen that from step 3.1 and 3.2：
(1) as the increase of matrix cracking depth and width, mesh stiffness and strain are gradually reduced.(2) consider and do not examine
Consider the interaction between crack surface, the mesh stiffness of Gear with Crack and strain are different.It is worth noting that with splitting
The increase of line depth, mesh stiffness and percent strain error are gradually reduced, and this is due to actual contact portion between crack surface
Be gradually reduced with the area ratio of whole crack surface with the increase of crack depth, at the same the contact on crack surface with
The increase of crack depth and be gradually reduced, on crack surface contact portion role be gradually reduced.In contrast, with splitting
The increase of line width, the contact on crack surface gradually increase, on crack surface contact portion role gradually increase, so
Mesh stiffness and percent strain error gradually increase with crack width.To sum up, for non-penetrating matrix cracking gear, consider
Interaction between crack surface make it that mesh stiffness and strain result are more accurate.Due to smaller matrix cracking depth with
And under conditions of larger matrix cracking width, percentage error is bigger, so mutual between at this time considering crack surface
Effect.
The above described is only a preferred embodiment of the present invention, being not the limitation that other forms are done to the present invention, appoint
What those skilled in the art changed or be modified as possibly also with the technology contents of the disclosure above equivalent variations etc.
Imitate embodiment.But it is every without departing from technical solution of the present invention content, the technical spirit according to the present invention is to above example institute
Any simple modification, equivalent variations and the remodeling made, still fall within the protection domain of technical solution of the present invention.
Claims (6)
1. a kind of gear meshing characteristic finite element method for considering matrix cracking and influenceing, it is characterised in that it includes following
Step：
S1, the gear pair basic parameter for obtaining driving wheel and driven pulley and the Crack Parameters containing matrix cracking gear；
S2, the gear three-dimensional finite element model containing the non-penetrating matrix cracking of parabola is established, including
S201, according to the gear pair basic parameter, using the APDL language programmed functions of ANSYS softwares, use Solid185
Unit simulation gear entity, establish healthy gear three-dimensional finite element model；
S202, on the basis of the healthy gear three-dimensional finite element model, to gear matrix carry out cut generation contain base
The gear FEM model of body crackle；
S203, the crack surface to the gear FEM model containing matrix cracking carry out mesh refinement, and according to crackle
Interaction between face, surface-to-surface contact elements Conta174 and Targe170 are established on the crack surface；
S3, according to the Crack Parameters, calculate gear meshing characteristic, and calculate to establish on crack surface and whether contact for calculating knot
The difference of fruit；Wherein, the Crack Parameters include crack depth, crack width, the gear meshing characteristic include mesh stiffness,
Strain.
2. the method as described in claim 1, it is characterised in that the gear pair basic parameter includes the number of teeth, modulus of elasticity, pool
Loose ratio, internal bore radius, base radius, modulus, the facewidth, pressure angle, addendum coefficient, tip clearance coefficient, coefficient of friction；The crackle
Parameter includes crack initiation site angle, crack width, crack depth, direction of crack propagation angle.
3. method as claimed in claim 2, it is characterised in that the step S201 comprises the following steps：
S20101, the gear in the gear pair basic parameter modulus of elasticity, Poisson's ratio, internal bore radius, basic circle
Radius, modulus, pressure angle, addendum coefficient, tip clearance coefficient, coefficient of friction, utilize the tooth of the single gear of ANSYS Software Creates
Exterior feature, the flank profil include involute and easement curve；
S20102, swivel replication is carried out to the single gear teeth, generate healthy gear two-dimensional finite element model；
S20103, the gear two-dimensional finite element model to generation stretch along gear centre axis, and its tensile elongation is described
The size of facewidth numerical value, generate healthy gear three-dimensional finite element model；
S20104, mesh refinement is carried out to the flank of tooth near path of contact.
4. method as claimed in claim 3, it is characterised in that the step S202 comprises the following steps：
S20201, in the healthy gear three-dimensional finite element model, according to the original position of matrix cracking, Crack Extension side
To selecting cracked gear body portion；
S20202, ordered using " VSBL " in ANSYS, by selected gear body portion according to the crack initiation site, crackle
Propagation direction is divided into two parts entity；
S20203, coordinate system is established on the divisional plane of two parts entity, worn according to the generation of crackle parabolic curve equation is non-
Saturating matrix cracking, the crackle parabolic curve equation are：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>q</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>x</mi>
<mo>&Element;</mo>
<mo>&lsqb;</mo>
<mi>L</mi>
<mo>-</mo>
<msub>
<mi>L</mi>
<mi>c</mi>
</msub>
<mo>,</mo>
<mi>L</mi>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>q</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
<msqrt>
<mfrac>
<mrow>
<msub>
<mi>L</mi>
<mi>c</mi>
</msub>
<mo>-</mo>
<mi>x</mi>
</mrow>
<msub>
<mi>L</mi>
<mi>c</mi>
</msub>
</mfrac>
</msqrt>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>x</mi>
<mo>&Element;</mo>
<mo>&lsqb;</mo>
<mn>0</mn>
<mo>,</mo>
<msub>
<mi>L</mi>
<mi>c</mi>
</msub>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, q (x) be optional position x at crack depth, q0For initial crack depth, LcFor crack width, L is gear width.
