Design method of rake face of hob for multiple-head double-conical surface second enveloping hourglass worm

Abstract

The present invention discloses a design method for the flank and clearance face of a toroidal worm hob, belonging to the field of mechanical transmission. One helix of the multi-start double conical surface second enveloping toroidal worm hob includes N cutter teeth, where N is a positive integer. The design method includes: determining the position of the straight flute rake face of at least one cutter tooth among the N cutter teeth on one helix of the multi-start basic worm; determining the centripetal vector of the straight flute rake face of at least one cutter tooth based on the position of the straight flute rake face; rotating the straight flute rake face of at least one cutter tooth by a first angle around its respective centripetal vector to obtain the helical flute rake face of at least one cutter tooth; configuring at least one cutter tooth on one helix to be circumferentially and equally spaced around the hob axis to obtain the helical flute rake faces of the cutter teeth on at least one other helix of the multi-start double conical surface second enveloping toroidal worm hob. The surface structure of the rake face obtained according to the design method of the present disclosure is simple and not affected by the parameters of the machining tool.

Description

Technical Field

[0001] The present invention relates to the field of mechanical transmission, and particularly to a design method for the rake face of a multi-head double-cone surface second-enveloping toroidal worm hob. Background Art

[0002] The double-cone surface second-enveloping toroidal worm drive is applicable to the occasions of multi-head and large transmission ratio. The worm wheel constituting the worm pair is hobbed by a double-cone surface second-enveloping toroidal worm hob. The double-cone surface second-enveloping toroidal worm hob is based on a double-cone enveloping toroidal worm as the basic body, and is obtained by machining the rake face, side relief face, top relief face, etc. The structure of the rake face affects the hobbing performance of the hob, and the hobbing performance can be measured by the magnitude of the side rake angle. Generally, it is desired that the magnitudes of the side rake angles on both sides of the cutter teeth of the hob are basically the same and are both positive values.

[0003] Since the helix angle of the multi-head hob is relatively large, in order to ensure that the difference in the side rake angles of the cutter teeth on both sides of the hob is not too large to ensure the consistency of the hobbing performance on both sides, a spiral groove rake face needs to be designed and machined. Different from the cylindrical hob, the structures of the cutter teeth of the toroidal worm hob are not the same as each other, and the lead angles on the same toroidal surface are also different everywhere. Therefore, the difference of each cutter tooth needs to be considered when designing the rake face of the toroidal worm hob. Summary of the Invention

[0004] In the related art, a method of machining a spiral groove rake face by variable transmission ratio milling with a cylindrical milling cutter according to the lead angle at the pitch toroidal surface of each cutter tooth is proposed. The rake face obtained based on this method is a complex variable helix angle helical surface. This method has a simple machining method, but insufficient consideration of the difference of the cutter teeth. Moreover, when the change law of the transmission ratio remains unchanged, if the diameter of the cylindrical milling cutter changes, the shape of the machined spiral groove rake face also changes, and it is impossible to ensure that the shapes of the spiral groove rake faces machined by cutters with different parameters are the same, that is, it has a strong dependence on the tool shape parameters. Therefore, the method cannot ensure the consistency of the obtained rake face when using milling cutters with different diameters.

[0005] Therefore, there is an urgent need for a design method for a spiral groove rake face with a simple curved surface structure, not affected by the machining tool parameters, and capable of making the difference in the side rake angles on both sides of the cutter teeth not too large.

[0006] In order to solve at least one of the above problems and defects existing in the prior art, an embodiment of the present invention provides a design method for the rake face of a multi-head double-cone surface second-enveloping toroidal worm hob. The design method of the embodiment of the present invention provides a design method for a spiral groove rake face with a simple curved surface structure and not affected by the machining tool parameters.

