Method for designing tooth profile of cutting edge of tooth turning tool

Abstract

The invention relates to a tooth profile design method for a cutting edge of a tooth turning cutter, which belongs to the technical field of transmission and comprises the following steps: S1, establishing a mathematical model of a tooth profile of a to-be-processed gear by using a single parameter s as an independent variable; s2, according to the parameters of the gear to be machined and the mathematical model of the tooth profile of the gear to be machined in the S1, the parameters of the gear turning cutter are designed, and the tooth profile design parameters of the cutting edge of the gear turning cutter are obtained through calculation; s3, establishing a coordinate system according to a gear plane meshing principle; s4, according to the tooth turning machining motion principle, a transformation matrix converted from the tooth profile coordinate system Sc (Oc-xc, yc) of the gear to be machined in the S3 to the tooth profile coordinate system Sh (Oh-xh, yh) of the cutting edge of the tooth turning cutter is deduced; s5, by means of a tooth profile normal method, the rotating angle # imgabs0 # of the gear turning cutter is obtained, and the tooth profile of the cutting edge of the gear turning cutter is obtained through the coordinate transformation matrix # imgabs1 # in the S5 and the mathematical model of the tooth profile of the gear to be machined in the S1; the motion principle of the tooth turning cutter is efficiently solved and met, the obtained tooth profile conforms to the machining generating principle, and the calculation efficiency is high; meanwhile, the cutting edge tooth profile precision is high.

Description

Technical Field

[0001] The invention belongs to the field of transmission technology and relates to a method for designing the tooth profile of a cutting edge of a gear turning tool. Background Art

[0002] Traditional gear processing methods include gear grinding, gear hobbing and gear shaping. Compared with these methods, gear turning has unique advantages. The gear turning method realizes cutting through the relative movement between the tool and the workpiece. During the processing, a certain angle is maintained between the rotation axis of the tool and the workpiece, and the two move around their respective rotation axes to realize the development movement. At the same time, the workpiece moves along the axial direction. These three movements cooperate with each other to complete the cutting process. Production efficiency and tool life can be increased by 2 to 6 times. In addition, the gear turning process is flexible and can cut various parts such as internal teeth, external teeth, spiral teeth, bevel teeth, etc. In particular, the internal gears are processed by the gear turning method, which is not limited by the processing size, and the cutting efficiency is high and the precision is close to the gear grinding process.

[0003] However, the existing design methods of the cutting edge tooth profile of gear turning tools are mainly based on the kinematic method and the envelope method, which have the following shortcomings:

[0004] 1. The most commonly used gear cutting tool is the bevel gear shape. The design and derivation of its cutting edge are mostly based on the kinematic method to establish the meshing equation ( ) and solve the nonlinear equations. In this process, many parameters are involved and complex coordinate transformations are required, so the meshing equations are very complicated to establish; multiple inversions are required to ensure the correct results when solving, so the calculation efficiency is low; in addition, when the kinematic method is applied to the design of tools with complex tooth shapes (such as asymmetric or modified tooth profiles), it is difficult to establish meshing equations in certain local conjugate areas of the tooth profile (asymmetric or modified areas).

[0005] 2. The envelope method uses the tooth profile for enveloping. The process of extracting data points from the envelope line is very cumbersome, with large computational workload and low computational efficiency. The tooth profile accuracy obtained by the envelope method is determined by the tooth profile rolling distance and its rolling angle, and the blade shape accuracy is low. It is not suitable for designing and machining the tooth profile of the cutting tool for high-precision gears. Summary of the invention

[0006] In view of this, in order to solve the above-mentioned technical problems, the present invention provides a method for designing the tooth profile of the cutting edge of a gear turning tool. The method is based on the tooth profile normal method, which simplifies the three processing motions into two-axis meshing and unfolding motions to derive the tooth profile of the cutting edge of the gear turning tool. The method has the characteristics of high calculation efficiency and high cutting edge tooth profile accuracy, and can be applied to the processing of any internal and external gear tooth profile and modified tooth profile.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A method for designing a tooth profile of a cutting edge of a gear turning tool comprises the following steps:

