CN107153736B - A kind of the considerations of amendment, rouses the gear pair meshing characteristic analysis method to correction of the flank shape - Google Patents
A kind of the considerations of amendment, rouses the gear pair meshing characteristic analysis method to correction of the flank shape Download PDFInfo
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Abstract
A kind of gear pair meshing characteristic analysis method of the considerations of the present invention relates to amendments drum to correction of the flank shape, this method is to obtain the basic parameter of gear pair and rouse to profile modifying parameters, it along facewidth Directional Decomposition is N number of independent and uniform web gear by the gear teeth of gear pair, based on the tooth profile error roused to profile modifying gear pair, using the gear pair meshing characteristic analysis method for considering that extension engagement influences, the time-variant mesh stiffness of every plate sheet gear pair is calculated；The engaging tooth wheel set threedimensional model containing drum to correction of the flank shape is established by three-dimensional drawing simulation softward, threedimensional model is imported into ANSYS software and establishes three-dimensional finite element contact model, solves the time-variant mesh stiffness data in the entire engagement process of gear；Analysis method modeling process of the invention is simple, and calculation amount is small, lower to computer requirement, and calculated result is accurately true.
Description
Technical field
The invention belongs to mechanical kinetics technical fields, and in particular to the gear pair roused the considerations of a kind of amendment to correction of the flank shape
Meshing characteristic analysis method.
Background technique
Currently, existing consideration drum mainly has following 2 kinds of methods to the gear pair meshing characteristic analysis method of correction of the flank shape:
1. based on commercial finite element analysis software
Three-dimensional CAD model is imported into commercial finite element analysis software or establishes three-dimensional mould directly in finite element software
Type selects suitable unit and material parameter, carries out grid dividing to threedimensional model, establishes the finite element contact of engaging tooth wheel set
Model, setting suitably constrain and method for solving appropriate are selected to analyze the meshing characteristic of gear pair.But it utilizes existing
Commercial finite element analysis software to considering that drum is engaged specificity analysis to the gear pair of correction of the flank shape when, modeling process is complicated and numerous
Weight, computational efficiency is low, more demanding to computer performance, and is nibbled using what different modeling pattern and cell type obtained
It closes characteristic and also has larger gap.
2. the modeling method based on cantilever beam
Gear tooth is simplified to Flexural cantilever model, rigidity modeling is engaged based on energy method.However existing consideration
Drum has ignored nonlinear contact rigidity, finite element amendment MATRIX STIFFNESS, extends to the gear pair meshing characteristic analysis method of correction of the flank shape
The influence of engagement can not accurately calculate the flexible deformation of the gear teeth, larger with the resultant error of FEM calculation, cannot be true
Reflect the meshing characteristic of gear pair.
Therefore, in the prior art the considerations of drum to the gear pair meshing characteristic analysis method of correction of the flank shape, not only modeling process is complicated
And it is heavy, computational efficiency is low, and it is more demanding to computer performance, and have ignored nonlinear contact rigidity, finite element amendment
MATRIX STIFFNESS, the influence for extending engagement, can not accurately calculate the flexible deformation of the gear teeth, the resultant error with FEM calculation
It is larger, it cannot really reflect the meshing characteristic of gear pair.
Summary of the invention
(1) technical problems to be solved
For existing technical problem, the considerations of present invention proposes a kind of amendment drum engaged to the gear pair of correction of the flank shape it is special
Property analysis method, solve that modeling process in the prior art is complicated and heavy, and computational efficiency is low, to computer performance requirement
The problems such as higher, the resultant error of calculating is larger, cannot really reflect the meshing characteristic of gear pair.
