A method for constructing a geometric structure of an enveloping toroidal worm gear hob with a single tooth constant rake angle

Abstract

The present invention discloses a method for constructing a geometric structure of an enveloping toroidal worm gear hob with a single tooth equal rake angle. Three-dimensional modeling software is used to make the rake angles of each tooth equal everywhere, and the rake surface of each tooth is designed as a separate free-form surface. Based on this method, CAD modeling of the worm gear hob is completed, which not only simplifies the design and manufacturing process of the toroidal worm gear hob, but also improves the overall cutting performance of the hob by improving the rake angle of each tooth.

Description

Technical Field

[0001] The invention relates to the technical field of design and manufacturing of worm gear hobs, in particular to a method for constructing a single tooth equal rake angle of an enveloping annular worm gear hob geometric structure. Background Art

[0002] Compared to cylindrical worm gears, toroidal worm gears offer advantages such as strong load-bearing 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 the meshing transmission performance is very sensitive to errors and deformation, requiring high-precision machining and manufacturing. The toroidal worm gear hob used to machine the worm gear is a special tool with a complex structure and is difficult to design and manufacture. The rake angles of the cutting edges on both sides of existing straight-chip-groove worm gear hobs differ significantly, with one side having a positive rake angle and the other having a negative rake angle. When the worm pair's transmission ratio is small, that is, when the number of hob heads is large, the tooth with the larger absolute value of the negative rake angle will increase the main cutting force, deteriorate the cutting conditions of the tooth, and seriously affect cutting efficiency and cutting quality. The rake face of the spiral-chip-groove worm gear hob can improve the rake angle at each point on the tooth indexing annulus, but the rake angles at the tooth top and tooth root are still not balanced. The traditional slotted design method of the integral worm gear hob cannot fundamentally overcome the above-mentioned difficulties, so it is necessary to propose a new design method of the enveloping annular worm gear hob.

[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-linked universal CNC milling machine. It is a method for automating the worm gear hob 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, and does not solve the disadvantage of the difference in the front angles on the left and right sides of the hob. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for constructing a geometric structure of an enveloping toroidal worm gear hob with equal rake angles for a single tooth, so as to achieve that the rake angles of each tooth are equal everywhere, and the rake surface of each tooth is designed as a separate free-form surface. Based on this method, the CAD modeling of the worm gear hob is completed, which not only simplifies the design and manufacturing process of the toroidal worm gear hob, but also improves the overall cutting performance of the hob by improving the rake angle of each tooth.

[0005] The object of the present invention is achieved by providing a method for constructing a geometric structure of a single tooth with equal rake angle of an enveloping toroidal worm gear hob. The method is executed based on a CAD three-dimensional modeling environment and includes the following steps:

[0006] A. According to the forming principle of the spiral surface of the toroidal worm gear hob, the point family of each toroidal spiral line on the left spiral surface of the hob is obtained, k spiral lines are selected (1), and a space curve is obtained. The space curve extends along the tooth height direction on the left spiral surface, and satisfies two constraints at the intersection with each toroidal spiral line: a. The angle between the tangent vector along the toroidal spiral line and the tangent vector along this space curve is a certain value; b. The curvature of this space curve at this point is minimum. At this time, this space curve can be uniquely determined, and the angle between this space curve and each toroidal spiral line on the left spiral surface is a certain value, which can satisfy that the front angle at each intersection (3) is equal everywhere, and the space curve is used as the left cutting edge curve (2) of the toroidal worm gear hob.

[0007] B. Repeat step A to obtain another space curve on the right helical surface as the right cutting edge curve of the toroidal worm gear hob (4);

[0008] C. The left cutting edge curve (2) intersects with the left tooth root spiral line (5) and the tooth top spiral line (6) to obtain the lower left point and the upper left point. The right cutting edge curve (4) intersects with the right tooth root spiral line (5) and the tooth top spiral line (6) to obtain the lower right point and the upper right point. The upper left point and the upper right point are connected, and the lower left point and the lower right point are connected to fit the top edge curve (7) and the groove bottom curve (8) respectively. The front cutting face (9) of a single tooth is fitted by the left cutting edge curve (2), the right cutting edge curve (4), the top edge curve (7) and the groove bottom curve (8), and the equal rake angle construction of the front cutting face (9) of a single tooth is completed.

