A design method for the tooth profile of the cutting edge of a gear turning tool

Abstract

The present invention relates to a gear turning tool cutting edge tooth profile design method, which belongs to the field of transmission technology. S1: using a single parameter s as an independent variable, a mathematical model of the gear tooth profile to be processed is established; 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 gear turning tool parameters are designed, and the gear turning tool cutting edge tooth profile design parameters are calculated; S3: according to the gear plane meshing principle, a coordinate system is established; S4: according to the gear turning processing motion principle, the gear tooth profile coordinate system of the gear to be processed in S3 is derived. Sc(Oc‑xc,yc) is converted to the gear skiving cutter cutting edge tooth profile coordinate system Sh(Oh‑xh,yh). S5: Using the tooth profile normal method, the angle #imgabs0# rotated by the gear skiving cutter is calculated. The gear skiving cutter cutting edge tooth profile is obtained by combining the coordinate transformation matrix #imgabs1# in S5 with the mathematical model of the gear tooth profile to be machined in S1. This method efficiently solves and satisfies the gear skiving cutter motion principle, and the resulting tooth profile conforms to the machining generation principle, achieving high computational efficiency and high cutting edge tooth profile accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of transmission, 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 achieves 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 achieve the unfolding motion. 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 components such as internal teeth, external teeth, spiral teeth, bevel teeth, etc. In particular, the gear turning method is used to process internal gears, which is not limited by the processing size. The cutting efficiency is high and the precision is close to that of 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 turning tools are bevel gears. The design and derivation of their cutting edges are mostly based on the kinematic method to establish the meshing equation ( ) and solve the nonlinear system of equations. This process involves numerous parameters and requires complex coordinate transformations, making the meshing equations very complex to establish. Multiple inversions are required to ensure the correct solution, resulting in low computational efficiency. Furthermore, when kinematic methods are applied to tool design for complex tooth profiles (such as asymmetric or modified tooth profiles), meshing equations are difficult to establish in certain local conjugate regions 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 a large amount of calculation and low calculation efficiency. Moreover, the tooth profile accuracy obtained by the envelope method is determined by the tooth profile rolling distance and its rolling angle. The blade shape accuracy is low and it is not suitable for designing and processing the tooth profile of the gear 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. This method is based on the tooth profile normal method, and simplifies the three processing motions into a two-axis meshing expansion motion to derive the tooth profile of the cutting edge of the gear turning tool. This method has the characteristics of high computational 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 cutting edge tooth profile of a gear turning tool comprises the following steps:

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

[0010] (1)

[0011] Where, is the vector of the gear tooth profile to be machined in the coordinate system, is the first section tooth profile control parameter, 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 machined, s is a continuous parameter, and the rest of the tooth profile is expressed by the parameter s. The mathematical model of the tooth profile is expressed by the single parameter s, and the gear cutting cutter tooth profile is derived.

[0012] S2: Design the parameters of the gear to be machined and the mathematical model of the gear tooth profile in S1, and calculate the design parameters of the gear cutting tool cutting edge tooth profile;

[0013] S3: Convert the three-dimensional spatial 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 starting point. Establish a coordinate system S2 (O2-x2, y2) for the origin; ③ Establish a gear tooth profile coordinate system Sc (Oc-xc, yc) fixedly connected to the workpiece motion, and a gear cutter cutting edge tooth profile coordinate system Sh (Oh-xh, yh) fixedly connected to the gear cutter motion;

[0015] S4: According to the motion principle of gear skiving, derive the transformation matrix from the gear profile coordinate system Sc (Oc-xc, yc) to the gear cutting tool cutting edge profile coordinate system Sh (Oh-xh, yh). The coordinate transformation matrix of the two coordinate systems is Expressed as:

[0016] (8)

[0017] (9)

[0018] Where, 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 machined and the gear cutting cutter;

[0019] S5: Determine the intersection point between the gear to be processed and the gear cutting tool For the meshing node, use the tooth profile normal method to calculate the angle that the gear cutting cutter rotates , the tooth profile of the cutting edge of the gear skiving 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 machined in S1, its point set is obtained, and the gear cutting tool 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 module of the gear cutting cutter designed by formula 2 is equal to the given module of the gear being processed, and the axis angle between the gear cutting cutter and the gear being processed 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] Where, is the module of the gear to be processed, is the module of the gear cutting tool;

[0025] (3)

[0026] Where, 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, Indicates internal gear machining;

[0027] (4)

[0028] (5)

[0029] (6)

[0030] Where, 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 tool are respectively 、 Around the origin of their respective fixed coordinate systems , After the gear and gear cutter rotate from the starting position for a period of time, the workpiece rotates around Turn the corner , gear cutting tool around Turn the corner , the coordinate system is 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] Where, Indicates the gear ratio.

