JP2011144916A - Wave gear device having three-dimensionally contacting positive shifted tooth profile - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a wave gear device having a three-dimensionally contacting positive shifted tooth profile continuously meshing in the tooth trace direction and having an increased tooth depth. <P>SOLUTION: The deflection coefficients κ of an opening end 34a of an external tooth 34 of a flexible external gear 3, a central principal section 30, and an inner end 34b in the harmonic drive gear device 1 are set at 1+2a, 1+a, and 1 respectively. An addendum tooth profile portion fs1 of the external tooth is obtained using a second similar curve AC obtained by similarly transforming part of a moving locus M0 obtained by a rack approximation of an inner end 34b of the external tooth 34 to define a straight line tooth profile portion fs2 connected thereto and a tooth profile FS1 having a tooth depth of 2mn(1+a) in the principal section 30 of tooth trace center of the external tooth by the addendum tooth profile portion fs3 connected thereto. As tooth profiles for the portion from the principal section 30 to the opening end 34a, and the portion from the principal section 30 to an inner end 34b, shifted tooth profiles FS2, FS3 which are obtained by shifting the tooth profile FS1 in the negative direction of the tooth depth are employed respectively. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  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, a three-dimensional contact state is formed in which both gears maintain a meshed state in the cross-section perpendicular to each axis in the tooth trace direction, and a large toothbrush that is advantageous for preventing ratcheting of both gears at high load torque is provided. The present invention relates to a wave gear device having a dimensional contact positive deviation tooth profile.

  The wave gear device is based on 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. For example, the inventor proposed in Patent Document 2 that the basic tooth profile is an involute tooth profile, and in 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. We have proposed a tooth profile design method that derives the tooth addendum of both gears that use wide area contact. Furthermore, the present inventor has proposed a tooth shape of high ratcheting torque capable of continuous meshing in a wave gear device in Patent Document 5.

  In general, a wave gear device includes an annular rigid internal gear, a flexible external gear disposed coaxially inside the ring-shaped rigid internal gear, and a wave generator fitted inside the gear. 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 in an elliptical shape by a wave generator, and meshes with the rigid internal gear at both ends of the major 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.

  A rational tooth profile setting method that takes into account the bending operation (corning) of the flexible external gear by the wave generator has not been sufficiently considered. Currently, there is a strong market demand to improve the load torque performance of wave gear devices. Achieving this requires a rational tooth profile that allows continuous meshing throughout the tooth trace, taking into account the tooth coning.

  In addition, one of the demands for the wave gear device is a countermeasure for ratcheting with a high reduction ratio. When the number of teeth of both gears exceeds 200, it is necessary to increase the tooth depth in order to prevent ratcheting at high load torque.

U.S. Pat. No. 2,906,143 Japanese Examined Patent Publication No. 45-41171 Japanese Unexamined Patent Publication No. 63-115943 JP-A 64-79448 JP 2007-211197 A

  The object of the present invention is to maintain a wide range of meshing in the main cross section (axial cross section) set at a predetermined position in the tooth trace direction, and partially in other axial perpendicular sections in the tooth trace direction. Proposal of a wave gear device having a positive displacement tooth profile with a three-dimensional contact, which has a large tooth retention capable of maintaining meshing and preventing ratcheting of both gears at high load torque even at a high reduction ratio There is to do.

The wave gear device (1) of the present invention comprises:
An annular rigid internal gear (2), a flexible external gear (3) disposed coaxially on the inside thereof, and a wave generator (4) fitted on the inside;
The flexible external gear (3) includes a flexible cylindrical body (31), a diaphragm (32) extending in a radial direction from a rear end of the cylindrical body, and the cylindrical body. External teeth (34) formed on the outer peripheral surface portion on the front end opening side of
The flexible external gear (3) is bent into an ellipse by the wave generator (4) and meshes with the internal teeth (24) of the rigid internal gear (2) at both ends of the long axis of the ellipse. And
The rigid internal gear (2) and the flexible external gear (3) are both spur gears of the module m,
The number of teeth of the flexible external gear (3) is 2n less (n is a positive integer) than the number of teeth of the rigid internal gear (2),
A rim neutral circle before bending at the long axis position (L1) of the elliptical rim neutral line of the flexible external gear (3) in an axial perpendicular section at an arbitrary position in the direction of the tooth trace of the external tooth (34). The amount of deflection with respect to is 2κmn using the deviation coefficient κ,
The amount of bending is along the direction of the tooth trace of the outer teeth (34) from the inner end (34b) on the diaphragm (32) side toward the opening end (34a) on the front end opening side. Increasing in proportion to the distance from the diaphragm (32),
When the meshing of the outer teeth (34) and the inner teeth (24) is approximated by rack meshing, the outer teeth (4) are rotated with the rotation of the wave generator (4) in the cross-section perpendicular to each axis. The movement trajectory (M) of the tooth (34) with respect to the internal tooth (24) is such that the x-axis is the translation direction of the rack, the y-axis is the direction perpendicular thereto, and the origin of the y-axis is the average of the amplitude of the movement trajectory (M). When set to the position, it is defined by Equation 1.
x = 0.5 mn (θ−κsin θ) (Formula 1)
y = κmncos θ

