Wave generator cam curve design method and device, equipment and storage medium

Abstract

This application provides a method, apparatus, device, and storage medium for designing a wave generator cam curve. The method includes: loading the radius of a true circle and the deformation of the cam to ensure that the circumference of the true circle is consistent with the circumference of the modified curve; constructing the tangent polar coordinate equation of the modified curve based on Fourier expansion, the equation containing a set of Fourier coefficients; determining candidate parameters and candidate polar diameters under the condition of satisfying a first constraint, based on the equation, the deformation, the extreme angles corresponding to the extreme values ​​of the curvature change, and the curvature ratio; calculating the difference between the candidate polar diameter and the standard ellipse polar diameter, the standard ellipse and the modified curve having the same semi-major axis and circumference; and finally, determining the target polar diameter and the contour parameters of the modified curve by combining the polar diameter difference, the corresponding polar angle, and the second constraint.

Description

Technical Field

[0001] This application relates to the field of wave generator technology, and in particular to a method, apparatus, device and storage medium for designing a wave generator cam curve. Background Technology

[0002] In harmonic gear transmissions, the profile curve of the wave generator cam directly determines the deformation shape and performance of the flexspline. Currently, the commonly used traditional elliptic curves or basic Fourier curves easily lead to stress concentration at the flexspline tooth roots and interference between meshing teeth, affecting transmission accuracy and fatigue life. To optimize performance, existing technologies such as the Ishikawa method propose using multiple Fourier coefficients to improve the curve. This method improves the cam profile to some extent, but it still struggles to precisely control the cam's "bulge" shape, further equalize stress distribution, and avoid tooth interference. Summary of the Invention

[0003] This application provides a method, apparatus, device, and storage medium for designing cam curves for wave generators, which can reduce the risk of tooth root stress concentration and tooth interference, and improve the smoothness of cam curves and transmission stability.

[0004] In a first aspect, embodiments of this application provide a method for designing a wave generator cam curve, the method comprising:

[0005] The true circle radius and the deformation of the cam are loaded, wherein the circumference of the circle corresponding to the true circle radius is the same as the circumference of the modified curve corresponding to the cam;

[0006] Based on Fourier expansion, the tangent polar coordinate equation of the improved curve is constructed according to the radius of the true circle and the tangent angle of the improved curve. The tangent angle of the improved curve is the angle between the improved curve and the preset coordinate axis. The tangent polar coordinate equation includes a set of Fourier expansion coefficients.

[0007] Based on the tangent polar coordinate equation, the deformation, the extreme angle, and the curvature ratio, the candidate parameters and candidate polar radius of the improved curve are determined. The candidate polar radius corresponds to a candidate polar angle. The extreme angle is the angle corresponding to the extreme value of the curvature change of the improved curve. The curvature ratio is the ratio of the extreme value of the curvature change of the improved curve to the curvature change located at the major axis position of the improved curve. The Fourier expansion coefficients, the extreme angle, and the curvature ratio are all subject to a preset first constraint condition.

[0008] Calculate the difference between the candidate polar radius and the polar radius of the standard ellipse. The semi-major axis of the standard ellipse is the same as the semi-major axis of the modified curve. The circumference of the standard ellipse is equal to the circumference of the modified curve. The semi-minor axis of the standard ellipse is determined according to the semi-major axis and a preset semi-minor axis calculation formula.

[0009] The target polar diameter is determined from the candidate polar diameters using the polar diameter difference, the candidate polar angles corresponding to the polar diameter difference, and the preset second constraint conditions. Then, the contour parameters of the improved curve are determined from the candidate parameters based on the target polar diameter.

[0010] In some embodiments, the polar equation of the tangent is:

[0011] ;

[0012] in, p Let be the perpendicular distance from the origin of the coordinate system to the tangent line at any point on the improved curve. r 0 is the radius of the true circle. φ The included angle of the tangents, a 1. a 2 and a 3 are all Fourier expansion coefficients.

