CN110725919A

CN110725919A - Flexible gear, rigid gear and harmonic reducer

Info

Publication number: CN110725919A
Application number: CN201911127021.9A
Authority: CN
Inventors: 邱楚锋
Original assignee: Guangzhou Xinhao Precision Technology Co Ltd
Current assignee: Guangzhou Xinhao Precision Technology Co Ltd
Priority date: 2019-11-18
Filing date: 2019-11-18
Publication date: 2020-01-24

Abstract

The utility model provides a gentle wheel and rigid gear and harmonic speed reducer ware, when not atress, the gentle wheel teeth on the gentle wheel and the rigid gear teeth on the rigid gear all keep face contact at complete mesh state or half mesh state, and after the atress, the gentle wheel teeth on the gentle wheel and the rigid gear teeth on the rigid gear become face contact at complete mesh state or half mesh state, consequently, can not produce edge mesh and sharp point meshing, the serious situation of flank of tooth wearing and tearing that produces when effectively having avoided the two to mesh mutually, not only be favorable to the formation of oil film, can also avoid forming stress concentration in wearing and tearing department, guarantee the bearing strength of gentle wheel and rigid gear, be favorable to prolonging the life of gentle wheel and rigid gear.

Description

Flexible gear, rigid gear and harmonic reducer

Technical Field

The invention relates to a flexible gear, a rigid gear matched with the flexible gear and a harmonic reducer comprising the flexible gear and the rigid gear.

Background

The harmonic reducer is mainly composed of four basic components of a wave generator, a flexible gear and a rigid gear, and is a gear transmission which is characterized in that the flexible gear generates controllable elastic deformation by assembling the flexible bearing on the wave generator and is meshed with the rigid gear to transmit motion and power. The existing harmonic reducer deforms the flexible gear under the action of the wave generator, so that the teeth of the flexible gear part are forced to be meshed with the teeth of the rigid gear part, and the meshing part usually has edge meshing and sharp point meshing, so that the edge meshing part and the sharp point meshing part are easily seriously abraded, the formation of oil films on the surfaces of the rigid gear and the flexible gear is not facilitated, and meanwhile, the abrasion part is also easily subjected to large stress concentration, so that the bearing capacity of the flexible gear and the rigid gear is weak, and the service life of the flexible gear and the rigid gear is short.

Disclosure of Invention

The invention aims to provide a flexible gear, a rigid gear and a harmonic reducer which have strong bearing capacity and long service life.

The flexible gear comprises a flexible gear body with a cavity at a core part, wherein a plurality of flexible gear teeth are continuously arranged on the outer side wall of the flexible gear body along the circumferential direction of the flexible gear body; a single flexbile gear tooth includes addendum circular arc R4 and two sections root circular arcs R3, and two sections root circular arcs R3 are located addendum circular arc R4 both sides, and addendum circular arc R4 all loops through circular arc R1 and circular arc R2 between the root circular arc R3 of both sides rather than and are connected as an organic wholely, circular arc R1 is the circular arc of evagination, circular arc R2 is the circular arc of indent, and adjacent gentle teeth of a cogwheel pass through root circular arc R3 and connect.

The rigid wheel comprises a rigid wheel body, wherein a through hole for inserting the flexible wheel is formed in the core part of the rigid wheel body, and a plurality of rigid wheel teeth are continuously arranged on the side wall of the through hole of the rigid wheel body along the circumferential direction of the through hole; a single rigid wheel tooth includes addendum plane D and two sections root circular arcs R5, and two sections root circular arcs R5 are located addendum plane D both sides, all loop through circular arc R6, circular arc R7 and circular arc R8 between addendum plane D and the root circular arc R5 of its both sides and connect as an organic wholely, circular arc R6 and circular arc R7 are the circular arc of evagination, circular arc R8 is the circular arc of indent, and adjacent just teeth of a cogwheel pass through root circular arc R5 and connect.

The harmonic reducer comprises a wave generator, the flexible gear and the rigid gear, wherein the flexible gear is inserted into a through hole of the rigid gear, the wave generator is embedded into an inner cavity of the flexible gear, and the wave generator deforms the flexible gear to enable the flexible gear to be meshed with the rigid gear.

