CA2128502C - Tertiary negative-deflection flexing contact gears of non-profile-shifted tooth profile - Google Patents
Tertiary negative-deflection flexing contact gears of non-profile-shifted tooth profile Download PDFInfo
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- CA2128502C CA2128502C CA002128502A CA2128502A CA2128502C CA 2128502 C CA2128502 C CA 2128502C CA 002128502 A CA002128502 A CA 002128502A CA 2128502 A CA2128502 A CA 2128502A CA 2128502 C CA2128502 C CA 2128502C
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Classifications
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
- F16H55/0833—Flexible toothed member, e.g. harmonic drive
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Abstract
In a cup-shaped flexing contact gear (1), both a rigid internal gear (2) and a flexible external gear (3) are made to be non-profile-shifted spur gears, an opening (3a) of the flexible external gear (3) is set in a state of negative deviation wherein a deflection of the opening is lower in value than a normal deflection; a moving locus is obtained through rack approximation of teeth of the external gear to the internal gear at respective sections of rotation of tooth trace of the flexible external gear (3), an envelope (e) is obtained by overlapping the moving locus on one of sections of rotation, another moving locus is obtained in a section of rotation at the end portion of tooth trace on the side of a diaphragm or in the vicinity of the outside of the end portion and is smoothly connected to the envelope to thereby obtain a composite curve (L). A curve (FE) is obtained by similarity transforming at a reduction ratio of 1/2 a portion from a starting point (A) of the envelope (e) to a terminating point (E) thereof corresponding to two times the working depth in the direction of the depth from an apex of a moving locus (~
o) when deviation is 0, using the terminating point as an original point, and this curve is made to be each of main portions of convex tooth profiles at tooth faces of the both gears (2, 3). Further, a composite curve (MFE) including a straight line (MF) having a limited pressure angle (.alpha.M) associated with a deflection value of the opening inserted in the vicinity of a datum point (M) of tooth profile and a transient curve smoothly connecting the straight line to the main portion of the convex tooth profile is made to he each of tooth profiles at the tooth faces of the both gears.
o) when deviation is 0, using the terminating point as an original point, and this curve is made to be each of main portions of convex tooth profiles at tooth faces of the both gears (2, 3). Further, a composite curve (MFE) including a straight line (MF) having a limited pressure angle (.alpha.M) associated with a deflection value of the opening inserted in the vicinity of a datum point (M) of tooth profile and a transient curve smoothly connecting the straight line to the main portion of the convex tooth profile is made to he each of tooth profiles at the tooth faces of the both gears.
Description
DFSCRI:°TiON
TITLE OF INVENTION
TERTIARY NEGATIVE-DEVIATION FLEXING CONTACT TYPE GE:AH DRIVE
OF NON-PROFILE-SHIFTED TOOTH PROFI1,F
Technical FiEld The present invention relates to 3 flexing~contact-type gear drive, pnd particularly to tooth profiles of a ri~r,id internal gear and a flexible external gear employed in this type of gear drive.
Background Art A flexing-contact-type gear drive typically consists of a rigid circuinr~ intarnal gear, a flexible exterwal gear which has 2n (n being a positive integer) less teeth than the internal gear and which is disposed inside the internal gear and flexed into an elliptical shape so as to mesh with the internal gear at ~Cwo places, and wave generator fitted inaic9e t;~~e external gear for flexing it. The basic tooth profile for the guars of a flexing contact gear drive is linear (see U.S. Patent No. 2,906,1t~3), On ~,tle other hard, an i.nvolc,te tooth profile has also been proposed (see Japanese Patent Publication No. S~IO 4~-111171). However, where the linear or the involute tooth profile is adapted as that o'f° each of the inr,ernal and external gears, the addendum faces of the gears ran ,~__ ~r"~Y(r44~ ,., c~ 'y~.i~ la ~7;
~:~.~~ i~<' cannot be Continuously meshed with each other.
For increasing load capacity the inventor of the present invention proposed in Japanese Patent Laid Opcn No.
SHO 6g-11593 a system using as the basis for the tooth face profile the curve obtained by similarity transfor~rninR the locus of motion at a reduction ratio of 1/2 over a prescribe range from the meshing limit point on the locus of motion basod on the rack approximation of the tooth of the external gees relative to Lloe internal gear determined by the shape o:' the wave generator. With the tooth profile disclosed ~.n this, publication, the addendum faces of the internal and external gears can be continuously meshed with each other.
In the meantime, as a flexing-contact-type gear drive, one having a cup-shaped flexible external gear has been known. If the internal and external gears of this type gear drive are designed to have the same tooth profiles as disclosed in the above Japanese Patent Laid Open No. SHO 53-w 115943, it cannot be realized to Form a continuous meshing between the teeth of the gears all along the tooth trace direction.
More specifically, in a cup°shaped, flexing-contact-type gear drive, the eup~shaped flexible external gear is subjected to deflection called honing, in which the deflection value of the external gear increases gradually in the direction from its diaphragm side to its opening side and :in proportional to a distance from the diaphragm (the deflection E/:~ r/:E~~.~ y~r~~G ~~GE ~7u'~ ny . ~ Y~O~~ fi~~00 h~~~U _ Yo ~~2~3~~~
being a difference .in the length between tho ma,~or axis and the minor axis of the el'iiptical shape of the external gear).
The change in the deflection along the axis of the external gear due to the coning is not considered in determination cf the tooth profiles disclosed in Japanese Patent Laid Open No.
SNO 63-1159~43~
Accordingly, where a cup--shaped, flexing-contact--type gear drive is provided with the internal and external gears of the tooth profiles as disclosed in the above publication, both gears can be meshed continuously with each~other only at a specific sectional portion along the tooth trace direction (for exanple, at such a sectional portion of non-deviation where a normal deflection occurs), while they may be improperly meshed to cause tooth interference or the like at the other sectional portions.
Measures to avoid the defect are disclosed, for example, in .lapanese Patent Laid Open Nos. SHO 62--75153 and HEl 2-62u61. rn these measures, however, it is required i;o apply special additional processings such as crowning, relieving and the like to t:he tenth of gears.
Tn order to achieve a wider range of meshing of the external and internal gears atang the tooth trace direction of the cup-shapod flexible external gear without tooth interference between the external and internal gears, the inventor of the present invention proposes a tooth profile disclosed in Japanese Patent Application No. II~I--3-357036.
~~d '! r ..~'Ef~~d Y~4~G ,4Gr ~0~'' ~G
~~~8~~%.
The invention diqclosed in this patent application was made based on the recognition that, in a flexing, contact type gear drive, moving lcci cf teeth of the cup-shaped flexible external gear at respective sections of rotation along tooth trace direction thereof are found to be changed and decreased in deflection along the tooth trace direction viewed Prom the opening side of the flexible external gear, and that th~se moving loci are found to form a single envelope when these moving loci are overlapped on a same plane. In this patent application, a rack approximation method is introduced to simplify the analysis in finding a formula of the obtained envelope. Moreover, a moving locus of the flexible external ge2r is obtained at a section of rotation near and outside the diaphragm--side end of the flexible external gear, and is Connected to the envelope to thereby form a composite curve.
