Harmonic reducer rigid gear tooth profile design method and harmonic reducer

Abstract

The invention relates to the technical field of speed reducers, and particularly discloses a harmonic speed reducer rigid gear tooth profile design method which comprises the following steps: giving a polar coordinate expression of a flexible gear neutral layer curve: r = p / cos (mu); assuming that the rotation angle of the undeformed end of the flexible gear is # imgabs0 # in unit time, according to the assumption that a neutral layer curve is not elongated before and after deformation of the flexible gear, the arc length of the deformed end of the flexible gear is equal to the arc length of the undeformed end of the flexible gear, and according to the Cauchy formula of the convex set perimeter, # imgabs1 # Zc is the tooth number of the rigid gear, and Zf is the tooth number of the flexible gear; a parameter equation of the tooth profile of the rigid gear can be obtained according to the envelope theory, the tooth profile of one tooth in the rigid gear is obtained, and then the whole tooth profile of the rigid gear is obtained through the array. When the rigid gear calculated through the method is used in the three-wave speed reducer, the transmission ratio is smaller than 10, and the meshing area of the rigid gear and the flexible gear exceeds 40%.

Description

Technical Field

[0001] The present invention relates to the technical field of speed reducers, and in particular to a design method for the tooth profile of a rigid gear of a harmonic speed reducer and a harmonic speed reducer. Background Art

[0002] As a precision transmission device, the harmonic speed reducer has the advantages of large transmission ratio, small volume, light weight, high transmission accuracy, etc., and is widely used in the fields of robots, aerospace, precision machine tools, etc. However, in traditional harmonic speed reducers, there are mainly double-wave speed reducers and triple-wave speed reducers. Among them, the larger the difference in the number of teeth between the flexible gear and the rigid gear, the smaller the transmission ratio. The transmission ratio of the existing triple-wave speed reducer is generally greater than 30; and the meshing ratio of the flexible gear and the rigid gear is between 20% - 30%, resulting in poor load-bearing capacity and not being suitable for high-rigidity application scenarios; in order to increase the meshing ratio of the flexible gear and the rigid gear, the deformation of the flexible gear will be too large, thus affecting the meshing accuracy and the stability of transmission.

[0003] Therefore, there is an urgent need to study a design method for the tooth profile of a rigid gear of a harmonic speed reducer and a harmonic speed reducer to solve the above problems. Summary of the Invention

[0004] The purpose of the present invention is to provide a design method for the tooth profile of a rigid gear of a harmonic speed reducer and a harmonic speed reducer to solve the problems in the prior art that the meshing area between the flexible gear and the rigid gear in the harmonic speed reducer is small, resulting in poor load-bearing capacity, not being suitable for high-rigidity application scenarios, and having a relatively high transmission ratio, and the transmission ratio is greater than 30, resulting in slow response.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A design method for the tooth profile of a rigid gear of a harmonic speed reducer, including:

[0007] Giving the polar coordinate expression of the neutral layer curve of the flexible gear:

[0008] r = p / cos(μ);

[0009] In the formula, p is the perpendicular distance from point O to the tangent of point q, point O is the center of the neutral layer curve of the flexible gear before deformation, and point q is a point on the neutral layer curve of the flexible gear after deformation; μ is the included angle between the center line of the flexible gear tooth and the radius vector;

[0010] According to the assumption that the neutral layer curve of the flexible gear does not elongate before and after deformation, the arc length of the deformed end circular arc of the flexible gear is equal to the arc length of the undeformed end circular arc, and combining with the Cauchy formula of the convex set perimeter It can be obtained that:

[0011]

[0012] The rotation angle of the rigid gear is Ф, and In the formula, Zc is the number of teeth of the rigid gear, Z f is the number of teeth of the flexible gear;

[0013] According to the envelope theory, the parametric equation of the rigid gear tooth profile can be obtained, and the tooth profile of one tooth of the rigid gear can be obtained;

[0014] The entire rigid gear tooth profile is obtained by array.

[0015] As an alternative technical solution of a design method for the rigid gear tooth profile of a harmonic reducer, the expression of the flexible gear neutral layer curve in tangent polar coordinates is:

[0016] p = r m+ mcos(Kθ), 0 ≤ θ ≤ 2π; where, m is the module, r m is the radius of the flexible gear neutral layer curve before deformation, and K is a constant.

