CN110162869A - A kind of modeling method of involute gear - Google Patents
A kind of modeling method of involute gear Download PDFInfo
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- CN110162869A CN110162869A CN201910406799.7A CN201910406799A CN110162869A CN 110162869 A CN110162869 A CN 110162869A CN 201910406799 A CN201910406799 A CN 201910406799A CN 110162869 A CN110162869 A CN 110162869A
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Abstract
The invention discloses a kind of modeling methods of involute gear, comprising the following steps: step 1, input gear parameter；Step 2, involute and mirror image involute are established；Step 3, merge involute and mirror image involute to form monodentate contour line by interpolation method；Step 4, by monodentate contour generating gear ring outer contour；Step 5, gear front and rear surfaces profile is established；Step 6, gear side surface configuration is established；Step 7, triangle gridding is generated on gear side surface configuration, carries out Delaunay triangulation on gear front surface profile and gear rear surface profile.The modeling method meets the demand of gear finite element analysis, the model of gear network of generation is reasonable, quality is higher, each section surface point is safeguarded using individual data structure, be conducive to simplify various front and back processing operations, it can be achieved that gear pair or planetary gear are to a variety of operations such as tooth, the displaying of gear stress distribution, gear stress and deformation analysis.
Description
Technical field
The present invention relates to gear modeling and processing technique field more particularly to a kind of modeling methods of involute gear.
Background technique
Machinery manufacturing industry is the basic industry of national economy, is the core of China's heavy industry development.The hair of machinery manufacturing industry
Exhibition level is the one of the important signs that of industrialization of the country degree, is the important mainstay industry of country, the developing water of machine-building
Flat is also the one of the important signs that for measuring a national science and technology level and the level of economic development.Wherein, the modeling of involute gear
Method is the core technology link in machine-building design and simulation system.Interior three about involute gear of engineering field at present
Dimension Modeling Method is less, and modeling process is complex, and functional limitation is big.
In the dimensional Modeling Technology of involute gear, crucial technical point can be divided into four.First, visualization problem,
I.e. given gear parameter, establishes the corresponding model of gear in graphical interfaces.Second, surface stress shows that is, the model of gear can
With according to requiring to show the stress intensity suffered by it, the general means using surface coloring at the different position of part.Third,
Mode motion deformation analysis, the i.e. model of gear can be according to requiring to deform under different operating conditions.4th, to tooth problem,
I.e. in gear pair or planetary gearing train structure, each gear can be formed correct gear engagement by some transformation and be closed
System.
In aforementioned four key technology point, after the three-dimensional visualization of first key technology point namely involute gear is
Whether the basis of continuous three key technology points, involute gear modeling are rationally subsequent to involute gear progress processing operation
Basis.How to realize the visualization of involute gear, and just executes a series of post-processing behaviour below its threedimensional model
Make, is a significant problem in mechanical industry emulation field.
Above- mentioned information disclosed in the background technique are used only for increasing the understanding to the application background technique, therefore,
It may include and do not constitute the prior art known to persons of ordinary skill in the art.
Summary of the invention
The present invention proposes that a kind of grid constitutes involute gear modeling method reasonable, that formation speed is fast, is executed with facilitating
Post-processing operation.
For achieving the above object, the present invention, which adopts the following technical solutions, is achieved:
The present invention provides a kind of modeling method of involute gear, comprising the following steps:
Step 1, input gear parameter；
Step 2, establish involute, rotation transformation done around x-axis to the involute of generation, will it is postrotational it is described gradually
It bursts at the seams and generates mirror image involute about xoy plane, the involute and the mirror image involute constitute the left and right side edge of monodentate；
Step 3, it establishes monodentate contour line: the involute and the mirror image involute is merged by shape by interpolation method
At monodentate contour line；
Step 4, it establishes gear ring outer contour: establishing monodentate contour line copy identical with the number of teeth, and successively to every
A monodentate contour line copy does rotation transformation about x-axis, if the number of each monodentate contour line copy is id, then each
The rotation angle of the monodentate contour line copy are as follows:
Wherein, z is the number of teeth；
Circumference interpolation is done between each monodentate contour line copy, generates gear ring outer contour；
Step 5, it establishes gear front and rear surfaces profile: generating wheel respectively according to system given parameters along internal diameter profile, former
Internal-and external diameter profile and wheel hub internal-and external diameter profile, by the wheel along internal diameter profile, the former internal-and external diameter profile and the wheel hub
Outer diameter profile and the gear ring outer contour combination producing gear front surface profile and gear rear surface profile；
Step 6, it establishes gear side surface configuration: establishing multiple gear ring outer profile copies, by the gear ring outer profile copy
Translation transformation is done in the z-axis direction and does rotation transformation about z-axis, generates gear side surface configuration, displacement s and rotation
Shown in the following formula of angle γ:
Wherein, w is the facewidth, and aa is helical angle, and d is reference diameter；
Step 7, triangle gridding is generated to the gear side surface configuration, to the gear front surface profile and the tooth
It takes turns rear surface profile and carries out Delaunay triangulation.
