CN105522227B - A kind of profile correction method for cycloid bevel gears processing cutter tooth main cutting edge - Google Patents
A kind of profile correction method for cycloid bevel gears processing cutter tooth main cutting edge Download PDFInfo
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- CN105522227B CN105522227B CN201510921328.1A CN201510921328A CN105522227B CN 105522227 B CN105522227 B CN 105522227B CN 201510921328 A CN201510921328 A CN 201510921328A CN 105522227 B CN105522227 B CN 105522227B
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- cutter tooth
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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 present invention relates to a kind of profile correction methods for cycloid bevel gears processing cutter tooth main cutting edge, belong to machine design and manufacture field.This method is based on gear teeth face process principle, using Principles of Gear Connection, the cutter tooth main cutting edge surface profile for processing the flank of tooth is modified, is changed to obtain tooth surface equation according to space coordinates.The gear processed using the engagement trace of the gear teeth of TCA analyticals new method processing with transmission error and with conventional method is compared, and the gear built herein is greatly lowered transmission error and obtains better contact point trace line simultaneously;By experimental verification analysis method, loading experiment is carried out to the gear of structure and analyzes its contacting zone position, the phenomenon that gear built herein can be to avoid stress concentration.Stress concentration phenomenon when avoiding the gear from engaging from root reduces transmission error, so as to reduce the noise of gear, improves transmission stability.
Description
Technical field
The present invention relates to a kind of profile correction methods for cycloid bevel gears processing cutter tooth main cutting edge, belong to machinery and set
Meter and manufacturing field.
Background technology
Overlikon spiral bevel gear (Klingelnberg) is one of currently used two canine tooth of spiral bevel gear, is especially being navigated
It is more and more extensive in the heavy duty of empty, automobile and heavy machine tool etc., high-power transmission field to be applied.As machinery passes
Dynamic system increasingly develops towards direction at a high speed, accurate, as the crucial transmission parts in transmission system, overlikon spiral bevel gear warp
Often it is operated under complex working condition, such as heavy duty, impact and varying load, therefore just produced therewith the problems such as flank of tooth vibration failur and noise
It is raw.Therefore overlikon spiral bevel gear is constantly subjected to extensive concern and the research of various countries relevant expert scholar, becomes in Gear Production
Key technology and commanding elevation.Gleason company formally delivered Tooth Contact Analysis (tooth contact in 1978
Analysis, TCA) principle and method, can be using this method on the premise of without considering load deflection and error component
Shape and the position of face spot are simulated on computer.TCA technologies have been widely used in various gears, Chinese scholar Zheng Chang
It opens, Mao Shimin etc. has also been successively performed the research work of TCA methods.Wang Xiaochun, Wu Xutang etc. propose three rank contact analysis reason
By instantaneous transmission ratio and acceleration can not only be obtained using this method, high-order acceleration can also be obtained.Wu Xuncheng etc. is also carried
Go out the concept of point gearing conjugate tooth profiles mismatch transmission performance pre-control and the active designs theory of hypoid gear etc., and use it
Theory is solved under conditions of the known flank of tooth 1 and thereon contact point trace line and transmission requirement, solves the unknown of Local conjugation therewith
The problem of flank of tooth 2.Once hiding for Central South University comprehensively has studied the algorithm of Gleason and TCA programs, discloses its compilation theory
And various calculation formula are derived.The gear teeth meshing under finite element model for solving load effect such as American scholar F.L.Litvin
The contact stress of situation and load action point, and by Local synthesis algorithm, TCA analyses and finite element stress analysis, reduce
Noise and vibration during gear drive.
But domestic and foreign scholars study the gear modification flank of tooth forming process be mostly by taking spur gear or bevel gear as an example into
What row illustrated.Since the tooth trace of overlikon spiral bevel gear heavy duty cycloid bevel gears along gear teeth tooth length direction is cyclo-palloid curve and is being taken turns
The high direction height of tooth of tooth is equal, because the particularity of overlikon spiral bevel gear tooth form, domestic and foreign scholars' analysing content is seldom related to
To overlikon spiral bevel gear.Herein by the traditional machine tool process principle of research overlikon spiral bevel gear, engaged and managed based on conventional gears
By by correction of the flank shape cutter, the flank of tooth of practicing Buddhism or Taoism of gear is obtained by coordinate transform, TCA analyses, finite element loading emulation are carried out to it
The gear analyzed and gone out with traditional processing tool sharpening is compared, it is known that the gear built herein can be to avoid stress concentration
Phenomenon.It is herein stress concentration phenomenon when can avoid the gear to engage with root, reduces transmission error, so as to reduce making an uproar for gear
Sound improves transmission stability.
