CN105522227A - Profile shaping method for machining cutter tooth main cutting edge according to cycloid bevel gear - Google Patents
Profile shaping method for machining cutter tooth main cutting edge according to cycloid bevel gear Download PDFInfo
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- CN105522227A CN105522227A CN201510921328.1A CN201510921328A CN105522227A CN 105522227 A CN105522227 A CN 105522227A CN 201510921328 A CN201510921328 A CN 201510921328A CN 105522227 A CN105522227 A CN 105522227A
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- gear
- cutting edge
- cutter tooth
- bevel gears
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F21/00—Tools specially adapted for use in machines for manufacturing gear teeth
- B23F21/12—Milling tools
- B23F21/16—Hobs
- B23F21/18—Taper hobs, e.g. for bevel gears
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Abstract
The invention relates to a profile shaping method for machining a cutter tooth main cutting edge according to a cycloid bevel gear, and belongs to the field of machine designing and manufacturing. The method is based on a gear tooth surface machining principle, a gear meshing principle is used, the surface profile of the cutter tooth main cutting edge of a machined tooth surface is modified, and a tooth surface equation is obtained according to space coordinate system changes. A meshing track and a transmission error of a gear tooth machined through a new method is analyzed through a TCA analysis method, and are compared with those of a gear machined through a traditional method, and the gear constructed in the invention is obtained, so that the transmission error is substantially reduced, and meanwhile the better contact track is obtained; and through an experimental verification and analysis method, the constructed gear conducts a loading experiment and analyzes the position of a contact zone, and stress concentration can be avoided through the gear constructed in the invention. Stress concentration during gear meshing is completely avoided, the transmission error is reduced, noise of the gear is reduced accordingly, and the transmission stability is improved.
Description
Technical field
The present invention relates to a kind of profile correction method for cycloid bevel gears processing cutter tooth main cutting edge, belong to machine design and manufacture field.
Background technology
Overlikon spiral bevel gear (Klingelnberg) is one of spiral bevel gear two canine tooth commonly used at present, and the heavy duty especially in aviation, automobile and heavy machine tool etc., high-power transmission are applied in field more and more widely.Along with machine driven system is day by day towards high speed, accurate future development, as the crucial drive disk assembly in transmission system, under overlikon spiral bevel gear is often operated in complex working condition, as heavy duty, impact and varying load etc., therefore the problem such as flank of tooth vibration failur and noise just produces thereupon.Therefore overlikon spiral bevel gear is subject to extensive concern and the research of various countries relevant expert scholar always, becomes the key technology in Gear Production and commanding elevation.Gleason company formally delivered Tooth Contact Analysis (toothcontactanalysis in 1978, TCA) principle and method, under the prerequisite not considering load deflection and error component, utilize the method can simulate shape and the position of face spot on computers.TCA technology has been widely used in various gear, and Chinese scholar Zheng Chang opens, Mao Shimin etc. also completes the research work of TCA method in succession.It is theoretical that Wang Xiaochun, Wu Xutang etc. propose three rank contact analysis, utilizes the method not only can obtain instantaneous transmission ratio and acceleration, can also obtain high-order acceleration.Wu Xuncheng etc. also proposed the concept of point gearing conjugate tooth profiles mismatch transmission performance pre-control and the active designs theory etc. of hypoid gear, and with its theory solve the known flank of tooth 1 and on contact point trace line and transmission requirement condition under, solve the problem of the unknown flank of tooth 2 of Local conjugation with it.Once the hide algorithm and TCA program that comprehensively have studied Gleason of Central South University, disclose its compilation theory and various computing formula of having derived.The contact stress of the gear teeth meshing situation under finite element model for solving load effect and load application point such as American scholar F.L.Litvin, and analyze and finite element stress analysis by Local synthesis algorithm, TCA, reduce noise and vibration during gear drive.
