Dual-type strain wave gearing

Abstract

An externally toothed gear of a dual-type strain wave gearing is provided with first and second external teeth having different teeth numbers. The first and second external teeth are flexed by a wave generator by the same flexing amount, into an ellipsoidal shape. The average pressure angle of main-tooth-surface sections of tooth profiles of the first external teeth having a low teeth number is less acute than the average pressure angle of main-tooth-surface sections of tooth profiles of the second external teeth having a high teeth number. Accordingly, a dual-type strain wave gearing can be achieved with which the first and second external teeth having different teeth numbers can be suitably flexed to form excellent meshing states with respective internally toothed gears.

Claims

1. A strain wave gearing comprising: a rigid first internally toothed gear formed with first internal teeth; a rigid second internally toothed gear formed with second internal teeth, the second internally toothed gear being disposed so as to be coaxially aligned in parallel with the first internally toothed gear; a flexible externally toothed gear in which first external teeth capable of meshing with the first internal teeth and second external teeth capable of meshing with the second internal teeth are formed in an outer-peripheral surface of a radially flexible cylindrical body, the second teeth differing in number from the first teeth, and the externally toothed gear being disposed coaxially inside the first and second internally toothed gears; and a wave generator for flexing the externally toothed gear in an ellipsoidal shape to cause the first external teeth to partially mesh with the first internal teeth and to cause the second external teeth to partially mesh with the second internal teeth, wherein, a relationship
Zf1=Zf2?2n is satisfied, where Zf1 is the number of first external teeth, Zf2 is the number of second external teeth, and n is a positive integer; wherein, a radial flexing amount d, which is a radial flexing amount of the first and second external teeth being flexed by the wave generator, satisfies
d<d.sub.1, and
d>d.sub.2, where m.sub.1 is a module of the first external teeth, m.sub.2 is a module of the second external teeth, n.sub.1 and n.sub.2 are positive integers, 2n.sub.1 is a difference in number of teeth between the first external teeth and the first internal teeth, and 2n.sub.2 is a difference in number of teeth between the second external teeth and the second internal teeth, and a theoretical value d.sub.1 of an amount by which the first external teeth are radially flexed at major-axis positions and a theoretical value d.sub.2 of an amount by which the second external teeth are radially flexed when the externally teethed gear is flexed in an ellipsoidal shape are respectively represented by
d.sub.1=m.sub.1n.sub.1 and
d.sub.2=m.sub.2n.sub.2; and wherein, a relationship
?1>?2 is satisfied, where a first average pressure angle ?1 is an average of angles that are formed by a tooth-profile center line and a tooth-profile tangent line that extends to individual portions of a tooth land within a range of 50% of a total tooth depth in a tooth profile of the first external teeth, the range being centered about a pitch circle of the first external teeth, and where a second average pressure angle ?2 is an average of angles that are formed by a tooth-profile center line of the second external teeth and a tooth-profile tangent line that extends to individual portions of a tooth land within a range of 50% of a total tooth depth in a tooth profile of the second external teeth, the range being centered about a pitch circle of the second external teeth.

2. The strain wave gearing according to claim 1, wherein the first and second average pressure angles ?1 and ?2 satisfy
0.29?1<?2<0.75?1.

3. The strain wave gearing according to claim 1 wherein first and second rim wall thicknesses t(1) and t(2) satisfy
t(1)<t(2), where the first rim wall thickness t(1) is a rim wall thickness of a tooth bottom rim of the first external teeth, and the second rim wall thickness t(2) is a rim wall thickness of a tooth bottom rim of the second external teeth.

4. The strain wave gearing according to claim 1, wherein the wave generator has: a rigid plug; an ellipsoidally contoured outer-peripheral surface formed in an outer-peripheral surface of the plug; a first wave bearing fitted to the outer-peripheral surface, the first wave bearing comprising ball bearings for supporting the first external teeth; and a second wave bearing fitted to the outer-peripheral surface, the second wave bearing comprising ball bearings for supporting the second external teeth.