Then, a portion of the composite curve which starts from a selected meshing limit point and corresponds to two times the working depth in the tooth depth direction is,sub,)ected to the simllarit-,y transformation at a reduction ratio of 1/2 to obtain a curve which is employed as convex tooth profiles of tooth faces of tho external and internal gears.
The present inventor also proposed in Japanese Patent Application iJo. HMI 3-357037 that a moving locus based on which tooth profiles are introduced is defined only by the above-mentioned envelope. The invention disclosed in this Japanese Patent Application eras made based on the recognition n 01d s,~~,~E~.~:.~Y~r4GG.kGE INOdd v~~00 ~~~~'~~Oi'0 ~~.2~ ~~~' that the envelope is similar to a curve obtained by sub,~ecting to the similarity transformation at a reduction ratio of 1/2 a moving locus of teeth of t:he flexible external gear at a rotational section of a non-deviated state. With this envelope, tooth profiles are determl.ned which are applicable to tooth profiles of both gears of a cup-shaped, flexing-contact-type gear drive wherein the difference in tooth number between the rigid internal gear and tha flexible external gear is four.
However, in the inventions disclosed~in Japanese Patent Application Nos. HEI 3-357036 and HEI ~-357p37, an opening of the cup-shaped flexible external gear is regarded as in a non-deviated state. Further, setting of a pressure angle at a datum point of tooth profiles is not specified.
While, recently there has been increased more and morea demand for enhanced performance of flexing contact type gear drives. In order Lo satisfy the demand, it is necessr,ry to further Pnhance strength and rigidity of the flexing Contact type gear drive, and at the same time it is necessary to further improve wear-resisting capability. For these purposes, the actual load distribution appeared on the teeth along the tooth traco direction must be equalized.
Disclosure of Tnvent:ion The present invention is directed to an improvement of , tooth profi2es disclosed in Japanese Patent AppJ.icatzon Nos.
~~2~~~
HFI 3-35703b and HEI 3°357037. The present invention is characterized by setting the deflection of an opening of a , cup-shaped flexible external gear of a flexing contact type gear drive to be a negative-deviated state wherein the amaunt of deflection is set smaller than that of a normal deflection.
Concept of positive and negative with resp~ct to deviation of teeth are described in Japanese Publication No. SHO u5-U1171 by the same inventor of the present invention.
Further, according to the present invention, tooth profiles are determined based on a composite curve formed by an envelope of moving loci of teeth of a flexibly external '~d gear and a moving locus pf teeth at a section of rotation which is located on an end of the diaphragm-side of the external gear along the tooth trace direction or located adjacent to the outside of the end portion thereof. This concept is similar to that disclosed in Japanese Patent Application Nos. HEI 3-357036 and HEI g-357037, except that the moving locus of teeth at the section of rotation located on the end of the oxternal gear is employed.
According to the present invention, different from the inventions disclosed in the above-cited Japanese Patent Application Nos. HFI ~-357036 and H~z ~-357037 in which the envelope employed includes the moving locus or. the section of non-deviated state, a clearly limited portion of the envelope is employed Which corresponds to an amount of negative deviation of teeth of each of rsSpect sections of rotation of ..«. ....~,~.:~.y~y.Ha:~.y:yaYlililuE;cYL518:i5;;kBfdbma~5~tueu°.a.~xt ~C;tiiFtiSs ~~.~~'J~ d the flexible external guar along its tooth trace direction.
In addition, the present; invention is characterized in that an pressure angle at a datum point of tooth is d!~fin~d in accordance with an amount. of negative deviation occurred on an opening of a flexible extornal gear, MorE specifically, according to the present invention, in a flexing contact type gear drive having a rigid internal gear, a cup-shaped flexible external gear disposed inside the internal gear, and a wave generator for deflecting the external gear into an elliptical shape such that the value of deflection is proportional to a distance from a diaphragm o,~ along the direction from the diaphragm to an opening of the external gear and for rotating the elliptica? shape of the external gear, whereby a relative rotation between the both gears IS generated by rotating the wave gear, tooth profiles of the rigid internal gear and the flexible external gear are defined as follows.
Firstly, both the rigid internal gear and the flexible external gear are made to be non-profile-shifted spar gears, '~J and an opening of the flexible external gear is set to be a negative-deviated state in which a deflection occurred is lower in volume than a normal deflection, Then, a moving locus is obtained through rack approximation of teeth of the external gear to the internal gear at respective sections of rotation along the tooth trace direction of ,the flexible external gear, and the obtained moving locus is overlapped on ~~~~'~~t~
one of sections of rotation, whereby an envelope i:a obtained.
Another moving locus in a section of rotation at an end portion of tooth trace on the side of a diaphragm or in the vicinity of the outside of the end portion is smoothly connected to the envelope so that a composite curve is obtained. A curve is obtained by subjecting to the similarity transformation at a reduction ratio of 1/2 a portion from a starting point of the envelope to a terminating point.
c~rresponditlg to two times the working depth in the direction of depth from an ape~c of a moving locus when the deviation is 0, using the terminating point as an original point. The curve thus obtained is made to be each of main portion:; of convex tooth profiles at the tooth faces of the both gears.
Furthermore, a composite curve is obtained which includes a straight line having a limited pressure angle associated with a deflection value of an opening and inserted in the vicinity of a datum point of tooth profile, and a transient curve smoothly connecting the above straight lina to the main portion of the convex tooth profile. This composite curve or its similar curves is made to be each of tooth profiles at the tooth faces of the both gears. While, tooth flanks of the both gears are defined by a composite tooth profile including a straight line and a concave curve which is symmetrical to the tooth proff:~e of each ef the tooth faces of the gears with respect to each of the datum points of tooth profiles of the gears, or are defined by a tooth profile which is obtained by 212 ~0~' \ providing the composite tooth profile with some amount of escape.
Brief' Description of Drawings Figure 1 is N perspective view of a cup-Shaped flexing coritaet type gear dr.ivo.
Figure 2 is a front view of~ the goat drive of Figure 1.
Figure 3 illustrates a state of a flexible external gear before deflection due to coning.
Figure ~1 illustrates a state of the flexible external gear on a major axis of elliptical shape after deflection due to contng.
Figure 5 illustrates a state of the flexible external gear on a minor axis of elliptical shape after deflection due to coning.
Figures 6, 7 and 8 show a locus of one of teeth of the flexible external gear when moving with respect to a tooth groove of a rigid internal gear, wherein Figure 6 shows a moving locus thereof at, a seotion of rotation on an opening of the flexible external gear, Figure 7 shows a moving locus thereof at a central section of rotation of tooth trace of the external gear, and Figure 8 shows a moving loons thereof at a section of rotation on an end portion of the diaphragm of the external gear.
Figure 9 is a composite curve by which a tooth profile SId s~;~ ~s~.r,.~4f~,~~,,~~G
. Y'a0~a ~5~00 BO"~_~;~o of the present invention is defined.
Figure 10 illustrates how to obtain the tooth profile of the present invention from the cornposite curve of Figure 9.
rJ
Figures 11, 12 and 13 show meshing condl.ti0ns of the tooth profiles of the present invention, respectively, whar~ein Figuro 11 shows a s'~ate of moshing at a section of rotatipn on the opening of the external gear, Figure 12 shows a state thereof at a central section of rotation of tooth , trace of the external gear, and Figure l~ shows a State thereof at a soetiori of rotation on an end of the diaphragm of tooth trace of the external gear.
