Active design method for cylindrical tooth turning cutter with given clearance angle

Abstract

The invention discloses an active design method for a cylindrical gear turning cutter with a given clearance angle, which belongs to the field of gear machining and cutter design thereof, and comprises the following steps of: giving a machining clearance angle, a front angle, a cutter tooth number and an initial helical angle, calculating mounting parameters, adjusting the helical angle of the cutter, calculating a cutter edge shape by a shape generating rack, and calculating a barrel-shaped enveloping surface conjugated with a workpiece gear. Checking whether the enveloping surface intersects with the curved surface of the cutter, determining the tooth width of the cutter, and obtaining design and installation parameters of the cylindrical tooth turning cutter. According to the parameters, gear turning machining of the workpiece gear can be achieved. In order to solve the problems that the machining precision of a bowl-shaped tooth turning cutter is high in attenuation speed along with the cutter sharpening condition, and a common cylindrical tooth turning cutter cannot realize active design of a machining rear angle, the designed tooth turning cutter has a given design rear angle, and the machining precision is constant after cutter sharpening.

Description

Technical Field

[0001] This invention relates to the field of gear machining and tool design, specifically to an active design method for a cylindrical gear turning tool with a given back angle. Background Technology Gears are a widely used and essential intelligent mechanical component. With the development of new energy vehicles and robots, the demand for internal gear rings has exploded. However, gear hobbing cannot machine internal gears, and gear shaping faces the challenge of low processing efficiency, failing to meet the high-precision and high-efficiency machining requirements of internal gear rings. Gear turning is a new gear machining process that can machine internal and external gears and double gears with short relief grooves, featuring high processing efficiency and high precision.

[0002] Gear turning cutters are crucial for ensuring gear turning accuracy, and structural parameters such as the rake angle and clearance angle are key parameters affecting tool life and cutting conditions. Currently, the most commonly used gear turning cutter is the cup-shaped cutter. This type of cutter is tapered along the tool axis. The clearance angle is achieved by changing the helix angle of the left and right tooth faces. However, in actual machining, as the cutting edge wears, the tool's outer diameter gradually decreases during sharpening, introducing machining errors. Cylindrical gear turning cutters are a new type of gear turning cutter, whose cutting edge shape remains unchanged along the tool axis. Therefore, they can maintain constant machining accuracy even after multiple sharpenings. However, current cylindrical gear turning cutter design methods achieve tool edge shape design by changing the position of the rake face while ensuring the tool and workpiece are conjugate. Although this allows for active design of the rake angle, the clearance angle cannot be guaranteed. Therefore, there is an urgent need for an active design method for cylindrical gear turning cutters capable of achieving a given clearance angle. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides an active design method for cylindrical turning cutters with a given back angle. The designed cutting cutter has standard helical surfaces on both the left and right sides and a given back angle, eliminating the need for multiple iterations.

[0004] The present invention achieves the above objectives through the following technical means: S1. Determine the tool clearance angle based on the gear workpiece parameters and the expected machining state. Front corner Number of teeth on the cutting tool and the initial helix angle of the tool ; Number of teeth of the cutting tool The selection principle is: the number of teeth on the cutting tool and the number of teeth on the workpiece should be coprime; tool back angle It is the difference between the helix angle of the tooth surface where the left and right cutting edges of the tool are located and the helix angle of the tooth surface of the workpiece gear that is in correct meshing.

[0005] S2. Based on the gear workpiece, establish a virtual production rack and determine the normal module of the production rack. Normal pressure angle and helix angle ; Based on the workpiece and tool parameters of S1, calculate the normal module of the virtual production rack. Normal pressure angle and helix angle The expressions are as follows: In the formula, Indicates the pitch circle radius of the gear in the workpiece; Indicates the number of teeth on the gear in the workpiece; Indicates the base circle radius of the workpiece gear; The pitch circle radius of the workpiece gear. The helix angle is the pitch circle of the gear on the workpiece.

[0006] S3. Calculate the cone angle between the tool axis and the virtual rack, and the angle between the tool axis and the tooth profile in the virtual rack pitch plane; Based on the given machining back angle, i.e., based on the back angle in S1 The angle between the projection of the tool axis onto the virtual rack pitch plane and the rack tooth profile, and the rack parameters in S2, is the initial helix angle of the tool. The cone angle between the tool axis and the virtual rack. The following relationship must be satisfied: Solve this equation to get .