5. The strain wave gearing according to claim 1, wherein a gap is formed between a tooth-trace-direction inner-end surface of the first external teeth and a tooth-trace-direction inner-end surface of the second external teeth, the gap having a prescribed width along a tooth trace direction, and the gap having a deepest part along a tooth depth direction at a tooth-trace-direction central portion; wherein a relationship
0.1L<L1<0.3L is satisfied, where L is a width from a tooth-trace-direction outer end of the first external teeth to a tooth-trace-direction outer end of the second external teeth, and L1 is a maximum width of the gap along the tooth trace direction; and, wherein relationships
0.9h1<t1<1.3h1 and
0.9h2<t2<1.3h2 are satisfied, where h1 is a tooth depth of the first external teeth, h2 is a tooth depth of the second external teeth, t1 is a tooth-depth-direction depth from a tooth top land of the first external teeth to the deepest part, and t2 is a tooth-depth-direction depth from a tooth top land of the second external teeth to the deepest part.

6. The strain wave gearing according to claim 5, wherein the wave generator has a first wave bearing comprising a ball bearing for supporting the first external teeth, and a second wave bearing comprising a ball bearing for supporting the second external teeth; wherein bearing-ball centers of the first wave bearing and the second wave bearing are located at positions that are equidistant, along the tooth trace direction, from a tooth-trace-direction center of the gap; and wherein, where an inter-ball-center distance Lo is a distance between the bearing-ball centers of the first and second wave bearings, the inter-ball-distance is set so as to increase correspondingly with an increase in the maximum width L1 of the gap, and satisfies a relationship
0. 35L<Lo<0.7L.

7. The strain wave gearing according to claim 1, wherein the number of the first external teeth differs from the number of the first internal teeth, and the number of second external teeth differs from the number of second internal teeth.

8. The strain wave gearing according to claim 1, wherein the number of first external teeth is less than the number of first internal teeth, and the number of first internal teeth and the number of second internal teeth are equal to each other.

9. The strain wave gearing according to claim 1, wherein the wave generator is a rotation-inputting element; and either one of the first internally toothed gear and second internally toothed gear is a stationary-side internally toothed gear secured so as not to rotate, and the other of the first internally toothed gear and second internally toothed gear is a drive-side internally toothed gear that is a reduced-rotation-outputting element.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1(A) and FIG. 1(B) are an end-surface view and a longitudinal cross-sectional view of a dual-type strain wave gearing to which the present invention is applied;

(2) FIG. 2 is a schematic diagram of the dual-type strain wave gearing shown in FIG. 1(A) and FIG. 1(B);

(3) FIG. 3 is a partial enlarged cross-sectional view of the strain wave gearing shown in FIG. 1(A) and FIG. 1(B);

(4) FIG. 4(A) and FIG. 4(B) are diagrams showing the flexed state of the externally toothed gear shown in FIG. 1(A) and FIG. 1(B); and

(5) FIG. 5(A) and FIG. 5(B) are pairs of graphs showing the tooth profiles of the first and second external teeth of the externally toothed gear shown in FIG. 1(A) and FIG. 1(B).

MODE FOR CARRYING OUT THE INVENTION

(6) An embodiment of a dual-type strain wave gearing to which the present invention is applied is described below with reference to the attached drawings.

(7) [Overall Configuration of Strain Wave Gearing]

(8) FIG. 1(A) and FIG. 1(B) are an end-surface view and a longitudinal cross-sectional view showing a dual-type strain wave gearing (referred to below simply as strain wave gearing) according to an embodiment of the present invention, and FIG. 2 is a schematic diagram of the same. The strain wave gearing 1, which is used as, e.g., a gear reducer, has an annular rigid first internally toothed gear 2, an annular rigid second internally toothed gear 3, a cylindrical flexible externally toothed gear 4 comprising a radially flexible thin-walled elastic body, and an ellipsoidally contoured wave generator 5.

(9) The first and second internally toothed gears 2, 3 are disposed so as to be coaxially aligned in parallel with each other, with a prescribed gap therebetween, along the direction of a central axis 1a. In the present example, the first internally toothed gear 2 is a stationary-side internally toothed gear secured so as not to rotate, the number of first internal teeth 2a thereof being indicated by Zc1. The second internally toothed gear 3 is a rotatably supported drive-side internally toothed gear, the number of second internal teeth 3a thereof being indicated by Zc2. The second internally toothed gear 3 is the reduced-rotation-outputting element of the strain wave gearing 1.

