A design method of high-load-bearing harmonic gear transmission circular-arc tooth profile

Abstract

The application discloses a design method of a high-bearing harmonic gear transmission circular-arc tooth profile, which comprises the following steps: firstly, calibrating the tooth profile parameters of a flexible gear and a rigid gear; then, determining the relationship and value range between other parameters of the rigid gear and the flexible gear; determining the circular-arc radius of the tooth profile of the flexible gear according to the tooth surface contact stress; and finally, calculating the circular-arc parameters of the tooth profile of the rigid gear according to the conjugate meshing condition. The circular-arc tooth profile established by the application not only has the advantages of the multi-tooth meshing of the circular-arc tooth profile, but also has the feature of separable center distance of the harmonic gear transmission, so that the correct meshing can be realized even if the flexible gear is deformed due to the taper. The circular-arc radius of the circular-arc tooth profile established by the application is larger, and the contact is incircle, so that the tooth surface contact area can be greatly increased, the tooth surface contact stress can be reduced, and the service life and the precision maintenance of the harmonic reducer can be improved.

Description

Technical Field

[0001] This invention relates to a method for designing the circular arc tooth profile of a high-load-bearing harmonic gear transmission, belonging to the field of harmonic gear transmission technology. Background Technology

[0002] Harmonic reducers mainly consist of a flexible gear, a rigid gear, and a wave generator. They are speed reduction devices that rely on the periodic, controllable elastic deformation of the flexible gear under the action of the wave generator to achieve gear meshing motion and complete motion and power transmission. They possess a series of advantages, including a large transmission ratio, a wide transmission ratio range, and high precision. Whether used as a precision transmission in a high-sensitivity servo system or as a power transmission for large loads, they exhibit excellent transmission performance and are widely used in precision transmission and control fields such as industrial robots, aerospace, bionics, and medical devices.

[0003] The core component of a harmonic reducer, the flexure, undergoes elastic deformation under load. Simultaneously, the meshing teeth also experience elastic deformation. When the deformation is sufficient to eliminate the backlash between adjacent teeth, multi-tooth meshing is formed. Multi-tooth meshing is one of the main reasons for the aforementioned advantages of harmonic drives. Therefore, novel tooth profiles and the deformation law of the flexure are the key research areas for harmonic gear drives. Currently, many domestic scholars and enterprises are dedicated to research related to harmonic drives. Examples include: Chinese invention patent application CN113361031A entitled "A Three-Dimensional Tooth Profile Design Method for a Harmonic Reducer Flexible Gear"; Chinese invention patent application CN107191570A entitled "Three-Circular Arc Tooth Profile Design of Continuous Conjugate Cup-Shaped or Top-Hat-Shaped Harmonic Gears"; and Chinese invention patent CN104074948B entitled "Cup-Shaped Harmonic Gear with Common Tangent-Type Double Circular Arc Tooth Profile and Its Tooth Profile Design Method." The working tooth profiles of these disclosed harmonic gears are composed of multiple circular arcs, which has the following drawbacks:

[0004] 1) The working arc radius is (1.4 to 2.0) times the gear module. A small arc radius is relatively small and relies on experience without theoretical basis;

[0005] 2) For the flexible gear, only the convex arc portion of the tooth tip participates in meshing contact, and the tooth surface contact area is small, approximately 50% of the tooth height;

[0006] 3) The convex arc of the tooth tip of the flexible gear and the convex arc of the tooth tip of the rigid gear are in external tangential contact, resulting in extremely high contact stress;

[0007] 4) The tapered deformation of the flexible gear causes different radial deformations on different cross sections, and the tooth meshing position deviates from the theoretical position, thus destroying the conjugate meshing condition.

[0008] The above problems result in high working stress on the tooth surface of harmonic gears, uneven stress distribution, and easy tooth surface wear, which reduces the accuracy and service life of the harmonic reducer. Summary of the Invention

[0009] This invention provides a design method for a high-load-bearing harmonic gear transmission with a circular arc tooth profile. The circular arc tooth profile established by this method not only has the advantages of multi-tooth meshing of circular arc tooth profiles, but also has the feature of separable center distance of involute gear transmission. Even if the flexible gear has tapered deformation, it can still achieve correct meshing. Under the same conditions, it can significantly improve the load-bearing capacity, life and accuracy retention of the harmonic reducer.

