Axial double-arc tooth cone worm gear pair and manufacturing method

Abstract

The invention discloses an axial double-arc tooth spiroid worm pair and a manufacturing method, and belongs to the technical field of gear transmission, and the manufacturing method comprises the following steps: S1, adopting a double-arc edge forming tool, and machining to form a spiroid worm helical surface with two sections of tangent arc tooth profiles under a preset fixed connection coordinate system through composite relative motion of the tool and a spiroid worm blank; s2, a conical hob which is in conjugate matching with the helical surface of the spiroid worm is adopted to perform multi-motion collaborative hobbing machining on the blank of the spiroid worm gear, and a double-arc tooth surface is generated; and S3, the double-arc tooth bevel worm and the double-arc bevel worm gear are assembled, and the axial double-arc tooth bevel worm pair in meshing transmission is formed. The double-arc tooth profile design is adopted, and the special double-arc blade forming tool is used for machining, so that the thread meshing length of the spiroid worm accounts for more than 95% of the total length, and the meshing contact ratio is improved; the coverage rate of the tooth surface contact area of the bevel worm gear reaches 90% or above, instantaneous contact lines are evenly distributed and are not crossed, the tooth surface contact stress is reduced, and the transmission stability and the heavy load bearing capacity are improved.

Description

Technical Field

[0001] This invention relates to the field of gear transmission technology, and in particular to an axial double circular arc bevel worm gear pair and its manufacturing method. Background Technology

[0002] As a special type of spatially interleaved shaft transmission, the bevel worm gear drive, with its advantages such as easily adjustable backlash and high transmission ratio and strong load-bearing capacity due to its single-sided offset structure, has a promising future in various mechanical systems. However, the traditional manufacturing methods of bevel worm gear pairs have many technical bottlenecks, which seriously restrict the improvement of their transmission performance.

[0003] First, the tooth profile design and machining adaptability are poor. Traditional bevel worm gears mostly use single circular arc or involute tooth profiles, and ordinary straight-edged or single circular arc-edged cutting tools are mostly used during machining. This results in low tooth surface meshing overlap. The effective meshing length of the bevel worm thread is only 80% to 90% of the total thread length. The contact area of ​​the bevel worm gear tooth surface is narrow, and the local stress concentration is severe, which easily leads to failure phenomena such as tooth surface wear and pitting.

[0004] Furthermore, the machining process lacks stability. The conjugate error between the production surface of the traditional conical hob and the helical surface of the conical worm gear is relatively large, usually between 0.01mm and 0.02mm. During hobbing, the motion coordination between the conical hob and the conical worm gear blank is poor, which easily produces defects such as tooth surface ripples and tooth direction deviation. In the assembly process, there is a lack of precise reference positioning methods, and the meshing clearance is difficult to control, resulting in poor transmission smoothness and high noise.

[0005] Furthermore, traditional manufacturing methods have poor adaptability to bevel worm gear pairs with different parameters, insufficient tool versatility, and the need to redesign and manufacture tools when changing parameters, resulting in low production efficiency and high costs. Therefore, there is an urgent need to develop a manufacturing method for axial double circular arc bevel worm gear pairs that can achieve high overlap, high conjugate accuracy, and excellent lubrication and heat dissipation performance to meet the high-performance requirements of modern industry for transmission systems. Summary of the Invention

[0006] To address the technical problems of poor tooth profile design and machining adaptability and insufficient machining process stability in traditional bevel worm gear manufacturing methods, this invention provides an axial double-circular-arc bevel worm gear pair and its manufacturing method. The transmission pair of this invention exhibits extremely high overlap, ensuring that over 95% of the total thread length of the bevel worm effectively participates in the meshing process. Simultaneously, the tooth surface of the bevel worm wheel is almost completely covered by the meshing area. The instantaneous contact lines of the worm pair are evenly and sparsely distributed, with no crossing phenomenon; this characteristic greatly improves heat dissipation and lubrication. The lubrication angle and induced principal curvature of this transmission are maintained at a low level, providing favorable conditions for the formation of a high-quality lubricating oil film between the teeth, while simultaneously reducing the contact stress level. In summary, the axial double-circular-arc bevel worm gear pair exhibits superior meshing performance.