E3est Mode for Carrying Out the Invention An example of the present invention will now be described with reference to the drawangs.
Figures 1 and 2 is a perspective view and a front view of a known cup-shaped fle5ting con'~aet type gear drive. The fleXing contact typo gear drive 1 comprises a circular rigid internal gear 2, a cup~shaped flexible external gear 3 disposed inside the internal gear, and an elliptically-shaped wave generator 4 fitted into the external gear. The cup-shaped flexible external gear 3 is in a state flexed into an elliptical shape by the elliptically-shaped wavy generator 1~.
~i8ures 3, ~t and 5 show a state of deflection of the fl.ext~ble external gear caused by coning, respectively, by 9Id s~7 ~s~.r"~y~4~G.~~.~ ~0~~ ~~~00 ~u?~~0~76 ~:~~~3~~)' means of a section taken along an axis of the flexible external gear, Figure 3 shows a state of deflection of the external gear before flexed by the wave generator ,1 (before def~,ection). Figure it is a sectional view taken along the ax is pf the external gear and along a major axis of the wave generator, showing a state flex~d by the wave generator U.
Whereas, Figure 6 .is a sectional view taken along the axis of the external gear and along a minor axis of the wave generator, showing a state flexed by the wave generator u.
As can be seen from these figures, the Cup~sraped flexible external gear 3 is deflected Owing to coning, so that the deflection in value is maximum on its openin 3a and $ . is gradually decreased toward the side of its diaphragm 3b, Figures 6, 7 and 8 show & moving locus. of one of teeth of the cup-shaped flexible external gear with respect to a tooth groove of the rigid internal gear 2 of the flexing contact type gear drive 1, the moving locus being obtained by the reek approximation provided that the numbers of the both gears 2 and 3 become infinite without changing the difference in number of teeth between the both gears, Each of the obtained moving loci is in a state of n~gative deviation.
Note that in these.figures, the teeth of the internal and external gears are provided with same tooth profiles provisionally<
In these figures, the moving locus of, Figuro C ~.s obtained at a section of rotation of a point 31 on the opening 2~~8~~~~~
3a of the teeth 30 of the cup-shaped flexible external gear 3. The moving locus of rigure 7 is obtained on a sQetion of rotation at a center of tooth trace of the~external gear, while that of Figure 8 is obtained at a section of r~otat:ior, of a point 33 on an end portion of the diaphragm 3b of tooth trace of the external gear.
As is apparent from these figures, a degree of tooth Interference of the both gears increases gradually toward the side of the diaphragm 3b From the opening 3a. To avoid the tooth interference, it, is necessary to apply an additiona.t processing such as cell~ving to the teeth of the gears, The moving locus on a desired section of rotation can be expressed by x = 0.5 mn( n - ,~ sin n ) (1) Y - mn(1 - ~ pOs wherein x is an orthogonal coordinate along a pitch line of a rack, y is an orthogonal coordin&te along a depth of the rack, m is a module of the tooth, n is 1/2 of the number of tooth difference between the rigid internal gear and the flexible external goar~, r~ is an angular parameter, ~; is a deflection ooofficient (,~ - 1 represents a state of non deviation, whereas ~ ~ 1 represents that of negative deviation).
The following expression (2) can be derived by eliminating tha term g ~n from the expression (1).
1 ?.
pe k.D ~J
x - 0.5mn [COS ~' ( ( ~ 'Y/m/n)/,~ f - ~c J- 1- ( ( 1~y/m/n)/ ~c } 4 7.
(2) Further, the following expression (3) can be obtained by solving x through a partial differential of the expression in terms of - ~ 1 -y/m/n (3) elimination of the term x from the expressipns (2) and (3) makes an expression defining an envelope a obtained by overlapping a moving locus with respect to each value of on an plane. That is, the following expression (4) can be obtained.
x - 0 . 5mn ~ cps - ~ f' 1 -y/m/n - ,r y/m/n ( 1 -y/m/n ) } _ 0 The definition of the above envelope leads t,o the following facts. If the constant ,~ is :;et to r,e a certain value, this means to select a section of rote.
>rion having a deflection in value corresponding to the value of x . On Lhis section of r4tation, the envelope is meant to contact; with the moving locus of teeth at the point of y obtained b Y
substituting the above value in the equation (3),for the co~fficient~ is . In other words, a portion of the envelope on or ad,~acent to this point of y represents a part of the r~
moving locus of teeth.
As mentioned before, the Inventor of the present tnvention found that the above envelope is not but a similar curve obtained by reducing a moving locus at a ratio of 1/2, the waving locus being obtained wYren x - 1 (non deviation) in the equation (2). However, it is insufficient to provide an effective tooth depth by.using only this envelope. This is especially apparent when n = 1, that is,.when the number of tooth difference between the rigid internal gear' and the flexible external gear is 2.
Therefore, according to the present invention, based on the inventions disclosed in the above-cited Japanese Patent Application Np. HEI 3 357036, a moving locus of teeth of the flexible external gear is obtained on a section of rotation of an erid portion of the diaphragm side of tooth trace or on a section of rotation in the vicinity of outside of the end portion (wherein the section of rotation is referred to hereinafter as the limit section), a'nd is smoothly connected to the envelope to form a composite Curve, so that the composite curve is made to a basis of deriving tooth profiles of the gears.
Figure 9 illi.istrates the thus formed composite curve L~ In this figure, there are illustrated five moving loci in total including a movipg locus Q a of teeth on a section corresponding to the state of non deviation and a moving locus .~ g of teeth on the section of rotation In the vicinity of 1 ~l outside of the end portion Of tooth tr&ce of the diaphragm (the fihove-mentioned 7.imit section), in ndditi.on t:o the respective moving loci ,P. a, ~ b and .~ c shown in Figures 6, '1 and g. Further, the respective points A, 5, C and D of Figure 9 represent th~ places where the moving loci .B a, a b and ,g c ~,re contacted with the envelope e, respectively.
Where the limit Section is selected on the ~nd portion of tooth trace of the diaphragm, the moving locus. g is in accordance with the uioving locus Figure 70 shows how to derive the tooth profiles of _ the present invention from the composite curve L. Now, a prescribed portion of this curve is selected from a point A to a point E. The starting point A is a point where the moving locus Q a of teeth on the section of rotation of the opening 3a of the flexible exter~nsl gear 3 is contacted with t;he envelope e. The terminating point E is a point where the value in y-ordinate is equal to the two times of working tooth depth, this pint being usually located on the moving locus ~ g of teEth on the limit section as mentioned above.
While, it was not specified in the inventions disclosed in Japanese Patent Application Nos. HEI 3-357036 and HEf 3-350737 how to settle the point p.
In contrast to this, according to the present invention, the point A can be Bottled as follows. Where the deafleetion constant of the opening 3a of the flexible external gear is ,~ , t?1e value of rc , < 1 , and therefore in ~d 2ceordance with the expression (~)~
Y = mn(1 - ~ ~ z) (5) can be obtained, gy applying this equation into the equation (2), the x and y coordinates of the point A cen be settled.