[0017] As an alternative technical solution of a design method for the rigid gear tooth profile of a harmonic reducer, r m = (0.5Z f - h f ) - 0.5t, where, Z f is the number of teeth of the flexible gear, h f is the tooth root height coefficient, and t is the wall thickness at the tooth root of the flexible gear.

[0018] As an alternative technical solution of a design method for the rigid gear tooth profile of a harmonic reducer, the angle μ between the center line of the flexible gear tooth and the radius vector is calculated according to the following formula:

[0019] μ = tan -1 [3msin(Kθ) / {r m + mcos(Kθ)}];

[0020] In the formula, m is the module, r m is the radius of the flexible gear neutral layer curve before deformation, and K is a constant.

[0021] As an alternative technical solution of a design method for the rigid gear tooth profile of a harmonic reducer, K ≥ 2.

[0022] As an alternative technical solution of a design method for the rigid gear tooth profile of a harmonic reducer, K = 3 or 4.

[0023] As an alternative technical solution of a design method for the rigid gear tooth profile of a harmonic reducer, let the parametric equation of the flexible gear tooth profile be:

[0024] According to the envelope theory, the parametric equation of the rigid gear tooth profile can be obtained:

[0025]

[0026] The tooth profile of one tooth of the rigid gear can be obtained from the above parametric equations.

[0027] As an alternative technical solution for the design method of the tooth profile of the rigid gear of a harmonic reducer, D = Z c - Z f ; D ≥ 2.

[0028] As an alternative technical solution for the design method of the tooth profile of the rigid gear of a harmonic reducer, D = 3 or D = 4.

[0029] A harmonic reducer includes a flexible gear, a rigid gear, and a harmonic generator. Among them, the rigid gear is designed by using the design method of the tooth profile of the rigid gear of the harmonic reducer described in any of the above technical solutions. The rigid gear is located on the outer periphery of the flexible gear, and the harmonic generator is located inside the flexible gear.

[0030] The present invention has at least the following beneficial effects:

[0031] The present invention provides a design method for the tooth profile of the rigid gear of a harmonic reducer and a harmonic reducer. In the design method for the tooth profile of the rigid gear of the harmonic reducer, when calculating the polar coordinates of the neutral layer curve of the flexible gear, the ratio of p and cos(μ) is used. Among them, p is the perpendicular distance from point O to the tangent line of point q. Point O is the center of the neutral layer curve of the flexible gear before deformation, and point q is a point on the neutral layer curve of the flexible gear after deformation; μ is the angle between the center line of the flexible gear tooth and the radial vector, so that the polar coordinates of the neutral layer curve of the flexible gear are more accurate. The rigid gear calculated by the above method is applied in a three-wave reducer, and the transmission ratio is less than 10, with a faster response. Compared with the existing three-wave reducer, under the same input premise, the output is faster. In addition, the meshing area between the flexible gear and the rigid gear is greater than 40%, so that the load-bearing capacity is greatly improved, and it can adapt to application scenarios with higher stiffness; and there are three meshing points between the flexible gear and the rigid gear in the three-wave reducer, and the deformation of the flexible gear is small, thus ensuring the meshing accuracy and the stability of transmission. Description of the Drawings

[0032] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments of the present invention. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to the content of the embodiments of the present invention and these drawings.

[0033] Figure 1 It is a schematic structural diagram of the neutral layer curve of the flexible gear before and after deformation in the embodiment of the present invention;

[0034] Figure 2 It is a coordinate schematic diagram of the flexible gear and the rigid gear in the embodiment of the present invention;

[0035] Figure 3Schematic diagram of half a tooth in the rigid gear profile designed based on the envelope theory in the embodiments of the present invention;

[0036] Figure 4 Schematic diagram of the meshing area between the flexible gear and the rigid gear in the embodiments of the present invention;

[0037] Figure 5 is Figure 4 partial enlarged view of. Detailed implementation manners

[0038] Before explaining any embodiment of the present application in detail, it should be understood that the present application is not limited to the structural details and component arrangements set forth in the following description or shown in the above drawings.

[0039] In the present application, the terms "include", "comprise", "have" or any other variant thereof are intended to cover non-exclusive inclusion, such that a process, method, article or device including a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the phrase "including a..." does not exclude the presence of additional identical elements in the process, method, article or device including the element.

[0040] In the present application, the term "and / or" describes the association relationship of associated objects and indicates that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " in the present application generally represents an "and / or" relationship between the associated objects before and after.