[0007] Furthermore, the tool pitch circle radius Calculated by the following formula: .

[0008] S4. Adjust the tool helix angle and determine the designed tool helix angle. ; Tool design helix angle The adjustment principle is to ensure that the clearance angles of the left and right cutting edges are equal, and the calculation formula is as follows: ; ; .

[0009] S5. Under the condition of ensuring accurate meshing between the gear workpiece and the cutting tool and the virtual production rack, calculate the installation parameters of the cutting tool in the machine tool coordinate system, including: the intersection angle (installation angle) between the cutting tool axis and the gear axis. The position of the intersection of the tool axis and the gear axis relative to the theoretical cutting position in the X, Y, and Z axes. , and ; Based on the tool helix angle in S4, the rack parameters in S2, and the cone angle in S3, the intersection angle (installation angle) between the tool axis and the gear axis. The tool axis should be parallel to the plane formed by the machine tool's Z-axis (gear axial motion axis) and Y-axis (gear tangential motion axis). The calculation formula is as follows: In the formula, Indicates the helix angle of the pitch circle of the gear in the workpiece; The rotation angle of the virtual rack around the gear axis is calculated using the following formula: ; According to the installation angle and virtual rack rotation angle It can calculate the offset distance of the machining position relative to the intersection of the gear axis and the tool axis. , and The calculation formula is as follows: In the formula, Let X be the angle between the line connecting the engagement point and the center of the tool's rake face and the X-axis. The calculation formula is as follows: .

[0010] S6. Based on the installation position relationship between the tool and the virtual feed rack and the tool rake angle, calculate the envelope surface and cutting edge curve of the virtual feed rack in the tool coordinate system. Furthermore, the cutting edge of the tool is the cross-section of the envelope surface of the virtual production rack in the tool coordinate system and the rake face; Furthermore, the envelope of the virtual generating rack can be represented as follows: In the formula, For virtual production rack in tool coordinate system The envelope surface in the middle; This is the transformation matrix from the virtual rack coordinate system to the tool coordinate system; For the virtual gear rack in the virtual gear rack coordinate system The equations in; For virtual production form rack along The distance the axis moves, For the virtual production rack tooth surface in the tool coordinate system The normal vector in; When the intersection of the tool pitch circle and the left and right cutting edges is relative to the tool coordinate system When the tool face is axisymmetric, the normal vector of the tool face can be expressed in the tool coordinate system as: Therefore, the cutting edge type can be represented as follows: In the formula, For the tool pitch circle and The intersection of the axes.

[0011] S7. Establish the barrel-shaped envelope surface of the workpiece gear and determine the tool tooth width. Check whether the envelope surface intersects with the tool surface; if they intersect, reduce the tool tooth width by the preset value.

[0012] S8. Based on the installation parameters determined in the above steps, the gear turning tool can be manufactured using the tool parameters determined in the above steps to realize gear turning on the gear turning machine.

[0013] Beneficial effects of the present invention This invention relates to a cylindrical gear cutting cutter. The left and right tooth surfaces of this type of gear cutting cutter are standard helical surfaces, and the cutting edge shape is consistent at all positions on the tool axis, which can ensure constant machining accuracy after the tool is sharpened.

[0014] This invention enables the proactive design of a key parameter of cylindrical gear turning cutters—the tool clearance angle—to improve cutting quality and ensure design efficiency. Attached Figure Description

[0015] Figure 1 This is a flowchart of the active design method for a cylindrical gear cutting tool with a given back angle according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the installation of the virtual production rack and the designed cutting tool according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the tool installation for machining a given workpiece according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the cutting edge shape of the tool designed according to an embodiment of the present invention; Figure 5 A schematic diagram of a cylindrical gear cutting tool designed for an embodiment of the present invention; Figure 6 This is a schematic diagram illustrating the machining surface error of the cylindrical gear turning cutter designed according to an embodiment of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0017] The gear workpiece is an involute internal gear ring with 112 teeth, a normal pressure angle of 20.85°, a normal module of 1.732, a pitch circle helix angle of 14.72 (left-handed), a tip circle diameter of 197.65 mm, and a root circle diameter of 204.82 mm.

