CN110766801A

CN110766801A - Three-dimensional modeling method for involute line contact conical worm transmission pair

Info

Publication number: CN110766801A
Application number: CN201911010251.7A
Authority: CN
Inventors: 呼咏; 郭锦洲; 张学成; 于丽娟; 杜雨欣; 王宇; 祝智强
Original assignee: Jilin University
Current assignee: Jilin University
Priority date: 2019-10-23
Filing date: 2019-10-23
Publication date: 2020-02-07
Anticipated expiration: 2039-10-23
Also published as: CN110766801B

Abstract

The invention discloses a three-dimensional modeling method of an involute contact conical worm transmission pair, which solves the problems of larger error, complexity and easy tooth surface deformation when a model is introduced into other software in the prior art, and comprises the following steps: 1) three-dimensional modeling of an involute line contact conical worm: (1) a part is newly built in CATIA software, the coordinate system of the part is a conical worm coordinate system, and the coordinate system is set as S₁I.e. O₁‑X₁,Y₁,Z₁Establishing α surfaces, (3) establishing β surfaces, (4) establishing a three-dimensional model of a conical worm, and (2) establishing a three-dimensional model of an involute contact conical worm gear, (1) newly establishing a part in CATIA software, wherein the coordinate system of the part is a conical worm gear coordinate system, and the coordinate system is set as S₂I.e. O₂‑X₂,Y₂,Z₂Establishing α 'surface, (3) establishing β' surface, (4) establishing a three-dimensional model of the cone worm wheel, and (3) gradually openingAnd (3) assembling the line contact conical worm and worm wheel.

Description

Three-dimensional modeling method for involute line contact conical worm transmission pair

Technical Field

The invention relates to a method belonging to the technical field of mechanical transmission parts, in particular to a three-dimensional modeling method of an involute line contact conical worm transmission pair.

Background

The traditional bevel worm transmission has the problems that the tooth profile has theoretical error, the calculation is difficult and the tooth surface can not be ground. To address these problems, scientists have proposed involute spiroid drives, including involute point, line contact spiroid drives, and involute line contact spiroid drive pairs. The involute line contact conical worm transmission pair has higher strength, so that much attention is paid. The involute line contact conical worm transmission pair is a new type space staggered shaft transmission with large transmission ratio and multiple tooth line contact characteristics. Because the involute line contact conical worm transmission pair has a plurality of contact teeth, compared with the common worm, the involute line contact conical worm transmission pair has the advantages of high transmission strength, stable transmission and good lubricating property, and is developed to a certain extent in China, but is at the laboratory level. The traditional conical worm transmission is applied to agricultural machinery, hoisting machinery, machine tools, missiles and various military purposes, and the involute line contact conical worm transmission pair has the advantages of the traditional conical worm transmission, so that the application prospect of the involute line contact conical worm transmission is wide.

The numerical control machining technology makes a great breakthrough nowadays, and the importance of a three-dimensional model to machining is also highlighted. Because the existing five-axis linkage numerical control machine tool can process corresponding parts according to the three-dimensional model, the modeling precision has great influence on the quality of the parts. In the traditional modeling method of the worm, the coordinates of a large number of points are calculated by utilizing a tooth surface parameter equation, and then a worm gear tooth surface is formed; or the established worm entity is utilized to simulate hob processing, and the three-dimensional Boolean operation is utilized to remove the material of the worm wheel blank model to establish the worm wheel model. The models established by the methods have larger errors and are more complicated, and the problem of tooth surface deformation is easy to occur when the models are introduced into other software. A simple and accurate three-dimensional model greatly helps the study of the performance of the transmission pair, and the correct three-dimensional modeling process can provide reference for the machining method and improve the machining efficiency. Therefore, it is necessary to provide a simple and efficient modeling method for the involute contact conical worm gear pair.

Disclosure of Invention

The invention aims to solve the technical problems that the prior art has larger errors and is more complicated, and the tooth surface deformation is easy to occur when a model is introduced into other software, and provides a three-dimensional modeling method of an involute contact conical worm transmission pair.

In order to solve the technical problems, the invention is realized by adopting the following technical scheme: the three-dimensional modeling method of the involute line contact conical worm transmission pair comprises the following steps:

1) three-dimensional modeling of an involute line contact conical worm:

(1) a part is newly built in CATIA software, the coordinate system of the part is a conical worm coordinate system, and the coordinate system is set as S₁I.e. O₁-X₁,Y₁,Z₁；

(2) Establishing α faces;

(3) establishing β faces;

(4) creating a conical worm three-dimensional model;

2) three-dimensional modeling of an involute line contact cone worm gear:

(1) a part is newly built in CATIA software, the coordinate system of the part is a cone worm gear coordinate system, and the coordinate system is set as S₂I.e. O₂-X₂,Y₂,Z₂；

(2) Establishing α' surface;

(3) establishing β' surface;

(4) establishing a three-dimensional model of the bevel worm gear;

3) the involute line contacts the bevel worm and worm gear assembly.

The establishment of the α plane in the technical scheme refers to:

(1) general formula (1)

Order to

Obtaining the coordinate value of the starting point

0，-l_αRespectively correspond to X₁,Y₁,Z₁Coordinate values of the axes;

order to

Obtaining a linear parameter equation, wherein the slope of the straight line is the slope of the No. 1 straight line;

create a plane I, which is Y₁Z₁Offset plane of plane according to starting point X₁The coordinate values of the axes define the offset direction and the offset distance of the plane I, i.e. the offset direction is X₁Positive direction, offset distance is base radius of face of worm α

Drawing No. 1 straight line in the plane I, head end of No. 1 straight line) at Z₁Axial negative direction and in X₁Z₁On the plane, with X₁Y₁A face distance of l_α-P_αAccording to

Determining the slope of line number 1, i.e. in Z₁The positive direction of the axis is from, the straight line is parallel to Z₁The clockwise included angle of the positive direction of the axis in the plane I is

The length of line No. 1 is 2d_1ca；

(2) Order to

The base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be obtained according to the equation_αAnd coordinates of points on the spiral line, for drawing the spiral line;

creating No. 1 spiral line, the head end of No. 1 spiral line is coincident with the head end of No. 1 straight line, and the axis is Z₁Axis, pitch P_αHeight of L +3 XP_α(ii) a According toDetermining the rotation direction of a No. 1 spiral line;

creating No. 2 spiral line, the head end of No. 2 spiral line is superposed with the head end of No. 1 straight line, and the axis is Z₁Axis, pitch P_αHeight of L +3 XP_αAccording to

Determining the rotating direction of No. 2 spiral line, wherein the extending direction of No. 2 spiral line is Z₁The negative axis direction;

(3) drawing No. 2 straight line in the plane I, wherein the head end of the No. 2 straight line is Z₁Axial negative direction and in X₁Z₁On the plane, the distance from the head end of the No. 1 straight line isWherein

Represents that 0.5 epsilon is rounded up; the head end of No. 2 straight line is far from X compared with the head end of No. 1 straight line₁Y₁Surface, slope of line No. 2 is the same as that of line No. 1, in Z₁The positive direction of the axis is the beginning, the No. 2 straight line and Z₁The clockwise included angle of the positive direction of the axis in the plane I is

Length of 2d_1caNo. 2 straight line end and No. 2 spiralOverlapping the spiral lines;

(4) and (3) taking the No. 1 spiral line and the No. 2 spiral line as guide lines, taking the No. 1 straight line and the No. 2 straight line as outlines, creating a net-shaped curved surface I by utilizing a command of 'net-shaped curved surface' in software, and obtaining α surfaces after the net-shaped curved surface I is subjected to the trimming process of the step (3) in the three-dimensional modeling step of the awl and the worm.