[0009] S1: The gear to be processed consists of 6 sections, namely, the tooth top transition section, the middle tooth profile section, and the tooth root transition section. The mathematical model of the tooth profile of the gear to be processed is established by using a single parameter s as the independent variable. The mathematical model of the tooth profile of the gear to be processed is:

[0010] (1)

[0011] In the formula, is the vector of the gear tooth profile to be processed in the coordinate system, is the control parameter of the first tooth profile, Y1 is the y-axis coordinate of the starting point, is the y-axis control parameter of the gear tooth profile to be processed, is the x-axis control parameter of the gear tooth profile to be processed, s is a continuous parameter, and the other segments of the tooth profile are expressed by the parameter s; the mathematical model of the tooth profile is expressed by a single parameter s, and the tooth profile of the gear cutting cutter is derived;

[0012] S2: According to the parameters of the gear to be processed and the mathematical model of the gear tooth profile to be processed in S1, the parameters of the gear skiving cutter are designed, and the design parameters of the gear skiving cutter cutting edge tooth profile are calculated;

[0013] S3: Convert the three-dimensional space-based meshing into a two-dimensional plane meshing. According to the gear plane meshing principle, establish the following coordinate system:

[0014] ①The center of the gear to be processed Establish a coordinate system S1 (O1-x1, y1) as the origin. S1 is used as its initial static coordinate system, that is, a fixed coordinate system connected to the gear to be processed; ② Take the center of the gear to be processed as the center. Establish a coordinate system S2 (O2-x2, y2) for the origin; ③ Establish a gear tooth profile coordinate system Sc (Oc-xc, yc) to be processed that is fixedly connected to the workpiece movement, and a gear cutter cutting edge tooth profile coordinate system Sh (Oh-xh, yh) that is fixedly connected to the gear cutter movement;

[0015] S4: According to the motion principle of gear cutting, the transformation matrix of the gear profile coordinate system Sc (Oc-xc, yc) to be processed in S3 is derived to transform the gear profile coordinate system Sh (Oh-xh, yh) of the gear cutting cutter cutting edge. The coordinate transformation matrix of the two coordinate systems is It is expressed as:

[0016] (8)

[0017] (9)

[0018] In the formula, represents the internal gear machining transformation matrix, represents the external gear machining transformation matrix, Indicates the turning angle of the gear cutting tool. Indicates the rotation angle of the gear to be processed, Indicates the center distance between the gear to be processed and the gear cutting cutter;

[0019] S5: Determine the intersection point between the gear to be processed and the gear cutting tool The tooth profile normal method is used to calculate the angle that the gear cutting cutter rotates. , the tooth profile of the cutting edge of the gear cutting cutter is obtained through the coordinate transformation matrix in S4 and the mathematical model of the gear tooth profile to be processed in S1.

[0020] Furthermore, through the mathematical model of the gear tooth profile to be processed in S1, its point set is obtained, and the gear cutting cutter parameters are designed according to its parameters.

[0021] Furthermore, the parameters of the gear cutting tool in S2 are designed as follows: the number of teeth of the designed gear cutting tool is defined Helix angle of gear cutting tool , the gear cutting cutter module is designed to be equal to the given module of the processed gear through formula 2, and the axis angle between the gear cutting cutter and the processed gear is calculated by formula 3 and formula 4 respectively and center distance a, which are the parameters required for designing the gear cutter tooth profile;

[0022] Formulas 2, 3, and 4 are:

[0023] (2)

[0024] In the formula, is the module of the gear to be processed, is the module of the gear cutting tool;

[0025] (3)

[0026] In the formula, represents the axis intersection angle, Indicates the helix angle of the workpiece being machined. Indicates the helix angle of the gear cutting tool, Indicates external gear processing, Indicated as internal gear machining;

[0027] (4)

[0028] (5)

[0029] (6)

[0030] In the formula, Indicates the pitch radius of the gear to be processed, Indicates the pitch radius of the gear cutting cutter. Indicates the number of teeth on the gear cutting tool. Indicates external gear processing, Indicates internal gear machining.