[0009] Furthermore, it also includes:

[0010] D. The intersection point of the left cutting edge curve (2) and each torus spiral is moved along the spiral direction by a length of (m / n)-2 points to obtain k points (10) located on each torus spiral, where m represents the number of equally spaced points on each spiral, and n represents the number of complete teeth on each spiral;

[0011] E. Use the k points after the movement to fit the left edge of the flank (11). Similarly, the right edge of the flank (12) is obtained.

[0012] F. Take the intersection point (13) of the left side line (11) of the flank face and the helical line of the left tooth top annular surface, and the intersection point (14) of the right side line (12) of the flank face and the helical line of the right tooth top annular surface, and fit to obtain the tooth top curve (15) of the flank face;

[0013] G. Take the intersection point (16) of the left side line (11) of the flank face and the left groove bottom spiral line, and the intersection point (17) of the right side line (12) of the right flank face and the right groove bottom spiral line, and fit to obtain the groove bottom curve (18) of the flank face;

[0014] H. The flank surface (19) is fitted by the left side line (11) of the flank surface, the right side line (12) of the flank surface, the tooth top curve (15) and the groove bottom curve (18), thereby completing the construction of the flank surface (19) of a single tooth.

[0015] Furthermore, it also includes:

[0016] I. Importing the calculated three-dimensional coordinate data of the left and right helical surface point families 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;

[0017] J. The tooth top surface (22) of a single cutter tooth is obtained by performing curved surface lofting by the helical lines of the tooth top annular surfaces on the left and right sides, and the groove bottom surface (23) of a single cutter tooth is obtained by performing curved surface lofting by the helical lines of the tooth root annular surfaces on the left and right sides.

[0018] Furthermore, it also includes:

[0019] K. Import 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) into the three-dimensional modeling software, and stitch 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) into a three-dimensional solid model of a complete tooth, thereby completing the equal rake angle construction of the geometric structure of a single tooth.

[0020] Furthermore, it also includes:

[0021] L. Select the intersection point L1 of the left cutting edge curve of the rake face of the first constructed tooth and the spiral line of the indexing annulus, move the intersection point along the spiral line direction by a length of m / n points, and obtain the intersection point L2 of the left cutting edge curve of the rake face of the second tooth and the spiral line of the indexing annulus, and then follow the AC steps (modeling method of the first tooth) to obtain the rake face of the second tooth, and complete the equal rake angle construction of the rake face of the second tooth. The rake face also satisfies the condition that the angle between the rake face and the left and right spiral surfaces is a certain value everywhere, that is, it also satisfies the condition that the rake angle at each intersection is equal everywhere;

[0022] M. Move the points on the left and right side lines of the flank of the first tooth along the spiral line by the length of m / n points, and then follow the EH steps (modeling method for the first tooth) to obtain the flank of the second tooth;

[0023] N. Follow steps IJ to complete the construction of the 3D model of the second tooth geometry.

[0024] Furthermore, the above method is repeated to complete the construction of all the teeth on the entire spiral line, and the remaining part of the spiral surface that is not sufficient to construct a tooth is trimmed and discarded; then, through the method of equally spaced circular arrays, all the teeth distributed on other spiral lines are constructed, and finally a complete three-dimensional solid model of the enveloping toroidal worm gear hob is obtained.

[0025] The beneficial effects of the present invention are:

[0026] Through this modeling method, the rake angles of all teeth on the hob model are made equal. This method not only simplifies the hob design and processing technology, but also ensures the position and shape of each tooth cutting edge. As a result, a three-dimensional model of the toroidal worm gear hob is obtained with more balanced performance of each cutting edge and better overall cutting performance, which facilitates the subsequent hob manufacturing process. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 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.

[0028] Figure 2 This is a schematic diagram showing the principle of constructing the equal rake angle of the single-tooth rake face of the toroidal worm gear hob of the present invention.

