Circular shock wave E-tooth shape decelerator and tooth shape design method thereof

Abstract

The application discloses a circular shock wave E-tooth-shaped speed reducer and a tooth shape design method thereof. The tooth shape of the steel wheel tooth of the harmonic reducer is a concave circular arc shape, and a rolling body is arranged in the circular arc of the steel wheel tooth. The rolling body is engaged with the tooth shape of the flexible wheel, so that the tooth of the flexible wheel and the tooth of the steel wheel are in pure rolling engagement through the rolling body. The rolling body can be a rigid component such as a roller or a steel ball. The outer surface of the cam can be an elliptical shape, a circular arc shape, a logarithmic spiral shape or the like. The specific tooth shape of the flexible wheel tooth designed by the design method provided by the application can realize that all the teeth are engaged, so that the load-carrying capacity is relatively high. The generalized tooth shape generation method includes general formulas of different cam outer surface shapes in the generalized tooth shape design. The tooth shape design method for calculating the specific tooth shape according to the shape of the outer surface of the cam is disclosed. Different tooth shapes can be obtained according to different cams, and the change rule of the pressure angle is also different. The smaller the pressure angle is, the stronger the load-carrying capacity is.

Description

Technical Field

[0001] This invention relates to the field of speed reducers, and more particularly to an E-tooth profile speed reducer, a generalized tooth profile generation method, and a tooth profile design method. Background Technology

[0002] Speed ​​reducers are a crucial component of the machinery industry, directly impacting production efficiency, operational performance, and product quality. However, due to the limited load-bearing capacity and short lifespan of modern high-precision transmission mechanisms, their transmission performance is inevitably affected, failing to simultaneously meet the requirements of precision, lifespan, and load-bearing capacity in industrial production. Harmonic gear reducers (harmonic reducers) are a new type of speed reducer developed using the principle of planetary gear transmission. They consist of a fixed internal gear, a flexible gear, and a wave generator that causes radial deformation of the flexible gear. They utilize the controllable elastic deformation wave generated by the flexible gear to induce relative tooth misalignment between the teeth of the gear and the flexible gear, thereby transmitting power and motion.

[0003] This transmission is fundamentally different from ordinary gear transmission, and has special characteristics in terms of meshing theory, set calculation and structural design. Harmonic gear reducers have the advantages of high precision and high load capacity. Compared with ordinary reducers, they use 50% less material, and their volume and weight are reduced by at least 1 / 3. For specific technology, please refer to [1] Wang Jiaxu, Yuan Pan, Li Junyang, et al. Research on tooth profile of harmonic transmission based on different meshing principles [J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2017(45):58-64. and [2] Yang Yong, Wang Jiaxu, Zhou Qinghua, et al. Accurate solution of conjugate tooth profile of zero backlash harmonic gear transmission by elliptical cam wave generator [J]. Journal of Central South University (Natural Science Edition), 2017. In practice, it has been found that existing harmonic reducers are prone to wear during the meshing of the flexible gear teeth and the steel gear teeth, leading to a decrease in the reducer's transmission accuracy and thus affecting its lifespan. Furthermore, harmonic reducers cannot achieve full engagement of all teeth, impacting their load-bearing capacity. Summary of the Invention

[0004] To address the aforementioned problems, the primary objective of this invention is to provide an E-tooth profile reducer that enables all teeth to engage in meshing and has a high load-bearing capacity. A secondary objective is to provide an E-tooth profile reducer with a tooth profile design, structure, and application that reduces friction and wear.

[0005] To achieve the above objectives, this invention provides an E-tooth profile reducer, a generalized tooth profile generation method, and a tooth profile design method. The steel wheel teeth of the harmonic reducer have an inwardly concave arc shape, and rolling elements are installed within the arc of the steel wheel teeth. These rolling elements mesh with the flexspline teeth, allowing the flexspline teeth and steel wheel teeth to engage in pure rolling meshing through the rolling elements. The rolling elements can be rollers, steel balls, etc., while the outer surface of the cam can be elliptical, arc-shaped, logarithmic spiral-shaped, etc. This invention enables all teeth to participate in meshing, resulting in a strong load-bearing capacity. The generalized tooth profile generation method and generalized tooth profile design include general formulas for different cam outer surface shapes. A tooth profile design method is also disclosed that calculates specific tooth profiles based on the cam outer surface shape. This allows for different tooth profiles to be obtained for different cams, with different pressure angle variation patterns. The smaller the pressure angle, the stronger the load-bearing capacity.

