CN104679941B - A kind of computational methods of tooth surface bending deformation quantity - Google Patents
A kind of computational methods of tooth surface bending deformation quantity Download PDFInfo
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- CN104679941B CN104679941B CN201510046255.6A CN201510046255A CN104679941B CN 104679941 B CN104679941 B CN 104679941B CN 201510046255 A CN201510046255 A CN 201510046255A CN 104679941 B CN104679941 B CN 104679941B
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Abstract
The present invention relates to a kind of computational methods of tooth surface bending deformation quantity, and gear teeth face flexural deformation softness factor matrix is extracted with reference to FInite Element and differential technique；Then, gear teeth face bending deformation quantity is established by coordinate transform and mapping and accurately solves computation model, a complicated space curved surface problem on deformation is reduced to a simple cantilever beam deformed problem；Finally, the bending deformation quantity of optional position on gear teeth face has been obtained by interpolation calculation.To realize that carrying out dynamic load contact analysis (LTCA) to gear by deformation compatibility condition lays a good foundation, and has also laid good place mat for the quasi-statics analysis method of gear.
Description
Technical field
The invention belongs to the mechanical analysis field of gear, and in particular to during a kind of gear drive, tooth during gear teeth stand under load
The computational methods of the bending deformation quantity in face.
Background technology
Dynamic load contact analysis (LTCA) is carried out, it is necessary to obtain gear to gear by deformation compatibility condition in order to realize
The flank of tooth bending deformation quantity and face deflection of secondary each time of contact.
At present in engineering, it is most common calculate gear drive process stressing conditions method be by finite element software such as
(ANSYS, ABAQUS etc.) carries out calculating analysis.This method by establishing gear finite element model, match somebody with somebody by luggage of going forward side by side, and passes through application
Load and constraint, then can obtain the static strength situation of gear, it is hereby achieved that the stress deformation situation of gear, tooth at this time
Deformation on face includes juxtaposition metamorphose and flexural deformation.But this method is calculated when needing substantial amounts of machine, and each contact position
Putting needs not only to adjust and calculate, the deflection of each position also bad extraction, and inaccurately on the flank of tooth.
However, face deflection can conveniently be calculated by Hertz theories, but the calculating of flank of tooth flexural deformation
Model did not had very deep research but.In those early years, someone, which mentions, regards the gear teeth as a cantilever beam to carry out the meter of flexural deformation
Calculate, but since tooth profiles are complicated, this computation model is simultaneously inaccurate.
The content of the invention
Technical problems to be solved
In order to avoid the shortcomings of the prior art, the present invention proposes a kind of calculating side of tooth surface bending deformation quantity
Method, gear teeth face flexural deformation softness factor matrix is extracted with reference to FInite Element and differential technique；Then, by coordinate transform with
Mapping establishes gear teeth face bending deformation quantity and accurately solves computation model, and this method deforms a complicated space curved surface
Problem reduction is a simple cantilever beam deformed problem；Finally, obtained by interpolation calculation any on gear teeth face
The bending deformation quantity of position.