According to the flexible gear and the rigid gear, as the circular arc R1 on the flexible gear tooth is an outward convex circular arc, the circular arc R2 is an inward concave circular arc, the circular arcs R6 and R7 on the rigid gear tooth are outward convex circular arcs, and the circular arc R8 is an inward concave circular arc, when the flexible gear is completely meshed with the rigid gear, the circular arc R1 on the flexible gear tooth is contacted with the circular arc R8 on the rigid gear tooth, the flexible gear is forced to deform along with the rotation of the wave generator, part of the flexible gear tooth on the flexible gear and part of the rigid gear tooth on the rigid gear are changed from a disengagement state or a half meshing state, when the rigid gear is in the half meshing state, the circular arc R1 on one side tooth surface of the flexible gear tooth on the flexible gear is gradually disengaged from the circular arc R8 on one side tooth surface of the rigid gear tooth on the flexible gear, and the circular arc R2 on one side tooth surface of the flexible gear tooth on the flexible gear is gradually contacted with the circular arcs R6 and R7, as the wave generator continues to rotate, the circular arc R2 on one side tooth surface of the flexible gear teeth on the flexible gear gradually disengages from the circular arcs R6 and R7 on one side tooth surface of the rigid gear teeth on the rigid gear until the engaged teeth disengage from each other; when the stress is not applied, the flexible gear teeth on the flexible gear and the rigid gear teeth on the rigid gear are in surface contact in a complete meshing state or a half meshing state, and when the stress is applied, the flexible gear teeth on the flexible gear and the rigid gear teeth on the rigid gear are in surface contact in the complete meshing state or the half meshing state, so that edge meshing and sharp point meshing cannot be generated, the situation that the tooth surfaces are seriously abraded when the flexible gear and the rigid gear are meshed with each other is effectively avoided, not only is the formation of an oil film facilitated, but also the stress concentration at the abrasion part can be avoided, and on the premise that the bearing strength of the flexible gear and the rigid gear is ensured, the stability of the transmission precision when the flexible gear and the rigid gear are matched is ensured, and the service lives of the flexible gear and the rigid gear.

The harmonic reducer is suitable for the structures of the flexible gear and the rigid gear, and has high bearing strength, so that the harmonic reducer not only can be long in service life, but also can be used for transmitting power with high precision.

Drawings

Fig. 1 is a schematic view of a flexspline of the present invention.

Fig. 2 is a schematic view of a flexible gear tooth structure according to the present invention.

FIG. 3 is a schematic view of the rigid wheel structure of the present invention.

FIG. 4 is a schematic view of a steel gear tooth structure according to the present invention.

FIG. 5 is a schematic view of the meshing structure of the flexible gear and the rigid gear.

FIG. 6 is a schematic diagram of a harmonic reducer according to the present invention.

Fig. 7 is an exploded view of fig. 6.

Detailed Description

A flexible gear, as shown in fig. 1 and 2, comprises a flexible gear body with a core provided with a cavity, wherein a plurality of flexible gear teeth are continuously arranged on the outer side wall of the flexible gear body along the circumferential direction of the flexible gear body; a single flexbile gear tooth includes addendum circular arc R4 and two sections root circular arcs R3, and two sections root circular arcs R3 are located addendum circular arc R4 both sides, and addendum circular arc R4 all loops through circular arc R1 and circular arc R2 between the root circular arc R3 of both sides rather than and are connected as an organic wholely, circular arc R1 is the circular arc of evagination, circular arc R2 is the circular arc of indent, and adjacent gentle teeth of a cogwheel pass through root circular arc R3 and connect. The circular arc R1 is a convex circular arc, i.e., the circular arc R1 on one flexspline tooth is convex toward the adjacent flexspline tooth, and the circular arc R2 is a concave circular arc, i.e., the circular arc R2 on one flexspline tooth is concave toward itself.