The content of the invention
The object of the present invention is to provide a kind of profile correction methods for cycloid bevel gears processing cutter tooth main cutting edge.Base
In gear teeth face process principle, using Principles of Gear Connection, the cutter tooth main cutting edge surface profile for processing the flank of tooth is modified,
Changed to obtain tooth surface equation according to space coordinates.Using the engagement trace of the gear teeth of TCA analyticals new method processing
The gear processed with transmission error and with conventional method is compared, and the gear built herein is greatly lowered transmission and misses
Difference obtains better contact point trace line simultaneously;By experimental verification analysis method, loading experiment is carried out simultaneously to the gear built herein
It analyzes its and contacts zone position, the phenomenon that gear built herein can be to avoid stress concentration.It is that can be avoided with root herein
Stress concentration phenomenon when gear engages reduces transmission error, so as to reduce the noise of gear, improves transmission stability.
The present invention is realized using following technological means:
1st, traditional line type cutter tooth cutting edge is built.
2nd, parabolic type cutter tooth cutting edge is built.
3rd, machining tool coordinate system and gear teeth modeling are established.
4th, in Matlab by discrete point set above to be preserved respectively in the form of Txt, and be conducted into three
It ties up in modeling software Pro/E, by being read out processing to these data, line is connected to according to from point, then the flank of tooth is expanded to by line,
Finally by face again to the construction thinking of body, the threedimensional model of the heavily loaded cycloid bevel gears of foundation.
5th, by taking 1 standard of table installs gear pair as an example, by the actual flank of tooth TCA programs of Matlab software programmings, with driving wheel
Gear ratio with driven wheel is 29:Exemplified by 29, TCA is carried out to the gear teeth that two kinds of cutter tooth cutting edges of different shapes process respectively
Analysis.
6th, under the load effect that torque is 500Nm, driven by the driving wheel of application parabolic type cutter tooth cutting edge processing
Dynamic driven wheel observes the position of its contact area.
Description of the drawings
Fig. 1 gears rotate perspective plane;
Fig. 2 gear teeth face discrete point schematic diagrames;
Fig. 3 gear teeth threedimensional models;
Fig. 4 linear pattern cutter tooth cutting edges process tooth contact area and transmission error curve;
Fig. 5 parabolic type cutter tooth cutting edges process tooth contact area and transmission error curve;
Fig. 6 is the implementing procedure figure of this method.
Specific embodiment
It by following description and is described with reference to the drawings, the present invention can become apparent from, and illustrate to explain the present invention
Method and embodiment.
The present invention provides a kind of profile correction method for cycloid bevel gears processing cutter tooth main cutting edge.Specific implementation step
It is rapid as follows:
1 traditional line type cutter tooth cutting edge model
Traditional processing cycloid bevel gears often select linear pattern cutter tooth cutting edge, then by adjusting lathe dimensional parameters to the gear teeth
It practices Buddhism or Taoism, so not only so that machined parameters are excessively complicated but also can influence flank profile.Linear pattern cutter tooth cutting edge surface
The concave and convex surface of gear, α are cut in profile, the convex surface and concave surface of cutter tooth respectivelygProfile angle, arc radius ρwIn machining
The fillet of gear surface is formed, cutter tooth main cutting edge surface is around reference axis zgIt is rotary motion, rotation angle θg, cutter head half
Footpath is Rg。
It can be obtained in blade coordinate system S by the geometrical relationship in Fig. 1gUnder, there is the coordinate column vector r of blade arbitrary pointg
(sg, θg) expression formula is
2 structure parabolic type cutter tooth cutting edge models
This method proposes a kind of new parabolic type cutter tooth cutting edge, by practicing Buddhism or Taoism to cutter tooth cutting edge, directly may be used
To process relatively good flank profile.In parabolic type cutter tooth cutting edge, cutter head is around rotation axis zgRotation, rotation angle are
θg, αgFor tangent line of the cutting edge at point M and the angle between the longitudinal centre line of blade, sg0Join for vertex of a parabola position
Number, the position of point M is by sg0It determines.