[0031] Furthermore, in step S3, the y2 axis coincides with the y1 axis, and S2 serves as its initial static coordinate system, that is, a fixed coordinate system connected to the gear cutting tool.

[0032] Furthermore, in step S3, during the gear cutting process, the gear to be processed and the gear cutting cutter are respectively moved at a uniform angular speed. , Around the origin of their respective fixed coordinate systems , After the gear and gear cutting cutter rotate from the starting position for a period of time, the workpiece rotates around Turn the corner , Gear cutting tool Turn the corner , the coordinate system established, in which the relationship between the rotation angle of the gear cutting cutter and the rotation angle of the gear to be processed is:

[0033] (7)

[0034] In the formula, Indicates the transmission ratio.

[0035] Furthermore, a total of 4 coordinate systems are established for the gear to be processed and the gear cutting tool.

[0036] Furthermore, in the established coordinate system, let Point is the instantaneous meshing point, and the point on the wheel The normal line of the tooth profile passes through the meshing node , (x1, y1) is any point on the gear tooth profile to be processed. The tooth profile normal line intersects with the pitch circle of the gear to be processed at point , using the tooth profile normal method, according to any point on the gear to be processed The angle between the tangent line at and the x1 axis , and then obtain The angle that the gear to be processed rotates to become the meshing point of the two tooth profiles , according to the meshing relationship of the internal gear, calculate the angle that the gear cutting cutter rotates .

[0037] Further, in order to make the point Become the meshing point, Points need The points coincide, so we can find (x1, y1) becomes the meshing equation required for the meshing point. The specific calculation formula of the meshing equation is as follows:

[0038] (10)

[0039] In the formula, is the tooth profile at point The tangent line t and The angle between the axes; Figure 3 The geometric relationship can be obtained:

[0040] (11)

[0041] O1L1 is Figure 3 midline segment length;

[0042] The calculation formula of the equivalent line segment length traversed by the meshing point, namely O1L1, is as follows:

[0043] (12)

[0044] The left side of the equation represents The equivalent line length of the meshing point is represented by the right side of the equation. Figure 3 The geometric relationship expression of O1L1 is obtained, and the final rotation angle is obtained when the two are equal. .

[0045] Furthermore, according to the meshing equation, the rotation angle when a certain point on the right half of the gear profile to be processed becomes the meshing point can be calculated. , according to the transmission relationship expressed by formula 7 in step S3

[0046] (7)

[0047] The turning angle of the gear cutting tool can be obtained , the two coordinate transformation matrices expressed in the two rotation angles step S4 are transformed using the following formula:

[0048] (13)

[0049] (14)

[0050] In the formula, represents the conjugate tooth profile of the internal gear, Represents the conjugate tooth profile of the external gear. The coordinates of the meshing point of the gear skiving cutter can be obtained to obtain the conjugate tooth profiles of the internal and external gears, that is, the tooth profile of the cutting edge of the gear skiving cutter.

[0051] The beneficial effects of the present invention are:

[0052] 1. The present invention discloses a method for designing the tooth profile of a cutting edge of a gear turning tool, which simplifies the complex gear turning processing motion, ignores the cutting speed that provides the axial feed depth, considers the meshing motion of the processed gear and the gear turning cutter in a two-dimensional plane, and does not need to establish complex meshing equations to derive the tooth shape of the gear turning cutter. A general design process for the tooth profile of the cutting edge of a gear turning tool is determined, which can efficiently solve and satisfy the motion principle of the gear turning cutter, and the obtained tooth profile conforms to the processing development principle.

[0053] 2. The present invention discloses a method for designing the tooth profile of a cutting edge of a gear turning tool. The method has high integration and high calculation efficiency. At the same time, the cutting edge tooth profile has high precision. The method is effective and practical, and has high practical significance and promotion value in this industry.