But the forming process of the Chinese scholars research gear modification flank of tooth is set forth for spur gear or bevel gear mostly.Because overlikon spiral bevel gear heavy duty cycloid bevel gears is cyclo-palloid curve and equal at the tooth depth direction height of the gear teeth along the tooth trace of gear teeth tooth length direction, because the particularity of overlikon spiral bevel gear profile of tooth, Chinese scholars is analyzed content and is seldom related to overlikon spiral bevel gear.Herein by the traditional machine tool process principle of research overlikon spiral bevel gear, based on conventional gears mesh theory, by correction of the flank shape cutter, the flank of tooth of practicing Buddhism or Taoism of gear is obtained through coordinate transform, TCA analysis is carried out to it, finite element loads simulation analysis and contrasts with the gear that traditional process tool processes, the phenomenon that the known gear built herein can avoid stress to concentrate.Herein for can root avoid gears meshing time stress concentration phenomenon, reduce transmission error, thus reduce the noise of gear, improve transmission stability.
Summary of the invention
The object of this invention is to provide a kind of profile correction method for cycloid bevel gears processing cutter tooth main cutting edge.Based on gear teeth face process principle, utilize Principles of Gear Connection, the cutter tooth main cutting edge surface profile of the processing flank of tooth is revised, obtain tooth surface equation according to space coordinates change.The engagement trace of the gear teeth of application TCA analytical new method processing and transmission error also contrast with the gear that conventional method processes, and the gear built herein significantly reduces transmission error and obtains better contact point trace line simultaneously; Check analysis method by experiment, carries out loading experiment to the gear built herein and analyzes its position, contact zone, the phenomenon that the gear built herein can avoid stress to concentrate.Herein for can root avoid gears meshing time stress concentration phenomenon, reduce transmission error, thus reduce the noise of gear, improve transmission stability.
The present invention adopts following technological means to realize:
1, traditional line type cutter tooth cutting edge is built.
2, parabolic type cutter tooth cutting edge is built.
3, machining tool coordinate system and gear teeth modeling is set up.
4, in Matlab, discrete point set is above preserved with the form respectively with Txt, and imported in 3 d modeling software Pro/E, by carrying out reading process to these data, line is linked according to from point, the flank of tooth is expanded to again by line, last by face again to the structure thinking of body, set up the threedimensional model of heavily loaded cycloid bevel gears.
5, for table 1 standard, gear pair is installed, by Matlab software programming actual flank of tooth TCA program, for the gear ratio of driving wheel and driven pulley for 29:29, respectively TCA analysis is carried out to the gear teeth that two kinds of difform cutter tooth cutting edges process.
6, under the load effect being 500Nm at moment of torsion, the driving wheel processed by application parabolic type cutter tooth cutting edge drives driven pulley to observe the position of its contact area.
Accompanying drawing explanation
Fig. 1 gear rotating and projection face;
Fig. 2 gear teeth face discrete point schematic diagram;
Fig. 3 gear teeth threedimensional model;
Fig. 4 linear pattern cutter tooth cutting edge processes tooth contact district and transmission error curve;
Fig. 5 parabolic type cutter tooth cutting edge processes tooth contact district and transmission error curve;
Fig. 6 is the implementing procedure figure of this method.
Detailed description of the invention
By description below and accompanying drawings, the present invention can be more clear, and accompanying drawing illustrates for explaining the inventive method and embodiment.
The invention provides a kind of profile correction method for cycloid bevel gears processing cutter tooth main cutting edge.Concrete implementation step is as follows:
1 traditional line type cutter tooth cutting edge model
Tradition processing cycloid bevel gears often selects linear pattern cutter tooth cutting edge, then is practiced Buddhism or Taoism to the gear teeth by adjustment lathe dimensional parameters, so not only makes machined parameters too complexity but also can affect flank profile.Linear pattern cutter tooth cutting edge surface profile, the concave surface of the convex surface of cutter tooth and concave surface difference cutting pinion and convex surface, α
gprofile angle, arc radius ρ
wthe fillet on formative gear surface when machining, cutter tooth main cutting edge surface is around reference axis z
gdo gyration, the anglec of rotation is θ
g, tip radius is R
g.
Can be obtained at blade coordinate system S by the geometrical relationship in Fig. 1
gunder, there is the coordinate column vector r of blade arbitrfary point
g(s
g, θ
g) expression formula is
2 build parabolic type cutter tooth cutting edge model
This method proposes a kind of novel parabolic type cutter tooth cutting edge, by practicing Buddhism or Taoism to cutter tooth cutting edge, directly can process reasonable flank profile.In parabolic type cutter tooth cutting edge, cutter head is around rotating shaft z
grotate, the anglec of rotation is θ
g, α
gfor cutting edge a tangent line at M place and and the longitudinal centre line of blade between angle, s
g0for parabola apex location parameter, the position of some M is by s
g0determine.