[0007] According to one aspect of the present disclosure, a design method for the rake face of a multi-headed double-cone quadratic envelope toroidal worm hob is provided. One helix of the multi-headed double-cone quadratic envelope toroidal worm hob includes N cutter teeth, where N is a positive integer. The design method includes:

[0008] Determine the position of the straight-groove rake face of at least one cutter tooth among the N cutter teeth on one helix of the multi-headed basic worm;

[0009] Based on the position of the straight-groove rake face, determine the centripetal vector of the straight-groove rake face of the at least one cutter tooth;

[0010] Rotate the straight-groove rake face of the at least one cutter tooth by a first angle around its respective centripetal vector to obtain the helical-groove rake face of the at least one cutter tooth;

[0011] At least one cutter tooth on one helix is configured to be circumferentially and angularly equally spaced around the hob axis to obtain the helical-groove rake faces of the cutter teeth on at least one other helix of the multi-headed double-cone quadratic envelope toroidal worm hob.

[0012] In some embodiments, determining the position of the straight-groove rake face of at least one cutter tooth among the N cutter teeth on one helix of the multi-headed basic worm includes:

[0013] Determine the first plane in which the straight-groove rake face of one cutter tooth D1 among the N cutter teeth on one helix lies. The first plane passes through the hob axis;

[0014] Form the straight-groove rake face Σ1 of the one cutter tooth D1 by the intersection of the first plane and the one helix.

[0015] In some embodiments, determining the position of the straight-groove rake face of at least one cutter tooth among the N cutter teeth on one helix of the multi-headed basic worm further includes:

[0016] Determine the phase difference φ0 between two adjacent cutter teeth on one helix;

[0017] Cause the first plane to rotate around the hob axis by a second angle φ i to obtain a rotated plane, where the second angle φ i =(i - 1)φ0, and i is any integer greater than 1;

[0018] Form the straight-groove rake face of the ith cutter tooth by the intersection of the rotated plane and the one helix.

[0019] In some embodiments, determining the centripetal vector of the straight-groove rake face of the at least one cutter tooth includes:

[0020] Determine a first reference point located in the straight flute rake face based on the center of the multi-head double-cone surface second envelope hourglass worm hob and the center distance a;

[0021] Determine a second reference point based on the pitch line of the multi-head double-cone surface second envelope hourglass worm hob.

[0022] In some embodiments, determine a centripetal vector based on the first reference point and the second reference point.

[0023] In some embodiments, set the distance between the first reference point and the center to be equal to the center distance a, and the line connecting the first reference point and the center is perpendicular to the hob axis.

[0024] In some embodiments, make the pitch line intersect with the corresponding tooth to form a left intersection point and a right intersection point, and the midpoint of the left intersection point and the right intersection point is the second reference point.

[0025] The direction of the centripetal vector is from the second reference point to the first reference point.

[0026] In some embodiments, the first angle is the lead angle at the midpoint.

[0027] In some embodiments, construct an O1-hjk rectangular coordinate system, where O1 is the center of the multi-head double-cone surface second envelope hourglass worm hob, and the k-axis coincides with the hob axis;

[0028] Determine the coordinates (x, y, z) of the midpoint in the O1-hjk rectangular coordinate system;

[0029] The lead angle at the midpoint is where f is the transmission ratio of the multi-head double-cone surface second envelope hourglass worm hob.

[0030] In some embodiments, the interval angle of the array is φ j = 2π / Z, where Z is the number of heads of the multi-head double-cone surface second envelope hourglass worm hob. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] These and / or other aspects and advantages of the present invention will become apparent and be readily understood from the following description of the preferred embodiments in conjunction with the accompanying drawings, in which:

[0032] Figure 1 is a flowchart of a design method for the rake face of a multi-head double-cone surface second envelope hourglass worm hob according to an embodiment of the present invention;

[0033] Figure 2 is a schematic diagram of the position determination of the straight flute rake face according to an embodiment of the present invention;

[0034] Figure 3Schematic diagram of the plane where the straight groove rake face of a single cutting tooth in the embodiment of the present invention is located;

[0035] Figure 4 Schematic diagram for constructing the helical groove rake face according to the embodiment of the present invention;

[0036] Figure 5 Construction model of a toroidal worm hob with a helical groove rake face according to the embodiment of the present invention. Detailed implementation manners

[0037] The technical solution of the present invention will be further specifically described below through embodiments in conjunction with the drawings. In the specification, the same or similar reference numerals indicate the same or similar components. The following description of the embodiments of the present invention with reference to the drawings is intended to explain the overall inventive concept of the present invention and should not be construed as a limitation of the present invention.