Further, for the purpose of latQr necessity, a value of ~ , corresponding to the point A is obtained at this point from the equations (1) and (5), r~ . - cos w, a straight line is drawn passing through the origin of the Coordinate axes and the point A. Then, a composite curve MFE is obtained by similarity transforming a composite curve OAE at a reduction ratio of 1 J2. ThP th"c "h,-~ ~ ~.,a __~_ . .
curve MFE is rounded at the point F so as. to smoothly connect the curve and the straight portions thereof, which in turn is madE to be convex tooth profiles at the tooth faces of the rigid internal gear 2. Thereafter, a curve MO which is sym~tetrical to the convex tooth profile with respect to the poitlt M (datum point) is obtained and is made to be convex tooth profiles at the tooth Faces of the flexible external gear 3. Accordingly, the tooth profiles of the present intention become linear tooth profiles on and near the datum points through the rack approximation. Then, the pressure '~ 2~2~~~;~
angl a a ~, is obtained of the straight .line, 'The value of a ,~
can be obtained by the following equ~ction, using the expressions (1) and (6).
a ~ - tan '' { 0.5( ~J 4 ' ~t , S1n r~ . )l( 1 -- rc The tooth profiles at the tooth faces of the gears are assured to contact with each other properly at sections corresponding to the values of ,~ associated with the values of y through which the teeth of the external, gear mpve in the _ tooth grooves of the internal gear. 'This is based on the facts that the tooth apex P of the flexible external gear is on the point obtained by extending two times the straight line EQ beyond the point Q from the point ~, and the inclinations of the tangents at the point Q of the both tooth profiJ,es are equal, which facts are derived from the fact l,het the tooth profiles of the both gears contacting with Each othsr~, for example, at the paint Q i.n the drawing are symmetrical with respect to the point Q when viewed through the rack approximation, and by the process of defining the tooth profiles at the tooth faces as mentioned 4bove.
Figures 11, 12 and 13 show the meshing of the tooth profiles of teeth when the limit sectzon ig selected on the end portion of tooth trace of the diaphragm. Figure 11 shows th'e meshing'thereof on the section of rotation at the opening, Figure 12 shows the meshing on the central section of ,. ~~.~Fv°~~
rotation of tooth trace, and F~jgur~e t3 shows thsa.t on the section of the end of tooth trace of the diaphragm. When viewed along t:he tooth trace direction, the portion of the composite curve defined by the envelope from the apex thereof corresponds to the meshing or contact oi' the teeth form the opening of the flexible external gear to the end portion of the diaphragm side or to the limit section in the vicinity of outsido of the end portion, while the remaining portion of the Composite Curve corresponds to a continuous contact of the tooth profiles within the limit section. l~Iowever, if th@
limit section is settled in the vicinity of outside of the end portion of the diaphragm side, no actual tcc~th exist. on this section and therEfore the meshing or contact: of the teeth within this limit section is a imaginary one. Although, the meshing of the tooth portions located on the end portion of th~ diaphragm sido can be regarded as like as that on the limit section. As seen from the drawings, according to th~
example of the present invention, in the sections shown in Figures 11 and 12, a part of the continuous contact of the '~
teeth can be reali2ed in accordance wl.th a degree of Contact between the envelope and the moving locus of the shown Section, and in Figure 13, a continuous contact of the toot profiles within the section can be realized.
Tndustria7 Applicabflity According to the present invention, a composite curve is --. ~~~8 ~~«
is obtained by an envelope of a moving locus of the teeth of the flexible external gear obtainod when the deflection of the Opening of t:he flexible external gear is set to be a stetc of negative deviation which is lower in value than a normal deflection, and a moving locus at; a section of rotation at an end portion of tooth trace on the side of a diaphragm or in the vicinity of the outside of the and portion, and the thus obtained composite curve is employed for def:(ning the tooth profiles of the both gears, Hence, it is possible to use a limited part of the envelope for the basis of the formation of the tooth profiles of teeth, the limited part of the envelope corresponding to the values of negative deviation of the respective sections of rotation of tooth trace of the flexible external gear. Furthermore, the pressure angle at the datum .point can be decided in connection with the value of the negative deviation of the opening of the flexible external gear.
~y employing the tooth profiles of the prQSent invention, in the cup-shaped flexing contact type gear drive, a smooth meshing of the teeth can be realized all along the tooth trace direction toward the end portion of the diaphragm side without need of additional processing such as crowning, relieving and the like applied on the exterhaa gear and with maintaining the thickness of tooth rim, whereby a natural or proper tooth contact can be realized along the tooth trace direction. Zn addition, if the limit section is selected on r-.
~~~~'1~~D
the end portion of tooth trace of the diaphragm side, the continuous meshing of tootp~ profiles within th~ s~ction can also be utilized. Tris produces an effect of~reducing sr,ress of tooth surface, and at the same 'time produces an effect of enhancing a rigidity of teeth. $Spocially where n = 2, in other words, the number of tooth dj.fference between the rigid internal gear and the flexible external gear is 4, a radius of Curvature of the tooth profile becomes larger in accordance with the increase of the tooth depth, and therefore a remarkable effect of reducing the stress of tooth surface can be obtained.
Moreovor, since the flexing contact type gear drive is driven in a state or negative deviation, the tooth rim bending stress caused by elliptical. deformati.0I1 Of t:he external gear can be greatly reduced. For instance, the bending stress occurred when ~c , - 1 (non deviation) can be reduced by 20 ~ by setting ,~ , .- O,g (negative deviation).
With the reasons mentioned above, according to the present invention, a tertiary flexing contact gear drive of the type having high strength, rigidity and precision can be reali2Qd. Further, the present invention can be applied Lrrespective of the value of the coning angle, and therefore it can be applied directly to a cup-shaped flexible external gear of the short. barrel type.
TITLE OF INVENTION
TERTIARY NEGATIVE-DEVIATION FLEXING CONTACT TYPE GE:AH DRIVE
OF NON-PROFILE-SHIFTED TOOTH PROFI1,F
Technical FiEld The present invention relates to 3 flexing~contact-type gear drive, pnd particularly to tooth profiles of a ri~r,id internal gear and a flexible external gear employed in this type of gear drive.
Background Art A flexing-contact-type gear drive typically consists of a rigid circuinr~ intarnal gear, a flexible exterwal gear which has 2n (n being a positive integer) less teeth than the internal gear and which is disposed inside the internal gear and flexed into an elliptical shape so as to mesh with the internal gear at ~Cwo places, and wave generator fitted inaic9e t;~~e external gear for flexing it. The basic tooth profile for the guars of a flexing contact gear drive is linear (see U.S. Patent No. 2,906,1t~3), On ~,tle other hard, an i.nvolc,te tooth profile has also been proposed (see Japanese Patent Publication No. S~IO 4~-111171). However, where the linear or the involute tooth profile is adapted as that o'f° each of the inr,ernal and external gears, the addendum faces of the gears ran ,~__ ~r"~Y(r44~ ,., c~ 'y~.i~ la ~7;
~:~.~~ i~<' cannot be Continuously meshed with each other.