(2) technical solution
In order to achieve the above object, the main technical schemes that the present invention uses include:
A kind of the considerations of amendment, rouses the gear pair meshing characteristic analysis method to correction of the flank shape, includes the following steps:
S1: it obtains the basic parameter of gear pair and rouses to profile modifying parameters；
S2: being based on gear pair total profile deviation, establishes and considers nonlinear contact, finite element amendment MATRIX STIFFNESS, extends engagement
The drum of influence is to profile modifying gear pair mesh stiffness computation model；
S2.1: along facewidth Directional Decomposition being N number of independent and uniform web gear by the gear teeth of gear pair, and L indicates the facewidth,
N indicates total thin slice number, as shown in Figure 2.Every plate sheet gear is calculated in the total profile deviation of each position of engagement；In Fig. 2 a and Fig. 2 c
In, dotted line indicates drum to modification curve (circular curve), and each plate sheet gear-profile deviation can indicate are as follows:
En=Ep,n+Eg,n
(1)
In formula,Respectively indicate driving wheel and driven wheel
Total profile deviation；znIt is each thin slice along the coordinate in facewidth direction；RpAnd RgIndicate that the drum of driving wheel and driven wheel is round to modification curve
Arc radius, they can be indicated are as follows:
In formula, L is the facewidth, as shown in Figure 3: cβIt is the profiling quantity of axial modification；
S2.2: rigid using consideration nonlinear contact, finite element amendment matrix based on drum to the total profile deviation of profile modifying gear pair
Degree extends the gear pair meshing characteristic analysis method that engagement influences, and the time-variant mesh stiffness of every plate sheet gear pair is calculated
kn, to obtain maximum deformation quantity of the thin slice spur gear pair in engagement process:
In formula, F is total engagement force, QmFor maximum deformation quantity, n is natural number, and N is the web gear number decomposed, EnIt is each
Plate sheet gear-profile deviation, knFor the time-variant mesh stiffness of each plate sheet gear pair.To make QmCalculated result is more accurate,
This method is by the way of iterating, knIt calculates according to the following formula and further substitutes into formula (3):
S2.3: according to maximum deformation quantity Q of the thin slice spur gear pair in engagement processm, drum is calculated to profile modifying gear
Time-variant mesh stiffness of the pair in each position of engagement of entire flank profil:
Consider to be expressed as follows containing drum to the spur gear pair of correction of the flank shape engagement global stiffness:
S3: the engaging tooth wheel set threedimensional model containing drum to correction of the flank shape is established, threedimensional model is imported into ANSYS software, is established
Three-dimensional finite element contact model solves the time-variant mesh stiffness data in the entire engagement process of gear；
S3.1: it is established containing drum by three-dimensional drawing software Autodesk Inventor Professional (AIP) to repairing
The engaging tooth wheel set threedimensional model of shape saves as " .sat " file that ANSYS can be identified, and imported into ANSYS software；
S3.2: defining contact type, and creation contact pair selects solid element Solid185, osculating element Conta174 wound
Contact pair is built, contact type is set as Standard contact, and contact stiffness coefficient is set as 1.0, and coefficient of friction is set as 0.2, considers to extend and nibble
It closes effect and creates 3 gear contacts pair, pass through ANSYS automatic identification contact condition；
S3.3: applying constraint, constrains all freedom degrees of driven gear inner hole boundary node, builds at driving gear inner hole center
A vertical node is defined as a rigid region as main controlled node, by driving gear inner hole boundary point and main controlled node, constrains
The translational degree of freedom of main controlled node retains its rotational freedom；
S3.4: defining load, applies tangential force F on all nodes in driving gear inner hole boundary and carrys out simulation torque:
In formula: T1For input torque, rint1For driving gear internal bore radius, n indicates driving gear inner hole boundary node number,
LeFor effective working flank width.The a certain gear teeth of driven gear have just been entered to the position of engagement as reference position, from this
The process that position starts to the lower gear teeth of driven wheel to enter engagement is a mesh cycle.In the process, driving wheel turns over
AngleBy driving gear turns in a mesh cycle angle bisecting at 120 parts, obtain 121 it is discrete
Angle position loads each discrete location.
