Design method of cylindrical gear turning tool without structured clearance angle

Abstract

The present invention relates to gear processing and its tools, specifically a method for designing a cylindrical gear turning tool with no structural back angle. The method includes: designing the angle between the number of tool teeth and the installation axis; calculating the barrel-shaped conjugate surface conjugate with the gear tooth surface to be processed; determining the distance of the tool front cutting edge deviating from the middle section of the barrel-shaped conjugate surface; designing the tool helix angle; designing the tool front angle; calculating the tool front cutting edge shape; obtaining the design parameters and installation parameters of the gear turning tool; manufacturing the tool according to the above tool design parameters, and performing gear turning on a gear turning machine according to the tool installation parameters. The present invention addresses the problem that the commonly used conical gear turning tools have a fast decline in accuracy and a short service life after regrinding, and proposes a gear turning method under spatial offset conjugate conditions. The designed cylindrical gear turning tool has a constant accuracy after regrinding; the tool can be regrinded many times and has a longer service life; the tool can be processed by forming grinding, and the manufacturing process is simple.

Description

Technical Field

[0001] The present invention relates to the technical field of gear processing and its cutting tools, and in particular to a design method for a cylindrical gear turning tool without a structural back angle. Background Art

[0002] Gears are critical components in numerous industries, and their processing technology is crucial for the development of high-end gear products. Gear skiving is an emerging gear processing technology that addresses the challenges of machining thin-walled or compact internal gear rings without undercuts in high-end precision harmonic reducers and automatic transmissions. It offers significant advantages such as high precision, high efficiency, and environmental friendliness. Currently, a growing number of companies are adopting gear skiving as an alternative to traditional gear rolling, inserting, broaching, honing, and grinding processes.

[0003] The key to gear turning technology lies in tool design. Currently, the most common gear turning tool is a conical gear turning tool. In order to avoid interference between the tool back face and the machined tooth surface, the tool is designed with a fixed structural back angle on the tool back face, and its structural appearance is similar to that of a gear shaping tool. However, because the tool has a fixed structural back angle, the outer diameter of the tool will continue to decrease during the regrinding process, the tool blade shape will change, and the tool blade shape and the gear tooth surface will no longer satisfy the conjugate relationship, resulting in a short tool life and reduced precision of the machined gear. Although some methods can design a conical tool blade shape without theoretical error, the tool back face designed by these methods is a free-form surface, the tool grinding and manufacturing process is complex, and it is difficult to apply in practice. Therefore, how to break through the fundamental defects of the existing conical gear turning tool design methods, such as rapid decline in regrinding accuracy and short service life, is a key issue that needs to be urgently addressed in gear turning technology. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention provides a design method for a cylindrical gear turning tool with no structural back angle. The designed cylindrical gear turning tool has constant accuracy after regrinding; the tool can be regrinded many times and has a longer service life; the tool can be processed by form grinding, and the manufacturing process is simple.

[0005] The present invention achieves the above technical objectives through the following technical means.

[0006] A design method for a cylindrical gear turning tool without a structured back angle, comprising:

[0007] S1: Design the number of tool teeth z according to the parameters of the gear to be processed t Angle Σ with the tool installation axis;

[0008] S2: Design the initial helix angle β of the tool t0 , calculate the tool installation center distance a;

[0009] S3: Calculate the barrel-shaped conjugate surface S that is conjugate with the gear tooth surface to be machined (2) , check the barrel-shaped conjugate surface S (2) Is there a surface intersection phenomenon? If yes, return to step S1 and modify the number of tool teeth or the tool installation axis intersection angle. If no, continue to step S4;

[0010] S4: Determine whether the tool rake face deviates from the barrel-shaped conjugate surface S (2) The distance z from the middle section off ;

[0011] S5: Design the helix angle β of the tool t , check whether there is interference between the tool back face and the gear tooth surface to be processed. If so, return to step S4 to reduce the deviation of the tool front face from the barrel-shaped conjugate surface S (2) The distance z from the middle section off If not, calculate the tool width b under the current parameters and proceed to step S6;

[0012] S6: Check whether the working clearance angles of the main cutting edges on both sides of the tool are symmetrical. If not, return to step S5 to modify the helix angle β of the tool. t , if yes, proceed to step S7;

[0013] S7: Design the structural rake angle γ0 of the tool;

[0014] S8: According to the structural rake angle γ0 of the tool, the tool rake face plane is constructed and the tool rake face edge shape is calculated;

[0015] S9: Get the design parameters and installation parameters of the gear cutting tool. The tool design parameters include: number of teeth z t , tool helix angle β t , width b, structural rake angle γ0, tool installation parameters include: installation axis intersection angle Σ, installation center distance a, distance z of the tool rake face from the middle section of the barrel conjugate surface off ;

[0016] S10: manufacturing a gear turning tool according to the tool design parameters and the tool rake face edge shape obtained in step S9, and performing gear turning processing on a gear turning machine according to the tool installation parameters.