As a kind of preferred embodiment, in the step 2 the following steps are included:
Calculate the initial angle startA and end angle endA of the involute, calculation method are as follows:
Wherein, df is root diameter, and da is tip diameter, and db is base circle diameter (BCD)；
It selectes discrete points n and generates the involute, the involute parametric equation according to involute parametric equation
Are as follows:
It is further comprising the steps of in the step 2 as a kind of preferred embodiment:
Rotation transformation, rotation angle α calculation formula are done around x-axis to the involute of generation are as follows:
As a kind of preferred embodiment, interpolation method described in the step 3 the following steps are included:
Step 3-1, establishes monodentate point set, and positive sequence traverses the involute point set of the involute and is successively saved in described
Monodentate point is concentrated；
Step 3-2 calculates tooth top central point, and the tooth top central point is saved in the monodentate point and is concentrated；
Step 3-3, inverted order traverse the mirror image involute point set of the mirror image involute and are successively saved in the monodentate
Point is concentrated.
As a kind of preferred embodiment, the circumference interpolation in the step 4 the following steps are included:
Step 4-1 calculates discrete root circle profile point set according to demand；
Step 4-2 extracts the first and last point of each monodentate point set, these points are respectively the monodentate right side and left side
Tooth root point；
Step 4-3 constructs KDTree, calculates the nearest tooth root of space length to two tooth root points of each monodentate
Circle contour point is simultaneously recorded in the subscript that the root circle profile point is concentrated；
Step 4-4, according to 4-3 walk in the subscript concentrated of the root circle profile point that obtains extract the root circle wheel
The section point set of wide point set；
Step 4-5 establishes gear ring outer profile point set, in order by the monodentate point set and the root circle profile point set
Section point set be saved in the gear ring outer profile point and concentrate.
As a kind of preferred embodiment, in the step 7 to the gear side surface configuration generate triangle gridding include with
Lower step:
If two adjacent gear ring outer profile numbers are respectively i and i+1, if the point number in gear ring is id=1,
2 ..., j ..., N, to id=1 ..., N is performed the following operations respectively:
(1) as j ≠ N, respectively the point j of gear ring i, point j+1, gear ring i+1 point j between and gear ring i point j+1, tooth
It encloses between point j, the point j+1 of i+1 and generates triangle gridding；
(2) as j==N, respectively between the point N of gear ring i, point 1, the point 1 of gear ring i+1 and point N, the gear ring of gear ring i
Triangle gridding is generated between the point N of i+1, point 1.
Compared with prior art, the advantages and positive effects of the present invention are:
The present invention proposes a kind of modeling method of involute gear, comprising the following steps: step 1, input gear parameter；
Step 2, involute and mirror image involute are established；Step 3, involute and mirror image involute are merged by interpolation method to be formed
Monodentate contour line；Step 4, by monodentate contour generating gear ring outer contour；Step 5, gear front and rear surfaces profile is established；Step
Rapid 6, establish gear side surface configuration；Step 7, triangle gridding is generated on gear side surface configuration, in gear front surface profile
Delaunay triangulation is carried out on gear rear surface profile.The modeling method meets the demand of gear finite element analysis, generates
Model of gear network rationally, quality it is higher, each section surface point using individual data structure maintenance, be conducive to
Simplify various front and back processing operations, it can be achieved that gear pair or planetary gear are to tooth, the displaying of gear stress distribution, gear stress deformation
A variety of operations such as analysis.
After a specific embodiment of the invention is read in conjunction with the figure, the other features and advantages of the invention will become more
It is clear.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will to embodiment or
Attached drawing needed to be used in the description of the prior art is briefly described, it should be apparent that, the accompanying drawings in the following description is this
Some embodiments of invention, for those of ordinary skill in the art, without any creative labor, also
Other drawings may be obtained according to these drawings without any creative labor.
