CN110766801A - Three-dimensional modeling method for involute line contact conical worm transmission pair - Google Patents
Three-dimensional modeling method for involute line contact conical worm transmission pair Download PDFInfo
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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
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 toObtaining the coordinate value of the starting point0,-lαRespectively correspond to X1,Y1,Z1Coordinate values of the axes;
order toObtaining 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 lα-PαAccording toDetermining 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 isThe length of line No. 1 is 2d1ca;
(2) Order toThe base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be obtained according to the equationαAnd 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 PαHeight of L +3 XPα(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 PαHeight of L +3 XPαAccording toDetermining 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 isWhereinRepresents 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 isLength of 2d1caNo. 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 toThe coordinate value of the starting point can be obtained0,-lβRespectively 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. 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 wormThen 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 lβ-PβAccording 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 2d1ca;
(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 equationβAnd 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 PβHeight of L +3 XPαAccording toDetermining 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 PβHeight of L +3 XPαAccording 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 2d1caThe 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 d1caThe 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 d1cfThe 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 E1cfThe 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 toObtaining the coordinate value of the starting point0,lα'Respectively correspond to X2,Y2,Z2Coordinate 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. 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 ofDrawing 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 lα'+Pα';
ByDetermining 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 isHas a length of
(2) Order toObtaining a base circle spiral line equation, and obtaining the rotation direction of the spiral line,Pitch P of the threadα'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 Pα'Height of 2Pα'According toDetermining 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 Pα'Height of 2Pα'According toDetermining 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 isThe 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 toObtaining the coordinate value of the starting point0,-lβ'Respectively correspond to X2,Y2,Z2Coordinate 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. 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 lβ'+Pβ'According toThe 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 isNo. 7 straight line length ofThe No. 7 straight line is marked with Z2Rotation angle of shaft as axisObtaining No. 7 rotating straight line with the rotating direction 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 equationβAnd 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 Pβ'Height of 2Pβ'According toDetermining 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 Pβ'Height of 2Pβ'According toDetermining 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 l2caThe radius of the big end of the top conical surface of the conical worm wheel is RαThe 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 RαThe 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 RiAnd a radius RaThe 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 respectivelyαAnd Ri;
(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 RαThe 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 uβIs 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 thetaαAnd thetaβIs 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 uβ'Is the parameters of α 'surface and β' surface, the geometric meaning is the length of the straight generatrix of the helical surface, thetaα'And thetaβ'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 toObtaining the coordinate value of the starting point0,-lαRespectively 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 lα-PαExamples of the examplesα-Pα18.8864mm, according toDetermining 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 isExamples of the embodimentsThe length of the No. 1 straight line 101 is 2d1caExample 2d1ca=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 equationαAnd 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 Pα=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 PαExamples Pα26.7171mm, height L +3 XPαExamples of L +3 XPα173.6614 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 PαExamples Pα26.7171mm, height L +3 XPαExamples of L +3 XPα173.6614mm, according toDetermining 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 isWhereinRepresents a rounding of 0.5 epsilon up, in the examplesNo. 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 isLength of 2d1caExamples of the embodimentsLength of 2d1ca83.5180mm, 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,-lβRespectively 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. 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 embodimentsLine 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 lβ-PβExamples of the examplesβ-Pβ9.5851mm, 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 embodimentsThe length of line 105 No. 3 is 2d1caExample 2d1ca=83.5180;
(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 equationβAnd 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 Pβ=23.1472mm;
Creating No. 3 helix 106, with No. 3 helix head 10601 coinciding with No. 3 straight head 10501, with axis Z1Axis, pitch PβExamples Pβ23.1472mm, height L +3 XPαExamples of L +3 XPα173.6614mm, according toDetermining 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 PβExamples Pβ23.1472mm, highDegree of L +3 XPαExamples of L +3 XPα173.6614mm, according toDetermining 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 2d1caExample 2d1ca83.5180mm, 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 d1caExamples Z1=-E=-38.8567,d1ca41.7590mm, 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 d1cfExamples Z1=-E=-38.8567,d1cf23.8509mm, 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 mm1cfThe 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 toThe coordinate value of the starting point can be obtained0,lα'Respectively correspond to X2,Y2,Z2Coordinate 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. 5 straight line 201;