The radius of the circular arc R1 is 0.72 mm-1.09 mm, such as 0.72mm, 0.73mm, 0.74mm, 0.75 mm, 0.76mm, 0.77 mm, 0.78 mm, 0.79 mm, 0.80mm, 0.81 mm, 0.82 mm, 0.83 mm, 0.84mm, 0.85 mm, 0.86 mm, 0.87 mm, 0.88mm, 0.89 mm, 0.90mm, 0.91 mm, 0.92 mm, 0.93 mm, 0.94 mm, 0.95mm, 0.96 mm, 0.97 mm, 0.98mm, 0.99 mm, 1.00 mm, 1.01mm, 1.02 mm, 1.03mm, 1.04 mm, 1.05mm, 1.06 mm, 1.07 mm, 1.08 mm or 1.09mm, the radius of the circular arc R1 mm, 0.43 mm, 0.38mm, 0.43 mm, 0.48mm, 0.43 mm, 0.38mm, 0.48mm, 0.38mm, 0.48mm, 0.45mm, 0.53mm, 0.54 mm or 0.55mm, the radius of the root circular arc R3 is 0.18mm < R3 < 0.28mm, such as 0.18mm, 0.19mm, 0.20mm, 0.21mm, 0.22mm, 0.23mm, 0.24mm, 0.25mm, 0.26mm, 0.27mm or 0.28mm, the radius of the top circular arc R4 is 0.18mm < R4 < 0.28mm, such as 0.18mm, 0.19mm, 0.20mm, 0.21mm, 0.22mm, 0.23mm, 0.24mm, 0.25mm, 0.26mm, 0.27mm or 0.28mm, the tooth thickness L1 mm < L1 mm, 0.73mm, such as 0.48mm, 0.49mm, 0.27mm, 0.28mm, 0.60mm, 0.65mm, 0.59 mm, 0.65mm, 0.59 mm, 0.60mm, 0.66mm, 0.60mm, 0.28mm, 0.48mm, 0.28mm, 0.71 mm, 0.72mm, 0.73mm, etc., the groove width L2 of the flexible gear teeth is 0.48mm < L2 < 0.72mm, such as 0.48mm, 0.49mm, 0.50mm, 0.51mm, 0.52mm, 0.53mm, 0.54 mm, 0.55mm, 0.56mm, 0.57mm, 0.58mm, 0.59 mm, 0.60mm, 0.61mm, 0.62 mm, 0.63mm, 0.64 mm, 0.65mm, 0.66mm, 0.67 mm, 0.68mm, 0.69mm, 0.70mm, 0.71 mm, or 0.72mm, etc., the radial height h1 of the circular arc R1 is 0.22mm < h < 56 < 0.33mm, such as 0.22mm, 0.23mm, 0.24mm, 0.25mm, 0.26mm, 0.29 mm, 0.30 mm, 0.32 mm, 0.30 mm, 0.590.32 mm, 0.30, 0.33mm, 0.34 mm, 0.35mm, 0.36mm or 0.37mm, and the like, and the height h from the tooth crest to the tooth root of the flexible gear teeth is 0.56mm < h < 0.84mm, such as 0.56mm, 0.57mm, 0.58mm, 0.59 mm, 0.60mm, 0.61mm, 0.62 mm, 0.63mm, 0.64 mm, 0.65mm, 0.66mm, 0.67 mm, 0.68mm, 0.69mm, 0.70mm, 0.71 mm, 0.72mm, 0.73mm, 0.74mm, 0.75 mm, 0.76mm, 0.77 mm, 0.78 mm, 0.79 mm, 0.80mm, 0.81 mm, 0.82 mm, 0.83 mm or 0.84mm, and the like, and by setting the parameters of the flexible gear teeth in the above ranges, the flexible gear teeth can effectively maintain the engagement between the sharp gear and the gear, thereby avoiding the occurrence of the contact between the sharp gear and the rigid gear, the occurrence of the contact between the hard gear and the hard gear, and the occurrence of the contact between the occurrence of the gear teeth, and, the bearing strength of the flexible gear is ensured, and the service life of the flexible gear is prolonged.

