A three-dimensional structure modeling method for a variable rake angle toroidal worm gear hob

Abstract

The present invention discloses a three-dimensional structural modeling method for a variable rake angle toroidal worm gear hob. The method considers designing the rake surface of each tooth as a separate free-form surface, so that the rake angle of each tooth can be varied according to the design requirements. The CAD modeling of the worm gear hob is completed based on this method, which not only simplifies the design and manufacturing process of the toroidal worm gear hob, but also improves the cutting performance at each position on the hob edge line according to the actual processing task by improving the rake angle at each position on the cutting edge line of each tooth.

Description

Technical Field

[0001] The invention relates to the technical field of design and manufacturing of toroidal worm gear hobs, in particular to a three-dimensional structure modeling method of a toroidal worm gear hob with a variable rake angle. Background Art

[0002] Compared to cylindrical worm gears, toroidal worm gears offer advantages such as greater load capacity, compact size, high transmission efficiency, and long service life. Therefore, they are widely used in high-efficiency, heavy-load applications. However, the meshing theory of toroidal worm gears is complex, and meshing transmission performance is highly sensitive to errors and deformation, requiring high-precision manufacturing. The toroidal worm gear hob used to machine the worm gear is a specialized tool with a complex structure and is difficult to design and manufacture. The rake angles of the cutting edges on both sides of the existing straight chip groove worm gear hob are too different, that is, one side has a positive rake angle and the other side has a negative rake angle; the rake face of the spiral chip groove worm gear hob can improve the rake angles on the tooth indexing annulus on the left and right sides, but the rake angles at the tooth top and tooth root are still not balanced, and it is even more impossible to design a hob with a specified rake angle according to actual processing requirements. In the actual processing of some worm gears, the cutting amount at each point on the hob tooth edge line is different, and the cutting force at each point is also different from the tooth top to the tooth root, which requires the rake angle on the cutting edge line to change everywhere. This traditional slotted design method of the integral worm gear hob cannot achieve the above design requirements. Therefore, it is necessary to propose a new enveloping annular worm gear hob design method to meet the cutting performance at different positions on the tooth cutting edge to meet the requirements of different cutting amounts, that is, to achieve that the rake angles on the left and right sides of the rake face can be freely controlled according to the needs of the tool under different working conditions.

[0003] Chinese patent ZL201710542592.3 "CAD / CAM method for toroidal worm gear hobs based on universal CNC milling machines" proposes a CAD method for the geometric structure of a toroidal worm gear hob, and a CAM method that can complete processing on a four-axis or higher-axis universal CNC milling machine. It is a method for automating worm gear hobs through only two clamping processes and one heat treatment process. However, this method mainly simplifies the worm gear hob processing process. The construction of the hob geometric model still uses the method of opening straight grooves or spiral grooves. It does not solve the disadvantage of the difference in the front angles on the left and right sides of the hob, and it is impossible to obtain a worm gear hob with a variable front angle according to the design requirements. Summary of the Invention

[0004] The purpose of the present invention is to provide a three-dimensional structural modeling method for a variable rake angle toroidal worm gear hob, that is, considering the front cutting surface of each tooth as a separate free-form surface for design, so that the rake angle of each tooth can be changed everywhere according to the design requirements, and completing the CAD modeling of the worm gear hob based on this method, which not only simplifies the design and manufacturing process of the toroidal worm gear hob, but also improves the cutting performance of each position on the hob edge line according to the actual processing task by improving the rake angle of each position on the cutting edge line of each tooth.

[0005] The object of the present invention is achieved by: a method for modeling a three-dimensional structure of a variable rake angle toroidal worm gear hob, comprising the following steps:

[0006] S1, a step of generating a left cutting edge curve on the left helical surface, wherein, in step S1, according to the helical surface forming principle of the toroidal worm gear hob, the point families of the toroidal spiral lines on the left helical surface of the hob are obtained respectively, k spiral lines (1) are selected, and a space curve (2) extending along the tooth height direction on the left helical surface is obtained, the space curve intersects with several spiral lines of the left helical surface and forms several intersection points, and the intersection points meet two constraints: S11, the angle between the tangent vector along the toroidal spiral line and the tangent vector along this space curve is variable everywhere according to design requirements (is a certain value and is not equal to each other); S12, the curvature of the space curve is minimum at the intersection point; at this time, the space curve can be uniquely determined, that is, the angle between the space curve (2) and the toroidal spiral lines on the left helical surface is a certain value and is not equal to each other, which can satisfy that the front angle at each intersection point (3) is variable everywhere according to design requirements;