[0007] The technical solution adopted in this invention, which relates to an axial double-circular-arc bevel worm gear pair and its manufacturing method, is as follows:

[0008] An axial double circular arc bevel tooth worm gear pair includes an axial double circular arc bevel tooth worm gear and a double circular arc bevel worm wheel for meshing transmission.

[0009] A method for manufacturing an axial double circular arc bevel worm gear pair includes the following steps:

[0010] S1. Using a double-circular-arc forming tool, a conical worm helical surface with two tangent circular arc tooth profiles is formed by the compound relative motion between the tool and the conical worm blank under a preset fixed coordinate system.

[0011] S2. A conical hob, which is conjugate to the spiral surface of the conical worm gear, is used to perform multi-motion coordinated hobbing on the conical worm gear blank to generate a double circular arc tooth surface.

[0012] S3. The axial double circular arc bevel worm gear machined in S1 and the double circular arc bevel worm wheel generated in S2 are aligned and assembled according to the preset center distance and assembly datum to form an axial double circular arc bevel worm gear pair for meshing transmission.

[0013] A further improvement to the technical solution of the present invention is that: in step S1, the two arc segments of the double-arc forming tool correspond to the tooth tip-indexing cone segment respectively. and pitch cone-tooth root section ,when When the cutting tool is used to turn the i-face of the bevel worm, the i-face is the helical surface facing the small end of the bevel worm; when When turning, the cutting tool is used to machine the e-face of the bevel worm, which is the helical surface facing the large end of the bevel worm.

[0014] A further improvement to the technical solution of the present invention lies in: the radius of the double-arc forming tool. and The value of is generally , and The value of is generally ,in Let be the module of the generatrix of the double-circular-arc bevel worm gear along the axial direction, and and .

[0015] A further improvement to the technical solution of this invention lies in the fact that the pressure angles of the i-face and e-face of the axial double-circular-arc bevel worm are not equal, with the pressure angle of the i-face being... The value of is generally e-face pressure angle The value of is generally .

[0016] A further improvement of the technical solution of the present invention is that: a fixed coordinate system is preset in step S1. It is rigidly connected to the axial double circular arc bevel worm gear, and the unit vector Aligned with the axis of the conical worm, pointing positively towards the large end of the conical worm; origin of coordinates. It is located on the axis of the tapered worm and coincides with the midpoint of the thread length.

[0017] A further improvement to the technical solution of this invention lies in the following: in step S1, the conical worm blank rotates relative to the double-circular-edge forming tool; any position can be considered as the initial position along the generatrix of the conical worm, i.e., the spherical vector. ,move Received, among which θ is the helical parameter of the tapered worm along its generatrix, and θ is the helical parameter of the double-circular-edge cutting tool around its axis. The angle through which the axis rotates.

[0018] The technological advancements achieved by this invention due to the adoption of the above technical solutions are as follows:

[0019] This invention employs a double-circular-arc tooth profile design and is processed using a special double-circular-arc forming tool, enabling more than 95% of the entire length of the conical worm thread to participate in meshing, thereby improving the meshing overlap. The contact area coverage of the conical worm gear tooth surface reaches more than 90%, and the instantaneous contact line is evenly distributed and does not cross, reducing the tooth surface contact stress and improving the transmission smoothness and heavy load bearing capacity.

