A flexible gear tooth structure of a harmonic reducer and a harmonic reducer

Abstract

This utility model discloses a flexible gear tooth profile structure and a harmonic reducer, relating to the technical field of harmonic reducers. It includes multiple teeth disposed on a flexible gear, each tooth having a first and / or second modified portion to increase the edge contact area during meshing. By configuring the first and second modified portions on the teeth, the radius of curvature of the tooth tip plane and the meshing point is increased, increasing the contact area during meshing, reducing impact load, and providing a larger area for the oil film to separate the tooth surface. This makes the actual metal contact area approach zero, increasing the contact area, reducing the maximum contact stress, and simultaneously reducing the probability of adhesion failure.

Description

Technical Field

[0001] This utility model belongs to the field of harmonic reducer technology, specifically relating to a flexible gear tooth structure of a harmonic reducer and a harmonic reducer. Background Technology

[0002] Currently, traditional harmonic reducers use a standard involute tooth profile for the flexure, with fixed tooth tip height and tooth thickness. The high tooth tip height concentrates stress at the tooth root during meshing. This root region is prone to microcracks, leading to fatigue fracture, shortened service life, and potential sudden failure under high load conditions, impacting equipment reliability. Insufficient tooth thickness results in insufficient load-bearing capacity and low transmission efficiency. Existing designs cannot balance flexure strength and transmission efficiency, leading to short lifespan and high noise. Furthermore, gear meshing is mostly line contact, with edge contact causing a sharp reduction in contact area and increased impact load. Additionally, due to the contact of metal micro-protrusions, the actual contact area is much smaller than the theoretical value, resulting in extremely high local stress and a tendency to cause scuffing or wear. To solve at least one of these technical problems, it is necessary to develop a new flexure tooth profile structure and a new harmonic reducer. Utility Model Content

[0003] The purpose of this utility model is to provide a flexible gear tooth structure and a harmonic reducer to solve the above-mentioned technical problems. By setting a first modified part and a second modified part on the gear teeth, the radius of curvature of the two points on the tooth tip plane and the meshing point is increased, which increases the contact area during meshing, reduces the impact load, and provides a larger area for the oil film to separate the tooth surface, so that the actual metal contact area approaches zero, increases the contact area, reduces the maximum contact stress, and reduces the probability of adhesion failure.

[0004] To achieve the above-mentioned objectives, the technical solution adopted by this utility model is as follows:

[0005] A flexible gear tooth structure for a harmonic reducer includes multiple teeth disposed on the flexible gear. The teeth are provided with a first modified portion and / or a second modified portion to increase the edge contact area during meshing. By providing the first and second modified portions on the teeth, the radius of curvature of the tooth tip plane and the meshing point is increased, thereby increasing the contact area during meshing, reducing impact load, and providing a larger area for the oil film to separate the tooth surface. This makes the actual metal contact area approach zero, increasing the contact area, reducing the maximum contact stress, and simultaneously reducing the probability of galling failure.

[0006] Preferably, the first shaping portion is provided at the tooth profile of the gear tooth.

[0007] Preferably, the second shaping portion is provided at the tooth direction of the gear teeth.

[0008] Preferably, the shape of the first modified portion is a first parabolic modified portion.

[0009] Preferably, the shape of the first parabola modification satisfies the following formula:

[0010] δ(x)=δ max *(1-x / L) 2 ,

[0011] In the formula, δ(x): the amount of shaping at a distance x from the shaping start point, in μm;

[0012] δ_max: Maximum shaping amount, which is at the end or beginning of the shaping process, in μm;

[0013] L: Length of the reshaping area, from the starting point to the ending point of the reshaping, in mm;

[0014] x: The distance along the tooth profile from the starting point of the modification, in mm. By modifying the tooth profile, the meshing position is adjusted to make the load distribution more uniform, reduce tooth profile errors, and avoid a sudden reduction in local contact area;

[0015] Preferably, the shape of the second modified portion is a second parabolic modified portion.