[0018] Please see Figure 1 The specific implementation steps of an active design method for a cylindrical turning tooth cutter with a given back angle are as follows: S1. Determine the basic parameters of the cutting tool; Determine the tool clearance angle based on the gear workpiece parameters and the expected machining conditions. Front corner Number of teeth on the cutting tool and the initial helix angle of the tool ; In this invention, the back angle of the cutting tool The tool rake angle is 1.8981°. The initial helix angle is 0°, the number of cutter teeth is 47, and the initial helix angle of the cutter is 3.28° (right-hand helix).

[0019] S2. Construct a virtual production rack; A virtual feed rack is created based on the gear workpiece, and the normal module of the feed rack is determined. Normal pressure angle and helix angle ; Based on the workpiece and tool parameters of S1, calculate the normal module of the virtual production rack. Normal pressure angle and helix angle The expressions are as follows: In the formula, Indicates the pitch circle radius of the gear in the workpiece; Indicates the number of teeth on the gear in the workpiece; Indicates the base circle radius of the workpiece gear; The pitch circle radius of the workpiece gear. The helix angle of the workpiece gear pitch circle; In this invention, the pitch circle radius of the gear meshing with the virtual production rack is determined. Consistent with the gear pitch circle, which is 100.2834 mm, the virtual production rack helix angle is determined. Normal module and normal pressure angle .

[0020] S3. Calculate the cone angle between the tool axis and the virtual rack, and the angle between the tool axis and the tooth profile in the virtual rack pitch plane; Based on the given machining back angle, i.e., based on the back angle in S1 The angle between the projection of the tool axis onto the virtual rack pitch plane and the rack tooth profile, and the rack parameters in S2, is the initial helix angle of the tool. The cone angle between the tool axis and the virtual rack. The following relationship must be satisfied: Solve this equation to get In this invention, .

[0021] Furthermore, the tool pitch circle radius Calculated by the following formula: .

[0022] S4. Adjust the tool helix angle and determine the designed tool helix angle. ; Tool design helix angle The adjustment principle is to ensure that the clearance angles of the left and right cutting edges are equal, and the calculation formula is as follows: In this invention, , ; When the helix angle of the tooth surfaces containing the left and right cutting edges of the tool is the theoretical helix angle, the clearance angle of the left and right cutting edges is 0°; while when the helix angle of the tooth surfaces containing the left and right cutting edges is the initial helix angle of the tool... At that time, the clearance angle of the left cutting edge is 1.9142° and the clearance angle of the right cutting edge is 1.8821°. Therefore, the helix angle of the tool needs to be adjusted to ensure that the clearance angles of the left and right cutting edges are equal.

[0023] Based on the rotation angle of the virtual rack around the gear axis in S5 The expression for calculating the helix angle of the tool design is: .

[0024] S5. Calculate the installation parameters of the cutting tool on the machine tool; Under the condition of ensuring accurate meshing between the gear workpiece and the cutting tool and the virtual production rack, calculate the installation parameters of the cutting tool in the machine tool coordinate system, including: the intersection angle (installation angle) between the cutting tool axis and the gear axis. The position of the intersection of the tool axis and the gear axis relative to the theoretical cutting position in the X, Y, and Z axes. , and ; Based on the tool helix angle in S4, the rack parameters in S2, and the cone angle in S3, the intersection angle (installation angle) between the tool axis and the gear axis. The tool axis should be parallel to the plane formed by the machine tool's Z-axis (gear axial motion axis) and Y-axis (gear tangential motion axis). The calculation formula is as follows: In the formula, Indicates the helix angle of the pitch circle of the gear in the workpiece; The rotation angle of the virtual rack around the gear axis is calculated using the following formula: ; According to the installation angle and virtual rack rotation angle It can calculate the offset distance of the machining position relative to the intersection of the gear axis and the tool axis. , and The calculation formula is as follows: In the formula, Let X be the angle between the line connecting the engagement point and the center of the tool's rake face and the X-axis. The calculation formula is as follows: ; Based on the determined virtual rack parameters, gear workpiece parameters, and tool parameters, the following is obtained: Figure 2 The diagram shows the installation of the cutting tool relative to the virtual feed rack. In the diagram, the coordinate system... Parallel to the machine tool coordinate system, axis , and The X, Y, and Z axes of the same gear turning machine are parallel; coordinate system Fixed to the virtual production rack; coordinate system Fixed to the tool; tool axis The angle between its projection line on the virtual production rack and the cone angle is the angle between the projection line and the cone angle. Therefore, the tool axis in the coordinate system The direction vector in is At this point, the tool axis intersects the plane formed by the machine tool's Y and Z motion axes, making it impossible to install in an actual machine tool. Therefore, it is necessary to... Figure 2 The virtual production rack and tool winding Rotation To ensure that the tool axis after rotation is in the coordinate system The X component of the direction vector in the vector is 0. Calculated by formula ; Furthermore, based on the workpiece gear pitch circle and Angle, to obtain as Figure 3 The diagram shows the installation of the tool relative to the workpiece gear; in Figure 2 Based on this, a machine tool coordinate system was introduced. Auxiliary coordinate system Based on the spatial relationship shown in the diagram, the representation of the tool axis direction vector in the machine tool coordinate system is calculated. This allows us to determine the angle between the tool axis and the gear axis, which is the installation angle. The installation angle is then calculated using the formula. ; Furthermore, the representation of the tool coordinate system X-axis in the machine tool coordinate system is calculated, and the angle between the tool coordinate system X-axis and the machine tool coordinate system X-axis is determined. The included angle is calculated using the formula. ; Furthermore, the offset distance of the machining position is calculated. The calculation is obtained according to the formula: , and .