[0020] This invention, through differentiated pressure angle design (different pressure angles on the i-side and e-side) and precise tooth surface conjugate machining, controls the inter-tooth lubrication angle to below 20°, which is conducive to the formation of a stable lubricating oil film and improves the lubrication effect; the evenly distributed contact line and wide contact area increase the heat dissipation area, reduce the maximum temperature of the tooth surface during operation, and extend the service life of the transmission pair. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of a double-circular-arc forming tool used to turn an axial double-circular-arc bevel worm gear according to a manufacturing method of an axial double-circular-arc bevel worm gear according to the present invention.

[0022] Figure 2 This is a schematic diagram of the axial double circular arc toothed bevel worm gear meshing coordinate system in the manufacturing method of the axial double circular arc toothed bevel worm gear pair of the present invention;

[0023] Figure 3 This is a projection view of the meshing area within the axial section of the conical worm gear when the i-face of the conical worm gear and the convex surface of the conical worm wheel mesh in an embodiment of the present invention;

[0024] Figure 4 This is a projection view of the meshing area within the axial section of the conical worm wheel when the i-face of the conical worm and the convex surface of the conical worm wheel mesh in an embodiment of the present invention;

[0025] Figure 5 This is a projection view of the meshing area within the axial section of the conical worm gear when the e-surface of the conical worm gear and the concave surface of the conical worm wheel mesh in an embodiment of the present invention;

[0026] Figure 6 This is a projection view of the meshing area within the axial section of the conical worm wheel when the e-surface of the conical worm gear and the concave surface of the conical worm wheel mesh in an embodiment of the present invention;

[0027] Figure 7 A schematic diagram of the structure of an axial double circular arc toothed bevel worm gear pair according to the present invention.

[0028] In the attached diagram: 1. Double circular arc bevel worm gear; 2. Double circular arc bevel worm wheel. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings. In the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessarily obscuring the concept of this invention.

[0030] like Figure 1-5 As shown, the present invention provides an axial double circular arc bevel worm gear pair and a manufacturing method thereof, used to manufacture an axial double circular arc bevel worm gear 1 and a double circular arc bevel worm wheel 2. The helical surface of the axial double circular arc bevel worm gear 1 is formed by turning with a double circular arc cutting tool; the double circular arc bevel worm wheel 2 is formed by generating with a double circular arc cutting conical hob that is consistent with the helical surface of the axial double circular arc bevel worm gear 1. The double circular arc bevel worm gear 1 and the double circular arc bevel worm wheel 2 mesh to form a double circular arc bevel worm gear pair.

[0031] This invention includes the following steps:

[0032] S1. Manufacturing axial double circular arc bevel worm gear 1:

[0033] Establish coordinate system It is fixedly connected to the axial double circular arc bevel worm gear 1, coordinate system unit vector It coincides with the axis of the conical worm, with its positive direction pointing towards the large end of the conical worm. The point is located on the axis of the tapered worm and coincides with the midpoint of its thread length;

[0034] At the initial position, the unit vector and Zhang Cheng's axial section of the helical surface of the double-circular-arc bevel worm gear 1, with the double-circular-arc cutting tool located within this axial section, unit vector The intersection point with the indexing cone of the double circular arc bevel worm gear along... and The distance between the points is equal to the radius of the midpoint of the pitch circle of the axial double-circular-arc bevel worm gear 1. The tool radius of the section from the worm tooth tip to the pitch cone and from the worm tooth pitch cone to the tooth root are respectively... and ;when When the cutting tool is used to turn the i-face of the bevel worm, the i-face is the helical surface facing the small end of the bevel worm; when When turning, the cutting tool is used to machine the e-face of the bevel worm, which is the helical surface facing the large end of the bevel worm; the two circular arcs of the double-circular-edge cutting tool are tangent at the worm's indexing cone, with the point of tangency along the spherical vector. With spherical vector The distance is equal to , The axial tooth thickness of the tapered worm gear. The cone half-angle of the tapered worm gear; the centers of the two arcs of the double-circular-edge cutting tool are respectively and And all of them lie on their common normal, the common normal and the spherical vector The included angle is equal to the pressure angle of the axial double circular arc bevel worm gear 1. ;

[0035] A double-circular-arc cutting tool turns a bevel worm blank to form the helical surface of an axial double-circular-arc bevel worm 1. The bevel worm blank rotates relative to the double-circular-arc cutting tool. Any position can be considered as the initial position along the generatrix of the bevel worm, i.e., the spherical vector. ,move Received, among which θ is the helical parameter of the tapered worm along its generatrix, and θ is the helical parameter of the double-circular-edge cutting tool. The angle through which the axis rotates.

