WO2016197909A1

WO2016197909A1 - Non-fully-symmetric involute gear and machining method therefor

Info

Publication number: WO2016197909A1
Application number: PCT/CN2016/085111
Authority: WO
Inventors: 颜力; 吴全衡; 刘忠伟; 文超
Original assignee: 中车戚墅堰机车车辆工艺研究所有限公司
Priority date: 2015-06-08
Filing date: 2016-06-07
Publication date: 2016-12-15
Also published as: CN104896061A; CN104896061B

Abstract

A non-fully-symmetric involute gear and a machining method and machining tool therefor. A tooth profile of an end-face tooth space of the non-fully-symmetric involute gear comprises an involute segment AB and an arc segment BC of a first-side tooth profile and an involute segment FE and an arc segment DE of a second-side tooth profile, wherein a point B is the starting point of the involute segment of the first-side tooth profile of the end-face tooth space of the non-fully-symmetric involute gear and the diameter of the involute segment at the starting point is rb, a point E is the starting point of the involute segment of the second-side tooth profile of the end-face tooth space of the non-fully-symmetric involute gear and the diameter the involute segment at the starting point is re, and rb≠re, so that the involute segment AB and the involute segment FE are non-fully symmetric about an axis III, and different tooth-root curvature strengths can be obtained at the two sides of teeth of the non-fully-symmetric involute gear.

Description

Incompletely symmetric involute gear and processing method thereof

Technical field

The invention relates to the technical field of involute gears, and relates to a non-completely symmetric involute gear and a processing method thereof, and a milling cutter for machining the incompletely symmetric involute gear.

Background technique

Gear transmission systems are commonly used for gears that mesh with two gears at the same time, such as intermediate idlers or planetary gears. Since their teeth are subjected to biaxial bending loads, the roots of the gears are most prone to bending and breaking, for example in GB/T 3480. -1997 "Involute Cylindrical Gear Load Capacity Calculation Method" P56 stipulates: For gears that are symmetrically bi-directionally curved (such as intermediate wheels or planetary gears), the bending fatigue limit of the gear should be multiplied by a factor of 0.7 when designing. The bending fatigue limit that such gears can withstand.

In addition, the left and right tooth surfaces of the intermediate idler gear or the planetary gear are respectively meshed with two different gears. Therefore, the bending strengths of the left and right tooth surfaces of the intermediate idler gear or the planetary gear are respectively different, and the tooth surface involute is required for meshing. The starting point is also different.

However, the traditional involute gear does not consider the difference between the starting point of the involute of the left and right tooth surfaces. The designed tooth profile is completely symmetrical for the left and right tooth faces and the tooth root. See GB/T 1356-2001 "General Machinery and The standard basic rack tooth profile of cylindrical gears for heavy machinery, which reveals that the involute gear has a completely symmetrical tooth profile, therefore, in order to ensure that the starting points of the left and right flank involutes are the same and have sufficient involute length to participate Engagement makes the curvature radius of the left and right tooth root curve small, which further reduces the root bending strength of the intermediate idler or planetary gear.

Summary of the invention

According to a first aspect of the invention, there is provided a non-fully symmetric involute gear (200, 400), the tooth profile of the face tooth groove comprising an involute segment AB and an arc of the first side tooth profile (210, 410) The segment BC and the involute segment FE and the arc segment DE of the second side tooth profile (230, 430), wherein the point B is the first side of the face tooth groove of the asymmetric involute gear (200, 400) The involute starting point of the tooth profile (210, 410) and its involute starting point diameter is r _b , the point E being the second side tooth of the face tooth slot of the asymmetric involute gear (200, 400) The involute starting point of the profile (230, 430) and its involute starting point diameter is r _e ;

Wherein the involute starting point diameter r _{b is} not equal to the involute starting point diameter r _e such that the involute segment AB and the involute segment FE are not completely symmetrical with respect to the axis (III), wherein An axis III is an angle bisector of a central angle corresponding to a face groove width of the incompletely symmetric involute gear (200, 400);

Further, the arc curvature radius r _{1 of the} arc segment BC is not equal to the arc curvature radius r _{2 of the} arc segment DE.