[0017] Furthermore, the tool installation axis intersection angle Σ in step S1 is selected according to the following principle: when the helix angle β of the gear to be machined is w When the tool installation axis angle Σ is within the range of 15° to 30°, the helix angle β of the gear to be machined w Equal; when the helix angle β of the gear to be processed w If it is not within the range of 15° to 30°, the selection range of the tool installation axis intersection angle Σ is 15° to 30°.

[0018] Furthermore, the initial helix angle β of the tool in step S2 is t0 The calculation formula is:

[0019] β t0 =|β w -Σ|

[0020] Among them, β t0 is the initial helix angle of the tool, β w is the helix angle of the gear to be machined, and Σ is the installation axis angle of the tool.

[0021] Furthermore, the calculation formula for the tool installation center distance a in step S2 is:

[0022] a=r pw -r pt

[0023] Among them, r pw is the pitch radius of the gear to be machined, r pt is the pitch radius of the tool, and z t is the number of teeth of the tool, z w is the number of teeth of the gear to be processed.

[0024] Furthermore, the barrel-shaped conjugate surface in step S3 is calculated using the following two formulas:

[0025] QM-mn M =0

[0026] Where QM is the vector length between the tooth meshing point M and a point Q on the conjugate surface, n M Represents the normal vector of the tooth surface meshing point M, where m is the proportional constant.

[0027]

[0028] Among them, S (2) is a barrel-shaped conjugate surface, S (1) is the helical surface of the gear to be machined, M tw is the coordinate transformation matrix, and M 2-1 =Rot(i,Σ)Tran(i,a), Indicates that the rotation angle around the tool z axis is The rotation matrix, Tran(k,z off ) indicates that the translation distance along the z-axis of the tool is z off The translation matrix of Rot(i,Σ) represents the rotation matrix of the gear to be processed with an angle of Σ around the x-axis. Tran(i,a) represents the translation matrix of the gear to be processed with a translation distance a along the x-axis. Indicates that the rotation angle around the z-axis of the gear to be processed is The rotation matrix of .

[0029] Furthermore, in step S6, the working clearance angle α of the main cutting edges on both sides of the tool e Using barrel-shaped conjugate surface S (2) It is expressed as the angle between the two normal vectors on the meshing line on the tool back face, and the calculation formula is:

[0030] α e =<N t ,N c >

[0031] Among them, N t is the normal vector of the barrel-shaped conjugate surface on the meshing line at a certain moment, N c is the normal vector of the tool flank face on the engagement line.

[0032] Furthermore, the selection range of the tool rake angle in step S7 is 5° to 15°.

[0033] Furthermore, in step S8, the tool rake face edge shape S γ The calculation formula is:

[0034] S γ =Tran(i,r t )Tran(k,z off )Rot(i,β t )Rot(j,-γ0)

[0035] Among them, r t The offset is z off Tool radius at time, Tran(i,r t ) indicates that the translation distance along the tool x-axis is r t The translation matrix, Tran(k,z off ) indicates that the translation distance along the z-axis of the tool is z off The translation matrix, Rot(i,β t ) indicates that the tool rotates around the x-axis by an angle of β t Rot(j,-γ0) represents the rotation matrix of the tool with an angle of -γ0 around the y-axis.

[0036] Beneficial effects of the present invention:

[0037] 1) Gear turning tools designed according to the present invention maintain consistent accuracy after regrinding, extending tool life. Because the gear turning tool is cylindrical, regrinding only requires regrinding the rake face without altering the tool's edge profile, resulting in extremely high precision and stability. Furthermore, compared to tapered gear turning tools, cylindrical gear turning tools offer a greater regrindable thickness, extending tool life.