[0036] S2. Manufacturing the double circular arc conical worm gear 2:

[0037] The blank of the double circular arc conical worm gear 2 is cut using an axial double circular arc bevel hob. The production surface of the hob is completely consistent with the helical surface of the axial double circular arc bevel worm 1 obtained in step one. The static coordinate system of the blank of the double circular arc conical worm gear 2 is: Unit basis vector The axis of the double circular arc conical worm gear 2 coincides with the axis of the double circular arc conical worm gear, and its positive direction points to the large end of the double circular arc conical worm gear. (Unit vector) Along the direction of the common perpendicular line between the axis of the conical worm and the axis of the double circular arc conical worm wheel 2; point and These are the feet of the perpendiculars on the axis of the conical worm and the axis of the double-circular-arc conical worm gear 2, respectively. The center distance of the axial double circular arc bevel worm gear pair is point From the worm shaft axis to the origin The distance is , and These are the installation distance and thread length of the tapered worm gear, respectively.

[0038] During the process of generating the double circular arc bevel worm gear 2 with a tapered hob, both the tapered hob and the blank of the double circular arc bevel worm gear 2 rotate around their respective axes, and the tapered hob performs a linear translational feed motion along the axis of the double circular arc bevel worm gear 2; when the distance between the axes of the tapered hob and the double circular arc bevel worm gear 2 along their common perpendicular is equal to the center distance of the axial double circular arc bevel worm gear pair... At this time, the tapered hob stops its feed motion.

[0039] S3. Assemble an axial double circular arc bevel worm gear pair:

[0040] The axial double-circular-arc bevel worm gear 1 manufactured according to S1 and the double-circular-arc bevel worm wheel 2 manufactured according to S2, with their center distances... The components are assembled to form an axial double circular arc toothed bevel worm gear pair.

[0041] Double-circular-edge turning tool radius and The value of is generally , and The value of is generally ,in Let be the module of the generatrix of the axial double-circular-arc bevel worm gear, and and .

[0042] The pressure angles on the i-face and e-face of the axial double-circular-arc bevel worm gear 1 are not equal; the pressure angle on the i-face is... The value of is generally e-face pressure angle The value of is generally .

[0043] Example 1

[0044] In this embodiment, the axial double-circular-arc bevel worm gear 1 is right-handed, with a number of... The bevel worm gear pair has a transmission ratio of 68. The manufacturing method of this embodiment adopts the following steps:

[0045] S1. Manufacturing axial double circular arc bevel worm gear 1:

[0046] Establish coordinate system It is fixedly connected to the axial double circular arc bevel worm gear 1, coordinate system unit vector It coincides with the axis of the conical worm, with its positive direction pointing towards the large end of the conical worm. The point is located on the axis of the tapered worm and coincides with the midpoint of its thread length;