(10) The cylindrical externally toothed gear 4 is disposed coaxially inside the first and second internally toothed gears 2, 3. The externally toothed gear 4 has a cylindrical body 6 that is a radially flexible thin-walled elastic body, first external teeth 7 and second external teeth 8 formed in the circular outer-peripheral surface of the cylindrical body 6, and a gap 9 (refer to FIG. 3) formed between the external teeth 7, 8 on either side, the gap 9 functioning as a cutter clearance area. The first external teeth 7 are formed on one side along the central axis 1a direction of the circular outer-peripheral surface of the cylindrical body 6, and the second external teeth 8 are formed on the other second-internal-teeth 3a side of the circular outer-peripheral surface. The first and second external teeth 7, 8 are formed such that the central-axis 1a direction is the tooth trace direction.

(11) Specifically, the first external teeth 7 are formed on the side opposing the first internal teeth 2a, and are capable of meshing with the first internal teeth 2a, the number of first external teeth 7 being indicated by Zf1. The second external teeth 8 are formed on the side opposing the second internal teeth 3a, and are capable of meshing with the second internal teeth 3a, the number of second external teeth 8 being indicated by Zf2. The numbers Zf1, Zf2 of teeth are different from each other.

(12) The wave generator 5 has an ellipsoidally contoured rigid plug 11, and a first wave bearing 12 and second wave bearing 13, the first and second wave bearings being fitted to the ellipsoidal outer-peripheral surface of the rigid plug 11. The first and second wave bearings 12, 13 are formed from ball bearings.

(13) The wave generator 5 is inserted into the inner-peripheral surface of the cylindrical body 6 of the externally toothed gear 4, and causes the cylindrical body 6 to flex in an ellipsoidal shape. Therefore, the first and second external teeth 7, 8 are also flexed in an ellipsoidal shape. The ellipsoidally flexed externally toothed gear 4 meshes with the first and second internally toothed gears 2, 3 at both end positions along the major axis Lmax of the ellipsoidal shape. Specifically, the first external teeth 7 mesh with the first internal teeth 2a at both end positions along the major axis of the ellipsoidal shape, and the second external teeth 8 mesh with the second internal teeth 3a at both end positions along the major axis.

(14) The wave generator 5 is the rotation-input element of the strain wave gearing 1. The rigid plug 11 of the wave generator 5 has a shaft hole 11c, in which an input rotation shaft 10 (refer to FIG. 2) is securely connected in a coaxial arrangement. For example, a motor output shaft may be securely connected in a coaxial arrangement in the shaft hole 11c. When the wave generator 5 rotates, the positions at which the first external teeth 7 of the externally toothed gear 4 and the stationary-side first internal teeth 2a mesh, and the positions at which the second external teeth of the externally toothed gear 4 and the drive-side second internal teeth 3a mesh, move along the circumferential direction.

(15) The number Zf1 of first external teeth 7 and the number Zf2 of second external teeth 8 differ from each other; in the present example, the number Zf2 of second external teeth is greater. The number Zc1 of first internal teeth 2a and the number Zf1 of first external teeth 7 also differ from each other; in the present example, the number Zc1 of first internal teeth 2a is greater. The number Zc2 of second internal teeth 3a and the number Zf2 of second external teeth 8 differ from each other; in the present example, the number Zc2 of second internal teeth 3a is less.