[0038] 2) Compared with the complex back face development grinding process of the conical gear turning tool during the manufacturing process, the cylindrical gear turning tool designed according to the design method of the present invention has an external structure similar to that of a cylindrical gear and can be processed by forming grinding, which can simplify the tool manufacturing process, improve the tool manufacturing efficiency, and reduce the tool manufacturing cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of a method for designing a cylindrical gear turning tool with no structured relief angle according to an embodiment of the present invention;

[0040] Figure 2 Schematic diagram of a barrel-shaped conjugate surface conjugated with an internal gear according to an embodiment of the present invention;

[0041] Figure 3 It is a part of the barrel-shaped conjugate surface in an embodiment of the present invention;

[0042] Figure 4 The working clearance angle change of the main cutting edges on both sides of the tool in the embodiment of the present invention;

[0043] Figure 5 The cutting edge shape of the tool rake face intercepted from the barrel-shaped conjugate surface in the embodiment of the present invention;

[0044] Figure 6 The projected edge shape of the rake face of the tool according to the embodiment of the present invention is on the end face;

[0045] Figure 7 A cylindrical gear turning tool designed for an embodiment of the present invention. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0047] The gear to be processed is an internal helical gear with an involute tooth profile and the number of teeth is z. w =97, modulus is m n =1.5875mm, pressure angle is α n =20°, helix angle β w=23.5° (right-hand rotation), tooth top circle diameter d a1 =139.78mm, tooth root diameter d f1 =147.82mm, span of rod is 135.593mm, and diameter of measuring rod is 3.5mm. The design method of cylindrical gear turning tool without structured clearance angle of the present invention is applied to design gear turning tool for internal meshing helical gear with involute tooth profile.

[0048] See also Figures 1 to 6 According to an embodiment of the present invention, a method for designing a cylindrical gear turning tool without a structured clearance angle comprises the following steps:

[0049] S1: Design the number of tool teeth z according to the parameters of the gear to be processed t =37, the intersection angle between the designed number of tool teeth and the tool installation axis Σ;

[0050] The tool installation axis angle Σ is selected according to the following principles: when the helix angle β of the gear to be machined is w When the tool installation axis angle Σ is within the range of 15° to 30°, the helix angle β of the gear to be machined w Equal, when the helix angle β of the gear to be processed w If the tool installation axis angle Σ is not within the range of 15° to 30°, the selection range is 15° to 30°. w =23.5°, and its value is within the range of 15° to 30°. Therefore, the tool installation axis intersection angle Σ=23.5° is selected.

[0051] S2: Design the initial helix angle β of the tool t0 , calculate the tool installation center distance a.

[0052] Because the helix angle β of the gear to be machined w The same as the tool installation axis angle Σ, according to the formula β t0 =|β w -Σ|Calculate the initial helix angle β of the tool t0 =0°; at the same time, using the formula a=r pw -r pt The tool installation center distance a under the current parameters is calculated to be 36.006 mm, where r pw is the pitch radius of the gear to be machined, r pt is the pitch radius of the tool, and z t is the number of teeth of the tool, z w is the number of teeth of the gear to be processed;

[0053] S3: Calculate the barrel-shaped conjugate surface S that is conjugate with the gear tooth surface to be machined (2) , and check the calculated barrel conjugate surface S (2)Is there a surface intersection phenomenon? If so, it indicates that the conjugate barrel-shaped conjugate surface S calculated by the current parameters (2) If there is a singular point, it is necessary to return to step S1 and modify the number of tool teeth or the tool installation axis angle until a barrel-shaped conjugate surface S is obtained. (2) There is no surface intersection phenomenon. If not, proceed to step S4;

[0054] Barrel-shaped conjugate surface S (2) Calculate using formulas (1) to (8). Figure 2 The diagram is a schematic diagram of a barrel-shaped conjugate surface conjugate with the internal gear. Establish a fixed coordinate system O1-x1, y1, z1 of the gear to be processed and a fixed coordinate system O2-x2, y2, z2 of the tool. The z1 axis coincides with the rotation axis of the gear to be processed, the z2 axis coincides with the rotation axis of the tool, and the angle between the z1 axis and the z2 axis is the tool installation axis intersection angle Σ; the x1 axis coincides with the x2 axis, and the shortest distance between the gear to be processed and the tool rotation axis is the initial installation center distance a of the tool; the gear to be processed is rotated at a uniform angular velocity ω (w) The tool rotates around the axis z1 at a uniform angular velocity ω (t) Rotate around axis z2. Point Q is a line in the gear fixed coordinate system that is perpendicular to the x-axis and passes through the gear pitch circle r. pw Point M is any point on the barrel-shaped conjugate surface in meshing state, QM is the vector length between meshing point M and point Q, n M Represents the normal vector of the meshing point M.