According to a second aspect of the present invention, there is provided a method of processing the above-described incompletely symmetric involute gear (200, 400), wherein a profile of a face tooth groove of the incompletely symmetric involute gear (200, 400) is provided The involute segment AB, the arc segment BC, the arc segment DE and the involute segment EF are used as the cutting tooth shape of the forming milling cutter, and the tooth milling is formed by using the milling cutter to divide the tooth to be machined by the indexing. The incompletely symmetric involute gear (200, 400) is thus produced.

According to a third aspect of the present invention, there is still further a method of processing the above-described incompletely symmetric involute gear (200, 400), wherein the teeth of the face groove of the incompletely symmetric involute gear (200, 400) are The involute segment AB, the arc segment BC, the arc segment DE and the involute segment EF of the profile are used as the cutting path of the wire cutting, and the indexing of the workpiece to be machined by the indexing line forms a tooth groove, thereby producing the incomplete symmetry Open gear (200,400).

According to a fourth aspect of the present invention, a milling cutter is provided, characterized in that the involute section AB, the arc segment BC, and the circle of the tooth profile of the face tooth groove of the incompletely symmetric involute gear described above are provided. The arc segment DE and the involute segment EF serve as the cutting tooth profile of the milling cutter.

The above features and operations of the present invention will become more apparent from the following description and drawings.

DRAWINGS

The above and other objects and advantages of the present invention will be more fully understood from the aspects of the appended claims.

1 is a schematic view showing a tooth profile of a face of a non-completely symmetric involute gear engaged with a first involute gear and a second involute gear, in accordance with an embodiment of the present invention.

2 is a schematic view showing the shape of two teeth of a non-completely symmetric involute gear according to an embodiment of the present invention.

3 is a schematic view showing a tooth profile of a face tooth groove of a non-completely symmetric involute gear according to an embodiment of the present invention.

4 is a schematic view showing a tooth profile of a face tooth groove of a non-completely symmetric involute gear according to still another embodiment of the present invention.

detailed description

The following is a description of some of the various possible embodiments of the invention, which are intended to provide a basic understanding of the invention and are not intended to identify key or critical elements of the invention or the scope of the invention. It is to be understood that, in accordance with the technical aspects of the present invention, those skilled in the art can suggest other alternatives that are interchangeable without departing from the spirit of the invention. Therefore, the following detailed description and the accompanying drawings are merely illustrative of the embodiments of the invention, and are not intended to

In the description, components of various embodiments described using directional terminology (e.g., "left", "right", etc.) and similar terms are used to refer to the directions shown in the drawings or to those skilled in the art. These directional terms are used for relative description and clarification, rather than limiting the orientation of any embodiment to a particular orientation or orientation that may vary correspondingly as the orientation of the hob or gear is placed. For example, the teeth of a non-fully symmetric involute gear are defined as "left side" and "right side" according to the orientation in the drawing. After the non-completely symmetric involute gear is turned axially, the left side of the original tooth is "left side". "The right side of the tooth corresponding to the new orientation, the "right side" of the original tooth will correspond to the "left side" of the tooth of the new orientation.

As used herein, "incompletely symmetric" means that one of the two objects is symmetrically disposed about a portion of the other object, and another portion of the other component is asymmetrically disposed about another portion of the other object. .

As shown in FIGS. 1 to 4, the tooth profile of the face tooth groove of the incompletely symmetric involute gear 200/400 includes an involute segment AB, a circular arc segment BC and a straight segment CD, a circular arc segment DE, and an involute segment EF. Wherein the involute segment AB and the arc segment BC can be used to form the left tooth profile 210/410, and the arc segment DE and the involute segment EF can be used to form the right tooth profile 230/430. The straight line segment CD is tangent to the arc segment BC and the arc segment DE, respectively, to points C and D.