[0006] In this invention, the outer surface of the cam can be elliptical, circular arc, logarithmic spiral, etc. Different cams can produce different tooth profiles, and the pressure angle variation patterns also differ. The smaller the pressure angle, the stronger the load-bearing capacity.

[0007] The beneficial effects of this invention are that it discloses a generalized tooth profile generation method and the structure obtained according to the above method; it also discloses an E-tooth profile reducer, which has rolling elements mounted on a steel wheel, and then the rolling elements make rolling contact with the flexible gear teeth.

[0008] Using the above technical solution, this invention designs the steel wheel tooth profile as a concave arc shape, with rolling elements (rollers, steel balls, etc.) installed within the arc. The rolling elements mesh with the flexible wheel tooth profile, and the interaction is purely rolling, reducing friction and wear. Because this invention allows all teeth to participate in meshing, its load-bearing capacity is strong. Furthermore, the outer surface of the cam in this invention can be elliptical, arc-shaped, logarithmic spiral-shaped, etc. Different cams can produce different tooth profiles, and the pressure angle variation also differs; the smaller the pressure angle, the stronger the load-bearing capacity. Attached Figure Description

[0009] Figure 1 Schematic diagram of tooth profile generation principle; Figure 2 This is a schematic diagram of the logarithmic spiral shock wave principle of an E-tooth reducer according to the present invention; Figure 3 Logarithmic spiral; Figure 4 A side sectional view of an E-tooth reducer according to the present invention; Figure 5 A front view of an E-tooth reducer according to the present invention; Figure 6 A schematic diagram of the flex wheel in an E-tooth reducer according to the present invention; Figure 7 A schematic diagram of the housing end face of an E-tooth reducer according to the present invention; Figure 8 This is a schematic diagram of an elliptical shock wave principle of an E-tooth reducer according to the present invention; Figure 9a -f is a schematic diagram of the elliptical shock wave tooth profile of an E-tooth reducer according to the present invention; Figure 10 This is a schematic diagram of the circular shock wave principle of an E-tooth reducer according to the present invention; Figure 11a -e is a schematic diagram of the circular shock wave tooth profile of an E-tooth reducer according to the present invention; Figure 12a -e is a schematic diagram of the logarithmic spiral shock wave tooth profile of an E-tooth reducer according to the present invention; Figure 13a -e is a schematic diagram of the cycloidal tooth profile of an E-tooth reducer according to the present invention; Figure 14 A schematic diagram of an embodiment of an E-tooth reducer with a steel wheel; in: 1. Positioning shaft, 2. Flexible wheel, 3. Bolt, 4. Cross bearing, 5. Screw, 6. Housing, 7. Retaining ring, 8. Needle roller, 9. Flexible bearing, 10. Input shaft, 11. Retaining ring, 12. Baffle, 13. Input shaft II, 14. Steel wheel II, 15. Flexible wheel II, 16. Flexible bearing II. Detailed Implementation

[0010] The technical solution of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

[0011] In view of the defects of the meshing of the flexible gear teeth and the steel gear teeth in the existing harmonic reducer, the present invention designs the steel gear teeth as a concave arc shape and installs rolling elements (rollers, steel balls, etc.) inside the arc. Then, by means of the meshing of the rolling elements with the flexible gear teeth, the combined motion is changed to pure rolling, thereby reducing friction and reducing wear.

[0012] In order to enable all teeth to participate in meshing in the above structure, the tooth profile of the flexible gear needs to be specially designed. To this end, the present invention further discloses a method for generating and designing the tooth profile of the above structure.

