WO2012153363A1 - 3次元連続接触歯形を有する波動歯車装置 - Google Patents
3次元連続接触歯形を有する波動歯車装置 Download PDFInfo
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- WO2012153363A1 WO2012153363A1 PCT/JP2011/002565 JP2011002565W WO2012153363A1 WO 2012153363 A1 WO2012153363 A1 WO 2012153363A1 JP 2011002565 W JP2011002565 W JP 2011002565W WO 2012153363 A1 WO2012153363 A1 WO 2012153363A1
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- tooth
- section
- external
- teeth
- tooth profile
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- 238000005452 bending Methods 0.000 claims description 12
- 230000007935 neutral effect Effects 0.000 claims description 7
- 230000002093 peripheral effect Effects 0.000 claims description 5
- 230000009466 transformation Effects 0.000 claims description 4
- 150000001875 compounds Chemical class 0.000 abstract description 4
- 230000017105 transposition Effects 0.000 abstract 2
- 238000000034 method Methods 0.000 description 8
- 238000006073 displacement reaction Methods 0.000 description 4
- 239000002131 composite material Substances 0.000 description 3
- 238000003754 machining Methods 0.000 description 1
- 210000003205 muscle Anatomy 0.000 description 1
- 230000001105 regulatory effect Effects 0.000 description 1
- 230000000717 retained effect Effects 0.000 description 1
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Classifications
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- 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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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
- Y10T74/00—Machine element or mechanism
- Y10T74/19—Gearing
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
- Y10T74/00—Machine element or mechanism
- Y10T74/19—Gearing
- Y10T74/19014—Plural prime movers selectively coupled to common output
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
- Y10T74/00—Machine element or mechanism
- Y10T74/19—Gearing
- Y10T74/19949—Teeth
- Y10T74/19963—Spur
- Y10T74/19967—Yieldable
Definitions
- the present invention relates to an improvement in the tooth profile of a rigid internal gear and a flexible external gear in a wave gear device. More specifically, the present invention relates to a wave gear device having a three-dimensional continuous contact tooth profile in which both gears are maintained in a predetermined meshing state on a cross section perpendicular to each axis in the tooth trace direction.
- Wave gear device is the founder C.I. W. Since the invention of Musser (Patent Document 1), various inventions of this apparatus have been made by many researchers including the present inventor to this day. There are various types of inventions related to the tooth profile.
- Patent Document 2 that the basic tooth profile is an involute tooth profile
- Patent Documents 3 and 4 a method of approximating the meshing of the teeth of the rigid internal gear and the flexible external gear with a rack.
- a wave gear device has an annular rigid internal gear, a flexible external gear arranged coaxially inside this, and a wave generator fitted inside this.
- the flexible external gear is formed on a flexible cylindrical body, a diaphragm extending in the radial direction from the rear end of the cylindrical body, and an outer peripheral surface portion on the front end opening side of the cylindrical body. With external teeth.
- the flexible external gear is bent into an ellipse by a wave generator, and meshes with the rigid internal gear at both ends of the long axis of the ellipse.
- the external teeth of the flexible external gear flexed in an elliptical shape increase in the amount of deflection substantially in proportion to the distance from the diaphragm from the diaphragm side toward the front end opening along the tooth trace direction. Yes. Further, as the wave generator rotates, each portion of the tooth portion of the flexible external gear repeatedly bends in the radial direction. However, a rational tooth profile setting method that takes into account the bending operation (corning) of the flexible external gear by such a wave generator has not been sufficiently considered.
- the present inventor has proposed a wave gear device having a tooth profile that enables continuous meshing in consideration of tooth coning in Patent Document 5.
- an arbitrary axis-perpendicular cross-sectional position in the tooth trace direction of the flexible external gear is defined as the main cross section, and the elliptical rim neutral of the flexible external gear in the main cross section.
- the meshing of the flexible external gear and the rigid internal gear is approximated by rack meshing, and in the cross-section perpendicular to the axis including the main cross section in the tooth trace direction of the flexible external gear, it is possible to accompany the rotation of the wave generator.