Can be obtained at blade coordinate system S by the geometrical relationship in Fig. 2
gunder, there is the coordinate column vector r of blade arbitrfary point
g(s
g, θ
g) expression formula is
In formula: ("+" is outer cutter, and "-" is interior cutter), a
cfor parabolic type main cutting edge surface profile quadratic term coefficient,
3 set up machining tool coordinate system and gear teeth modeling:
Dextrorotation cycloid bevel gears Cutter coordinate system is set up, wherein coordinate system S according to KNC type tooth milling machine
m2being connected with lathe is lathe coordinate system, coordinate system S in the process of machining gears
m2remain static; S
c2take turns axle center with product shape to connect firmly, S during initial position
c2with S
m2position overlaps; S
a2for position of wheel auxiliary coordinates; S
2for crossing gear reference cone apex, with the coordinate system of processed wheel blank consolidation, its initial position and coordinate system S
b2overlap; If angular velocity of rotation is ω during workpiece work
1; Any time, the rotational angle of processed gear was still ψ
2; Δ E
m2for workhead offset; Δ X
b2for berth; Δ X
d2for horizontal position of wheel; γ
m2for processed gear established angle, be numerically equal to reference cone angle; ψ
c2for the angle that cage chair any time rotates.By blade arbitrfary point at S
c2column vector r under coordinate system
c2(s
g, θ
g) obtain blade arbitrfary point at S by the matrixing of coordinate
2vector under coordinate system i.e. gear teeth face equation.Corresponding transformation matrix of coordinates is M
m2c2, M
a2m2, M
2a2, M
b22expression is equation
r
b2(s
g,θ
g,ψ
2)＝M
b22·M
2a2·M
a2m2·M
m2c2·r
g(s
g，θ
g)(3)
In formula: M
b22, M
2a2, M
a2m2, M
m2c2for corresponding transformation matrix of coordinates.
R
b2(s
b, θ, ψ
2) corresponding unit normal vector is
Obtaining flank engagement equation by Principles of Gear Connection is
S respectively owing to there being three unknown numbers in flank engagement equation
b, θ, ψ
2.So the discrete point on gear teeth face will be obtained, need to set up three equations and combine and solve.The boundary condition by the flank of tooth is now needed to set up equation.The axial plane crossing gear shaft does the rotating and projection face of gear, as shown in Figure 1, solving to more be convenient to, first setting up coordinate system S
p(o
p; x
p, y
p), O
pfor wheel blank conical point is as the origin of coordinates, x
pspend dividing of gear and chase after bus.
The tooth surface equation of driving gear can be obtained according to above-mentioned derivation:
For one of Beijing first Machine Tools Plant group of heavy duty cycloid bevel gears, the secondary basic parameter of cycloid bevel gears that Beijing first Machine Tools Plant provides in table 1 with detailed Machine-settings in table 2.These parameters are brought in the tooth surface equation group 3-19 of gear, and with quasi_Kantorovich operator, equation is carried out discrete in Matlab software and solve.
The secondary basic parameter of table 1 cycloid bevel gears
The secondary basic machined parameters of table 2 cycloid bevel gears
Table2Basicprocessingparametersofcycloidbevelgearpair
Because the threedimensional model that will construct in Pro/E, thus to the division of gear teeth face grid as much as possible evenly or gradual change as Fig. 5 be gear teeth face discrete point schematic diagram.Can know from Fig. 2 and get 37 points along the tooth length direction of gear teeth face, 10 points are got in the facewidth direction along gear teeth face, and the working gear flank of tooth is got 370 points altogether.
Convex surface and the concave surface of driven pulley and driving wheel can be obtained respectively according to the flank of tooth discrete co-ordinate values of driven pulley and driving wheel.Fig. 5 is the discrete point of driven gear concave surface and the discrete point of driven gear convex surface.