In the present invention, in the wave gear device (1) configured as described above,
The amount of deflection of the inner end (34b) of the external tooth (34) is the amount of deflection in an unshifted state with a displacement coefficient κ = 1, and the amount of deflection of the main cross section (30) is the displacement coefficient κ =. 1 + a (0 <a <0.5) is the deflection amount in the positive deflection state, and the deflection amount of the opening end portion (34a) is the deflection amount in the positive deflection state with the deflection position coefficient κ = 1 + 2a,
The first curve portion (AB) from the vertex (A) to the next bottom point (B) in the movement locus (M0) obtained at the inner end portion (34b) of the outer tooth (34) is the bottom point. (B) is reduced to λ times (0.5 <λ <1) with the center of similarity as the center of similarity, and a first similarity curve (BC) defined by Equation 2 is obtained,
x _Ca = 0.5 mn {(1-λ) π + λ (θ−sin θ)}
y _Ca = mn {λ (1 + cos θ) −1} (0 ≦ θ ≦ π) (Formula 2)
A second curve obtained by rotating the first similarity curve (BC) by 180 degrees around the end point (C) opposite to the bottom point (B) in the first similarity curve (BC), The end point (C) is multiplied by (1-λ) / λ with the center of similarity as the center of similarity to obtain a second similarity curve (AC) defined by Equation 3;
x _Fa = 0.5 mn (1-λ) (π−θ + sin θ)
y _Fa = mn {λ (1 + cos θ) −cos θ} (0 ≦ θ ≦ π) (Formula 3)
By moving the first similarity curve (BC) by a in the negative direction of the y-axis, a third curve (B1C1) defined by Equation 2a is obtained,
_{x Ca1 = 0.5mn {(1-} λ) π + λ (θ-sinθ)} ( Equation 2a)
_yCa1 = mn {λ (1 + cos θ) -1-a}
(0 ≦ θ ≦ π)
A fourth curve (A1C2) defined by Equation 3a is obtained by moving the second similarity curve (AC) by a in the positive direction of the y-axis,
x _Fa1 = 0.5 mn (1-λ) (π-sin θ) (Formula 3a)
y _Fa1 = mn {λ (1 + cos θ) −cos θ + a}
(0 ≦ θ ≦ π)
On the fourth curve (A1C2), the slope of the tangent line drawn on the curve with respect to the y-axis is from the end point (A1) at 90 degrees to the contact point (C3) at α degrees (0 <α <10). The defined tooth addendum portion (fs1), the straight tooth profile portion (fs2) defined by the tangent with an inclination angle of α degrees drawn to the contact (C3), and the other end of the straight tooth profile portion (fs2) The tooth has a tooth root of 2 (1 + a) mn with a tooth root portion (fs3) made of a curve that does not participate in the meshing of both teeth set so as not to interfere with the internal tooth (24) connected to the tooth. Forming a basic external tooth profile (FS1),
On the third curve (B1C1), the main cross section set at the center in the tooth trace direction of the external teeth (34) from the end point (B1) where the inclination angle of the tangent drawn on the curve with respect to the y-axis is 90 degrees ( 30) cutting out the curved portion to the end point (C4) that does not interfere with the movement locus (M1) drawn by the basic external tooth profile (FS1) as a fifth curve (B1C4),
Specified by an end tooth portion (cs1) defined by the fifth curve (B1C4) and a straight line inclined by the angle α with respect to the y axis connected to the end point (C2) of the end tooth portion (cs1). A tooth having a straight tooth profile portion (cs2) and a curve that does not participate in the meshing of both teeth set so as not to interfere with the external tooth (34) connected to the other end of the straight tooth profile portion (cs2). A tooth profile curve having a tooth depth of 2 (1 + a) mn is formed by the original tooth profile portion (cs3), and the tooth profile curve is adopted as a tooth profile (CS) of the internal tooth (24),
As the tooth profile of the main cross section (30) in the external tooth (34), the basic external tooth profile (FS1) is adopted,
The movement drawn by the basic external tooth profile (FS1) on the cross-section perpendicular to each axis as the tooth profile on the cross-section perpendicular to each axis from the main cross section (30) to the open end (34a) of the external teeth (34). Until the linear tooth profile portion (fs2) in the locus coincides with the linear tooth profile portion (fs2) in the movement locus drawn by the basic external tooth profile (F1) in the main cross section (30), on each axis perpendicular cross section. Adopting the dislocation tooth profile (FS2) obtained by performing dislocation in the negative direction of tooth depth with respect to the basic external tooth profile (FS1),
As the tooth profile on each cross section perpendicular to the axis from the main cross section (30) to the inner end (34b) of the external tooth, the movement locus drawn by the basic external tooth profile (FS1) on each cross section perpendicular to the axis is: Displacement in the negative direction of the tooth gap with respect to the basic external tooth profile (FS1) on the cross section perpendicular to each axis so as to contact the bottom of the movement locus drawn by the basic external tooth profile (FS1) in the main cross section (30) The dislocation tooth profile (FS3) obtained by applying is used.