[0016] Preferably, the shape of the second parabola modification satisfies the following formula:

[0017] δ(y)=C*[1-(2y / b) 2 ],

[0018] In the formula, δ(y): the amount of protrusion at a distance y from the center line of the tooth width, in mm;

[0019] C: Maximum protrusion, located at the center of tooth width y=0, in mm;

[0020] b: Effective tooth width of the gear, in mm;

[0021] y: The distance along the tooth width direction from the centerline, ranging from -b / 2 to +b / 2, with y=0 at the center, in mm. After the corresponding modifications of the first and second modification parts, the meshing position shifts upward, increasing the pressure angle at the meshing point, thereby increasing the radius of curvature, increasing the contact area at the meshing point, and decreasing the contact stress. At the same time, due to the increased contact area, the oil film has a larger distribution area between the tooth surfaces, reducing the pressure borne by the oil film per unit area and reducing the risk of tooth surface scuffing.

[0022] Preferably, the gear tooth is provided with a third shaping portion in the axial direction of the flexible gear, and the third shaping portion satisfies the tooth tip height coefficient of 0.65-0.85.

[0023] Preferably, the gear teeth are provided with a third modified portion in the axial direction of the flexible gear, and the third modified portion satisfies a tooth addendum coefficient of 0.7-0.8. Adjusting the tooth addendum coefficient from 1.0 to 0.7-0.8 achieves stress reduction by changing the pressure angle; the short tooth structure matches the tooth profile of the double circular arc wave generator, reducing interference and impact during meshing. The short tooth structure increases the root thickness and reduces the tooth tip thickness, balancing the strength and flexibility of the flexible gear. Load-bearing capacity is improved, and transmission efficiency is enhanced compared to traditional long teeth. The short tooth design reduces unnecessary contact areas, optimizes the energy transfer path, and improves efficiency.

[0024] A harmonic reducer includes a rigid wheel, a flexible bearing, and a flexible wheel tooth structure as described above.

[0025] This application has achieved beneficial technical effects:

[0026] This invention increases the radius of curvature of the tooth tip plane and the meshing point by setting a first and a second shaping part on the gear teeth, thereby increasing the contact area during meshing, reducing the impact load, and providing a larger area for the oil film to separate the tooth surface, making the actual metal contact area close to zero, increasing the contact area, reducing the maximum contact stress, and reducing the probability of adhesive failure. Attached Figure Description

[0027] Figure 1 The diagram shown is a load diagram of gear teeth meshing;

[0028] Figure 2 The diagram shown is a stress diagram at the tooth root.

[0029] Figure 3 The diagram shown is a schematic of the structure before the modification.

[0030] Figure 4 The diagram shown is a schematic of the reshaped structure.

[0031] Figure 5 The diagram shown is a tooth meshing diagram of the prior art;

[0032] Figure 6 The diagram shown is the meshing diagram of the short-tooth design in this technical solution;

[0033] Figure 7 The diagram shown is a schematic representation of the modified structure of this technical solution;

[0034] Figure 8 The diagram shown is an exploded structural diagram of a harmonic reducer.

[0035] Figure 9 The diagram shown is a structural schematic of a harmonic reducer.

[0036] Figure Labels

[0037] Rigid wheel-10, flexible bearing-8, flexible wheel-7, coupling one-11, bearing-9, fixing screw one-6, oil seal-5, coupling two-4, fixing flange-3, bearing housing-2, fixing screw two-1, third shaping part-12, first shaping part-13, second shaping part-14. Detailed Implementation

[0038] To more clearly illustrate the technical solutions in the embodiments of this utility model or the prior art, the specific implementation methods of this utility model will be described below with reference to the accompanying drawings. Obviously, the drawings described below are merely some embodiments of this utility model. For those skilled in the art, other drawings and other implementation methods can be obtained based on these drawings without any creative effort.

[0039] The technical solution of this utility model will be described in detail below with specific embodiments.

[0040] Reference Figures 1 to 9 A flexible gear tooth structure for a harmonic reducer includes multiple teeth disposed on the flexible gear. The teeth are provided with a first modified portion 13 and / or a second modified portion 14 to increase the edge contact area during meshing. By providing the first modified portion 13 and the second modified portion 14, the radius of curvature of the tooth tip plane and the meshing point is increased, thereby increasing the contact area during meshing, reducing impact load, and providing a larger area for the oil film to separate the tooth surface. This makes the actual metal contact area approach zero, increasing the contact area, reducing the maximum contact stress, and decreasing the probability of adhesion failure. Both the first modified portion 13 and the second modified portion 14 are configured with a module in the range of 0.3-0.5.