[0013] In the above structure, the outer surface of the cam in this invention can be elliptical, circular arc, logarithmic spiral, etc., and different tooth profiles and pressure angle variation laws can be obtained according to different cams. Therefore, this invention discloses a generalized tooth profile generation method and a specific tooth profile design method for E-tooth profile reducers with different cam outer surfaces. The tooth profile generation method of this invention is deduced based on the generalized tooth profile design. However, since the cam (input shaft 10) adopts different outer surface shapes, the external shape expression is different, and the specific derivation process is also different, requiring different design methods. There is a one-to-one correspondence between the steel wheel, the flexible wheel, and the cam. When the cam rotates, it drives the teeth on the flexible wheel to mesh with the needle rollers on the steel wheel, realizing the reducer's deceleration rotation.

[0014] 1. Generalized tooth profile generation method Figure 1 The diagram illustrates the principle of tooth profile generation. The theoretical tooth profile of the flexspline's outer surface is as follows: ; in, ρ ( θ () is the radius vector of the tooth shape. ε The angle through which the radius vector rotates. θ The radius vector rotates through the angle relative to the input axis. θ Solve according to the following formula. ; in, φ The angle through which the output shaft rotates relative to the input shaft. S c For point B The distance traveled along the outer surface of the cam.

[0015] The curvature formula is ; Differentiating the theoretical tooth profile coordinates ;

[0016] The actual tooth profile equation is ;

[0017] in, r This is the offset distance. .

[0018] The actual tooth profile is E-shaped.

[0019] The pressure angle is the angle between the common normal to a point on the actual tooth profile curve and the circumferential direction. The formula for the pressure angle is as follows: ;

[0020] in, ,x , y Let be the coordinates of a point on the theoretical tooth profile curve. , x s , y s These are the coordinates of a point on the actual tooth profile curve.

[0021] The present invention will be further described in detail below with reference to the accompanying drawings. The following embodiments applying the method are used to illustrate the present invention, but are not intended to limit the scope of the invention.

[0022] 2. Tooth profile design of an E-tooth reducer according to the present invention When the outer cylindrical surface of the cam (input shaft 10) is a logarithmic helix, the schematic diagram is as follows: Figure 2 and Figure 3 As shown.

[0023] For a number of spiral shock waves, the theoretical tooth profile equation is:

[0024] when θ d When = 0, the coordinate point is ( x 1. y 1); when θ d = π When / 2, the coordinates are ( x 2. y 2). The intersection of the common normals at the two points above is ( x 0、 y 0).

[0025] ρ L ( θ d As shown below

[0026] in, R a Length parameter, k Exponential parameters.

[0027] θ d and β The relationship between them is as follows: ;

[0028] in R The radius of the circle that is the same length as the logarithmic spiral on the shock generator.

[0029] right ρ L ( θ d )middle β Taking the derivative, we get

[0030] right θ d beg β The first and second derivatives can be obtained as follows:

[0031] in, .

[0032] θ and θ d Relationship

[0033] in, , , . , , , , flo Indicates no greater than 2 θ / π The largest integer, .

[0034] vector diameter ρ ( θ )for

[0035] right θ beg β First derivative and second derivative ;

[0036] in, , .

[0037] right β The derivative is

[0038]

[0039] right β The derivative is ;

[0040] in, .

[0041] The curvature of the tooth profile, the actual tooth profile, and the pressure angle can be obtained from the above formulas.

[0042] 3. Structural design of an E-tooth reducer according to the present invention As attached Figures 4 to 7 As shown, an E-tooth reducer of the present invention includes a positioning shaft 1, a flexible wheel 2, a bolt 3, a cross bearing 4, a screw 5, a housing 6, a retaining ring 7, a needle roller 8, a flexible bearing 9, an input shaft 10, a retaining ring 11, and a baffle 12. The flexible bearing 9 is installed on the outer surface of the input shaft 10 and inside the flexible wheel 2. The cross bearing 4 is fixed to the end face of the housing 6 by screws 5, and the flexible wheel 2 is fixed to the end face of the cross bearing 4 by bolts 3. The coaxiality of the flexible wheel 2 and the cross bearing 4 is ensured by the positioning shaft 1. The inner surface of the housing 6 has a cylindrical surface, and multiple arc grooves (steel wheel teeth) are machined on the inner cylindrical surface of the inner surface of the housing 6. The needle roller 8 is installed in the arc grooves. The outer surface of the flexible wheel 2 has a cylindrical surface, and multiple E-shaped teeth with logarithmic helical pitch circles are machined on the cylindrical surface of the outer surface of the flexible wheel 2. The needle roller 8 meshes with the teeth on the flexible wheel 2. The outer surface of the input shaft 10 is a logarithmic helical curved surface. The baffle 12 restricts the axial movement of the needle roller 8, and the retaining ring 7 restricts the radial and axial movement of the needle roller 8.