S3.5: it solves processor and the gear engagement model data of each position of engagement is solved；
S3.6: result is extracted in processing: being extracted the driving wheel corner deflection of each discrete location, is acquired often according to formula 8
The mesh stiffness k of one discrete location, to obtain the time-variant mesh stiffness in the entire engagement process of gear；
In formula, T1For torque suffered by gear, Δ θ is the corner deflection of gear, rb1For driving gear base radius；
S4: the root-mean-square error based on analytical Calculation result and finite element solving result:
In formula, λ is the independent variable of error function；kA-AMAnd kB-AMIt is analytical Calculation result respectively in bidentate class mark position A
With the mesh stiffness of monodentate class mark position B；
kA-FEMAnd kB-FEMIt is that engagement of the finite element solving result in bidentate class mark position A and monodentate class mark position B is rigid
Degree；
With the minimum target of root-mean-square error, different drums are obtained to profiling quantity cβTime-variant mesh stiffness analytic method it is rigid
Spend correction factor λk, λ is acquired using quadratic function approximating methodkAnd cβBetween relational expression:
In formula, a, b, c are the coefficient of quadratic equation；
S5: any drum is given to profiling quantity cβ, gear pair time-variant mesh stiffness K is calculated by S2T, pass through the calculating pair of formula 8
The correction factor λ answeredk, obtain accurate time-variant mesh stiffness result K=λk·KT, further obtain time-variant mesh stiffness curve
Figure.
(3) beneficial effect
The beneficial effects of the present invention are: the considerations of amendment provided by the invention drum is analyzed to the gear pair meshing characteristic of correction of the flank shape
Method, modeling process is simple, and calculation amount is small, lower to computer performance requirement, and considers nonlinear contact rigidity, has
Limit member amendment MATRIX STIFFNESS, the influence for extending engagement, therefore can accurately calculate the flexible deformation of the gear teeth, at the same with it is limited
The resultant error that member calculates is small, can really reflect the meshing characteristic of gear pair.
Detailed description of the invention
Gear pair meshing characteristic analysis method of the considerations of Fig. 1 is the amendment in the specific embodiment of the invention drum to correction of the flank shape
Flow chart；
Fig. 2 is model of gear schematic diagram of the consideration drum in the specific embodiment of the invention to correction of the flank shape, wherein (a) is indicated
The entire gear teeth are (b) the gear thin slice after discrete, (c) are to rouse to modification curve schematic diagram；
Fig. 3 is the structural schematic diagram of driving gear in the specific embodiment of the invention；
Fig. 4 is drum in the specific embodiment of the invention to profiling quantity cβRespectively 0 μm, 5 μm, 10 μm, 15 μm, 20 μm
The parsing of gear time-variant mesh stiffness and result of finite element, wherein (a) indicates parsing result, (b) indicates finite element result；
Fig. 5 is the stiffness modification being fitted using quadratic function approximating method in the specific embodiment of the invention
Curve；
Fig. 6 is (c under any given profiling quantity in the specific embodiment of the inventionβ=2.5 μm, 7.5 μm, 12.5 μm and
17.5 μm), it is calculated using finite element method and using the gear pair meshing characteristic analysis method meter roused the considerations of amendment to correction of the flank shape
Obtained time-variant mesh stiffness curve comparison figure (b) indicates finite element result wherein (a) indicates parsing result.
Specific embodiment
In order to preferably explain the present invention, in order to understand, with reference to the accompanying drawing, by specific embodiment, to this hair
It is bright to be described in detail.
The considerations of present embodiment discloses a kind of amendments as shown in Figure 1: is roused to the gear pair meshing characteristic analysis side of correction of the flank shape
Method, comprising the following steps:
S1: it obtains the basic parameter of gear pair and rouses to profile modifying parameters；
In the present embodiment, basic parameter and the drum for obtaining gear pair are as shown in table 1 to profile modifying parameters:
Table 1 is roused to profile modifying gear pair basic parameter
In the present embodiment, drum is 0~20 μm to profiling quantity, and it is expected to be quickly obtained within the scope of this any drum to profiling quantity
The time-variant mesh stiffness of lower tooth wheel set.