The establishment of the β plane in the technical scheme refers to:

(1) general formula (2)

Order to

The coordinate value of the starting point can be obtained

0，-l_βRespectively correspond to X₁,Y₁,Z₁Coordinate values of the axes; order to

A linear parameter equation can be obtained, and the slope of the straight line is the slope of the No. 3 straight line;

create plane II, which is Y₁Z₁Offset plane of plane according to starting point X₁The coordinate values of the axes define the offset direction and the offset distance of the plane II, i.e. the offset direction is X₁In the positive direction, the offset distance is the base radius of β surfaces on the conical worm

Then drawing No. 3 straight line in the plane II, wherein the head end of the No. 3 straight line is Z₁In the negative axial direction, with X₁Y₁A face distance of l_β-P_βAccording to the determination of the slope of the line No. 3, i.e. in Z₁The positive direction of the axis is the beginning, the No. 3 straight line and Z₁The clockwise included angle of the positive direction of the axis in the plane I isThe length of line 105 No. 3 is 2d_1ca；

(2) Order to

The base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be known according to the equation_βAnd the coordinates of points on the spiral line can be used for drawing the spiral line;

creating No. 3 spiral line, the head end of No. 3 spiral line is coincident with the head end of No. 3 straight line, and the axis is Z₁Axis, pitch P_βHeight of L +3 XP_αAccording to

Determining the rotation direction of a No. 3 spiral line; the extension direction of No. 3 helical line is Z₁The negative axis direction;

creating No. 4 spiral line, the head end of No. 4 spiral line is coincided with the tail end of No. 3 straight line, and the axis is Z₁Axis, pitch P_βHeight of L +3 XP_αAccording toThe rotating direction of No. 3 spiral line is determined, and the extending direction of No. 3 spiral line is Z₁The negative axis direction;

(3) creating a No. 4 straight line which is a tangent of the No. 3 spiral line, wherein the head end of the No. 4 straight line is superposed with the tail end of the No. 3 spiral line, and the length of the No. 4 straight line is 2d_1caThe tail end of the No. 4 straight line is superposed with the tail end of the No. 4 spiral line;

(4) and (3) taking the No. 3 spiral line and the No. 4 spiral line as guide lines, taking the No. 3 straight line and the No. 4 straight line as outlines, creating a net-shaped curved surface II by utilizing a command of 'net-shaped curved surface' in software, and obtaining β surfaces after the net-shaped curved surface II is subjected to the trimming process of the step (3) in the three-dimensional modeling step of the conical worm.

The technical scheme is that the establishment of the conical worm three-dimensional model refers to the following steps:

(1) creating a conic surface of a spiroid

The axis of the conical surface of the top of the conical worm is Z₁Shaft, half cone angle delta₁At Z₁The diameter of the conical surface at the tip of the conical worm at the position E is d_1caThe whole body passes through the net-shaped curved surface I and the net-shaped curved surface II;

(2) creating a root cone of a spiroid worm

The axis of the conical surface of the top of the conical worm is Z₁Shaft, half cone angle delta₁At Z₁The diameter of the conical section of the worm root at the position E is d_1cfThe whole body passes through the net-shaped curved surface I and the net-shaped curved surface II;

(3) cutting curved surface

Cutting the reticular curved surface I and the reticular curved surface II to ensure that the head and the tail of the two curved surfaces are positioned in the plane I, filling the plane by utilizing the boundary lines of the head and the tail of the two curved surfaces to form a filling plane I and a filling plane II, and reserving the parts of the two curved surfaces between the conical surface of the top of the conical worm and the conical surface of the root of the conical worm, wherein the cut curved surfaces of the reticular curved surface I and the reticular curved surface II are α surfaces and β surfaces;

(4) generating conic worm entity

Cutting the conical worm top conical surface and conical worm root conical surface, reserving α surfaces, β surfaces, filling plane I and filling plane II parts, namely conical worm top conical cutting surface and conical worm root conical cutting surface, using 'joining' command in software to join α surfaces, β surfaces, filling plane I, filling plane II, conical worm top conical cutting surface and conical worm root conical cutting surface, creating a joining curved surface I, using 'closed curved surface' command in software to fill solid in the joining curved surface I to form conical worm gear tooth solid I, using the conical worm gear tooth solid I as object, using Z as object₁In a circular array with axis as center, the number of arrays being z₁Obtaining a gear tooth entity II of the conical worm; establishing a root cone model of the conical worm, wherein the half cone angle of the root cone is delta₁At Z₁Diameter d of cross section at E_1cfThe overall length is greater than the gear tooth entity I and the gear tooth entity II of the conical worm; finally cut off Z₁> -E and Z₁And the entity at < -E-L is completed by modeling the conical worm.

The establishment of the α' plane in the technical scheme is as follows:

(1) general formula (3)

Order to

Obtaining the coordinate value of the starting point0，l_α'Respectively correspond to X₂,Y₂,Z₂Coordinate values of the axes; order to

A linear parameter equation can be obtained, and the slope of the straight line is the slope of the No. 5 straight line;

establishing a plane III, plane III being Y₂Z₂Offset from the plane by X from the starting point₂The values of the axes determine the direction and distance of the offset of the plane III, i.e. the direction of the offset is X₂Negative direction, offset distance of

Drawing No. 5 straight line in the plane III, wherein the head end of the No. 5 straight line is Z₂Positive axial direction, and in X₂Z₂On the plane, the head end of No. 5 straight line and X₂Y₂Distance of face is l_α'+P_α'；

By

Determining the slope of line No. 5 by Z₂The positive direction of the axis is the beginning, the No. 5 straight line and Z₂The clockwise included angle of the positive axial direction on the plane III is

Has a length of

(2) Order to

Obtaining a base circle spiral line equation, and obtaining the rotation direction of the spiral line,Pitch P of the thread_α'And coordinates of points on the spiral line, for drawing the spiral line;

creating No. 5 spiral line, the head end of No. 5 spiral line is coincided with the head end of No. 5 straight line, and the axis is Z₂Axis, direction of extension Z₂Axial negative direction, pitch P_α'Height of 2P_α'According to

Determining the rotation direction of No. 5 spiral line;

creating No. 6 spiral line, the head end of No. 6 spiral line is coincided with the tail end of No. 5 straight line, and the axis is Z₂Axis, direction of extension Z₂Axial negative direction, pitch P_α'Height of 2P_α'According to

Determining the rotation direction of No. 6 spiral line;

(3) creating No. 6 straight line, the straight line is tangent to No. 5 spiral line, the head end of No. 6 straight line is coincided with the tail end of No. 5 spiral line, and the length is

The tail end of the No. 6 straight line is positioned on the No. 6 spiral line;

(4) and (3) taking the No. 5 spiral line and the No. 6 spiral line as guide lines and the No. 5 straight line and the No. 6 straight line as outlines, creating a net-shaped curved surface III by utilizing a ' net-shaped curved surface ' command in software, and obtaining an α ' surface after the net-shaped curved surface III is subjected to the trimming process of the step (4) in the three-dimensional modeling step of the bevel worm gear.

The establishment of the β' plane in the technical scheme is as follows:

(1) general formula (4)

Order to

Obtaining the coordinate value of the starting point

0，-l_β'Respectively correspond to X₂,Y₂,Z₂Coordinate values of the axes; order to

A linear parameter equation can be obtained, and the slope of the straight line is the slope of the No. 7 straight line;

create plane IV, which is Y₂Z₂Using the starting point X₂Coordinate values determine the offset direction and offset distance of plane IV, and the offset direction is X₂Negative direction, offset distance of

Drawing No. 7 straight line in the plane IV, wherein the head end of the No. 7 straight line is Z₂Axial negative semi-axis, with X₂Y₂Distance of axis l_β'+P_β'According to

The slope of line 7 can be determined, i.e. in Z₂The positive direction of the axis is from, the straight line is parallel to Z₂The clockwise included angle of the positive axial direction on the plane IV is

No. 7 straight line length of

The No. 7 straight line is marked with Z₂Rotation angle of shaft as axis

Obtaining No. 7 rotating straight line with the rotating direction along Z₂The positive direction of the axis looks at anticlockwise rotation;

(2) order to

The base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be known according to the equation_βAnd points on the helixCoordinates for drawing a spiral line;

creating No. 7 spiral line, the head end of No. 7 spiral line is coincided with the head end of No. 7 rotating straight line, and the axis is Z₂Axis, direction of extension Z₂Positive axial direction, pitch P_β'Height of 2P_β'According to

Determining the rotation direction of a No. 7 spiral line;

creating No. 8 spiral line, the head end of No. 8 spiral line is coincided with the tail end of No. 7 rotating straight line, and the axis is Z₂Axis, direction of extension Z₂Positive axial direction, pitch P_β'Height of 2P_β'According to

Determining the rotation direction of the No. 8 spiral line;

(3) creating No. 8 straight line, wherein the No. 8 straight line is a tangent line of the No. 7 spiral line, the head end of the No. 8 straight line is coincided with the tail end of the No. 7 spiral line, and the length of the No. 8 straight line isThe tail end of the No. 8 straight line is superposed with the No. 8 spiral line;

(4) and (3) taking the No. 7 spiral line and the No. 8 spiral line as guide lines, taking the No. 7 rotating straight line and the No. 8 straight line as outlines, creating a net-shaped curved surface IV by utilizing a ' net-shaped curved surface ' command in software, and obtaining an β ' surface after the net-shaped curved surface IV is subjected to the trimming process of the step (4) in the three-dimensional modeling step of the bevel gear.