[0007] S2, step of generating the right cutting edge curve (4), step S2 is the same as step S1;

[0008] S3, a step of fitting a front top edge curve (7) and a front groove bottom curve (8), wherein the left cutting edge curve (2) intersects with the left tooth top spiral line (6) to form an upper left point, the right cutting edge curve (4) intersects with the right tooth top spiral line (6) to form an upper right point, and the upper left point and the lower right point are connected along the tooth top surface to fit the front top edge curve (7); the left cutting edge curve (2) intersects with the left tooth root spiral line (5) to form a lower left point, the right cutting edge curve (4) intersects with the right tooth root spiral line (5) to form a lower right point, and the lower left point and the lower right point are connected along the tooth root surface to fit the front groove bottom curve (8);

[0009] S4, the step of fitting the left cutting edge curve (2), the right cutting edge curve (4), the front top edge curve (7) and the front groove bottom curve (8) into the rake face (9) of a single tooth, thereby completing the variable rake angle construction of the rake face (9) of the single tooth.

[0010] Furthermore, it also includes:

[0011] S5, moving the intersection of the left cutting edge curve (2) and each annular spiral line backward along the spiral line by a length of (m / n)-2 points, wherein m represents the number of equally spaced points contained in each spiral line, and n represents the number of complete teeth contained in each spiral line;

[0012] S6, obtaining a plurality of points (10) located on the spiral lines of each annular surface, and fitting the moved plurality of points (10) to obtain a left edge line (11) of the back cutting surface;

[0013] S7, similarly obtain the right edge line of the flank (12);

[0014] S8, taking the intersection point (13) of the left side line (11) and the left tooth top helix line (6), and the intersection point (14) of the right side line (12) and the right tooth top helix line (6), and fitting to obtain the tooth top curve (15) of the flank face;

[0015] S9, taking the intersection point (16) of the left side line (11) and the left tooth root helix line (5), and the intersection point (17) of the right side line (12) and the right tooth root helix line (5), and fitting to obtain the groove bottom curve (18) of the flank face;

[0016] S10, fitting the flank surface (19) by the left side line (11), the right side line (12), the tooth top curve (15) and the groove bottom curve (18), completing the construction of the flank surface (19) of a single tooth.

[0017] Furthermore, it also includes:

[0018] S11, importing the calculated three-dimensional coordinate data of the left helical surface point family and the right helical surface point family of the hob into a three-dimensional modeling software, and fitting the left helical surface (20) and the right helical surface (21) of the hob respectively;

[0019] S12, performing curved surface lofting by the helical lines of the tooth top annular surfaces on the left and right sides to obtain the tooth top surface (22) of a single cutter tooth, and performing curved surface lofting by the helical lines of the tooth root annular surfaces on the left and right sides to obtain the groove bottom surface (23) of a single cutter tooth.

[0020] Furthermore, it also includes:

[0021] S13, the front cutting edge (9), the back cutting edge (19), the left helical surface (20), the right helical surface (21), the tooth top surface (22), and the groove bottom surface (23) are all imported into the three-dimensional modeling software, and the front cutting edge (9), the back cutting edge (19), the left helical surface (20), the right helical surface (21), the tooth top surface (22), and the groove bottom surface (23) are combined into a three-dimensional solid model of a complete tooth, thereby completing the variable rake angle construction of the geometric structure of a single tooth.

[0022] Furthermore, it also includes:

[0023] S14, selecting the intersection point L1 of the left cutting edge curve (2) of the first tooth rake face (9) and the indexing annular spiral line, moving the intersection point along the spiral line by a length of m / n points to obtain the intersection point L2 of the left cutting edge curve of the second tooth rake face and the indexing annular spiral line, and modeling the second tooth based on the position of the intersection point;

[0024] S15, repeating steps S1-S4 to complete the modeling operation of the rake face of the second tooth, so that the angles between the rake face and the left and right helical surfaces are of a certain value and are not equal, that is, the rake angles at each intersection are variable according to the design requirements;

[0025] S16, moving the points on the left and right side lines of the flank surface of the first tooth along the spiral direction by the same length (i.e., the length of m / n points), thereby fitting the left and right side lines of the flank surface of the second tooth;

[0026] S17. The construction method of the left and right spiral surfaces, tooth top surface, and groove bottom surface of the second tooth is exactly the same as the construction method of the first tooth in steps S11-12, and then the three-dimensional model construction of the second tooth geometric structure is completed.

[0027] Also includes:

[0028] Repeat the above steps to complete the construction of n teeth on the entire spiral line, and discard the remaining spiral surface that is not enough to construct a tooth;

[0029] Then, all the teeth distributed on other spiral lines are constructed by means of an equidistant circular array, and finally a complete three-dimensional solid model of the enveloping toroidal worm gear hob is obtained.

