CN109887079A - Spiral bevel gear three-dimensional modeling method - Google Patents
Spiral bevel gear three-dimensional modeling method Download PDFInfo
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- CN109887079A CN109887079A CN201910217747.5A CN201910217747A CN109887079A CN 109887079 A CN109887079 A CN 109887079A CN 201910217747 A CN201910217747 A CN 201910217747A CN 109887079 A CN109887079 A CN 109887079A
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- tooth
- flank
- point
- gear
- bevel gear
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Abstract
The invention discloses a kind of spiral bevel gear three-dimensional modeling methods, comprising the following steps: Step 1: establishing spiral bevel gear two dimension gear blank figure；Step 2: carrying out discrete, several equally distributed sample points of generation to the flank region in two-dimentional gear blank figure；Step 3: acquiring the corresponding true tooth point of each sample point according to the explicit expression of flank of tooth point mapping relations and the spiral bevel gear flank of tooth；Step 4: two-dimentional gear blank and true tooth point are imported 3 d modeling software, two-dimentional gear blank is rotated into the three-dimensional gear blank of generation around Gear axis, each true tooth point line is generated into the single flank of tooth；Step 5: carrying out annular array to the single flank of tooth on the basis of Gear axis, institute's geared surface is obtained, and trimmed with three-dimensional gear blank and complete to model.It is expressed using the display of the flank of tooth, rapid Optimum solves flank of tooth point, simplifies calculating process；And the solution acquired is bound to be a point in true tooth, does not interfere with final flank of tooth modeling accuracy regardless of whether for completely accurate solution.
Description
Technical field
The invention belongs to spiral bevel gears to model field, in particular to a kind of spiral bevel gear three-dimensional modeling method.
Background technique
The three-dimensional modeling of spiral bevel gear generally comprises two key steps at present:
1) it is expressed according to the flank of tooth of spiral bevel gear, calculates a series of regularities of distribution on the spiral bevel gear flank of tooth
Flank of tooth discrete point；
2) discrete point of calculating is imported into commercial 3 d modeling software and carries out three-dimensional modeling.
In above-mentioned two step, step 1) mainly includes following four step.
A) discrete to the flank region progress of gear blank according to spiral bevel gear two dimension gear blank figure, generate a series of uniform points
The sample point of cloth.
Any one of 1) b) for sample point, there is a flank of tooth point corresponding respectively in flank of tooth two sides, accordingly
Corresponding relationship is herein referred to as flank of tooth point mapping relations, i.e., the flank of tooth point is in true tooth.
C) according to flank of tooth point mapping relations, corresponding math equation can be established based on flank of tooth expression, solves the mathematics side
Journey.
D) solution obtained in step c) is substituted into flank of tooth expression, a flank of tooth point can be obtained.If the solution in step c)
It is completely accurate solution, corresponding all set for actually seeking flank of tooth point are herein referred as true tooth.If in step c)
Solution is not exclusively accurate solution, actually seeks flank of tooth point accordingly not in true tooth, that is, there is certain error, error is big
It is small associated with solution error size in step c).
When math equation of the existing technical method in establishment step c), the flank of tooth of use is expressed as a kind of implicit table
It reaches, correspondingly has following problems during solving the flank of tooth.
1, equation is complicated.
2, it is approximate solution that step c), which solves the solution come, is existed with theoretic true solution (completely accurate solution) certain
Error, what corresponding step d) was obtained actually seek flank of tooth point, and not only there are certain errors with default flank of tooth point, and not true
On the flank of tooth, final spiral bevel gear modeling accuracy will affect.
3, when to solving, error precision requirement is higher, and the solution time is longer accordingly.
Summary of the invention
The purpose of the present invention is to solve the shortcomings of the prior art place, provide it is a kind of simplify calculate while again not
It will affect the spiral bevel gear three-dimensional modeling method of final precision.