The technical scheme is that the establishment of the three-dimensional model of the bevel worm gear comprises the following steps:

(1) creating a tapered worm gear tip cone

The axis of the top cone surface of the cone worm wheel is Z₂Shaft, half cone angle delta₂With vertex at Z₂Axial negative semi-axis and X₂Y₂Plane distance of | Δ l_2caThe radius of the big end of the top conical surface of the conical worm wheel is R_αThe opening direction is Z₂The shaft is in the positive direction;

(2) creating a root cone of a bevel worm gear

The axis of the conical surface of the conical worm gear root is Z₂Shaft, half cone angle delta₂(ii) a The normal distance between the root conical surface of the bevel worm wheel and the top conical surface of the bevel worm wheel is h, and the offset direction is Z₂In the positive axial direction, the radius of the big end of the conical surface of the root of the conical worm wheel is R_αThe opening direction is Z₂The shaft is in the positive direction;

(3) creating a curved surface of an inner ring of a bevel worm wheel and a curved surface of an outer ring of the bevel worm wheel

Respectively creating a radius of R_iAnd a radius R_aThe cylindrical curved surfaces are the inner ring curved surface of the bevel worm wheel and the outer ring curved surface of the bevel worm wheel, and the axes are Z₂The shaft and the two cylindrical curved surfaces need to pass through the reticular curved surface III and the reticular curved surface IV, and the radiuses are R respectively_αAnd R_i；

(4) Cutting curved surface

Cutting the net-shaped curved surface III and the net-shaped curved surface IV, and keeping the parts of the two curved surfaces in the middle of the conical surface at the top of the bevel worm wheel, the conical surface at the root of the bevel worm wheel, the curved surface at the inner ring of the bevel worm wheel and the curved surface at the outer ring of the bevel worm wheel, namely α 'surface and β' surface;

cutting the conical worm gear inner ring curved surface and the conical worm gear outer ring curved surface, and remaining the conical worm gear top cone cutting surface, the conical worm gear root cone cutting surface, the α 'surface and the β' surface, namely the conical worm gear inner ring cutting curved surface and the conical worm gear outer ring cutting curved surface;

jointing α 'surface, β' surface, bevel gear top cone cutting surface, bevel gear root cone cutting surface, bevel gear inner ring cutting curved surface and bevel gear outer ring cutting curved surface by using a 'jointing' command in software to create a jointing curved surface II;

(5) generating bevel worm gear tooth surface entity

Filling the joining curved surface II with a solid by means of a software 'closed curved surface' command to complete a bevel worm gear tooth, which is taken as an object, Z₂Circular array z with axis as axis of rotation₂The entity establishes a three-dimensional model of the root cone of the bevel worm gear by utilizing a 'rotator' command in software, and the axis of the root cone model of the bevel worm gear is Z₂Shaft, half cone angle delta₂(ii) a Conic worm gear root and conic wormThe normal distance of the top cone surface of the wheel is h, and the offset direction is Z₂In the positive axial direction, the radius of the large end is R_αThe opening direction is Z₂The shaft is forward, finally, an entity in the curved surface of the inner ring of the bevel worm gear is removed, and the modeling of the bevel worm gear is completed;

the assembly of the involute line contact conical worm and conical worm gear in the technical scheme is as follows:

(1) newly-built assembly body file, and part coordinate system S displayed in combination software₁And S₂Assembling, inserting the built three-dimensional models of the worm wheel and the worm, giving fixed constraint to the worm wheel, and giving Y to the worm₁Z₁Plane and cone worm wheel Y₂Z₂Plane offset constraint, wherein the offset is A;

(2) given conical worm X₁Y₁Plane and conic worm gear Z₂X₂Plane coincidence constraint, giving to conic worm Z₁X₁Flat and tapered worm gear X₂Y₂Plane coincidence constraint;

(3) satisfy the conical worm Y₁Z₁Planar on-cone worm gear X₂Negative axle shaft, conic worm Y₁Positive axial direction and bevel worm gear Z₂The positive direction of the axis is opposite, the conical worm Z₁Positive axial direction and conic worm wheel Y₂The positive directions of the axes are the same, and the conical worm X₁Shaft and bevel worm gear X₂The positive direction of the axis is the same.

Compared with the prior art, the invention has the beneficial effects that:

1. the three-dimensional modeling method of the involute line contact conical worm transmission pair can avoid parametric modeling and improve modeling efficiency and modeling precision;

2. because the tooth surfaces of the worm and the worm wheel in the three-dimensional modeling method of the involute line contact conical worm transmission pair are involute helicoids, the modeling methods of the worm and the worm wheel are similar, the penetration can be realized only by understanding the modeling method of one part, and the technical requirement of modeling is reduced;

3. according to the three-dimensional modeling method of the involute contact conical worm transmission pair, the assembly of the involute contact worm gear and the involute contact worm is completed by using the coordinate plane and the coordinate system in software, manual subjective adjustment is not needed, and the method is beneficial to subsequent programming.

Drawings

The invention is further described with reference to the accompanying drawings in which:

FIG. 1 is a block diagram of a modeling flow of a three-dimensional modeling method of an involute contact conical worm transmission pair according to the invention;

FIG. 2 is a block diagram of a three-dimensional modeling process of a conical worm in the three-dimensional modeling method of the involute contact conical worm transmission pair;

FIG. 3 is a graph of the relationship between the positions of curves required by modeling the face of the awl worm α in the three-dimensional modeling method of the involute contact awl worm transmission pair;

FIG. 4 is a graph of the relationship between the positions of curves required by modeling the face of the awl worm β in the three-dimensional modeling method of the involute contact awl worm transmission pair;

FIG. 5 is an axonometric view of the conical worm structure in the three-dimensional modeling method of the involute contact conical worm transmission pair according to the invention;

FIG. 6 is a graph of the relationship between the positions of curves required by modeling the surface of a bevel worm wheel α' in the three-dimensional modeling method of the involute contact bevel worm gear pair;

FIG. 7-1 is a graph of the relationship between the positions of curves required for modeling the surface β' of the bevel worm wheel in the three-dimensional modeling method of the involute contact bevel worm gear pair according to the present invention;

FIG. 7-2 is an enlarged partial view taken at A in FIG. 7-1;

FIG. 8 is an axonometric view of the gear tooth structure of the worm wheel of the bevel gear in the three-dimensional modeling method of the involute contact bevel worm gear transmission pair according to the present invention;

FIG. 9 is an axonometric view of the conical worm gear structure in the three-dimensional modeling method of the involute contact conical worm gear transmission pair according to the invention;

FIG. 10 is a perspective view of the bevel worm gear pair in the three-dimensional modeling method of the involute contact bevel worm gear pair according to the present invention;

FIG. 11-1 is a schematic diagram of the meshing of the α plane and the α' plane of the awl worm transmission pair in the three-dimensional modeling method of the involute contact awl worm transmission pair of the invention;

FIG. 11-2 is a schematic diagram of the meshing of the β plane and the β' plane of the awl worm transmission pair in the three-dimensional modeling method of the involute contact awl worm transmission pair of the invention;

in the figure, 1. a conic worm, No. 101.1 straight line head, No. 102.1 spiral line, No. 103.2 spiral line, No. 104.2 straight line, No. 109 straight line head, No. 102.1 straight line, No. 105.3 straight line, No. 6 straight line tail, No. 106.3 spiral line, No. spiral line head, No. 107.4 spiral line, No. spiral line head, No. number spiral line tail, No. 108.4 straight line, No. straight line head, No. 109 straight line tail, No. 110 face, No. 2 conic worm wheel, No. 201.5 straight line, No. 1 straight line head, No. # straight line tail, No. 202.5 spiral line, No. spiral line head, No. spiral line tail, No. 203.6 spiral line, No. 204.6 straight line, No. straight line head, No. 205.7 straight line, No. 206.7 straight line head, No. 206.7 head, No. rotary straight line tail, No. 207.7 head, No. 208.8 straight line tail, No. 208, No. 8 spiral line, No. 210 spiral line face, No. 210 worm gear tooth face.

