CN105718651B - A kind of involute bevel gears tooth end relief and parametric modeling method - Google Patents
A kind of involute bevel gears tooth end relief and parametric modeling method Download PDFInfo
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- CN105718651B CN105718651B CN201610035683.3A CN201610035683A CN105718651B CN 105718651 B CN105718651 B CN 105718651B CN 201610035683 A CN201610035683 A CN 201610035683A CN 105718651 B CN105718651 B CN 105718651B
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- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
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- G06F30/17—Mechanical parametric or variational design
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
Abstract
The present invention relates to a kind of involute bevel gears tooth end relief and parametric modeling methods, the following steps are included: S1, the involute bevel gears progress finite element analysis to non-correction of the flank shape, obtain the circumferentially displaced difference of gear and the equivalent distribution of contact figure of the flank of tooth of each crucial position of engagement；S2, based on the circumferentially displaced difference of the gear, determine the profiling quantity of tooth end relief, based on the equivalent distribution of contact figure of the flank of tooth determine correction of the flank shape length；S3, using correction of the flank shape length and profiling quantity as variable, establish the equation of tooth end relief curve and the correction of the flank shape flank of tooth；S4, according to tooth end relief curve and the threedimensional model of the establishing equation profile modifying gear of the correction of the flank shape flank of tooth.The present invention effectively improves the gear load as caused by tooth surface elasticity and is unevenly distributed and stress concentration status, improves transmission accuracy, and the vibrating noise for reducing gear engagement is horizontal, so that the service life of gear improves.
Description
Technical field
The present invention relates to the correction of the flank shape of gear and modeling methods, more specifically to a kind of involute bevel gears tooth
Hold correction of the flank shape and parametric modeling method.
Background technique
In the actual use process due to involute bevel gears, by the accuracy of manufacture, mismachining tolerance and load
The influence of the factors such as distribution situation causes actual mesh tooth face to deviate from the spherical involute of its Theoretical Design, therefore gear
Vibration, noise increase in the process of running, seriously reduce the NVH quality of gear.Tooth is obtained by the means of finite element analysis
The tooth surface elasticity amount after loaded is taken turns, the parameters such as profiling quantity and the correction of the flank shape length of gear face is further determined that, finally changes
It is horizontal to reduce the vibrating noise that gear engagement generates for the loaded situation of kind gear teeth face.
The correction method of traditional involute bevel gears mainly includes profile modification, axial modification, tooth end relief etc..
Publication number CN1936749A uses the comprehensive correction of the flank shape method of increment, flank profil and teeth directional and carries out correction of the flank shape to involute bevel gears,
But reasonable dismissal is not made to the determination process of its profile modifying parameters, only gives the experience recommended range of profile modifying parameters.It is open
Number CN101937211A uses flank profil, axial modification method and carries out correction of the flank shape to involute bevel gears, uses limited dynamics
First simulation method determines bevel gear big end profile modification amount, makes correction of the flank shape exterior feature in gear teeth central cross-section using 3D sculpting software first
Shape, and correction of the flank shape profile is equidistantly stretched to the modeling process for realizing teeth directional modification of equidistance gear to the flank of tooth, finally by numerically-controlled machine tool
It realizes profile modifying gear processing, is a kind of relatively reasonable profile modifying gear processing method, but its shortcoming is that teeth directional etc. only can be achieved
Away from correction of the flank shape, parametrization correction of the flank shape cannot be carried out according to actual needs, change profile modifying parameters.Publication number CN85102760B passes through to humorous
Wave gear carries out electrochemical corrosion, to achieve the purpose that correction of the flank shape.
Summary of the invention
The technical problem to be solved in the present invention is that providing a kind of involute bevel gears tooth end relief and parametrization is built
Mould method.