As can be seen from Figures 3 and 4, the involute segment AB and the involute segment EF are not completely symmetrical with respect to the axis III, wherein the axis III is the face cogging width M of the incompletely symmetric involute gear 200/400. The angle bisector of the central angle corresponding to N; point A and point F are the tooth vertices of the left and right tooth faces of the face groove of the incompletely symmetric involute gear 200/400, respectively; point B is the incompletely symmetric involute The involute starting point of the left side tooth profile 210/410 of the face tooth groove of the gear 200/400, r _b is the gradual change of the left side tooth profile 210/410 of the face tooth groove of the incompletely symmetric involute gear 200/400 The starting point diameter of the opening line; the point E is the involute starting point of the right side tooth profile 230/430 of the face tooth groove of the incompletely symmetric involute gear 200/400, and r _{e is the} incompletely symmetric involute gear 200/ The involute starting point diameter of the right side tooth profile 230/430 of the face tooth groove of 400.

Wherein, the straight line segment CD is perpendicular to the axis III and is tangent to the root circle, and the arc segment BC is tangent to the straight line segment CD and the straight line I, and the arc segment DE is simultaneously tangent to the straight line segment CD and the straight line II, wherein the straight line I is a tangent that passes through point B and is tangent to the involute segment AB, and the straight line II is a tangent that passes through the point E and is tangent to the involute segment EF.

To facilitate the description of the coordinate positional relationship of the points in the tooth profile, as shown in FIGS. 3 and 4, the y-axis is established along the axis III, and the x-axis is established with a line perpendicular to the y-axis and tangential to the root circle. Further, the coordinates of the defined point B are (-x _b , y _b ), the coordinates of the defined point E are (x _e , y _e ), the radius of curvature of the arc of the arc segment BC is r ₁ , and the circle of the arc segment DE The radius of curvature of the arc is r ₂ and r ₁ ≠r ₂ . Here, in the embodiment shown in Fig. 3, r ₂ > r ₁ , in the embodiment shown in Fig. 4, r ₂ < r ₁ .

3, when y _b <y _e, this time, r _b <r _e, the radius of the arc of curvature of the arc segment BC relationship arc radius r ₁ of curvature of the arc segment DE and r ₂ is:

And, the involute segment AB of the left tooth profile 210 is longer than the involute segment EF of the right tooth profile 230, and the involute segment AB is composed of the involute segment AE' and the involute segment E'B, and the involute segment AE' It is completely symmetrical with respect to the involute segment EF with respect to the axis III, wherein the point E' is the boundary point of the circumference of the involute segment AB corresponding to the diameter r _e .

When y _b >y _e (in the incompletely symmetric involute gear 400 of the embodiment shown in FIG. 4), at this time, r _b >r _e , the radius of curvature of the arc of the arc segment BC r ₁ and the arc The relationship between the curvature radius r ₂ of the arc of the segment DE is:

Moreover, the involute segment AB of the left tooth profile 410 is shorter than the involute segment EF of the right tooth profile 430, and the involute segment EF is composed of the involute segment EB' and the involute segment B'F, and the involute segment B' F and the involute segment AB are completely symmetrical about the axis III, wherein the point B' is the boundary point of the circumference of the involute segment EF corresponding to the diameter r _b .

Continuing with FIG. 1, FIG. 3 and FIG. 4, the involute segment AB of the left side tooth profile 210 of the face groove of the incompletely symmetric involute gear 200/400 is a non-completely symmetric involute gear. The involute section of the 200/400 end face tooth shape meshing with the end face tooth profile of the first involute gear 100, the involute section EF of the right side tooth profile of the face groove of the incompletely symmetric involute gear 200 is incomplete An involute section in which the end face profile of the symmetric involute gear 200/400 meshes with the face profile of the second involute gear 300. Therefore, the left and right tooth faces of the incompletely symmetric involute gear 200/400 of the embodiment of the present invention respectively engage two different gears, which can be specifically used as an intermediate idle gear or a planetary gear or the like.