[0041] In the present application, the terms "connect", "combine", "couple", "mount" may be direct connection, combination, coupling or mounting, or may be indirect connection, combination, coupling or mounting. Among them, by way of example, direct connection means that two parts or components are connected together without setting an intermediate member, and indirect connection means that two parts or components are respectively connected to at least one intermediate member, and these two parts or components are connected through the intermediate member. In addition, "connect" and "couple" are not limited to physical or mechanical connection or coupling, and may include electrical connection or coupling.

[0042] In this application, those of ordinary skill in the art will understand that relative terms used in connection with quantities or conditions (e.g., "about", "approximately", "substantially", etc.) are intended to include the recited value and have the meaning indicated by the context. For example, such relative terms include at least the degree of error associated with the measurement of a particular value, tolerances resulting from manufacturing, assembly, use in relation to a particular value, etc. Such terms should also be considered to disclose ranges defined by the absolute values of two endpoints. The relative terms may refer to plus or minus a certain percentage (e.g., 1%, 5%, 10% or more) of the indicated value. Numerical values that do not employ relative terms should also be disclosed as specific values with tolerances. In addition, when expressing relative angular positional relationships (e.g., substantially parallel, substantially perpendicular), "substantially" may refer to plus or minus a certain number of degrees (e.g., 1 degree, 5 degrees, 10 degrees or more) from the indicated angle.

[0043] In this application, those of ordinary skill in the art will understand that the functions performed by a component can be performed by one component, multiple components, one part, or multiple parts. Similarly, the functions performed by a part can also be performed by one part, one component, or a combination of multiple parts.

[0044] In this application, the orientation terms such as "upper", "lower", "left", "right", "front", "rear", etc. are described based on the orientation and positional relationship shown in the drawings, and should not be construed as limiting the embodiments of this application. In addition, in the context, it should also be understood that when it is mentioned that one element is connected "above" or "below" another element, it can not only be directly connected "above" or "below" another element, but also be indirectly connected "above" or "below" another element through an intermediate element. It should also be understood that the orientation terms such as the upper side, the lower side, the left side, the right side, the front side, the rear side, etc. not only represent the positive orientation, but can also be understood as the side orientation. For example, the lower side can include directly below, lower left, lower right, front lower, and rear lower, etc.

[0045] This embodiment provides a design method for the profile of the rigid gear of a harmonic reducer, as Figure 1 shown, the circular curve is the neutral layer curve of the flexspline before deformation, the elliptical curve is the neutral layer curve of the flexspline deformed under the action of the harmonic generator, point O is the center of the neutral layer curve of the flexspline before deformation, point q is a point on the neutral layer curve after the flexspline is deformed, r is the radial vector of point q, p is the perpendicular distance from point O to the tangent line of point q, w is the radial deformation amount, μ is the angle between the center line of the flexspline tooth and the radial vector; ζ is the angle between the radial vector of point q and the major axis; the design method for the profile of the rigid gear of this harmonic reducer includes:

[0046] Giving the polar coordinate expression of the neutral layer curve of the flexspline:

[0047] r = p / cos(μ);

[0048] Taking the rotation center O of the harmonic generator as the origin and the major axis of the harmonic generator as the y-axis, the kinematic geometric relationships of the harmonic generator, the flexspline, and the rigid ring are combined Figure 2 as shown in the figure, where L1 is the tooth of the flexspline, L2 is the tooth of the rigid ring, the c-axis is the center line of the tooth slot of the rigid ring, the e-axis is the center line of the tooth of the flexspline, ξ is the angle between the c-axis and the e-axis, ε is the angle between the c-axis and the vector radius of point q, Ф is the rotation angle of the rigid ring, S is the arc length from point q to the major axis; w is the radial deformation, and ζ is the angle between the vector radius of point q and the major axis.

[0049] Assume that within a unit time, the rotation angle of the non-deformed end of the flexspline is According to the assumption that the neutral layer curve of the flexspline does not elongate before and after deformation, the arc length of the deformed end of the flexspline is equal to the arc length of the non-deformed end. Combining with the Cauchy formula of the convex set perimeter It can be obtained that:

[0050]

[0051] In the formula, Z c is the number of teeth of the rigid ring, and Z f is the number of teeth of the flexspline;

[0052] According to the envelope theory, the parametric equation of the tooth profile of the rigid ring can be obtained, and the tooth profile of one tooth in the rigid ring can be obtained, and then the entire tooth profile of the rigid ring can be obtained by array.