It can be obtained in blade coordinate system S by the geometrical relationship in Fig. 2gUnder, there is the coordinate column vector r of blade arbitrary pointg
(sg, θg) expression formula is
In formula:("+" is outer knife, and "-" is interior knife), acFor the secondary term coefficient of parabolic type main cutting edge surface profile,
3 establish machining tool coordinate system and gear teeth modeling:
Dextrorotation cycloid bevel gears Cutter coordinate system, wherein coordinate system S are established according to KNC type tooth milling machinesm2Being connected with lathe is
Lathe coordinate system, the coordinate system S during gear is processedm2Remain static;Sc2It is connected firmly with production shape wheel axle center, initial bit
S when puttingc2With Sm2Position overlaps;Sa2To take turns position auxiliary coordinates;S2To cross gear reference cone apex, with processed wheel blank consolidation
Coordinate system, initial position and coordinate system Sb2It overlaps;Angular velocity of rotation is ω when if workpiece works1;Any time is processed tooth
The rotational angle of wheel is still ψ2;ΔEm2For workhead offset;ΔXB2For bed;ΔXD2For horizontal wheels position;γm2To be processed gear
Established angle is numerically equal to reference cone angle;ψc2The angle rotated for cage chair any time.By blade arbitrary point in Sc2Coordinate system
Lower column vector rc2(sg,θg) blade arbitrary point obtained in S by the matrixing of coordinate2Vector i.e. gear teeth under coordinate system
Face equation.Corresponding transformation matrix of coordinates is Mm2c2, Ma2m2, M2a2, Mb22Expression is that equation is
rb2(sg,θg,ψ2)=Mb22·M2a2·Ma2m2·Mm2c2·rg(sg, θg) (3)
In formula:Mb22, M2a2, Ma2m2, Mm2c2For corresponding transformation matrix of coordinates.
rb2(sb,θ,ψ2) corresponding unit normal vector is
Obtaining flank engagement equation by Principles of Gear Connection is
Due in flank engagement equation there are three unknown number be s respectivelyb, θ, ψ2.So it to obtain discrete on gear teeth face
Point solves, it is necessary to establish three equation joints.It needs to establish equation by the boundary condition of the flank of tooth at this time.Cross the axial plane of gear shaft
The rotation perspective plane of gear is done, as shown in Figure 1, being solved to easily facilitate, initially sets up coordinate system Sp(op;xp,yp), OpFor wheel
Base conical point is as coordinate origin, xpIt spends dividing for gear and chases after busbar.
It can obtain the tooth surface equation of driving gear according to above-mentioned derivation:
By taking one group of heavy duty cycloid bevel gears of Beijing first Machine Tools Plant as an example, the cycloid that Beijing first Machine Tools Plant provides bores tooth
Wheel set basic parameter is shown in Table 1 and is shown in Table 2 with detailed Machine-settings.These parameters are brought into the tooth surface equation group 3-19 of gear
In, and with quasi_Kantorovich operator equation is carried out discrete in Matlab softwares and solved.
1 cycloid bevel gears pair basic parameter of table
The secondary basic machined parameters of 2 cycloid bevel gears of table
Table 2Basic processing parameters of cycloid bevel gear pair
Because the threedimensional model to be constructed in Pro/E, to the division of gear teeth face grid as far as possible uniformly or
Person is gradual change if Fig. 5 is gear teeth face discrete point schematic diagram.From Fig. 2 it is known that rectangular along the tooth of gear teeth face
To 37 points are taken, 10 points are taken along the facewidth direction of gear teeth face, take 370 points altogether on the working gear flank of tooth.
According to the flank of tooth discrete co-ordinate values of driven wheel and driving wheel can respectively obtain driven wheel and driving wheel convex surface and
Concave surface.Fig. 5 is the discrete point of driven gear concave surface and the discrete point on driven gear convex surface.
4 structure cycloid bevel gears threedimensional models
By discrete point set above to be preserved respectively in the form of Txt in Matlab, and it is conducted into three-dimensional
In modeling software Pro/E, by being read out processing to these data, line is connected to according to from point, then the flank of tooth is expanded to by line, most
Afterwards by face again to the construction thinking of body, the threedimensional model of the heavily loaded cycloid bevel gears of foundation.Such as the threedimensional model that Fig. 3 is the gear teeth, figure
It is middle a) for the driven wheel gear teeth, b) for the driving wheel gear teeth, c) be single pair gear teeth meshing.