[0038] According to the overall inventive concept of the present invention, a design method for the rake face of a multi - head double - conical surface second - enveloping toroidal worm hob is proposed. One helix of the multi - head double - conical surface second - enveloping toroidal worm hob includes N cutting teeth, where N is a positive integer. The design method includes: determining the position of the straight groove rake face of at least one cutting tooth among the N cutting teeth on one helix of the multi - head basic worm; determining the centripetal vector of the straight groove rake face of the at least one cutting tooth based on the position of the straight groove rake face; rotating the straight groove rake face of the at least one cutting tooth around its respective centripetal vector by a first angle to obtain the helical groove rake face of the at least one cutting tooth; and arranging at least one cutting tooth on one helix in an equidistant array around the hob axis at a circumferential angle to obtain the helical groove rake faces of the cutting teeth on at least one other helix of the multi - head double - conical surface second - enveloping toroidal worm hob.

[0039] In the design method of the embodiment of the present invention, a simple plane is used as the design basis for the rake face. By rotating the straight groove rake face around the constructed centripetal vector, the helical groove rake face is obtained, which can effectively reduce the difference in the side rake angles on both sides of the cutting tooth and avoid the generation of a large negative side rake angle.

[0040] The rake face designed by the design method of the embodiment of the present invention is a spatial plane, which is easier to achieve precise grinding compared to a complex variable - helix - angle helical surface.

[0041] The design method of the embodiment of the present invention allows a generating - surface tool formed with a straight line as the generatrix to machine a plane with the same spatial position, such as a cylindrical milling cutter, a conical milling cutter, etc. When the tool parameters change, only the tool - setting point needs to be adjusted to ensure the shape and spatial position of the plane, which can ensure the consistency of the rake face and reduce the dependence on the tool shape parameters.

[0042] Specifically, a design method for the rake face of a multi-start double conical enveloping toroidal worm hob with a spiral body including N cutting teeth is proposed, where N is a positive integer. As Figure 1 shown, the design method includes:

[0043] Step S1: Determine the position of the straight flute rake face of at least one cutting tooth among the N cutting teeth on one spiral body of the multi-start basic worm.

[0044] The multi-start toroidal worm hob is manufactured with the multi-start basic worm as the basic body. Thus, the number of spiral bodies of the multi-start toroidal worm hob is equal to the number of spiral bodies of the multi-start basic worm, and the number of cutting teeth included in one spiral body of the multi-start toroidal worm hob is equal to the number of cutting teeth included in the spiral body of the multi-start basic worm, that is, each spiral body includes N cutting teeth. Since all the cutting teeth of the hob are the circumferential array of the cutting teeth on one spiral head along the axis S of the hob, therefore, any one spiral body on the multi-start basic worm can be selected for the design of the rake face.

[0045] As Figure 2 shown, determining the position of the straight flute rake face of at least one cutting tooth among the N cutting teeth on one spiral body of the multi-start basic worm includes:

[0046] Determine the first plane P1 where the straight flute rake face of one cutting tooth D1 among the N cutting teeth on one spiral body A is located, and the axis S of the hob is within the first plane P1;

[0047] The straight flute rake face Σ1 of the one cutting tooth D1 is formed by the intersection of the first plane P1 and the one spiral body A.

[0048] Thus, the straight flute rake face of one cutting tooth D1 on one spiral body A can be obtained. For the spiral body A, it can be any one of the spiral bodies in the multi-start basic worm. For one cutting tooth D1 on the spiral body A, it can be any one of the cutting teeth on the spiral body A, for example, it can be the first cutting tooth on the left side of the spiral body A.

[0049] In order to obtain the straight flute rake faces of other cutting teeth on one spiral body A, determining the position of the straight flute rake face of at least one cutting tooth among the N cutting teeth on one spiral body of the multi-start basic worm further includes:

[0050] Determine the phase difference φ0 between two adjacent cutting teeth on the one spiral body A, and the phase difference φ0 can be set as needed;

[0051] Rotate the first plane P1 around the axis S of the hob by a second angle φ i to obtain the rotated plane P i , where the second angle φ i =(i - 1)φ0, and i is any integer greater than 1;

[0052] Through the rotation plane P i Intersects with the spiral A to form the straight flute rake face Σ of the ith tooth i .