[0043] Among them, the cylindrical surface of the inner surface of the outer shell 6 is machined with Z 1 with a diameter of d The circular arc groove teeth described in 1, Z One circular arc groove tooth is evenly distributed on a radius of R On the circle, an arc groove is installed with a diameter of d r The needle roller 8, and d r < d 1, d r / 2> r .

[0044] Among them, the cylindrical surface of the outer surface of the flexible wheel 2 is machined with Z Two of the aforementioned E-shaped teeth, and satisfying Z 1> Z 2 or Z 1= Z 2 or Z 1< Z 2; The input shaft 10 rotates, and the input shaft 10 pushes the flexible wheel 2 to deform through the flexible bearing 9. The flexible wheel 2 pushes the needle roller 8, and the needle roller 8 reacts to the flexible wheel 2. The flexible wheel 2 rotates at low speed under the pushing action of the input shaft 10 and the limiting action of the needle roller 8. The needle roller 8 slides in the arc groove. The flexible wheel 2 drives the inner ring of the cross bearing 4 to rotate, and outputs power to the output shaft to realize the deceleration motion of the reducer.

[0045] Transmission ratio .

[0046] See Figure 12, which is a schematic diagram of the logarithmic spiral shock wave tooth profile of an E-tooth reducer according to the present invention.

[0047] 4. Specific application examples of the present invention index k =arccot93°, number of needle rollers Z 1 = 100, number of teeth Z 2=98, base circle of logarithmic spiral R a =31.284mm.

[0048] One hundred arc-shaped grooves with a diameter of 1.34 mm are machined on the cylindrical surface of the inner surface of the outer shell 6. The 100 arc-shaped grooves are evenly distributed on a circle with a radius of 32.653 mm. A needle roller 8 with a diameter of 1.32 mm is installed in the arc-shaped groove. The cylindrical surface of the outer surface of the flexible wheel 2 is machined with 98 E-shaped teeth, which are obtained according to the derived formula.

[0049] The transmission ratio i = -49.

[0050] Tooth shape Figure 12a Pressure angle such as Figure 12b The minimum pressure angle is less than 20°, which is less than the minimum pressure angle in the cycloidal tooth profile. Figure 13b ), and significantly smaller than the pressure angle of the toothed shock wave using an elliptical shock wave ( Figure 11b Therefore, the E-tooth reducer using logarithmic spiral shock waves exhibits excellent performance.

[0051] 5. The E-tooth reducer of the present invention adopts an elliptical shock wave tooth profile design. See Figure 1 The theoretical tooth profile of the flexible wheel outer surface using elliptical shock waves is: ; in, , , , a It is the semi-major axis of the ellipse. b The minor half-axis of the ellipse has a transmission ratio of [missing information]. i = Z 1 / ( Z 1- Z 2), θ Solve according to the following formula. ; in, .

[0052] The curvature formula is ; Taking the derivative of formula (2), we can obtain θ right φ derivative ; in,

[0053] right φ The derivative is ; right φ The derivative is ; For formula (1) φ Differentiation ; Substituting formulas (4) to (12) into formula (3), we can obtain the curvature formula of the tooth profile; The actual tooth profile equation is ; in, , .

[0054] pressure angle ; in, , r This represents the offset distance.

[0055] Z 1 = 100 Z 1=98、 e =0.5、 S 2 = 0.5 r =0.5、 R 1=30, and the tooth shape is shown in Figure 9.