[0041] In one embodiment, the first shaping portion 13 is provided at the tooth profile of the gear teeth.

[0042] In one embodiment, the second shaping portion 14 is disposed at the tooth direction of the gear teeth.

[0043] In one embodiment, the shape of the first shaping portion 13 is a first parabolic shape.

[0044] In one embodiment, the shape of the first parabolic trim satisfies the following formula:

[0045] δ(x)=δ max *(1-x / L) 2 ,

[0046] In the formula, δ(x): the amount of shaping at a distance x from the shaping start point, in μm;

[0047] δ_max: Maximum shaping amount, which is at the end or beginning of the shaping process, in μm;

[0048] L: Length of the reshaping area, from the starting point to the ending point of the reshaping, in mm;

[0049] x: The distance along the tooth profile from the starting point of the modification, in mm. By modifying the tooth profile, the meshing position is adjusted to make the load distribution more uniform, reduce tooth profile errors, and avoid a sudden reduction in local contact area;

[0050] In one embodiment, the shape of the second shaping portion 14 is a second parabolic shape.

[0051] In one embodiment, the shape of the second parabolic modification satisfies the following formula:

[0052] δ(y)=C*[1-(2y / b) 2 ],

[0053] In the formula, δ(y): the amount of protrusion at a distance y from the center line of the tooth width, in mm;

[0054] C: Maximum protrusion, located at the center of tooth width y=0, in mm;

[0055] b: Effective tooth width of the gear, in mm;

[0056] y: The distance along the tooth width direction from the center line, ranging from -b / 2 to +b / 2, with the center y = 0, in mm. After the corresponding modifications of the first modification part 13 and the second modification part 14, the meshing position moves upward, increasing the pressure angle at the meshing point, thereby increasing the radius of curvature, increasing the contact area at the meshing point, and reducing the contact stress. At the same time, due to the increased contact area, the oil film has a larger distribution area between the tooth surfaces, reducing the pressure borne by the oil film per unit area and reducing the risk of tooth surface scuffing.

[0057] In one embodiment, the gear tooth is provided with a third shaping part 12 in the axial direction of the flexible gear, and the third shaping part 12 satisfies the tooth tip height coefficient of 0.65-0.85, that is, the third shaping part is shaped according to the tooth tip height coefficient.

[0058] In one embodiment, the gear teeth are provided with a third modified portion 12 in the axial direction of the flexible gear. The third modified portion 12 satisfies a tooth addendum coefficient of 0.7-0.8, meaning that the third modified portion is modified according to the tooth addendum coefficient. Adjusting the tooth addendum coefficient from 1.0 to 0.7-0.8 reduces the tooth addendum by 20%-30%. Simultaneously, due to the short tooth meshing, the load pressure angle increases, and the axial load on the tooth root decreases, thus reducing stress by changing the pressure angle. The short tooth structure matches the tooth profile of the double circular arc wave generator, reducing interference and impact during meshing. The increased tooth root thickness and decreased tooth tip thickness of the short tooth structure balance the strength and flexibility of the flexible gear. The load-bearing capacity is improved, and the transmission efficiency is enhanced compared to traditional long teeth. The short tooth design reduces unnecessary contact areas, optimizes the energy transfer path, and improves efficiency.

[0059] This embodiment also provides a harmonic reducer, including a rigid wheel 10, a flexible bearing 8, and a flexible wheel 7 with the aforementioned flexible wheel tooth structure. It also includes a coupling 11, a bearing 9, a fixing screw 6, an oil seal 5, a second coupling 4, a fixing flange 3, a bearing housing 2, and a second fixing screw 1, thereby assembling the harmonic reducer.

[0060] The implementation scheme of this utility model will be described in detail below with reference to specific embodiments.

[0061] Example 1

[0062] To solve the following technical problems existing in the prior art:

[0063] (1) The tooth tip height is relatively high, and the stress is concentrated at the tooth root during meshing. Microcracks are easily generated in the tooth root area, leading to fatigue fracture and shortening the service life.

[0064] (2) The long tooth structure has a large deformation under high speed or high frequency load, which affects the transmission accuracy and transmission efficiency.

[0065] (3) When gears mesh, they are mostly in line contact. When meshing, edge contact leads to a sharp reduction in area and an increase in impact load. At the same time, since it is a metal micro-protrusion contact, the actual contact area is much smaller than the theoretical value, and the local stress is extremely high, which can easily cause scuffing or wear.