4 build cycloid bevel gears threedimensional model
In Matlab, discrete point set is above preserved with the form respectively with Txt, and imported in 3 d modeling software Pro/E, by carrying out reading process to these data, line is linked according to from point, the flank of tooth is expanded to again by line, last by face again to the structure thinking of body, set up the threedimensional model of heavily loaded cycloid bevel gears.If Fig. 3 is the threedimensional model of the gear teeth, a) being the driven pulley gear teeth in figure, b) is the driving wheel gear teeth, c) is single to gear teeth meshing.
5TCA analyzes:
For table 1 standard, gear pair is installed, by Matlab software programming actual flank of tooth TCA program, for the gear ratio of driving wheel and driven pulley for 29:29, respectively TCA analysis is carried out to the gear teeth that two kinds of difform cutter tooth cutting edges process.Fig. 4 be the Gear Contact district that draws of TCA methods analyst that linear pattern cutter tooth cutting edge processes the gear teeth and engagement time transmission error curve.
Analysis result contrast can draw: the degree of (1) transmission error reduces to 41 μ rad by 355.5 μ rad, approximately reduces 88.4%, achieves the significantly reduction of transmission error; (2) parabolic type cutter tooth cutting edge obtains better parabola shaped transmission error, makes transmission more steady; (3) obtain along the flank of tooth longitudinally upper better contact point trace line.
6 experimental verifications:
Under the load effect that moment of torsion is 500Nm, the driving wheel processed by application parabolic type cutter tooth cutting edge drives driven pulley to observe the position of its contact area.
In order to the position of more clear observation tooth contact zone, after rolling inspection experiment terminates, with the change of the red lead powder of the lower gear teeth of a blank sheet of paper print.
Draw the cycloid bevel gears of application parabolic type cutter tooth cutting edge processing, the position, contact zone when being subject to moment of torsion and being 500Nm is positioned at the centre of the flank of tooth, and the phenomenon that nib contacts and stress are concentrated does not occur.
Summed up by above instance analysis: the cycloid bevel gears of application parabolic type cutter tooth cutting edge processing achieves parabola shaped driving error curve, reduces the amplitude of transmission error.And the cycloid bevel gears of application parabolic type cutter tooth cutting edge processing is avoided occurring that stress concentrates the phenomenon with nib contacts when engaging, thus the noise reduced in gear drive process and vibration.
Claims (3)
1., for a profile correction method for cycloid bevel gears processing cutter tooth main cutting edge, it is characterized in that: it comprises the steps:
1) traditional line type cutter tooth cutting edge model is built
2) parabolic type cutter tooth cutting edge model is built
3) machining tool coordinate system and gear teeth modeling is set up
4) cycloid bevel gears threedimensional model is built
5) TCA analyzes:
For table 1 standard, gear pair is installed, by Matlab software programming actual flank of tooth TCA program, for the gear ratio of driving wheel and driven pulley for 29:29, respectively TCA analysis is carried out to the gear teeth that two kinds of difform cutter tooth cutting edges process;
The secondary basic parameter of table 1 cycloid bevel gears
6) experimental verification:
Under the load effect that moment of torsion is 500Nm, the driving wheel processed by application parabolic type cutter tooth cutting edge drives driven pulley to observe the position of its contact area.In order to the position of more clear observation tooth contact zone, after rolling inspection experiment terminates, with the change of the red lead powder of the lower gear teeth of a blank sheet of paper print.
2. as claimed in claim 1 for the profile correction method of cycloid bevel gears processing cutter tooth main cutting edge, it is characterized in that: the cycloid bevel gears of application parabolic type cutter tooth cutting edge processing achieves parabola shaped driving error curve, reduces the amplitude of transmission error.
3. as claimed in claim 1 for the profile correction method of cycloid bevel gears processing cutter tooth main cutting edge, it is characterized in that: the cycloid bevel gears of application parabolic type cutter tooth cutting edge processing is avoided occurring that stress concentrates the phenomenon with nib contacts when engaging, thus the noise reduced in gear drive process and oscillation phenomenon.