In the incompletely involute gear of the incompletely symmetrical involute gear of the present invention, the involute starting point of the left and right tooth surfaces and the curvature radius of the left and right tooth root arcs are different, so the left and right teeth of the entire tooth of the incompletely symmetric involute gear The starting point of the involute and the radius of curvature of the left and right root arcs are different. The designer can design different curvature curves of the left and right root curves according to the position of the starting point of the involute of the left and right tooth surfaces, so that the left and right sides of the tooth obtain different roots. The bending strength ensures that the gear of the present invention can better adapt to the effect of the biaxial bending load, thereby improving the reliability of the gear. The invention is particularly applicable to intermediate idlers or planet gears in which the teeth are subjected to a bi-directional bending load.

A specific example shape of the tooth profile of the face tooth groove of the incompletely symmetric involute gear 200/400 of the embodiment of the present invention is further explained below.

(1) The coordinates of point B (-x _b , y _b ) satisfy the following formulas (1-1) and (1-2):

Where r _{b is} the involute starting point diameter of the left side tooth profile 210 of the face tooth groove of the asymmetric involute gear 200/400, and r _{f is the} root radius of the asymmetric involute gear 200/400, β ₁ represents the central angle of the groove width on the circumference corresponding to the diameter r _b , which is calculated by the following formulas (1-3) to (1-7):

Wherein, m and α respectively represent the end face modulus and the end face pressure angle of the incompletely symmetric involute gear 200/400, and a ₁ represents the first involute gear 100 of the incompletely symmetric involute gear 200/400 meshing therewith The center distance, r _a1 represents the tip circle diameter of the first involute gear 100, and z ₁ represents the number of teeth of the first involute gear 100.

(2) The coordinates (x _e , y _e ) of point E satisfy the following formulas (2-1) and (2-2):

Where r _{e is} the involute starting point diameter of the right side tooth profile 230/430 of the face tooth groove of the asymmetric involute gear 200/400, and r _{f is the} root circle of the asymmetric involute gear 200/400 The radius, β ₂ represents the central angle of the groove width on the circumference corresponding to the diameter r _e , which is calculated by the following formulas (2-3) to (2-7):

Wherein m and α respectively represent the end face modulus and the end face pressure angle of the incompletely symmetric involute gear 200/400, and a ₂ represents the second involute gear 300 of the incompletely symmetric involute gear 200/400 meshing therewith. The center distance, r _a2 represents the tip circle diameter of the second involute gear 300, and z ₂ represents the number of teeth of the second involute gear 300.

(3) The curve coordinate (x, y) of the arc segment BC is determined by the following equation (3-1):

Where r ₁ represents the radius of curvature of the arc segment BC, which is calculated by the following formula and equation:

Wherein β ₁ represents the central angle of the tooth groove width on the circumference corresponding to the diameter r _b , which can be calculated by the above formula (1-3), and x _b and y _b respectively represent the x coordinate and the y coordinate of the point B, It can be calculated by the above formula (1-1), α _b is calculated by the above formula (1-4), and s _{1 is the} maximum value of the solution of equation (3-3).

(4) The curve coordinate (x, y) of the arc segment DE is determined by the following equation (4-1):

Where r ₂ represents the radius of curvature of the arc segment DE, which is calculated by the following formula and equation:

Wherein, β ₂ represents the central angle of the cogging width on the circumference corresponding to the diameter r _e , which can be calculated by the above formula (2-3), and x _e and y _e respectively represent the x coordinate and y of the E point. The coordinates can be calculated by the above formula (2-1), α _e is calculated by the above formula (2-4), and s _{2 is the} minimum value of the solution of equation (4-3).