[0054] 3. The present invention discloses a method for designing the tooth profile of a cutting edge of a gear turning tool. The method can be applied to the processing of any internal and external gear tooth profiles, and realizes the integrated design and calculation of gear geometric parameters, basic parameters of tooth blanks, and gear tooth processing parameters.

[0055] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0057] Figure 1 It is a schematic diagram of a mathematical model of a gear tooth profile to be processed in a method for designing a cutting edge tooth profile of a gear turning tool according to the present invention;

[0058] Figure 2 A schematic diagram of a gear cutting tool cutting edge tooth profile design method of the present invention;

[0059] Figure 3 A schematic diagram of a mathematical simulation coordinate system for two-dimensional gear turning in a gear turning tool cutting edge tooth profile design method of the present invention;

[0060] Figure 4 A schematic diagram of a tooth profile of a gear cutting tool cutting edge in a method for designing a tooth profile of a gear cutting tool cutting edge of the present invention;

[0061] Figure 5 It is a schematic diagram of the comparison between the tooth profile of the internal gear to be processed after enveloping and the tooth profile of the cutting edge of the gear cutting tool in a method for designing the tooth profile of the cutting edge of a gear cutting tool of the present invention;

[0062] Figure 6 It is a schematic diagram comparing the tooth profile of the external gear to be processed after enveloping and the tooth profile of the cutting edge of the gear cutting tool in a method for designing the tooth profile of the cutting edge of a gear cutting tool of the present invention. DETAILED DESCRIPTION

[0063] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0064] like Figure 1-Figure 6 The figure shows a design method for the cutting edge tooth profile of a gear turning tool. This design method starts from the gear tooth profile to be processed, simplifies the complex gear turning processing motion, ignores the cutting speed that provides the axial feed depth, and considers the meshing motion of the two in a two-dimensional plane; the gear turning tool tooth profile is derived from the three-dimensional coordinate system and transformed into the two-dimensional coordinate system. Using the tooth profile normal method and considering the geometric relationship during meshing, the gear turning tool cutting edge tooth profile is obtained.

[0065] The specific steps include:

[0066] S1: The gear to be processed consists of 6 sections: the tooth top transition section, the middle tooth profile section, and the tooth root transition section. Using a single parameter s as the independent variable, establish the following Figure 1 The mathematical model of the gear tooth profile to be machined is shown.

[0067] The mathematical model of the gear tooth profile to be processed is:

[0068] (1)

[0069] In the formula, is the vector of the gear tooth profile to be processed in the coordinate system, is the control parameter of the first tooth profile, Y1 is the y-axis coordinate of the starting point, is the y-axis control parameter of the gear tooth profile to be processed, is the x-axis control parameter of the gear tooth profile to be processed, s is a continuous parameter, and the remaining segments of the tooth profile are expressed by the parameter s. The mathematical model of the tooth profile is expressed by a single parameter s, and the tooth profile of the gear cutting cutter is derived.

[0070] S2: According to the parameters of the gear to be processed and the mathematical model of the gear tooth profile to be processed in S1, its point set is obtained, and the parameters of the gear cutting cutter are designed according to its parameters, and the design parameters of the gear cutting cutter cutting edge tooth profile are calculated.

[0071] The parameters of the gear cutting tool are designed as follows: Helix angle of gear cutting tool , the gear cutting cutter module is designed to be equal to the given module of the processed gear through formula 2, and the axis angle between the gear cutting cutter and the processed gear is calculated by formula 3 and formula 4 respectively and center distance a, which are the parameters required for designing the gear cutter tooth profile;

[0072] Formulas 2, 3, and 4 are:

[0073] (2)

[0074] In the formula, is the module of the gear to be processed, is the module of the gear cutting tool;

[0075] (3)

[0076] In the formula, represents the axis intersection angle, Indicates the helix angle of the workpiece being processed. represents the helix angle of the gear cutting tool, Indicates external gear processing, Indicated as internal gear machining;

[0077] (4)

[0078] (5)

[0079] (6)

[0080] In the formula, Indicates the center distance between the gear to be processed and the gear cutting cutter. Indicates the pitch radius of the gear to be processed, Indicates the pitch radius of the gear cutting cutter. Indicates the number of teeth on the gear cutting tool. Indicates external gear processing, Indicates internal gear machining.

