WO2017094195A1 - 2応力分離の波動歯車装置 - Google Patents
2応力分離の波動歯車装置 Download PDFInfo
- Publication number
- WO2017094195A1 WO2017094195A1 PCT/JP2015/084198 JP2015084198W WO2017094195A1 WO 2017094195 A1 WO2017094195 A1 WO 2017094195A1 JP 2015084198 W JP2015084198 W JP 2015084198W WO 2017094195 A1 WO2017094195 A1 WO 2017094195A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- tooth
- gear
- section
- external
- tooth profile
- Prior art date
Links
Images
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
- F16H49/00—Other gearings
- F16H49/001—Wave gearings, e.g. harmonic drive transmissions
-
- 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
- F16H1/00—Toothed gearings for conveying rotary motion
- F16H1/28—Toothed gearings for conveying rotary motion with gears having orbital motion
- F16H1/32—Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear
-
- 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
-
- 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
-
- 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
- F16H3/00—Toothed gearings for conveying rotary motion with variable gear ratio or for reversing rotary motion
- F16H3/44—Toothed gearings for conveying rotary motion with variable gear ratio or for reversing rotary motion using gears having orbital motion
- F16H3/70—Toothed gearings for conveying rotary motion with variable gear ratio or for reversing rotary motion using gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear
Definitions
- the present invention relates to a wave gear device in which a flexible external gear is bent elliptically by a wave generator and partially meshes with a rigid internal gear. More specifically, the transmission torque capacity is improved by avoiding the superposition of bending stress caused by bending and tensile stress caused by load torque due to meshing with the internal gear at both ends of the major axis of the elliptical shape of the external gear.
- the present invention relates to the wave gear device shown.
- a wave gear device has a rigid internal gear, a flexible external gear disposed coaxially inside the rigid gear, and a wave generator fitted inside the rigid gear.
- the flat wave gear device includes an external gear having external teeth formed on the outer peripheral surface of a flexible cylinder.
- the external gear of the cup-type and top-hat type wave gear device includes a flexible cylindrical body, a diaphragm extending radially from the rear end of the cylindrical body, and a front end opening of the cylindrical body. And external teeth formed on the outer peripheral surface portion.
- a circular external gear is bent elliptically by a wave generator, and both end portions in the major axis direction of the elliptically bent external gear mesh with the internal gear.
- 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.
- the flexible external gear is bent from the perfect circle state to an ellipse by the wave generator, so that bending stress is generated at both ends of the long axis of the elliptical shape due to the bending. Further, since the external gear bent in an elliptical shape meshes with the internal gear at both end portions of the long axis, tensile stress is generated due to the load torque transmitted through the meshing portion. For this reason, a large stress acts on both end portions of the long axis of the external gear (portion rim portion) by superimposing both stresses.
- the maximum amount of bending in the radial direction when the external gear is deformed into an ellipse (the amount of bending in the radial direction at the long axis position) is standard. Is set to a deflection amount ⁇ mn ( ⁇ ⁇ 1) smaller than the normal deflection amount mn.
- n is a positive integer
- the number of teeth difference between both gears is 2n.
- m is a module of both gears.
- the case of the radial deflection amount ⁇ mn ( ⁇ ⁇ 1) is called negative deflection, and the case of the radial deflection amount ⁇ mn ( ⁇ > 1) larger than mn is called positive deflection.
- the object of the present invention is to superimpose the bending stress and tensile stress generated at both ends of the long axis of the external gear, and to determine the amount of bending of the external gear (the average amount of bending at each position in the tooth trace direction) from the normal amount of bending. It is another object of the present invention to provide a wave gear device that can be avoided without reducing the size.
- the wave gear device of the present invention is A rigid internal gear, a flexible external gear disposed coaxially on the inside thereof, and a wave generator fitted on the inside,
- the external gear is bent elliptically by the wave generator, and the external teeth of the external gear bent elliptically mesh with the internal teeth of the internal gear in the vicinity of both end portions in the major axis direction.