This spiral bevel gear three-dimensional modeling method provided by the invention, comprising the following steps:
Step 1: establishing spiral bevel gear two dimension gear blank figure；
Step 2: carrying out discrete, several equally distributed sample points of generation to the flank region in two-dimentional gear blank figure；
Step 3: it is corresponding to acquire each sample point according to the explicit expression of flank of tooth point mapping relations and the spiral bevel gear flank of tooth
True tooth point；
Step 4: two-dimentional gear blank and each true tooth point are imported 3 d modeling software, by two-dimentional gear blank around Gear axis
Rotation generates three-dimensional gear blank, and each true tooth point line is generated the single flank of tooth；
Step 5: carrying out annular array to the single flank of tooth on the basis of Gear axis, obtain institute's geared surface, and with three-dimensional
Gear blank, which is trimmed, completes modeling.
In said step 1, it consults spiral bevel gear design manual and chooses gear blank parameter, determine spiral bevel gear two dimension
Gear blank figure.
In the step 2, the boundary of flank region is quadrangle, and zone of dispersion is selected as comprising flank region when discrete
Similar quadrangle.
For any one sample point q in the step 3, around the postrotational track of Gear axis and flank of tooth two sides
Intersection point be default true tooth point, solution procedure is as follows:
Firstly, establishing coordinate system sg, origin OgFor bevel gear pitch cone vertex, ZgAxis is overlapped with bevel gear axis, XgAxis
In two-dimentional gear blank plane with ZgAxis is vertical, YgIt is determined by the right-hand rule；
Secondly, any sample point q is chosen, in coordinate system sgIt is middle according to the gear blank parameter coordinate be (Rq, 0,Zq)；
Then, it is assumed that the coordinate of default true tooth point is Wei (Sx,Sy,Sz), according to flank of tooth point mapping relations, have:
Then, each flank of tooth point can be expressed as to one according to the explicit expression of the spiral bevel gear flank of tooth and includes two changes
Measure h withFunction, then have:
The formula is a Nonlinear System of Equations, can be converted into and state optimization problem and solved
I.e.
Can solve h withValue, be set as h* withBy h* withThe explicit expression for substituting into the flank of tooth has obtained sample
The corresponding true tooth point coordinate (S of this qx*,Sy*,Sz* the corresponding true tooth point of sample point q) is acquired；
Finally repeating the step can be obtained the corresponding true tooth point of each sample point；
Wherein Rq=(Ao-f) sin Γ+dcos Γ, Zq=(Ao-f) cos Γ+dsin Γ.0≤f≤F ,-bf
≤d≤af；F is the face width of tooth, AoIt is in OgThe outer cone distance measured between A；afAnd bfIt is that q point corresponding with parameter f arrives respectively
The distance of tooth top and tooth root.
Each true tooth point is imported into 3 d modeling software in the step 4, with a line, the mode that line connects face is raw
At the single flank of tooth.
Spiral bevel gear two dimension gear blank figure is established when the present invention models first；Then to the tooth in two-dimentional gear blank figure
Face region carries out discrete, several equally distributed sample points of generation；Then according to flank of tooth point mapping relations and spiral bevel gear tooth
The explicit expression in face acquires the corresponding true tooth point of each sample point；Two-dimentional gear blank and each true tooth point are imported again three-dimensional
Modeling software, two-dimentional gear blank rotate the three-dimensional gear blank of generation around Gear axis, and each true tooth point line generates the single flank of tooth；Most
Annular array is carried out to the single flank of tooth on the basis of Gear axis afterwards, obtains institute's geared surface, and trimmed i.e. with three-dimensional gear blank
It can.It is expressed using the display of the flank of tooth, rapid Optimum solves flank of tooth point, simplifies calculating process；And it is acquired using display expression
Solution only be will cause and actually seek flank of tooth point and default flank of tooth point there are certain error regardless of whether for completely accurate solution, but one
Surely it can be a point in true tooth, not interfere with final flank of tooth modeling accuracy.
Detailed description of the invention
Fig. 1 is two dimension gear blank schematic diagram selected by a preferred embodiment of the invention.
Fig. 2 is discrete obtained sample point schematic diagram in the present embodiment.
Fig. 3 is flank of tooth point mapping relations schematic diagram.
Fig. 4 is to generate the schematic diagram after the single flank of tooth in three-dimensional gear blank.
Fig. 5 is the schematic diagram after generation institute's geared surface in three-dimensional gear blank.