[0053] The rigid ring calculated by the above method is applied in a three-wave reducer, and the transmission ratio is less than 10, with faster response. Compared with the existing three-wave reducer, under the same input premise, the output is faster. In addition, the meshing area of the flexspline and the rigid ring accounts for more than 40%, that is, more than 40% of the teeth in the flexspline mesh with the rigid ring, resulting in a significant improvement in the load-bearing capacity and being able to adapt to application scenarios with higher stiffness; and there are three meshing points between the flexspline and the rigid ring in the three-wave reducer, and the deformation of the flexspline is smaller, thus ensuring the meshing accuracy and the stability of the transmission. Since the smaller the reduction ratio and the fewer the number of teeth, the larger the value of cos(μ), therefore, in the above method, r is obtained by p / cos(μ), and under the premise of a smaller reduction ratio, the result of r is more accurate, and thus the meshing area between the rigid teeth and the flexible teeth is larger.

[0054] In some embodiments, the expression of the neutral layer curve of the flexspline in tangent polar coordinates is:

[0055] p = r m+ mcos(Kθ), 0 ≤ θ ≤ 2π; where m is the module, r m is the radius of the neutral layer curve of the flexspline before deformation, and K is a constant. Specifically, K ≥ 2. Exemplarily, when calculating a three-wave reducer, K is specified as 3, that is, substituting K = 3 into the above formula gives: p = r m+m cos(3θ), 0 ≤ θ ≤ 2π; ζ = θ - μ. When calculating a four-wave reducer, K is specified as 4. Where, r m =(0.5Z f -h f ) - 0.5t, where, Z f is the number of teeth of the flexspline, h f is the addendum coefficient, and t is the wall thickness at the root of the flexspline teeth. Determining the radius of the neutral layer curve of the flexspline before deformation through the specific number of teeth, addendum coefficient of the flexspline, and the wall thickness of the flexspline at the tooth root can ensure the proportion of the meshing area between the flexspline and the rigid spline. Substituting p = r m+ m cos(3θ) into r = p / cos(μ) gives r = {r m + m cos(3θ)} / cos(μ).

[0056] In some embodiments, the angle μ between the center line of the flexspline teeth and the radius vector is calculated according to the following formula:

[0057] μ = tan -1 [3m sin(Kθ) / {r m + m cos(Kθ)}]; in the formula, m is the module, r m is the radius of the neutral layer curve of the flexspline before deformation, and K is a constant. Specifically, K ≥ 2. Exemplarily, when calculating a three-wave reducer, K is specified as 3, that is, substituting K = 3 into the above formula gives:

[0058] μ = tan -1 [3m sin(3θ) / {r m + m cos(3θ)}].

[0059] In other embodiments, when calculating a four-wave reducer, K is specified as 4.

[0060] Let the parametric equation of the flexspline tooth profile be: According to the envelope theory, the parametric equation of the rigid spline tooth profile can be obtained:

[0061]

[0062] From the above parametric equations, the tooth profile of one tooth of the rigid spline can be obtained.

[0063] Where, D = Z c - Z f ; D ≥ 2. In the embodiment of calculating a three-wave reducer, D = 3. In other embodiments, D can also be 4, 5, 6, 7, 8, 9. In some embodiments, D can also be 20.

[0064] Using the above method, specific parameters are given, r mWhen \(p = 17.023\) and \(m = 0.23\), the expression of the neutral layer curve of the flexspline after deformation in the tangent polar coordinates can be obtained: \(p=17.023 + 0.23\times\cos(3\theta)\);

[0065] Then, the number of teeth \(Z\) of the rigid spline is given c as 33, and the number of teeth \(Z\) of the flexspline f is 30. Among them, the parametric equation can be set according to the preset flexspline structure, which is obvious to those skilled in the art, so it will not be elaborated here.

[0066] Combined with Figure 3 as shown, substituting five data points into \(\theta\) to obtain the tooth profile of the rigid spline designed based on the envelope theory. Among them, \(A1\), \(A2\), \(A3\), \(A4\) and \(A5\) respectively represent five positions of the flexspline. The connecting lines of the positions tangent to the flexspline at the five positions form half of the tooth profile \(A0\) of the rigid tooth. The entire tooth profile of the rigid tooth is obtained by mirroring, and then the complete tooth profile of the rigid tooth is obtained by circular array. Among them, after assigning a value to \(\theta\), a position of the flexspline is obtained. Assigning a value to \(\theta\) five times obtains five positions of the flexspline, and the range of the five assignments is \(60^{\circ}\).