(16) In the present example, the externally toothed gear 4 is caused to flex in an ellipsoidal shape, and meshes with the internally toothed gears 2, 3 at two locations along the circumferential direction. Therefore, the difference between the number Zc1 of first internal teeth 2a and the number Zf1 of first external teeth 7 is 2n.sub.1, where n.sub.1 is a positive integer. The difference between the number Zc2 of second internal teeth 3a and the number Zf2 of second external teeth 8 is 2n.sub.2, where n.sub.2 is a positive integer.
Zc1=Zf1+2n.sub.1
Zc2=Zf2?2n.sub.2

(17) In a specific example, the numbers of teeth are set as follows (n.sub.1=n.sub.2=1):
Zc1=62
Zf1=60
Zc2=62
Zf2=64

(18) The speed ratio R1 between the first internally toothed gear 2 and the first external teeth 7, and the speed ratio R2 between the second internally toothed gear 3 and the second external teeth 8, are respectively defined as follows:
i1=1/R1=(Zf1?Zc1)/Zf1=(60?62)/60=?1/30
i2=1/R2=(Zf2?Zc2)/Zf2=(64?62)/64=1/32

(19) Therefore, R1=?30, and R2=32.

(20) The speed ratio R of the strain wave gearing 1 is represented by the following formula using the speed ratios R1, and R2. Thus, according to the present invention, a strain wave gearing having a dramatically low speed ratio (low reduction ratio) can be realized (a negative speed ratio indicates that output rotation progresses in the direction opposite that of input rotation).

(21) $\begin{array}{c}R=\left(R1?R2-R1\right)/\left(-R1+R2\right)\\ =\left(-30?32+30\right)/\left(30+32\right)\\ =-930/62\\ =-15\end{array}$

(22) Thus, according to the strain wave gearing 1 in the present example, it is possible to obtain a speed ratio of less than 50, e.g., a speed ratio appreciably lower than 30. Additionally, unlike in the prior art, first external teeth 7 and second external teeth 8 that differ in number and module are formed as the external teeth of the externally toothed gear. Accordingly, there is a greater degree of freedom in the design for setting the speed ratio, and a strain wave gearing having a low speed ratio can be realized more easily than in the prior art.

(23) [Configuration of Externally Toothed Gear]

(24) FIG. 3 is a partial enlarged cross-sectional view of the strain wave gearing 1 shown in FIG. 1(A) and FIG. 1(B). The first and second external teeth 7, 8 formed in the externally toothed gear 4 shall now be described in detail with reference primarily to FIG. 3. In the present example, the tooth width of the first and second external teeth 7, 8 is substantially equal to that of the first and second internal teeth 2a, 3a, with which the first and second external teeth 7, 8 are capable of meshing. Therefore, the first external teeth 7 and second external teeth 8, which have the same tooth width, are formed symmetrically about a tooth-trace-direction central position 6a on the cylindrical body 6. In cases when the first internal teeth 2a and second internal teeth 3a differ in terms of tooth width, the first external teeth 7 and second external teeth 8 are also configured with different tooth widths in a corresponding manner.

(25) The gap 9, which has a prescribed width along the tooth trace direction, is formed between the first and second external teeth 7, 8. The gap 9 functions as a cutter clearance area for tooth-cutting cutters used for cutting the first and second external teeth 7, 8.

(26) (Rim Wall Thickness of First and Second External Teeth)

(27) The rim wall thickness of the tooth bottom rim of the first external teeth 7 and second external teeth 8 is set as follows. The second rim wall thickness t(2) of the second external teeth 8, of which there are a greater number, is set so as to be greater than the first rim wall thickness t(1) of the first external teeth 7, of which there are a smaller number, where the first rim wall thickness t(1) is the rim wall thickness of the first external teeth 7, and the second rim wall thickness t(2) is the rim wall thickness of the second external teeth 8.
t(1)<t(2)

(28) (Amount by Which First and Second External Teeth are Flexed)

(29) The first and second external teeth 7, 8 of the externally toothed gear 4 in the present example are both caused to flex in an ellipsoidal shape by the wave generator 5 having the two rows of wave bearings 12, 13. m.sub.1 is the module of the first external teeth 7, and m.sub.2 is the module of the second external teeth 8. 2n.sub.1 is the difference in number between the first external teeth 7 and the first internal teeth 2a, and 2n.sub.2 is the difference in number between the second external teeth 8 and the second internal teeth 3a. Therefore, the theoretical value d.sub.1 of the amount by which the first external teeth 7 are radially flexed at major-axis positions Lmax and the theoretical value d.sub.2 of the amount by which the second external teeth 8 are radially flexed when the external teeth are flexed in an ellipsoidal shape are respectively represented by the following.
d.sub.1=m.sub.1n.sub.1
d.sub.2=m.sub.2n.sub.2

(30) In the case of the first and second external teeth 7, 8 that differ in number and are formed in the outer-peripheral surface of the same cylindrical body 6, the pitch circle diameters of the teeth on both sides are approximately equal. Accordingly, the theoretical value mn of the amount of radial flexing is normally less when the number of teeth is greater.