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|---|---|---|---|
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| CN105522227B CN105522227B (en) | 2018-05-25 |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108241764A (en) * | 2016-12-26 | 2018-07-03 | 宝沃汽车（中国）有限公司 | The three-dimensional modeling method and device of hypoid gear |
| CN108256174A (en) * | 2017-12-27 | 2018-07-06 | 西安建筑科技大学 | Modeling method is engaged on the shaving that tooth form quality influences for analyzing shaving process |
| CN108345744A (en) * | 2018-02-09 | 2018-07-31 | 西北工业大学 | A kind of cutter profile design space computational methods |
| CN108873809A (en) * | 2018-07-02 | 2018-11-23 | 中南大学 | A kind of high-order tooth surface error modification method of spiral bevel gear |
| CN109101754A (en) * | 2018-08-31 | 2018-12-28 | 西安交通大学 | A kind of full step process of spiral bevel gear |
| CN109241613A (en) * | 2018-08-31 | 2019-01-18 | 西安交通大学 | A kind of cutter root relief parameter determination method of spiral bevel gear |
| CN109396567A (en) * | 2018-11-06 | 2019-03-01 | 重庆大学 | The digital envelope method of worm abrasion wheel profile is determined in correction of the flank shape cycloid gear generating grinding |
| CN110788413A (en) * | 2019-10-29 | 2020-02-14 | 西安交通大学 | Method for optimizing cutter edge curve of milling cutter disc at end of cycloid gear bevel gear |
| CN112182803A (en) * | 2020-09-29 | 2021-01-05 | 南京高速齿轮制造有限公司 | Excitation calibration method of dynamic model |
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| CN103223533A (en) * | 2013-05-10 | 2013-07-31 | 中国农业大学 | Method for designing side rear angle surfaces of double-enveloping ring surface worm gear hob |
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Cited By (17)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108241764A (en) * | 2016-12-26 | 2018-07-03 | 宝沃汽车（中国）有限公司 | The three-dimensional modeling method and device of hypoid gear |
| CN108256174A (en) * | 2017-12-27 | 2018-07-06 | 西安建筑科技大学 | Modeling method is engaged on the shaving that tooth form quality influences for analyzing shaving process |
| CN108256174B (en) * | 2017-12-27 | 2021-05-11 | 西安建筑科技大学 | Shaving engagement modeling method for analyzing influence of shaving process on tooth profile quality |
| CN108345744A (en) * | 2018-02-09 | 2018-07-31 | 西北工业大学 | A kind of cutter profile design space computational methods |
| CN108345744B (en) * | 2018-02-09 | 2019-02-01 | 西北工业大学 | A kind of cutter profile design space calculation method |
| CN108873809A (en) * | 2018-07-02 | 2018-11-23 | 中南大学 | A kind of high-order tooth surface error modification method of spiral bevel gear |
| CN108873809B (en) * | 2018-07-02 | 2020-12-04 | 中南大学 | High-order tooth surface error correction method for spiral bevel gear |
| CN109101754B (en) * | 2018-08-31 | 2020-01-14 | 西安交通大学 | Full-process machining method for spiral bevel gear |
| CN109241613B (en) * | 2018-08-31 | 2020-07-28 | 西安交通大学 | Method for determining cutter root trimming parameters of spiral bevel gear |
| CN109241613A (en) * | 2018-08-31 | 2019-01-18 | 西安交通大学 | A kind of cutter root relief parameter determination method of spiral bevel gear |
| CN109101754A (en) * | 2018-08-31 | 2018-12-28 | 西安交通大学 | A kind of full step process of spiral bevel gear |
| CN109396567A (en) * | 2018-11-06 | 2019-03-01 | 重庆大学 | The digital envelope method of worm abrasion wheel profile is determined in correction of the flank shape cycloid gear generating grinding |
| CN109396567B (en) * | 2018-11-06 | 2020-04-28 | 重庆大学 | Digital envelope method for determining profile of worm grinding wheel in generating grinding of shape-modified cycloid gear |
| CN110788413A (en) * | 2019-10-29 | 2020-02-14 | 西安交通大学 | Method for optimizing cutter edge curve of milling cutter disc at end of cycloid gear bevel gear |
| CN110788413B (en) * | 2019-10-29 | 2020-08-18 | 西安交通大学 | Method for optimizing cutter edge curve of milling cutter disc at end of cycloid gear bevel gear |
| CN112182803A (en) * | 2020-09-29 | 2021-01-05 | 南京高速齿轮制造有限公司 | Excitation calibration method of dynamic model |
| CN112182803B (en) * | 2020-09-29 | 2024-05-14 | 南京高速齿轮制造有限公司 | Excitation calibration method of dynamic model |
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