[0025] S6. Calculate the cutting edge curve of the tool; Based on the installation position relationship between the tool and the virtual feed rack and the tool rake angle, calculate the envelope surface and cutting edge curve of the virtual feed rack in the tool coordinate system; Furthermore, the cutting edge of the tool is the cross-section of the envelope surface of the virtual production rack in the tool coordinate system and the rake face; Furthermore, the envelope of the virtual generating rack can be represented as follows: In the formula, For virtual production rack in tool coordinate system The envelope surface in the middle; This is the transformation matrix from the virtual rack coordinate system to the tool coordinate system; For the virtual gear rack in the virtual gear rack coordinate system The equations in; For virtual production form rack along The distance the axis moves, For the virtual production rack tooth surface in the tool coordinate system The normal vector in; When the intersection of the tool pitch circle and the left and right cutting edges is relative to the tool coordinate system When the tool face is axisymmetric, the normal vector of the tool face can be expressed in the tool coordinate system as: Therefore, the cutting edge type can be represented as follows: In the formula, Tool pitch circle and The intersection of the axes; S7. Remove the tooth width of the cutting tool and check it; Establish the barrel-shaped envelope of the workpiece gear and determine the tool tooth width. Check whether the envelope surface intersects with the tool surface; if they intersect, reduce the tool tooth width by the preset value.

[0026] S8. Output the design results and manufacture the cutting tools; Based on the installation parameters determined in the above steps, the gear turning tool can be manufactured using the tool parameters determined in the above steps to achieve gear turning on the gear turning machine.

[0027] Ultimately, we obtained the following: Figure 4 The cutting edge type shown; Based on the helix angle of the tool design ,Will Figure 4 The obtained cutting edge is swept to determine the tool tooth surface, such as Figure 5 As shown; The workpiece gear is machined using the calculated cutting edge according to the predetermined installation parameters, until... Figure 6 The machining error shown is from Figure 6 It can be seen that the cylindrical gear turning cutter designed in this invention can achieve high-precision gear machining, and the active design method of the tool back angle is effective, which can control the machining error at the micrometer level. At the same time, the tool has good wear compensation capability and is suitable for high-precision and high-efficiency gear machining scenarios.

[0028] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the concept and scope of the present invention. Without departing from the design concept of the present invention, all modifications and improvements made by those skilled in the art to the technical solutions of the present invention should fall within the protection scope of the present invention. The technical content for which protection is sought in the present invention has been fully described in the claims.

Claims

1. A method for actively designing a cylindrical turning cutter with a given back angle, characterized in that, Includes the following steps: S1. Determine the tool clearance angle based on the gear workpiece parameters and the expected machining state. Front corner Number of teeth on the cutting tool and the initial helix angle of the tool ; S2. Based on the gear workpiece, establish a virtual production rack and determine the normal module of the production rack. Normal pressure angle and helix angle ; S3. Based on the given tool clearance angle Calculate the cone angle between the virtual production rack pitch plane and the tool axis. And the angle between the tool axis and the tooth profile in the virtual rack pitch plane; S4. Calculate the machining clearance angle of the left and right cutting edges of the tool, adjust the tool helix angle, and determine the tool design helix angle. ; S5. Under the condition of ensuring accurate meshing between the gear workpiece and the cutting tool and the virtual production rack, calculate the installation parameters of the cutting tool in the machine tool coordinate system; S6. Based on the installation position relationship between the tool and the virtual feed rack and the tool rake angle, calculate the envelope surface and cutting edge curve of the virtual feed rack in the tool coordinate system. S7. Establish the barrel-shaped envelope surface of the workpiece gear and determine the tool tooth width. Check whether the envelope surface intersects with the tool surface; if they intersect, reduce the tool tooth width by the preset value. S8. Based on the installation parameters determined in the above steps, the gear turning tool can be manufactured using the tool parameters determined in the above steps to realize gear turning on the gear turning machine.