- Both the internal gear and the external gear before being deformed into an elliptical shape are spur gears of the module m,
- the number of teeth of the external gear is 2n less than the number of teeth of the internal gear, where n is a positive integer,
- n is a positive integer
- the tooth profile of the tooth base of each of the internal gear and the external gear is set to an arbitrary tooth profile that does not interfere with the tooth profile of the end of the
- the tooth profile of the end of the internal gear is defined by the above-described formula a in each axis perpendicular to the tooth trace direction, and the tooth shape of the end of the external gear. Is defined by the above-mentioned formula b in each cross section perpendicular to the tooth trace direction.
- the external gear includes a flexible cylindrical body and a diaphragm extending in the radial direction from the rear end of the cylindrical body.
- the outer teeth are formed on the outer peripheral surface portion of the cylindrical body on the front end opening side, and the amount of bending of the outer teeth is the outer teeth on the diaphragm side along the tooth trace direction.
- the main cross section changes in proportion to the distance from the diaphragm from the inner end portion toward the outer tooth opening end portion on the front end opening side, and the main cross section is the outer tooth opening end portion and the outer teeth in the outer teeth. The center position in the direction of the tooth trace between the inner ends.
- the tooth profile of the external gear in the main cross section is defined by the addendum tooth profile defined by the formula b.
- the tooth profile of each axis perpendicular section other than the main section in the tooth trace direction of the external gear is a dislocation tooth profile in which the dislocation corresponding to the deflection amount of each axis perpendicular section is applied to the tooth profile of the main section.
- the tooth profile in each axis perpendicular section in the tooth trace direction from the main section of the external gear to the end of the external tooth opening is the top of the movement locus of ⁇ > 1 drawn by the tooth profile in each axis perpendicular section.
- the flat type wave gear device does not employ a negative deflection with a deviation coefficient ⁇ ⁇ 1, and the cup type or top hat type wave gear device is displaced throughout the tooth trace direction. It is possible to improve the transmission torque capacity of the wave gear device without adopting negative deflection of coefficient ⁇ ⁇ 1.
- FIG. 1 It is a schematic front view which shows an example of the wave gear apparatus to which this invention is applied. It is explanatory drawing which shows the bending condition of the external gear of a cup shape and a top hat shape, (a) shows the state before a deformation
- FIG. 1 is a front view of a wave gear device that is an object of the present invention.
- 2 (a) to 2 (c) are cross-sectional views showing a state in which the opening of the flexible external gear is bent in an elliptical shape
- FIG. 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. 2C illustrates a cross section including the minor axis of the elliptic curve after deformation.
- the solid lines indicate the diaphragm and boss portions of the cup-shaped flexible external gear
- the broken lines indicate the diaphragm and boss portions of 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 having an elliptical profile fitted on the inner side.
- Generator 4 The internal gear 2 and the external gear 3 before deformation are spur gears of the module m.
- the difference in the number of teeth between the internal gear 2 and the external gear 3 is 2n (n is a positive integer), and the circular external gear 3 of the wave gear device 1 is bent elliptically by a wave generator 4 having an elliptical contour. ing.
- the external teeth 34 of the external gear 3 (hereinafter sometimes simply referred to as “teeth 34”) are internal gears 2.
- the inner teeth 24 (hereinafter sometimes simply referred to as “teeth 24”).
- the external gear 3 includes a flexible cylindrical body 31, a diaphragm 32 that extends in a radial direction continuously to a rear end 31 b that is one end of the cylindrical body 31, and a boss that is continuous to the diaphragm 32. 33 and external teeth 34 formed on the outer peripheral surface portion on the side of the front end opening 31a which is the other end of the cylindrical body 31.
- the wave generator 4 having an elliptical contour is fitted into the inner peripheral surface portion of the outer tooth forming portion of the cylindrical body portion 31.
- the wave generator 4 gradually increases the amount of bending outward or inward in the radial direction from the diaphragm-side rear end 31b toward the front end opening 31a.
- FIG. 2B in the cross section including the major axis La (see FIG. 1) of the elliptical curve, the amount of outward deflection gradually increases in proportion to the distance from the rear end 31b to the front end opening 31a.
- FIG. 2C in the cross section including the minor axis Lb (see FIG.
- the amount of inward bending gradually increases in proportion to the distance from the rear end 31b to the front end opening 31a.
- the outer teeth 34 formed on the outer peripheral surface portion on the front end opening 31a side are also substantially proportional to the distance from the rear end 31b from the outer tooth inner end portion 34b toward the outer tooth opening end portion 34a in the tooth trace direction. As a result, the amount of deflection gradually increases.