[0013] In some embodiments, before determining the candidate parameters and candidate polar radius of the improved curve based on the tangent polar coordinate equation, the deformation, the extreme angle of the curvature change, and the curvature ratio, the method further includes:

[0014] The curvature change is determined based on the tangential polar radius of curvature of the improved curve and the radius of the true circle, using the following formula:

[0015] ;

[0016] ;

[0017] in, The tangential polar coordinate radius of curvature, The change in curvature is the amount of curvature.

[0018] The extreme angle of the curvature change and the curvature ratio are determined based on the curvature change.

[0019] In some embodiments, determining the candidate parameters and candidate polar radius of the improved curve based on the tangent polar coordinate equation, the deformation, the extreme angle of the curvature change, and the curvature ratio includes:

[0020] The normal angle is calculated based on the polar coordinate equation of the tangent, using the following formula:

[0021] ;

[0022] in, η The normal angle is...

[0023] Based on the normal angle and the perpendicular distance, the candidate polar radius and candidate polar angle of the improved curve are calculated using the following formulas:

[0024] ;

[0025] ;

[0026] in, For the candidate polar radius, the θ The candidate polar angle is denoted as .

[0027] Within a preset parameter range, iterate through various combinations of the curvature ratio and the extreme angle;

[0028] For each of the combinations, the Fourier expansion coefficients that satisfy the first constraint are solved to determine a set of candidate parameters and corresponding candidate polar trajectories.

[0029] In some embodiments, the first constraint includes the following system of equations:

[0030] ;

[0031] in, e It is the amount of deformation of the cam. β It is the extreme angle of the curvature change. λ The curvature ratio is given.

[0032] In some embodiments, calculating the polar radius difference between the candidate polar radius and the polar radius of the standard ellipse includes:

[0033] Calculate the polar radius of the standard ellipse at the candidate polar angle based on the major semi-axis and the minor semi-axis of the standard ellipse.

[0034] The polar diameter difference is determined based on the candidate polar diameter and the elliptical polar diameter.

[0035] In some embodiments, the polar radius of the standard ellipse is calculated using the following formula:

[0036] ;

[0037] in, r t Let be the polar radius of the standard ellipse. a Let be the semi-major axis of the standard ellipse. b Let be the minor semi-axis of the standard ellipse.

[0038] In some embodiments, the specific formula for determining the polar radius difference based on the candidate polar radius and the elliptical polar radius is as follows:

[0039] ;

[0040] in, r f For the difference in polar radius, the r g To improve the polar radius of the curve, the r t This is the polar radius of a standard ellipse.

[0041] In some embodiments, the second constraint includes the following system of equations:

[0042] ;

[0043] in, To maximize the difference in polar radius between the improved curve and the standard ellipse, This is the angle corresponding to the maximum value of the polar radius difference. For the desired bulge angle, Tolerance for the bulge angle, For the required amount of bulging; The tolerance for the required bulge amount is the maximum design value of the polarity difference. The polar angle corresponding to the minimum even-numbered polar radius difference is 90°.

[0044] In some embodiments, the preset formula for calculating the minor semi-axis is:

[0045] ;

[0046] ;

[0047] Where 'a' is the semi-major axis of the standard ellipse. Let be the radius of the true circle, e be the amount of deformation, and b be the minor semi-axis of the standard ellipse.