For increasing load capacity the inventor of the present invention proposed in Japanese Patent Laid Opcn No.
SHO 6g-11593 a system using as the basis for the tooth face profile the curve obtained by similarity transfor~rninR the locus of motion at a reduction ratio of 1/2 over a prescribe range from the meshing limit point on the locus of motion basod on the rack approximation of the tooth of the external gees relative to Lloe internal gear determined by the shape o:' the wave generator. With the tooth profile disclosed ~.n this, publication, the addendum faces of the internal and external gears can be continuously meshed with each other.
In the meantime, as a flexing-contact-type gear drive, one having a cup-shaped flexible external gear has been known. If the internal and external gears of this type gear drive are designed to have the same tooth profiles as disclosed in the above Japanese Patent Laid Open No. SHO 53-w 115943, it cannot be realized to Form a continuous meshing between the teeth of the gears all along the tooth trace direction.
More specifically, in a cup°shaped, flexing-contact-type gear drive, the eup~shaped flexible external gear is subjected to deflection called honing, in which the deflection value of the external gear increases gradually in the direction from its diaphragm side to its opening side and :in proportional to a distance from the diaphragm (the deflection E/:~ r/:E~~.~ y~r~~G ~~GE ~7u'~ ny . ~ Y~O~~ fi~~00 h~~~U _ Yo ~~2~3~~~
being a difference .in the length between tho ma,~or axis and the minor axis of the el'iiptical shape of the external gear).
The change in the deflection along the axis of the external gear due to the coning is not considered in determination cf the tooth profiles disclosed in Japanese Patent Laid Open No.
SNO 63-1159~43~
Accordingly, where a cup--shaped, flexing-contact--type gear drive is provided with the internal and external gears of the tooth profiles as disclosed in the above publication, both gears can be meshed continuously with each~other only at a specific sectional portion along the tooth trace direction (for exanple, at such a sectional portion of non-deviation where a normal deflection occurs), while they may be improperly meshed to cause tooth interference or the like at the other sectional portions.
Measures to avoid the defect are disclosed, for example, in .lapanese Patent Laid Open Nos. SHO 62--75153 and HEl 2-62u61. rn these measures, however, it is required i;o apply special additional processings such as crowning, relieving and the like to t:he tenth of gears.
Tn order to achieve a wider range of meshing of the external and internal gears atang the tooth trace direction of the cup-shapod flexible external gear without tooth interference between the external and internal gears, the inventor of the present invention proposes a tooth profile disclosed in Japanese Patent Application No. II~I--3-357036.
~~d '! r ..~'Ef~~d Y~4~G ,4Gr ~0~'' ~G
~~~8~~%.
The invention diqclosed in this patent application was made based on the recognition that, in a flexing, contact type gear drive, moving lcci cf teeth of the cup-shaped flexible external gear at respective sections of rotation along tooth trace direction thereof are found to be changed and decreased in deflection along the tooth trace direction viewed Prom the opening side of the flexible external gear, and that th~se moving loci are found to form a single envelope when these moving loci are overlapped on a same plane. In this patent application, a rack approximation method is introduced to simplify the analysis in finding a formula of the obtained envelope. Moreover, a moving locus of the flexible external ge2r is obtained at a section of rotation near and outside the diaphragm--side end of the flexible external gear, and is Connected to the envelope to thereby form a composite curve.
Then, a portion of the composite curve which starts from a selected meshing limit point and corresponds to two times the working depth in the tooth depth direction is,sub,)ected to the simllarit-,y transformation at a reduction ratio of 1/2 to obtain a curve which is employed as convex tooth profiles of tooth faces of tho external and internal gears.
The present inventor also proposed in Japanese Patent Application iJo. HMI 3-357037 that a moving locus based on which tooth profiles are introduced is defined only by the above-mentioned envelope. The invention disclosed in this Japanese Patent Application eras made based on the recognition n 01d s,~~,~E~.~:.~Y~r4GG.kGE INOdd v~~00 ~~~~'~~Oi'0 ~~.2~ ~~~' that the envelope is similar to a curve obtained by sub,~ecting to the similarity transformation at a reduction ratio of 1/2 a moving locus of teeth of t:he flexible external gear at a rotational section of a non-deviated state. With this envelope, tooth profiles are determl.ned which are applicable to tooth profiles of both gears of a cup-shaped, flexing-contact-type gear drive wherein the difference in tooth number between the rigid internal gear and tha flexible external gear is four.
However, in the inventions disclosed~in Japanese Patent Application Nos. HEI 3-357036 and HEI ~-357p37, an opening of the cup-shaped flexible external gear is regarded as in a non-deviated state. Further, setting of a pressure angle at a datum point of tooth profiles is not specified.
While, recently there has been increased more and morea demand for enhanced performance of flexing contact type gear drives. In order Lo satisfy the demand, it is necessr,ry to further Pnhance strength and rigidity of the flexing Contact type gear drive, and at the same time it is necessary to further improve wear-resisting capability. For these purposes, the actual load distribution appeared on the teeth along the tooth traco direction must be equalized.
Disclosure of Tnvent:ion The present invention is directed to an improvement of , tooth profi2es disclosed in Japanese Patent AppJ.icatzon Nos.
~~2~~~
HFI 3-35703b and HEI 3°357037. The present invention is characterized by setting the deflection of an opening of a , cup-shaped flexible external gear of a flexing contact type gear drive to be a negative-deviated state wherein the amaunt of deflection is set smaller than that of a normal deflection.
Concept of positive and negative with resp~ct to deviation of teeth are described in Japanese Publication No. SHO u5-U1171 by the same inventor of the present invention.
Further, according to the present invention, tooth profiles are determined based on a composite curve formed by an envelope of moving loci of teeth of a flexibly external '~d gear and a moving locus pf teeth at a section of rotation which is located on an end of the diaphragm-side of the external gear along the tooth trace direction or located adjacent to the outside of the end portion thereof. This concept is similar to that disclosed in Japanese Patent Application Nos. HEI 3-357036 and HEI g-357037, except that the moving locus of teeth at the section of rotation located on the end of the oxternal gear is employed.
According to the present invention, different from the inventions disclosed in the above-cited Japanese Patent Application Nos. HFI ~-357036 and H~z ~-357037 in which the envelope employed includes the moving locus or. the section of non-deviated state, a clearly limited portion of the envelope is employed Which corresponds to an amount of negative deviation of teeth of each of rsSpect sections of rotation of ..«. ....~,~.:~.y~y.Ha:~.y:yaYlililuE;cYL518:i5;;kBfdbma~5~tueu°.a.~xt ~C;tiiFtiSs ~~.~~'J~ d the flexible external guar along its tooth trace direction.
In addition, the present; invention is characterized in that an pressure angle at a datum point of tooth is d!~fin~d in accordance with an amount. of negative deviation occurred on an opening of a flexible extornal gear, MorE specifically, according to the present invention, in a flexing contact type gear drive having a rigid internal gear, a cup-shaped flexible external gear disposed inside the internal gear, and a wave generator for deflecting the external gear into an elliptical shape such that the value of deflection is proportional to a distance from a diaphragm o,~ along the direction from the diaphragm to an opening of the external gear and for rotating the elliptica? shape of the external gear, whereby a relative rotation between the both gears IS generated by rotating the wave gear, tooth profiles of the rigid internal gear and the flexible external gear are defined as follows.