Specifically, in the above formula and equation, m and α respectively represent the end face modulus and the end face pressure angle of the incompletely symmetric involute gear 200/400; z, z ₁ , and z ₂ are respectively represented as the incomplete symmetry. The number of teeth of the involute gear 200/400, the first involute gear 100, and the second involute gear 300; r _a1 , r _a2 represent the teeth of the first involute gear 100 and the second involute gear 300, respectively The top circle diameter; a ₁ , a ₂ respectively represent the center distance of the incompletely symmetric involute gear 200/400 and the first involute gear 100 and the incompletely symmetric involute gear 200/400 and the second involute The center distance of the line gear 300; r _b , r _e , r _f respectively represent the starting point radius of the left flank involute of the face tooth profile of the incompletely symmetric involute gear 200/400, and the face tooth The shape of the right flank involute starting point radius and the root circle radius; r ₁ and r ₂ respectively represent the radius of curvature of the arc segment BC and the arc segment DE.

Further, the point coordinate equations on the involute segment AB and the involute segment EF of the incompletely symmetric involute gear 200/400 can be determined by Equation 1-27 of "Working Principles of Grinding" published by the Mechanical Industry Press in 1977. .

The present invention also provides a method of processing a non-completely symmetric involute gear as shown in Figures 3 and 4.

In an embodiment, the involute segment AB, the arc segment BC, the straight segment CD, the arc segment DE, and the involute segment EF of the face tooth profile of the incompletely symmetric involute gear 200/400 are used as forming milling The cutting tooth profile of the tooth cutter is formed by pitching the tooth to be machined to form a tooth groove, and a non-completely symmetric involute gear 200/400 is obtained. This processing method is highly efficient and is very suitable for mass production.

In still another embodiment, the involute segment AB, the arc segment BC, the straight segment CD, the arc segment DE, and the involute segment EF of the face tooth tooth profile of the incompletely symmetric involute gear 200/400 are taken as a line The cutting path of the cutting, the indexing of the workpiece to be machined to form a tooth groove, and a non-completely symmetric involute gear 200/400 is obtained. In this way, special tools are not required, but the efficiency is low, suitable for single or small batch production. This eliminates the need for special tools, but is relatively inefficient and suitable for single or small batch production.

The design determination process of the tooth profiles AB, BC, CD, DE, EF of the face tooth grooves of the incompletely symmetric involute gear 400 is specifically illustrated below.

The non-completely symmetric involute gear 400 and the meshing first involute gear 100 and the second involute gear 300 have the main parameter values: m=7, α=20°, z=26, z ₁ = 17, z ₂ = 89, r _a1 = 69.37, r _a2 = 314.37, a ₁ = 157, a ₂ = 402, r _f = 85.88.

In the first step, a coordinate system is established, with the axis of symmetry of the cogging being the y-axis, and the line perpendicular to the y-axis and tangential to the root circle being the x-axis.

In the second step, the coordinates of the point B (-x _b , y _b ), the coordinates of the point E (x _e , y _e ), and the curve equation of the arc segment BC and the arc segment DE are determined as follows.

(1) The coordinates of point B (-x _b , y _b ) are calculated according to the above formulas (1-1) to (1-6), and the corresponding parameter values are substituted into formulas (1-1) to (1-6). Calculated:

among them,

Therefore, the coordinates (-x _b , y _b ) of the point B are obtained as (-4.977, 3.692).

(2) The coordinates of point E (-x _b , y _b ) are calculated according to the above formulas (2-1) to (2-6), and the corresponding parameter values are substituted into formulas (2-1) to (2-6). Calculated:

among them,

Therefore, the coordinates (x _e , y _e ) of the point E are calculated to be (4.464, 2.187).

(3) The curve equation of the arc segment BC is determined according to the equation (3-1) and is calculated according to the above formula (3-3), formula (3-4) and equation (3-3):

s ₁ takes the above equation to solve the maximum value of 7.525;

Thus, the curve equation (x-7.525) ² + (y-2.725) ² = 7.425 of the arc segment BC is determined.