- the circle passing through the center in the thickness direction of the root rim of the external tooth 34 before being bent into an elliptical shape in the axially perpendicular section at an arbitrary position in the direction of the tooth trace of the external tooth 34 is a rim neutral circle.
- an elliptical curve passing through the center in the thickness direction of the root rim after being bent in an elliptical shape is referred to as a rim neutral curve.
- the amount of deflection w in the major axis direction with respect to the rim neutral circle at the major axis position of the elliptical rim neutral curve is represented by 2 ⁇ mn, where ⁇ (a real number including 1) is a deviation coefficient.
- the number of teeth of the external teeth 34 of the external gear 3 is Z F
- the number of teeth of the internal teeth 24 of the internal gear 2 is Z C
- a tooth profile that provides a greater deflection amount ( ⁇ > 1) than the normal deflection amount is referred to as a positive deflection tooth profile.
- FIG. 3A is a diagram showing a movement trajectory of the teeth 34 of the external gear 3 with respect to the teeth 24 of the internal gear 2 obtained when the relative motion of both the gears 2 and 3 of the wave gear device 1 is approximated by a rack.
- the x axis indicates the translation direction of the rack
- the y axis indicates a direction perpendicular thereto.
- the origin of the y axis is the average position of the amplitude of the movement trajectory.
- the curve Ma is a movement locus obtained at the outer tooth opening end portion 34a
- the curve Mb is a movement locus obtained at the outer tooth inner end portion 34b.
- a curved line Mc is a movement locus obtained at an arbitrary position between the external tooth opening end portion 34a and the external tooth inner end portion 34b in the tooth trace direction, in this example, the central portion in the tooth trace direction.
- the cross section perpendicular to the axis at this position is referred to as a main cross section 34c.
- the movement locus of the teeth 34 of the external gear 3 with respect to the teeth 24 of the internal gear 2 is expressed by the following equation.
- a first curve AB in which the parameter ⁇ is in the range from ⁇ to 0 is taken in the movement locus Mc on the main cross section 34c in FIG. 3A.
- the first curve AB is transformed into ⁇ times (0 ⁇ ⁇ 1) with the point B as the center of similarity to obtain a first similarity curve BC (see FIG. 4A).
- the first similarity curve BC is employed as the tooth addendum of the internal tooth 24 of the rigid internal gear 2.
- ⁇ 0.5 is set.
- FIG. 4A shows a first similarity curve BC given by Equation 2A.
- ⁇ Tooth profile of internal gear teeth> (Formula 2A)
- x Ca 0.25 ( ⁇ + ⁇ sin ⁇ )
- y Ca 0.5 (-1 + cos ⁇ )
- the first similarity curve BC is rotated 180 degrees around the point C, which is the end point opposite to the point B in the first similarity curve BC, to obtain a curve obtained by similarity conversion of (1 ⁇ ) times.
- FIG. 4B shows a curve AD given by Equation 3B.
- the tooth profile of the tooth bases of both gears 2 and 3 may be any tooth profile that does not interfere with the tooth profile of the end of the mating gear.
- the tooth profile of the tooth base of the internal gear 2 has a maximum tooth thickness of the internal gear 2 that is created by the internal gear 2 while the end tooth profile of the external gear 3 moves from the top to the bottom of the movement locus Mc. It can be determined as the root tooth profile.
- This root tooth profile is given by the following equation 4.
- FIG. 4D shows the tooth profile curve of the tooth root given by Equation 5.
- x Fa ⁇ / 2 ⁇ / 2 ⁇ 0.25 ( ⁇ + sin ⁇ cos ( ⁇ / 2)
- y Fa ⁇ 0.5 (1-cos ⁇ )
- FIG. 5 shows an external tooth profile 34 ⁇ / b> C and an internal tooth profile 24 ⁇ / b> C defined by combining the individual tooth profiles in the main cross section 34 c of the external gear and the internal gear.
- the tooth profile of the cross section perpendicular to each axis in the tooth trace direction of the internal gear 2 is the same as the tooth profile at the position of the main cross section 34c set as described above. It is.
- the tooth profile of each axis perpendicular section other than the main section 34c in the tooth trace direction of the external gear 3 is a dislocation tooth profile in which the dislocation corresponding to the deflection amount of each axis perpendicular section is applied to the tooth profile of the main section 34c.