A rigid wheel, as shown in fig. 3 and 4, comprises a rigid wheel body, wherein a through hole for inserting a flexible wheel is arranged at the core part of the rigid wheel body, and a plurality of rigid wheel teeth are continuously arranged on the side wall of the through hole of the rigid wheel body along the circumferential direction of the through hole; a single rigid wheel tooth includes addendum plane D and two sections root circular arcs R5, and two sections root circular arcs R5 are located addendum plane D both sides, all loop through circular arc R6, circular arc R7 and circular arc R8 between addendum plane D and the root circular arc R5 of its both sides and connect as an organic wholely, circular arc R6 and circular arc R7 are the circular arc of evagination, circular arc R8 is the circular arc of indent, and adjacent just teeth of a cogwheel pass through root circular arc R5 and connect. The circular arc R6 and the circular arc R7 are convex circular arcs, that is, the circular arc R6 and the circular arc R7 on one rigid gear tooth are convex toward the adjacent rigid gear tooth, and the circular arc R8 is a concave circular arc, that is, the circular arc R8 on one rigid gear tooth is concave toward itself. After the shape and the parameters of the gear teeth of the flexible gear are determined, the shape and the parameters of the gear teeth of the rigid gear can be obtained through the envelope principle. The number of the rigid gear teeth on the rigid wheel is two more than that of the flexible gear teeth on the flexible wheel.

The radius of the tooth root circular arc R5 is 0.18mm ≤ R5 ≤ 0.27mm, such as 0.18mm, 0.19mm, 0.20mm, 0.21mm, 0.22mm, 0.23mm, 0.24mm, 0.25mm, 0.26mm or 0.27mm, the radius of the circular arc R6 is 0.13mm ≤ R6 ≤ 0.19mm, such as 0.13mm, 0.14mm, 0.15mm, 0.16mm, 0.17 mm, 0.18mm or 0.19mm, the radius of the circular arc R7 is 0.38mm ≤ R7 ≤ 0.57mm, such as 0.38mm, 0.39 mm, 0.40mm, 0.41 mm, 0.42mm, 0.43 mm, 0.44 mm, 0.45mm, 0.46 mm, 0.47mm, 0.48mm, 0.40mm, 0.41 mm, 0.42mm, 0.43 mm, 0.55mm, 1.01mm, 1.55 mm, 1.5 mm, 1.06 mm, 1.53 mm, 1.5 mm, 1.55 mm, 1mm, 1.3 mm, 1mm, 1.19 mm, 1mm, 1.08 mm, 1.09mm, 1.10 mm, 1.11 mm, 1.12 mm, 1.13 mm, 1.14 mm, 1.15 mm, 1.16 mm, 1.17 mm, 1.18 mm, 1.19 mm, 1.20 mm, 1.21 mm, 1.22 mm, 1.23mm, 1.24mm, 1.25 mm, 1.26mm, 1.27 mm, 1.28 mm, 1.29 mm, 1.30 mm, 1.31mm, 1.32 mm, 1.33 mm, 1.34 mm, 1.35 mm, 1.36 mm, 1.37 mm, 1.38 mm, 1.39 mm, 1.40 mm, 1.41 mm, 1.42 mm, 1.43mm, 1.44 mm, 1.45 mm, 1.46 mm, 1.47 mm, 1.48 mm, 1.49 mm, 1.50 mm, 1.51 mm, 1.42 mm, 1.43mm, 1.44 mm, 1.45 mm, 1.47 mm, 1.48 mm, 0.51mm, 0.52mm, 0.53mm, 0.52mm, 0.53mm, 0.65mm, 0.66mm, 0.67 mm, 0.68mm, 0.69mm, 0.70mm, 0.71 mm, 0.72mm, 0.73mm, 0.74mm, 0.75 mm, 0.76mm and the like, the tooth thickness L4 of the rigid gear teeth is 0.45mm < L4 < 0.68mm, such as 0.45mm, 0.46 mm, 0.47mm, 0.48mm, 0.49mm, 0.50mm, 0.51mm, 0.52mm, 0.53mm, 0.54 mm, 0.55mm, 0.56mm, 0.57mm, 0.58mm, 0.59 mm, 0.60mm, 0.61mm, 0.62 mm, 0.63mm, 0.64 mm, 0.65mm, 0.66mm, 0.67 mm or 0.68mm and the like, the radial height of the R8 is 0.34 mm, 0.26mm, 0.32 mm, 0.34 mm, 0.26mm, 0.32 mm, 0.34 mm, 0.32 mm, 0.30 mm, 0.32 mm, such as 0.14mm, 0.15mm, 0.16mm, 0.17 mm, 0.18mm, 0.19mm, 0.20mm, 0.21mm or 0.22mm, the height H from the tooth crest to the tooth root of said rigid gear teeth is 0.49mm ≦ H ≦ 0.74mm, such as 0.49mm, 0.50mm, 0.51mm, 0.52mm, 0.53mm, 0.54 mm, 0.55mm, 0.56mm, 0.57mm, 0.58mm, 0.59 mm, 0.60mm, 0.61mm, 0.62 mm, 0.63mm, 0.64 mm, 0.65mm, 0.66mm, 0.67 mm, 0.68mm, 0.69mm, 0.70mm, 0.71 mm, 0.72mm, 0.73mm or 0.74mm, by setting the parameters of the rigid gear teeth in the range of said gear teeth, the effective meshing between the flexible gear and the sharp gear is maintained, thereby not only avoiding the occurrence of severe meshing between the sharp gear and the hard gear, and sharp gear, and the occurrence of the hard gear, and the occurrence of the tooth surfaces, and the occurrence of the engagement of the contact between the hard gear teeth, and stress concentration at the abrasion part can be avoided, the bearing strength of the rigid wheel is ensured, and the service life of the rigid wheel is prolonged.