[0081] The three-dimensional space-generated meshing is converted into a two-dimensional plane meshing. According to the gear plane meshing principle, the following coordinate system is established:

[0082] ①The center of the gear to be processed Establish a coordinate system S1 (O1-x1, y1) as the origin. S1 is used as its initial static coordinate system, that is, a fixed coordinate system connected to the gear to be processed; ② Take the center of the gear to be processed as the center. The coordinate system S2 (O2-x2, y2) is established as the origin. The y2 axis of the new coordinate system coincides with the y1 axis. S2 is used as its initial static coordinate system, that is, the fixed coordinate system connected to the gear cutting tool. ③ During the gear cutting process, the gear to be processed and the gear cutting tool move at a uniform angular speed. , Around the origin of their respective fixed coordinate systems , After the gear and gear cutting cutter rotate from the starting position for a period of time, the workpiece rotates around Turn the corner , Gear cutting tool Turn the corner ; Establish the gear profile coordinate system Sc (Oc-xc, yc) to be processed which is fixedly connected to the workpiece movement, and the gear cutter cutting edge tooth profile coordinate system Sh (Oh-xh, yh) to be fixedly connected to the gear cutter movement. The relationship between the rotation angle of the gear cutter and the rotation angle of the gear to be processed is established as follows:

[0083] (7)

[0084] In the formula, Indicates the transmission ratio, Indicates the turning angle of the gear cutting tool. Indicates the gear angle to be processed.

[0085] A total of 4 coordinate systems are established for the gears to be processed and the gear cutting cutter, refer to Figure 2 The coordinate system shown.

[0086] S4: According to the motion principle of gear cutting, the transformation matrix of the gear profile coordinate system Sc (Oc-xc, yc) to be processed in S3 is derived to transform the gear profile coordinate system Sh (Oh-xh, yh) of the gear cutting cutter cutting edge. The coordinate transformation matrix of the two coordinate systems is It is expressed as:

[0087] (8)

[0088] (9)

[0089] In the formula, represents the internal gear machining transformation matrix, Represents the external gear machining transformation matrix.

[0090] S5: Determine the intersection point between the gear to be processed and the gear cutting tool The tooth profile normal method is used to calculate the meshing node according to any point on the gear to be processed. The angle between the tangent line at and the x1 axis , and then obtain The angle that the gear to be processed rotates to become the meshing point of the two tooth profiles , according to the meshing relationship of the internal gear, calculate the angle that the gear cutting cutter rotates , through the coordinate transformation matrix in S4 The tooth profile of the cutting edge of the gear skiving cutter is obtained by using the mathematical model of the gear tooth profile to be machined in S1.

[0091] Reference Figure 3 In the established coordinate system, it is assumed that the right half of the gear profile to be processed is the meshing profile for derivation. Point is the instantaneous meshing point, and the point on the gear to be processed The normal line of the tooth profile passes through the meshing node , (x1, y1) is any point on the gear tooth profile to be processed. The tooth profile normal line intersects with the pitch circle of the gear to be processed at point , in order to make the point Become the meshing point, Points and The points coincide, so we can find (x1, y1) becomes the meshing equation required for the meshing point. The specific calculation formula of the meshing equation is as follows:

[0092] (10)

[0093] In the formula, is the tooth profile at point The tangent line t and The angle of the axis;

[0094] according to Figure 3 The geometric relationship can be obtained:

[0095] (11)

[0096] O1L1 is Figure 3 midline segment length;

[0097] The calculation formula of the equivalent line segment length traversed by the meshing point, namely O1L1, is as follows:

[0098] (12)

[0099] The left side of the equation represents The equivalent line length of the meshing point is represented by the right side of the equation. Figure 3 The geometric relationship expression of O1L1 is obtained, and the final rotation angle is obtained when the two are equal. .