(4) The curve equation of the arc segment DE is determined according to the equation (4-1) and is calculated according to the above formula (4-3), formula (4-4) and equation (4-3):

Wherein, the minimum value of the solution of s ₂ taking the above equation is 4.137;

further,

Thus, the curve equation of the arc segment DE is determined: (x-4.137) ² + (y-1.121) ² =1.254

(5) Calculated:

At this time, the arc curvature radius r ₁ of the arc segment BC is 2.43 times the curvature radius r ₂ of the arc segment DE. Therefore, the left and right sides of the incompletely involute gear have different roots. The bending strength, and the tooth side where the side of the arc segment BC is located has a higher root bending strength.

The above examples mainly illustrate the incompletely symmetric involute gear of the present invention and a method of processing the same. Although only a few of the embodiments of the present invention have been described, it will be understood by those skilled in the art that the invention may be practiced in many other forms without departing from the spirit and scope of the invention. Accordingly, the present invention is to be construed as illustrative and not restrictive, and the invention may cover various modifications without departing from the spirit and scope of the invention as defined by the appended claims With replacement.

Claims

A non-fully symmetric involute gear (200, 400) having a tooth profile of the face tooth groove including an involute segment AB and a circular arc segment BC of the first side tooth profile (210, 410) and a second side tooth profile ( 230, 430) an involute segment FE and a circular arc segment DE, wherein the point B is the gradual progression of the first side tooth profile (210, 410) of the face tooth groove of the asymmetric involute gear (200, 400) The starting point of the opening line and the involute starting point diameter is r b , and the point E is the involute of the second side tooth profile (230, 430) of the face tooth groove of the asymmetric involute gear (200, 400) Line starting point and its involute starting point diameter is r e ;

The involute starting point diameter r b is not equal to the involute starting point diameter r e , such that the involute segment AB and the involute segment FE are not completely symmetrical about the axis (III), wherein The axis III is an angle bisector of a central angle corresponding to a face groove width of the incompletely symmetric involute gear (200, 400);

Further, the arc curvature radius r 1 of the arc segment BC is not equal to the arc curvature radius r 2 of the arc segment DE.
The incompletely symmetric involute gear (200, 400) of claim 1 wherein the y-axis is established with an axis III to be perpendicular to the y-axis and to the incompletely symmetric involute gear (200, 400) The tangential line of the root circle establishes the x-axis, the coordinate of the point B is (-x b , y b ), and the coordinate of the point E is (x e , y e );

When y b> y e, r b > r e, the radius of curvature of the circular arc of the circular arc segment BC relationship arc radius r 1 of curvature of the arc segment DE and r 2 is:
Also, the involute segment EF is composed of an involute segment EB' and an involute segment B'F, the involute segment B'F and the involute segment AB being completely symmetrical about the axis III.
The incompletely symmetric involute gear (200, 400) of claim 1 wherein the y-axis is established with an axis III to be perpendicular to the y-axis and to the incompletely symmetric involute gear (200, 400) The tangential line of the root circle establishes the x-axis, the coordinate of the point B is (-x b , y b ), and the coordinate of the point E is (x e , y e );