(31) In the present example, the amounts by which the first and second external teeth 7, 8 are radially flexed by the wave generator 5 are both set to amount d. The amount d of radial flexing is represented by the following.
d<d.sub.1
d>d.sub.2

(32) FIG. 4(A) and FIG. 4(B) are diagrams showing the flexed state of the externally toothed gear 4. In FIG. 4(A) and FIG. 4(B), the rim-neutral circle C is the circle passing through the thickness center of the cylindrical body (tooth bottom rim) 6 in a state in which the externally toothed gear 4 is perfectly circular prior to being flexed in an ellipsoidal shape. The rim-neutral circle C is deformed in an ellipsoidal shape due to the externally toothed gear 4 being flexed in an ellipsoidal shape. This deformed circle is referred to as the ellipsoidal rim-neutral curve C1.

(33) The amount d by which the externally toothed gear 4 is radially flexed is the difference between the radius of the major axis Lmax of the ellipsoidal rim-neutral curve C1 and the radius of the rim-neutral circle C. This amount d is represented by ?mn, where m is the module of the externally toothed gear, 2n is the difference in number of teeth with respect to the internally toothed gears (n being a positive integer), and ? is the deflection coefficient. The amount mn of radial flexing when ? equals 1 is a value obtained by dividing the pitch circle diameter of the externally toothed gear by the reduction ratio from when the rigid internally toothed gear is secured; this is the theoretical value (amount of flexing at a standard deflection) of the amount of radial flexing.

(34) In the present example, the state of flexing of the first external teeth 7, of which there are a smaller number, is set to an amount of flexing less than the theoretical value (an amount of flexing at a negative deflection angle where ?<1), as described above. Conversely, the state of flexing of the second external teeth 8, of which there are a greater number, is set to an amount of flexing greater than the theoretical value (an amount of flexing at a positive deflection angle where ?>1).

(35) (Average Pressure Engles of First and Second External Teeth)

(36) FIG. 5(A) is a graph showing the pressure angle of the tooth profile that defines the first external teeth 7, and FIG. 5(B) is a graph showing the pressure angle of the tooth profile that defines the second external teeth 8. The pressure angles of the tooth profiles of the first and second external teeth 7 and 8 in the present example are described with reference to these graphs.

(37) In FIG. 5(A), which shows one tooth profile 70 of the first external teeth 7, a principal tooth land region A1 is the tooth land region that defines a range of 50% of the total tooth depth hl of the tooth profile 70, the principal tooth land region A1 being centered about the pitch circle PC1. The average of the angles that are formed by a tooth-profile center line of the tooth profile 70 and a tooth-profile tangent line that extends to individual portions of the principal tooth land region A1 is determined, this average being a first average pressure angle ?1.

(38) Similarly, in FIG. 5(B), which shows one tooth profile 80 of the second external teeth 8, a principal tooth land region A2 is the tooth land region that defines a range of 50% of the total tooth depth h2 of the tooth profile 80, the principal tooth land region A2 being centered about the pitch circle PC2. The average of angles that are formed by a tooth-profile center line of the tooth profile and a tooth-profile tangent line that extends to individual portions of the principal tooth land region A2 is determined, this average being a second average pressure angle ?2.