- the tooth profile shape of each cross section in the tooth trace direction other than the main cross section in the external gear 3 is set as follows. As shown in FIG. 3B, in a cross section perpendicular to the axis of the deviation coefficient ⁇ > 1 from the main cross section 34c to the external tooth opening end 34a, the movement locus of the external gear 3 teeth 34 by rack approximation to the internal gear 2 teeth 24.
- FIG. 6 is a graph showing an example of the amount of dislocation near the main cross section of the external gear 3 in the tooth trace direction.
- the horizontal axis indicates the distance from the central portion (main cross section 34c) of the external teeth 34 in the tooth trace direction
- the vertical axis indicates the dislocation amount h.
- the dislocation amount h is indicated by dislocation lines L1 and L2 having the same inclination.
- the dislocation straight line L1 indicates the amount of dislocation from the main cross section 34c to the external tooth opening end 34a
- the dislocation straight line L2 indicates the amount of dislocation from the main cross section 34c to the external tooth inner end 34b.
- FIG. 6 also shows a quartic curve C1 having the main cross section 34c as a vertex and in contact with the dislocation lines L1 and L2.
- a substantially flat portion is formed at the central portion of the external teeth 34 including the main cross section 34c in the tooth trace direction.
- FIG. 7 is an explanatory diagram showing tooth profile contours in the tooth trace direction of the internal teeth 24 and the external teeth 34 that have been displaced as described above.
- the tooth profile profile of the external teeth 34 in the tooth trace direction is defined by the above-mentioned quartic curve C1 in the central portion of the tooth trace direction including the main cross section 34c, and between this center portion and the external tooth opening end 34a.
- the portion is defined by the dislocation straight line L1
- the portion between the central portion and the outer tooth inner end 34b is defined by the dislocation straight line L2.
- FIG. 8 to 10 are explanatory views showing the appearance of the meshing between the external teeth 34 and the internal teeth 24 having the tooth profile as described above by rack approximation.
- FIG. 8 shows the engagement of the external teeth 34 with the internal teeth 24 at the external tooth opening end 34 a of the external teeth 34.
- FIG. 9A shows the same engagement in the main cross section 34c of the external teeth 34, and
- FIG. 9B is a partially enlarged view thereof.