[0055] Formula (1) indicates that when the workpiece tooth surface and the barrel-shaped conjugate surface rotate to a certain meshing moment, the vector length QM and the normal vector n of the meshing point M are M In parallel, m represents a proportionality constant.

[0056] QM-mn M =0 (1)

[0057] The vector length QM is the difference between the vector length O1Q and the vector length O1M. In the gear machining coordinate system, O1Q and O1M are:

[0058] O1Q=x q i+y q j+z q k (2)

[0059]

[0060] in, Indicates that the rotation angle around the z-axis of the gear to be processed is Rot(k,θ) represents the rotation matrix of the gear to be processed with an angle of θ around the z-axis.

[0061] From formulas (2) and (3), we can get the expression equation of vector length QM:

[0062] QM=O1M-O1Q (4)

[0063] When the meshing point M is in meshing state, its normal vector can be obtained by rotating the normal vector n of the gear tooth surface to be machined around its rotation axis. Therefore, the normal vector n of the meshing point M is M The expression equation is:

[0064]

[0065] Substituting formula (4) and formula (5) into formula (1), we can get the normal vector n of the meshing point M: M The expression equation is:

[0066]

[0067] From the three equations in formula (6), the parameters τ and m in formula (6) are eliminated by elimination method, and a formula containing only the parameters The equation is:

[0068]

[0069] The gear surface S to be machined is known (1) The helicoidal parameters (u, θ) are substituted into formula (7) to solve the rotation angle of the meshing point M around the axis of the gear to be processed. Therefore, all meshing points on the gear tooth surface that meet the meshing conditions can be solved, and then the meshing points on the gear tooth surface are transformed from the workpiece coordinate system to the tool coordinate system through the coordinate transformation of formula (8), and the barrel-shaped conjugate surface S is obtained. (2) ,Right now:

[0070]

[0071] Among them, S (2) is a barrel-shaped conjugate surface, S (1) is the helical surface of the gear to be machined, M tw is the coordinate transformation matrix, and M 2-1 =Rot(i,Σ)Tran(i,a), Indicates that the rotation angle around the tool z axis is The rotation matrix, Tran(k,z off ) indicates that the translation distance along the z-axis of the tool is z off The translation matrix of the gear to be processed is Rot(i,Σ), which is the rotation matrix of the gear to be processed with an angle of Σ around the x-axis. Tran(i,a) is the translation matrix of the gear to be processed with a translation distance a along the x-axis. Indicates that the rotation angle around the z-axis of the gear to be processed is The rotation matrix of .

[0072] like Figure 3 , is the local part of the calculated barrel-shaped conjugate surface. After inspection, the calculated barrel-shaped conjugate surface S (2) If there is no surface intersection phenomenon, proceed to step S4.

[0073] S4: Determine whether the tool rake face deviates from the barrel-shaped conjugate surface S (2) The distance z from the middle section off =-30mm;

[0074] S5: Design the helix angle β of the tool t , and check whether there is interference between the tool back face and the gear tooth surface to be processed. If so, it is necessary to return to step S4 to reduce the deviation of the tool front face from the barrel-shaped conjugate surface S (2) The distance z from the middle section off , until there is no interference between the tool back face and the gear tooth surface to be machined. If not, continue to step S6 and at the same time calculate the tool width b under the current parameters.

[0075] The initial helix angle β of the tool in this embodiment is t0 =0°, after checking, there is no interference between the back face of the tool and the tooth surface of the gear to be processed, and the tool width b under the current parameters is 40mm.