[0053] The ith tooth is the ith tooth arranged in sequence with a tooth D1 corresponding to the first plane P1 as the first tooth, where i is any integer greater than 1. For example, if the tooth D1 is the first tooth on the left, then the ith tooth is the ith tooth arranged from the left. For another example, if the tooth D1 is the rth tooth from the left, then the ith tooth can be the (r + i)th tooth arranged from the left, or the (r - i)th tooth arranged from the left, where r is any integer.

[0054] In this way, the straight flute rake faces of at least one other tooth on the spiral A can be obtained. Of course, this step can be repeated until the straight flute rake faces of all other teeth on the spiral A are obtained.

[0055] In an example, the phase difference φ0 between two adjacent teeth refers to the difference in the phase angles of two adjacent teeth. The phase angle of a tooth is the phase angle between the plane where the straight flute rake face of the tooth is located and the coordinate plane h - O1 - k. The coordinate plane h - O1 - k is a plane in the O1 - hjk rectangular coordinate system, where O1 is the center of the multi - head double - cone face quadratic envelope toroidal worm hob, the k - axis coincides with the hob axis S, as Figure 2 shown. For example,[[]] Figure 2 φ in h represents the phase angle between the first plane P1 and the coordinate plane h - O1 - k.

[0056] Step S2 determines the centripetal vector g of the straight flute rake face of the at least one tooth based on the position of the straight flute rake face.

[0057] Specifically, step S2 includes:

[0058] Step S21 determines the first reference point O2 located in the straight flute rake face based on the center O1 of the multi - head double - cone face quadratic envelope toroidal worm hob and the center distance a i .

[0059] In an example, the distance between the first reference point O2 i and the center O1 (as shown by the circle in Figure 3 ) is set to be equal to the center distance a, and the line Q between the first reference point O2 i and the center O1 is perpendicular to the hob axis S, as Figure 3 shown.

[0060] Step S22 determines a second reference point based on the indexing line T of the multi-head double-cone surface second enveloping hourglass worm hob.

[0061] In one example, the indexing line T (for example, with a radius of r2) intersects the corresponding tooth flank to form a left intersection point L i and a right intersection point R i , and the midpoint M i of the left intersection point L i and the right intersection point R i (as shown by the solid dot in Figure 3 ) is the second reference point, as shown in Figure 3 .

[0062] Step S23 determines the centripetal vector g based on the first reference point O2 i and the second reference point.

[0063] In one example, the direction vector of the line formed by the first reference point and the second reference point is the centripetal vector g, as shown by the dashed line in Figure 3 . The direction of the centripetal vector g is from the second reference point to the first reference point O2 i .

[0064] Step S3 rotates the straight flute rake face Σ i of at least one tooth flank by a first angle φ e around their respective centripetal vectors g to obtain the helical flute rake face Σ i s of the at least one tooth flank, as shown in Figure 4 .

[0065] In one example, the first angle φ e is the lead angle at the midpoint M i . Based on this, each obtained helical flute rake face takes into account the lead angle of each tooth flank itself, and the designed rake face can reduce the distribution range of the side rake angles of each tooth flank with different shapes, which is beneficial to equalizing the forces on both sides of the tooth flanks.

[0066] The lead angle at the midpoint M i is determined through the following steps:

[0067] Construct an O1-hjk rectangular coordinate system, where O1 is the center of the multi-head double-cone surface second enveloping hourglass worm hob, and the k-axis coincides with the hob axis S;

[0068] Determine the coordinates (x, y, z) of the midpoint M i in the O1-hjk rectangular coordinate system;

[0069] The lead angle at the midpoint M i is where f is the transmission ratio of the hob for double enveloping hourglass worm with multiple heads and double conical surfaces.

[0070] In one example, for a hob of a worm wheel with a left-handed helix, the straight flute rake face Σ of at least one tooth i can be rotated clockwise by a first angle φ around its respective centripetal vector g e to obtain the helical flute rake face Σ of the at least one tooth. i s For a hob of a worm wheel with a right-handed helix, the straight flute rake face Σ of at least one tooth i can be rotated counterclockwise by a first angle φ around its respective centripetal vector g e to obtain the helical flute rake face Σ of the at least one tooth. i s .