Fig. 1 is the algorithm flow chart of the modeling method embodiment of involute gear of the present invention；
Fig. 2 is the model schematic of involute embodiment of the present invention；
Fig. 3 is the model schematic of the postrotational involute embodiment of the present invention；
Fig. 4 is the model schematic of monodentate contour line embodiment of the present invention；
Fig. 5 is the model schematic of gear ring outer contour embodiment of the present invention；
Fig. 6 is the model schematic of gear front surface profile embodiment of the present invention；
Fig. 7 is the model schematic of gear front surface profile of the present invention and gear rear surface profile embodiment；
Fig. 8 is the model schematic of gear side surface configuration embodiment of the present invention；
Fig. 9 is the model schematic for the pinion embodiment that the present invention generates after grid；
Figure 10 is the model schematic of gear three-dimensional visualization embodiment of the present invention.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, ordinary skill people
Member's every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
It should be noted that in the description of the present invention, term " on ", "lower", "left", "right", " perpendicular ", " cross ",
The direction of the instructions such as "inner", "outside" or the term of positional relationship are direction based on the figure or positional relationship, this is only
For ease of description, rather than indication or suggestion described device or element must have a particular orientation, with specific orientation structure
It makes and operates, therefore be not considered as limiting the invention.In addition, term " first ", " second " are used for description purposes only,
It is not understood to indicate or imply relative importance.
The present invention discloses a kind of modeling method of involute gear, modeling procedure referring to Fig.1, the modeling method include with
Lower step:
Step 1, input gear parameter.Parameter mainly includes number of teeth z, helical angle aa, facewidth w, reference diameter d, tooth root
Circular diameter df, tip diameter da, base circle diameter (BCD) db, wheel are along internal diameter (namely former outer diameter) lyD, hub outside diameter (namely former
Internal diameter) lgD1, wheel hub internal diameter lgD2, former bias fbOff, wheel hub bias lgOff, the wide fbW of former and the wide lgW of wheel hub.
When reference diameter d, root diameter df, tip diameter da, base circle diameter (BCD) db are unknown can also by with
Lower formula carrys out calculating parameter:
M is modulus in above formula, and bwxs is modification coefficient, and haa is addendum coefficient, and xjl is tooth top reduction, and cc is top
Gap coefficient.
The parameter of the present embodiment middle gear is respectively as follows: modulus 16mm, the number of teeth 29, and 22.5 ° of rotation angle, tip clearance coefficient 0.4,
Addendum coefficient 1, facewidth 315mm, wheel is along thickness 20mm, former width 250mm, hub outside diameter 250mm, wheel hub internal diameter
100mm, hub width 380mm, reference diameter 464mm, base circle diameter (BCD) 428.68mm, tip diameter 500mm, root circle
Diameter 435.2mm.
The present embodiment uses vtk as three-dimensional visualization picture frame, and illustrates the coordinate of current part in the lower left corner
Direction mark, referring to Fig. 2 to Figure 10.
Step 2, involute is established, referring to Fig. 2, rotation transformation is done around x-axis to the involute of generation, after rotation
The involute generate mirror image involute about xoy plane, referring to Fig. 3, the involute and the mirror image involute are constituted
The left and right side edge of monodentate.
Step 3, it establishes monodentate contour line: the involute and the mirror image involute is merged by shape by interpolation method
At monodentate contour line, referring to Fig. 4.
Step 4, gear ring outer contour is established by monodentate contour line: monodentate contour line need to be implemented backup operation in order to
Monodentate contour line backup sequence is successively executed rotation process, and is done using root circle for monodentate by the generation of gear ring outer contour
Interpolation, to constitute entire gear ring outer contour.Specifically, monodentate contour line copy identical with the number of teeth of gear is established, and
Rotation transformation successively is done about x-axis to each monodentate contour line copy, if the number of each monodentate contour line copy is
Id, the then rotation angle of each monodentate contour line copy are as follows:
Wherein, z is the number of teeth；
Circumference interpolation is done between each monodentate contour line copy, generates gear ring outer contour, referring to Fig. 5.
Step 5, it establishes gear front and rear surfaces profile: generating wheel respectively according to system given parameters along internal diameter profile, former
Internal-and external diameter profile and wheel hub internal-and external diameter profile, by the wheel along internal diameter profile, the former internal-and external diameter profile and the wheel hub
Outer diameter profile and the gear ring outer contour combination producing gear front surface profile and gear rear surface profile, referring to Fig. 6 and figure
7。
Step 6, it establishes gear side surface configuration: generating gear side surface configuration by backing up multiple gear ring outer profiles, and
Rotation process is executed to it according to helical angle, rear surface is also coped with after contralateral surface executes rotation process and executes rotation process.