[0048] This application provides a method for designing a wave generator cam curve. The method includes: loading a true circle radius and a cam deformation, wherein the circumference of the circle corresponding to the true circle radius is the same as the circumference of the modified curve corresponding to the cam; based on Fourier expansion, constructing a tangent polar coordinate equation for the modified curve according to the angle between the tangents of the true circle radius and the modified curve, wherein the tangent angle is the angle between the modified curve and a preset coordinate axis, and the tangent polar coordinate equation includes a set of Fourier expansion coefficients; determining candidate parameters and candidate polar radii for the modified curve based on the tangent polar coordinate equation, the deformation, the extreme angle, and the curvature ratio, wherein a candidate polar radii corresponds to a candidate polar angle, and the extreme angle is the angle corresponding to the extreme value of the curvature change of the modified curve. The curvature ratio is the ratio of the extreme value of the curvature change of the improved curve to the curvature change located at the position of the major axis of the improved curve. The Fourier expansion coefficients, extreme angles, and curvature ratios are all subject to the preset first constraint condition. The difference between the candidate polar diameter and the polar diameter of the standard ellipse is calculated. The semi-major axis of the standard ellipse is the same as the semi-major axis of the improved curve, the circumference of the standard ellipse is equal to the circumference of the improved curve, and the semi-minor axis of the standard ellipse is determined according to the semi-major axis and the preset semi-minor axis calculation formula. The target polar diameter is determined from the candidate polar diameter through the polar diameter difference, the candidate polar angle corresponding to the polar diameter difference, and the preset second constraint condition. Then, the contour parameters of the improved curve are determined from the candidate parameters according to the target polar diameter. In the above method, by loading the radius and deformation of the true circle, constructing the polar coordinate equation of the tangent based on Fourier expansion, determining the candidate parameters and candidate polar diameter under the first constraint, calculating the polar diameter difference with the standard ellipse, and filtering the target polar diameter and contour parameters through the second constraint, the optimization of full parameter scanning and polar diameter difference guidance is realized, which effectively reduces the risk of tooth root stress concentration and tooth interference, and improves the smoothness of the cam curve and transmission stability. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 A schematic flowchart illustrating a wave generator cam curve design method provided in this application embodiment;

[0051] Figure 2 A schematic diagram of design parameters provided for embodiments of this application;

[0052] Figure 3 A schematic diagram illustrating the relationship between a modified curve and a true circle, provided in an embodiment of this application;

[0053] Figure 4A schematic diagram of the amount of curvature change provided in an embodiment of this application;

[0054] Figure 5 A schematic diagram illustrating the relationship between extreme angles and curvature ratios provided in this application embodiment;

[0055] Figure 6 This application provides a schematic diagram illustrating the change in the relative radius of two curves to a true circle in an embodiment of the present application.

[0056] Figure 7 This is a schematic diagram illustrating the variation of the polar radius difference in an embodiment of this application.

[0057] Figure 8 This is a schematic diagram of a constraint solution set provided in an embodiment of this application. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described below with reference to the accompanying drawings.

[0059] The terms "first" and "second," etc., used in the specification, claims, and drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0060] The term "embodiment" as used herein means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0061] It should be understood that in this application, "at least one (item)" means one or more, "more than one" means two or more, "at least two (items)" means two or three or more, and "and / or" is used to describe the relationship between related objects, indicating that there can be three relationships. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the related objects before and after are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0062] Please see Figure 1 , Figure 1 This is a schematic flowchart illustrating a wave generator cam curve design method provided in an embodiment of this application. Figure 1 As shown, the specific steps of the wave generator cam curve design method include: S101-S105.

[0063] S101, Load the true circle radius and the deformation of the cam. The circumference of the circle corresponding to the true circle radius is the same as the circumference of the modified curve corresponding to the cam.

[0064] For example, the deformation of the cam is the maximum acceptable deformation for designing the improved curve. Before designing the improved curve, input such as... Figure 2 The diagram shows the design requirements for the improved curve. Using the wave generator cam curve design method provided in this application embodiment, a solution set of the contour parameters of the improved curve that meets the above design requirements can be obtained. The contour parameters of this improved curve conform to the following... Figure 2 The design requirements for the improved curve are shown.

[0065] S102. Based on Fourier expansion, construct the polar coordinate equation of the tangent of the improved curve according to the radius of the true circle and the included angle of the tangent of the improved curve. The included angle of the tangent of the improved curve is the angle between the improved curve and the preset coordinate axis. The polar coordinate equation of the tangent includes a set of Fourier expansion coefficients.

[0066] For example, such as Figure 3 As shown, the dashed line is a true circle with the same circumference as the modified curve of the cam. r 0 is the radius of the true circle before deformation. H It is located on the improved curve r g A point on the surface. φ express x The angle between the axis and the tangent at H.p From the origin O to point H The perpendicular distance to the tangent at that point. Therefore, it can be determined by using... φ The function, used as a parameter, defines the tangent polar equation of the profile curve of the modified cam in tangent polar coordinates.