(39) In the present example, the first average pressure angle ?l of the first external teeth 7, of which there are a smaller number, is set so as to be greater than the second average pressure angel ?2 of the second external teeth 8, of which there are a greater number (i.e., ?1>?2). For example, the relationship between the first and second average pressure angles ?1, ?2 may be established as follows.
?2?0.31?1

(40) According to the experiments carried out by the inventors, it was confirmed that the relationship between the first and second average pressure angles ?1, ?2 is preferably established as follows.
0.29?1<?2<0.75?1

(41) By setting the average pressure angles of the first and second external teeth 7 and 8 differing in number as described above, the both first and second external teeth 7 and 8 can be meshed in a satisfactory manner with the corresponding internally toothed gears. In addition, it was confirmed that the wear resistance of the first and second external teeth 7 and 8 is improved, and that the balance of the tooth bottom fatigue strengths between the first and second external teeth 7 and 8 is improved. It was also confirmed that the bearing-ball load distribution of the two rows of the wave bearings 12 and 13 of the wave generator 5 for supporting the first and second external teeth 7 and 8 can be made uniform, and that the lifetimes of the wave bearings 12 and 13 can be elongated.

(42) (Gap: Cutter Clearance Area)

(43) The gap 9 formed between the first and second external teeth 7, is described next with reference to FIG. 3. As described previously, the gap 9 functions as a cutter clearance area for tooth-cutting cutters used for cutting the first and second external teeth 7, 8.

(44) The gap 9 has a prescribed width along the tooth trace direction; the deepest part, which is the part of the gap 9 that is formed deepest along the tooth depth direction, is formed in the tooth-trace-direction central portion. In the present example, the deepest part 9a is a portion at which the tooth-trace-direction central portion is defined by a straight line extending parallel to the tooth trace direction, as viewed from the tooth-thickness direction. At the two tooth-trace-direction ends of the deepest part 9a, a concave arcuate curve that defines the tooth-trace-direction inner-end surface 7a of the first external teeth 7 and a concave arcuate curve that defines the tooth-trace-direction inner-end surface 8a of the second external teeth 8 are smoothly connected. It is also possible to adopt a configuration in which the deepest part 9a is defined by a concave curved surface and the two inner-end surfaces 7a, 8a are defined by inclined straight lines. It is furthermore possible to adopt a configuration in which the deepest part 9a is defined by a straight line and the two inner-end surfaces 7a, 8a are defined by inclined straight lines.

(45) The tooth-trace-direction width of the gap 9 in the present example gradually increases from the deepest part 9a along the tooth depth direction. The maximum width L1 in the tooth trace direction is the distance, along the tooth trace direction, from the tooth-trace-direction inner end 7b of the addendum circle of the first external teeth 7 to the tooth-trace-direction inner end 8b of the addendum circle of the second external teeth 8.

(46) The relationship
0.1L<L1<0.3L

(47) is established, where L is the width from the tooth-trace-direction outer end 7c of the first external teeth 7 to the tooth-trace-direction outer end 8c of the second external teeth 8, and L1 is the tooth-trace-direction maximum width of the gap 9.

(48) The depth of the deepest part 9a of the gap 9 is set as follows. The relationships
0.9h1<t1<1.3h1 and
0.9h2<t2<1.3h2

(49) are established, where h1 is the tooth depth of the first external teeth 7, h2 is the tooth depth of the second external teeth 8, t1 is the tooth-depth-direction depth from the top land 7d of the first external teeth 7 to the deepest part 9a, and t2 is the tooth-depth-direction depth from the top land 8d of the second external teeth 8 to the deepest part 9a.

(50) In the externally toothed gear 4 of the dual-type strain wave gearing 1, the tooth-cutting cutters used for cutting the first and second external teeth 7, 8 are also different from each other. Therefore, the gap 9, which functions as a cutter clearance area, is formed in the tooth-trace-direction central portion of the externally toothed gear 4; i.e., between the first external teeth 7 and the second external teeth 8.

(51) The manner in which the gap 9 is formed has a prominent effect on the tooth contact of the first external teeth 7 with respect to the first internal teeth 2a along the tooth trace direction, as well as the tooth land load distribution. The manner in which the gap 9 is formed similarly has a prominent effect on the tooth contact of the second external teeth 8 with respect to the second internal teeth 3a along the tooth trace direction, as well as the tooth land load distribution.