[0030] All of the above steps are performed in CAD software, utilizing the 3D modeling function of the CAD software.

[0031] The beneficial effects of the present invention are:

[0032] The method proposed in the present invention can facilitate the design of a toroidal worm gear hob with a variable rake angle, that is, the rake angles of the cutting edges on the left and right sides of a single tooth on the hob can be changed everywhere according to the design requirements. This method simplifies the hob design and processing technology while ensuring that the rake angles on the cutting edge lines of each tooth can be changed everywhere, thereby obtaining a three-dimensional model of the toroidal worm gear hob in which the cutting performance at different processing positions of each cutting edge meets the actual cutting amount and cutting force requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a schematic diagram showing the principle of constructing a variable rake angle for a single-tooth rake face of a toroidal worm gear hob according to the present invention.

[0034] Figure 2 This is a diagram showing the key features of the rake and flank surfaces of a single tooth of the toroidal worm gear hob of the present invention.

[0035] Figure 3 This is a diagram showing the location of the helix line and throat point of the toroidal worm gear hob of the present invention.

[0036] Figure 4 This is a three-dimensional model diagram of 12 teeth on a spiral line of the toroidal worm gear hob established by the present invention.

[0037] Figure 5 This is a three-dimensional model diagram of the 4 heads and 48 teeth of the toroidal worm gear hob established by the present invention.

[0038] Figure 6 This is a complete three-dimensional model diagram of the toroidal worm gear hob established by the present invention. DETAILED DESCRIPTION

[0039] The following is combined with Figure 1-6 The present invention is further described with reference to the accompanying drawings and specific examples.

[0040] Taking the plane double enveloping toroidal worm gear hob as an example, its relevant parameters are: the center distance of the toroidal worm pair a=131.5mm, the radius of the hob tooth top circle R a0 =40mm, hob tooth root circle radius R f0 =34.5mm, there are 4 hob heads, and the hob has a total of 48 teeth. The hob with a 0° rake angle and better cutting performance is used as an example.

[0041] Step 1: Construction of equal rake angle of the front cutting edge of a single tooth: Based on the geometric structure construction method of the toroidal worm gear hob, it specifically includes: using the forming principle of the spiral surface and side relief angle surface of the toroidal worm gear hob, respectively obtain the point family of each indexing toroidal spiral line on the left spiral surface of the hob, export it into a text in txt format, import the coordinates of the 91 points in the text into the 3D modeling software, and fit it into a spiral line (the spiral line is fitted by 91 equally spaced points) and select 11 equally spaced spiral lines for fitting. Combine the helical surfaces on one side and find a space curve 2. This curve is distributed on the helical surface and along the tooth height direction. The intersection of this curve and each toroidal helical line satisfies the following conditions: ① The angle between the tangent vector along the toroidal helical line at this point and the tangent vector along this space curve varies in the range of [89°, 91°], and the variation pattern is uniformly decreasing from the tooth top to the tooth root. The angle is 90° at the indexing toroidal helical line (the rake angle variation range at this time is [-1°, 1°]); ② The curvature of this space curve at this point is the smallest. This curve 2 is formed by fitting 11 intersection points 3 with each toroidal spiral line. This spatial curve is used as the left cutting edge curve 2 of the toroidal worm gear hob. The same method is used to obtain another spatial curve as the right cutting edge curve 4 of the toroidal worm gear hob. Then, the top edge curve 7 and the groove bottom curve 8 are fitted from the intersection points of the two spatial curves with the root toroidal spiral line 5 and the tooth top toroidal spiral line 6 respectively. Finally, the rake face 9 of a single tooth is fitted from these four curves, completing the construction of the rake face 9 of a single tooth with a variable rake angle.

[0042] Step 2: Construction of the flank face of a single tooth: According to the construction method of the front face of a single tooth described in step 1, the intersection of the left cutting edge curve on the constructed front face and each annular spiral line is moved along the spiral direction by a length of (m / n)-2=5 points to obtain 11 points 10 located on each annular spiral line, and the 11 moved points are used to fit the left side line 11 of the flank face. Similarly, the right side line 12 of the flank face is obtained. The intersection point 13 of the left side line and the left tooth top annular spiral line, and the intersection point 14 of the right side line and the right tooth top annular spiral line are taken to fit the tooth top curve 15 of the flank face; the intersection point 16 of the left spiral line and the left groove bottom spiral line, and the intersection point 17 of the right spiral line and the right groove bottom spiral line are taken to fit the groove bottom curve 18 of the flank face, and the flank face 19 is fitted from the left side line 11, the right side line 12 and the tooth top curve 15 and the groove bottom curve 18 to complete the construction of the flank face 19 of a single tooth.