Detailed Description

The invention is described in detail below with reference to the attached drawing figures:

for purposes of making the objects, aspects and advantages of the present invention more apparent, the following detailed modeling and assembling process is set forth in conjunction with the drawings and one embodiment, it being understood that the specific embodiments described herein are for purposes of illustration only and are not intended to be limiting. The specific parameters of the involute contact conical worm gear pair of the embodiment are shown in the following table

TABLE 1 three-dimensional modeling parameters of example involute line contact conical worm gear pair

The left tooth surface and the right tooth surface of the involute line contact awl worm are respectively an α surface and a β surface, wherein the vector expressions of any point on a α surface and a β surface are respectively as follows:

in the formula: i.e. i₁、j₁And k₁Respectively is the coordinate axis X of the coordinate system where the involute conical worm is positioned₁,Y₁,Z₁Direction vector of (u)_αAnd u_βIs a parameter of α planes and β planes and is greater than or equal to 0, and the geometric meaning is the length of a straight generatrix of the spiral plane theta_αAnd theta_βIs the angle parameters of α planes and β planes, and has the geometric meaning of the tangent point of the straight generatrix of the spiral plane and the spiral line of the base circle and the origin O of a coordinate system₁Connecting line with X₁The angle in the positive direction, positive being defined as from Z₁The involute-taper worm gear tooth surfaces matched with the involute-taper worm are α 'surfaces and β' surfaces respectively, wherein the vectors of any point on the α 'surface and the β' surface are respectively expressed as

In the formula: i.e. i₂、j₂And k₂Respectively is the coordinate axis X of the coordinate system where the involute cone worm gear is positioned₂,Y₂,Z₂Direction vector of (u)_α'And u_β'Is the parameters of α 'surface and β' surface, the geometric meaning is the length of the straight generatrix of the helical surface, theta_α'And theta_β'Is the angle parameters of α 'plane and β' plane, and has the geometric meaning of the tangent point of the straight generatrix of the spiral plane and the spiral line of the base circle and the origin O of the coordinate system₂Connecting line with X₂The angle in the positive direction, positive being defined as from Z₂Viewed in the positive direction, the counterclockwise direction is positive.

The example steps of the three-dimensional modeling of the involute line contact conical worm transmission pair are carried out under CATIA V5R 21 software, and the environment language of the software is simplified Chinese.

Referring to fig. 1, the three-dimensional modeling method of the involute contact conical worm transmission pair includes: modeling of an involute contact spiroid, modeling of an involute contact spiroid gear, and assembly of the involute contact spiroid gear.

1. Involute line contact conical worm three-dimensional modeling

Referring to fig. 2, the three-dimensional modeling of the involute contact conical worm comprises the following steps:

1) a part is newly built in CATIA software, a part coordinate system in the software is a conical worm coordinate system, and the coordinate system is set as S₁I.e. O₁-X₁,Y₁,Z₁；

2) Creating α face 109

Referring to fig. 2 and 3, the steps for establishing α face 109 are as follows:

(1) general formula (1)

Order to

Obtaining the coordinate value of the starting point

0，-l_αRespectively correspond to X₁,Y₁,Z₁Coordinate values of the axes; order toA linear parameter equation can be obtained, and the slope of the straight line is the slope of the No. 1 straight line 101;

create a plane I, which is Y₁Z₁Offset plane of plane according to starting point X₁The coordinate values of the axes define the offset direction and the offset distance of the plane I, i.e. the offset direction is X₁Positive direction, offset distance is base radius of face of worm αExamples of the embodiments

Drawing a No. 1 straight line 101 in a plane I, wherein the head end 10101 of the No. 1 straight line is in Z₁Axial negative direction and in X₁Z₁On the plane, with X₁Y₁A face distance of l_α-P_αExamples of the examples_α-P_α18.8864mm, according to

Determining the slope of line 101 No. 1, i.e. in Z₁The positive direction of the axis is from, the straight line is parallel to Z₁The clockwise included angle of the positive direction of the axis in the plane I is

Examples of the embodiments

The length of the No. 1 straight line 101 is 2d_1caExample 2d_1ca＝83.5180mm；

(2) Order toThe base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be known according to the equation_αAnd coordinates of points on the spiral line can be used for drawing the spiral line, in the embodiment, the rotation direction of the base circle spiral line is right-handed, and the thread pitch is P_α＝26.7171mm；

Creating a No. 1 spiral line 102, wherein the head end 10201 of the No. 1 spiral line is coincident with the head end 10101 of a No. 1 straight line, and the axis is Z₁Axis, pitch P_αExamples P_α26.7171mm, height L +3 XP_αExamples of L +3 XP_α173.6614 mm; according toDetermining the rotation direction of a No. 1 spiral line, wherein the rotation direction is right rotation in the embodiment; the extending direction of No. 1 spiral line 102 is Z₁The negative axis direction;

creating No. 2 spiral line 103, wherein the head end 10301 of the No. 2 spiral line is superposed with the head end 10102 of the No. 1 straight line, and the axis is Z₁Axis, pitch P_αExamples P_α26.7171mm, height L +3 XP_αExamples of L +3 XP_α173.6614mm, according to

Determining the rotation direction of a No. 2 spiral line 103, wherein the rotation direction is right rotation; no. 2 helix 103 extends in the direction Z₁The negative axis direction;

(3) drawing No. 2 straight line 104 in the plane I, with the head 10401 of No. 2 straight line in Z₁Axial negative direction and in X₁Z₁On the plane, the distance from the head end 10101 of No. 1 straight line is

Wherein

Represents a rounding of 0.5 epsilon up, in the examples

No. 2 straight line head 10401 is far from X compared with No. 1 straight line head 10101₁Y₁Surface, line No. 2 104 has the same slope as line No. 1 101, in Z₁The positive direction of the axis is the beginning, the No. 2 straight line and Z₁The clockwise included angle of the positive direction of the axis in the plane I is

Length of 2d_1caExamples of the embodiments

Length of 2d_1ca83.5180mm, the No. 2 straight end 10402 coincides with the No. 2 spiral line 103;

(4) taking the No. 1 spiral line 102 and the No. 2 spiral line 103 as guide lines, taking the No. 1 straight line 101 and the No. 2 straight line 104 as outlines, creating a net-shaped curved surface I by utilizing a command of 'net-shaped curved surface' in software, and obtaining α surfaces after the net-shaped curved surface I is subjected to the trimming process of the step (3) in the conical worm three-dimensional modeling step 4);

3) creating β faces 110

Referring to fig. 2 and 4, the steps for creating β planes 110 are as follows:

(1) general formula (2)

Order toObtaining the coordinate value of the starting point0，-l_βRespectively correspond to X₁,Y₁,Z₁Coordinate values of the axes; order to