  In the present invention, the first and the second for inducing the basic tooth addendum of both gears by using the movement path (M0) without displacement with respect to the rigid internal gear at the inner end of the flexible external gear. Two similar curves are obtained. Using the first and second similarity curves, in the main cross section set at the center in the direction of the tooth trace of the flexible external gear, the basic internal teeth with 2κmn = 2 (1 + a) mn which is larger than the standard 2 mn Tooth profile and basic external tooth profile are specified. And the internal tooth profile is set to the basic internal tooth profile over the entire tooth trace direction. On the other hand, about a flexible external gear, the basic external tooth form is employ | adopted as an external tooth form on the main cross section. Considering Corning as the external tooth profile on the open end side from the main cross-section and the external tooth profile on the inner end side from the main cross-section, respectively, the negative direction of the tooth relative to the basic external tooth profile The dislocation tooth profile obtained by dislocation is applied.

  As a result, according to the present invention, in the main cross section in the tooth trace direction of both gears, the meshing of the tooth addendums of both gears and the contact of the linear tooth profile portions are performed. From the main cross section to the open end, the contact between the linear tooth profile parts is maintained, and from the main cross section to the inner end, the continuous engagement between the end tooth forms is approximately due to the nature of the similar curve adopted for the addendum tooth form. Maintained.

  Therefore, according to the present invention, effective meshing (three-dimensional contact) is realized over the entire range of tooth traces of both gears, unlike the conventional case where simple relieving is applied to avoid tooth profile interference of both gears. can do. In addition, since the tooth profile (positive deviation tooth profile) of the tooth larger than the standard tooth is used, even when the number of teeth exceeds 200, ratcheting does not occur and the desired torque transmission is achieved. Can be maintained.

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 a flexible external gear, (a) shows the state before a deformation | transformation, (b) shows the state of the cross section containing the major axis of the flexible external gear deform | transformed into the ellipse. (C) shows the state of the cross section including the minor axis of the flexible external gear deformed into an elliptical shape. External obtained by approximating the relative motion of both gears at the inner end (κ = 1), central main section (κ = 1 + a) and open end (κ = 1 + 2a) of the external teeth in the rack It is explanatory drawing which shows the movement locus | trajectory of a tooth | gear. It is explanatory drawing which shows the similar curve which prescribes | regulates the basic tooth profile of each tooth end of both gears derived | led-out from the movement locus | trajectory of the external tooth in the axial orthogonal cross section of the inner end part of an unbiased position. It is explanatory drawing which shows an example of the tooth profile of both the gears in a main cross section. It is explanatory drawing which shows the both-tooth form in the axial cross section from a main cross section to an opening edge part, and the state of these meshing. It is explanatory drawing which shows the both-tooth form in an axial orthogonal cross section from the main cross section to an inner end part, and the state of these meshing. It is explanatory drawing which shows the outline of the tooth trace direction of the tooth | gear of the flexible external gear by dislocation.

(Configuration of wave gear device)
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 in a cross-section including a shaft, and FIG. 2 (a) is a state before deformation. 2 (b) shows a cross section including the major axis of the ellipse after deformation, and FIG. 2 (c) shows a cross section including the minor axis of the ellipse after deformation. 2A to 2C, a solid line indicates a cup-shaped flexible external gear, and a broken line indicates a top hat-shaped flexible external gear.

  As shown in these drawings, a 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 difference in the number of teeth between the rigid internal gear 2 and the flexible external gear 3 is 2n (n is a positive integer), and the flexible external gear 3 of the wave gear device 1 is elliptical by a wave generator 4 having an elliptical profile. And is engaged with the rigid internal gear 2 in the vicinity of both ends of the elliptical long axis L1. When the wave generator 4 is rotated, the meshing position of the two gears 2 and 3 moves in the circumferential direction, and relative rotation according to the difference in the number of teeth of the two gears is generated between the two gears 2 and 3. 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.