- Each movement trajectory of the teeth of the flexible external gear with respect to the teeth of the rigid internal gear is obtained, and the curved portion from the point A at the top to the point B at the next bottom in the non-displacing movement trajectory obtained in the main cross section is represented by point B.
- a first similarity curve BC reduced to ⁇ times ( ⁇ ⁇ 1) is obtained as the center of similarity, and the first similarity curve BC is adopted as the basic tooth profile of the end of the rigid internal gear.
- a curve obtained by rotating the first similarity curve BC around the end point C of the first similarity curve BC by 180 degrees is multiplied by (1 ⁇ ) / ⁇ times with the end point C as the center of similarity.
- Two similar curves are obtained, and the second similar curve is adopted as the basic tooth profile of the end of the flexible external gear.
- each negative excursion side movement locus obtained in the cross section perpendicular to each axis deflected in the negative excursion state (deflection coefficient ⁇ ⁇ 1) on the diaphragm side from the main cross section, and the front end opening side from the main cross section So that both the positive displacement side movement trajectories obtained in the cross sections perpendicular to the respective axes deflected in the positive displacement state (flexure coefficient ⁇ > 1) at the bottom of the non-deviation movement trajectory in the main cross section are drawn.
- the tooth profile of the flexible external gear the main cross section is sandwiched, and the tooth profile portions on both sides in the tooth trace direction are shifted.
- the tooth profile extending from the main cross section to the opening and the tooth extending from the main cross section to the diaphragm is centered on the meshing of the continuous tooth profile over a wide range in the main cross section. Effective engagement can be achieved in the entire range of the muscle. Therefore, more torque can be transmitted compared to the wave gear device meshing in the conventional narrow tooth trace range.
- the problem of the present invention is that the required displacement is applied to the tooth trace of the flexible external gear, and the amount of deflection is changed from the positive deviation to the negative deviation along the tooth trace direction.
- the tooth profile in the cross section perpendicular to each axis of the flexible external gear is defined by subjecting the tooth profile of the similar curve derived from the tooth movement trajectory to the required dislocation, thereby forming a three-dimensional contact state of both gears and transmitting torque. It is an object to propose a wave gear device that can increase the ratcheting torque by setting both gears to high teeth.
- tooth profile of the open end cross section of the external tooth of the flexible external gear it is defined from the addendum tooth profile defined as described above, the linear tooth profile connected to the tooth profile, and the appropriate tooth root profile that avoids interference.
- a high-tooth composite tooth profile As a tooth profile of the internal teeth of the rigid internal gear, a compound tooth profile of a high tooth defined by an end tooth profile defined as described above, a linear tooth profile connected to the tooth profile, and an appropriate root tooth profile that avoids interference Is used.
- the relative movement trajectory of the rigid internal gear with respect to the internal teeth obtained in each cross section in the tooth trace direction of the external teeth of the flexible external gear is The dislocation tooth profile obtained by shifting the compound tooth profile adopted as the tooth profile of the open end section so as to share the movement trajectory of the open end section and the bottom thereof is changed from the open end section of the external teeth of the flexible external gear. It is adopted as a tooth profile at each position in the tooth trace direction up to the inner end cross section.
- FIG. 1 is a front view of a wave gear device that is the subject of the present invention
- FIGS. 2 (a) to 2 (c) show the situation in which the opening of the flexible external gear is bent in an elliptical shape in an axial section.
- 2 (a) is a state before deformation
- FIG. 2 (b) is a cross section including the major axis of the elliptic curve after deformation
- FIG. 2 (c) is a short view of the elliptic curve after deformation.
- Each cross section including the axis is shown.
- 2A to 2C the solid line indicates the cup-shaped flexible external gear
- the broken line indicates the top hat-shaped flexible external gear.