[0010] The technical solution of this invention: a method for designing the circular arc tooth profile of a high-load-bearing harmonic gear transmission, comprising the following steps:

[0011] Step 1: Calibrate the tooth profile parameters of the flexible and rigid gears:

[0012] The inner radius r0 of the flexible gear is equal to the outer radius of the flexible bearing. The flexible gear tooth profile parameters are: gear module m1, number of teeth Z1, pitch circle r1, tooth root wall thickness 2t, process tooth profile angle γ1, tooth profile arc radius ρ1, total tooth height h1, tooth thickness Sa, and tooth tip transition radius r. a1 Tooth root transition fillet r f1， Neutral layer radius r m ;

[0013] The tooth profile parameters of the rigid wheel are: gear module m2, number of teeth Z2, pitch circle r2, process tooth profile angle γ2, tooth profile arc radius ρ2, total tooth height h2, tooth space width Sf, and tooth tip fillet r. a2 Tooth root transition fillet r f2 ;

[0014] Step 2: Determine the relationship and value range of other parameters between the rigid wheel and the flexible wheel:

[0015] Modulus m1=m2=m

[0016] Number of teeth z2 = z1 + 2

[0017] The root wall thickness is 2t, where t = (0.008 ~ 0.015) * r0

[0018] Neutral layer radius r m =r0+t

[0019] Pitch circles r1 = z1 * m, r2 = z2 * m

[0020] The radius of the working tooth profile arc of the flexible gear is ρ1, and the radius of the working tooth profile arc of the rigid gear is ρ2.

[0021] Tooth profile process angle, γ1=(6~35)°, γ2=(6~35)°, γ1 takes a smaller value when the speed ratio is large, and a larger value when the speed ratio is small, γ2 is obtained from the conjugate calculation.

[0022] The total tooth height h1 = (1.4~1.8) m, h2 = (1.4~1.8) m

[0023] The tooth thickness ratio K = Sf / Sa = (1.2~2.0), with a smaller value for a larger speed ratio and a larger value for a smaller speed ratio.

[0024] Flexible gear tooth thickness Sa=π*m / (K+1)

[0025] Rigid wheel tooth groove width Sf=π*m-Sa

[0026] Transition fillet r a1 = (0.5~1)*m, r f1 = (1~2)*m, r a2 = (0.5~1)*m,

[0027] r f2 = (0.5~1)*m;

[0028] Step 3: Calculate the radius ρ1 of the flexible gear tooth profile arc:

[0029] The contact between the flexible gear tooth profile and the rigid gear tooth profile can be simplified to an internal tangential contact of a cylinder. The output torque of the harmonic reducer is T (Nm), the flexible gear tooth width is B (mm), the material elastic modulus is E (MPa), and the working load on the tooth surface is F (N). Assuming that 10% of the gear teeth participate in the contact transmission of torque, and that each pair of teeth bears an equal load, ρ2≈1.05*ρ1; according to Hertzian contact stress theory, the contact stress σ on the flexible gear tooth surface is:

[0030]

[0031] Allowable specific pressure [σ] (MPa) for flexible gear material, and conditions for determining the radius ρ1 of the flexible gear tooth profile:

[0032] σ≤[σ] (2)

[0033] That is, the radius ρ1 of the flexible gear tooth profile arc is:

[0034]

[0035] Step 4: Calculate the radius ρ2 of the tooth profile of the rigid wheel:

[0036] Given the parameters of the flexible gear tooth profile, the parameters of the flexible gear structure, and the deformation parameters of the wave generator, the arc length of the flexible gear tooth profile is discretized into several points. Each point can be used to determine the discrete point of the rigid gear tooth profile conjugate with the flexible gear tooth profile using Wills' theorem. The obtained discrete points of the rigid gear tooth profile are then subjected to coordinate transformation and arc fitting to obtain the arc radius ρ2 of the rigid gear tooth profile and the process tooth profile angle γ2.