[0035] Furthermore, a total of four 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 point The tooth profile normal just passes through the meshing node , (x1, y1) is any point on the gear tooth profile to be processed. The tooth profile normal intersects the pitch circle of the gear to be machined 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 when it becomes 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, to make the point Become the meshing point, Points of need 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:

[0038] (10)

[0039] Where, 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 for 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 length of the equivalent line segment that the meshing point passes through 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 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 step S4 of the two rotation angles are converted using the following formula:

[0048] (13)

[0049] (14)

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

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

[0052] 1. The present invention discloses a method for designing the tooth profile of a gear turning tool cutting edge, which simplifies the complex gear turning machining motion, ignores the cutting speed that provides the axial feed depth, and considers the meshing motion of the machined gear and the gear turning tool in a two-dimensional plane. It does not require the establishment of complex meshing equations to derive the gear turning tool tooth profile. A general design process for the tooth profile of a gear turning tool cutting edge is determined, which can efficiently solve and satisfy the gear turning tool motion principle, and the obtained tooth profile conforms to the machining generation 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 computational efficiency. At the same time, the tooth profile of the cutting edge 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 gear turning tool cutting edge. This method can be applied to the tooth profile processing of any internal or external gear, and realizes the integrated design and calculation of gear geometric parameters, basic parameters of tooth blanks, and gear tooth processing parameters.

[0055] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may 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 with reference to the accompanying drawings, in which:

[0057] Figure 1 Schematic diagram of the mathematical model of the gear tooth profile to be machined in a gear turning tool cutting edge tooth profile design method of the present invention;

[0058] Figure 2 Schematic diagram of a gear turning tool cutting edge tooth profile design method according to 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 according to the present invention;

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

[0061] Figure 5 A schematic diagram showing a comparison between the tooth profile of an internal gear to be machined after enveloping and the tooth profile of the cutting edge of a gear skiving tool in a method for designing the tooth profile of a gear skiving tool according to the present invention;

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

[0063] The following describes the embodiments of the present invention by means of 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 are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0064] like Figures 1-6 The design method for the cutting edge tooth profile of a gear skiving tool is shown. Starting from the gear tooth profile to be machined, this method simplifies the complex gear skiving motion, ignoring the cutting speed that determines the axial feed depth and considering the meshing motion of the two in a two-dimensional plane. The gear skiving tool tooth profile is derived by transforming the three-dimensional coordinate system into a two-dimensional coordinate system. Using the tooth profile normal method, the cutting edge tooth profile is obtained by considering the geometric relationship during meshing.

[0065] The specific steps include:

[0066] S1: The gear to be processed consists of 6 sections: tooth top transition section, middle tooth profile section, and 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 machined is:

[0068] (1)

[0069] Where, is the vector of the gear tooth profile to be machined in the coordinate system, is the first section tooth profile control parameter, 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 gear cutting cutter tooth profile 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 tool are designed according to its parameters, and the design parameters of the gear cutting tool 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 module of the gear cutting cutter designed by formula 2 is equal to the given module of the gear being processed, and the axis angle between the gear cutting cutter and the gear being processed 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] Where, is the module of the gear to be processed, is the module of the gear cutting tool;

[0075] (3)

[0076] Where, 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, Indicates internal gear machining;

[0077] (4)

[0078] (5)

[0079] (6)

[0080] Where, 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] Convert the three-dimensional spatial meshing into a two-dimensional plane meshing. According to the gear plane meshing principle, establish the following coordinate system:

[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 starting point. Establish a coordinate system S2 (O2-x2, y2) for the origin. The y2 axis of the new coordinate system coincides with the y1 axis. S2 serves as its initial static coordinate system, that is, a 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 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 tooth profile coordinate system Sc (Oc-xc, yc) that is fixedly connected to the workpiece motion, and the gear cutter cutting edge tooth profile coordinate system Sh (Oh-xh, yh) that is fixedly connected to the gear cutter motion. The relationship between the rotation angle of the gear cutter and the rotation angle of the gear to be processed in the established coordinate system is:

[0083] (7)

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

[0085] There are 4 coordinate systems for the gear to be processed and the gear cutting tool, refer to Figure 2 The coordinate system shown.

[0086] S4: According to the motion principle of gear skiving, derive the transformation matrix from the gear profile coordinate system Sc (Oc-xc, yc) to the gear cutting tool cutting edge profile coordinate system Sh (Oh-xh, yh). The coordinate transformation matrix of the two coordinate systems is Expressed as:

[0087] (8)

[0088] (9)

[0089] Where, 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 For meshing nodes, use 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 when it becomes 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 gear cutting edge 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 tooth profile to be processed is the meshing tooth profile for deduction. Point is the instantaneous meshing point, and the point on the gear to be processed The tooth profile normal just passes through the meshing node , (x1, y1) is any point on the gear tooth profile to be processed. The tooth profile normal intersects the pitch circle of the gear to be machined at point , in order to make the point Become the meshing point, Points of need 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] Where, is the tooth profile at point The tangent line t and The angle between the axes;

[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 for 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 length of the equivalent line segment that the meshing point passes through 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 a point on the gear tooth profile to be processed The meshing equation required for (x1, y1) to become the meshing point. Based on this equation, the rotation angle when a certain point on the right half of the gear 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 step S4 of the two rotation angles are converted using the following formula:

[0103] (13)

[0104] (14)

[0105] Where, represents the conjugate tooth profile of the internal gear, Representing the conjugate tooth profile of the external gear, the coordinates of the gear cutter engagement point can be obtained to obtain the conjugate tooth profiles of the internal and external gears, that is, the gear cutter cutting edge tooth profile (example diagram for processing internal gears) as shown in the figure. Figure 4 As shown; and according to the gear turning tool processing motion principle, the envelope verification is carried out, and after the envelope, it is completely aligned with the gear turning tool cutting edge tooth profile, as shown Figure 5 、 6 As shown in the figure, 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 solutions of the present invention and are not limiting. 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 solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for designing the tooth profile of a gear turning tool cutting edge, characterized in that: The following steps are involved: S1: The gear to be processed consists of 6 sections: tooth top transition section, intermediate tooth profile section, and tooth root transition section. Using a single parameter s as the independent variable, a mathematical model of the gear tooth profile to be processed is established. The mathematical model of the gear tooth profile to be processed is: （1） Where, is the vector of the gear tooth profile to be machined in the coordinate system, is the first section tooth profile control parameter, 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 machined, s is a continuous parameter, and the rest of the tooth profile is expressed by the parameter s. The mathematical model of the tooth profile is expressed by the single parameter s, and the gear cutting cutter tooth profile is derived. S2: Design the parameters of the gear to be machined and the mathematical model of the gear tooth profile in S1, and calculate the design parameters of the gear cutting tool cutting edge tooth profile; S3: Convert the three-dimensional spatial 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 starting point. Establish a coordinate system S2 (O2-x2, y2) for the origin; ③ Establish a gear tooth profile coordinate system Sc (Oc-xc, yc) fixedly connected to the workpiece motion, and a gear cutter cutting edge tooth profile coordinate system Sh (Oh-xh, yh) fixedly connected to the gear cutter motion; S4: According to the motion principle of gear skiving, the transformation matrix of the gear tooth profile coordinate system Sc (Oc-xc, yc) to be processed in S3 is derived to transform the gear tooth profile coordinate system Sh (Oh-xh, yh) of the gear skiving cutter cutting edge. The coordinate transformation matrix of the two coordinate systems is expressed as: （8） （9） Where, 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 angle of the gear to be processed, Indicates the center distance between the gear to be machined and the gear cutting cutter; S5: Determine the intersection point between the gear to be processed and the gear cutting tool For the meshing node, use the tooth profile normal method to calculate the angle that the gear cutting cutter rotates , the tooth profile of the cutting edge of the gear skiving 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. The method for designing the tooth profile of a gear turning tool cutting edge according to claim 1, wherein: The point set of the gear tooth profile to be machined is obtained through the mathematical model of the gear tooth profile in S1, and the parameters of the gear cutting tool are designed according to the parameters of the point set.

3. The method for designing the tooth profile of a gear turning tool cutting edge according to claim 1, wherein: The gear cutting tool parameter design in S2 is specifically as follows: defining the number of teeth of the designed gear cutting tool Helix angle of gear cutting tool , the module of the gear cutting cutter designed by formula 2 is equal to the given module of the gear being processed, and the axis angle between the gear cutting cutter and the gear being processed 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） Where, is the module of the gear to be processed, is the module of the gear cutting tool; （3） Where, 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, Indicates internal gear machining; （4） （5） （6） Where, 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 the tooth profile of a gear turning tool cutting edge according to 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. The method for designing the tooth profile of the cutting edge of a gear turning tool according to claim 4, wherein: In 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 cutter rotate from the starting position for a period of time, the workpiece rotates around Turn the corner , gear cutting tool around Turn the corner , the coordinate system is 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） Where, Indicates the gear ratio.

6. The method for designing the tooth profile of a gear turning tool cutting edge according to claim 5, wherein: A total of four coordinate systems are established for the gear to be processed and the gear cutting tool.

7. The method for designing the tooth profile of a gear turning tool cutting edge according to claim 5, wherein: In step S5, in the established coordinate system, set Point is the instantaneous meshing point, just on the wheel The tooth profile normal just passes through the meshing node , (x1, y1) is any point on the gear tooth profile to be processed. The tooth profile normal intersects the pitch circle of the gear to be machined 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 when it becomes 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. The method for designing the tooth profile of a gear turning tool cutting edge according to claim 7, wherein: To make the point Become the meshing point, Points of need 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） Where, is the tooth profile at point The tangent line t and The angle between the axes; The formula for calculating the length of the equivalent line segment that becomes the meshing point is as follows: （12）。 9. The method for designing the tooth profile of a gear turning tool cutting edge according to claim 8, wherein: According to the meshing equation, the rotation angle when a certain point on the right half of the gear 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 step S4 of the two rotation angles are converted using the following formula: （13） （14） Where, represents the conjugate tooth profile of the internal gear, It represents the conjugate tooth profile of the external gear, that is, the tooth profile of the cutting edge of the gear cutting tool.

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