[0100] This formula is the point on the gear tooth profile to be processed (x1, y1) is the meshing equation required to be established as the meshing point. Based on this equation, the rotation angle when a certain point on the right half of the gear profile to be processed becomes the meshing point can be calculated. , according to the transmission relationship expressed by formula 7 in step S3

[0101] (7)

[0102] The turning angle of the gear cutting tool can be obtained , the two coordinate transformation matrices expressed in the two rotation angles step S4 are transformed using the following formula:

[0103] (13)

[0104] (14)

[0105] In the formula, represents the conjugate tooth profile of the internal gear, Represents the conjugate tooth profile of the external gear, and the meshing point coordinates of the gear skiving cutter can be obtained to obtain the conjugate tooth profiles of the internal and external gears, that is, the tooth profile of the cutting edge of the gear skiving cutter (example diagram for machining internal gears) as shown in Figure 4 As shown; and according to the principle of gear cutting tool processing movement, the envelope verification is carried out. After the envelope, it is completely in line with the tooth profile of the gear cutting tool cutting edge, as shown in Figure 5 , 6 As shown, the derivation is successful and the reliability of the method is verified.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A method for designing a cutting edge tooth profile of a gear turning tool, characterized in that: The following steps are involved: S1: The gear to be processed consists of 6 sections, namely, the tooth top transition section, the middle tooth profile section, and the tooth root transition section. The mathematical model of the tooth profile of the gear to be processed is established by using a single parameter s as the independent variable. The mathematical model of the tooth profile of the gear to be processed is: （1） In the formula, is the vector of the gear tooth profile to be processed in the coordinate system, is the control parameter of the first tooth profile, Y1 is the y-axis coordinate of the starting point, is the y-axis control parameter of the gear tooth profile to be processed, is the x-axis control parameter of the gear tooth profile to be processed, s is a continuous parameter, and the other segments of the tooth profile are expressed by the parameter s; the mathematical model of the tooth profile is expressed by a single parameter s, and the tooth profile of the gear cutting cutter is derived; S2: According to the parameters of the gear to be processed and the mathematical model of the gear tooth profile to be processed in S1, the parameters of the gear skiving cutter are designed, and the design parameters of the gear skiving cutter cutting edge tooth profile are calculated; S3: Convert the three-dimensional space-based meshing into a two-dimensional plane meshing. According to the gear plane meshing principle, establish the following coordinate system: ①The center of the gear to be processed Establish a coordinate system S1 (O1-x1, y1) as the origin. S1 is used as its initial static coordinate system, that is, a fixed coordinate system connected to the gear to be processed; ② Take the center of the gear to be processed as the center. Establish a coordinate system S2 (O2-x2, y2) for the origin; ③ Establish a gear tooth profile coordinate system Sc (Oc-xc, yc) to be processed that is fixedly connected to the workpiece movement, and a gear cutter cutting edge tooth profile coordinate system Sh (Oh-xh, yh) that is fixedly connected to the gear cutter movement; S4: According to the motion principle of gear cutting, the transformation matrix of the gear profile coordinate system Sc (Oc-xc, yc) to be processed in S3 is derived to transform the gear profile coordinate system Sh (Oh-xh, yh) of the gear cutting cutter cutting edge. The coordinate transformation matrix of the two coordinate systems is expressed as: （8） （9） In the formula, represents the internal gear machining transformation matrix, represents the external gear machining transformation matrix, Indicates the turning angle of the gear cutting tool. Indicates the rotation angle of the gear to be processed, Indicates the center distance between the gear to be processed and the gear cutting cutter; S5: Determine the intersection point between the gear to be processed and the gear cutting tool The tooth profile normal method is used to calculate the angle that the gear cutting cutter rotates. , the tooth profile of the cutting edge of the gear cutting cutter is obtained through the coordinate transformation matrix in S4 and the mathematical model of the gear tooth profile to be processed in S1.