(52) In view of these points, the maximum width L1 of the gap is set within a range of 0.1-0.3 times the width L of the externally toothed gear 4, and the maximum depths t1, t2 are set within a range of 0.9-1.3 times the tooth depths h1, h2 of the first and second external teeth 7, 8, as described above. It was confirmed that forming the gap 9 in this manner makes it possible to maintain uniformity in the tooth-trace-direction tooth land load distributions of the first and second external teeth 7, 8, and to maintain a satisfactory state for the tooth contact of the first and second external teeth 7, 8 with respect to the first and second internal teeth 2a, 3a at each tooth-trace-direction position.

(53) [Distance Between Bearing-Ball Centers in Wave Generator]

(54) The distance between the bearing-ball centers of the first and second wave bearings 12, 13 are described next with reference to FIG. 3.

(55) In the rigid plug 11 of the wave generator 5, an ellipsoidally contoured first outer-peripheral surface 11a of fixed width is formed on one central-axis-direction side, and an ellipsoidally contoured second outer-peripheral surface 11b of fixed width is formed on the other central-axis-direction side. The first outer-peripheral surface 11a and the second outer-peripheral surface 11b are ellipsoidal outer-peripheral surfaces having the same shape and the same phase.

(56) The first wave bearing 12 is fitted to the first outer-peripheral surface 11a in a state of being flexed in an ellipsoidal shape, and the second wave bearing 13 is fitted to the second outer-peripheral surface 11b in a state of being flexed in an ellipsoidal shape. The first and second wave bearings 12, 13 are of the same size.

(57) The bearing centers 12a, 13a of the first wave bearing 12 and second wave bearing 13 are located at positions that are equidistant, along the tooth width direction, from the tooth-trace-direction central position 6a on the externally toothed gear 4. The distance between bearing-ball centers is set so as to increase correspondingly with an increase in the maximum width L1 of the gap 9. Furthermore, the inter-ball-center distance Lo is set so as to reach a value within the range indicated by the following formula, Lo being the distance between bearing-ball centers.
0.35L<Lo<0.7L

(58) In the prior art, a wave generator having two rows of ball bearings is used in order to increase the area in which the externally toothed gear is supported. The two rows of ball bearings were arranged with respect to the tooth-width-direction central portion of the externally toothed gear, irrespective of the inter-ball-center distance.

(59) In the present example, the inter-ball-center distance Lo between two rows of wave bearings 12, 13 is increased such that it is possible to increase rigidity for supporting first and second external teeth 7, 8 differing in number, and to improve the tooth contact of each of the external teeth 7, 8 with respect to internal teeth 2a, 3a at each tooth-trace-direction position. Specifically, as described above, a configuration is adopted in which the inter-ball-center distance Lo lengthens (increases) correspondingly with an increase in the tooth-trace-direction maximum length L1 of the gap 9, which is formed between the first and second external teeth 7, 8 and functions as a cutter clearance area. The range of increase of the inter-ball-center distance Lo is set to 0.35-0.7 times the width L of the externally toothed gear 4.

(60) This makes it possible to arrange the first and second wave bearings 12, 13 such that the ball centers are positioned at suitable tooth-trace-direction positions with respect to each of the first and second external teeth 7, 8, in accordance with the width of the gap 9 that is formed. This makes it possible to reliably support the first and second external teeth 7, 8, using the first and second wave bearings 12, 13, at each tooth-trace-direction position of each of the first and second external teeth 7, 8 (i.e., to increase the supporting rigidity of the wave generator 5).

(61) As a result, it is possible to improve the tooth contact of the first and second external teeth 7, 8 at each tooth-trace-direction position, and to increase the tooth bottom fatigue strength thereof. It is also possible to average the bearing-ball load distribution of each of the wave bearings 12, 13 of the wave generator 5, and to reduce the maximum load; therefore, the service life of the wave generator 5 can be improved.

Other Embodiments

(62) In the example described above, the first internally toothed gear 2 is configured as a stationary-side internally toothed gear, and the second internally toothed gear 3 is configured as a drive-side internally toothed gear (reduced-rotation-outputting member). However, it is possible to instead configure the first internally toothed gear 2 as a drive-side internally toothed gear (reduced-rotation-outputting member), and configure the second internally toothed gear 3 as a stationary-side internally toothed gear.