[0067] In some embodiments, the polar equation of the tangent is:

[0068] ;

[0069] in, p Let be the perpendicular distance from the origin of the coordinate system to the tangent line at any point on the improved curve. r 0 is the radius of the true circle. φ The angle between the tangents, a 1. a 2 and a 3 are all Fourier expansion coefficients.

[0070] S103. Based on the tangent polar coordinate equation, deformation, extreme angle, and curvature ratio, determine the candidate parameters and candidate polar radius of the improved curve. The candidate polar radius corresponds to a candidate polar angle. The extreme angle is the angle corresponding to the extreme value of the curvature change of the improved curve. The curvature ratio is the ratio of the extreme value of the curvature change of the improved curve to the curvature change located at the position of the major axis of the improved curve. The Fourier expansion coefficients, extreme angle, and curvature ratio are all subject to the preset first constraint condition.

[0071] In some embodiments, before determining the candidate parameters and candidate polar radius of the improved curve based on the polar coordinate equation of the tangent, the amount of deformation, the extreme angle of the curvature change and the curvature ratio, the method further includes: S1031-S1032.

[0072] S1031. Determine the curvature change based on the tangential polar coordinate radius of curvature and the radius of the true circle of the improved curve. The calculation formula is as follows:

[0073] ;

[0074] ;

[0075] in, Let be the radius of curvature in tangential polar coordinates. This represents the change in curvature.

[0076] For example, in the above steps, such as Figure 4 As shown, by traversing the Fourier expansion coefficients ( a 1. a 2 and a 3) Possible combinations at different tangent angles φ In the process, the curvature changes of a set of improved curves were obtained respectively. The change in curvature of a conventional ellipse (also known as a standard ellipse) Each possible combination of Fourier expansion coefficients will generate a... Figure 4 In subsequent processes, the curvature change is used. At that time, the default value is the change in curvature of the improved curve. . Figure 4 Change in curvature It is proportional to the stress at the tooth root.

[0077] S1032. Determine the extreme angle and curvature ratio of the curvature change based on the curvature change.

[0078] For example, according to such Figure 4 The curvature change shown The solution set, the change in curvature The angle corresponding to the maximum value is the extreme angle. β curvature ratio λ The change in curvature Maximum value and curvature change The ratio of the values ​​on the major axis.

[0079] According to such Figure 4 The curvature change shown The curve is used to determine the extreme angle of the curvature change. β and curvature ratio λ The solution between, this solution is Figure 5 The above is a point. In the above process, each curvature change is generated. The curves will all be in Figure 5 Generate a point on the top, thus obtaining Figure 5 Intermediate extreme angle β The ratio of curvature of the two λ Relationship curve. This relationship curve can be used to solve for candidate parameters and candidate polar radius of the improved curve.

[0080] In some embodiments, determining candidate parameters and candidate polar radii for the improved curve based on the polar coordinate equation of the tangent, the deformation, the extreme angle of the curvature change, and the curvature ratio includes:

[0081] The normal angle is calculated using the polar equation of the tangent. The formula is as follows:

[0082] ;

[0083] in, η It is the normal angle.

[0084] Based on the normal angle and the perpendicular distance, the candidate polar radius and candidate polar angle of the improved curve are calculated using the following formulas:

[0085] ;

[0086] ;

[0087] in, As candidate polar diameters, θ This is a candidate polar angle.

[0088] Within the preset parameter range, it iterates through various combinations of curvature ratios and extreme angles.

[0089] For each combination, solve for the Fourier expansion coefficients that satisfy the first constraint to determine a set of candidate parameters and the corresponding candidate polar radius.

[0090] It should be noted that the candidate parameters include at least: candidate polar angle. θ and Fourier expansion coefficients ( a 1. a 2 and a 3) Parameters used to specifically describe the improved curve.

[0091] In some embodiments, the first constraint includes the following system of equations:

[0092] ;

[0093] in, e It is the amount of deformation of the cam. β It is the extreme angle of the change in curvature. λ This represents the curvature ratio.

[0094] S104. Calculate the difference between the polar radius of the candidate polar radius and the polar radius of the standard ellipse. The semi-major axis of the standard ellipse is the same as the semi-major axis of the modified curve. The circumference of the standard ellipse is equal to the circumference of the modified curve. The semi-minor axis of the standard ellipse is determined according to the semi-major axis and the preset semi-minor axis calculation formula.