[0047] At the initial position, the unit vector and Zhang Cheng's axial section of the helical surface of the double-circular-arc bevel worm gear 1, with the double-circular-arc cutting tool located within this axial section, unit vector The intersection point with the indexing cone of the double circular arc bevel worm gear along... and The distance between the points is equal to the radius of the midpoint of the pitch circle of the axial double-circular-arc bevel worm. ,Pick The tool radius of the section from the worm tooth tip to the pitch cone and from the worm tooth pitch cone to the tooth root are respectively... and ,Pick , , , ;when When the cutting tool is used to turn the i-face of the bevel worm, the i-face is the helical surface facing the small end of the bevel worm; when When turning, the cutting tool is used to machine the e-face of the bevel worm, which is the helical surface facing the large end of the bevel worm; the two circular arcs of the double-circular-edge cutting tool are tangent at the worm's indexing cone, with the point of tangency along the spherical vector. With spherical vector The distance is equal to , The axial tooth thickness of the tapered worm gear. Let be the cone half-angle of the conical worm, take , The centers of the two arcs of the double-circular-edge cutting tool are respectively and And all of them lie on their common normal, the common normal and the spherical vector The included angle is equal to the pressure angle of the axial double circular arc bevel worm. ,Pick , ;

[0048] A double-circular-arc cutting tool turns a bevel worm blank to form the helical surface of an axial double-circular-arc bevel worm 1. The bevel worm blank rotates relative to the double-circular-arc cutting tool. Any position can be considered as the initial position along the generatrix of the bevel worm, i.e., the spherical vector. ,move Received, among which θ is the helical parameter of the tapered worm along its generatrix, and θ is the helical parameter of the double-circular-edge cutting tool. The angle through which the axis rotates is taken. .

[0049] S2. Manufacturing the double circular arc conical worm gear 2:

[0050] The blank of the double circular arc conical worm gear 2 is cut using an axial double circular arc bevel hob. The production surface of the hob is completely consistent with the helical surface of the axial double circular arc bevel worm 1 obtained in step one. The static coordinate system of the blank of the double circular arc conical worm gear 2 is: Unit basis vector The axis of the double circular arc conical worm gear 2 coincides with the axis of the double circular arc conical worm gear, and its positive direction points to the large end of the double circular arc conical worm gear. (Unit vector) Along the direction of the common perpendicular line between the axis of the conical worm and the axis of the double circular arc conical worm wheel 2; point and These are the feet of the perpendiculars on the axis of the conical worm and the axis of the double-circular-arc conical worm gear 2, respectively. The center distance of the axial double circular arc bevel worm gear pair is point From the worm shaft axis to the origin The distance is , and These are the installation distance and thread length of the tapered worm gear, respectively. , , ;

[0051] During the process of generating the double circular arc bevel worm gear 2 with a tapered hob, both the tapered hob and the blank of the double circular arc bevel worm gear 2 rotate around their respective axes, and the tapered hob performs a linear translational feed motion along the axis of the double circular arc bevel worm gear 2; when the distance between the axes of the tapered hob and the double circular arc bevel worm gear 2 along their common perpendicular is equal to the center distance of the axial double circular arc bevel worm gear pair... At this time, the tapered hob stops its feed motion.

[0052] S3. Assemble an axial double circular arc bevel worm gear pair:

[0053] The axial double-circular-arc bevel worm gear 1 manufactured according to S1 and the double-circular-arc bevel worm wheel 2 manufactured according to S2, with their center distances... The components are assembled to form an axial double circular arc toothed bevel worm gear pair.

[0054] Double-circular-edge turning tool radius and The value of is generally , and The value of is generally ,in Let be the module of the generatrix of the axial double-circular-arc bevel worm gear, and and In this embodiment , , , , ;

[0055] The pressure angles on the i-face and e-face of the axial double-circular-arc bevel worm gear 1 are not equal; the pressure angle on the i-face is... The value of is generally e-face pressure angle The value of is generally In this embodiment, , ;

[0056] The axial double circular arc toothed bevel worm gear pair manufactured according to the above manufacturing method.

[0057] The aforementioned axial double-circular-arc bevel worm gear pair has the bevel worm i-face meshing with the bevel worm wheel convex surface. The projection diagrams of the meshing area within the axial sections of the bevel worm and bevel worm wheel are shown below. Figures 3 to 4 As shown; the conical worm gear's e-surface meshes with the concave surface of the conical worm wheel, and the projections of the meshing area within the axial sections of the conical worm gear and conical worm wheel are respectively shown in the figures below. Figures 5 to 6 As shown.