2. A method for designing a cutting edge tooth profile of a gear turning tool according to claim 1, characterized in that: The point set is obtained through the mathematical model of the gear tooth profile to be processed in S1, and the gear cutting tool parameters are designed according to the parameters.

3. A method for designing a cutting edge tooth profile of a gear turning tool according to claim 1, characterized in that: The gear cutting tool parameter design in S2 is specifically as follows: the number of teeth of the designed gear cutting tool is defined Helix angle of gear cutting tool , the module of the gear cutting cutter is designed to be equal to the given module of the processed gear through formula 2, and the axis angle between the gear cutting cutter and the processed gear is calculated by formula 3 and formula 4 respectively and center distance a, which are the parameters required for designing the gear cutter tooth profile; Formulas 2, 3, and 4 are: （2） In the formula, is the module of the gear to be processed, is the module of the gear cutting tool; （3） In the formula, represents the axis intersection angle, Indicates the helix angle of the workpiece being processed. represents the helix angle of the gear cutting tool, Indicates external gear processing, Indicated as internal gear machining; （4） （5） （6） In the formula, Indicates the pitch radius of the gear to be processed, Indicates the pitch radius of the gear cutting cutter. Indicates the number of teeth on the gear cutting tool. Indicates external gear processing, Indicates internal gear machining.

4. A method for designing a cutting edge tooth profile of a gear turning tool as claimed in claim 3, characterized in that: In step S3, the y2 axis coincides with the y1 axis, and S2 serves as its initial static coordinate system, that is, a fixed coordinate system connected to the gear cutting tool.

5. A method for designing a cutting edge tooth profile of a gear turning tool as claimed in claim 4, characterized in that: In the step S3, during the gear cutting process, the gear to be processed and the gear cutting cutter are respectively driven at a uniform angular speed. , Around the origin of their respective fixed coordinate systems , After the gear and gear cutting cutter rotate from the starting position for a period of time, the workpiece rotates around Turn the corner , Gear cutting tool Turn the corner , the coordinate system established, in which the relationship between the rotation angle of the gear cutting cutter and the rotation angle of the gear to be processed is: （7） In the formula, Indicates the transmission ratio.

6. A method for designing a cutting edge tooth profile of a gear turning tool as claimed in claim 5, characterized in that: A total of four coordinate systems are established for the gear to be processed and the gear cutting tool.

7. A method for designing a cutting edge tooth profile of a gear turning tool as claimed in claim 5, characterized in that: In step S5, in the established coordinate system, set Point is the instantaneous meshing point, and the point on the wheel The normal line of the tooth profile passes through the meshing node , (x1, y1) is any point on the gear tooth profile to be processed. The tooth profile normal line intersects with the pitch circle of the gear to be processed at point , using the tooth profile normal method, according to any point on the gear to be processed The angle between the tangent line at and the x1 axis , and then obtain The angle that the gear to be processed rotates to become the meshing point of the two tooth profiles , according to the meshing relationship of the internal gear, calculate the angle that the gear cutting cutter rotates .

8. A method for designing a cutting edge tooth profile of a gear turning tool as claimed in claim 7, characterized in that: In order to make the point Become the meshing point, Points and The points coincide, so we can find (x1, y1) becomes the meshing equation required for the meshing point. The specific calculation formula of the meshing equation is as follows: （10） In the formula, is the tooth profile at point The tangent line t and The angle of the axes; The formula for calculating the length of the equivalent line segment that the meshing point passes through is as follows: （12）。 9. A method for designing a cutting edge tooth profile of a gear turning tool as claimed in claim 8, characterized in that: According to the meshing equation, the rotation angle when a certain point on the right half of the gear profile to be processed becomes the meshing point can be calculated. , according to the transmission relationship expressed by formula 7 in step S3 （7） The turning angle of the gear cutting tool can be obtained , the two coordinate transformation matrices expressed in the two rotation angles step S4 are transformed using the following formula: （13） （14） In the formula, represents the conjugate tooth profile of the internal gear, It represents the conjugate tooth profile of the external gear, that is, the cutting edge tooth profile of the gear cutting cutter.

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