S2: being based on gear pair tooth profile error, establishes and considers nonlinear contact, finite element amendment MATRIX STIFFNESS, extends engagement
The drum of influence is to profile modifying gear pair mesh stiffness computation model；
S2.1: drum is chosen to profile modifying parameters cβFor 0 μm, 5 μm, 10 μm, 15 μm, 20 μm, by the gear teeth of gear pair along the facewidth
Directional Decomposition is 40 independences and uniform web gear.Every plate sheet gear is calculated in each engagement according to formula (1)~(2)
The total profile deviation E of positionn；
S2.2: rigid using consideration nonlinear contact, finite element amendment matrix based on drum to the total profile deviation of profile modifying gear pair
Degree extends the gear pair meshing characteristic analysis method that engagement influences, and the time-variant mesh stiffness of every plate sheet gear pair is calculated
kn, to obtain maximum deformation quantity Q of the thin slice spur gear pair in engagement processm；By the way of iterating, according to formula
(4) k is calculatednAnd formula (3) further are substituted into, to obtain more accurate Qm；
S2.3: according to maximum deformation quantity Q of the thin slice spur gear pair in engagement processm, calculated by formula (5) or (6)
Obtain time-variant mesh stiffness K of the drum to profile modifying gear pair in each position of engagement of entire flank profilT, stiffness curve is as shown in fig. 4 a；
S3: the engaging tooth wheel set threedimensional model containing drum to correction of the flank shape is established, driving wheel threedimensional model is as shown in figure 3, by three-dimensional
Model imported into ANSYS software, establishes three-dimensional finite element contact model, and the time-varying engagement solved in the entire engagement process of gear is rigid
Degree evidence, finite element solving result are as shown in Figure 4 b；
Specifically, it S3.1: is built respectively by three-dimensional drawing software Autodesk Inventor Professional (AIP)
The vertical drum that contains is to profiling quantity cβEngaging tooth wheel set threedimensional model when being 0 μm, 5 μm, 10 μm, 15 μm, 20 μm, saving as ANSYS can
With " .sat " file of identification, and it is directed respectively into ANSYS software；
S3.2: defining contact type, and creation contact pair selects solid element Solid185, osculating element Conta174 wound
Contact pair is built, contact type is set as Standard contact, and contact stiffness coefficient is set as 1.0, and coefficient of friction is set as 0.2, considers to extend and nibble
It closes effect and creates 3 gear contacts pair, pass through ANSYS automatic identification contact condition.
S3.3: applying constraint, constrains all freedom degrees of driven gear inner hole boundary node, builds at driving gear inner hole center
A vertical node is defined as a rigid region as main controlled node, by driving gear inner hole boundary point and main controlled node, constrains
The translational degree of freedom of main controlled node retains its rotational freedom.
S3.4: defining load, applies tangential force F (calculating by formula 7) on all nodes in driving gear inner hole boundary
Carry out simulation torque, using a certain gear teeth of driven gear just enter engagement position as reference position, since this position to
The process that the lower gear teeth of driven wheel enter engagement is a mesh cycle.In the process, the angle that driving wheel turns overBy driving gear turns in a mesh cycle angle bisecting at 120 parts, 121 discrete angles are obtained
Position loads each discrete location；
S3.5: it solves processor and the gear engagement model data of each position of engagement is solved；
S3.6: extraction is handled as a result, extracting the driving wheel corner deflection of each discrete location, is acquired according to formula (8)
The mesh stiffness k of each discrete location, to obtain the time-variant mesh stiffness in the entire engagement process of gear；
S4: based on analytical Calculation result and finite element solving result in bidentate class mark position A and monodentate class mark position B
Mesh stiffness, as shown in table 2, root-mean-square error function representation are as follows:
In formula, λ is the independent variable of error function；kA-AMAnd kB-AMIt is analytical Calculation result respectively in bidentate class mark position A
With the mesh stiffness of monodentate class mark position B；kA-FEMAnd kB-FEMIt is finite element solving result in bidentate class mark position A and list
The mesh stiffness of tooth class mark position B.
Using root-mean-square error minimum value as target, different drums are obtained to profiling quantity cβTime-variant mesh stiffness analytic method
Stiffness modification λk(being shown in Table 2) acquires λ using quadratic function approximating methodkAnd cβBetween relational expression:
In formula, the coefficient of quadratic equation is respectively a=5.065 × 10-4, b=-1.255 × 10-3, c=0.9954, fitting
Curve is shown in Fig. 5.