  By the wave generator 4 having an elliptical contour fitted into the inner peripheral surface portion of the outer tooth forming portion of the cylindrical body 31, the cylindrical body 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. As shown in FIG. 2 (b), in the cross section including the elliptical long axis L1, the outward deflection amount gradually increases in proportion to the distance from the rear end 31b to the opening end 31a, and is shown in FIG. 2 (c). Thus, in the cross section including the elliptical short axis L2, the amount of inward bending gradually increases in proportion to the distance from the rear end 31b to the opening end 31a. Accordingly, the external teeth 34 formed on the outer peripheral surface portion on the opening end 31a side are also proportional to the distance from the rear end 31a from the inner end portion 34b in the tooth trace direction toward the opening end portion 34a on the opening side. As a result, the amount of deflection gradually increases.

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 when the relative motion of both the gears 2 and 3 of the wave gear device 1 is approximated by a rack. FIG. In the figure, the x axis indicates the translation direction of the rack, and 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 difference in the number of teeth between the rigid internal gear 2 and the flexible external gear 3 is 2n (n is a positive integer). Assuming that the total amplitude of the movement trajectory of the flexible external gear 3 relative to the rigid internal gear 2 in an arbitrary axis-perpendicular section is 2κmn (κ is a deviation coefficient, a real number including 1 and m is a module), The movement locus of the external teeth 34 of the gear 3 is given by Equation 1.
x = 0.5 mn (θ−κsin θ) (Formula 1)
y = κmncos θ

For the sake of simplicity, assuming that m = 1 and n = 1 (the number of teeth difference is 2), the movement trajectory is as shown in Equation 1A. FIG. 3 shows the movement locus in this case.
x = 0.5 (θ−κsinθ) (Formula 1A)
y = κcos θ

  Here, a cross section perpendicular to the axis of the inner end 34b of the flexible external gear 3, a cross section perpendicular to the center in the direction of the tooth trace (a cross section perpendicular to the position indicated by reference numeral 30 in FIG. 2), and the axis of the open end 34a. The deviation coefficients κ in the cross section at right angles are 1, 1 + a, 1 + 2a (0 <a <0.5), respectively. In FIG. 3, the movement trajectory M0 is obtained at the inner end portion 34b in the standard deflection state without displacement with the displacement coefficient κ = 1. The movement locus M1 is obtained in the main section 30 in the positive deflection state where the deflection coefficient κ = 1 + a, and the movement locus M2 is the open end of the deflection state in the positive deflection state where the deflection coefficient κ = 1 + 2a. It is obtained in the part 34a. Thus, the amount of bending is set so that a positive deflection state is obtained over the entire tooth trace direction.

(Method of forming tooth profile in main section)
FIG. 4 is an explanatory diagram showing a method for setting the tooth profiles of the external teeth 34 and the internal teeth 24 in the main cross section 30. In the present invention, the movement locus M0 obtained in the cross section perpendicular to the axis of the inner end portion 34b of the non-deflection (κ = 1) in the flexible external gear 3 is used for the tooth addendum in the main section 30.

  First, in the movement locus M0, the first curve AB in the range from the parameter θ of π (point B: the bottom point of the movement locus) to 0 (point A: the vertex of the movement locus) is taken, and the point B is the center of similarity. Then, the first curve AB is transformed to λ times (0.5 <λ <1) to obtain a first similarity curve BC. The end tooth form of the rigid internal gear is defined using the first similar curve BC as described later.

  Next, the first similarity curve BC is rotated by 180 degrees around the end point C of the first similarity curve BC to obtain a second curve B′C indicated by an imaginary line. The second curve is transformed to (1-λ) / λ times with the end point C as the center of similarity to obtain a second similarity curve AC. The second similarity curve AC is adopted as the basic tooth profile of the end tooth shape portion of the flexible external gear 3.

  FIG. 4 shows a case where λ = 0.6. In the present invention, the value of the similarity magnification λ for obtaining the first similarity curve BC adopted as a curve for defining the tooth addendum portion of the rigid internal gear 2 is λ> 0.5. The reason for this is to alleviate the reduction of the end tooth profile portion of the tooth profile of the internal tooth 24 caused by the linear tooth profile portion that defines a part of the tooth profile of the external tooth 34 of the flexible external gear 3 as will be described later. .