[0067] Combined with Figure 4 and Figure 5 as shown, it is the result obtained by computer simulation. Figure 5 In it, \(B0\) is the rigid tooth, \(B1\), \(B2\), \(B3\), \(B4\), \(B5\) are five adjacent teeth in the flexspline. Taking the center of the rigid spline as the origin, an arbitrary sector area with a radian of \(\alpha = 60^{\circ}\) is selected. The meshing area of the flexspline and the rigid spline is \(\beta = 49.091^{\circ}\), and the proportion of the meshing area of the flexspline and the rigid spline is \(49.091\times3 / 360 = 0.409\), that is, the proportion of the meshing area of the flexspline and the rigid spline can be as high as \(40.9\%\), and the reduction ratio of the above three-wave speed reducer is 10.

[0068] Obviously, the above embodiments of the present invention are only examples for clearly explaining the present invention, rather than limiting the implementation manners of the present invention. For those of ordinary skill in the art, various obvious changes, re-adjustments and substitutions can be made without departing from the protection scope of the present invention. It is not necessary and impossible to enumerate all the implementation manners here. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A method for designing a tooth profile of a harmonic reducer rigid wheel, characterized in that: include: The polar coordinate expression of the neutral layer curve of the flexible wheel is given as: r = p / cos(μ); Where, p is the vertical distance from the tangent line at point O to point q, point O is the center of the neutral layer curve before the flexspline is deformed, and point q is a point on the neutral layer curve after the flexspline is deformed; μ is the angle between the center line of the flexspline tooth and the radius vector; Based on the assumption that the neutral layer curve does not stretch before and after the flexspline deformation, the arc length of the flexspline deformation end is equal to the arc length of the undeformed end. Combined with the Cauchy formula of the convex set perimeter We can get: The rigid wheel rotation angle is Ф, and In the formula, Z c is the number of teeth on the steel wheel, Z f is the number of flexspline teeth; According to the envelope theory, the parameter equation of the wheel tooth shape can be obtained, and the tooth shape of one tooth of the wheel can be obtained; The entire rigid wheel tooth profile is obtained through the array.

2. The method for designing the tooth profile of a harmonic reducer according to claim 1, characterized in that: The expression of the neutral layer curve of the flexible wheel in tangent polar coordinates is: p=r m+ mcos(Kθ), 0≤θ≤2π; where m is the modulus, r m is the curve radius of the neutral layer of the flexible wheel before deformation, and K is a constant.

3. The method for designing the tooth profile of a harmonic reducer according to claim 2, characterized in that: r m =(0.5Z f -h f )-0.5t, where Z f is the number of flexspline teeth, h f is the tooth root height coefficient, and t is the wall thickness at the root of the flexspline tooth.

4. The method for designing the tooth profile of a harmonic reducer according to claim 3, characterized in that: The angle μ between the center line of the flexspline tooth and the radius vector is calculated according to the following formula: μ=tan -1 [3msin(Kθ) / {r m +mcos(Kθ)}]; In the formula, m is the modulus, r is m is the curve radius of the neutral layer of the flexible wheel before deformation, and K is a constant.

5. The method for designing the tooth profile of a harmonic reducer according to claim 4, characterized in that: K≥2。 6. The method for designing the tooth profile of a harmonic reducer according to claim 4, characterized in that: K=3 or 4.

7. The method for designing the tooth profile of a harmonic reducer according to claim 4, characterized in that: Assume the parametric equation of the flexspline tooth shape is: According to the envelope theory, the parameter equation of the rigid wheel tooth shape can be obtained: The tooth shape of one tooth of the rigid wheel can be obtained from the above parametric equation.

8. The method for designing the tooth profile of a harmonic reducer according to claim 1, characterized in that: D=Z c -Z f ;D≥2。 9. The method for designing the tooth profile of a harmonic reducer according to claim 8, characterized in that: D=3 or D=4.

10. Harmonic reducer, characterized in that: It comprises a flexible spline, a rigid spline and a harmonic generator, wherein the rigid spline is designed by adopting the design method of the harmonic reducer rigid spline tooth profile according to any one of claims 1 to 9, the rigid spline is located at the outer periphery of the flexible spline, and the harmonic generator is located inside the flexible spline.

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