The technical solution adopted by the present invention to solve the technical problems is: constructing a kind of involute bevel gears increment and repairs
Shape and parametric modeling method, comprising the following steps:
S1, finite element analysis is carried out to the involute bevel gears of non-correction of the flank shape, obtains the gear of each crucial position of engagement
Circumferentially displaced difference and the equivalent distribution of contact figure of the flank of tooth；
S2, based on the circumferentially displaced difference of the gear, determine the profiling quantity of tooth end relief, answered with the equivalent contact of the flank of tooth
Correction of the flank shape length is determined based on power distribution map；
S3, using correction of the flank shape length and profiling quantity as variable, establish the equation of tooth end relief curve and the correction of the flank shape flank of tooth；
S4, according to tooth end relief curve and the threedimensional model of the establishing equation profile modifying gear of the correction of the flank shape flank of tooth.
In above scheme, the equation of the tooth end relief curve is as follows:
In formula: r is gear start radius；RciIt (i=1,2) is the arc radius of modification curve；R be outer cone away from；B is tooth
It is wide；ΔLiIt (i=1,2) is correction of the flank shape length；
In above scheme, which is characterized in that the correction of the flank shape tooth surface equation is as follows:
Z=r cos (β sin α) cos α
In formula: r is gear start radius；α is cone generating angle；β be the field of conjugate action between initial segment and instantaneous rotating shaft
Angle, wherein involute start angle is 0 on base cone；RciIt (i=1,2) is the arc radius of modification curve；To be parallel to
The unit vector of base cone axis；AndRespectively unit vectorX, y to projection coordinate.
In above scheme, the key position of engagement includes four single bi-tooth gearing transfer points.
Implement involute bevel gears tooth end relief and parametric modeling method of the invention, has below beneficial to effect
Fruit:
1, the invention proposes a kind of based on the circumferentially displaced difference of gear and the equivalent distribution of contact figure of teeth directional gradually
Burst at the seams straight bevel gear correction method, is built by means of the three-dimensional that mathematical analysis software and 3D sculpting software realize profile modifying gear
Mold process.
2, the present invention effectively improve the gear load as caused by tooth surface elasticity be unevenly distributed and stress concentrate
Situation improves transmission accuracy, and the vibrating noise for reducing gear engagement is horizontal, so that the service life of gear improves.
3, the present invention is directed to the characteristics of gear mesh flexible deformation, uses increment unsymmetric shape modification, driven tooth to driving gear
Wheel does not make correction of the flank shape.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing:
Fig. 1 is the schematic diagram of theoretical spherical involute；
Fig. 2 is the three-dimensional model diagram of the non-correction of the flank shape straight bevel gear of standard；
Fig. 3 is standard straight bevel gear limited element calculation model schematic diagram；
Fig. 4 is gear mesh schematic diagram mesh cycle；
Fig. 5 is the circumferentially displaced difference schematic diagram of key position gear；
Fig. 6 is the non-correction of the flank shape straight bevel gear facewidth to equivalent distribution of contact figure；
Fig. 7 is straight bevel gear tooth end relief parameter schematic diagram；
Fig. 8 is the correction of the flank shape flank of tooth model established in Matlab；
Fig. 9 is the three-dimensional model diagram into the straight bevel gear for crossing correction of the flank shape；
Figure 10 be after correction of the flank shape the straight bevel gear facewidth to equivalent distribution of contact figure.
Specific embodiment
For a clearer understanding of the technical characteristics, objects and effects of the present invention, now control attached drawing is described in detail
A specific embodiment of the invention.
It is as follows in involute bevel gears tooth end relief and parametric modeling method specific embodiment of the invention:
On the basic circle conical surface a little or basic circle reference cone face on a little on the basic circle conical surface rotary at spherical involute.Such as Fig. 1
It is shown, a point P in tangent plane0Spherical involute PP is formed behind the rotation β angle of base cone face0.It is starting with big end spherical involute
Line, small end spherical involute are terminated line, and the non-correction of the flank shape straight bevel gear flank of tooth of standard can be obtained using variable cross-section sweeping order,
And non-profile modifying gear threedimensional model as shown in Figure 2 is established using array commands.