- FIG. 10 shows the same engagement at the external tooth inner end 34b of the external tooth 34.
- the flat wave gear device since the separation of two stresses (bending stress and tensile stress) is realized, the flat wave gear device does not employ a negative deflection with a deviation coefficient ⁇ ⁇ 1, In the top hat type wave gear device, it is possible to improve the transmission torque capacity of the wave gear device without adopting a negative displacement deflection with a displacement coefficient ⁇ ⁇ 1 throughout the tooth trace direction.
Landscapes
- Engineering & Computer Science (AREA)
- General Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Retarders (AREA)
- Gears, Cams (AREA)
Abstract
Description
剛性の内歯車と、この内側に同軸状に配置された可撓性の外歯車と、この内側に嵌めた波動発生器とを有し、
前記外歯車は前記波動発生器によって楕円状に撓められ、楕円状に撓められた前記外歯車の外歯は、その長軸方向の両端部分の近傍において前記内歯車の内歯にかみ合っており、
前記内歯車および、楕円状に変形する前の前記外歯車は共にモジュールmの平歯車であり、
前記外歯車の歯数は、nを正の整数とすると、前記内歯車の歯数より2n枚少なく、
前記外歯の歯筋方向の所定の位置の軸直角断面における前記外歯車の楕円状のリム中立曲線における長軸位置において、その撓み前のリム中立円に対する半径方向撓み量は、κを偏位係数とすると、2κmnであり、前記外歯の歯筋方向の所定の位置に設定した軸直角断面を主断面とすると、当該主断面は偏位係数κ=1の無偏位撓みの断面であり、
前記主断面において、前記外歯車の前記内歯車に対する歯のかみ合いをラックかみ合いとみなした場合に得られる前記外歯車の歯の前記内歯車の歯に対するκ=1の移動軌跡に基づいて、
前記内歯車の歯末の歯形が次式aで規定され、
(式a)
xCa=0.25mn(π+θ-sinθ)
yCa=0.5mn(-1+cosθ)
但し、0≦θ≦π
前記外歯車の歯末の歯形が次式bで規定されており、
(式b)
xFa=0.25mn(π-θ+sinθ-εcos(θ/2))
yFa=0.5mn(1―cosθ)
但し、0<ε≦0.1
0≦θ≦π
前記内歯車および前記外歯車のそれぞれの歯元の歯形は、相手歯車の前記歯末の歯形と干渉しない任意の歯形に設定されていることを特徴としている。
図1は本発明の対象である波動歯車装置の正面図である。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のダイヤフラムおよびボスの部分を示し、破線はシルクハット状の可撓性外歯車のダイヤフラムおよびボスの部分を示す。
xFa=0.5mn(θ-κsinθ)
yFa=κmncosθ
(式1)
xFa=0.5(θ-κsinθ)
yFa=κcosθ
主断面34c(偏位係数κ=1)における内歯24のラック近似による歯末の歯形について説明する。主断面34cにおける内歯24の歯末歯形を規定するために、外歯34における主断面34cにおいて得られる移動軌跡Mcを利用する。
(式2)
xCa=0.5{(1-λ)π+λ(θ-κsinθ)}
yCa=κ{λ(1+cosθ)-1}
但し、0≦θ≦π
<内歯車の歯末の歯形>
(式2A)
xCa=0.25(π+θ-sinθ)
yCa=0.5(-1+cosθ)
但し、0≦θ≦π
(式3)
x(θ)=0.5{(1-λ)(π-θ+κsinθ)}
y(θ)=κ{(λ-1)(1-cosθ)}
但し、0≦θ≦π
(式3A)
x(θ)=0.25(π-θ+sinθ)
y(θ)=0.5(1-cosθ)
但し、0≦θ≦π
ここで、外歯34の歯末の歯形を次の式3Bによって規定する。図4Bには式3Bで与えられる曲線ADを示してある。
xFa=0.25(π-θ+sinθ-εcos(θ/2))
yFa=0.5(1-cosθ)
但し、0<ε≦0.1
0≦θ≦π
両歯車2、3の歯元の歯形は、相手歯車の歯末の歯形と干渉しない任意の歯形とすればよい。例えば、内歯車2の歯元の歯形は、外歯車3の歯末歯形が移動軌跡Mcの頂点から底点まで移動する間に、内歯車2に創成する曲線を、内歯車2の最大歯厚の歯元歯形として定めることができる。この歯元歯形は、次の式4で与えられる。図4Cには、式4で与えられる歯元の歯形曲線を示してある。
(式4)
xCa=0.25(π-θ+sinθ)
yCa=0.5(1-cosθ)
但し、0≦θ≦π
(式5)
xFa=π/2-ε/2-0.25(π-θ+sinθ-εcos(θ/2))
yFa=-0.5(1-cosθ)
但し、0<ε≦0.1
0≦θ≦π
ここで、フラット型波動歯車装置においては、内歯車2および外歯車3の歯筋方向の各軸直角断面の歯形は上記のように設定された主断面34cにおける歯形と同一である。
h=λ(κ)(κ-1)
(式A)
xFa=0.5(θ―κsinθ)
yFa=κcosθ
(式B)
tanακ=0.5(1-κcosθκ)/κsinθκ
(式C)
tanα1=0.5(1-cosθ1)/sinθ1
(式D)
(1-κcosθκ)/κsinθκ - (1-cosθ1)/sinθ1 =0
(式E)