On the xy coordinate plane in FIG. 4, the first similarity curve BC and the second similarity curve AC are expressed by Expression 2 and Expression 3.
(First similarity curve BC)
x _Ca = 0.5 {(1-λ) π + λ (θ−sin θ)}
y _Ca = λ (1 + cos θ) −1 (Formula 2)
(0 ≦ θ ≦ π)
(Second similarity curve AC)
x _Fa = 0.5 (1-λ) (π−θ + sin θ)
y _Fa = λ (1 + cos θ) −cos θ (Formula 3)
(0 ≦ θ ≦ π)

Next, the first similarity curve BC and the second similarity curve AC are calculated on the main cross section 30 where the displacement coefficient κ = κ _o = 1 + a, and the tooth depth is 2κ _o mn and the internal teeth and external teeth larger than the standard are obtained. Adopted as an addendum tooth profile. On the xy coordinate plane, the y coordinate of the tooth addendum of both gears is decreased by a for the rigid internal gear and increased by a for the flexible external gear. Therefore, the tooth addendum portion of the tooth profile of the inner tooth 24 in the main cross section 30 is defined by the third curve B1C1 represented by the equation 2a, and the tooth addendum portion of the tooth profile of the external tooth 34 is represented by the equation 3a It is defined by the curve A1C2 (when m = 1, n = 1).
(Basic formula of the tooth addendum of the rigid internal gear)
_xCa1 = 0.5 {(1-λ) π + λ (θ−sin θ)}
y _Ca1 = λ (1 + cos θ) -1-a (Formula 2a)
(0 ≦ θ ≦ π)
(Basic formula of tooth addendum of flexible external gear)
x _Fa1 = 0.5 (1-λ) (π-sin θ)
y _Fa1 = λ (1 + cos θ) −cos θ + a (Formula 3a)
(0 ≦ θ ≦ π)

  In this case, the pressure angle α (angle formed by the tangent to the y-axis) of the end points (end points C1 and C2 in FIG. 4) of the tooth addendum portions of both teeth 24 and 34 is 0 degree. It is better to avoid from. Therefore, in the external tooth 34, the end on the side of the end point C2 is replaced with a linear tooth profile portion whose pressure angle α is defined by a tangent of, for example, about 9 degrees, and the end point of the fourth curve A1C2 at the pressure angle α = 90. The end tooth profile portion is defined using a curved portion from A1 to a point C3 where the pressure angle α is around 9 degrees. Since the root tooth profile part of the external tooth 34 does not participate in meshing with the internal tooth 24, the tooth base tooth part can be defined by an arbitrary curve that does not interfere with the tooth addendum part of the counterpart internal tooth 24. Therefore, the shape of the root tooth portion of the external tooth 34 can be freely set after ensuring the required total tooth depth (= 2κomn).

  Similarly, in the internal tooth 24, the end portion on the side of the end point C1 is replaced with a linear tooth profile portion whose pressure angle α is defined by, for example, a tangent of about 9 degrees, and the pressure angle α = 90 in the third curve B1C1. The tooth addendum portion is defined using the curved portion B1C3a from the end point B1 to the end point C3a having a pressure angle α in the vicinity of 9 degrees. Since the root tooth profile portion of the internal tooth 24 does not participate in meshing with the external tooth 34, the root tooth shape portion can be defined by an arbitrary curve that does not interfere with the tooth addendum portion of the counterpart external tooth 34. Therefore, it is possible to freely set the shape of the root tooth profile portion of the internal tooth 24 while ensuring the required total tooth depth (= 2κomn).

  FIG. 5 shows an example of the tooth profile of the external tooth 34 with the toothpick thus defined 2κomn = 2κo = 2 (1 + a). The tooth profile FS1 of the external teeth 34 of the flexible external gear 3 on the main cross section 30 has an addendum tooth shape portion fs1 composed of a curved portion A1C3 and a pressure angle α connected to the end point C3 of the addendum tooth shape portion fs1 is approximately 9. Degree linear tooth profile portion fs2 and a tooth base tooth shape portion fs3 connected to the end point E of the linear tooth profile portion fs2.

  Next, the tooth profile of the internal tooth 24 of the rigid internal gear 2 is the same as that of the external tooth 24, and the end tooth profile portion defined by the curved portion B1C3a (see FIG. 4) and the pressure connected to this end point C3a. It can be provisionally defined by a linear tooth profile portion having an angle α of approximately 9 degrees and an arbitrarily shaped tooth root portion connected to the linear tooth profile portion.

  Here, on the main cross section 30, the point of the tooth addendum of the flexible external gear 3 moves along the movement locus M1 shown in FIG. The external teeth 34 of the flexible external gear 3 are closest to the external teeth 24 of the rigid internal gear 2 in the x-axis direction at the projecting point (D point, pressure angle α = 0) of the top of the movement locus M1. To do.

  At this time, the linear tooth profile portion fs2 of the tooth profile FS1 set as the tooth profile of the external tooth 34 violates a part of the provisional tooth profile adopted as the tooth profile of the internal tooth 24. Therefore, as shown in FIG. 4, by using the curved portion B1C4 after slightly removing the portion on the end point C3a side that interferes with the linear tooth shape portion fs2 of the external tooth 24 in the curved portion B1C3a, Defines the tooth addendum part of the tooth profile.