Fig. 6 is gained model schematic.
Specific embodiment
This spiral bevel gear three-dimensional modeling method provided by the embodiment, specific steps are as follows:
Step 1: consulting spiral bevel gear design manual (A.Standard, Design manual for bevel
(2005) 2005-D03 of gears, ANSI/AGMA) therefrom choose gear blank parameter outer cone distance (O in Fig. 1gThe distance of A), the facewidth (figure
The distance of AF in 1), gear wheel and the respective height of teeth top of pinion gear (the corresponding a in facewidth middle in Fig. 1fDistance), tooth root
High (the corresponding b in facewidth middle in Fig. 1fDistance), face cone angle (г in Fig. 1oAnd γo), dedendum angle (г in Fig. 1RAnd γR), really
Determine spiral bevel gear two dimension gear blank figure, two-dimentional gear blank figure is as shown in Figure 1.
Step 2: as shown in Figure 1, the boundary of flank region is quadrangle BCDE in two-dimentional gear blank figure, to region progress
It is discrete to obtain a series of equally distributed sample points, it is realized when discrete by uniform discrete parameter d and f, zone of dispersion is selected as
Similar quadrangle comprising flank region, as shown in Fig. 2, zone of dispersion area is slightly larger and flank region is so as to subsequent three-dimensional
Modeling.
Step 3: it is corresponding to acquire each sample point according to the explicit expression of flank of tooth point mapping relations and the spiral bevel gear flank of tooth
True tooth point, the intersection point q for any one sample point q, around the postrotational track of Gear axis and flank of tooth two sidesi、
qoTo preset true tooth point, qiFor the intersection point with flank of tooth convex surface, qoFor the intersection point with flank of tooth concave surface, as shown in Figure 3；Solve tooth
Millet cake detailed step are as follows:
Firstly, establishing coordinate system sg, its origin of origin OgFor the bevel gear vertex of a cone, XgAxis is in OgWith sample point q line and
Bevel gear center line institute is in the plane perpendicular to bevel gear center line, ZgAxis is bevel gear rotation centerline, YgBy the right-hand rule
It determines；
Secondly, any sample point q is chosen, in coordinate system sgIt is middle according to the gear blank parameter coordinate be (Rq, 0,Zq)；
Then, it is assumed that the coordinate of default true tooth point is Wei (Sx,Sy,Sz), according to flank of tooth point mapping relations, have:
Then, according to the explicit expression of the spiral bevel gear flank of tooth (Zhou Y, Chen ZC (2015) A new geometric
meshing theory for a closed-form vector representation of the face-milled
generated gear tooth surface and its curvature analysis.Mech.Mach.Theory,83
(2015): each flank of tooth point can 91-108.) be expressed as one comprising two variable h withFunction, then have:
Further according to formula Can solve h withValue, be set as h* withBy h* withSubstitute into the explicit of the flank of tooth
Expression formula obtains the corresponding true tooth point of sample point q；
Finally repeating the step can be obtained the corresponding true tooth point of each sample point；
Wherein Rq=(Ao-f) sin Γ+dcos Γ, Zq=(Ao-f) cos Г+dsin Г.0≤f≤F ,-bf
≤d≤af；F is the face width of tooth, AoIt is in OgThe outer cone distance measured between A；afAnd bfIt is that q point corresponding with parameter f arrives respectively
The distance of tooth top and tooth root.
Step 4: two-dimentional gear blank and each true tooth point are imported 3 d modeling software, two-dimentional gear blank is revolved around Gear axis
Reincarnation is at three-dimensional gear blank, and for each true tooth point with a line, the mode that line connects face generates the single flank of tooth；As shown in Figure 4.
Step 5: carrying out annular array to the single flank of tooth on the basis of Gear axis, institute's geared surface is obtained as shown in Fig. 5,
And trimming is carried out with three-dimensional gear blank, threedimensional model as shown in FIG. 6 can be obtained.
The present invention is expressed using the display of the flank of tooth, and rapid Optimum solves flank of tooth point, simplifies calculating process, solves flank of tooth point
Speed is fast, calculates and stablizes, and modeling efficiency is high；And the solution for using display expression to acquire is regardless of whether for completely accurate solution, centainly
Can in true tooth, only can there are certain errors without falling in outside true tooth with default flank of tooth point, do not interfere with most
Whole flank of tooth modeling accuracy.