The tooth profile parameters of the rigid wheel and the flexible wheel are obtained by creative labor of the inventor, and the rigid wheel and the flexible wheel are matched with each other under the parameters, so that edge meshing and sharp point meshing between the rigid wheel and the flexible wheel can be further effectively avoided, serious abrasion of a meshing part is avoided, formation of an oil film is facilitated, stress concentration at the abrasion part can be avoided, the bearing strength of the flexible wheel and the rigid wheel is ensured, and the service life of the flexible wheel and the rigid wheel is prolonged.

The utility model provides a harmonic speed reducer ware, as shown in fig. 5 to 7, includes wave generator, flexible bearing 4 and foretell flexible gear 1 and all technical characteristics of rigid gear 2, flexible gear 1 inserts in the through-hole of rigid gear 2, wave generator embedding flexible gear 1's inner chamber, still be provided with flexible bearing 4 between wave generator and the flexible gear 1, wave generator makes flexible gear 1 take place deformation, makes flexible gear 1 and rigid gear 2 mesh mutually. Because the harmonic reducer has all the technical characteristics of the flexible gear 1 and the rigid gear 2, the harmonic reducer also has all the beneficial technical effects of the flexible gear 1 and the rigid gear 2, so that the power transmission precision of the harmonic reducer is higher, and the service life of the harmonic reducer is longer.

The wave generator is prior art, and it includes wheel hub 5 and oval cam 6 that the cover is connected on wheel hub 5, set up flexible bearing 4 between the inner chamber wall of cam 6 and flexbile gear 1, force flexbile gear 1 to take place to warp through the shape of cam 6, make flexbile gear 1 and mesh with rigid wheel 2 mutually. The bottom of the flexible gear 1 is tightly pressed on the inner ring of the crossed roller bearing 3 through a flexible gear press ring 7, and the bottom of the rigid gear 2 is connected with the outer ring of the crossed roller bearing 3 through a screw.

The present invention is further illustrated by the following specific embodiments of harmonic reducers, which are preferred embodiments of the present invention but are not to be construed as being limited thereto.

Example one

A harmonic reducer adopts above-mentioned technical scheme, and wherein the flexspline parameter is: r1 is 0.72mm, R2 is 0.36mm, R3 is 0.23mm, R4 is 0.24mm, L1 is 0.48mm, L2 is 0.48mm, h1 is 0.22mm, h2 is 0.25mm, h is 0.70 mm; the rigid wheel parameters are as follows: r5 is 0.22mm, R6 is 0.16mm, R7 is 0.38mm, R8 is 1.01mm, L3 is 0.51mm, L4 is 0.45mm, H3 is 0.25mm, H4 is 0.14mm, and H is 0.61 mm.