  As a result, as shown in FIG. 5, the tooth profile CS of the internal tooth 24 of the rigid internal gear 2 includes the end tooth portion cs1 formed of the curved portion B1C4 and the pressure angle α connected to the end point C4 of the end tooth portion cs1. Is defined by a linear tooth profile portion cs2 of approximately 9 degrees and a tooth root profile portion cs3 connected to the end point F of the linear tooth profile portion cs2.

  The meshing on the main cross section 30 by the tooth profile CS of the internal tooth 24 and the tooth profile FS1 of the external tooth 34 defined as described above is the meshing between the tooth addendum portions of both teeth 24 and 34 and the linear tooth profile portions. It becomes a meshing. When the external teeth 34 of the flexible external gear 3 move with respect to the internal teeth 24 of the rigid internal gear 2 along the movement locus M1, the tooth addendum portions are both defined by a similar curve derived from the movement locus M0. Continuous contact is guaranteed.

(Method of forming tooth profile at a position other than the main cross section)
With reference to FIG. 6, FIG. 7, the formation method of the tooth profile of an axial cross section other than the main cross section 30 is demonstrated. First, the internal tooth 24 has the tooth profile CS set in the main cross section 30 as described above over the entire tooth trace direction. As for the external teeth 34, the dislocation tooth profile obtained by performing dislocation in the negative direction of the tooth as follows according to the position of the tooth trace with respect to the tooth profile FS1 of the external tooth 34 set in the main section 30 as described above. Is adopted as a tooth profile other than the main cross section 30.

  In the portion from the main cross section 30 to the open end 34a of the outer tooth 34, the tooth profile is such that the straight tooth profile portion of the tooth profile FS1 in the cross section perpendicular to each axis coincides with the straight tooth profile portion of the tooth profile FS1 in the main cross section 30. A dislocation is applied to FS1 in the negative y-axis direction. The obtained dislocation tooth profile FS2 is employed as a tooth profile at a portion perpendicular to each axis from the main cross section 30 to the opening end 34a.

FIG. 6 shows the shape of the tooth profile CS of the internal tooth 2 and the dislocation tooth profile FS2 of the external tooth 3 and the meshing state thereof in one axial cross section taken between the main cross section 30 and the open end 34a. It is. If the amount of dislocation in the negative direction applied to the tooth profile FS1 of the external tooth 34 is mnh, the amount of dislocation when m = 1 and n = 1 is h, and the value of h is the displacement coefficient κ _o ( = 1 + a) is given by Equation 4.

（式４）

(Formula 4)

  Next, in each axis perpendicular section from the main cross section 30 to the inner end 34b of the external tooth 34, the deviation coefficient κ is 1 <κ <1 + a, and the point on the tooth profile FS1 of the external tooth 34 is the main cross section 30. A movement trajectory of a loop with a small amount of protrusion in the x-axis direction is drawn as compared with the loop of the movement trajectory M1 in FIG. Therefore, the interference by the loop like the external tooth profile FS1 on the opening end 34a side of the main cross section 30 does not occur.

  However, since the amount of deflection is less than 2κomn of the main cross section 30, the external tooth profile FS1 interferes with the tooth profile CS of the internal tooth 24 at the bottom of the movement locus, and the meshing cannot be maintained as it is. That is, in each axial perpendicular section of the external tooth 24 from the main cross section 30 to the inner end portion 34b, the displacement coefficient κ is smaller than κo in the main cross section 30, and therefore the movement of the external tooth profile on these axial orthogonal sections. The trajectory interferes with the movement trajectory M1 in the main cross section 30, and the meshing as in the main cross section 30 cannot be maintained.

  Therefore, in the tooth profile of the external tooth 34 from the main cross section 30 to the inner end portion 34b, the movement locus of the tooth profile FS1 in the cross section perpendicular to each axis moves in the main cross section 30 according to the deviation coefficient κ in the cross section perpendicular to each axis. Dislocation is applied to the tooth profile FS1 in the negative direction of the tooth so as to contact the bottom of the locus M1. The obtained dislocation tooth profile FS3 is employed as a tooth profile at a portion perpendicular to each axis extending from the main cross section 30 to the inner end 34b.