- the wave gear device 1 includes an annular rigid internal gear 2, a flexible external gear 3 disposed on the inner side thereof, and a wave generator having an elliptical profile fitted on the inner side. 4.
- the rigid internal gear 2 and the flexible external gear 3 are both spur gears of the module m. Further, the difference in the number of teeth of both gears is 2n (n is a positive integer), and the rigid internal gear 2 is more common.
- the flexible external gear 3 is bent in an elliptical shape by a wave generator 4 having an elliptical outline, and meshes with the rigid internal gear 2 at both end portions in the direction of the elliptical long axis L1.
- the flexible external gear 3 includes a flexible cylindrical body 31, a diaphragm 32 that extends continuously in the radial direction from the rear end 31 b, a boss 33 that continues to the diaphragm 32, and the cylindrical body 31. External teeth 34 formed on the outer peripheral surface portion on the opening end 31a side.
- the cylindrical body portion 31 is directed from the diaphragm-side rear end 31b toward the opening end 31a.
- the amount of bending outward or inward in the radial direction is gradually increased.
- the amount of outward deflection gradually increases in proportion to the distance from the rear end 31b to the open end 31a, as shown in FIG. 2 (c).
- the amount of inward bending gradually increases in proportion to the distance from the rear end 31b to the opening end 31a. Therefore, the amount of deflection of the external teeth 34 formed on the outer peripheral surface portion on the opening end 31a side changes in each axis perpendicular to the tooth trace direction. That is, the amount of deflection gradually increases in proportion to the distance from the rear end 31b from the inner end section 34b on the diaphragm side toward the opening end section 34a on the opening end 31a side in the tooth trace direction of the outer teeth 34.
- FIG. 3 shows the movement trajectory of the external teeth 34 of the flexible external gear 3 with respect to the internal teeth 24 of the rigid internal gear 2 obtained by approximating the relative movement of the teeth of the two gears 2 and 3 of the wave gear device 1 with a rack.
- the x axis indicates the translation direction of the rack
- the y axis indicates a direction perpendicular thereto.
- the external teeth 34 at the long axis position L1 in the elliptical rim neutral line of the external teeth 34 are elliptical.
- the amount of bending with respect to the rim neutral circle before bending to 2 is 2 ⁇ mn, where ⁇ is the bending coefficient.
- the origin of the y-axis in FIG. 3 is the average position of the amplitude of the movement trajectory.
- the positive deviation movement trajectory Mo is a deflection coefficient ⁇ >.
- the main section 34c is set at a position indicated by a straight line passing through the center of the ball 4a of the bearing of the wave generator 4.
- the deflection coefficient of the movement trajectory in each cross section from the main cross section 34c to the opening end cross section 34a is ⁇ > 1
- the movement trajectory in each cross section from the main cross section 34c to the inner end cross section 34b on the diaphragm side is ⁇ 1.
- the tooth profile of the open end section 34a of the external teeth 34 is a convex curved external tooth end tooth portion 41, an external tooth linear tooth portion 42 continuous thereto, and a concave curve external tooth root continuous therewith. It is defined by a tooth profile portion 43 and an external tooth bottom portion 44 continuous therewith.
- the tooth profile shape of the outer teeth 34 from the opening end cross section 34a to the inner end cross section 34b is a dislocation tooth profile shape in which minus dislocation is applied to the illustrated tooth profile shape as will be described later.
- the tooth profile of the internal tooth 24 is the same in the direction of the tooth trace, and the convex tooth-shaped internal tooth end tooth portion 51, the internal tooth linear tooth portion 52 continuous thereto, and the concave curved internal tooth continuous therewith. It is prescribed
- tooth profile at the open end cross section of external teeth (Tooth profile at the open end cross section of external teeth)
- the tooth profiles of the internal teeth 24 and the external teeth 34 are formed by the following procedure.
- the internal tooth profile of the rigid internal gear is defined by the basic end tooth profile defined above, the linear tooth profile connected to the basic tooth profile, and an appropriate root tooth profile that avoids interference. Use a high-tooth composite tooth profile.