[0076] S6: Check whether the working clearance angles of the main cutting edges on both sides of the tool are symmetrical. If not, return to step S5 to modify the tool's helix angle β t , until the working clearance angles of the main cutting edges on both sides of the tool are symmetrical. If so, proceed to step S7;

[0077] Using formula α e =<N t ,N c >Calculate the working clearance angle of the main cutting edges on both sides of the tool, where N t Indicates the normal vector of the barrel-shaped conjugate surface on the meshing line at a certain moment, N c Indicates the normal vector of the tool back face on the meshing line. After calculation, when the initial helix angle β of the tool t0 = 0°, such as Figure 4 As shown, when the tool installation axis angle Σ=23.5°, the tool structure rake angle γ0=15°, and the distance z from the tool rake face to the middle section of the barrel conjugate surface is off= -30mm, the working clearance angle of the left main cutting edge is 1°, and the working clearance angle of the right main cutting edge is 2.73°. In other words, the working clearance angles of the main cutting edges on both sides of the tool are asymmetrical, which will cause uneven wear of the main cutting edges on both sides during cutting, thereby reducing the service life of the tool. Therefore, it is necessary to return to step S5 and modify the helix angle β of the tool. t , until the working clearance angles of the main cutting edges on both sides of the tool are symmetrical, and the helix angle of the tool at this time is β t =0.7°, such as Figure 4 At this time, the main cutting edges on both sides of the tool have equal working clearance angles, which is conducive to improving the uneven wear of the main cutting edges on both sides of the tool.

[0078] S7: Design the tool’s structural rake angle γ0 = 15°;

[0079] S8: According to the tool's structural rake angle γ0 = 15°, the tool rake face plane is constructed and the formula S is used. γ =Tran(i,r t )Tran(k,Z off )Rot(i,β t )Rot(j,-γ0) calculates the cutting edge shape of the tool rake face, where z off is the offset of the tool along the axial direction, r t is the offset z off Tool radius at time, β t is the helix angle of the tool, and γ0 is the rake angle of the tool. t ) indicates that the translation distance along the tool x-axis is r t The translation matrix, Tran(k,z off ) indicates that the translation distance along the z-axis of the tool is z off The translation matrix of Rot(i,β t ) indicates that the tool rotates around the x-axis by an angle of β t Rot(j,-γ0) represents the rotation matrix of the tool with an angle of -γ0 around the y-axis. Figure 5 , is the cutting edge shape of the tool rake face cut from the barrel-shaped conjugate surface using the rake face calculation formula. Figure 6 , is the projected edge shape of the tool's rake face on the end face.

[0080] S9: Complete the design of the tool and obtain the design parameters and installation parameters of the gear turning tool. The tool design parameters include: number of teeth z t =37, tool helix angle β t=0.7°, width b = 40mm, structural rake angle γ0 = 15°, tool installation parameters include: installation axis intersection angle Σ = 23.5°, installation center distance a = 36.01mm, distance z of the tool rake face from the middle section of the barrel conjugate surface off =-30mm;

[0081] S10: Manufacturing a gear turning tool according to the tool design parameters and the tool rake face edge shape in step S9. Gear turning is performed on a gear turning machine according to the tool installation parameters in step S9.

[0082] Compared with the complex back face development grinding process of conical gear turning tools during the manufacturing process, the cylindrical gear turning tool proposed in the present invention has an external structure similar to that of a cylindrical gear and can be processed by forming grinding, which can simplify the tool manufacturing process, improve the tool manufacturing efficiency, and reduce the tool manufacturing cost.

[0083] During use, the cylindrical gear turning tool designed using the present invention's cylindrical structure allows only the rake face to be reground during regrinding, without changing the tool's edge profile. This ensures extremely high precision and stability. Furthermore, compared to tapered gear turning tools, cylindrical gear turning tools offer a greater regrindable thickness, extending tool life.

[0084] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A design method for a cylindrical gear turning tool without a structured back angle, characterized in that: include: S1: Design the number of tool teeth z according to the parameters of the gear to be processed t Angle Σ with the tool installation axis; S2: Design the initial helix angle β of the tool t0 , calculate the tool installation center distance a; S3: Calculate the barrel-shaped conjugate surface S that is conjugate with the gear tooth surface to be machined (2) , check the barrel-shaped conjugate surface S (2) Is there a surface intersection phenomenon? If yes, return to step S1 and modify the number of tool teeth or the tool installation axis intersection angle. If no, continue to step S4; S4: Determine whether the tool rake face deviates from the barrel-shaped conjugate surface S (2) The distance z from the middle section off ; S5: Design the helix angle β of the tool t , check whether there is interference between the tool back face and the gear tooth surface to be processed. If so, return to step S4 to reduce the deviation of the tool front face from the barrel-shaped conjugate surface S (2) The distance z from the middle section off If not, calculate the tool width b under the current parameters and proceed to step S6; S6: Check whether the working clearance angles of the main cutting edges on both sides of the tool are symmetrical. If not, return to step S5 to modify the helix angle β of the tool. t , if yes, proceed to step S7; S7: Design the structural rake angle γ0 of the tool; S8: According to the structural rake angle γ0 of the tool, the tool rake face plane is constructed and the tool rake face edge shape is calculated; S9: Get the design parameters and installation parameters of the gear cutting tool. The tool design parameters include: number of teeth z t , tool helix angle β t , width b, structural rake angle γ0, tool installation parameters include: installation axis angle Σ, installation center distance a, distance z of the tool rake face from the middle section of the barrel conjugate surface off ; S10: manufacturing a gear turning tool according to the tool design parameters and the tool rake face edge shape obtained in step S9, and performing gear turning processing on a gear turning machine according to the tool installation parameters.