A linear parameter equation can be obtained, and the slope of the straight line is the slope of the No. 3 straight line 105;

create plane II, which is Y₁Z₁Offset plane of plane according to starting point X₁The coordinate values of the axes define the offset direction and the offset distance of the plane II, i.e. the offset direction is X₁In the positive direction, the offset distance is the base radius of β surfaces on the conical worm 1Examples of the embodiments

Line No. 3 is then drawn in plane II with line No. 3 leading 10501 at Z₁In the negative axial direction, with X₁Y₁A face distance of l_β-P_βExamples of the examples_β-P_β9.5851mm, based on determining the slope of line 105 # 3, i.e. in Z₁Line 105 and Z in No. 3 with the positive direction of the axis as the start₁The clockwise included angle of the positive direction of the axis in the plane I isExamples of the embodiments

The length of line 105 No. 3 is 2d_1caExample 2d_1ca＝83.5180；

(2) Order to

The base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be known according to the equation_βAnd coordinates of points on the spiral line can be used for drawing the spiral line, in the embodiment, the rotation direction of the base circle spiral line is right-handed, and the thread pitch is P_β＝23.1472mm；

Creating No. 3 helix 106, with No. 3 helix head 10601 coinciding with No. 3 straight head 10501, with axis Z₁Axis, pitch P_βExamples P_β23.1472mm, height L +3 XP_αExamples of L +3 XP_α173.6614mm, according to

Determining the rotation direction of a No. 3 spiral line 106, wherein the rotation direction is right rotation; the extending direction of the No. 3 spiral line 106 is Z₁The negative axis direction;

creating No. 4 helix 107, with No. 4 helix head 10701 coinciding with No. 3 straight line end 10502, axis Z₁Axis, pitch P_βExamples P_β23.1472mm, highDegree of L +3 XP_αExamples of L +3 XP_α173.6614mm, according to

Determining the rotation direction of a No. 3 spiral line 107, wherein the rotation direction is right rotation; the extending direction of No. 3 spiral line 107 is Z₁The negative axis direction;

(3) creating a No. 4 straight line 108 that is tangent to the No. 3 helix 106, the No. 4 straight line head 10801 coinciding with the No. 3 helix end 10602 and having a length of 2d_1caExample 2d_1ca83.5180mm, number 4 straight end 10802 coincides with number 4 helical end 10702;

(4) taking the No. 3 spiral line 106 and the No. 4 spiral line 107 as guide lines, taking the No. 3 straight line 105 and the No. 4 straight line 108 as outlines, creating a net-shaped curved surface II by using a command of 'net-shaped curved surface' in software, and obtaining β surfaces 110 after the net-shaped curved surface II is subjected to the trimming process of the step (3) in the step 4) of the conical worm three-dimensional modeling;

4) creating a three-dimensional model of a spiroid

Referring to fig. 5, the steps for creating the conical worm three-dimensional model are as follows:

(1) creating a conic surface of a spiroid

The axis of the conical surface of the top of the conical worm is Z₁Shaft, half cone angle delta₁Example δ₁7.2477 °; at Z₁The diameter of the conical surface at the tip of the conical worm at the position E is d_1caExamples Z₁＝-E＝-38.8567，d_1ca41.7590mm, and the whole body passes through the net-shaped curved surface I and the net-shaped curved surface II;

(2) creating a root cone of a spiroid worm

The axis of the conical surface of the top of the conical worm is Z₁Shaft, half cone angle delta₁Example δ₁7.2477 °; at Z₁The diameter of the conical section of the worm root at the position E is d_1cfExamples Z₁＝-E＝-38.8567，d_1cf23.8509mm, and the whole body passes through the net-shaped curved surface I and the net-shaped curved surface II;

(3) cutting curved surface

Cutting the net-shaped curved surface I and the net-shaped curved surface II to enable the head and the tail of the two curved surfaces to be positioned in the plane I, filling the plane by utilizing the boundary lines of the head and the tail of the two curved surfaces to form a filling plane I and a filling plane II, reserving the parts of the two curved surfaces between the top conical surface of the worm and the root conical surface of the worm, and obtaining α surfaces 109 and β surfaces 110 after the net-shaped curved surface I and the net-shaped curved surface II are cut;

(4) generating conic worm entity

Cutting the conical worm top conical surface and the conical worm root conical surface, reserving α surfaces 109, β surfaces 110, a filling plane I and a filling plane II, namely the conical worm top conical cutting surface and the conical worm root conical cutting surface, joining α surfaces 109, β surfaces 110, the filling plane I, the filling plane II, the conical worm top conical cutting surface and the conical worm root conical cutting surface by using a 'joining' command in software, creating a joining curved surface I, filling a solid in the joining curved surface I to form a conical worm gear tooth solid I by using a 'closed curved surface' command in the software, taking the conical worm gear tooth solid I as an object, and taking Z as an object₁In a circular array with axis as center, the number of arrays being z₁In the example z₁Obtaining a conical worm gear tooth entity II; establishing a root cone model of the conical worm, wherein the half cone angle of the root cone is delta₁At Z₁Diameter d of section at-E-38.8567 mm_1cfThe overall length is greater than the gear tooth entity I and the gear tooth entity II of the conical worm; finally cut off Z₁> -E and Z₁And the entity at < -E-L is completed by modeling the conical worm.

2. Involute line contact cone worm gear three-dimensional modeling

Referring to fig. 2, since the bevel worm wheel 2 and the bevel worm 1 are both involute helicoids, the main three-dimensional modeling steps of the bevel worm wheel and the bevel worm are similar, and the involute line contact bevel worm wheel three-dimensional modeling steps are as follows:

1) a part is newly built in CATIA software, the coordinate system of the part is a cone worm gear coordinate system, and the coordinate system is set as S₂I.e. O₂-X₂,Y₂,Z₂；

2) Creation α' of face 211

Referring to fig. 6, the steps for establishing α' plane are as follows:

(1) general formula (3)

Order to

The coordinate value of the starting point can be obtained0，l_α'Respectively correspond to X₂,Y₂,Z₂Coordinate values of the axes; order to

A linear parameter equation can be obtained, and the slope of the straight line is the slope of the No. 5 straight line 201;

Examples of the embodimentsDrawing a No. 5 straight line 201 in a plane III, and drawing the head end 20101 of the No. 5 straight line in Z₂Positive axial direction, and in X₂Z₂On the plane, the head end of No. 5 straight line 20101 and X₂Y₂Distance of face is l_α'+P_α'Examples of the examples_α'+P_α'1077.6594mm, made of

Determine the slope of line 201 # 5 in Z₂Line 201 and Z in No. 5 with the positive axial direction as the start₂The clockwise included angle of the positive axial direction on the plane III is

Examples of the embodimentsHas a length of

Examples of the embodiments

(2) Order to

The base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be known according to the equation_α'And coordinates of points on the spiral line can be used for drawing the spiral line, in the embodiment, the spiral direction of the base circle is left-handed, and the thread pitch is P_α'＝990.2444mm；

Creating a No. 5 helix 202, with the No. 5 helix head 20201 coinciding with the No. 5 straight head 20101, with the axis Z₂Axis, direction of extension Z₂Axial negative direction, pitch P_α'Examples P_α'990.2444mm, height 2P_α'Example 2P_α'1980.4888mm, according to

Determining the rotation direction of the No. 5 spiral line 202, wherein the rotation direction is left rotation in the embodiment;

creating No. 6 helix 203, with No. 6 helix head 20301 coinciding with No. 5 straight end 20102, axis Z₂Axis, direction of extension Z₂Axial negative direction, pitch P_α'Examples P_α'990.2444mm, height 2P_α'Example 2P_α'1980.4888mm, according to

Determining the rotation direction of a No. 6 spiral line 203, wherein the rotation direction is left rotation;

(3) a No. 6 straight line 204 is created, the straight line is tangent to the No. 5 spiral line 202, the head end 20401 of the No. 6 straight line is superposed with the tail end 20202 of the No. 5 spiral line, and the length of the straight line is

Examples of the embodiments

Number 6 straight end 20402 should be located on number 6 spiral 203.