FIG. 7 shows the shapes of the tooth profile CS of the internal tooth 2 and the dislocation tooth profile FS3 of the external tooth 3 and their meshing states in one axial cross section taken between the main cross section 30 and the inner end 34b. It is. When the amount of shift in the negative direction applied to the tooth profile FS3 of the external teeth 34 and mnh _1, dislocation amount in the case of m = 1, n = 1 becomes _{h 1,} the value of _{h 1} is deviation coefficient in the main section 30 It is given by the following equation using κ _o (= 1 + a) and takes a negative value.
h ₁ = κ−κ _o

  The movement trajectory of the point on the tooth profile FS3 of the external tooth 34 after such dislocation is in contact with the movement trajectory M1 of the main cross section 30 at the bottom (point P in FIG. 3), and the trajectory of the portion near the bottom. Well approximates the movement trajectory M1. This has been found by the present inventors. Based on this knowledge, the present invention secures continuous contact between the tooth addendum portions by shifting from the main section 30 to the inner end 34b in the negative direction of the toothpaste.

(Correction of tooth profile direction)
FIG. 8 is an explanatory view showing the contour of the external tooth profile of the external gear 3 obtained by applying the shift as described above in the tooth trace direction. As shown in this figure, the contour of the external teeth 34 in the tooth trace direction is the position of the main cross section 30 due to the difference in dislocation applied to the opening end 34a side and the inner end 34b side with the main cross section 30 as a boundary. It has a polygonal line shape that apex. In order to avoid a polygonal outline in which clear vertices appear, the vertices surrounded by circles in the figure are replaced by small arcs 34c, and the arcs 34c are changed to outlines 34d and 34e on both sides of the main cross section 30. It is desirable to have a smoothly continuous shape.

DESCRIPTION OF SYMBOLS 1 Wave gear apparatus 2 Rigid internal gear 3 Flexible external gear 4 Wave generator 24 Internal tooth 30 Main cross section 34 External tooth 34a Open end part 34b Inner end part 34c Arc 34d, 34e Tooth trace outline M0, M1, M2 Movement locus

Claims (4)