Technical solution
A kind of computational methods of tooth surface bending deformation quantity, it is characterised in that step is as follows：
Step 1, extraction flank of tooth flexural deformation softness factor matrix：
Monodentate finite element model is established, obtains node coordinate, the node serial number on working flank, while pass through Differential Geometry
Method obtain the normal vector of each node location on the flank of tooth；
One unit force is decomposed on the normal vector of each node, forms the specific loading vector on each node；
Monodentate finite element model is imported in finite element software, to the institute on the bottom surface and two sides of monodentate finite element model
There is node to apply full free degree constraint；
According to node serial number, apply specific loading vector to each node on working flank successively, and extract work tooth
The deflection of all nodes on face, obtains a comprehensive softness factor matrix [Cz]n×n×3, wherein：N is represented one on working flank
N node is shared,
First dimension of the matrix is represented applies specific loading vector in i-th of node；Second dimension is represented in j-th of node
The deflection of upper generation；Third dimension first row represent j-th of node X to deflection, third dimension secondary series represents j-th of section
The deflection in Y-direction is put, the row of the third dimension the 3rd represent deflection of j-th of node in Z-direction；
Apply the full free degree to node on monodentate finite element model bottom surface and two sides again to constrain, meanwhile, to inoperative tooth
All nodes apply full free degree constraint on face；
According to node serial number, apply specific loading vector to each node on working flank successively, and extract work tooth
The deflection of all nodes on face, obtains a juxtaposition metamorphose softness factor matrix [CC]n×n×3；
Two coefficient matrixes are done into additive operation and obtain the flexural deformation softness factor matrix of single gear teeth working flank：
[Cf]n×n×3=[Cz]n×n×3-[Cc]n×n×3；
Step 2, establish flank of tooth bending deformation quantity computation model：Monodentate finite element model tooth is obtained by gear generating method
The parameter of any node represents r on facei(ui,vi), by coordinate projection and mapping, by the section on finite element model working flank
Point transformation is under plane coordinate system, and two axis of plane coordinate system are respectively u, v, by monodentate finite element model under constraints
Physical model is expressed as a plane cantilever sheet model, and plane cantilever sheet model is used as using flexural deformation softness factor matrix
Mechanical characteristic, obtain flank of tooth bending deformation quantity computation model；
Step 3, calculate flank of tooth bending deformation quantity：Each contact is obtained instantaneously according to Tooth Contact Analysis method, work tooth
The distribution of contact position and contact on face, then by the institute of the contact Equivalent Distributed of each contact area to the region
Have on node, obtain the loading matrix of whole flank of tooth bending deformation quantity computation model, by loading matrix and bending softness factor square
Battle array is multiplied, and obtains the bending deformation quantity on arbitrary node；
For not a node position on working flank, the method that linear interpolation is carried out to node near the location point is tried to achieve.
Beneficial effect
A kind of computational methods of tooth surface bending deformation quantity proposed by the present invention, are extracted with reference to FInite Element and differential technique
Gear teeth face flexural deformation softness factor matrix；Then, gear teeth face flexural deformation is established by coordinate transform and mapping
Amount is accurate to solve computation model, and a complicated space curved surface problem on deformation is reduced to a simple cantilever beam deformed
Problem；Finally, the bending deformation quantity of optional position on gear teeth face has been obtained by interpolation calculation.Pass through compatibility of deformation to realize
Condition carries out dynamic load contact analysis (LTCA) to gear and lays a good foundation, and is also the quasi-statics analysis side of gear
Method has laid good place mat.
Brief description of the drawings
The limited element calculation model of Fig. 1 (a) non-working flanks non-displacement constraint；
A- working faces
Fig. 1 (b) non-working flanks have the limited element calculation model of displacement constraint；
B- non-working surfaces
Fig. 2 gear teeth flank of tooth bending deformation quantity computation models；
Fig. 3 face pressure equivalent process
Embodiment
In conjunction with embodiment, attached drawing, the invention will be further described：
Step 1, flank of tooth flexural deformation softness factor matrix is extracted：
The finite element model of the single gear teeth is established, determines node coordinate, node serial number on working flank, while by micro-
The method of geometry is divided to obtain the normal vector of each node location on the flank of tooth.
One unit force is decomposed on the normal vector of each node of working flank, forms the specific loading on each node
Vector.