[0066] The specific improvements to this technical solution are as follows;

[0067] (1) Short tooth tip height design: The tooth tip height coefficient is adjusted from 1.0 to 0.7-0.8 to reduce stress by changing the pressure angle; Finite element analysis shows that the root stress of the short tooth structure can be reduced by about 20%-30%, and the fatigue life of the flexure is increased by more than 1.5 times.

[0068] (2) The short-tooth structure matches the tooth profile of the double circular arc wave generator, reducing interference and impact during meshing. The short-tooth structure increases the root thickness and decreases the tip thickness, balancing the strength and flexibility of the flexspline. The load-bearing capacity is increased by 25%, and the transmission efficiency is increased from 85% of the traditional long-tooth structure to 92%.

[0069] (3) Asymmetric modification of flexible gear tooth tip: By modifying the tooth profile of the flexible gear, the radius of curvature of the two points on the tooth tip plane and the meshing point is increased, which increases the contact area during meshing, reduces the impact load, and provides a larger area for the oil film to separate the tooth surface, making the actual metal contact area close to zero, increasing the contact area by 15%, reducing the maximum contact stress by 20%, and reducing the probability of adhesive failure by about 35%.

[0070] This technical solution can achieve the following technical effects:

[0071] (1) Reduce tooth root stress and increase lifespan

[0072] When the teeth mesh at the tooth tip, they are in the double-pair meshing zone, where the two pairs of teeth share the load. The stress at the tooth root is not the greatest. According to the analysis, the bending stress generated at the tooth root is the greatest when the load is applied at the highest point of the single-pair meshing zone, as shown in the gear meshing load diagram and the tooth root stress diagram.

[0073] Based on the fatigue strength calculation of the tooth root, the stress at the tooth root is:

[0074]

[0075] In the formula: F n For the applied load,

[0076] γ is the pressure angle at the tooth tip when the load is applied.

[0077] h is the total tooth height, b is the tooth width, and s is the tooth root length.

[0078] The tooth addendum coefficient of the short-tooth design is adjusted from 1.0 to 0.7-0.8, resulting in a 20%-30% reduction in tooth addendum. Simultaneously, due to the shorter tooth meshing, the load pressure angle increases, reducing the axial load on the tooth root. Combined with a wave generator, the short tooth structure matches the double-circular-arc tooth profile, further reducing meshing impact and the impact load on the tooth root. Under the same design conditions, with other parameters unchanged, the product of tooth height and load in the short-tooth design is 30% smaller than that of the traditional tooth profile design, and the stress value at the critical section of the tooth root is also reduced by 30%, thus improving service life.

[0079] (2) Improve transmission efficiency

[0080] The design of the addendum directly affects friction loss, contact stress, and dynamic performance during meshing, thus impacting gear transmission efficiency. A larger addendum increases the contact line length during gear meshing, leading to a larger friction area, increased friction loss, and decreased transmission efficiency. When the addendum coefficient decreases from 1.0 to 0.7, the meshing contact area decreases by approximately 30%, and friction loss decreases by 15%-20%. Short tooth designs reduce unnecessary contact areas, optimize energy transfer paths, and improve efficiency.

[0081] The greater the tooth tip height, the higher the relative sliding speed between the meshing tooth surfaces, which intensifies frictional heat generation and energy loss. According to the transmission efficiency formula:

[0082]

[0083] P in the formula loss Frictional power loss is directly related to sliding speed and inversely proportional to transmission efficiency. P in For input power, P out The output power is determined by the sliding speed, normal load, and coefficient of friction.

[0084] P loss =μ·F n ·V s

[0085] Where: μ: coefficient of sliding friction, which is related to lubrication conditions and materials;

[0086] Fn: Normal load between meshing tooth surfaces;

[0087] Vs: Sliding speed, which is determined by the gear geometry and rotational speed.

[0088] The sliding speed in the above relationship is directly related to the tooth tip height coefficient. This design indirectly affects the transmission efficiency by changing the tooth tip height coefficient to influence the sliding speed.