[0029] 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.

[0030] 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.

[0031] 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.

[0032] Figure 6 This is a complete three-dimensional model diagram of the toroidal worm gear hob established by the present invention. DETAILED DESCRIPTION

[0033] The following is combined with Figure 1-6 The present invention is further described with reference to the accompanying drawings and specific examples.

[0034] 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.

[0035] 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 as 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 11 equally spaced spiral lines 1 are selected to fit the spiral surface on one side. A spatial curve is obtained. The curve is distributed on the spiral surface and along the tooth height direction. The intersection of this curve and each toroidal spiral line satisfies: ① The tangent vector along the toroidal spiral line at this point and the tangent vector along this spatial curve are the same. The angle between the tangent vectors is 90° (the rake angle is 90°-90°=0° at this point); ② The curvature of this spatial curve at this point is minimum. This curve is fitted by 11 intersection points 3 with each toroidal spiral line, that is, this spatial curve is orthogonal to each toroidal spiral line 1 on the left helical surface. This spatial curve is used as the left cutting edge curve 2 of the toroidal worm gear hob. Using the same method, another spatial curve is obtained as the right cutting edge curve 4 of the toroidal worm gear hob. The top edge curve 7 and the groove bottom curve 8 are then fitted by the intersection points of the two spatial curves with the tooth root toroidal spiral line 5 and the tooth top toroidal spiral line 6, respectively. Finally, these four curves are used to fit the rake face 9 of a single tooth, completing the construction of the rake face 9 of a single tooth with a 0° rake angle.

[0036] Step 2: Construction of the back cutting surface of a single tooth: According to the construction method of the front cutting surface of a single tooth described in step 1, the intersection of the left cutting edge curve on the constructed front cutting surface 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. The 11 moved points are used to fit the left side line 11 of the back cutting surface. Similarly, the right side line 12 of the back cutting surface is obtained. The intersection point 13 of the left side line 11 and the left tooth top annular spiral line, as well as the intersection point 14 of the right side line 12 and the right tooth top annular surface, are taken to fit the tooth top curve 15 of the back cutting surface; the intersection point 16 of the left spiral line and the left groove bottom spiral line, as well as 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 back cutting surface. The back cutting surface 19 is fitted out by the left side line 11, the right side line 12, the tooth top curve 15 and the groove bottom curve 18 to complete the construction of the back cutting surface 19 of the single tooth.

[0037] 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.

[0038] Step 4: Constructing a 3D model of a single tooth: Import the rake face 9 of step 1, the flank face 19 of step 2, the left helical face 20 and the right helical face 21 of 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 1 ) to complete the construction of a single tooth 3D model.

[0039] 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 second tooth rake face left cutting edge curve The intersection point L2 with the dividing annular surface spiral line and the intersection point R2 with the right cutting edge curve of the second tooth rake face and the dividing 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. Then, the intersection points 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 orthogonality of the rake face and the spiral surfaces on the left and right sides, that is, the rake angle at each intersection is 0°. 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.

[0040] 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 ).

[0041] 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 method for constructing a geometric structure of a single tooth with constant rake angle for an enveloping toroidal worm gear hob, wherein the method is executed in a CAD-based three-dimensional modeling environment and is characterized in that: The process includes the following: A. Obtain the point family of each toroidal spiral line on the left helical surface of the hob, select k spiral lines from them (1), and calculate a space curve, wherein the space curve extends along the tooth height direction on the left helical surface and satisfies two constraints at the intersection with each toroidal spiral line: a. The angle between the tangent vector along the toroidal spiral line and the tangent vector along this space curve is a certain value; b. The curvature of this space curve at this point is minimum; and the space curve is used as the left cutting edge curve of the toroidal worm gear hob (2). B. Repeat step A to obtain another space curve on the right helical surface as the right cutting edge curve of the toroidal worm gear hob (4); C. The left cutting edge curve (2) intersects with the left tooth root spiral line (5) and the tooth top spiral line (6) to obtain the lower left point and the upper left point. The right cutting edge curve (4) intersects with the right tooth root spiral line (5) and the tooth top spiral line (6) to obtain the lower right point and the upper right point. The upper left point and the upper right point are connected, and the lower left point and the lower right point are connected to fit the top edge curve (7) and the groove bottom curve (8) respectively. The front cutting face (9) of a single tooth is fitted by the left cutting edge curve (2), the right cutting edge curve (4), the top edge curve (7) and the groove bottom curve (8), and the equal rake angle construction of the front cutting face (9) of a single tooth is completed.