[0071] At least one tooth on one helix A in step S4 is configured to be circumferentially arrayed at equal angular intervals around the hob axis S to obtain the helical flute rake faces of the teeth on at least one other helix of the hob for double enveloping hourglass worm with multiple heads and double conical surfaces.

[0072] In one example, the interval angle of the array is φ j = 2π / Z, where Z is the number of heads of the hob for double enveloping hourglass worm with multiple heads and double conical surfaces, such as two heads, three heads or more.

[0073] Since all the teeth of the hob are the circumferential array of the teeth on one helical head along the hob axis S, the helical flute rake faces of the teeth on other helices can be obtained by means of circumferential array. For example, the helical flute rake faces of the teeth on all helices can be obtained by circumferential array, or the helical flute rake faces of the teeth on some helices can be obtained by circumferential array.

[0074] In one example, the circumferential array can be realized by software such as Solidworks.

[0075] Only a part of the embodiments of the present invention is shown below, which is only for illustrative purposes; those skilled in the art can understand other feasible embodiments of the present invention, and will not be repeated here.

[0076] Taking a hob for double enveloping hourglass worm with six heads as an example, its parameters are: center distance a = 125 mm, transmission ratio f = 6, right-handed worm, number of heads Z = 6, number of tooth rows U = 6 of the hob, number of teeth N = 5 on each helix, addendum arc radius R a = 90 mm, dedendum arc radius R f = 99.95 mm

[0077] Figure 2 Schematic diagram for determining the position of the straight flute rake face according to an embodiment of the present invention. The multi-start toroidal worm hob is manufactured with a multi-start basic worm as the basic body. O1 is the center of the hob, and S is the axis of the hob, that is, the rotational axis of the hob. Taking O1 as the coordinate origin, a right-handed rectangular coordinate system is established, and the coordinate axes are h, j, and k respectively. Among them, the k-axis coincides with the S axis and is horizontal to the right, the h-axis is perpendicular to the paper surface and outward, and the j-axis is vertically downward.

[0078] First, a first plane P1 where the straight flute rake face of the leftmost first tooth D1 is determined by a selected helix A. The first plane P1 passes through the hob axis S (i.e., the hob axis S lies in the first plane P1) and the phase angle between the first plane P1 and the coordinate plane h - O1 - k is φ h = 2.129 rad. The first plane P1 intersects with the helix A to form the straight flute rake face Σ1 of the tooth D1. Assuming the phase difference between two adjacent teeth is φ0 = 0.1047 rad, the first plane P1 is rotated by an angle φ i = (i - 1)φ0 to obtain the rotated plane P i , and the rotated plane P i intersects with the selected helix A to form the rake face Σ i of the ith tooth on the selected helix A, where i = 2, 3, 4, 5.

[0079] Figure 3 Schematic diagram of the plane where the straight flute rake face of a single tooth according to an embodiment of the present invention is located. For the tooth D i whose rake face is the straight flute rake face Σ i , there is a point O2 i in the plane determined by the straight flute rake face Σ i (i.e., the first reference point O2 i ), such that the line Q connecting O2 i and the center O1 is perpendicular to the hob axis S, and the distance from O2 i to O1 is the center distance a. The pitch line T with a radius of r2 intersects the two sides of the tooth at points L i and R i . The midpoint of L i and R i is M i , whose coordinates are (x, y, z). The midpoint M i is the second reference point. The centripetal vector g is determined by the second reference point (i.e., the midpoint M i ) and the point O2 i . The lead angle γ i at the midpoint M i is determined by the following formula:

[0080]

[0081] According to the above formula, the lead angles from the cutting tooth D1 to the cutting tooth D5 are calculated as: 0.476 rad, 0.520 rad, 0.550 rad, 0.525 rad, 0.492 rad.

[0082] Figure 4 It is a schematic diagram for constructing the helical flute rake face according to an embodiment of the present invention. For the straight flute rake face Σ of any cutting tooth i , rotate it counterclockwise by the first angle φ around the centripetal vector g e to obtain the helical flute rake face Σ i s . For different cutting teeth, from the cutting tooth D1 to the cutting tooth D5, make the first angle φ e equal to the calculated lead angle γ of the corresponding cutting tooth i .