[0095] In some embodiments, the preset formula for calculating the minor semi-axis is:

[0096] ;

[0097] ;

[0098] Where 'a' is the semi-major axis of the standard ellipse. Let be the radius of the true circle, e be the deformation, and b be the minor semi-axis of the standard ellipse.

[0099] For example, such as Figure 6 As shown, the changes in the minor semi-axis of the standard ellipse relative to the radius of the true circle, and the changes in the modified curve relative to the radius of the true circle, are both expressed as... It means that, through Figure 6 This makes it easier to observe the changes in the relative radius of the two curves to the true circle.

[0100] In some embodiments, calculating the polar radius difference between the candidate polar radius and the polar radius of the standard ellipse includes: calculating the elliptical polar radius of the standard ellipse at the candidate polar angle based on the major semi-axis and minor semi-axis of the standard ellipse; and determining the polar radius difference based on the candidate polar radius and the elliptical polar radius.

[0101] In some embodiments, the polar radius of a standard ellipse is calculated using the following formula:

[0102] ;

[0103] in, r t The polar radius of a standard ellipse. a The semi-major axis of a standard ellipse. b It is the minor semi-axis of a standard ellipse.

[0104] In some embodiments, the polar radius difference is determined based on the candidate polar radius and the elliptical polar radius, using the following formula:

[0105] ;

[0106] in, r f This is the difference in polar radius, also known as the change in polar radius. r f , r g To improve the polar radius of the curve, r t This is the polar radius of a standard ellipse.

[0107] For example, such as Figure 7 As shown, the change in polar diameter r f (polar diameter difference) r f ) in the candidate polar angle θ The maximum value (0.0302) is reached at 33.06°, and the change in polar radius is... r f At candidate polar angle θ The value at 90° is -0.0406. The table above can be used to solve for the profile parameters of the improved curve in conjunction with the second constraint condition.

[0108] S105. Using the polar radius difference, the candidate polar angle corresponding to the polar radius difference, and the preset second constraint conditions, determine the target polar radius from the candidate polar radius, and then determine the contour parameters of the improved curve from the candidate parameters based on the target polar radius.

[0109] In some embodiments, the second constraint includes the following system of equations:

[0110] ;

[0111] in, The maximum value of the difference between the polar radius of the improved curve and the standard ellipse can also be called the maximum bulge. This is the angle corresponding to the maximum value of the extreme diameter difference, which can also be called the maximum bulge angle required for the design. For the desired bulge angle, Tolerance for the bulge angle, For the required amount of bulging. The tolerance for the required bulge amount is the maximum design value of the polarity difference. (By...) =π / 2 This limits the minimum polar angle corresponding to the difference between the polar radius of the modified curve and the standard ellipse to 90°.

[0112] For example, based on the above process, the following was obtained: Figure 8 The solution set shown, Figure 8 The solution set shown is consistent with the following: Figure 1 The solution set for the design requirements shown supports visual analysis of the results, facilitating engineering applications. From, for example... Figure 8 The solution set shown selects the target polar radius and the candidate polar angle corresponding to the target polar radius. Then, by reverse-engineering the candidate parameters, the contour parameters of the improved curve can be obtained.

[0113] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A wave generator cam curve design method characterized by, The method includes: The true circle radius and the deformation of the cam are loaded, wherein the circumference of the circle corresponding to the true circle radius is the same as the circumference of the modified curve corresponding to the cam; Based on Fourier expansion, the tangent polar coordinate equation of the improved curve is constructed according to the radius of the true circle and the tangent angle of the improved curve. The tangent angle of the improved curve is the angle between the improved curve and the preset coordinate axis. The tangent polar coordinate equation includes a set of Fourier expansion coefficients. Based on the tangent polar coordinate equation, the deformation, the extreme angle, and the curvature ratio, the candidate parameters and candidate polar radius of the improved curve are determined. The candidate polar radius corresponds to a candidate polar angle. The extreme angle is the angle corresponding to the extreme value of the curvature change of the improved curve. The curvature ratio is the ratio of the extreme value of the curvature change of the improved curve to the curvature change located at the major axis position of the improved curve. The Fourier expansion coefficients, the extreme angle, and the curvature ratio are all subject to a preset first constraint condition. Calculate the difference between the candidate polar radius and the polar radius of the standard ellipse. The semi-major axis of the standard ellipse is the same as the semi-major axis of the modified curve. The circumference of the standard ellipse is equal to the circumference of the modified curve. The semi-minor axis of the standard ellipse is determined according to the semi-major axis and a preset semi-minor axis calculation formula. The target polar diameter is determined from the candidate polar diameters using the polar diameter difference, the candidate polar angles corresponding to the polar diameter difference, and the preset second constraint conditions. Then, the contour parameters of the improved curve are determined from the candidate parameters based on the target polar diameter.