The time-variant mesh stiffness and rigidity that analytic method and finite element method are calculated at the single, double tooth class mark of table 2 are repaired
Positive coefficient
S5: any drum is given to profiling quantity cβ=2.5 μm, 7.5 μm, 12.5 μm and 17.5 μm, gear pair is calculated by S2
Time-variant mesh stiffness KT, corresponding correction factor λ is calculated by formula 8k, then accurate time-variant mesh stiffness result K=can be obtained
λk·KT, time-variant mesh stiffness curve graph is obtained, such as Fig. 6 a, the error of the modification method and finite element method is as shown in table 3, most
Big error is only 2.1%.
3 analytic modell analytical model of table amendment front and back time-variant mesh stiffness and finite element method compare
From the present embodiment it can be seen that drum is to the gear pair meshing characteristic of correction of the flank shape point the considerations of the amendment of offer of the invention
Analysis method, modeling process is simple, and calculation amount is small, lower to computer performance requirement, and it is rigid to have considered nonlinear contact
Degree finite element amendment MATRIX STIFFNESS, extends the influence of engagement, therefore can accurately calculate the flexible deformation of the gear teeth, simultaneously
It is small with the resultant error of FEM calculation, it can really reflect the meshing characteristic of gear pair.
The technical principle of the invention is described above in combination with a specific embodiment, these descriptions are intended merely to explain of the invention
Principle shall not be construed in any way as a limitation of the scope of protection of the invention.Based on explaining herein, those skilled in the art
It can associate with other specific embodiments of the invention without creative labor, these modes fall within this hair
Within bright protection scope.
Claims (7)
1. a kind of the considerations of amendment, rouses the gear pair meshing characteristic analysis method to correction of the flank shape, which comprises the following steps:
S1: it obtains the basic parameter of gear pair and rouses to profile modifying parameters；
S2: being based on gear pair total profile deviation, establishes and considers that nonlinear contact, finite element amendment MATRIX STIFFNESS, extension engagement influence
Drum to profile modifying gear pair mesh stiffness computation model；
S3: the engaging tooth wheel set threedimensional model containing drum to correction of the flank shape is established by three-dimensional drawing simulation softward, and threedimensional model is led
Enter to ANSYS software and establish three-dimensional finite element contact model, solves the time-variant mesh stiffness data in the entire engagement process of gear；
S4: different drums are obtained to profiling quantity cβTime-variant mesh stiffness analytic method correction factor λk, using quadratic interpolation method
Acquire λkAnd cβBetween relational expression；
S5: any drum is given to profiling quantity cβ, calculate gear pair time-variant mesh stiffness KTAnd corresponding correction factor λk, obtain essence
True time-variant mesh stiffness result K=λk·KT, obtain time-variant mesh stiffness curve graph；
The step S2 further include:
S2.1: along facewidth Directional Decomposition it is N number of independent and uniform web gear by the gear teeth of gear pair, and calculates every plate sheet
Tooth profile error of the gear in each position of engagement；
S2.2: using the gear pair meshing characteristic point for considering that nonlinear contact, finite element amendment MATRIX STIFFNESS, extension engagement influence
The time-variant mesh stiffness k of every plate sheet gear pair is calculated in analysis methodn；
S2.3: on the basis of being in meshing state by all web gear pairs, drum is calculated to profile modifying gear pair in entire tooth
The time-variant mesh stiffness of wide each position of engagement.
2. the considerations of amendment according to claim 1 rouses the gear pair meshing characteristic analysis method to correction of the flank shape, feature exists
In the step S3 further include:
S3.1: it is established containing bulging by three-dimensional drawing software Autodesk Inventor Professional (AIP) to correction of the flank shape
Engaging tooth wheel set threedimensional model；
S3.2: defining contact type, and creation contact pair selects solid element Solid185, osculating element Conta174 creation to connect
Touching pair, contact type are set as Standard contact, and contact stiffness coefficient is set as 1.0, and coefficient of friction is set as 0.2, consider to extend engagement effect
3 gear contacts pair should be created, ANSYS automatic identification contact condition is passed through；
S3.3: applying constraint, constrains all freedom degrees of driven gear inner hole boundary node, establishes one at driving gear inner hole center
A node is defined as a rigid region as main controlled node, by driving gear inner hole boundary point and main controlled node, constrains master control
The translational degree of freedom of node retains its rotational freedom；
S3.4: defining load, applies tangential force F on all nodes in driving gear inner hole boundary and carrys out simulation torque:
In formula: T1For input torque, rint1For driving gear internal bore radius, n indicates driving gear inner hole boundary node number, LeFor
Effective working flank width；
S3.5: it solves processor and the gear engagement model data of each position of engagement is solved；
S3.6: processing is extracted as a result, the driving wheel corner deflection of each discrete location is extracted, according to formulaIt acquires
The mesh stiffness k of each discrete location obtains the time-variant mesh stiffness data in the entire engagement process of gear；
In formula, T1For torque suffered by gear, Δ θ is the corner deflection of gear, rb1For driving gear base radius.