θκ - κsinθκ - θ1+sinθ1=0
(式F)
h=κcosθκ-cosθ1
h=κ-1
Claims (6)
- 剛性の内歯車と、この内側に同軸状に配置された可撓性の外歯車と、この内側に嵌めた波動発生器とを有し、
前記外歯車は前記波動発生器によって楕円状に撓められ、楕円状に撓められた前記外歯車の外歯は、その長軸方向の両端部分の近傍において前記内歯車の内歯にかみ合っており、
前記内歯車および、楕円状に変形する前の前記外歯車は共にモジュールmの平歯車であり、
前記外歯車の歯数は、nを正の整数とすると、前記内歯車の歯数より2n枚少なく、
前記外歯の歯筋方向の所定の位置の軸直角断面における前記外歯車の楕円状のリム中立曲線における長軸位置において、その撓み前のリム中立円に対する半径方向撓み量は、κを偏位係数とすると、2κmnであり、前記外歯の歯筋方向の所定の位置に設定した軸直角断面を主断面とすると、当該主断面の偏位係数κ=1であり、その半径方向撓み量はmnであり、
前記主断面において、前記外歯車の前記内歯車に対する歯のかみ合いをラックかみ合いとみなした場合に得られる前記外歯車の歯の前記内歯車の歯に対するκ=1の移動軌跡に基づいて、
前記内歯車の歯末の歯形が次の式a
(式a)
xCa=0.25mn(π+θ-sinθ)
yCa=0.5mn(-1+cosθ)
但し、0 ≦ θ ≦ π
で与えられており、
前記外歯車の歯末の歯形が次の式b
(式b)
xFa=0.25mn(π-θ+sinθ-εcos(θ/2))
yFa=0.5mn(1―cosθ)
但し、0 < ε ≦ 0.1
0 ≦ θ ≦ π
で与えられており、
前記内歯車および前記外歯車の歯元の歯形は、相手歯車の歯末の歯形と干渉しない任意の歯形に設定されている波動歯車装置。 - 請求項1において、
前記内歯車の歯元の最大歯厚の歯形は次の式c
(式c)
xCa=0.25mn(π-θ+sinθ)
yCa=0.5mn(1-cosθ)
但し、0 ≦ θ ≦ π
で与えられており、
前記外歯車の歯元の最大歯厚の歯形は次の式d
(式d)
xFa=mn(π/2-ε/2―0.25(π-θ+sinθ-εcos(θ/2)))
yFa=0.5mn(1-cosθ)
但し、0 < ε ≦ 0.1
0 ≦ θ ≦ π
で与えられている波動歯車装置。 - 請求項1において、
前記内歯車の歯末の歯形が、その歯筋方向の各軸直角断面において、前記の式aによって規定され、
前記外歯車の歯末の歯形が、その歯筋方向の各軸直角断面において、前記の式bによって規定されている波動歯車装置。 - 請求項1において、
前記外歯車は、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を備え、前記円筒状胴部の前端開口の側の外周面部分に、前記外歯が形成されており、
前記外歯の撓み量は、その歯筋方向に沿って、前記ダイヤフラムの側の外歯内端部から前記前端開口の側の外歯開口端部に向けて、前記ダイヤフラムからの距離に比例して変化しており、
前記主断面は、前記外歯における前記外歯開口端部と前記外歯内端部の間の歯筋方向の中央の位置であり、
前記主断面における前記外歯車の歯形は、前記の式bによって規定される歯末の歯形を含み、
前記外歯車における歯筋方向の前記主断面以外の各軸直角断面の歯形は、前記主断面の歯形に対して各軸直角断面の前記撓み量に応じた転位が施された転位歯形であり、
前記外歯車の前記主断面から前記外歯開口端部に至る歯筋方向の各軸直角断面の歯形は、各軸直角断面における歯形が描くκ>1の前記移動軌跡の頂部が、前記主断面におけるκ=1の前記移動軌跡の頂部に接するように、前記主断面の歯形に転位を施すことによって得られたものであり、
前記外歯の前記主断面から前記外歯内端部に至る歯筋方向の各軸直角断面の歯形は、各軸直角断面における歯形が描くκ<1の前記移動軌跡の底部が前記主断面におけるκ=1の前記移動軌跡の底部に接するように、前記主断面の歯形に転位を施すことによって得られたものである波動歯車装置。 - 請求項4において、
前記外歯車の前記主断面から前記外歯開口端部に至る歯筋方向の各軸直角断面の歯形は、前記主断面の歯形に対して、次式で与えられる転位が施されており、
h=κcosθκ-cosθ1
ここに、θκ、θ1は連立方程式
(1-κcosθκ)/κsinθκ - (1-cosθ1)/sinθ1 =0
θκ - κsinθκ - θ1+sinθ1=0
の解である波動歯車装置。 - 請求項5において、
前記外歯車の前記主断面から前記外歯内端部に至る歯筋方向の各軸直角断面の歯形は、前記主断面の歯形に対して、次式
h=κ-1
で与えられる転位が施されている波動歯車装置。
Priority Applications (7)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
DE112015000726.1T DE112015000726T5 (de) | 2015-12-04 | 2015-12-04 | Zwei-Spannungs-Trennungs-Verformungswellgetriebe |
US15/112,467 US10883589B2 (en) | 2015-12-04 | 2015-12-04 | Two stress-separation strain wave gearing |
JP2016543095A JP6104474B1 (ja) | 2015-12-04 | 2015-12-04 | 2応力分離の波動歯車装置 |
PCT/JP2015/084198 WO2017094195A1 (ja) | 2015-12-04 | 2015-12-04 | 2応力分離の波動歯車装置 |
KR1020167021603A KR101758607B1 (ko) | 2015-12-04 | 2015-12-04 | 2응력분리의 파동기어장치 |
CN201580004422.9A CN108291611B (zh) | 2015-12-04 | 2015-12-04 | 2应力分离的波动齿轮装置 |