Example two

On the basis of the first embodiment, the parameters of the flexible wheel part are changed into: r1 is 1.09mm, R2 is 0.55mm, L1 is 0.73mm, L2 is 0.72mm, h1 is 0.33mm, h2 is 0.37 mm; part of parameters of the rigid wheel are changed into the following parameters: r7 is 0.57mm, R8 is 1.52mm, L3 is 0.76mm, L4 is 0.68mm, h3 is 0.38mm, h4 is 0.22 mm.

EXAMPLE III

On the basis of the first embodiment, the parameters of the flexible wheel part are changed into: r1 is 0.90mm, R2 is 0.45mm, L1 is 0.60mm, L2 is 0.61mm, h1 is 0.27mm, h2 is 0.31 mm; part of parameters of the rigid wheel are changed into the following parameters: r7 is 0.47mm, R8 is 1.26mm, L3 is 0.63mm, L4 is 0.56mm, h3 is 0.31mm, and h4 is 0.18 mm.

Example four

On the basis of the first embodiment, the parameters of the flexible wheel part are changed into: r1 is 0.88mm, R2 is 0.40mm, L1 is 0.55mm, L2 is 0.58mm, h1 is 0.25mm, h2 is 0.28 mm; part of parameters of the rigid wheel are changed into the following parameters: r7 is 0.45mm, R8 is 1.23mm, L3 is 0.60mm, L4 is 0.52mm, h3 is 0.28mm, and h4 is 0.15 mm.

EXAMPLE five

On the basis of the first embodiment, the parameters of the flexible wheel part are changed into: r1 is 0.95mm, R2 is 0.50mm, L1 is 0.65mm, L2 is 0.66mm, h1 is 0.31mm, h2 is 0.35 mm; part of parameters of the rigid wheel are changed into the following parameters: r7 is 0.52mm, R8 is 1.31mm, L3 is 0.68mm, L4 is 0.61mm, h3 is 0.35mm, h4 is 0.21 mm.

Comparative example 1

A harmonic reducer is structurally the same as the harmonic reducer, but the flexible gear parameters are as follows: r1 is 0.65mm, R2 is 0.3mm, R3 is 0.23mm, R4 is 0.24mm, L1 is 0.40mm, L2 is 0.40mm, h1 is 0.20mm, h2 is 0.23mm, h is 0.70 mm; the rigid wheel parameters are that R5 is 0.22mm, R6 is 0.16mm, R7 is 0.35mm, R8 is 0.98mm, L3 is 0.48mm, L4 is 0.42mm, H3 is 0.22mm, H4 is 0.11mm, and H is 0.61 mm.

Comparative example No. two

On the basis of the first comparative example, the parameters of the flexible wheel part are modified as follows: l1 is 0.60mm, L2 is 0.61 mm; the parameters of the rigid wheel part are modified as follows: l3 was 0.63mm and L4 was 0.56 mm.

The harmonic reducers in the above examples one to five and comparative examples one and two were subjected to a half-year actual running-in test under a load of 50n.m, and the results are shown in the following table (in mm):

as is clear from the above table, after the running-in test, from 3 months, it is obvious that the clearance between the flexible gear and the rigid gear of the harmonic reducer in the comparative example is larger and larger, while the clearance between the flexible gear and the rigid gear of the harmonic reducer in the present application is always stable and always maintained in the national standard "191105: in an arc part (converted into 0.086mm in the test) required by GBT 30819-. It should be noted that, in the comparative example, after the clearance between the rigid gear and the flexible gear is greater than 0.2, no continuous test is necessary, and if the test is continued, the flexible gear is directly broken, and the motor is damaged.

Claims

1. A flexible gear comprises a flexible gear body with a cavity at a core part, wherein a plurality of flexible gear teeth are continuously arranged on the outer side wall of the flexible gear body along the circumferential direction of the flexible gear body; the method is characterized in that: a single flexbile gear tooth includes addendum circular arc R4 and two sections root circular arcs R3, and two sections root circular arcs R3 are located addendum circular arc R4 both sides, and addendum circular arc R4 all loops through circular arc R1 and circular arc R2 between the root circular arc R3 of both sides rather than and are connected as an organic wholely, circular arc R1 is the circular arc of evagination, circular arc R2 is the circular arc of indent, and adjacent gentle teeth of a cogwheel pass through root circular arc R3 and connect.