Select a pair of involute bevel gears with basic parameter in table 1:
Table 1
Grid is carried out to non-profile modifying gear model using Solid185 unit in finite-element preprocessing software Hypermesh
Divide, and import in ANSYS be arranged corresponding material properties (wherein material properties be 40Cr, elastic modulus E=2.1 ×
105Mpa, Poisson's ratio ν=0.3) and boundary condition (gear pair is contacted to friction coefficient μ=0.2, driving wheel torque T=50N.m,
All freedom degree staff cultivations of driven wheel axis hole node, the radial and axial freedom degree of driving wheel axis hole node is all fixed, only discharges
Circumferential free degree), finally obtain finite element model as shown in Figure 3.
According to gear schematic diagram mesh cycle, as shown in figure 4, determining four key positions in Meshing Process of Spur Gear: P1、
P2、P3、P4, i.e., single bi-tooth gearing transfer point.
For 4 key positions listed above, with reference to finite element stimulation as a result, obtaining the circumferentially displaced difference of its gear
It is worth schematic diagram, as shown in Figure 5.
The circumferentially displaced difference schematic diagram of gear according to figure 5, it is known that P3Occurs teeth directional displacement difference at position most
Big value, respectively 10.2 μm (corresponding gear small ends) and 14.12 μm (corresponding gear big end), it is thus determined that gear small end correction of the flank shape
Measure △ T1=11 μm, gear big end profiling quantity △ T2=15 μm.The facewidth emulated according to FEM calculation is answered to equivalent contact
Power distribution map, as shown in fig. 6, determining correction of the flank shape length △ L1=△ L2=0.975mm.
Tooth end relief parameter schematic diagram is as shown in Figure 7.Wherein the arc radius calculation formula of modification curve is as follows:
Rci=Δ Li 2/2ΔTi
The equation of modification curve G'N' is as follows:
Modification curve GN equation is as follows:
Wherein variable i=1 represents circular curve G'N'；I=2 represents circular curve GN；RciFor arc radius；B is the facewidth；
△TiFor profiling quantity；△LiFor correction of the flank shape length；R be outer cone away from.
Here the unit vector for being parallel to straight line PG is introducedIt can be acquired by following formula:
Therefore correction of the flank shape flank of tooth Σ 1 and 2 equation of Σ are as follows:
Z=r cos (β sin α) cos α
Wherein i=1,2.
Following procedure code is inputted in Matlab for constructing the correction of the flank shape flank of tooth:
clear all
close all
[l, k]=meshgrid (21:0.5:34,0:0.05:pi/3)；Space networks ruling
A=0.18044026*pi；Cone generating angle
B=k*sin (a)；Angle on the field of conjugate action between initial segment and instantaneous rotating shaft
C=1188.28125-sqrt (1188.28125*1188.28125- (l-27.634908) .* (l-
27.634908))；Profiling quantity
X=(l.*cos (b) .*cos (k) .*sin (a)+l.*sin (k) .*sin (b)+c.* (cos (k) .*sin (b)-
cos(b).*sin(k).*sin(a))./sqrt(cos(b).^2.*sin(a).^2+sin(b).^2))-sin(U1).*(l.*
cos(b).*sin(k).*sin(a)-l.*cos(k).*sin(b)+c.*(cos(b).*cos(k).*sin(a)+sin(k).*
sin(b))./sqrt(cos(b).^2.*sin(a).^2+sin(b).^2))；X-coordinate
Y=(l.*cos (b) .*sin (k) .*sin (a)-l.*cos (k) .*sin (b)+c.* (cos (b) .*cos (k) .*
sin(a)+sin(k).*sin(b))./sqrt(cos(b).^2.*sin(a).^2+sin(b).^2))+sin(U1).*(l.*
cos(b).*cos(k).*sin(a)+l.*sin(k).*sin(b)+c.*(cos(k).*sin(b)-cos(b).*sin(k).*
sin(a))./sqrt(cos(b).^2.*sin(a).^2+sin(b).^2))；Y-coordinate
Z=l.*cos (b) .*cos (a)；Z coordinate
surf(x,y,z)；Construct correction of the flank shape curved surface
By the point cloud data export of the MATLAB correction of the flank shape curved surface established, and use using 3D sculpting software Proe in straight-tooth
On the basis of bevel gear surface equation, building straight bevel gear axial modification curved surface is mixed by boundary, and further construct tooth
Slot entity and gear entity obtain the correction of the flank shape flank of tooth as shown in Figure 9.