5. method as claimed in claim 4, it is characterised in that carrying out mesh refinement to crack surface in the step S203 includes
Three boundary curves for forming crack surface are subjected to equidistant partition first with " LESIZE " order, recycle " VMESH " order pair
Crack surface is refined.
6. method as claimed in claim 5, it is characterised in that the step S3 includes：
S301, according to matrix cracking depth, calculate the gear meshing characteristic, comprise the following steps：
S30101, enter row constraint, the way of restraint to gear in the gear three-dimensional finite element model that step S2 is established
Including making master and slave wheel inner ring node and respective geometric center be coupled, Complete Bind driven pulley central point, constraint is actively
Wheel central point is allowed to can only be around central axis；Apply mode of loading and be included in the application torque of driving wheel geometric center, led
The angular displacement of driving wheel；According to the calculation formula of mesh stiffness, obtain when establishing contact on crack surface and not establishing contact, it is different
Matrix cracking depth conditions lower gear mesh stiffness, wherein, the calculation formula of the mesh stiffness is：
<mrow>
<mi>K</mi>
<mo>=</mo>
<mfrac>
<mi>T</mi>
<mrow>
<mi>&Delta;</mi>
<mi>&theta;</mi>
<mo>*</mo>
<msubsup>
<mi>r</mi>
<mi>b</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, K represents mesh stiffness, and T represents the torque being applied on driving wheel, and Δ θ represents the angular displacement of driving wheel, rbBased on
Driving wheel base radius；
During according to being contacted on line face during contactless unit on rigidity-crack surface of Stiffness amount=healthy gear without foundation
The rigidity of Gear with Crack, establish and connect on rigidity-crack surface of Stiffness amount=healthy gear when having osculating element on crack surface
The rigidity of Gear with Crack when touching, calculate to obtain and contact is established on crack surface and is not established in the case of contact, mesh stiffness slippage
Percentage error, percentage error=[(Stiffness during contactless unit on crack surface of the mesh stiffness slippage
Stiffness amount when having osculating element on amount-crack surface) Stiffness amount during contactless unit on/crack surface] × 100%；
Meanwhile using the post-processing function of ANSYS softwares, obtain the displacement cloud atlas of Gear with Crack under the conditions of different crack depths with
And the contact distribution on crack surface；
S30102, according to different matrix crack depth, calculate the strain of tooth root：Select the crackle gear teeth close to tooth root position a bit
Q, in each position of engagement of gear, using the post-processing function of ANSYS softwares, extracts the Q points as strain extraction point
Strain；According to Q points strain contactless list on slippage=healthy gear Q points strain-crack surface during contactless unit on crack surface
First Gear with Crack Q points strain, Q points strain slippage=healthy gear Q points strain-crack surface when having osculating element on crack surface
On have the strain of osculating element Gear with Crack Q points, obtain the percentage error of Q points strain, the percentage error of Q points strain=[(split
Q points strain slippage when having osculating element on Q points strain slippage-crack surface during contactless unit on line face) on/crack surface
Q points strain slippage during contactless unit] × 100%；
S302, according to matrix cracking width, calculate the gear meshing characteristic, including：
S30201, according to matrix cracking width, calculate the Gear Meshing Stiffness：The constrained procedure of the gear and the application
Mode of loading is with the S30101, and Gear Meshing Stiffness formula is the same as the S30101 under the conditions of different matrix crack width；
Meanwhile using the post-processing function of ANSYS softwares, obtain the contact point on crack surface under the conditions of different crack widths
Cloth；
S30202, according to matrix cracking width, calculate the Gear Root strain：Computational methods are the same as the step S30102.
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| CN109063613A (en) * | 2018-07-20 | 2018-12-21 | 东北大学 | Based on the synchronous nonstationary random response method for extracting transformation of Generalized parametering |
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| CN109684655B (en) * | 2018-11-01 | 2023-04-07 | 沈阳工业大学 | Method for calculating meshing stiffness of straight gear with non-penetrating cracks |
| CN109726520A (en) * | 2019-02-01 | 2019-05-07 | 东北大学 | Consider the spur gear mesh stiffness calculation method of complicated substrate and crack propagation path |
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| CN109977617B (en) * | 2019-04-25 | 2023-06-09 | 南京钢铁股份有限公司 | APDL language-based steel plate flame cutting thermal-force coupling simulation analysis method |
| CN112855922A (en) * | 2021-02-11 | 2021-05-28 | 中国人民解放军陆军装甲兵学院 | Planetary gear crack depth evaluation method |
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Application publication date: 20171208 Assignee: Beijing Xindian Hengyi Technology Co.,Ltd. Assignor: Northeastern University Contract record no.: X2022210000070 Denomination of invention: A Finite Element Analysis Method of Gear Meshing Characteristics Considering the Effect of Matrix Crack Granted publication date: 20200414 License type: Common License Record date: 20221213 |