As shown in Fig. 1 (a), in finite element software (such as ANSYS), by the bottom surface and two sides of monodentate finite element model
The all directions frees degree of all nodes all constrains, then, first node on the flank of tooth is applied corresponding specific loading to
Amount, extracts the deflection of all nodes under single specific loading vector, next deletes load, and it is corresponding to apply next node
Specific loading vector, extracts the deflection of all nodes under single specific loading vector, next ..., it is assumed that on working flank
One shares n node, then is repeated in n times.This makes it possible to obtain a comprehensive softness factor matrix [Cz]n×n×3.Wherein, matrix
The first dimension represent and apply specific loading vector in i-th node；Second dimension represents the deflection produced on j-th of node；
Third dimension first row represent j-th of node X to deflection, third dimension secondary series represents deformation of j-th of node in Y-direction
Amount, the row of the third dimension the 3rd represent deflection of j-th of node in Z-direction.
As shown in Fig. 1 (b), in finite element software (such as ANSYS), by the bottom surface and two sides of monodentate finite element model
The all directions free degree of all nodes all constrains, meanwhile, by all directions of all nodes on gear teeth non-working flank certainly
By degree all constraints.Then, corresponding specific loading vector is applied to first node on working flank, extracts single unit and carry
The deflection of all nodes under lotus vector, next deletes load, applies the corresponding specific loading vector of next node, extraction
The deflection of all nodes under single specific loading vector, next ..., is repeated in n times.This makes it possible to obtain a contact
Deform softness factor matrix [CC]n×n×3。
Then, the flexural deformation softness factor square of single gear teeth working flank can then be obtained by doing additive operation by both
Battle array：
[Cf]n×n×3=[Cz]n×n×3-[Cc]n×n×3
(1) flank of tooth bending deformation quantity computation model is established
Gear teeth face is usually a spatial complex curved surface, and direct applying power calculates the model of flexural deformation on gear teeth face
It is complex.In general, space curved surface can be represented with parametric form, there is r (u, v) to represent to study the parameter side of the flank of tooth herein below
Journey.Then it can represent r to the parameter of any node on the monodentate finite element model flank of toothi(ui,vi).As shown in Fig. 2, in the following, establish
One plane coordinate system, its two axis are respectively u, v, then by coordinate projection and mapping, by all node transformations on the flank of tooth
To under plane coordinate system, then a Plane Gridding Model is obtained, fixed constraint is applied to one end of grid, then monodentate can be had
Limit physical model of the meta-model under constraints and be expressed as a plane cantilever thin plate bending computation model.Meanwhile plane is hanged
Bending softness factor on the node of series of discrete on arm thin plate is it is known that so far, whole gear teeth flank of tooth flexural deformation gauge
Calculate model to have completely set up, it is the plane grid computation model of a gear teeth flank of tooth bending deformation quantity.
(2) flank of tooth bending deformation quantity is calculated
The each contact of a pair of of gear pair can be obtained instantaneously according to existing Tooth Contact Analysis (TCA) technology, work tooth
The distributed areas of contact position and contact on face.
It is known that when locally being contacted, the contact of the flank of tooth is similar to Hertz pressure, and the distribution of its pressure can be expressed
For：
P=p0{1-(r/a)2}1/2
Then, its pressure distribution curve of the arbitrary section of central axes excessively can be as shown in curve in Fig. 3.《Material power
Learn》In, pressure is linear with amount of deflection, can be evenly distributed to contact on Contact Ellipse immediate vicinity node below
Method carry out simplifying calculating, as shown in figure 3, when square region area be equal to curve and axis include area when, tooth
The calculating of each point bending deformation quantity is substantially accurate on face.
Method is simplified with this, by each node of the contact Equivalent Distributed of each contact area to the region, this
Sample can be obtained by the stressing conditions of whole flank of tooth bending deformation quantity computation model, can be in the hope of with reference to bending softness factor matrix
Go out the bending deformation quantity on arbitrary node.For not a node position on working flank, by being carried out to node near the location point
The method of linear interpolation can try to achieve, by《The mechanics of materials》Understand in the case of small deformation, had using linear interpolation higher
Computational accuracy.