2. The active design method for a cylindrical turning cutter with a given back angle according to claim 1, characterized in that: The number of teeth of the cutting tool in S1 The selection principle is to ensure that the number of teeth on the cutting tool and the number of teeth on the workpiece are coprime.

3. The active design method for a cylindrical turning cutter with a given back angle according to claim 1, characterized in that: The tool back angle in S1 It is the difference between the helix angle of the tooth surface where the left and right cutting edges of the tool are located and the helix angle of the tooth surface of the workpiece gear that is in correct meshing.

4. The active design method for a cylindrical turning cutter with a given back angle according to claim 1, characterized in that: The normal module of the gear rack is determined in S2. Normal pressure angle and helix angle The calculation formulas are as follows: In the formula, Indicates the pitch circle radius of the gear in the workpiece; Indicates the number of teeth on the gear in the workpiece; Indicates the base circle radius of the workpiece gear; The pitch circle radius of the workpiece gear. The helix angle is the pitch circle of the gear on the workpiece.

5. The active design method for a cylindrical turning cutter with a given back angle according to claim 1, characterized in that: In S3, the angle between the projection of the tool axis onto the virtual rack plane and the tooth profile is the initial helix angle of the tool. ; Cone angle between the tool axis and the virtual rack The following relationship must be satisfied: 。 6. The active design method for a cylindrical turning cutter with a given back angle according to claim 1, characterized in that: In S4, the tool is designed with a helix angle. The adjustment principle is to ensure that the clearance angles of the left and right cutting edges are equal. The calculation formulas are as follows: ； ； Tool design helix angle The expression is as follows: 。 7. The active design method for a cylindrical turning cutter with a given back angle according to claim 1, characterized in that: In step S5, the installation parameters of the tool in the machine tool coordinate system are calculated, including the intersection angle between the tool axis and the gear axis. The position of the intersection of the tool axis and the gear axis relative to the theoretical cutting position in the X, Y, and Z axes. , and ; The angle of intersection between the tool axis and the gear axis The tool axis should be parallel to the plane formed by the Z-axis and Y-axis of the machine tool. The calculation formula is as follows: In the formula, Indicates the helix angle of the pitch circle of the gear in the workpiece; The rotation angle of the virtual rack around the gear axis is calculated using the following formula: According to the installation angle and virtual rack rotation angle It can calculate the offset distance of the machining position relative to the intersection of the gear axis and the tool axis. , and The calculation formula is as follows: In the formula, The tool pitch circle radius; The angle between the line connecting the engagement point and the center of the tool's rake face and the X-axis is calculated using the following formula: 。 8. The active design method for a cylindrical turning cutter with a given back angle according to claim 7, characterized in that: The tool pitch circle radius The expression is as follows: 。 9. The active design method for a cylindrical turning cutter with a given back angle according to claim 1, characterized in that: In S6, the cutting edge of the tool is the cross-section of the envelope surface of the virtual production rack in the tool coordinate system and the rake face; The envelope of the virtual generating rack can be represented as follows: In the formula, For virtual production rack in tool coordinate system The envelope surface in the middle; This is the transformation matrix from the virtual rack coordinate system to the tool coordinate system; For the virtual gear rack in the virtual gear rack coordinate system The equations in the text; For virtual production form rack along The distance the axis moves, For the virtual production rack tooth surface in the tool coordinate system The normal vector in; When the intersection of the tool pitch circle and the left and right cutting edges is relative to the tool coordinate system When the tool face is axisymmetric, the normal vector of the tool face can be expressed in the tool coordinate system as: Therefore, the cutting edge type can be represented as follows: In the formula, For the tool pitch circle and The intersection of the axes.

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