[0089] The formula for calculating the sliding speed Vs is:

[0090] V s =|V1-V2|,

[0091] In the formula: V1=ω1·ρ1, which is the linear velocity of gear 1 at the meshing point;

[0092] V2 = ω2·ρ2, which is the linear velocity of gear 2 at the meshing point;

[0093] ρ1 and ρ2 are the distances from the meshing point to the center of their respective gears. Related to tooth tip height;

[0094] In the formula, ρ is the distance from the meshing point to the center of the gear;

[0095] r b Let r be the base circle radius. b =rcosα;

[0096] r a The radius of the tooth tip circle;

[0097] α is the pressure angle.

[0098] The meshing point shifts towards the tooth tip (ρ increases), leading to an increase in sliding speed Vs; frictional loss and Proportional to the pitch circle, efficiency decreases significantly. As the meshing point approaches the pitch circle (ρ decreases), the sliding speed decreases, and efficiency increases.

[0099] Integrating the above formulas, P loss This can be approximated as:

[0100]

[0101] In the formula, Z1 is the number of teeth on the flexible gear, and Z2 is the number of teeth on the rigid gear.

[0102] The larger the tooth tip height coefficient, the lower the transmission efficiency. Short tooth design increases transmission efficiency by reducing the tooth tip height coefficient, while reducing meshing impact force and making the transmission smoother.

[0103] (3) Reduce contact stress and decrease the risk of adhesive bonding.

[0104] Tooth surface scuffing occurs because during transmission, high pressure and relative sliding speed between tooth surfaces cause localized temperature rise due to friction, leading to oil film rupture and direct metal-to-metal contact, resulting in adhesion. This design employs short tooth profile modification. By modifying the tooth profile and adjusting the meshing position, the load distribution becomes more uniform, reducing tooth profile errors and preventing sudden reductions in localized contact area.

[0105] A mathematical model of stress and area is established based on Hertzian contact theory:

[0106]

[0107] In the formula: F is the normal load, E* is the equivalent elastic modulus (related to the material), R* is the equivalent radius of curvature, and L is the contact line length.

[0108] meshing contact area Therefore, we can conclude that... When the load is constant, the larger the contact area, the smaller the contact stress; conversely, the smaller the contact area, the more significant the stress concentration.

[0109] The gears use involute gear meshing, and the radius of curvature ρ at the meshing point is equal to the base circle radius r. b And the actual pressure angle α at the meshing pointp Decision: ρ = r b ·tanα p Its radius of curvature at the pitch circle is:

[0110]

[0111] The formula for calculating the equivalent radius of curvature at the meshing point is:

[0112]

[0113] In the formula, m is the module and z is the number of teeth.

[0114] Before and after the procedure Figure 3 , Figure 4 As shown, by combining and modifying the flexible gear teeth, a parabolic modification δ(x) = δ is performed on the gear tooth profile when the module is 0.3-0.5. max *(1-x / L) 2

[0115] In the formula: δ(x): the amount of shaping at a distance x from the shaping start point (μm).

[0116] δ_max: Maximum shaping amount (at the end or beginning of the shaping process, μm).

[0117] L: Length of the reshaping area (from the starting point to the ending point of the reshaping, mm).

[0118] x: Distance (mm) along the tooth profile from the starting point of the modification. x ranges from 0 (starting point) to L (ending point).

[0119] The same parabolic shaping is applied to the tooth direction: δ(y)=C*[1-(2y / b)]. 2 ],

[0120] In the formula: δ(y): the amount of protrusion at a distance y from the center line of the tooth width; the unit is mm.

[0121] C: Maximum convexity (at the center of tooth width y=0); unit is mm.

[0122] b: Effective tooth width of the gear (mm).

[0123] y: Distance (mm) from the center line along the tooth width direction.

[0124] The range of y is from -b / 2 to +b / 2, with the center y = 0.

[0125] After this reshaping, the meshing position shifts upward, increasing the pressure angle at the meshing point, which in turn increases the radius of curvature and the contact area at the meshing point. According to Hull's contact theory... It can be concluded that the contact stress is reduced, and at the same time, due to the increase in contact area, the oil film has a larger distribution area between the tooth surfaces, and the pressure borne by the oil film per unit area is reduced, thus reducing the risk of tooth surface scuffing.