Claims (1)
1. a kind of computational methods of tooth surface bending deformation quantity, it is characterised in that step is as follows：
Step 1, extraction flank of tooth flexural deformation softness factor matrix：
Monodentate finite element model is established, obtains node coordinate, the node serial number on working flank, while the side for passing through Differential Geometry
Method obtains the normal vector of each node location on the flank of tooth；
One unit force is decomposed on the normal vector of each node, forms the specific loading vector on each node；
Monodentate finite element model is imported in finite element software, to all sections on the bottom surface and two sides of monodentate finite element model
Point applies full free degree constraint；
According to node serial number, apply specific loading vector to each node on working flank successively, and extract on working flank
The deflection of all nodes, obtains a comprehensive softness factor matrix [Cz]n×n×3, wherein：N represents a shared n on working flank
A node,
First dimension of the matrix is represented applies specific loading vector in i-th of node；Second dimension is represented produces on j-th of node
Raw deflection；Third dimension first row represent j-th of node X to deflection, third dimension secondary series represents j-th of node and exists
The deflection of Y-direction, the row of the third dimension the 3rd represent deflection of j-th of node in Z-direction；
Apply the full free degree to node on monodentate finite element model bottom surface and two sides again to constrain, meanwhile, on non-working flank
All nodes apply full free degree constraint；
According to node serial number, apply specific loading vector to each node on working flank successively, and extract on working flank
The deflection of all nodes, obtains a juxtaposition metamorphose softness factor matrix [CC]n×n×3；
Two coefficient matrixes are done into additive operation and obtain the flexural deformation softness factor matrix of single gear teeth working flank：
[Cf]n×n×3=[Cz]n×n×3-[Cc]n×n×3；
Step 2, establish flank of tooth bending deformation quantity computation model：Obtained by gear generating method on the monodentate finite element model flank of tooth
The parameter of any node represents ri(ui,vi), by coordinate projection and mapping, the node on finite element model working flank is become
Change under plane coordinate system, two axis of plane coordinate system are respectively u, v, by entity of the monodentate finite element model under constraints
Model is expressed as a plane cantilever sheet model, the power using flexural deformation softness factor matrix as plane cantilever sheet model
Characteristic is learned, obtains flank of tooth bending deformation quantity computation model；
Step 3, calculate flank of tooth bending deformation quantity：Each contact is obtained instantaneously according to Tooth Contact Analysis method, on working flank
The distribution of contact position and contact, then by all sections of the contact Equivalent Distributed of each contact area to the region
On point, the loading matrix of whole flank of tooth bending deformation quantity computation model is obtained, by loading matrix with bending softness factor matrix phase
Multiply, obtain the bending deformation quantity on arbitrary node；
For not a node position on working flank, the method that linear interpolation is carried out to node near the not a node is tried to achieve.
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| CN105912793B (en) * | 2016-04-18 | 2019-01-04 | 清华大学 | A kind of finite element method obtaining the bending deformation of the hypoid gear gear teeth |
| CN106021689B (en) * | 2016-05-16 | 2019-12-31 | 中国航空工业集团公司西安飞机设计研究所 | Method for calculating contact force after structure deformation |
| CN109488303B (en) * | 2018-10-30 | 2020-10-09 | 湘潭大学 | Bionic crawler tooth, design method thereof and deep-sea ore collector |
| CN109190324B (en) * | 2018-11-12 | 2023-04-18 | 中南大学 | Tooth surface load contact deformation numerical calculation method for spiral bevel gear with errors |
| CN109657389B (en) * | 2018-12-28 | 2023-04-18 | 山东农业大学 | Dynamic bending calculation method for plant stems and leaves under action of airflow |
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| CN104021303A (en) * | 2014-06-19 | 2014-09-03 | 中国北方车辆研究所 | Spiral bevel gear profiled tooth surface profiling method based on actual measurement load spectrum |
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| CN104021303A (en) * | 2014-06-19 | 2014-09-03 | 中国北方车辆研究所 | Spiral bevel gear profiled tooth surface profiling method based on actual measurement load spectrum |
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