- Tooth profile at a position other than the open end cross section of the external teeth Considering the coning of the flexible external gear, the internal teeth of the rigid internal gear obtained at each cross section in the tooth trace direction of the external teeth of the flexible external gear.
- the dislocation tooth profile obtained by applying dislocation to the composite tooth profile adopted as the tooth profile of the open end cross section is flexible so that the relative trajectory of the external tooth shares the bottom of the open end cross section of the external tooth. It is adopted as a tooth profile at each position in the tooth trace direction from the opening end cross section of the external teeth of the external external gear to the inner end cross section thereof.
- the parameters ⁇ is [pi: from 0 (B point the bottom of the movement trajectory) range from up to (A point top of the movement locus).
- the curve AB is transformed into ⁇ times (similarity ratio ⁇ ⁇ 1) with the point B as the center of similarity to obtain a first similarity curve BC.
- the curve B 1 C 1 obtained by moving the first similar curve BC by ( ⁇ o ⁇ 1) mn in the end direction of the rigid internal gear 2 (minus direction on the y-axis in FIG. 4) is a temporary end tooth profile of the rigid internal gear. Adopted as the basic tooth addendum.
- the curve C 2 A 2 obtained by moving the second similar curve CA by ( ⁇ o ⁇ 1) mn in the end direction of the flexible external gear (the positive direction in the y-axis in FIG. 4) is given to the flexible external gear. Adopted as an end tooth profile (basic end tooth profile).
- an external tooth profile in the open end cross section 34a of the external tooth 34 is formed as follows. First, a straight line L 1 that intersects at a pressure angle ⁇ is drawn with respect to a curve C 2 A 2 that defines the tooth addendum of the flexible external gear, and an intersection D between the end point A 2 and the straight line L 1 in the curve C 2 A 2 . The curve portion A 2 D until is obtained.
- the external tooth addendum portion 41 is defined by the curved portion A 2 D. Further, the external tooth straight tooth portion 42 is defined by a straight line L 1 extending from the intersection D.
- the external tooth bottom surface defined by the external tooth straight tooth portion 42 and the predetermined external tooth bottom curve E so that the external tooth straight tooth portion 42 can secure a predetermined apex space with respect to the internal teeth 24.
- the external tooth root portion 43 is defined by a concave curve F connecting the portion 44.
- an intersection point G between the internal tooth linear tooth profile portion 52 and the curve B 1 C 1 is obtained, and the internal tooth addendum tooth profile portion using the curve portion B 1 G from the end point B 1 to the intersection point G in the curve B 1 C 1 . 51 is defined. Furthermore, the internal tooth linear tooth profile portion 52 and the internal tooth root portion 54 defined by the predetermined tooth root curve H so that a predetermined apex space is secured with respect to the external teeth. An internal tooth root portion 53 is defined by a concave curve I connecting the two.
- the tooth profile of the tooth base of both gears does not participate in meshing. Accordingly, the tooth forms (curves E, F, curves H, I) of the respective tooth bases do not interfere with the other tooth addendums 51, 52, 41, 42, and can be freely set.
- FIG. 6 shows an example of the tooth profile at the position of the open end cross section of both gears 2 and 3 as described above.
- the pressure angle ⁇ of the linear tooth profile is 9 degrees. It is desirable to avoid the part where the pressure angle of the tooth addendum is close to 0 degrees from the viewpoint of gear machining, and make the straight tooth form from the point where the pressure angle is around 6 degrees to 10 degrees and connect it to the tooth profile of the tooth root. That's fine.
- the tooth profile of the outer tooth 34 from the opening end cross section 34a to the inner end cross section 34b is a dislocation tooth profile set as follows. That is, the movement trajectory by rack approximation to the internal teeth 24 of the external teeth 34 obtained in the cross section perpendicular to the shaft leading to the inner end section 34b from the opening end section 34a is, relative to the movement locus M o obtained at the opening end section 34a, in contact at its bottom B 1, it has a dislocation tooth profile which has been subjected to negative dislocations external teeth tooth profile of the opening end section 34a.