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 ofExamples 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 lα'+Pα'Examples of the examplesα'+Pα'1077.6594mm, made ofDetermine 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 isExamples of the embodimentsHas a length ofExamples of the embodiments
(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 equationα'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 Pα'=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 Pα'Examples Pα'990.2444mm, height 2Pα'Example 2Pα'1980.4888mm, according toDetermining 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 Pα'Examples Pα'990.2444mm, height 2Pα'Example 2Pα'1980.4888mm, according toDetermining 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 isExamples of the embodimentsNumber 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 toObtaining the coordinate value of the starting point0,-lβ'Respectively correspond to X2,Y2,Z2Coordinate 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. 7 straight line 205;
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 ofExamples 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 lβ'+Pβ'Examples of the examplesβ'+Pβ'1308.5095mm, according toThe 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 isExamples of the embodimentsLine No. 7 205 has a length ofExamples of the embodimentsLine No. 7 is marked with Z2Rotation angle of shaft as axisExamples of the embodimentsObtain 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 equationβAnd 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 Pβ'=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 Pβ'Examples Pβ'1240.9817mm, height 2Pβ'Example 2Pβ'2481.9634mm, according toDetermining 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 Pβ'Examples Pβ'1240.9817mm, height 2Pβ'Example 2Pβ'2481.9634mm, according toDetermining 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 ofExamples of the embodimentsNumber 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 l2caI, example | Δ l2ca4.2998mm, the radius of the big end of the top conical surface of the conical worm wheel is RαExamples of Rα169.7689mm, 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 RαExamples of Rα169.7689mm, opening direction 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 RiAnd a radius RaThe 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 respectivelyαAnd RiIn the embodiment, R is created separatelyi106.3041mm and Rα169.7689mm 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 RαExamples of the embodimentsOpening 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 (8)
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:
(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 (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:
(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' 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 toObtaining the coordinate value of the starting point0,-lαRespectively correspond to X1,Y1,Z1Coordinate values of the axes;
order toObtaining a linear parameter equation, wherein 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 α
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 lα-PαAccording toDetermining 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 2d1ca;
(2) Order toThe base circle helix equation can be obtained, and the rotation direction and the pitch P of the helix can be obtained according to the equationαAnd coordinates of points on the spiral line, for drawing the spiral line;
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 PαHeight of L +3 XPα(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 PαHeight of L +3 XPαAccording 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 isWhereinRepresents 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 2d1caThe 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 obtained0,-lβRespectively 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. 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 lβ-PβAccording 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 isThe length of line 105 No. 3 is 2d1ca;
(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 equationβAnd 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 PβHeight of L +3 XPαAccording toDetermining 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 PβHeight of L +3 XPαAccording toThe 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 2d1caThe 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
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 d1caThe 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 d1cfThe 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, 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 E1cfThe 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 toObtaining the coordinate value of the starting point0,lα'Respectively correspond to X2,Y2,Z2Coordinate 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. 5 straight line (201);
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 ofDrawing 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 lα'+Pα';
ByDetermining 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 isHas a length of
(2) Order toObtaining a base circle helix equation, and obtaining the rotation direction and the pitch P of the helix according to the equationα'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 Pα'Height of 2Pα'According toDetermining 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 Pα'Height of 2Pα'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 toObtaining the coordinate value of the starting point0,-lβ'Respectively correspond to X2,Y2,Z2Coordinate 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. 7 straight line (205);
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 (205) in plane IV, and the head end (20501) of No. 7 straight line in Z2Axial negative semi-axis, with X2Y2Distance of axis lβ'+Pβ'According toThe 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 isThe length of the No. 7 straight line (205) isThe No. 7 straight line (205) is divided by Z2Rotation angle of shaft as axisObtaining a No. 7 rotating straight line (206) with the rotating direction 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 equationβAnd 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 Pβ'Height of 2Pβ'According toDetermining 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 Pβ'Height of 2Pβ'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 lineThe 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
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 l2caThe radius of the big end of the top conical surface of the conical worm wheel is RαThe 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 RαThe 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 RiAnd a radius RaThe 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 respectivelyαAnd Ri;
(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 RαThe 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:
(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.
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