An annular rigid internal gear (2), a flexible external gear (3) disposed coaxially on the inside thereof, and a wave generator (4) fitted on the inside;
The flexible external gear (3) includes a flexible cylindrical body (31), a diaphragm (32) extending in a radial direction from a rear end of the cylindrical body, and the cylindrical body. External teeth (34) formed on the outer peripheral surface portion on the front end opening side of
The flexible external gear (3) is bent into an ellipse by the wave generator (4) and meshes with the internal teeth (24) of the rigid internal gear (2) at both ends of the long axis of the ellipse. And
The rigid internal gear (2) and the flexible external gear (3) are both spur gears of the module m,
The number of teeth of the flexible external gear (3) is 2n less (n is a positive integer) than the number of teeth of the rigid internal gear (2),
A rim neutral circle before bending at the long axis position (L1) of the elliptical rim neutral line of the flexible external gear (3) in an axial perpendicular section at an arbitrary position in the direction of the tooth trace of the external tooth (34). The amount of deflection with respect to is 2κmn using the deviation coefficient κ,
The amount of bending is along the direction of the tooth trace of the outer teeth (34) from the inner end (34b) on the diaphragm (32) side toward the opening end (34a) on the front end opening side. Increasing in proportion to the distance from the diaphragm (32),
When the meshing of the outer teeth (34) and the inner teeth (24) is approximated by rack meshing, the outer teeth (4) are rotated with the rotation of the wave generator (4) in the cross-section perpendicular to each axis. The movement trajectory (M) of the tooth (34) with respect to the internal tooth (24) is such that the x-axis is the translation direction of the rack, the y-axis is the direction perpendicular thereto, and the origin of the y-axis is the average of the amplitude of the movement trajectory (M). In the wave gear device (1) defined by Equation 1 when set to the position,
x = 0.5 mn (θ−κsin θ) (Formula 1)
y = κmncos θ (−π ≦ θ ≦ π)
The amount of deflection of the inner end (34b) of the external tooth (34) is the amount of deflection in an unshifted state with a displacement coefficient κ = 1, and the amount of deflection of the main cross section (30) is the displacement coefficient κ =. 1 + a (0 <a <0.5) is the deflection amount in the positive deflection state, and the deflection amount of the opening end portion (34a) is the deflection amount in the positive deflection state with the deflection position coefficient κ = 1 + 2a,
The first curve portion (AB) from the vertex (A) to the next bottom point (B) in the movement locus (M0) obtained at the inner end portion (34b) of the outer tooth (34) is the bottom point. (B) is reduced to λ times (0.5 <λ <1) with the center of similarity as the center of similarity, and a first similarity curve (BC) defined by Equation 2 is obtained,
x _Ca = 0.5 mn {(1-λ) π + λ (θ−sin θ)}
y _Ca = mn {λ (1 + cos θ) −1} (0 ≦ θ ≦ π) (Formula 2)
A second curve obtained by rotating the first similarity curve (BC) by 180 degrees around the end point (C) opposite to the bottom point (B) in the first similarity curve (BC), The end point (C) is multiplied by (1-λ) / λ with the center of similarity as the center of similarity to obtain a second similarity curve (AC) defined by Equation 3;
x _Fa = 0.5 mn (1-λ) (π−θ + sin θ)
y _Fa = mn {λ (1 + cos θ) −cos θ} (0 ≦ θ ≦ π) (Formula 3)
By moving the first similarity curve (BC) by a in the negative direction of the y-axis, a third curve (B1C1) defined by Equation 2a is obtained,
_{x Ca1 = 0.5mn {(1-} λ) π + λ (θ-sinθ)} ( Equation 2a)
_yCa1 = mn {λ (1 + cos θ) -1-a}
(0 ≦ θ ≦ π)
A fourth curve (A1C2) defined by Equation 3a is obtained by moving the second similarity curve (AC) by a in the positive direction of the y-axis,
x _Fa1 = 0.5 mn (1-λ) (π-sin θ) (Formula 3a)
y _Fa1 = mn {λ (1 + cos θ) −cos θ + κo}
(0 ≦ θ ≦ π)
On the fourth curve (A1C2), the slope of the tangent line drawn on the curve with respect to the y-axis is from the end point (A1) at 90 degrees to the contact point (C3) at α degrees (0 <α <10). The defined tooth addendum portion (fs1), the straight tooth profile portion (fs2) defined by the tangent with an inclination angle of α degrees drawn to the contact (C3), and the other end of the straight tooth profile portion (fs2) The tooth has a tooth root of 2 (1 + a) mn with a tooth root portion (fs3) made of a curve that does not participate in the meshing of both teeth set so as not to interfere with the internal tooth (24) connected to the tooth. Forming a basic external tooth profile (FS1),
On the third curve (B1C1), the main cross section set at the center in the tooth trace direction of the external teeth (34) from the end point (B1) where the inclination angle of the tangent drawn on the curve with respect to the y-axis is 90 degrees ( 30) cutting out the curved portion to the end point (C4) that does not interfere with the movement locus (M1) drawn by the basic external tooth profile (FS1) as a fifth curve (B1C4),
Specified by an end tooth portion (cs1) defined by the fifth curve (B1C4) and a straight line inclined by the angle α with respect to the y axis connected to the end point (C4) of the end tooth portion (cs1). A tooth having a straight tooth profile portion (cs2) and a curve that does not participate in the meshing of both teeth set so as not to interfere with the external tooth (34) connected to the other end of the straight tooth profile portion (cs2). A tooth profile curve having a tooth depth of 2 (1 + a) mn is formed by the original tooth profile portion (cs3), and the tooth profile curve is adopted as a tooth profile (CS) of the internal tooth (24),
As the tooth profile of the main cross section (30) in the external tooth (34), the basic external tooth profile (FS1) is adopted,
The movement drawn by the basic external tooth profile (FS1) on the cross-section perpendicular to each axis as the tooth profile on the cross-section perpendicular to each axis from the main cross section (30) to the open end (34a) of the external teeth (34). Until the linear tooth profile portion (fs2) in the locus coincides with the linear tooth profile portion (fs2) in the moving locus drawn by the basic external tooth profile (FS1) in the main cross section (30), the cross section is perpendicular to each axis. Adopting the dislocation tooth profile (FS2) obtained by performing dislocation in the negative direction of tooth depth with respect to the basic external tooth profile (FS1),
As the tooth profile on each cross section perpendicular to the axis from the main cross section (30) to the inner end (34b) of the external tooth, the movement locus drawn by the basic external tooth profile (FS1) on each cross section perpendicular to the axis is: Displacement in the negative direction of the tooth gap with respect to the basic external tooth profile (FS1) on the cross section perpendicular to each axis so as to contact the bottom of the movement locus drawn by the basic external tooth profile (FS1) in the main cross section (30) Adopting the dislocation tooth profile (FS3) obtained by applying
A wave gear device (1) having a positive displacement tooth profile with a three-dimensional contact. In claim 1,
A wave gear characterized in that the amount of transition applied to each portion of the external teeth (34) from the main cross section (30) to the opening end (34a) is h × mn, and the value h is defined by Equation 4. Device (1).

(Formula 4) In claim 2,
The amount of dislocation applied to each part from the main cross section (30) to the inner end (34b) in the outer teeth (34) is h ₁ × mn,
When the displacement coefficient κ = κo (= 1 + a) in the main cross section (30),
Wave gear device characterized by a value h ₁ to κ-κo (1). In any one of claims 1 to 3,
A polygonal tooth trace having a vertex at the position of the main cross section (30) generated by dislocation applied to the open end (34a) side and the inner end (34b) side with the main cross section (30) as a boundary A wave gear device (1) characterized in that the contours (34d, 34e) are contours in which portions including the apexes are smoothly connected by an arc (34c).

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