Specifically, establishing multiple gear ring outer profile copies, the gear ring outer profile copy is done translation transformation in the z-axis direction and closing
Rotation transformation is done in z-axis, generates gear side surface configuration, referring to Fig. 8, displacement s and the rotation following formula institute of angle γ
Show:
Wherein, w is the facewidth, and aa is helical angle, and d is reference diameter.
Step 7, triangle gridding is generated to the gear side surface configuration, to the gear front surface profile and the tooth
It takes turns rear surface profile and carries out Delaunay triangulation, referring to Fig. 9 and Figure 10.
As a kind of preferred embodiment, in the generation of step 2 involute, need first to calculate the initial angle of involute
StartA and end angle endA, and corresponding involute is generated according to angular range.Initial angle startA and end angle endA meter
Calculation method are as follows:
Wherein, df is root diameter, and da is tip diameter, and db is base circle diameter (BCD).
Then, it selectes discrete points n and generates the involute, the involute parameter according to involute parametric equation
Equation are as follows:
It is further comprising the steps of in step 2 as a kind of preferred embodiment:
Rotation transformation, rotation angle α calculation formula are done around x-axis to the involute of generation are as follows:
As a kind of preferred embodiment, interpolation method described in step 3 the following steps are included:
Step 3-1, establishes monodentate point set, and positive sequence traverses the involute point set of the involute and is successively saved in described
Monodentate point is concentrated；
Step 3-2 calculates tooth top central point, and the tooth top central point is saved in the monodentate point and is concentrated；
Step 3-3, inverted order traverse the mirror image involute point set of the mirror image involute and are successively saved in the monodentate
Point is concentrated.
As a kind of preferred embodiment, the circumference interpolation in step 4 the following steps are included:
Step 4-1 calculates discrete root circle profile point set according to demand；
Step 4-2 extracts the first and last point of each monodentate point set, these points are respectively the monodentate right side and left side
Tooth root point；
Step 4-3 constructs KDTree, calculates the nearest tooth root of space length to two tooth root points of each monodentate
Circle contour point is simultaneously recorded in the subscript that the root circle profile point is concentrated；
Step 4-4, according to 4-3 walk in the subscript concentrated of the root circle profile point that obtains extract the root circle wheel
The section point set of wide point set；
Step 4-5 establishes gear ring outer profile point set, in order by the monodentate point set and the root circle profile point set
Section point set be saved in the gear ring outer profile point and concentrate.
Triangle gridding is generated on the gear side surface configuration as a kind of preferred embodiment, in the step 7 includes
Following steps:
If two adjacent gear ring outer profile numbers are respectively i and i+1, if the point number in gear ring is id=1,
2 ..., j ..., N, to id=1 ..., N is performed the following operations respectively:
(1) as j ≠ N, respectively the point j of gear ring i, point j+1, gear ring i+1 point j between and gear ring i point j+1, tooth
It encloses between point j, the point j+1 of i+1 and generates triangle gridding；
(2) as j==N, respectively between the point N of gear ring i, point 1, the point 1 of gear ring i+1 and point N, the gear ring of gear ring i
Triangle gridding is generated between the point N of i+1, point 1.
Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；To the greatest extent
Present invention has been described in detail with reference to the aforementioned embodiments for pipe, those skilled in the art should understand that: it is still
It is possible to modify the technical solutions described in the foregoing embodiments, or part of technical characteristic is equally replaced
It changes；And these are modified or replaceed, the essence for technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution
Mind and range.