[0037] In the above method, the tooth profiles of the rigid wheel and the flexible wheel are fitted according to the involute law. For the flexible wheel tooth profile curve ρ1, there is an involute curve L1 with a module of m, a number of teeth of Z1, a pressure angle of α, and a displacement coefficient of x1. For the rigid wheel tooth profile curve ρ2, there is an involute curve L2 with a module of m, a number of teeth of Z2, a pressure angle of α, and a displacement coefficient of x2. The module m and pressure angle α of the two involute curves L1 and L2 are equal, which satisfies the continuous meshing condition. The number of teeth is the same as the corresponding number of teeth of the rigid wheel and the flexible wheel. The displacement coefficients x1 and x2 are adapted to the correct installation under the deformation conditions of the wave generator.

[0038] Because of the adoption of the above technical solution, the advantages of the present invention are as follows:

[0039] ① The condition for determining the radius of the circular arc tooth profile established in this invention is: Hertzian contact stress on the tooth surface ≤ allowable specific pressure of the flexible wheel material, which is a more reasonable value.

[0040] ② The circular arc tooth profile established in this invention not only has the advantage of multi-tooth meshing of circular arc tooth profiles, but also has the feature of separable center distance of involute gear transmission, so that correct meshing can still be achieved even if the flexible gear has tapered deformation.

[0041] ③ The circular arc tooth profile established in this invention has a radius of approximately (20-50) of the flexible gear module. The radius of the circular arc is larger, and the flexible gear tooth profile and the rigid gear tooth profile are in tangential contact, which can significantly increase the tooth surface contact area, reduce the tooth surface contact stress, and improve the life and accuracy retention of the harmonic reducer. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of a harmonic reducer;

[0043] Figure 2 Here is a cross-sectional view of the flexspline:

[0044] Figure 3 This is a schematic diagram of the flexible gear tooth profile;

[0045] Figure 4 This is a cross-sectional view of the rigid wheel;

[0046] Figure 5 This is a schematic diagram of the tooth profile of a rigid wheel.

[0047] The labels in the attached diagram are: 1-rigid wheel, 2-flexible wheel, 3-flexible bearing, 4-cam. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0049] Embodiments of the present invention:

[0050] This invention is an optimized design for existing harmonic reducers, see [link / reference]. Figure 1 The harmonic reducer includes a rigid wheel 1, a flexible wheel 2, a cam 4, and a flexible bearing 3. The rigid wheel 1 is a rigid cylindrical internal gear, and the flexible wheel 2 is a flexible thin-walled cylindrical spur gear. The flexure wheel 2 and the rigid wheel 1 have the same pitch, but the number of teeth on the flexible wheel 2 is two fewer than that on the rigid wheel 1. The outer contour of the cam 4 is elliptical, and the flexible bearing 3 is mounted on the outer circumference of the cam 4 to form a wave generator. The inner hole of the gear ring of the flexible wheel 2 contacts the outer ring of the wave generator, forcing the flexible wheel 2 to deform according to the outer contour shape of the wave generator. The flexible wheel 2, the rigid wheel 1, and the wave generator are coaxially mounted. The rotation of the wave generator forces the flexible wheel 2 to deform continuously. Due to the difference in the number of teeth between the rigid wheel 1 and the flexible wheel 2, differential gear meshing reduction transmission is achieved.

[0051] The present invention provides a method for designing a circular arc tooth profile for a high-load-bearing harmonic gear transmission, comprising the following steps:

[0052] Step 1, see Figures 2-5 Calibrate the tooth profile parameters of the flexible and rigid gears:

[0053] The inner radius r0 of the flexible gear is equal to the outer radius of the flexible bearing. The flexible gear tooth profile parameters are: gear module m1, number of teeth Z1, pitch circle r1, tooth root wall thickness 2t, process tooth profile angle γ1, tooth profile arc radius ρ1, total tooth height h1, tooth thickness Sa, and tooth tip transition radius r. a1 Tooth root transition fillet r f1 Neutral layer radius r m ;

[0054] The tooth profile parameters of the rigid wheel are: gear module m2, number of teeth Z2, pitch circle r2, process tooth profile angle γ2, tooth profile arc radius ρ2, total tooth height h2, tooth space width Sf, and tooth tip fillet r. a2 Tooth root transition fillet r f2 ;