Finite Element Simulation Analysis is carried out to correction of the flank shape backgear, obtains after correction of the flank shape the straight bevel gear facewidth to equivalent contact stress
Distribution map, as shown in Figure 10, it is seen that the back-geared equivalent contact stress maximum value of correction of the flank shape declines, stress at increment and tooth root
Situation is concentrated to be improved.
The embodiment of the present invention is described with above attached drawing, but the invention is not limited to above-mentioned specific
Embodiment, the above mentioned embodiment is only schematical, rather than restrictive, those skilled in the art
Under the inspiration of the present invention, without breaking away from the scope protected by the purposes and claims of the present invention, it can also make very much
Form, all of these belong to the protection of the present invention.
Claims (3)
1. a kind of involute bevel gears tooth end relief and parametric modeling method, which comprises the following steps:
S1, finite element analysis is carried out to the involute bevel gears of non-correction of the flank shape, the gear for obtaining each crucial position of engagement is circumferential
Shift differences and the equivalent distribution of contact figure of the flank of tooth；
S2, based on the circumferentially displaced difference of the gear, the profiling quantity of tooth end relief is determined, with the equivalent contact stress of the flank of tooth point
Correction of the flank shape length is determined based on Butut；
S3, using correction of the flank shape length and profiling quantity as variable, establish the equation of tooth end relief curve and the correction of the flank shape flank of tooth；
S4, according to tooth end relief curve and the threedimensional model of the establishing equation profile modifying gear of the correction of the flank shape flank of tooth；The tooth end relief is bent
The equation of line is as follows:
In formula: r is gear start radius；RciFor the arc radius of modification curve, wherein i=1,2；R be outer cone away from；B is tooth
It is wide；△LiFor correction of the flank shape length, wherein i=1,2.
2. involute bevel gears tooth end relief according to claim 1 and parametric modeling method, which is characterized in that
The correction of the flank shape tooth surface equation is as follows:
Z=rcos (β sin α) cos α
In formula: r is gear start radius；α is cone generating angle；β is the angle on the field of conjugate action between initial segment and instantaneous rotating shaft,
Wherein involute start angle is 0 on base cone；RciFor the arc radius of modification curve, wherein i=1,2；To be parallel to base
The unit vector of circular cone axis；AndRespectively unit vectorX, y to projection coordinate.
3. involute bevel gears tooth end relief according to claim 1 and parametric modeling method, which is characterized in that
The key position of engagement includes four single bi-tooth gearing transfer points.
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| CN108389252B (en) * | 2018-01-31 | 2021-09-03 | 厦门理工学院 | Three-dimensional modeling method for processing involute gear tooth profile surface by gear shaping |
| CN113309843B (en) * | 2021-06-03 | 2022-07-26 | 株洲九方装备驱动技术有限公司 | Crinnberg gear for gear box and shaping method thereof |
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|---|---|---|---|---|
| CN1936749A (en) * | 2006-10-18 | 2007-03-28 | 华中科技大学 | Evolent straight-gear conic-gear direct-finishing method |
| CN101504035A (en) * | 2009-02-27 | 2009-08-12 | 华南理工大学 | Heavy-duty sliding bearing and its abrasion-resistant correction method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US7191521B2 (en) * | 2003-02-07 | 2007-03-20 | American Axle & Manufacturing, Inc. | Advanced geometry of skew and straight bevel gears produced by forging |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1936749A (en) * | 2006-10-18 | 2007-03-28 | 华中科技大学 | Evolent straight-gear conic-gear direct-finishing method |
| CN101504035A (en) * | 2009-02-27 | 2009-08-12 | 华南理工大学 | Heavy-duty sliding bearing and its abrasion-resistant correction method |
Non-Patent Citations (3)
| Title |
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| 双圆弧齿轮齿端修形与冷精锻成形技术研究;张贺;《中国优秀硕士学位论文全文数据库-工程科技Ⅰ辑》;20111215(第S1期);第B022-377页 |
| 渐开线直齿圆锥齿轮修形研究;黄海浪;《万方学术论文库》;20090902;第1-78页 |
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