Firstly, both the rigid internal gear and the flexible external gear are made to be non-profile-shifted spar gears, '~J and an opening of the flexible external gear is set to be a negative-deviated state in which a deflection occurred is lower in volume than a normal deflection, Then, a moving locus is obtained through rack approximation of teeth of the external gear to the internal gear at respective sections of rotation along the tooth trace direction of ,the flexible external gear, and the obtained moving locus is overlapped on ~~~~'~~t~
one of sections of rotation, whereby an envelope i:a obtained.
Another moving locus in a section of rotation at an end portion of tooth trace on the side of a diaphragm or in the vicinity of the outside of the end portion is smoothly connected to the envelope so that a composite curve is obtained. A curve is obtained by subjecting to the similarity transformation at a reduction ratio of 1/2 a portion from a starting point of the envelope to a terminating point.
c~rresponditlg to two times the working depth in the direction of depth from an ape~c of a moving locus when the deviation is 0, using the terminating point as an original point. The curve thus obtained is made to be each of main portion:; of convex tooth profiles at the tooth faces of the both gears.
Furthermore, a composite curve is obtained which includes a straight line having a limited pressure angle associated with a deflection value of an opening and inserted in the vicinity of a datum point of tooth profile, and a transient curve smoothly connecting the above straight lina to the main portion of the convex tooth profile. This composite curve or its similar curves is made to be each of tooth profiles at the tooth faces of the both gears. While, tooth flanks of the both gears are defined by a composite tooth profile including a straight line and a concave curve which is symmetrical to the tooth proff:~e of each ef the tooth faces of the gears with respect to each of the datum points of tooth profiles of the gears, or are defined by a tooth profile which is obtained by 212 ~0~' \ providing the composite tooth profile with some amount of escape.
Brief' Description of Drawings Figure 1 is N perspective view of a cup-Shaped flexing coritaet type gear dr.ivo.
Figure 2 is a front view of~ the goat drive of Figure 1.
Figure 3 illustrates a state of a flexible external gear before deflection due to coning.
Figure ~1 illustrates a state of the flexible external gear on a major axis of elliptical shape after deflection due to contng.
Figure 5 illustrates a state of the flexible external gear on a minor axis of elliptical shape after deflection due to coning.
Figures 6, 7 and 8 show a locus of one of teeth of the flexible external gear when moving with respect to a tooth groove of a rigid internal gear, wherein Figure 6 shows a moving locus thereof at, a seotion of rotation on an opening of the flexible external gear, Figure 7 shows a moving locus thereof at a central section of rotation of tooth trace of the external gear, and Figure 8 shows a moving loons thereof at a section of rotation on an end portion of the diaphragm of the external gear.
Figure 9 is a composite curve by which a tooth profile SId s~;~ ~s~.r,.~4f~,~~,,~~G
. Y'a0~a ~5~00 BO"~_~;~o of the present invention is defined.
Figure 10 illustrates how to obtain the tooth profile of the present invention from the cornposite curve of Figure 9.
rJ
Figures 11, 12 and 13 show meshing condl.ti0ns of the tooth profiles of the present invention, respectively, whar~ein Figuro 11 shows a s'~ate of moshing at a section of rotatipn on the opening of the external gear, Figure 12 shows a state thereof at a central section of rotation of tooth , trace of the external gear, and Figure l~ shows a State thereof at a soetiori of rotation on an end of the diaphragm of tooth trace of the external gear.
E3est Mode for Carrying Out the Invention An example of the present invention will now be described with reference to the drawangs.
Figures 1 and 2 is a perspective view and a front view of a known cup-shaped fle5ting con'~aet type gear drive. The fleXing contact typo gear drive 1 comprises a circular rigid internal gear 2, a cup~shaped flexible external gear 3 disposed inside the internal gear, and an elliptically-shaped wave generator 4 fitted into the external gear. The cup-shaped flexible external gear 3 is in a state flexed into an elliptical shape by the elliptically-shaped wavy generator 1~.
~i8ures 3, ~t and 5 show a state of deflection of the fl.ext~ble external gear caused by coning, respectively, by 9Id s~7 ~s~.r"~y~4~G.~~.~ ~0~~ ~~~00 ~u?~~0~76 ~:~~~3~~)' means of a section taken along an axis of the flexible external gear, Figure 3 shows a state of deflection of the external gear before flexed by the wave generator ,1 (before def~,ection). Figure it is a sectional view taken along the ax is pf the external gear and along a major axis of the wave generator, showing a state flex~d by the wave generator U.
Whereas, Figure 6 .is a sectional view taken along the axis of the external gear and along a minor axis of the wave generator, showing a state flexed by the wave generator u.
As can be seen from these figures, the Cup~sraped flexible external gear 3 is deflected Owing to coning, so that the deflection in value is maximum on its openin 3a and $ . is gradually decreased toward the side of its diaphragm 3b, Figures 6, 7 and 8 show & moving locus. of one of teeth of the cup-shaped flexible external gear with respect to a tooth groove of the rigid internal gear 2 of the flexing contact type gear drive 1, the moving locus being obtained by the reek approximation provided that the numbers of the both gears 2 and 3 become infinite without changing the difference in number of teeth between the both gears, Each of the obtained moving loci is in a state of n~gative deviation.
Note that in these.figures, the teeth of the internal and external gears are provided with same tooth profiles provisionally<
In these figures, the moving locus of, Figuro C ~.s obtained at a section of rotation of a point 31 on the opening 2~~8~~~~~
3a of the teeth 30 of the cup-shaped flexible external gear 3. The moving locus of rigure 7 is obtained on a sQetion of rotation at a center of tooth trace of the~external gear, while that of Figure 8 is obtained at a section of r~otat:ior, of a point 33 on an end portion of the diaphragm 3b of tooth trace of the external gear.
As is apparent from these figures, a degree of tooth Interference of the both gears increases gradually toward the side of the diaphragm 3b From the opening 3a. To avoid the tooth interference, it, is necessary to apply an additiona.t processing such as cell~ving to the teeth of the gears, The moving locus on a desired section of rotation can be expressed by x = 0.5 mn( n - ,~ sin n ) (1) Y - mn(1 - ~ pOs wherein x is an orthogonal coordinate along a pitch line of a rack, y is an orthogonal coordin&te along a depth of the rack, m is a module of the tooth, n is 1/2 of the number of tooth difference between the rigid internal gear and the flexible external goar~, r~ is an angular parameter, ~; is a deflection ooofficient (,~ - 1 represents a state of non deviation, whereas ~ ~ 1 represents that of negative deviation).
The following expression (2) can be derived by eliminating tha term g ~n from the expression (1).
1 ?.
pe k.D ~J
x - 0.5mn [COS ~' ( ( ~ 'Y/m/n)/,~ f - ~c J- 1- ( ( 1~y/m/n)/ ~c } 4 7.