[0055] Step 2: Determine the relationship and value range of other parameters between the rigid wheel and the flexible wheel:

[0056] Modulus m1=m2=m

[0057] Number of teeth z2 = z1 + 2

[0058] The root wall thickness is 2t, where t = (0.008 ~ 0.015) * r0

[0059] Neutral layer radius r m =r0+t

[0060] Pitch circles r1 = z1 * m, r2 = z2 * m

[0061] The radius of the working tooth profile arc of the flexible gear is ρ1, and the radius of the working tooth profile arc of the rigid gear is ρ2.

[0062] Tooth profile process angle, γ1=(6~35)°, γ2=(6~35)°, γ1 takes a smaller value when the speed ratio is large, and a larger value when the speed ratio is small, γ2 is obtained from the conjugate calculation.

[0063] The total tooth height h1 = (1.4~1.8) m, h2 = (1.4~1.8) m

[0064] The tooth thickness ratio K = Sf / Sa = (1.2~2.0), with a smaller value for a larger speed ratio and a larger value for a smaller speed ratio.

[0065] Flexible gear tooth thickness Sa=π*m / (K+1)

[0066] Rigid wheel tooth groove width Sf=π*m-Sa

[0067] Transition fillet r a1 = (0.5~1)*m, r f1 = (1~2)*m, r a2 = (0.5~1)*m,

[0068] r f2 = (0.5~1)*m;

[0069] Step 3: Calculate the radius ρ1 of the flexible gear tooth profile arc:

[0070] The contact between the flexible gear tooth profile and the rigid gear tooth profile can be simplified to an internal tangential contact of a cylinder. The output torque of the harmonic reducer is T (Nm), the flexible gear tooth width is B (mm), the material elastic modulus is E (MPa), and the working load on the tooth surface is F (N). Assuming that 10% of the gear teeth participate in the contact transmission of torque, and that each pair of teeth bears an equal load, ρ2≈1.05*ρ1; according to Hertzian contact stress theory, the contact stress σ on the flexible gear tooth surface is:

[0071]

[0072] Allowable stress [σ] (MPa) for flexible gear material, and conditions for determining the radius ρ1 of the flexible gear tooth profile:

[0073] σ≤[σ] (2)

[0074] That is, the radius ρ1 of the flexible gear tooth profile arc is:

[0075]

[0076] Step 4: Calculate the radius ρ2 of the tooth profile of the rigid wheel:

[0077] Given the parameters of the flexible gear tooth profile, the parameters of the flexible gear structure, and the deformation parameters of the wave generator, the arc length of the flexible gear tooth profile is discretized into several points. Each point can be used to determine the discrete point of the rigid gear tooth profile conjugate with the flexible gear tooth profile using Wills' theorem. The obtained discrete points of the rigid gear tooth profile are then subjected to coordinate transformation and arc fitting to obtain the arc radius ρ2 of the rigid gear tooth profile and the process tooth profile angle γ2.

[0078] In the above method, the tooth profiles of the rigid wheel and the flexible wheel are fitted according to the involute law. For the flexible wheel tooth profile curve ρ1, there is an involute curve L1 with a module of m, a number of teeth of Z1, a pressure angle of α, and a displacement coefficient of x1. For the rigid wheel tooth profile curve ρ2, there is an involute curve L2 with a module of m, a number of teeth of Z2, a pressure angle of α, and a displacement coefficient of x2. The module m and pressure angle α of the two involute curves L1 and L2 are equal, which satisfies the continuous meshing condition. The number of teeth is the same as the corresponding number of teeth of the rigid wheel and the flexible wheel. The displacement coefficients x1 and x2 are adapted to the correct installation under the deformation conditions of the wave generator.