(4) Taking the No. 5 spiral line 202 and the No. 6 spiral line 203 as guide lines, taking the No. 5 straight line 201 and the No. 6 straight line 204 as outlines, creating a net-shaped curved surface III by utilizing a ' net-shaped curved surface ' command in software, and obtaining an α ' surface 211 after the net-shaped curved surface III is subjected to the trimming process of the step (4) in the cone worm wheel three-dimensional modeling step 4);

3) creation β' of face 212

Referring to fig. 7-1 and 7-2, the steps for creating the β' plane are as follows:

(1) general formula (4)

Order to

Obtaining the coordinate value of the starting point

A linear parameter equation can be obtained, and the slope of the straight line is the slope of the No. 7 straight line 205;

Examples of the embodiments

Drawing No. 7 straight line 205 in plane IV, with No. 7 straight line head end 20501 in Z₂Axial negative semi-axis, with X₂Y₂Distance of axis l_β'+P_β'Examples of the examples_β'+P_β'1308.5095mm, according to

The slope of line 205 # 7 can be determined, i.e., in Z₂The positive direction of the axis is from, the straight line is parallel to Z₂The clockwise included angle of the positive axial direction on the plane IV is

Examples of the embodiments

Line No. 7 205 has a length ofExamples of the embodiments

Line No. 7 is marked with Z₂Rotation angle of shaft as axis

Examples of the embodiments

Obtain No. 7 rotation line 206, the rotation direction is along Z₂The positive direction of the axis looks at anticlockwise rotation;

(2) order toThe base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be known according to the equation_βAnd coordinates of points on the spiral line can be used for drawing the spiral line, in the embodiment, the rotation direction of the base circle spiral line is right-handed, and the thread pitch is P_β'＝1240.9817mm；

CreatingNo. 7 helix 207, No. 7 helix head 20701 coincides with No. 7 rotation straight head 20601, the axis is Z₂Axis, direction of extension Z₂Positive axial direction, pitch P_β'Examples P_β'1240.9817mm, height 2P_β'Example 2P_β'2481.9634mm, according to

Determining the rotation direction of a No. 7 spiral line, wherein the rotation direction is right rotation;

creating No. 8 spiral line 208, wherein the head end 20801 of the No. 8 spiral line is superposed with the tail end 20602 of the No. 7 rotating straight line, and the axis is Z₂Axis, direction of extension Z₂Positive axial direction, pitch P_β'Examples P_β'1240.9817mm, height 2P_β'Example 2P_β'2481.9634mm, according to

Determining the rotation direction of a No. 8 spiral line, wherein the rotation direction is right rotation;

(3) creating a No. 8 straight line 209, the No. 8 straight line 209 being a tangent to the No. 7 helix 207, the No. 8 straight line head end 20901 coinciding with the No. 7 helix end 20702 and having a length of

Examples of the embodiments

Number 8 straight end 20902 coincides with number 8 helix 208;

(4) taking the No. 7 spiral line 207 and the No. 8 spiral line 208 as guide lines, taking the No. 7 rotating straight line 206 and the No. 8 straight line 209 as outlines, and creating a net-shaped curved surface IV by using a ' net-shaped curved surface ' command in software, wherein the net-shaped curved surface IV obtains β ' surface 212 after the trimming process of the step (4) in the cone worm wheel three-dimensional modeling step 4);

4) creating a three-dimensional model of a pyramidal worm gear

The steps for creating the three-dimensional model of the bevel worm gear are as follows:

(1) creating a tapered worm gear tip cone

The axis of the top cone surface of the cone worm wheel is Z₂Shaft, half cone angle delta₂With vertex at Z₂Axial negative semi-axis and X₂Y₂Plane distance of | Δ l_2caI, example | Δ l_2ca4.2998mm, the radius of the big end of the top conical surface of the conical worm wheel is R_αExamples of R_α169.7689mm, opening direction Z₂The shaft is in the positive direction;

(2) creating a root cone of a bevel worm gear

The axis of the conical surface of the conical worm gear root is Z₂Shaft, half cone angle delta₂Example δ₂79.9132 °; the normal distance between the root conical surface of the bevel worm wheel and the top conical surface of the bevel worm wheel is h, in the embodiment, h is 8.8825mm, and the offset direction is Z₂In the positive axial direction, the radius of the big end of the conical surface of the root of the conical worm wheel is R_αExamples of R_α169.7689mm, opening direction Z₂The shaft is in the positive direction;

Respectively creating a radius of R_iAnd a radius R_aThe cylindrical curved surfaces are the inner ring curved surface of the bevel worm wheel and the outer ring curved surface of the bevel worm wheel, and the axes are Z₂The shaft and the two cylindrical curved surfaces need to pass through the reticular curved surface III and the reticular curved surface IV, and the radiuses are R respectively_αAnd R_iIn the embodiment, R is created separately_i106.3041mm and R_α169.7689mm cylindrical curved surface;

(4) cutting curved surface

Cutting the reticular curved surface III and the reticular curved surface IV, reserving the parts of the two curved surfaces in the middle of the conical surface at the top of the bevel worm wheel, the conical surface at the root of the bevel worm wheel, the curved surface at the inner ring of the bevel worm wheel and the curved surface at the outer ring of the bevel worm wheel, namely α 'surface 211 and β' surface 212, reserving the parts of the conical surface at the top of the bevel worm wheel and the conical surface at the root of the bevel worm wheel between α 'surface 211 and β' surface 212, namely the conical surface at the top of the bevel worm wheel and the conical surface at the root of the bevel worm wheel, cutting the curved surface at the inner ring of the bevel worm wheel, cutting the curved surface at the outer ring of the bevel worm wheel, reserving the parts of the conical surface at the top of the bevel worm wheel, cutting the conical surface at the root of the bevel worm wheel, cutting the curved surface at the α 'surface 211 and the β' surface 212, namely the cutting curved surface at the inner ring of the bevel gear and the outer ring of the bevel worm wheel;

(5) generating bevel worm gear tooth surface entity

Referring to FIGS. 8 and 9, the filling of the mating curved surface II with entities using the software "closed surface" command completes a worm gear tooth 210, which is the target of Z₂Circular array z with axis as axis of rotation₂Individual entities, examples z₂Obtaining all gear teeth of the bevel worm wheel, then establishing a three-dimensional model of the bevel worm wheel root cone by utilizing a 'rotator' command in software, wherein the axis of the model of the bevel worm wheel root cone is Z₂Shaft, half cone angle delta₂Example δ₂79.9132 °; the normal distance between the root conical surface of the bevel worm wheel and the top conical surface of the worm wheel is h, in the embodiment, h is 8.8825mm, and the offset direction is Z₂In the positive axial direction, the radius of the large end is R_αExamples of the embodiments

Opening direction Z₂The shaft is forward, finally, an entity in the curved surface of the inner ring of the bevel worm gear is removed, and the modeling of the bevel worm gear is completed;

3. involute line contact taper worm and cone worm gear assembly

Referring to fig. 10, the assembling steps of the involute line contact conical worm and conical worm gear are as follows:

1) newly-built assembly body file, and part coordinate system S displayed in combination software₁And S₂Assembling, inserting the built three-dimensional model of the conical worm wheel, and using 'fixed constraint' in software to give fixed constraint to the conical worm wheel, limit the whole freedom of the conical worm wheel and give Y-shaped conical worm for convenient assembly₁Z₁Plane and cone worm wheel Y₂Z₂Plane offset constraint, the offset is A, in the embodiment, A is-100 mm;

2) given conical worm X₁Y₁Plane and conic worm gear Z₂X₂Plane coincidence constraint, giving to conic worm Z₁X₁Flat and tapered worm gear X₂Y₂Plane coincidence constraint;

3) at the same time, it should also be satisfied that the conical worm Y₁Z₁Planar on-cone worm gear X₂Negative axle shaft, conic worm Y₁Positive axial direction and bevel worm gear Z₂The positive direction of the axis is opposite, the conical worm Z₁Positive axial direction and conic worm wheel Y₂The positive directions of the axes are the same, and the conical worm X₁Shaft and bevel worm gear X₂The positive direction of the axis is the same.