[0058] exist Figure 3 In the context of the tapered worm gear, the projection of the contact area on the i-face into its axial section is the region. ,in The conjugate line of the small end of the conical worm gear on the helical surface of the conical worm. The conjugate line of the bevel worm gear tooth tip on the helical surface of the bevel worm. The conjugate line of the large end of the conical worm gear on the helical surface of the conical worm. For the tip line of the conical worm gear, This is the dividing line between the two circular arc helical surfaces of the conical worm. Figure 4 In the middle, the contact area of ​​the convex surface of the conical worm gear is the region. ,in For the small end line of the conical worm gear, For the tip line of the bevel worm gear, For the large end line of the conical worm gear, The conjugate line between the tip of the conical worm tooth and the tooth surface of the worm wheel is denoted as . It is the conjugate line of the dividing line between the two circular arc helical surfaces of the conical worm on the tooth surface of the worm wheel.

[0059] exist Figure 5 In the context of the conical worm gear, the projection of the contact area on the e-surface into its axial section is the region. ,in For the small end line of the tapered worm, The conjugate line of the bevel worm gear tooth tip on the helical surface of the bevel worm. The conjugate line of the large end of the conical worm gear on the helical surface of the conical worm. For the tip line of the conical worm gear, This is the dividing line between the two circular arc helical surfaces of the conical worm. Figure 6 In the middle, the contact area of ​​the concave surface of the conical worm gear is a region. ,in The conjugate line of the small end of the conical worm on the tooth surface of the conical worm gear. For the tip line of the bevel worm gear, For the large end line of the conical worm gear, The conjugate line between the tip of the conical worm tooth and the tooth surface of the worm wheel is denoted as . It is the conjugate line of the dividing line between the two circular arc helical surfaces of the conical worm on the tooth surface of the worm wheel.

[0060] Combination Figure 3 and Figure 5 It can be seen that the working lengths of both helical surfaces of the tapered worm are relatively long, close to the total length of its thread. In comparison, the working length of the i-face of the tapered worm is slightly longer than that of the e-face.

[0061] Combination Figure 4 and Figure 6 It can be seen that the contact areas of the convex and concave surfaces of the conical worm gear are relatively wide, almost covering the entire tooth surface of the conical worm gear. Moreover, the instantaneous contact lines are evenly distributed without intersection within the contact area of ​​the entire tooth surface of the conical worm gear, which is beneficial to the heat dissipation and lubrication of the conical worm pair.

[0062] To further illustrate the meshing performance of the axial double-circular-arc bevel worm gear pair obtained above, three meshing points (a, b, and c) are sequentially selected along the direction from the tooth tip to the tooth root on each instantaneous contact line of the bevel worm gear tooth surface, and the induced principal curvature at these meshing points is calculated. and lubrication angle Some of the numerical results are listed in Table 1:

[0063] Table 1

[0064]

[0065] Table 1 shows that the induced principal curvature of the axial double-circular-arc bevel worm gear pair maintains a consistent sign throughout the entire meshing region and is always positive, indicating that no curvature interference boundaries appear on the entire tooth surface, thus avoiding undercutting of the bevel worm wheel. The low value of the induced principal curvature across the entire contact area indicates the absence of significant high-stress contact points. On the same tooth height line of the bevel worm wheel, the value of the induced principal curvature decreases from the small end to the large end, correspondingly reducing the tooth surface contact stress while gradually increasing the tooth surface load-bearing capacity. Furthermore, the values ​​of the lubrication angles throughout the entire meshing region are generally small, all less than 20°, indicating that an effective lubricating oil film easily forms between the teeth of the bevel worm gear pair, resulting in superior lubrication performance of the transmission pair.