[0056] 6. The E-tooth reducer of the present invention adopts a circular shock wave tooth profile design. When the outer cylindrical surface of the cam is circular, the schematic diagram is as follows: Figure 10 As shown.

[0057] ; in, , ρ ( θ () represents the pole diameter. Transmission ratio. i = Z 1 / ( Z 1- Z2), ρ ( θ )as follows ; in, e For the eccentricity, h Half width, R 1 represents the radius of the arc. θ as follows ; Where O is the cam rotation center, A is the starting endpoint of the arc segment (corresponding interval) of the flex wheel theoretical tooth profile, B is the connection point between the arc segment and the straight line segment (corresponding interval), C is the midpoint of the straight line segment, OC is the distance from O to C, i.e., half width; S1 is the arc length from point A to point B on the flex wheel theoretical tooth profile, and S2 is the length of the straight line segment from point B to point C. .

[0058] When the outer cylindrical surface of the cam is circular, the schematic diagram is as follows: Figure 10 As shown.

[0059] Polar diameter in this application The piecewise function is the extreme diameter equation of the tooth profile in the flexural theory, not the equation of the cam profile; the statement that 'the outer cylindrical surface of the cam is round' is a limitation on the structural characteristics of the cam (input shaft) itself, that is, the outer surface of the cam is cylindrical and its cross-section is circular. The two belong to the geometric characteristics of different components and there is no contradiction.

[0060] The curvature formula is ; Taking the derivative of formula (3), we can obtain θ right φ derivative ; in, , , , , , , .

[0061] right φ The derivative is ; For formula (1) φ Differentiation ; Substituting formulas (4) to (12) into formula (3), we obtain the curvature formula for the tooth profile. The actual tooth profile equation is: ; in, , , pressure angle ; in, , r This represents the offset distance.

[0062] Z 1 = 100 Z 2=98、 e =0.5、 S 2 = 0.5 r =0.5、 R 1=30, and the tooth profile is shown in Figure 11.

[0063] in, .

[0064] pressure angle ; in, , r This represents the offset distance.

[0065] Tooth shape Figure 11a Pressure angle such as Figure 11b The minimum pressure angle is significantly smaller than the pressure angle of the E-tooth shape using an elliptical shock wave. Figure 9b Therefore, the E-tooth reducer using circular shock waves has superior performance.

[0066] 7. The present invention provides an E-tooth profile reducer with a steel wheel of logarithmic spiral shock wave as the E-tooth profile. The steel wheel II14 teeth of the harmonic reducer have an E-shaped tooth profile, while the flexible wheel teeth have a convex circular arc curve. The E-shaped teeth of the steel wheel mesh with the circular arc teeth of the flexible wheel. The structure is as follows: Figure 14 As shown.

[0067] The outer surface of the input shaft II13 is a logarithmic spiral surface.

[0068] Among them, the cylindrical surface of the inner surface of steel wheel II14 is machined with Z 3 E-shaped teeth, flexible gear II 15 plus Z There are 4 circular arc teeth, which mesh with E-shaped teeth, and all teeth participate in the meshing.

[0069] The number of teeth satisfies Z 3> Z 4 or Z 3= Z 4 or Z 3< Z 4.

[0070] The input shaft II13 rotates, and the input shaft II13 pushes the flexible wheel II15 to deform through the flexible bearing II16. The arc teeth of the flexible wheel II15 act on the E-shaped teeth on the inner surface of the steel wheel II14. Under the push of the input shaft II13 and the restriction of the E-shaped teeth, the flexible wheel II15 rotates at a low speed, and the output shaft rotates, realizing the deceleration motion of the reducer.

[0071] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A tooth profile design method for an E-tooth reducer, characterized in that, The E-tooth reducer uses a circular shock wave, and its cam's outer cylindrical surface is circular. The theoretical tooth profile equation is: in, , ρ ( θ ( ) represents the extreme diameter, and the transmission ratio is... i = Z 1 / ( Z 1- Z 2), ρ ( θ )as follows ； in, e For the eccentricity, h Half width, R 1 represents the radius of the arc; θ as follows ； in, S 1 is , S 2 is BC , h for OC , , ; The curvature formula is ； right θ Taking the derivative, we get θ right φ derivative ； in, , , , , , , ; right φ The derivative is ； In the theoretical tooth profile equation φ Differentiation ； Substituting the above into the curvature formula, we obtain the curvature formula for the tooth profile. The actual tooth profile equation is: in, , ; The actual tooth profile obtained according to the above formula is the E-tooth profile; Pressure angle: ； in, , , r This represents the offset distance.