Claims (6)
1. a kind of modeling method of involute gear, which comprises the following steps:
Step 1, input gear parameter；
Step 2, involute is established, rotation transformation is done around x-axis to the involute of generation, the postrotational involute is closed
Mirror image involute is generated in xoy plane, the involute and the mirror image involute constitute the left and right side edge of monodentate；
Step 3, it establishes monodentate contour line: merging the involute and the mirror image involute to form monodentate by interpolation method
Contour line；
Step 4, it establishes gear ring outer contour: establishing monodentate contour line copy identical with the number of teeth of the gear, and successively right
Each monodentate contour line copy does rotation transformation about x-axis, if the number of each monodentate contour line copy is id, then
The rotation angle of each monodentate contour line copy are as follows:
Wherein, z is the number of teeth；
Circumference interpolation is done between each monodentate contour line copy, generates gear ring outer contour；
Step 5, it establishes gear front and rear surfaces profile: generating wheel respectively according to system given parameters inside and outside internal diameter profile, former
Diameter profile and wheel hub internal-and external diameter profile, by the wheel along internal diameter profile, the former internal-and external diameter profile and the wheel hub internal-and external diameter
Profile and the gear ring outer contour combination producing gear front surface profile and gear rear surface profile；
Step 6, it establishes gear side surface configuration: establishing multiple gear ring outer profile copies, by the gear ring outer profile copy in z-axis
Translation transformation is done on direction and does rotation transformation about z-axis, generates gear side surface configuration, displacement s and rotation angle γ
Shown in following formula:
Wherein, w is the facewidth, and aa is helical angle, and d is reference diameter；
Step 7, triangle gridding is generated to the gear side surface configuration, to table after the gear front surface profile and the gear
Facial contour carries out Delaunay triangulation.
2. the modeling method of involute gear according to claim 1, which is characterized in that include following in the step 2
Step:
Calculate the initial angle startA and end angle endA of the involute, calculation method are as follows:
Wherein, df is root diameter, and da is tip diameter, and db is base circle diameter (BCD)；
It selectes discrete points n and generates the involute, the involute parametric equation according to involute parametric equation are as follows:
3. the modeling method of involute gear according to claim 2, which is characterized in that further include in the step 2 with
Lower step:
Rotation transformation, rotation angle α calculation formula are done around x-axis to the involute of generation are as follows:
4. the modeling method of involute gear according to claim 1, which is characterized in that interpolation described in the step 3
Method the following steps are included:
Step 3-1, establishes monodentate point set, and positive sequence traverses the involute point set of the involute and is successively saved in the monodentate
Point is concentrated；
Step 3-2 calculates tooth top central point, and the tooth top central point is saved in the monodentate point and is concentrated；
Step 3-3, inverted order traverse the mirror image involute point set of the mirror image involute and are successively saved in the monodentate point set
In.
5. the modeling method of involute gear according to claim 4, which is characterized in that the circle in the step 4
All interpolation the following steps are included:
Step 4-1 calculates discrete root circle profile point set according to demand；
Step 4-2 extracts the first and last point of each monodentate point set, these points are respectively the tooth root of the monodentate right side and left side
Point；
Step 4-3 constructs KDTree, calculates the nearest tooth root circle contour of space length to two tooth root points of each monodentate
Point is simultaneously recorded in the subscript that the root circle profile point is concentrated；
Step 4-4, according to 4-3 walk in the subscript concentrated of the root circle profile point that obtains extract the root circle profile point set
Section point set；
Step 4-5 establishes gear ring outer profile point set, in order by the section of the monodentate point set and the root circle profile point set
Point set is saved in the gear ring outer profile point and concentrates.
6. the modeling method of involute gear according to claim 1, which is characterized in that the tooth in the step 7
Take turns side surface configuration generate triangle gridding the following steps are included:
If two adjacent gear ring outer profiles numbers are respectively i and i+1, if the point number in gear ring is id=1,2 ...,
J ..., N, to id=1 ..., N is performed the following operations respectively:
(1) as j ≠ N, respectively the point j of gear ring i, point j+1, gear ring i+1 point j between and gear ring i point j+1, gear ring i+1
Point j, point j+1 between generate triangle gridding；
(2) as j==N, respectively between the point N of gear ring i, point 1, the point 1 of gear ring i+1 and the point N of gear ring i, gear ring i+1
Triangle gridding is generated between point N, point 1.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103678818A (en) * | 2013-12-23 | 2014-03-26 | 昆明理工大学 | Precise modeling method for biarc correction cycloidal gear |
| US20150106063A1 (en) * | 2013-10-14 | 2015-04-16 | Airbus Operations Limited | Gear construction method and digital apparatus |
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2019
- 2019-05-16 CN CN201910406799.7A patent/CN110162869B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20150106063A1 (en) * | 2013-10-14 | 2015-04-16 | Airbus Operations Limited | Gear construction method and digital apparatus |
| CN103678818A (en) * | 2013-12-23 | 2014-03-26 | 昆明理工大学 | Precise modeling method for biarc correction cycloidal gear |
Non-Patent Citations (1)
| Title |
|---|
| 潘子健等: "利用UG建立全参数化渐开线直齿圆柱齿轮", 《长春理工大学学报(自然科学版)》 * |
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