2. The design method of a cylindrical gear turning tool with no structured clearance angle according to claim 1, characterized in that: In step S1, the tool installation axis intersection angle Σ is selected according to the following principle: when the helix angle β of the gear to be machined is w When the tool installation axis angle Σ is within the range of 15° to 30°, the helix angle β of the gear to be machined w Equal; when the helix angle β of the gear to be processed w If it is not within the range of 15° to 30°, the selection range of the tool installation axis intersection angle Σ is 15° to 30°.

3. The design method of a cylindrical gear turning tool with no structured clearance angle according to claim 1, characterized in that: The initial helix angle β of the tool in step S2 t0 The calculation formula is: b t0 =|β w -S| Among them, β t0 is the initial helix angle of the tool, β w is the helix angle of the gear to be machined, and Σ is the installation axis angle of the tool.

4. The design method of a cylindrical gear turning tool with no structured clearance angle according to claim 1, characterized in that: The calculation formula for the tool installation center distance a in step S2 is: a＝r pw -r pt Among them, r pw is the pitch radius of the gear to be machined, r pt is the pitch radius of the tool, and z t is the number of teeth of the tool, z w is the number of teeth of the gear to be processed.

5. The design method of a cylindrical gear turning tool with no structured clearance angle according to claim 1, characterized in that: The barrel-shaped conjugate surface in step S3 is calculated using the following two formulas: QM-mn M =0 Where QM is the vector length between the tooth meshing point M and a point Q on the conjugate surface, n M Represents the normal vector of the tooth surface meshing point M, where m is the proportional constant; Among them, S (2) is a barrel-shaped conjugate surface, S (1) is the helical surface of the gear to be machined, M tw is the coordinate transformation matrix, and M 2-1 =Rot(i,Σ)Tran(i,a), Indicates that the rotation angle around the tool z axis is The rotation matrix, Tran(k,z off ) indicates that the translation distance along the z-axis of the tool is z off The translation matrix of Rot(i,Σ) represents the rotation matrix of the gear to be processed with an angle of Σ around the x-axis. Tran(i,a) represents the translation matrix of the gear to be processed with a translation distance a along the x-axis. Indicates that the rotation angle around the z-axis of the gear to be processed is The rotation matrix of .

6. The design method of a cylindrical gear turning tool with no structured clearance angle according to claim 1, characterized in that: The working clearance angle α of the main cutting edges on both sides of the tool in step S6 e Using barrel-shaped conjugate surface S (2) It is expressed as the angle between the two normal vectors on the meshing line on the tool back face, and the calculation formula is: a e =<N t ,N c > Among them, N t is the normal vector of the barrel-shaped conjugate surface on the meshing line at a certain moment, N c is the normal vector of the tool flank face on the engagement line.

7. The design method of a cylindrical gear turning tool with no structured clearance angle according to claim 1, characterized in that: The selection range of the tool rake angle in step S7 is 5° to 15°.

8. The method for designing a cylindrical gear turning tool with no structured clearance angle according to claim 1, characterized in that: In step S8, the tool rake face edge shape S γ The calculation formula is: S γ =Tran(i,r t )Tran(k,z off )Rot(i,β t )Rot(j,-γ0) Among them, r t The offset is z off Tool radius at time, Tran(i,r t ) indicates that the translation distance along the tool x-axis is r t The translation matrix, Tran(k,z off ) indicates that the translation distance along the z-axis of the tool is z off The translation matrix, Rot(i,β t ) indicates that the tool rotates around the x-axis by an angle of β t Rot(j,-γ0) represents the rotation matrix of the tool with an angle of -γ0 around the y-axis.

Images