TW105121770A TWI648486B (zh) | 2015-12-04 | 2016-07-11 | 2應力分離的諧波齒輪裝置 |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
PCT/JP2015/084198 WO2017094195A1 (ja) | 2015-12-04 | 2015-12-04 | 2応力分離の波動歯車装置 |
Publications (1)
Publication Number | Publication Date |
---|---|
WO2017094195A1 true WO2017094195A1 (ja) | 2017-06-08 |
Family
ID=58796623
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/JP2015/084198 WO2017094195A1 (ja) | 2015-12-04 | 2015-12-04 | 2応力分離の波動歯車装置 |
Country Status (7)
Country | Link |
---|---|
US (1) | US10883589B2 (ja) |
JP (1) | JP6104474B1 (ja) |
KR (1) | KR101758607B1 (ja) |
CN (1) | CN108291611B (ja) |
DE (1) | DE112015000726T5 (ja) |
TW (1) | TWI648486B (ja) |
WO (1) | WO2017094195A1 (ja) |
Families Citing this family (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP3404291B1 (en) * | 2016-01-15 | 2020-09-30 | Harmonic Drive Systems Inc. | Strain wave gearing device with pure separation of two stresses |
JP6830736B2 (ja) | 2017-06-05 | 2021-02-17 | 株式会社ハーモニック・ドライブ・システムズ | 2応力純分離の波動歯車装置 |
KR102146753B1 (ko) * | 2019-09-03 | 2020-08-21 | 숭실대학교산학협력단 | 물림률이 향상된 하모닉 드라이브 기어 |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO2010070712A1 (ja) * | 2008-12-18 | 2010-06-24 | 株式会社ハーモニック・ドライブ・システムズ | 3次元接触可能な転位歯形を有する波動歯車装置 |
JP2011144916A (ja) * | 2010-01-18 | 2011-07-28 | Harmonic Drive Systems Inc | 3次元接触の正偏位歯形を有する波動歯車装置 |
WO2015079576A1 (ja) * | 2013-11-29 | 2015-06-04 | 株式会社ハーモニック・ドライブ・システムズ | 2度接触の負偏位歯形を有する波動歯車装置 |
Family Cites Families (11)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US2906143A (en) | 1955-03-21 | 1959-09-29 | United Shoe Machinery Corp | Strain wave gearing |
JPH0784896B2 (ja) | 1986-11-05 | 1995-09-13 | 株式会社ハーモニック・ドライブ・システムズ | 撓み噛み合い式歯車装置 |
JP2503027B2 (ja) | 1987-09-21 | 1996-06-05 | 株式会社ハーモニック・ドライブ・システムズ | 撓みかみ合い式歯車装置 |
JP3739017B2 (ja) | 1995-12-15 | 2006-01-25 | 株式会社ハーモニック・ドライブ・システムズ | 非干渉広域かみ合い歯形を有する撓みかみ合い式歯車装置 |
JP4165810B2 (ja) | 2001-03-29 | 2008-10-15 | 株式会社ハーモニック・ドライブ・システムズ | 3次元偏位噛み合い歯形を有する波動歯車装置 |
WO2005124189A1 (ja) | 2004-06-21 | 2005-12-29 | Harmonic Drive Systems Inc. | 負偏位噛み合い歯形を有する波動歯車装置 |
US8661940B2 (en) | 2011-05-09 | 2014-03-04 | Harmonic Drive Systems Inc. | Wave gear device having three-dimensional continuous contact tooth profile |
JP5840214B2 (ja) * | 2011-09-16 | 2016-01-06 | 株式会社ハーモニック・ドライブ・システムズ | 振動発電を行う波動歯車装置 |
US9534681B2 (en) * | 2011-09-29 | 2017-01-03 | Harmonic Drive Systems Inc. | Wave gear device having tapered flexible external gear |
KR101782041B1 (ko) * | 2012-01-10 | 2017-10-23 | 가부시키가이샤 하모닉 드라이브 시스템즈 | 림 두께를 고려한 인벌류트 양편위 치형을 갖는 파동 기어 장치 |