2. The method of claim 1, wherein, The polar equation of the tangent is: ； wherein p r is the distance from the coordinate origin to the perpendicular of the tangent at an arbitrary point on the modified curve, r 0 is the radius of the true circle, φ a is the included angle of the tangent, a 1, a 2 and a 3 are the Fourier expansion coefficients.

3. The method according to claim 2, characterized in that, Before determining the candidate parameters and candidate polar radius of the improved curve based on the tangent polar coordinate equation, the deformation, the extreme angle of the curvature change, and the curvature ratio, the method further includes: The curvature change is determined based on the tangential polar radius of curvature of the improved curve and the radius of the true circle, using the following formula: ； ； in, Let be the tangential polar coordinate radius of curvature. The change in curvature; The extreme angle of the curvature change and the curvature ratio are determined based on the curvature change.

4. The method according to claim 3, characterized in that, The process of determining the candidate parameters and candidate polar radius of the improved curve based on the tangent polar coordinate equation, the deformation, the extreme angle of the curvature change, and the curvature ratio includes: The normal angle is calculated based on the polar coordinate equation of the tangent, using the following formula: ； in, η The normal angle is... Based on the normal angle and the perpendicular distance, the candidate polar radius and candidate polar angle of the improved curve are calculated using the following formulas: ； ； in, For the candidate polar radius, the θ The candidate polar angle; Within a preset parameter range, iterate through various combinations of the curvature ratio and the extreme angle; For each of the combinations, the Fourier expansion coefficients that satisfy the first constraint are solved to determine a set of candidate parameters and corresponding candidate polar trajectories.

5. The method according to claim 2, characterized in that, The first constraint condition includes the following system of equations: ； in, e It is the amount of deformation of the cam. β It is the extreme angle of the curvature change. λ The curvature ratio is given.

6. The method according to claim 4, characterized in that, The calculation of the polar radius difference between the candidate polar radius and the polar radius of the standard ellipse includes: Calculate the polar radius of the standard ellipse at the candidate polar angle based on the major semi-axis and the minor semi-axis of the standard ellipse. The polar diameter difference is determined based on the candidate polar diameter and the elliptical polar diameter.

7. The method according to claim 6, characterized in that, The formula for calculating the polar radius of the standard ellipse is: ； in, r t The polar radius of a standard ellipse. a Let be the semi-major axis of the standard ellipse. b Let be the minor semi-axis of the standard ellipse.

8. The method according to claim 7, characterized in that, The polar radius difference is determined based on the candidate polar radius and the elliptical polar radius using the following formula: ； in, r f For the difference in polar radius, r g The polar radius of the improved curve is... r t Let be the polar radius of the standard ellipse.

9. The method according to claim 1, characterized in that, The second constraint includes the following system of equations: ； in, To maximize the difference in polar radius between the improved curve and the standard ellipse, This is the angle corresponding to the maximum value of the polar radius difference. For the desired bulge angle, Tolerance for the bulge angle, For the required bulge amount, The tolerance for the required bulge amount is the maximum design value of the polarity difference. The polar angle corresponding to the minimum even-numbered polar radius difference is 90°.

10. The method according to claim 1, characterized in that, The preset formula for calculating the minor semi-axis is: ； ； Where 'a' is the semi-major axis of the standard ellipse. Let be the radius of the true circle, e be the amount of deformation, and b be the minor semi-axis of the standard ellipse.

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