- the bending amount of the flexible external gear 3 is a bending amount substantially proportional to the distance from the diaphragm on the long axis from the diaphragm side to the opening.
- the movement locus M o of the opening end cross section 34a interferes with the movement locus at other positions (the movement locus M 1 of the main cross section, the movement locus M i of the inner end cross section, etc.), and thus normal engagement cannot be maintained.
- FIG. 8 shows three types of movement trajectories M o , M 1a , and M ia of the open end cross section 34a, the main cross section 34c, and the inner end cross section 34b of the external teeth 34 that have been subjected to dislocation in this way. It is a thing. Movement locus M 1a, M ia is in contact at the positive excursion movement locus M o and the bottom B 1 of the opening end section 34a, yet except for some of the top approximates well trajectory. This shows the possibility that the tooth profile of the present invention derived from the movement trajectory can mesh over the entire tooth trace except for a part of the apex.
- FIG. 9A, FIG. 9B, and FIG. 9C show the appearance of the meshing of the tooth profile in the cross section perpendicular to each axis of the tooth profile of this example by rack approximation.
- FIG. 9A is an explanatory view showing the state of engagement in the opening end section 34a
- FIG. 9B is an explanatory view showing the state of engagement in the main section 34c
- FIG. 9C is an explanatory view showing the state of engagement in the inner end section 34b. It is.
- the movement trajectories of the tooth profiles in the respective cross sections are in good agreement with the movement trajectory portions reaching their bottoms, indicating the possibility of meshing over the entire tooth trace of the tooth profile of this example.
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Abstract
Description