(2) Further, the following expression (3) can be obtained by solving x through a partial differential of the expression in terms of - ~ 1 -y/m/n (3) elimination of the term x from the expressipns (2) and (3) makes an expression defining an envelope a obtained by overlapping a moving locus with respect to each value of on an plane. That is, the following expression (4) can be obtained.
x - 0 . 5mn ~ cps - ~ f' 1 -y/m/n - ,r y/m/n ( 1 -y/m/n ) } _ 0 The definition of the above envelope leads t,o the following facts. If the constant ,~ is :;et to r,e a certain value, this means to select a section of rote.
>rion having a deflection in value corresponding to the value of x . On Lhis section of r4tation, the envelope is meant to contact; with the moving locus of teeth at the point of y obtained b Y
substituting the above value in the equation (3),for the co~fficient~ is . In other words, a portion of the envelope on or ad,~acent to this point of y represents a part of the r~
moving locus of teeth.
As mentioned before, the Inventor of the present tnvention found that the above envelope is not but a similar curve obtained by reducing a moving locus at a ratio of 1/2, the waving locus being obtained wYren x - 1 (non deviation) in the equation (2). However, it is insufficient to provide an effective tooth depth by.using only this envelope. This is especially apparent when n = 1, that is,.when the number of tooth difference between the rigid internal gear' and the flexible external gear is 2.
Therefore, according to the present invention, based on the inventions disclosed in the above-cited Japanese Patent Application Np. HEI 3 357036, a moving locus of teeth of the flexible external gear is obtained on a section of rotation of an erid portion of the diaphragm side of tooth trace or on a section of rotation in the vicinity of outside of the end portion (wherein the section of rotation is referred to hereinafter as the limit section), a'nd is smoothly connected to the envelope to form a composite Curve, so that the composite curve is made to a basis of deriving tooth profiles of the gears.
Figure 9 illi.istrates the thus formed composite curve L~ In this figure, there are illustrated five moving loci in total including a movipg locus Q a of teeth on a section corresponding to the state of non deviation and a moving locus .~ g of teeth on the section of rotation In the vicinity of 1 ~l outside of the end portion Of tooth tr&ce of the diaphragm (the fihove-mentioned 7.imit section), in ndditi.on t:o the respective moving loci ,P. a, ~ b and .~ c shown in Figures 6, '1 and g. Further, the respective points A, 5, C and D of Figure 9 represent th~ places where the moving loci .B a, a b and ,g c ~,re contacted with the envelope e, respectively.
Where the limit Section is selected on the ~nd portion of tooth trace of the diaphragm, the moving locus. g is in accordance with the uioving locus Figure 70 shows how to derive the tooth profiles of _ the present invention from the composite curve L. Now, a prescribed portion of this curve is selected from a point A to a point E. The starting point A is a point where the moving locus Q a of teeth on the section of rotation of the opening 3a of the flexible exter~nsl gear 3 is contacted with t;he envelope e. The terminating point E is a point where the value in y-ordinate is equal to the two times of working tooth depth, this pint being usually located on the moving locus ~ g of teEth on the limit section as mentioned above.
While, it was not specified in the inventions disclosed in Japanese Patent Application Nos. HEI 3-357036 and HEf 3-350737 how to settle the point p.
In contrast to this, according to the present invention, the point A can be Bottled as follows. Where the deafleetion constant of the opening 3a of the flexible external gear is ,~ , t?1e value of rc , < 1 , and therefore in ~d 2ceordance with the expression (~)~
Y = mn(1 - ~ ~ z) (5) can be obtained, gy applying this equation into the equation (2), the x and y coordinates of the point A cen be settled.
Further, for the purpose of latQr necessity, a value of ~ , corresponding to the point A is obtained at this point from the equations (1) and (5), r~ . - cos w, a straight line is drawn passing through the origin of the Coordinate axes and the point A. Then, a composite curve MFE is obtained by similarity transforming a composite curve OAE at a reduction ratio of 1 J2. ThP th"c "h,-~ ~ ~.,a __~_ . .
curve MFE is rounded at the point F so as. to smoothly connect the curve and the straight portions thereof, which in turn is madE to be convex tooth profiles at the tooth faces of the rigid internal gear 2. Thereafter, a curve MO which is sym~tetrical to the convex tooth profile with respect to the poitlt M (datum point) is obtained and is made to be convex tooth profiles at the tooth Faces of the flexible external gear 3. Accordingly, the tooth profiles of the present intention become linear tooth profiles on and near the datum points through the rack approximation. Then, the pressure '~ 2~2~~~;~
angl a a ~, is obtained of the straight .line, 'The value of a ,~
can be obtained by the following equ~ction, using the expressions (1) and (6).
a ~ - tan '' { 0.5( ~J 4 ' ~t , S1n r~ . )l( 1 -- rc The tooth profiles at the tooth faces of the gears are assured to contact with each other properly at sections corresponding to the values of ,~ associated with the values of y through which the teeth of the external, gear mpve in the _ tooth grooves of the internal gear. 'This is based on the facts that the tooth apex P of the flexible external gear is on the point obtained by extending two times the straight line EQ beyond the point Q from the point ~, and the inclinations of the tangents at the point Q of the both tooth profiJ,es are equal, which facts are derived from the fact l,het the tooth profiles of the both gears contacting with Each othsr~, for example, at the paint Q i.n the drawing are symmetrical with respect to the point Q when viewed through the rack approximation, and by the process of defining the tooth profiles at the tooth faces as mentioned 4bove.
Figures 11, 12 and 13 show the meshing of the tooth profiles of teeth when the limit sectzon ig selected on the end portion of tooth trace of the diaphragm. Figure 11 shows th'e meshing'thereof on the section of rotation at the opening, Figure 12 shows the meshing on the central section of ,. ~~.~Fv°~~
rotation of tooth trace, and F~jgur~e t3 shows thsa.t on the section of the end of tooth trace of the diaphragm. When viewed along t:he tooth trace direction, the portion of the composite curve defined by the envelope from the apex thereof corresponds to the meshing or contact oi' the teeth form the opening of the flexible external gear to the end portion of the diaphragm side or to the limit section in the vicinity of outsido of the end portion, while the remaining portion of the Composite Curve corresponds to a continuous contact of the tooth profiles within the limit section. l~Iowever, if th@
limit section is settled in the vicinity of outside of the end portion of the diaphragm side, no actual tcc~th exist. on this section and therEfore the meshing or contact: of the teeth within this limit section is a imaginary one. Although, the meshing of the tooth portions located on the end portion of th~ diaphragm sido can be regarded as like as that on the limit section. As seen from the drawings, according to th~
example of the present invention, in the sections shown in Figures 11 and 12, a part of the continuous contact of the '~
teeth can be reali2ed in accordance wl.th a degree of Contact between the envelope and the moving locus of the shown Section, and in Figure 13, a continuous contact of the toot profiles within the section can be realized.
Tndustria7 Applicabflity According to the present invention, a composite curve is --. ~~~8 ~~«
is obtained by an envelope of a moving locus of the teeth of the flexible external gear obtainod when the deflection of the Opening of t:he flexible external gear is set to be a stetc of negative deviation which is lower in value than a normal deflection, and a moving locus at; a section of rotation at an end portion of tooth trace on the side of a diaphragm or in the vicinity of the outside of the and portion, and the thus obtained composite curve is employed for def:(ning the tooth profiles of the both gears, Hence, it is possible to use a limited part of the envelope for the basis of the formation of the tooth profiles of teeth, the limited part of the envelope corresponding to the values of negative deviation of the respective sections of rotation of tooth trace of the flexible external gear. Furthermore, the pressure angle at the datum .point can be decided in connection with the value of the negative deviation of the opening of the flexible external gear.