And (3) modeling accuracy verification:

referring to fig. 11-1 and 11-2, by using a 'cutting' command in software, a plane I and a plane II are respectively used as geometric targets to cut the assembly body, if a α surface and a α 'surface, and a β surface and a β' surface are respectively meshed simultaneously by taking a plurality of straight lines as instantaneous contact lines, the modeling is proved to be correct, and at this time, the assembly of the involute line contact bevel worm gear is completed.

According to the invention, the characteristic that the involute line contacts the tooth surface of the bevel worm gear and the bevel worm is a spiral involute surface is utilized, the tooth surface is generated by sweeping around a base circle spiral line by using a tooth surface generatrix based on CATIA software, and the assembly is completed by utilizing a CATIA coordinate system. The modeling principles of the worm gear and the worm cone are the same, the modeling method is similar, the modeling method does not depend on parametric modeling, the property of the tooth surface is tightly combined according to a curved surface equation, the modeling and assembling method is simple, efficient and systematic, the auxiliary processing and manufacturing can be realized, and a good foundation can be laid for the subsequent research on the aspects of mechanical property, efficiency and the like.

Claims

1. A three-dimensional modeling method of an involute contact conical worm transmission pair is characterized by comprising the following steps:

1) three-dimensional modeling of an involute line contact conical worm:

(2) Establishing α faces (109);

(3) establishing β faces (110);

(4) creating a conical worm three-dimensional model;

2) three-dimensional modeling of an involute line contact cone worm gear:

(2) Establishing α' face (211);

(3) establishing β' face (212);

(4) establishing a three-dimensional model of the bevel worm gear;

3) the involute line contacts the bevel worm and worm gear assembly.

2. The method for three-dimensional modeling of an involute contact spiroid drive pair according to claim 1, wherein the establishing α planes (109) is:

(1) general formula (1)

Order to

Obtaining the coordinate value of the starting point

order to

Obtaining a linear parameter equation, wherein the slope of the straight line is the slope of the No. 1 straight line (101);

Drawing a No. 1 straight line (101) in a plane I, wherein the head end (10101) of the No. 1 straight line is arranged in Z₁Axial negative direction and in X₁Z₁On the plane, with X₁Y₁A face distance of l_α-P_αAccording to

Determining the slope of line No. 1 (101), i.e. in Z₁The positive direction of the axis is from, the straight line is parallel to Z₁The clockwise included angle of the positive direction of the axis in the plane I isThe length of the No. 1 straight line (101) is 2d_1ca；

(2) Order to

creating a No. 1 spiral line (102), wherein the head end (10201) of the No. 1 spiral line is superposed with the head end (10101) of the No. 1 straight line, and the axis is Z₁Axis, pitch P_αHeight of L +3 XP_α(ii) a According toDetermining the rotation direction of a No. 1 spiral line;

creating a No. 2 spiral line (103), wherein the head end (1030)1 of the No. 2 spiral line is superposed with the head end (10102) of the No. 1 straight line, and the axis is Z₁Axis, pitch P_αHeight of L +3 XP_αAccording toThe rotation direction of No. 2 spiral line (103) is determined, and the extension direction of No. 2 spiral line (103) is Z₁The negative axis direction;

(3) drawing a No. 2 straight line (104) in a plane I, wherein the head end (10401) of the No. 2 straight line is arranged in a Z direction₁Axial negative direction and in X₁Z₁On the plane, the distance from the head end (10101) of the No. 1 straight line is

Wherein

Represents that 0.5 epsilon is rounded up; the head end of No. 2 straight line (10401) is far from X than the head end of No. 1 straight line (10101)₁Y₁Surface, slope of line No. 2 (104) is the same as line No. 1 (101), and is represented by Z₁The positive direction of the axis is the beginning, the No. 2 straight line and Z₁The clockwise included angle of the positive direction of the axis in the plane I isLength of 2d_1caThe tail end (10402) of the No. 2 straight line is superposed with the No. 2 spiral line (103);

(4) and (3) taking the No. 1 spiral line (102) and the No. 2 spiral line (103) as guide lines and the No. 1 straight line (101) and the No. 2 straight line (104) as outlines, creating a net-shaped curved surface I by using a 'net-shaped curved surface' command in software, wherein α surfaces (109) are obtained after the net-shaped curved surface I is subjected to a trimming process of the step (3) in the three-dimensional modeling step of the conical worm.

3. The method for three-dimensional modeling of an involute contact spiroid drive pair of claim 1, wherein said creating β planes (110) comprises:

(1) general formula (2)

Order toThe coordinate value of the starting point can be obtained

A linear parameter equation can be obtained, and the slope of the straight line is the slope of the No. 3 straight line (105);

create plane II, which is Y₁Z₁Offset plane of plane according to starting point X₁The coordinate values of the axes define the offset direction and the offset distance of the plane II, i.e. the offset direction is X₁In the positive direction, the offset distance is the base radius of β surfaces on the conical worm (1)

Then drawing No. 3 straight line (105) in the plane II, wherein the head end (10501) of the No. 3 straight line is arranged in Z₁In the negative axial direction, with X₁Y₁A face distance of l_β-P_βAccording to the determination of the slope of the line (105) No. 3, i.e. in Z₁Line No. 3 (105) and Z in the positive direction of the axis₁The clockwise included angle of the positive direction of the axis in the plane I is

The length of line 105 No. 3 is 2d_1ca；

(2) Order toThe base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be known according to the equation_βAnd the coordinates of points on the spiral line can be used for drawing the spiral line;

creating a No. 3 spiral line (106), wherein the head end (10601) of the No. 3 spiral line is superposed with the head end (10501) of the No. 3 straight line, and the axis is Z₁Axis, pitch P_βHeight of L +3 XP_αAccording to

Determining the rotation direction of a No. 3 spiral line (106); no. 3 helical line(106) The direction of extension is Z₁The negative axis direction;

creating No. 4 spiral line (107), wherein the head end (10701) of the No. 4 spiral line is superposed with the tail end (10502) of the No. 3 straight line, and the axis is Z₁Axis, pitch P_βHeight of L +3 XP_αAccording to

The rotating direction of the No. 3 spiral line (107) is determined, and the extending direction of the No. 3 spiral line (107) is Z₁The negative axis direction;

(3) creating a No. 4 straight line (108) which is a tangent of the No. 3 spiral line (106), wherein the head end (10801) of the No. 4 straight line is superposed with the tail end (10602) of the No. 3 spiral line, and the length of the No. 4 straight line is 2d_1caThe No. 4 straight line end (10802) is superposed with the No. 4 spiral line end (10702);

(4) and (3) taking the No. 3 spiral line (106) and the No. 4 spiral line (107) as guide lines and taking the No. 3 straight line (105) and the No. 4 straight line (108) as outlines, and creating a net-shaped curved surface II by using a command of 'net-shaped curved surface' in software, wherein β surfaces (110) are obtained after the net-shaped curved surface II is subjected to the trimming process of the step (3) in the three-dimensional modeling step of the conical worm.

4. The method for three-dimensional modeling of an involute contact spiroid transmission pair according to claim 1, wherein the creating of the spiroid three-dimensional model is:

(1) creating a conic surface of a spiroid

(2) creating a root cone of a spiroid worm

(3) cutting curved surface

Cutting the reticular curved surface I and the reticular curved surface II to ensure that the head and the tail of the two curved surfaces are positioned in the plane I, filling the plane by utilizing the boundary lines of the head and the tail of the two curved surfaces to form a filling plane I and a filling plane II, reserving the parts of the two curved surfaces between the conical surface of the top of the conical worm and the conical surface of the root of the conical worm, and obtaining α surfaces (109) and β surfaces (110) after the reticular curved surface I and the reticular curved surface II are cut;

(4) generating conic worm entity

Cutting the conical worm top conical surface and the conical worm root conical surface, reserving α surfaces (109), β surfaces (110), a filling plane I and a filling plane II, namely the conical worm top conical cutting surface and the conical worm root conical cutting surface, utilizing a 'joint' command in software to joint α surfaces (109), β surfaces (110), the filling plane I, the filling plane II, the conical worm top conical cutting surface and the conical worm root conical cutting surface, creating a joint curved surface I, utilizing a 'closed curved surface' command in the software to fill a solid in the joint curved surface I to form a conical worm gear tooth solid I, taking the conical worm gear tooth solid I as an object, and taking Z as the object₁In a circular array with axis as center, the number of arrays being z₁Obtaining a gear tooth entity II of the conical worm; establishing a root cone model of the conical worm, wherein the half cone angle of the root cone is delta₁At Z₁Diameter d of cross section at E_1cfThe overall length is greater than the gear tooth entity I and the gear tooth entity II of the conical worm; finally cut off Z₁> -E and Z₁And the entity at < -E-L is completed by modeling the conical worm.