Claims

1. A method for designing the circular arc tooth profile of a high-load-bearing harmonic gear transmission, characterized in that... Includes the following steps: Step 1: Calibrate the tooth profile parameters of the flexible and rigid gears: The inner radius r0 of the flexible gear is equal to the outer radius of the flexible bearing. The flexible gear tooth profile parameters are: gear module m1, number of teeth Z1, pitch circle r1, tooth root wall thickness 2t, process tooth profile angle γ1, tooth profile arc radius ρ1, total tooth height h1, tooth thickness Sa, and tooth tip transition radius r. a1 Tooth root transition fillet r f1 Neutral layer radius r m ; The tooth profile parameters of the rigid wheel are: gear module m2, number of teeth Z2, pitch circle r2, process tooth profile angle γ2, tooth profile arc radius ρ2, total tooth height h2, tooth space width Sf, and tooth tip transition radius r. a2 Tooth root transition fillet r f2 ; Step 2: Determine the relationship and value range of other parameters between the rigid wheel and the flexible wheel: ① Modulus m1=m2=m ② Number of teeth z2=z1+2 ③ The root wall thickness is 2t, t=(0.008~0.015)*r0 ④ Neutral layer radius r m =r0+t ⑤ Pitch circle r1 = z1*m, r2 = z2*m ⑥ The radius of the working tooth profile arc of the flexible gear is ρ1, and the radius of the working tooth profile arc of the rigid gear is ρ2. ⑦ Tooth profile process angle, γ1=(6~35)°, γ2=(6~35)°, γ1 takes a smaller value when the speed ratio is large, and takes a larger value when the speed ratio is small, γ2 is obtained from the conjugate calculation. ⑧ Total tooth height h1 = (1.4~1.8)*m, h2 = (1.4~1.8)*m ⑨ Gear thickness ratio K = Sf / Sa = (1.2~2.0), take the smaller value when the speed ratio is large, and take the larger value when the speed ratio is small. ⑩ Flexible gear tooth thickness Sa=π*m / (K+1) Rigid wheel tooth groove width Sf=π*m-Sa Transition fillet r a1 = (0.5~1)*m, r f1 = (1~2)*m, r a2 = (0.5~1)*m, r f2 ＝(0.5～1)*m； Step 3: Calculate the radius ρ1 of the flexible gear tooth profile arc: The contact between the flexible gear tooth profile and the rigid gear tooth profile can be simplified to an internal tangential contact of a cylinder. The output torque of the harmonic reducer is T (Nm), the flexible gear tooth width is B (mm), the material elastic modulus is E (MPa), and the working load on the tooth surface is F (N). Assuming that 10% of the gear teeth participate in the contact transmission of torque, and that each pair of teeth bears an equal load, ρ2≈1.05*ρ1; according to Hertzian contact stress theory, the contact stress σ on the flexible gear tooth surface is: Allowable specific pressure [σ] (MPa) for flexible gear material, and conditions for determining the radius ρ1 of the flexible gear tooth profile: σ≤[σ] (2) That is, the radius ρ1 of the flexible gear tooth profile arc is: Step 4: Calculate the radius ρ2 of the tooth profile of the rigid wheel: Given the parameters of the flexible gear tooth profile, the parameters of the flexible gear structure, and the deformation parameters of the wave generator, the arc length of the flexible gear tooth profile is discretized into several points. Each point can be used to determine the discrete point of the rigid gear tooth profile conjugate with the flexible gear tooth profile using Wills' theorem. The obtained discrete points of the rigid gear tooth profile are then subjected to coordinate transformation and arc fitting to obtain the arc radius ρ2 of the rigid gear tooth profile and the process tooth profile angle γ2.

2. The high-load-bearing harmonic gear transmission circular arc tooth profile design method according to claim 1, characterized in that: The tooth profiles of the rigid wheel and the flexible wheel are fitted according to the involute law. For the flexible wheel tooth profile curve ρ1, there exists an involute curve L1 with a module of m, a number of teeth of Z1, a pressure angle of α, and a displacement coefficient of x1. For the rigid wheel tooth profile curve ρ2, there exists an involute curve L2 with a module of m, a number of teeth of Z2, a pressure angle of α, and a displacement coefficient of x2. The module m and pressure angle α of the two involute curves L1 and L2 are equal, which satisfies the continuous meshing condition. The number of teeth is the same as the corresponding number of teeth of the rigid wheel and the flexible wheel. The displacement coefficients x1 and x2 are adapted to the correct installation under the deformation conditions of the wave generator.

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