~y employing the tooth profiles of the prQSent invention, in the cup-shaped flexing contact type gear drive, a smooth meshing of the teeth can be realized all along the tooth trace direction toward the end portion of the diaphragm side without need of additional processing such as crowning, relieving and the like applied on the exterhaa gear and with maintaining the thickness of tooth rim, whereby a natural or proper tooth contact can be realized along the tooth trace direction. Zn addition, if the limit section is selected on r-.
~~~~'1~~D
the end portion of tooth trace of the diaphragm side, the continuous meshing of tootp~ profiles within th~ s~ction can also be utilized. Tris produces an effect of~reducing sr,ress of tooth surface, and at the same 'time produces an effect of enhancing a rigidity of teeth. $Spocially where n = 2, in other words, the number of tooth dj.fference between the rigid internal gear and the flexible external gear is 4, a radius of Curvature of the tooth profile becomes larger in accordance with the increase of the tooth depth, and therefore a remarkable effect of reducing the stress of tooth surface can be obtained.
Moreovor, since the flexing contact type gear drive is driven in a state or negative deviation, the tooth rim bending stress caused by elliptical. deformati.0I1 Of t:he external gear can be greatly reduced. For instance, the bending stress occurred when ~c , - 1 (non deviation) can be reduced by 20 ~ by setting ,~ , .- O,g (negative deviation).
With the reasons mentioned above, according to the present invention, a tertiary flexing contact gear drive of the type having high strength, rigidity and precision can be reali2Qd. Further, the present invention can be applied Lrrespective of the value of the coning angle, and therefore it can be applied directly to a cup-shaped flexible external gear of the short. barrel type.
Claims (3)
1. A tertiary negative-deviated flexing contact type gear drive having a rigid internal gear, a cup-shaped flexible external gear disposed inside the internal gear, and a wave generator for flexing the external gear into an elliptical shape so that a deflection occurred in the external gear along a direction from a diaphragm to an opening thereof is proportional in value to a distance measured from the diaphragm, a relative rotation of the both gears being generated by the rotation of the wave generator;
wherein both the rigid internal gear and the flexible external gear are made to be non-profile-shifted spur gears;
wherein the opening of the flexible external gear is set in a state of negative deviation wherein a deflection of the opening is lower in value than a normal deflection; a moving locus is obtained through rack approximation of teeth of the external gear to the internal gear at respective sections of rotation of tooth trace of the flexible external gear; an envelope is obtained by overlapping the moving locus on one of sections of rotation; another moving locus is obtained in a section of rotation at an end portion of tooth trace on a side of the diaphragm or in the vicinity of an outside of the end portion and is smoothly connected to the envelope to thereby obtain a composite curve; a curve is obtained by similarity transforming at a reduction ratio of a portion from a starting point of the envelope to a terminating point thereof corresponding to two times the working depth in the direction of the depth from an apex of a moving locus when deviation is 0, using the terminating point as an original point; and this curve is made to be each of main portions of convex tooth profiles at tooth faces of the both gears; and wherein a composite curve including a straight line having a limited pressure angle associated with a deflection value of the opening inserted in the vicinity of a datum point of tooth profile and a transient curve smoothly connecting the straight line to the main portion of the convex tooth profile is made to be each of tooth profiles at the tooth faces of the both gears.
wherein both the rigid internal gear and the flexible external gear are made to be non-profile-shifted spur gears;
wherein the opening of the flexible external gear is set in a state of negative deviation wherein a deflection of the opening is lower in value than a normal deflection; a moving locus is obtained through rack approximation of teeth of the external gear to the internal gear at respective sections of rotation of tooth trace of the flexible external gear; an envelope is obtained by overlapping the moving locus on one of sections of rotation; another moving locus is obtained in a section of rotation at an end portion of tooth trace on a side of the diaphragm or in the vicinity of an outside of the end portion and is smoothly connected to the envelope to thereby obtain a composite curve; a curve is obtained by similarity transforming at a reduction ratio of a portion from a starting point of the envelope to a terminating point thereof corresponding to two times the working depth in the direction of the depth from an apex of a moving locus when deviation is 0, using the terminating point as an original point; and this curve is made to be each of main portions of convex tooth profiles at tooth faces of the both gears; and wherein a composite curve including a straight line having a limited pressure angle associated with a deflection value of the opening inserted in the vicinity of a datum point of tooth profile and a transient curve smoothly connecting the straight line to the main portion of the convex tooth profile is made to be each of tooth profiles at the tooth faces of the both gears.
2. A tertiary negative deviated flexing contact type gear drive as claimed in claim 1 characterized in that tooth flanks of said rigid internal gear and said flexible external gear are defined by a composite tooth profile including a straight line and a concave curve which is symmetrical to the tooth profile of said tooth faces of both said gears with respect to said datum point of said tooth profile of said gears.
3. A tertiary negative deviated flexing contact-type gear drive as claimed in claim 1 of claim 2, wherein the tooth flanks of the rigid internal gear and the flexible external gear are defined by a tooth profile which is obtained by providing the composite tooth profile with a certain amount of escape.
Priority Applications (4)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| PCT/JP1992/001535 WO1994012808A1 (en) | 1992-11-24 | 1992-11-24 | Tertiary negative-deflection flexing contact gears of non-profile-shifted tooth profile |
| EP92924005A EP0622565B1 (en) | 1992-11-24 | 1992-11-24 | Tertiary negative-deflection flexing contact gears of non-profile-shifted tooth profile |
| CA002128502A CA2128502C (en) | 1992-11-24 | 1992-11-24 | Tertiary negative-deflection flexing contact gears of non-profile-shifted tooth profile |
| US08/256,721 US5485766A (en) | 1992-11-24 | 1992-11-24 | Tertiary negative-deviation flexing contact type gear drive of non-profile-shifted tooth profile |
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| PCT/JP1992/001535 WO1994012808A1 (en) | 1992-11-24 | 1992-11-24 | Tertiary negative-deflection flexing contact gears of non-profile-shifted tooth profile |
| CA002128502A CA2128502C (en) | 1992-11-24 | 1992-11-24 | Tertiary negative-deflection flexing contact gears of non-profile-shifted tooth profile |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CA2128502A1 CA2128502A1 (en) | 1994-06-09 |
| CA2128502C true CA2128502C (en) | 2004-08-31 |
Family
ID=32913605
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA002128502A Expired - Lifetime CA2128502C (en) | 1992-11-24 | 1992-11-24 | Tertiary negative-deflection flexing contact gears of non-profile-shifted tooth profile |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA2128502C (en) |
-
1992
- 1992-11-24 CA CA002128502A patent/CA2128502C/en not_active Expired - Lifetime
Also Published As
| Publication number | Publication date |
|---|---|
| CA2128502A1 (en) | 1994-06-09 |
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| EEER | Examination request | ||
| MKEX | Expiry |