2. The tooth profile design method for an E-tooth reducer according to claim 1, characterized in that, The E-tooth reducer has E-shaped teeth on the steel wheel and convex circular arc teeth on the flexible wheel. The E-shaped teeth on the steel wheel mesh with the circular arc teeth on the flexible wheel.

3. An E-type tooth reducer, which is a harmonic reducer, wherein the steel wheel teeth of the harmonic reducer have an inwardly concave arc shape, and a rolling element is installed within the arc of the steel wheel teeth, the rolling element meshing with the flexible wheel teeth, so that the flexible wheel teeth and the steel wheel teeth are in pure rolling meshing through the rolling element, characterized in that, The flexible gear tooth profile obtained by the tooth profile design method described in claim 1.

4. The E-tooth reducer according to claim 3, characterized in that, It includes: Positioning shaft (1), flexible wheel (2), bolt (3), cross bearing (4), housing (6), needle roller (8), flexible bearing (9), input shaft (10); Among them, the flexible bearing (9) is installed on the outer surface of the input shaft (10), the flexible bearing (9) is installed in the flexible wheel (2), the cross bearing (4) is fixed on the end face of the outer shell (6), the flexible wheel (2) is fixed on the end face of the cross bearing (4), and the coaxiality of the flexible wheel (2) and the cross bearing (4) is ensured by the positioning shaft (1); the inner surface of the outer shell (6) has a cylindrical surface, and the steel wheel teeth are multiple arc grooves machined on the inner cylindrical surface of the inner surface of the outer shell (6), and the rolling element is installed in the arc groove; the outer surface of the flexible wheel (2) has a cylindrical surface, and multiple teeth with elliptical pitch circles are machined on the cylindrical surface of the outer surface of the flexible wheel (2), and the rolling element meshes with the teeth on the flexible wheel (2); When the input shaft (10) rotates, the input shaft (10) pushes the flexible wheel (2) to deform through the flexible bearing (9). The flexible wheel (2) pushes the rolling element, and the rolling element reacts to the flexible wheel (2). The flexible wheel (2) rotates at low speed under the push of the input shaft (10) and the restriction of the rolling element. The rolling element slides in the arc groove. The flexible wheel (2) drives the inner ring of the cross bearing (4) to rotate, output shaft power, and realize the deceleration motion of the reducer.

5. The E-tooth reducer according to claim 4, characterized in that, The rolling element is a rigid needle roller or a steel ball.

6. The E-tooth reducer according to claim 4, characterized in that, It also includes a retaining ring (11) and a baffle (12), screws (5), bolts (3) and a retaining ring (7). The cross bearing (4) is fixed to the end face of the housing (6) by screws (5); the flexible wheel (2) is fixed to the end face of the cross bearing (4) by bolts (3); the baffle (12) restricts the axial movement of the rolling element, and the retaining ring (7) restricts the radial and axial movement of the rolling element.

7. The E-tooth reducer according to claim 3, characterized in that: The cylindrical surface of the inner surface of the outer shell (6) is machined with Z 1 with a diameter of d 1. Circular arc groove teeth, Z One circular arc groove tooth is evenly distributed on a radius of R On the circle, the rolling element with a diameter of [missing information] is installed in the arc groove. d r The needle roller (8), and d r < d 1, d r / 2> r , Among them, the cylindrical surface of the outer surface of the flexible wheel (2) is machined with Z Two of the aforementioned teeth, and satisfying Z 1> Z 2 or Z 1= Z 2 or Z 1< Z 2; Transmission ratio .

8. An E-tooth reducer according to any one of claims 3-7, characterized in that: The outer surface of the input shaft (10) is arc-shaped.

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