(1)撓み係数κ=1の無偏位の主断面における可撓性外歯車の外歯の剛性内歯車の内歯に対する移動軌跡から、両歯車の歯の歯末歯形を規定するために用いるそれぞれの相似曲線歯形を求める。
(2)可撓性外歯車の外歯における歯筋方向の開口端断面の撓み係数κo(>1)と主断面の撓み係数κ(=1)との差に相当する転位を、内歯および外歯のそれぞれの相似曲線歯形に施し、これによって得られた各歯形をそれぞれ内歯および外歯の歯末歯形として採用する。
(3)可撓性外歯車の外歯の開口端断面の歯形として、上記のように規定した歯末歯形と、これに接続した直線歯形と、干渉を回避する適宜の歯元歯形から規定される高歯の複合歯形を用いる。
(4)剛性内歯車の内歯の歯形として、上記のように規定した歯末歯形と、これに接続した直線歯形と、干渉を回避する適宜の歯元歯形から規定される高歯の複合歯形を用いる。
(5)可撓性外歯車のコーニングを考慮し、可撓性外歯車の外歯における歯筋方向の各断面において得られる剛性内歯車の内歯に対する相対的な移動軌跡が、当該外歯の開口端断面の移動軌跡とその底部を共有するように、開口端断面の歯形として採用した複合歯形に対して転位を施した転位歯形を、可撓性外歯車の外歯の開口端断面からその内端断面までの間の歯筋方向における各位置の歯形として採用する。
図1は本発明の対象である波動歯車装置の正面図であり、図2(a)~(c)はその可撓性外歯車の開口部を楕円状に撓ませた状況を含軸断面で示す断面図であり、図2(a)は変形前の状態、図2(b)は変形後における楕円状曲線の長軸を含む断面、図2(c)は変形後における楕円状曲線の短軸を含む断面をそれぞれ示してある。なお、図2(a)~(c)において実線はカップ状の可撓性外歯車を示し、破線はシルクハット状の可撓性外歯車を示す。
x=0.5mn(θ-κsinθ) (1)
y=κmncosθ
x=0.5(θ-κsinθ) (1A)
y=κcosθ
歯形形状の形成方法の説明に先立って、図6を参照して本発明による両歯車2、3の歯形の例を説明する。まず、外歯34における開口端断面34aの歯形形状は、凸曲線状の外歯歯末歯形部分41、これに連続する外歯直線歯形部分42、これに連続する凹曲線状の外歯歯元歯形部分43、および、これに連続する外歯歯底部分44によって規定されている。外歯34における開口端断面34aから内端断面34bに至る部分の歯形形状は、図示の歯形形状に後述のようにマイナス転位を施した転位歯形形状となっている。
(外歯の開口端断面における歯形形状)
本発明では、上記の内歯24および外歯34の歯形は次の手順で形成している。
(1)相似曲線歯形
撓み係数κ=1の無偏位の主断面における可撓性外歯車の外歯の剛性内歯車の内歯に対する移動軌跡から、両歯車の歯の歯末歯形を規定するために用いるそれぞれの相似曲線歯形を求める。
(2)基本歯末歯形
可撓性外歯車の外歯における歯筋方向の開口端断面の撓み係数κo(>1)と主断面の撓み係数κ(=1)との差に相当する転位を、内歯および外歯のそれぞれの相似曲線歯形に施し、これによって得られた各歯形をそれぞれ内歯および外歯の基本歯末歯形として採用する。
(3)外歯の開口端断面の歯形形状
可撓性外歯車の外歯の開口端断面の歯形として、上記のように規定した歯末歯形と、これに接続した直線歯形と、干渉を回避する適宜の歯元歯形から規定される高歯の複合歯形を用いる。
(4)内歯の歯形形状
剛性内歯車の内歯の歯形として、上記のように規定した基本歯末歯形と、これに接続した直線歯形と、干渉を回避する適宜の歯元歯形から規定される高歯の複合歯形を用いる。
(5)外歯における開口端断面以外の位置における歯形形状
可撓性外歯車のコーニングを考慮し、可撓性外歯車の外歯における歯筋方向の各断面において得られる剛性内歯車の内歯に対する相対的な移動軌跡が、当該外歯の開口端断面の移動軌跡とその底部を共有するように、開口端断面の歯形として採用した複合歯形に対して転位を施した転位歯形を、可撓性外歯車の外歯の開口端断面からその内端断面までの間の歯筋方向における各位置の歯形として採用する。
図4、図5において、符号M1は主断面34c(無偏位断面:κ=1)における外歯34の移動軌跡である。この移動軌跡M1において、パラメーターθがπ(B点:移動軌跡の底部)から0(A点:移動軌跡の頂部)までの範囲を取る。この曲線ABを、B点を相似の中心としてλ倍(相似比λ<1)に相似変換して第1相似曲線BCを得る。
剛性内歯車の基本歯末歯形を形成するために用いる曲線の基本式:
xCa=0.5{(1-λ)π+λ(θ-sinθ)}
yCa=λ(1+cosθ)-κo (0≦θ≦π) (2)
可撓性外歯車の基本歯末歯形を形成するために用いる曲線の基本式:
xFa=0.5(1-λ)(π-θ+sinθ)
yFa=(λ-1)(1+cosθ)+κo (0≦θ≦π) (3)
次に、基本歯末歯形(曲線C2A2)を用いて、次のように外歯34の開口端断面34aにおける外歯歯形を形成する。まず、可撓性外歯車の歯末歯形を規定する曲線C2A2に対して圧力角αで交わる直線L1を引き、曲線C2A2における端点A2から直線L1との交点Dまでの間の曲線部分A2Dを求める。この曲線部分A2Dによって外歯歯末歯形部分41を規定する。また、交点Dから延びている直線L1によって外歯直線歯形部分42を規定する。さらに、外歯直線歯形部分42が内歯24に対して所定の頂隙が確保されるように、当該外歯直線歯形部分42と所定の外歯歯底曲線Eによって規定される外歯歯底部分44との間を繋ぐ凹曲線Fによって外歯歯元歯形部分43を規定する。
次に、図5に示すように、外歯34の開口端断面34aにおいて、上記のように形成した外歯歯形が移動軌跡Moに沿って移動した場合において、当該移動軌跡Moの頂点A2を過ぎて内歯側に最大に食い込む位置を求める。すなわち、外歯歯形が移動軌跡Moの頂部のループにおける圧力角度が0度の点A3に移動したときの位置を求める。この位置を示す直線L2によって内歯直線歯形部分52を規定する。また、内歯直線歯形部分52と曲線B1C1との交点Gを求め、当該曲線B1C1における端点B1から交点Gまでの曲線部分B1Gを用いて内歯歯末歯形部分51を規定する。さらに、内歯直線歯形部分52が外歯に対して所定の頂隙が確保されるように、当該内歯直線歯形部分52と所定の歯底曲線Hによって規定される内歯歯底部分54との間を繋ぐ凹曲線Iによって内歯歯元歯形部分53を規定する。
次に、外歯34における開口端断面34aから内端断面34bに至る部分の歯形形状は次のようにして設定した転位歯形となっている。すなわち、開口端断面34aから内端断面34bに至る各軸直角断面において得られる外歯34の内歯24に対するラック近似による移動軌跡が、開口端断面34aにおいて得られる移動軌跡Moに対して、その底部B1で接するように、開口端断面34aの外歯歯形にマイナス転位を施した転位歯形形状となっている。
h=κ-κo (4)
図7にはこの場合の外歯の形状を示している。
Claims (2)
- 円環状の剛性内歯車と、この内側に同軸状に配置された可撓性外歯車と、この内側に嵌めた波動発生器とを有し、
前記可撓性外歯車は、可撓性の円筒状胴部と、この円筒状胴部の後端から半径方向に延びているダイヤフラムと、前記円筒状胴部の前端開口の側の外周面部分に形成された外歯とを備えており、
前記可撓性外歯車の外歯は前記波動発生器によって楕円状に撓められ、その楕円状曲線の長軸方向の両端部において前記剛性内歯車の内歯に噛み合っており、
楕円状に撓められた前記可撓性外歯車の前記外歯は、その歯筋方向に沿って、前記ダイヤフラムの側から前記前端開口の側に向けて、前記ダイヤフラムからの距離にほぼ比例して撓み量が増加しており、
前記可撓性外歯車の外歯および前記剛性内歯車の内歯は共にモジュールmの平歯車であり、
前記可撓性外歯車の歯数は、nを正の整数として、前記剛性内歯車の歯数より2n枚少ない歯数に設定されており、
前記外歯の歯筋方向における任意の位置の軸直角断面において、当該外歯の楕円状リム中立線における長軸位置における当該外歯が楕円状に撓む前のリム中立円に対する半径方向の撓み量は、κを撓み係数として、κmnであり、
前記可撓性外歯車の前記外歯の歯筋方向において、前記前端開口の側の端の軸直角断面を開口端断面とし、前記ダイヤフラムの側の端の軸直角断面を内端断面とし、前記開口端断面から前記内端断面までの間の任意の位置に定めた軸直角断面を主断面とすると、
前記主断面の前記撓み係数はκ=1であり、前記開口端断面の前記撓み係数はκ=κo>1であり、前記内端断面の前記撓み係数はκ=κi<1であり、
前記外歯の前記開口端断面上における開口端歯形形状は、凸曲線状の外歯歯末歯形部分、これに連続する外歯直線歯形部分、これに連続する凹曲線状の外歯歯元歯形部分、および、これに連続する外歯歯底部分によって規定されており、当該開口端断面から前記内端断面に至る部分の歯形形状は、前記開口端歯形形状にマイナス転位を施した転位歯形形状となっており、