[0043] Step 3: Construction of the left and right spiral surfaces, tooth top surfaces, and groove bottom surfaces: According to the left and right spiral surface construction method described in step 1, the calculated three-dimensional coordinate data of the left and right spiral surface point families of the hob are imported into the three-dimensional modeling software, and the left and right spiral surfaces 20 and 21 of the hob are fitted respectively. The tooth top surface 22 of a single tooth is obtained by surface lofting using the left and right tooth root annular spiral lines; the groove bottom surface 23 of a single tooth is obtained by surface lofting using the left and right tooth root annular spiral lines.

[0044] Step 4: Construction of a 3D model of a single tooth: Import the rake face 9 in step 1, the flank face 19 in step 2, the left helical face 20 and the right helical face 21 in step 3, the tooth top face 22, and the groove bottom face 23 into the 3D modeling software. The rake face 9, the flank face 19, the left helical face 20, the right helical face 21, the tooth top face 22, and the groove bottom face 23 form a 3D solid model of the tooth ( Figure 2 ) to complete the construction of a single tooth 3D model.

[0045] Step 5: Select the intersection point L1 (-16.1127915795434, 28.3245041496308, -4.70390000000024) of the first tooth rake face left cutting edge curve and the indexing annular spiral line, and the intersection point R1 (-16.1127915795434, 28.3245041496308, 4.70390000000024) of the first tooth rake face right cutting edge curve and the indexing annular spiral line, and move the two intersection points along the spiral line direction by 84 / 12 = 7 points to obtain the intersection point L1 (-16.1127915795434, 28.3245041496308, 4.70390000000024) of the second tooth rake face left cutting edge curve and the indexing annular spiral line. The intersection L2 and the intersection R2 of the right cutting edge curve of the second tooth rake face and the indexing annular surface spiral line are used to construct the left cutting edge curve of the second tooth rake face according to the method of constructing the left cutting edge curve of the rake face described in step 1. Similarly, the right cutting edge curve of the second tooth rake face is obtained, and then the intersection of these two curves and the tooth top annular surface spiral line and the tooth root annular surface spiral line are selected to fit the tooth top curve and groove bottom curve of the second tooth rake face. The rake face of the second tooth is obtained by fitting these four curves. The rake face also satisfies the change range of the angle between the rake face and the left and right spiral surfaces is [89°, 91°], that is, the change range of the rake angle is [-1°, 1°]. After completing the construction of the second tooth's rake face, move the points on the left and right side lines of the first tooth's flank face by the same length (i.e., the length of 7 points) along the spiral direction to fit the left and right side lines of the second tooth's flank face. The construction method of the left and right side spiral surfaces, tooth top surface, and groove bottom surface of the second tooth is exactly the same as step three, and then complete the establishment of the second tooth's three-dimensional model.

[0046] Repeat step 5 to complete the construction of all the teeth on the entire spiral line (a total of 12 teeth), and discard the remaining spiral surface that is not enough to construct a tooth. Then, through the method of evenly spaced circular array, all the teeth distributed on other spiral lines are constructed, and finally a complete three-dimensional solid model of the hob (containing a total of 48 teeth) is obtained ( Figure 6 ).

[0047] The above are preferred embodiments of the present invention. Those skilled in the art may make various changes or improvements based on the above. Without departing from the overall concept of the present invention, these changes or improvements should fall within the scope of protection required by the present invention.

Claims

1. A three-dimensional structure modeling method for a variable rake angle toroidal worm gear hob, characterized in that: The steps include: S1. A step of generating a left cutting edge curve (2) on the left helical surface, wherein in step S1, a space curve extending along the tooth height direction on the left helical surface is obtained, the space curve intersects with a plurality of spiral lines of the left helical surface and forms a plurality of intersection points, and the intersection points satisfy two constraints: S11. The angle between the tangent vector along the toroidal spiral line and the tangent vector along the space curve is a certain value and is not equal; S12. The curvature of the space curve is minimum at the intersection point; S2, step of generating the right cutting edge curve (4), step S2 is the same as step S1; S3, a step of fitting a front top edge curve (7) and a front groove bottom curve (8), wherein the left cutting edge curve (2) intersects with the left tooth top spiral line (6) to form an upper left point, the right cutting edge curve (4) intersects with the right tooth top spiral line (6) to form an upper right point, and the upper left point and the lower right point are connected along the tooth top surface to fit the front top edge curve (7); the left cutting edge curve (2) intersects with the left tooth root spiral line (5) to form a lower left point, the right cutting edge curve (4) intersects with the right tooth root spiral line (5) to form a lower right point, and the lower left point and the lower right point are connected along the tooth root surface to fit the front groove bottom curve (8); S4, the step of fitting the left cutting edge curve (2), the right cutting edge curve (4), the front top edge curve (7) and the front groove bottom curve (8) into the rake face (9) of a single tooth.

2. A three-dimensional structure modeling method for a variable rake angle toroidal worm gear hob according to claim 1, characterized in that: Also includes: S5, moving the intersection of the left cutting edge curve (2) and each annular spiral line backward along the spiral line by a length of (m / n)-2 points, wherein m represents the number of equally spaced points contained in each spiral line, and n represents the number of complete teeth contained in each spiral line; S6, obtaining a plurality of points (10) located on the spiral lines of each annular surface, and fitting the moved plurality of points (10) to obtain a left edge line (11) of the back cutting surface; S7, similarly obtain the right edge line of the flank (12); S8, taking the intersection point (13) of the left side line (11) and the left tooth top helix line (6), and the intersection point (14) of the right side line (12) and the right tooth top helix line (6), and fitting to obtain the tooth top curve (15) of the flank face; S9, taking the intersection point (16) of the left side line (11) and the left tooth root helix line (5), and the intersection point (17) of the right side line (12) and the right tooth root helix line (5), and fitting to obtain the groove bottom curve (18) of the flank face; S10, fitting the flank surface (19) by the left side line (11), the right side line (12), the tooth top curve (15) and the groove bottom curve (18), completing the construction of the flank surface (19) of a single tooth.

3. The method for modeling the three-dimensional structure of a variable rake angle toroidal worm gear hob according to claim 2, characterized in that: Also includes: S11, importing the calculated three-dimensional coordinate data of the left helical surface point family and the right helical surface point family of the hob into a three-dimensional modeling software, and fitting the left helical surface (20) and the right helical surface (21) of the hob respectively; S12, performing curved surface lofting by the helical lines of the tooth top annular surfaces on the left and right sides to obtain the tooth top surface (22) of a single cutter tooth, and performing curved surface lofting by the helical lines of the tooth root annular surfaces on the left and right sides to obtain the groove bottom surface (23) of a single cutter tooth.

4. The method for modeling the three-dimensional structure of a variable rake angle toroidal worm gear hob according to claim 3, characterized in that: Also includes: S13, the front cutting edge (9), the back cutting edge (19), the left helical surface (20), the right helical surface (21), the tooth top surface (22), and the groove bottom surface (23) are all imported into the three-dimensional modeling software, and the front cutting edge (9), the back cutting edge (19), the left helical surface (20), the right helical surface (21), the tooth top surface (22), and the groove bottom surface (23) are combined to form a three-dimensional solid model of a complete tooth.

5. The method for modeling the three-dimensional structure of a variable rake angle toroidal worm gear hob according to claim 4, characterized in that: Also includes: S14, selecting the intersection point L1 of the left cutting edge curve (2) of the first tooth rake face (9) and the indexing annular spiral line, moving the intersection point along the spiral line by a length of m / n points to obtain the intersection point L2 of the left cutting edge curve of the second tooth rake face and the indexing annular spiral line, and modeling the second tooth based on the position of the intersection point; S15, repeating steps S1-S4 to complete the modeling operation of the rake face of the second tooth, so that the angles between the rake face and the left and right helical surfaces are a certain value and are not equal; S16, moving the points on the left and right side lines of the flank surface of the first tooth along the spiral direction by the same length (i.e., the length of m / n points), thereby fitting the left and right side lines of the flank surface of the second tooth; S17. The construction method of the left and right spiral surfaces, tooth top surface, and groove bottom surface of the second tooth is exactly the same as the construction method of the first tooth in steps S11-12, and then the three-dimensional model construction of the second tooth geometric structure is completed.

6. The method for modeling the three-dimensional structure of a variable rake angle toroidal worm gear hob according to claim 5, characterized in that: Also includes: Repeat the above steps to complete the construction of n teeth on the entire spiral line, and discard the remaining spiral surface that is not enough to construct a tooth; Then, all the teeth distributed on other spiral lines are constructed by means of an equidistant circular array, and finally a complete three-dimensional solid model of the enveloping toroidal worm gear hob is obtained.

7. A method for modeling a three-dimensional structure of a variable rake angle toroidal worm gear hob according to any one of claims 1 to 6, characterized in that: All the above steps are performed in CAD software.

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