[0083] Perform a circular array of the cutting teeth on a single helix A around the hob axis S, and the interval angle of the array is the rotation angle φ j = 2π / Z = 1.0472 rad, and the total number of circular arrays is the number of heads Z = 6 of the hob. After the array, the helical flute rake faces of the cutting teeth of the multi-head toroidal worm hob are obtained.

[0084] Figure 5 It is a construction model of a toroidal worm hob with a helical flute rake face according to an embodiment of the present invention. When designing the rake face using the design method described in the embodiment of the present invention, by virtual measurement of the side rake angle size of each cutting tooth from the tooth tip to the tooth root, the size distribution range of the obtained side rake angle is [-7.97°, 8.21°]. The interval range of this side rake angle meets the design requirements and is beneficial to equalizing the forces on both cutting edges when the hob cuts the tooth surface of the worm.

[0085] Although some embodiments of the general inventive concept have been shown and described, those of ordinary skill in the art will understand that changes can be made to these embodiments without departing from the principles and spirit of the general inventive concept, and the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A design method for the rake face of a multi-head double conical surface second enveloping toroidal worm hob, where one helix of the multi-head double conical surface second enveloping toroidal worm hob includes N cutting teeth, where N is a positive integer, and where, The design method includes: Determining the position of the straight flute rake face of at least one tooth among the N teeth on one helix of the multi-start basic worm, including: determining the first plane where the straight flute rake face of one tooth D1 among the N teeth on one helix is located, the first plane passing through the hob axis, and forming the straight flute rake face of the one tooth D1 by the intersection of the first plane and the one helix; Determining the centripetal vector of the straight flute rake face of the at least one tooth based on the position of the straight flute rake face, including: determining a first reference point located in the straight flute rake face based on the center of the multi-start double conical surface second envelope toroidal worm hob and the center distance a, and determining a second reference point based on the pitch line of the multi-start double conical surface second envelope toroidal worm hob, such that the pitch line intersects the corresponding tooth to form a left intersection point and a right intersection point, and the midpoint of the left intersection point and the right intersection point is the second reference point, wherein the direction of the centripetal vector is from the second reference point to the first reference point; Rotating the straight flute rake face of the at least one tooth by a first angle around its respective centripetal vector to obtain the helical flute rake face of the at least one tooth, wherein the first angle is the lead angle at the midpoint; At least one tooth on one helix is configured to be circumferentially and equally spaced around the hob axis to obtain the helical flute rake faces of the teeth on at least one other helix of the multi-start double conical surface second envelope toroidal worm hob.

2. The design method according to claim 1, wherein, Determining the position of the straight flute rake face of at least one tooth among the N teeth on one helix of the multi-start basic worm further includes: Determining the phase difference φ0 between two adjacent teeth on one helix; Rotate the first plane about the hob axis by a second angle φ i to obtain a rotated plane, where the second angle φ i =(i - 1)φ 0， and i is an arbitrary integer greater than 1; Forming the straight flute rake face of the ith tooth by the intersection of the rotating plane and the one helix.

3. The design method according to claim 2, wherein, Determining the centripetal vector based on the first reference point and the second reference point.

4. The design method according to claim 3, wherein, Setting the distance between the first reference point and the center to be equal to the center distance a, and the connection line between the first reference point and the center is perpendicular to the hob axis.

5. The design method according to claim 4, wherein, Constructing an O1-hjk rectangular coordinate system, where O1 is the center of the multi-start double conical surface second envelope toroidal worm hob, and the k-axis coincides with the hob axis; Determining the coordinates (x, y, z) of the midpoint in the O1-hjk rectangular coordinate system; The lead angle at the midpoint is , where f is the transmission ratio of the hob for double enveloping hourglass worm with multiple threads and conical surfaces.

6. The design method according to any one of claims 1-5, wherein, The spacing angle of the array is φ j = 2π / Z, where Z is the number of starts of the multi-start double conical surface second enveloping toroidal worm hob.

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