5TCA is analyzed:
By taking 1 standard of table installs gear pair as an example, by the actual flank of tooth TCA programs of Matlab software programmings, with driving wheel and
The gear ratio of driven wheel is 29:Exemplified by 29, TCA points are carried out to the gear teeth that two kinds of cutter tooth cutting edges of different shapes process respectively
Analysis.Fig. 4 is transmission when linear pattern cutter tooth cutting edge processes Gear Contact area and the engagement that the TCA methods analysis of the gear teeth is drawn
Error curve.
Analysis result comparison can be drawn:(1) degree of transmission error reduces to 41 μ rad by 355.5 μ rad, about subtracts
Low 88.4%, realize being greatly lowered for transmission error;(2) parabolic type cutter tooth cutting edge obtains preferably parabola shaped
Transmission error makes transmission more steady;(3) obtain along the upper better contact point trace line in flank of tooth longitudinal direction.
6 experimental verifications:
Under the load effect that torque is 500Nm, by the active wheel drive of application parabolic type cutter tooth cutting edge processing
Driven wheel observes the position of its contact area.
In order to become apparent from the position of observation tooth contact zone, after rolling inspection experiment, lower whorl is printed with a blank sheet of paper
The variation of the red lead powder of tooth.
It draws the cycloid bevel gears using the processing of parabolic type cutter tooth cutting edge, is connect when being 500Nm be subject to torque
The phenomenon that touching the centre that zone position is located at the flank of tooth, nib contacts and stress concentration not occurring.
Gone out by above example analysis and summary:The cycloid bevel gears processed using parabolic type cutter tooth cutting edge realize throwing
The linear driving error curve of object reduces the amplitude of transmission error.And the cycloid of application parabolic type cutter tooth cutting edge processing
The phenomenon that bevel gear avoids the occurrence of stress concentration and nib contacts in engagement, so as to reduce the noise during gear drive
And vibration.
Claims (1)
1. a kind of profile correction method for cycloid bevel gears processing cutter tooth main cutting edge, the cycloid bevel gears process cutter tooth
For Gear Milling, it is characterised in that:It includes the following steps:
1) linear pattern cutter tooth cutting edge model is built;
2) parabolic type cutter tooth cutting edge model is built;
By the correction of the flank shape to cutter tooth cutting edge, flank profile is directly processed;In parabolic type cutter tooth cutting edge, cutter head is around rotation
Shaft zgRotation, rotation angle θg, αgFor tangent line of the cutting edge at point M and the angle between the longitudinal centre line of blade,
sg0For vertex of a parabola location parameter, the position of point M is by sg0It determines;
It is obtained by geometrical relationship in blade coordinate system SgUnder, there is the coordinate column vector r of blade arbitrary pointg(sg, θg) expression formula is
In formula:"+" be outer knife, "-" be interior knife, acFor the secondary term coefficient of parabolic type main cutting edge surface profile, RgFor cutter head half
Footpath;
3) machining tool coordinate system and gear teeth modeling are established;
4) cycloid bevel gears threedimensional model is built;
5) experimental verification;
Under the load effect that torque is 500Nm, the active wheel drive by application parabolic type cutter tooth cutting edge processing is driven
Wheel observes the position of its contact area;In order to become apparent from the position of observation tooth contact zone, after rolling inspection experiment, use
The variation of the red lead powder of the lower gear teeth of a blank sheet of paper print.
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CN1781637A (en) * | 2005-10-10 | 2006-06-07 | 西安建筑科技大学 | Method for shaping gear shaver |
CN102554365A (en) * | 2012-03-08 | 2012-07-11 | 江苏大学 | Involute gear-shaving cutter |
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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Patent Citations (8)
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DE1934021B2 (en) * | 1969-07-04 | 1976-01-15 | W. Ferd. Klingelnberg Söhne, 5630 Remscheid | MULTIPLE HOLLOW MILL |
CN86100544A (en) * | 1986-03-28 | 1987-02-11 | 中国纺织大学 | Gear with parabolic shaped tooth and hobboing cutter thereof |
US5580298A (en) * | 1994-09-27 | 1996-12-03 | The Gleason Works | Method of producing tooth flank surface modifications |
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