WO2015075781A1 (ja) * | 2013-11-19 | 2015-05-28 | 株式会社ハーモニック・ドライブ・システムズ | 波動歯車装置、摩擦係合式の波動装置、および波動発生器 |
-
2015
- 2015-12-04 JP JP2016543095A patent/JP6104474B1/ja active Active
- 2015-12-04 CN CN201580004422.9A patent/CN108291611B/zh active Active
- 2015-12-04 KR KR1020167021603A patent/KR101758607B1/ko active IP Right Grant
- 2015-12-04 US US15/112,467 patent/US10883589B2/en active Active
- 2015-12-04 DE DE112015000726.1T patent/DE112015000726T5/de active Pending
- 2015-12-04 WO PCT/JP2015/084198 patent/WO2017094195A1/ja active Application Filing
-
2016
- 2016-07-11 TW TW105121770A patent/TWI648486B/zh active
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO2010070712A1 (ja) * | 2008-12-18 | 2010-06-24 | 株式会社ハーモニック・ドライブ・システムズ | 3次元接触可能な転位歯形を有する波動歯車装置 |
JP2011144916A (ja) * | 2010-01-18 | 2011-07-28 | Harmonic Drive Systems Inc | 3次元接触の正偏位歯形を有する波動歯車装置 |
WO2015079576A1 (ja) * | 2013-11-29 | 2015-06-04 | 株式会社ハーモニック・ドライブ・システムズ | 2度接触の負偏位歯形を有する波動歯車装置 |
Also Published As
Publication number | Publication date |
---|---|
US20180259053A1 (en) | 2018-09-13 |
US10883589B2 (en) | 2021-01-05 |
TWI648486B (zh) | 2019-01-21 |
TW201721038A (zh) | 2017-06-16 |
CN108291611B (zh) | 2021-01-22 |
KR20170081132A (ko) | 2017-07-11 |
JPWO2017094195A1 (ja) | 2017-11-30 |
KR101758607B1 (ko) | 2017-07-17 |
CN108291611A (zh) | 2018-07-17 |
JP6104474B1 (ja) | 2017-03-29 |
DE112015000726T5 (de) | 2017-08-24 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
JP5165120B2 (ja) | 3次元連続接触歯形を有する波動歯車装置 | |
WO2017122362A1 (ja) | 2応力純分離の波動歯車装置 | |
JP6830736B2 (ja) | 2応力純分離の波動歯車装置 | |
JP5456941B1 (ja) | 3次元接触歯形を有する波動歯車装置 | |
TWI638105B (zh) | Harmonic gear device with negative offset tooth profile with 2 degree contact | |
TWI690665B (zh) | 伴隨著齒面一致的複合嚙合諧波齒輪裝置 | |
JP6104474B1 (ja) | 2応力分離の波動歯車装置 |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
ENP | Entry into the national phase |
Ref document number: 2016543095 Country of ref document: JP Kind code of ref document: A |
|
WWE | Wipo information: entry into national phase |
Ref document number: 15112467 Country of ref document: US |
|
WWE | Wipo information: entry into national phase |
Ref document number: 1020167021603 Country of ref document: KR |
|
WWE | Wipo information: entry into national phase |
Ref document number: 112015000726 Country of ref document: DE |
|
121 | Ep: the epo has been informed by wipo that ep was designated in this application |
Ref document number: 15909825 Country of ref document: EP Kind code of ref document: A1 |
|
122 | Ep: pct application non-entry in european phase |
Ref document number: 15909825 Country of ref document: EP Kind code of ref document: A1 |