前記内歯の軸直角断面上における歯形形状は、凸曲線状の内歯歯末歯形部分、これに連続する内歯直線歯形部分、これに連続する凹曲線状の内歯歯元歯形部分、および、これに連続する内歯歯底部分によって規定されており、
前記外歯および前記内歯の噛み合いをラック噛み合いで近似し、前記外歯の歯筋方向における各軸直角断面において、前記波動発生器の回転に伴う前記可撓性外歯車の外歯の前記剛性内歯車の内歯に対する移動軌跡を求め、
前記主断面において得られた前記移動軌跡M1における頂部の点Aから次の底部の点Bに至る曲線部分ABを、相似比λ<1として、点Bを相似の中心としてλ倍に相似変換して、第1相似曲線BCを求め、当該第1相似曲線BCを前記剛性内歯車の歯末方向に(κo-1)mnだけ移動した曲線B1C1を求め、
前記第1相似曲線BCの端点Cを中心として当該第1相似曲線BCを180度回転することにより得られた曲線を、当該端点Cを相似の中心として(1-λ)/λ倍に相似変換して第2相似曲線CAを求め、当該第2相似曲線CAを前記可撓性外歯車の歯末方向に(κo-1)mnだけ移動した曲線C2A2を求め、
前記曲線C2A2に対して圧力角αで交わる直線L1を引き、前記曲線C2A2における端点A2から直線L1との交点Dまでの間の曲線部分A2Dを求め、
前記曲線部分A2Dによって前記外歯歯末歯形部分を規定し、
前記交点Dから延びている前記直線L1によって、前記外歯直線歯形部分を規定し、
前記外歯直線歯形部分が前記内歯に対して所定の頂隙が確保されるように、当該外歯直線歯形部分と所定の外歯歯底曲線によって規定される前記外歯歯底部分との間を繋ぐ凹曲線によって前記外歯歯元歯形部分を規定し、
前記外歯直線歯形部分を備えた前記外歯が前記開口端断面において得られる前記移動軌跡Moに沿って移動した場合において、当該移動軌跡Moの頂点を過ぎて前記内歯に最大に食い込む位置を求め、当該位置にある前記外歯直線歯形部分を用いて前記内歯直線歯形部分を規定し、
前記内歯直線歯形部分と前記曲線B1C1との交点Gを求め、当該曲線B1C1における端点B1から交点Gまでの曲線部分B1Gを用いて前記内歯歯末歯形部分を規定し、
前記内歯直線歯形部分が前記外歯に対して所定の頂隙が確保されるように、当該内歯直線歯形部分と所定の歯底曲線によって規定される前記内歯歯底部分との間を繋ぐ凹曲線によって前記内歯歯元歯形部分を規定し、
前記外歯における前記開口端断面から前記内端断面に至る部分の歯形形状は、前記内端断面から前記開口端断面に至る各軸直角断面において得られる前記移動軌跡が前記開口端断面において得られる前記移動軌跡Moに対してそれらの底部の点Bで接するように、前記開口端歯形形状にマイナス転位を施した転位歯形形状となっていることを特徴とする波動歯車装置。 - 請求項1において、
前記外歯に施す転位の量はhmnであり、
h=κ-κoであることを特徴とする波動歯車装置。
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CN105822725A (zh) * | 2015-01-06 | 2016-08-03 | 上银科技股份有限公司 | 可提升传动精度的谐波减速机 |
CN107835906A (zh) * | 2015-07-07 | 2018-03-23 | 谐波传动***有限公司 | 具有波动齿轮装置的旋转传递机构 |
CN107835906B (zh) * | 2015-07-07 | 2020-05-05 | 谐波传动***有限公司 | 具有波动齿轮装置的旋转传递机构 |
CN112119243A (zh) * | 2018-05-14 | 2020-12-22 | 谐波传动***有限公司 | 波动齿轮装置 |
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US20120285283A1 (en) | 2012-11-15 |
JP5165120B2 (ja) | 2013-03-21 |
JPWO2012153363A1 (ja) | 2014-07-28 |
DE112011105127T5 (de) | 2014-02-13 |
US8661940B2 (en) | 2014-03-04 |
DE112011105127B4 (de) | 2017-01-19 |
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