2. The method for constructing a geometric structure of an enveloping toroidal worm gear hob with a single tooth constant rake angle according to claim 1, characterized in that: Also includes: D. The intersection point of the left cutting edge curve (2) and each torus spiral is moved along the spiral direction by a length of (m / n)-2 points to obtain k points (10) located on each torus spiral, where m represents the number of equally spaced points on each spiral, and n represents the number of complete teeth on each spiral; E. Use the k points after the movement to fit the left edge of the flank (11). Similarly, the right edge of the flank (12) is obtained. F. Take the intersection point (13) of the left side line (11) of the flank face and the helical line of the left tooth top annular surface, and the intersection point (14) of the right side line (12) of the flank face and the helical line of the right tooth top annular surface, and fit to obtain the tooth top curve (15) of the flank face; G. Take the intersection point (16) of the left side line (11) of the flank face and the left groove bottom spiral line, and the intersection point (17) of the right side line (12) of the right flank face and the right groove bottom spiral line, and fit to obtain the groove bottom curve (18) of the flank face; H. The flank surface (19) is fitted by the left side line (11) of the flank surface, the right side line (12) of the flank surface, the tooth top curve (15) and the groove bottom curve (18), thereby completing the construction of the flank surface (19) of a single tooth.

3. The method for constructing a geometric structure of a single tooth with equal rake angle of an enveloping toroidal worm gear hob according to claim 2, characterized in that: Also includes: I. Importing the calculated three-dimensional coordinate data of the left and right helical surface point families 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; J. The tooth top surface (22) of a single cutter tooth is obtained by performing curved surface lofting by the helical lines of the tooth top annular surfaces on the left and right sides, and the groove bottom surface (23) of a single cutter tooth is obtained by performing curved surface lofting by the helical lines of the tooth root annular surfaces on the left and right sides.

4. The method for constructing a geometric structure of an enveloping toroidal worm gear hob with a single tooth constant rake angle according to claim 3, characterized in that: Also includes: K. Import the front cutting edge (9), the rear cutting edge (19), the left helical surface (20), the right helical surface (21), the tooth top surface (22), and the groove bottom surface (23) into a three-dimensional modeling software, and stitch the front cutting edge (9), the rear cutting edge (19), the left helical surface (20), the right helical surface (21), the tooth top surface (22), and the groove bottom surface (23) into a three-dimensional solid model of a complete tooth.

5. The method for constructing a geometric structure of an enveloping toroidal worm gear hob with a single tooth constant rake angle according to claim 4, characterized in that: Also includes: L. Select the intersection point L1 of the left cutting edge curve of the rake face of the first tooth and the spiral line of the indexing annulus, move the intersection point along the spiral line by a length of m / n points, and obtain the intersection point L2 of the left cutting edge curve of the rake face of the second tooth and the spiral line of the indexing annulus. Then, follow steps AC to obtain the rake face of the second tooth, and complete the equal rake angle construction of the rake face of the second tooth. M. Move the points on the left and right side lines of the flank of the first tooth along the spiral line by the length of m / n points, and then follow steps EH to obtain the flank of the second tooth; N. Follow steps IJ to complete the construction of the 3D model of the second tooth geometry.

6. The method for constructing a geometric structure of a single tooth with equal rake angle of an enveloping toroidal worm gear hob according to claim 5, characterized in that: Repeat the above method to complete the construction of all the teeth on the entire spiral line, and discard the remaining spiral surface that is not sufficient to construct a tooth; then, through the method of equally spaced circular array, all the teeth distributed on other spiral lines are constructed, and finally a complete three-dimensional solid model of the enveloping toroidal worm gear hob is obtained.

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