When y b <y e, r b <r e, the radius of curvature of the circular arc of the circular arc segment BC relationship arc radius r 1 of curvature of the arc segment DE and r 2 is:
The involute segment AB consists of an involute segment AE' and an involute segment E'B, the involute segment AE' being completely symmetrical with respect to the involute segment EF with respect to the axis III.
The incompletely symmetrical involute gear (200, 400) of claim 1 wherein the tooth profile of the face groove of the incompletely symmetric involute gear (200, 400) further comprises a straight section CD The straight line segment CD is connected tangentially to the circular arc segment BC by a point C, which is connected tangentially to the circular arc segment DE by a point D, the straight line segment CD and the axis III is vertical and tangent to the root circle.
The incompletely symmetrical involute gear (200, 400) according to claim 1 or 4, wherein the arc segment BC is tangent to the straight line I passing through the point B, the arc segment DE and the passing point E is tangent to the straight line I, which is a tangent to the point B and tangent to the involute line AB, which is a tangent to the point E and tangent to the involute line EF.
The incompletely symmetric involute gear (200, 400) according to claim 1 or 4, wherein said point A is a tooth apex of said first side tooth profile (210, 410), said point F is the tooth apex of the second side tooth profile (230, 430).
The incompletely symmetric involute gear (200, 400) of claim 1 wherein said incompletely symmetric involute gear (200, 400) is an intermediate idler or planet gear for bidirectional engagement. .
The incompletely symmetrical involute gear (200, 400) according to claim 2 or 3, characterized in that the involute section AB of the face groove of the incompletely symmetric involute gear (200, 400) The involute segments FE mesh with the tooth faces of the first involute gear (100) and the first involute gear (300), respectively.
The incompletely symmetric involute gear (200, 400) according to claim 8, wherein the coordinates (-x b , y b ) of the point B satisfy the following formulas (1-1) and (1) 2):

Where r f is the root circle radius of the asymmetric involute gear (200, 400), and β 1 represents the center angle of the groove width on the circumference corresponding to the involute starting point diameter r b , which passes the following formula (1-3) to (1-7) calculation:

Wherein m and α respectively represent the end face modulus and the end face pressure angle of the incompletely symmetric involute gear (200, 400), and a 1 denotes the first intermeshing of the incompletely symmetric involute gear (200, 400) a center distance of the involute gear (100), r a1 represents a tip circle diameter of the first involute gear (100), and z 1 represents a number of teeth of the first involute gear (100);

The coordinates (x e , y e ) of the point E satisfy the following formulas (2-1) and (2-2):

Wherein β 2 represents the central angle of the cogging width on the circumference corresponding to the involute starting point diameter r e , which is calculated by the following formulas (2-3) to (2-7):

Wherein a 2 represents the center distance of the incompletely symmetric involute gear (200, 400) and the second involute gear (300) with which it meshes, and r a2 represents the tip circle of the second involute gear (300) Diameter, z 2 represents the number of teeth of the second involute gear (300).
The incompletely symmetric involute gear (200, 400) according to claim 9, wherein the curve coordinate (x, y) of the circular arc segment BC is determined by the following equation (3-1):

Wherein r 1 represents the radius of curvature of the circular arc segment BC, which is calculated by the following formulas (3-2), (3-4), and equation (3-3):

Where s 1 takes the maximum value of the solution of equation (3-3);

The curve coordinate (x, y) of the arc segment DE is determined by the following equation (4-1):

Where r 2 represents the radius of curvature of the arc segment DE, which is calculated by the following formulas (4-2), (4-4) and equation (4-3):

Where s 2 takes the solution minimum of equation (4-3).
A method of processing a non-fully symmetric involute gear (200, 400) according to any one of claims 1 to 10, characterized in that the face cogging of the incompletely symmetric involute gear (200, 400) The involute section AB, the arc segment BC, the arc segment DE and the involute segment EF of the tooth profile are used as the cutting tooth profile of the forming milling cutter, and the milling tool is used to form the workpiece to be machined by indexing. The cogging, thereby producing the incompletely symmetric involute gear (200, 400).
A method of processing a non-completely symmetric involute gear (200, 400) according to any one of claims 1 to 10, characterized in that the face cogging of the incompletely symmetric involute gear (200, 400) The involute segment AB, the arc segment BC, the arc segment DE and the involute segment EF of the tooth profile serve as a cutting path for the wire cutting, and the indexing of the workpiece to be machined by the indexing line forms a tooth groove, thereby making the incompleteness Symmetric involute gear (200, 400).
A milling cutter characterized by an involute section AB, a circular arc section of a tooth profile of a face tooth groove of the incompletely symmetric involute gear (200, 400) according to any one of claims 1 to 10. BC, the arc segment DE and the involute segment EF serve as the cutting profile of the milling cutter.