3. the considerations of amendment according to claim 1 rouses the gear pair meshing characteristic analysis method to correction of the flank shape, feature exists
In the time-variant mesh stiffness k of every plate sheet gear pair is calculated in the methodn, thus obtain thin slice spur gear pair and nibbling
Maximum deformation quantity Q during conjunctionmAre as follows:
In formula, F is total engagement force, QmFor maximum deformation quantity, n is natural number, and N is the web gear number decomposed, EnIt is every a piece of thin
Plate gear total profile deviation, knFor the time-variant mesh stiffness of each plate sheet gear pair.
4. the considerations of amendment according to claim 3 rouses the gear pair meshing characteristic analysis method to correction of the flank shape, feature exists
In, the method also includes: to make QmCalculated result is more accurate, and Q is acquired by the way of iteratingm, knCalculation formula
It is as follows:
In formula, knFor the time-variant mesh stiffness of each plate sheet gear pair, QmFor maximum deformation quantity, knFor each plate sheet gear
Secondary time-variant mesh stiffness, EnFor every plate sheet gear-profile deviation, θ indicates the corner in Meshing Process of Spur Gear, reflects gear
Change in location in engagement process, i.e. kn(θ) indicates the rigidity at the θ of the position of engagement.
5. the considerations of amendment according to claim 1 rouses the gear pair meshing characteristic analysis method to correction of the flank shape, feature exists
In time-variant mesh stiffness K of the drum to profile modifying gear pair in each position of engagement of entire flank profilTAre as follows:
It is described to consider to be expressed as follows containing drum to the spur gear pair of correction of the flank shape engagement global stiffness:
In formula, QmFor maximum deformation quantity, KTTime-varying engagement for drum to profile modifying gear pair in each position of engagement of entire flank profil is rigid
Degree, F are total engagement force, QmFor maximum deformation quantity, n is natural number, and N is the web gear number decomposed, EnFor each plate sheet gear
Total profile deviation, knFor the time-variant mesh stiffness of each plate sheet gear pair.
6. the considerations of amendment according to claim 1 rouses the gear pair meshing characteristic analysis method to correction of the flank shape, feature exists
In analytical Calculation result and the resulting root-mean-square error function of finite element solving result in step S4 are as follows:
In formula, λ is the independent variable of error function, kA-AMAnd kB-AMIt is analytical Calculation result respectively in bidentate class mark position A and list
The mesh stiffness of tooth class mark position B, kA-FEMAnd kB-FEMIt is finite element solving result respectively in bidentate class mark position A and list
The mesh stiffness of tooth class mark position B.
7. the considerations of amendment according to claim 1 rouses the gear pair meshing characteristic analysis method to correction of the flank shape, feature exists
In different drums are calculated to profiling quantity cβTime-variant mesh stiffness analytic method stiffness modification λk, using quadratic function
Approximating method acquires λkAnd cβBetween relational expression:
In formula, a, b, c are the coefficient of quadratic equation.
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Application publication date: 20170912 Assignee: JIANGSU JINXIANG TRANSMISSION EQUIPMENT Co.,Ltd. Assignor: Northeastern University Contract record no.: X2020210000037 Denomination of invention: A modified meshing characteristic analysis method of gear pair considering drum modification Granted publication date: 20190719 License type: Common License Record date: 20201223 |
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