Claims (5)
1. a kind of spiral bevel gear three-dimensional modeling method, which is characterized in that method includes the following steps:
Step 1: establishing spiral bevel gear two dimension gear blank figure；
Step 2: carrying out discrete, several equally distributed sample points of generation to the flank region in two-dimentional gear blank figure；
Step 3: it is corresponding true to acquire each sample point according to the explicit expression of flank of tooth point mapping relations and the spiral bevel gear flank of tooth
Pleodont millet cake；
Step 4: two-dimentional gear blank and each true tooth point are imported 3 d modeling software, two-dimentional gear blank is rotated around Gear axis
Three-dimensional gear blank is generated, each true tooth point line is generated into the single flank of tooth；
Step 5: carrying out annular array to the single flank of tooth on the basis of Gear axis, obtain institute's geared surface, and with three-dimensional gear blank into
Modeling is completed in row trimming.
2. spiral bevel gear three-dimensional modeling method as described in claim 1, it is characterised in that: in said step 1, consult
Spiral bevel gear design manual chooses gear blank parameter, determines spiral bevel gear two dimension gear blank figure.
3. spiral bevel gear three-dimensional modeling method as described in claim 1, it is characterised in that: in the step 2, the flank of tooth
The boundary in region is quadrangle, and zone of dispersion is selected as the similar quadrangle comprising flank region when discrete.
4. spiral bevel gear three-dimensional modeling method as described in claim 1, which is characterized in that for appointing in the step 3
Anticipate a sample point q, is default true tooth point around the intersection point of the postrotational track of Gear axis and flank of tooth two sides, solves step
It is rapid as follows:
Firstly, establishing coordinate system sg, origin OgFor bevel gear pitch cone vertex, ZgAxis is overlapped with bevel gear axis, XgAxis is in two dimension
In gear blank plane with ZgAxis is vertical, YgIt is determined by the right-hand rule；
Secondly, any sample point q is chosen, in coordinate system sgIt is middle according to the gear blank parameter coordinate be (Rq,0,Zq)；
Then, it is assumed that the coordinate of default true tooth point is Wei (Sx,Sy,Sz), according to flank of tooth point mapping relations, have:
Then, according to the explicit expression of the spiral bevel gear flank of tooth each flank of tooth point can be expressed as one comprising two variable h with
Function, then have:
The formula is a Nonlinear System of Equations, can be converted into and state optimization problem and solved
I.e.
Can solve h withValue, be set as h* withBy h* withThe explicit expression for substituting into the flank of tooth has obtained sample point q
Corresponding true tooth point coordinate (Sx*,Sy*,Sz* the corresponding true tooth point of sample point q) is acquired；
Finally repeating the step can be obtained the corresponding true tooth point of each sample point；
Wherein Rq=(Ao-f) sin Γ+dcos Γ, Zq=(Ao-f) cos Γ+dsin Γ, 0≤f≤F ,-bf≤d≤
af；F is the face width of tooth, AoIt is in OgThe outer cone distance measured between A；afAnd bfQ point corresponding with parameter f respectively to tooth top and
The distance of tooth root.
5. spiral bevel gear three-dimensional modeling method as described in claim 1, which is characterized in that will be each true in the step 4
Pleodont millet cake imports 3 d modeling software, and with a line, the mode that line connects face generates the single flank of tooth.
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Cited By (2)
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| CN111666641A (en) * | 2020-05-25 | 2020-09-15 | 重庆青山工业有限责任公司 | Method for calculating tooth surface parameters of straight bevel gear |
| CN114239300A (en) * | 2021-12-21 | 2022-03-25 | 中国航发中传机械有限公司 | Full-process-method-based tooth root transition fillet modeling method and system for spiral bevel gear |
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| CN114239300A (en) * | 2021-12-21 | 2022-03-25 | 中国航发中传机械有限公司 | Full-process-method-based tooth root transition fillet modeling method and system for spiral bevel gear |
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