2. The flexspline of claim 1, wherein: the radius of the circular arc R1 is 0.72mm or more and R1 or less and 1.09mm or less, the radius of the circular arc R2 is 0.36mm or more and R2 or less and 0.55mm or less, the tooth thickness L1 of the flexible gear tooth is 0.48mm or more and L1 or less and 0.73mm or less, the tooth groove width L2 of the flexible gear tooth is 0.48mm or more and L2 or less and 0.72mm or less, the radial height h1 of the circular arc R1 is 0.22mm or more and h1 or less and 0.33mm or less, and the tooth root height h2 of the flexible gear tooth is 0.25mm or more and h2 or less and 0.37mm or less.

3. The flexspline of claim 2, wherein: the radius of the tooth root circular arc R3 is more than or equal to 0.18mm and less than or equal to R3 and less than or equal to 0.28mm, the radius of the tooth top circular arc R4 is more than or equal to 0.18mm and less than or equal to R4 and less than or equal to 0.28mm, and the height h from the tooth top to the tooth root of the flexible gear tooth is more than or equal to 0.56mm and less than or equal to h and less than or equal to 0.84 mm.

4. A rigid wheel comprises a rigid wheel body, wherein a through hole for inserting a flexible wheel is formed in the core part of the rigid wheel body, and a plurality of rigid wheel teeth are continuously arranged on the side wall of the through hole of the rigid wheel body along the circumferential direction of the through hole; the method is characterized in that: a single rigid wheel tooth includes addendum plane D and two sections root circular arcs R5, and two sections root circular arcs R5 are located addendum plane D both sides, all loop through circular arc R6, circular arc R7 and circular arc R8 between addendum plane D and the root circular arc R5 of its both sides and connect as an organic wholely, circular arc R6 and circular arc R7 are the circular arc of evagination, circular arc R8 is the circular arc of indent, and adjacent just teeth of a cogwheel pass through root circular arc R5 and connect.

5. A rigid wheel according to claim 4, wherein: the number of the rigid gear teeth on the rigid wheel is two more than that of the flexible gear teeth on the flexible wheel.

6. A rigid wheel according to claim 4 or 5, wherein: the radius of the circular arc R7 is more than or equal to 0.38mm and less than or equal to R7 and less than or equal to 0.57mm, the radius of the circular arc R8 is more than or equal to 1.01mm and less than or equal to R8 and less than or equal to 1.52mm, the tooth width L3 of the steel gear teeth is more than or equal to 0.51mm and less than or equal to L3 and less than or equal to 0.76mm, the tooth thickness L4 of the steel gear teeth is more than or equal to 0.45mm and less than or equal to L4 and less than or equal to 0.68mm, the radial height h3 of the circular arc R8 is more than or equal to 0.25mm and less than or equal to h3 and less than or equal to 0.38 mm.

7. A rigid wheel according to claim 6, wherein: the radius of the tooth root circular arc R5 is more than or equal to 0.18mm and less than or equal to R5 and less than or equal to 0.27mm, the radius of the circular arc R6 is more than or equal to 0.13mm and less than or equal to R6 and less than or equal to 0.19mm, and the height H from the tooth crest to the tooth root of the rigid gear is more than or equal to 0.49mm and less than or equal to H and less than or equal to 0.74 mm.

8. A harmonic reducer comprises a wave generator and a flexible bearing, and is characterized in that: the flexible gear comprises a flexible gear according to any one of claims 1 to 3 and a rigid gear according to any one of claims 4 to 7, wherein the flexible gear is inserted into a through hole of the rigid gear, the wave generator is embedded into an inner cavity of the flexible gear, a flexible bearing is further arranged between the wave generator and the flexible gear, and the wave generator deforms the flexible gear to enable the flexible gear to be meshed with the rigid gear.

9. A harmonic reducer according to claim 8 in which: the bottom of the flexible wheel is tightly pressed on the inner ring of the crossed roller bearing through a flexible wheel pressing ring, and the bottom of the rigid wheel is connected with the outer ring of the crossed roller bearing through a screw.