[0066] In the above embodiments, an axial double-circular-arc bevel worm gear pair and its manufacturing method are provided. This invention employs a double-circular-arc tooth profile design and is processed using a dedicated double-circular-arc cutting tool, enabling the entire length of the bevel worm thread to participate in meshing, thus improving the meshing overlap ratio. The bevel worm gear tooth surface contact area coverage reaches over 90%, with uniform and non-intersecting instantaneous contact lines, reducing tooth surface contact stress and improving transmission smoothness and heavy-load capacity. This invention utilizes a differentiated pressure angle design (… Face and Different surface pressure angles and precise tooth surface conjugate machining keep the inter-tooth lubrication angle below 20°, which helps to form a stable lubricating oil film and improve the lubrication effect; the evenly distributed contact line and wide contact area increase the heat dissipation area, reduce the maximum temperature of the tooth surface during operation, and extend the service life of the transmission pair.

[0067] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the concept and scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the inventive concept should fall within the protection scope of the present invention. All technical contents for which protection is sought in this invention are fully described in the claims.

Claims

1. An axial double-circular-arc bevel worm gear pair, characterized in that: It includes an axial double circular arc bevel worm gear (1) and a double circular arc bevel worm wheel (2) for meshing transmission.

2. A method for manufacturing an axial double-circular-arc bevel worm gear pair, characterized in that, The method for manufacturing the axial double circular arc bevel worm gear pair according to claim 1 includes the following steps: S1. Using a double-circular-arc forming tool, a conical worm helical surface with two tangent circular arc tooth profiles is formed by the compound relative motion between the tool and the conical worm blank under a preset fixed coordinate system. S2. A conical hob, which is conjugate to the spiral surface of the conical worm gear, is used to perform multi-motion coordinated hobbing on the conical worm gear blank to generate a double circular arc tooth surface. S3. The axial double circular arc bevel worm gear (1) machined in S1 and the double circular arc bevel worm wheel (2) generated in S2 are aligned and assembled according to the preset center distance and assembly datum to form an axial double circular arc bevel worm gear pair for meshing transmission.

3. The manufacturing method of an axial double-circular-arc bevel worm gear pair according to claim 2, characterized in that: In step S1, the two arcs of the double-arc forming tool correspond to the tooth tip and the indexing cone section, respectively. and pitch cone-tooth root section ,when When the cutting tool is used to turn the i-face of the bevel worm, the i-face is the helical surface facing the small end of the bevel worm; when When turning, the cutting tool is used to machine the e-face of the bevel worm, which is the helical surface facing the large end of the bevel worm.

4. A method for manufacturing an axial double-circular-arc bevel worm gear pair according to claim 3, characterized in that: The radius of the double-circular-arc forming tool and The value of is generally , and The value of is generally ,in Let be the module of the generatrix of the double circular arc bevel worm (1) along the axial direction, and and .

5. A method for manufacturing an axial double-circular-arc bevel worm gear pair according to claim 3, characterized in that: The pressure angles of the i-face and e-face of the axial double circular arc bevel worm (1) are not equal, and the pressure angle of the i-face is... The value of is generally e-face pressure angle The value of is generally .

6. A method for manufacturing an axial double-circular-arc bevel worm gear pair according to claim 2, characterized in that, In step S1, a fixed coordinate system is preset. It is rigidly connected to the axial double circular arc bevel worm (1), and the unit vector Aligned with the axis of the conical worm, pointing positively towards the large end of the conical worm; origin of coordinates. It is located on the axis of the tapered worm and coincides with the midpoint of the thread length.

7. A method for manufacturing an axial double-circular-arc bevel worm gear pair according to claim 2, characterized in that: In step S1, the conical worm blank rotates relative to the double-circular-edge forming tool; any position can be considered as the initial position along the generatrix of the conical worm, i.e., the spherical vector. ,move Received, among which θ is the helical parameter of the tapered worm along its generatrix, and θ is the helical parameter of the double-circular-edge cutting tool around its axis. The angle through which the axis rotates.

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