[0126] This technical solution has the following features:

[0127] Short tooth tip height design: The tooth tip height coefficient is adjusted from 1.0 to 0.7-0.8, reducing the meshing contact area and stress; by adopting a short tooth structure, the meshing contact area is reduced by reducing the tooth tip height, thereby significantly reducing stress concentration at the tooth root, which will greatly improve the fatigue life of the flexspline and the transmission efficiency.

[0128] Gradual tooth thickness distribution: The thickness changes linearly from the tooth root to the tooth tip, balancing strength and flexibility;

[0129] Double circular arc tooth profile matching: Co-optimization with the double circular arc profile of the wave generator to reduce meshing interference.

[0130] Short tooth asymmetric modification: tooth profile according to δ(x)=δ max *(1-x / L) 2 δ(y)=C*[1-(2y / b)] 2 The relationship between the two parts needs to be modified to reduce the risk of glue bonding.

[0131] Example 2

[0132] This embodiment only describes the differences from the above embodiment; other technical features are the same. In this embodiment, the tooth tip height coefficient can be adjusted from 0.65 to 0.85, and the tooth thickness gradient can be adjusted to a non-linear distribution, but the load-bearing capacity will decrease by 5% to 8%.

[0133] Example 3

[0134] This embodiment only describes the differences from the above embodiment, while other technical features are the same. In this embodiment, only the tooth tip height is adjusted without optimizing the tooth thickness, resulting in limited improvement in lifespan, and the fatigue life of the flexspline is improved by about 1.5 times.

[0135] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0136] The embodiments described above are merely illustrative of several implementations of this utility model, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the utility model patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this utility model, and these all fall within the protection scope of this utility model. Therefore, the protection scope of this utility model patent should be determined by the appended claims.

[0137] The above provides a detailed description of the flexible gear tooth structure and embodiments of the harmonic reducer provided by this utility model. Specific examples have been used to illustrate the principle and implementation of this utility model. The descriptions of the embodiments above are only for the purpose of helping to understand the core idea of ​​this utility model. It should be noted that those skilled in the art can make various improvements and modifications to this utility model without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this utility model.

Claims

1. A flexible gear tooth structure for a harmonic reducer, comprising a plurality of teeth disposed on a flexible gear (7), characterized in that, The gear teeth are provided with a first modified portion (13) and / or a second modified portion (14) to increase the edge contact area in the meshing state.

2. The flexible gear tooth structure according to claim 1, characterized in that, The first shaping part (13) is provided at the tooth profile of the gear teeth.

3. The flexible gear tooth structure according to claim 1, characterized in that, The second shaping part (14) is provided at the tooth direction of the gear teeth.

4. The flexible gear tooth structure according to claim 1, characterized in that, The shape of the first modified part (13) is a first parabolic modified part.

5. The flexible gear tooth structure according to claim 4, characterized in that, The shape of the first parabola after modification satisfies the following formula: ， In the formula, δ(x): the amount of shaping at a distance x from the shaping start point, in μm; δ_max: Maximum shaping amount, which is at the end or beginning of the shaping process, in μm; L: Length of the reshaping area, from the starting point to the ending point, in mm; x: The distance along the tooth profile from the starting point of the modification, in mm.

6. The flexible gear tooth structure according to claim 3, characterized in that, The shape of the second shaping part (14) is a second parabolic shape.

7. The flexible gear tooth structure according to claim 6, characterized in that, The shape of the second parabola modification satisfies the following formula: ， In the formula, δ(y): the amount of protrusion at a distance y from the center line of the tooth width, in mm; C: Maximum protrusion, located at the center of tooth width y=0, in mm; b: Effective tooth width of the gear, in mm; y: The distance along the tooth width direction from the center line. The range of y is -b / 2 to +b / 2, with y=0 at the center. The unit is mm.

8. The flexible gear tooth structure according to claim 1, characterized in that, The gear tooth is provided with a third shaping part (12) in the axial direction of the flexible gear, and the third shaping part (12) satisfies the tooth tip height coefficient of 0.65-0.

85.

9. The flexible gear tooth structure according to claim 8, characterized in that, The gear tooth is provided with a third shaping part (12) in the axial direction of the flexible gear, and the third shaping part (12) satisfies the tooth tip height coefficient of 0.7-0.

8.

10. A harmonic reducer, comprising a rigid wheel and a flexible bearing, characterized in that, It also includes the flexible gear tooth structure as described in any one of claims 1 to 9.

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