5. The method for three-dimensional modeling of an involute contact spiroid drive pair according to claim 1, wherein said creating α' plane (211) is:

(1) general formula (3)

Order to

Obtaining the coordinate value of the starting point

0，l_α'Respectively correspond to X₂,Y₂,Z₂Coordinate values of the axes; order to

A linear parameter equation can be obtained, and the slope of the straight line is the slope of the No. 5 straight line (201);

Drawing a No. 5 straight line (201) in a plane III, wherein the head end (20101) of the No. 5 straight line is arranged in Z₂Positive axial direction, and in X₂Z₂On the plane, the head end of No. 5 straight line (20101) and X₂Y₂Distance of face is l_α'+P_α'；

By

Determining the slope of line No. 5 (201) as Z₂The positive direction of the axis is the beginning, the No. 5 straight line (201) and the Z₂The clockwise included angle of the positive axial direction on the plane III is

Has a length of

(2) Order to

Obtaining a base circle helix equation, and obtaining the rotation direction and the pitch P of the helix according to the equation_α'And coordinates of points on the spiral line, for drawing the spiral line;

creating a No. 5 spiral line (202), wherein the head end (20201) of the No. 5 spiral line is superposed with the head end (20101) of the No. 5 straight line, and the axis is Z₂Shaft, extensionIn the direction Z₂Axial negative direction, pitch P_α'Height of 2P_α'According to

Determining the rotation direction of a No. 5 spiral line (202);

creating a No. 6 spiral line (203), wherein the head end (20301) of the No. 6 spiral line is superposed with the tail end (20102) of the No. 5 straight line, and the axis is Z₂Axis, direction of extension Z₂Axial negative direction, pitch P_α'Height of 2P_α'According toDetermining the turning direction of a No. 6 spiral line (203);

(3) creating a No. 6 straight line (204) which is a tangent of the No. 5 spiral line (202), wherein the head end (20401) of the No. 6 straight line is superposed with the tail end (20202) of the No. 5 spiral line, and the length of the straight line is equal to that of the No. 5 spiral lineThe No. 6 straight line end (20402) is positioned on the No. 6 spiral line (203);

(4) and (3) taking the No. 5 spiral line (202) and the No. 6 spiral line (203) as guide lines and the No. 5 straight line (201) and the No. 6 straight line (204) as outlines, creating a net-shaped curved surface III by using a ' net-shaped curved surface ' command in software, wherein the net-shaped curved surface III obtains α ' surface (211) after the trimming process of the step (4) in the cone-worm three-dimensional modeling step.

6. The method for three-dimensional modeling of an involute contact spiroid drive pair according to claim 1, wherein said creating β' plane (212) is:

(1) general formula (4)

Order to

Obtaining the coordinate value of the starting point

A linear parameter equation can be obtained, and the slope of the straight line is the slope of the No. 7 straight line (205);

Drawing No. 7 straight line (205) in plane IV, and the head end (20501) of No. 7 straight line in Z₂Axial negative semi-axis, with X₂Y₂Distance of axis l_β'+P_β'According to

The slope of line # 7 (205) can be determined, i.e., in Z₂The positive direction of the axis is from, the straight line is parallel to Z₂The clockwise included angle of the positive axial direction on the plane IV is

The length of the No. 7 straight line (205) is

The No. 7 straight line (205) is divided by Z₂Rotation angle of shaft as axis

Obtaining a No. 7 rotating straight line (206) with the rotating direction along Z₂The positive direction of the axis looks at anticlockwise rotation;

(2) order to

The base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be known according to the equation_βAnd coordinates of points on the spiral line, for drawing the spiral line;

creating No. 7 spiral line (207), wherein the head end (20701) of the No. 7 spiral line is superposed with the head end (20601) of the No. 7 rotating straight line, and the axis is Z₂Axis, direction of extension Z₂Positive axial direction, pitch P_β'Height of 2P_β'According to

Determining the rotation direction of a No. 7 spiral line;

creating a No. 8 spiral line (208), wherein the head end (20801) of the No. 8 spiral line is superposed with the tail end (20602) of the No. 7 rotating straight line, and the axis is Z₂Axis, direction of extension Z₂Positive axial direction, pitch P_β'Height of 2P_β'According toDetermining the rotation direction of the No. 8 spiral line (208);

(3) creating a No. 8 straight line (209), wherein the No. 8 straight line (209) is a tangent of the No. 7 spiral line (207), the head end (20901) of the No. 8 straight line is superposed with the tail end (20702) of the No. 7 spiral line, and the length of the No. 8 straight line is equal to that of the No. 7 spiral line

The end (20902) of the No. 8 straight line is superposed with the No. 8 spiral line (208);

(4) and (3) taking the No. 7 spiral line (207) and the No. 8 spiral line (208) as guide lines and the No. 7 rotating straight line (206) and the No. 8 straight line (209) as outlines, and creating a net-shaped curved surface IV by using a ' net-shaped curved surface ' command in software, wherein the net-shaped curved surface IV obtains β ' surface (212) after the trimming process of the step (4) in the cone worm gear three-dimensional modeling step.

7. The method for three-dimensional modeling of an involute contact spiroid transmission pair according to claim 1, wherein the creating of the spiroid wheel three-dimensional model is:

(1) creating a tapered worm gear tip cone

(2) creating a root cone of a bevel worm gear

(4) Cutting curved surface

Cutting the net-shaped curved surface III and the net-shaped curved surface IV, and keeping the parts of the two curved surfaces in the middle of the conical surface at the top of the bevel worm wheel, the conical surface at the root of the bevel worm wheel, the curved surface at the inner ring of the bevel worm wheel and the curved surface at the outer ring of the bevel worm wheel, namely α 'surface (211) and β' surface (212);

cutting the conical worm gear top conical surface and the conical worm gear root conical surface, and reserving the parts of the conical worm gear top conical surface and the conical worm gear root conical surface between a α 'surface (211) and a β' surface (212), namely the conical worm gear top conical cutting surface and the conical worm gear root conical cutting surface;

jointing α 'surface (211), β' surface (212), the bevel gear top cone cutting surface, the bevel gear root cone cutting surface, the bevel gear inner ring cutting curved surface and the bevel gear outer ring cutting curved surface by utilizing a 'jointing' command in software to create a jointing curved surface II;

(5) generating bevel worm gear tooth surface entity

By means of a software "closed curve" command, the joining curve II is filled with a solid body to complete a bevel worm gear tooth (210), subject to this tooth, Z₂Circular array z with axis as axis of rotation₂The entity establishes a three-dimensional model of the root cone of the bevel worm gear by utilizing a 'rotator' command in software, and the axis of the root cone model of the bevel worm gear is Z₂Shaft, half cone angle delta₂(ii) a The normal distance between the root conical surface of the bevel worm wheel and the top conical surface of the bevel worm wheel is h, and the offset direction is Z₂In the positive axial direction, the radius of the large end is R_αThe opening direction is Z₂And (5) the shaft is forward, and finally, the entity in the curved surface of the inner ring of the bevel worm gear is removed, and the modeling of the bevel worm gear is completed.

8. The three-dimensional modeling method of the involute contact bevel worm gear pair according to claim 1, wherein the assembling of the involute contact bevel worm gear is as follows: