CN102102670B - Three-plane concurrent construction method and star wheel of single-screw compressor constructed by same - Google Patents

Three-plane concurrent construction method and star wheel of single-screw compressor constructed by same Download PDF

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CN102102670B
CN102102670B CN 201010279194 CN201010279194A CN102102670B CN 102102670 B CN102102670 B CN 102102670B CN 201010279194 CN201010279194 CN 201010279194 CN 201010279194 A CN201010279194 A CN 201010279194A CN 102102670 B CN102102670 B CN 102102670B
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CN102102670A (en
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李锦上
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Abstract

The invention discloses a star wheel (1). The star wheel (1) comprises a front side face (2), a tooth crestal face (3) and a rear side face (4) of star wheel teeth, and is characterized in that: the front side face, the tooth crestal face and the rear side face of the star wheel teeth are generated by a three-plane concurrent construction method. The three-plane concurrent construction method comprises the following steps of: constructing the front side face of the star wheel by using an axial plane theta Lj and a radial plane uk of a front enveloping surface; constructing the rear side face of the star wheel by using an axial plane theta Lj and a radial plane uk of a rear enveloping surface; and constructing the tooth crestal face of the star wheel by using an axial plane theta Lj and a radial plane theta lk of a tooth crestal enveloping surface.

Description

Three concurrent structured approaches and with the star-wheel of the single screw compressor of this method structure
Technical field
The present invention relates to software development, Machine Design and manufacturing technology field, particularly three concurrent structured approaches of space conjugation engagement pair secondary enveloping surface and adopt the star-wheel of the single screw compressor of this method construct.
Background technique
The field that space conjugation mesh theory is suitable for is very extensive, as the cutter in the machining, grinding tool, emery wheel; Crowded wheel in the material forming, roll, mould; Cam in the mechanical transmission, gear, worm and gear and anchor ring worm and gear; Single screw compressor in the fluid machinery, single-screw expander, helical-lobe compressor and pump class; The mechanism of precision instrumentation, conjugation engagement and other need the device of conjugation engagement; Etc..
The design of space conjugation engagement pair and manufacturing can realize with envelope method.
In a mechanical system that comprises three space O, I, II, wherein the O representative is with reference to space or static space, and I, II represent space, and I, II space with respect to O with reference to the motion in space respectively are If profile A is in the I space, when I space and profile A press with reference to the space with respect to O
Figure BSA00000265930100012
Motion, the II space is done with reference to the space with respect to O During motion, Profile A envelope in the II space goes out curved surface B, if satisfy meshing condition, this process is called the first enveloped of space conjugation engagement profile, and curved surface B then is called the first enveloped face B[1 of space conjugation engagement profile].
When the II space be included in the II space the first enveloped face B that come out by envelope with respect to O with reference to the space by φ 2Motion, the I space is φ with respect to O with reference to the space 1During motion,
Figure BSA00000265930100015
First enveloped face B envelope in the I space goes out curved surface
Figure BSA00000265930100016
Then this process is called the twice-enveloping of space conjugation engagement profile, curved surface
Figure BSA00000265930100017
The secondary enveloping surface that then is called space conjugation engagement profile
Figure BSA00000265930100018
The amphitypy body engagement that obtains through first and second envelope is exactly a pair of space conjugation engagement pair, and single screw compressor, single-screw expander and anchor ring worm and gear etc. are exactly typical space conjugation engagement pair.
At present, the design of screw rod in space conjugation engagement pair such as single screw compressor and the decompressor and the worm screw in the anchor ring worm and gear etc. and make and all to have mature technique, but as the design and fabrication technology famine of the secondary enveloping surfaces such as worm gear in the star-wheel in single screw compressor and the decompressor and the anchor ring worm and gear.When engineering circle relates to this technology, or be to avoid as " concerning enveloping worm pair, can not also there is no need all Line of contact are calculated and study.Usually only representational Line of contact is discussed, as entrance Line of contact, outlet Line of contact, a certain Line of contact instantaneous the time.[2] " or be the profile of really not designing star-wheel; can only obtain the profile of star-wheel according to the special plane rolling cut processing of the motion principle manufacturing of screw rod and star-wheel; " star-wheel is equivalent to globoid worm gear, and its flank of tooth is the envelope surface of screw tooth surface, can only process with rolling cut.[3]”
There are many defectives in the secondary enveloping surface of the star-wheel of employing rolling cut processing method Manufacture Order helical-lobe compressor (or single-screw expander) and the worm gear of anchor ring worm and gear, and the first needs special plane, so processing cost is very high, and manufacturing efficiency is very low; It two is that machining accuracy is difficult to control, because any machinery is all gapped, the engagement pair precision that the processing of the rolling cut of gapped tape error obtains is difficult to guarantee; It three is to produce difficulty in batches.
The desired location of multi-faceted cylindrical milling cutter when now also having by the processing screw rotor, get the surface that can touch the screw rotor flank of tooth on each milling cutter cylinder, these narrow strip surfaces are placed by former orientation, and with per two adjacently situated surfaces with the smooth connection of circumscribed straight line, [4] of handling by the approximation method of curve match with computer again.This method can not accurately obtain 5,10 in this Figure of description 2 and contact sealing work area with 13, more can not get 6,7,11,12, the 13 and 14 instantaneous contact areas that indicate, deviate from the engagement rule of space conjugation engagement pair in essence, can not obtain accurate engagement pair.
1, the new conjugate curved surface principle of Chen Zhi and application thereof--the new collection of thesis of Chen Zhi China Science Tech Publishing House 2008.5
2, all good Yong toroid helicoids worms are repaiied type principle and publishing house of the manufacturing technology National University of Defense technology 2005.9
3, Fang Yirong looks into comprehensive breakthrough mechanical development 1997.6 of single screw compressor technology such as generation beam
4, CN100408240C polycylindser milling envelope single screw compressor tooth face molded lines constructive method
Summary of the invention
Serious disappearance and deficiency at space conjugation engagement pair design and fabrication technology, the objective of the invention is to, three concurrent structured approaches of a kind of space conjugation engagement pair secondary enveloping surface are provided, intersect to produce the profile of the worm gear of the star-wheel of intersection point structure single screw compressor (or single-screw expander) and anchor ring worm and gear with secondary enveloping surface by constructing two auxiliary planes, design the three-dimensional stereo model of star-wheel then, the accurate conjugation engagement of implementation space conjugation engagement pair processes entity with turnning and milling Compositions of metal-working machines or five coordinate lathes etc. again in computer.To achieve these goals, the technology used in the present invention solution is as follows:
1, a kind of three concurrent structured approaches comprise the mechanical system of three space O, I, II, and wherein the O representative is with reference to space or static space, and I, II represent space, are r at I space vector function 1(u, profile v) is generating surface A to=A, presses with reference to the space with respect to O Motion, the II space is done with reference to the space with respect to O
Figure BSA00000265930100022
Motion, Generating surface A envelope in the II space generates first enveloped face B, and the vector function of first enveloped face B is Comprise the II space of making generating surface of first enveloped face B, press φ with respect to O with reference to the space 2Motion, the I space is φ with respect to O with reference to the space 1Motion,
Figure BSA00000265930100025
First enveloped face B envelope in the I space goes out secondary enveloping surface Secondary enveloping surface
Figure BSA00000265930100027
Vector function be
Figure BSA00000265930100028
It is characterized in that: the structure secondary enveloping surface With the following method:
(1), three faces of structure:
The structure envelope surface
Figure DEST_PATH_RE-GSB00000584207000011
According to secondary enveloping surface
Figure DEST_PATH_RE-GSB00000584207000012
Vector function
Figure DEST_PATH_RE-GSB00000584207000013
Get
Figure DEST_PATH_RE-GSB00000584207000014
(i=1,2 ..., n), obtain secondary enveloping surface
Figure DEST_PATH_RE-GSB00000584207000015
Vector function family
Figure DEST_PATH_RE-GSB00000584207000016
(i=1,2 ..., n) Biao Shi a n envelope surface, wherein the i envelope surface is called for short envelope surface
Figure DEST_PATH_RE-GSB00000584207000017
Structure axial plane θ Lj: with the line (a) at the center of described I space and II space or be parallel to the I space and the straight line of the line at II space center (b) is axis L and is done coaxial plane family, be r with vector function for sake of convenience j=θ (θ Lj) (j=1,2 ..., m) expression, θ LjBe family of planes r j=θ (θ Lj) (j=1,2 ..., m) in the characteristic angle on j plane, θ LjValue by selected reference level and j determines that wherein axial plane θ is called for short on the j plane Lj
Structure radial plane u kOr construct another axial plane θ Lk: making the family of planes perpendicular to described axis L, is r with vector function for sake of convenience k=u (u k) (k=1,2 ..., w) expression, u kBe family of planes r k=u (u k) (k=1,2 ..., w) in the intersection point of k plane and axis L along axis L to the I space or the distance of II space coordinate plane, wherein radial plane u is called for short on the k plane kPerhaps in the central plane of I space, making the straight line l perpendicular to described axis L, do the family of planes that axis was made described axis l with straight line l, is r with vector function for sake of convenience k=θ (θ Lk) (k=1,2 ..., w) expression, θ LkBe family of planes r k=θ (θ Lk) (k=1,2 ..., w) in the characteristic angle on k plane, θ LkValue by selected reference level and k determines that wherein axial plane θ is called for short on the k plane LkThe central plane of described I space was the central point of I space and perpendicular to the plane of the axis of I space.
(2), the intersection point d of three faces of structure Ijk min:
Utilize envelope surface
Figure DEST_PATH_RE-GSB00000584207000018
Axial plane θ LjWith radial plane u kThe intersection point d of these three faces of structure Ijk, according to intersection point d IjkDistance to axis L | d Ijk| value determine intersection point d for minimum principle Ijk minPerhaps utilize envelope surface
Figure DEST_PATH_RE-GSB00000584207000019
Axial plane θ LjWith axial plane θ LkThe intersection point d of these three faces of structure Ijk, according to intersection point d IjkArrive the distance at the center of I space | d Ijk| value determine intersection point d for minimum principle Ijk min
With graphical solution or three crossing intersection point d of analytic method structure Ijk min
Graphical solution is to utilize three-dimensional software in computer: at first construct envelope surface
Figure DEST_PATH_RE-GSB000005842070000110
Axial plane θ LjWith radial plane u kNext draws envelope surface
Figure DEST_PATH_RE-GSB000005842070000111
With axial plane θ LjIntersection l Ij, axial plane θ LjWith radial plane u kIntersection l Jk, radial plane u kAnd envelope surface
Figure DEST_PATH_RE-GSB000005842070000112
Intersection l KiThe 3rd draws three intersection l Ij, l JkAnd l KiIntersect the intersection point d that produces Ijk, envelope surface family
Figure DEST_PATH_RE-GSB000005842070000113
(i=1,2 ..., n) with intersection l JkN intersection point arranged; At last according to intersection point d IjkDistance to axis L | d Ijk| value determine intersection point d for minimum principle Ijk minPerhaps at first construct envelope surface
Figure DEST_PATH_RE-GSB000005842070000114
Axial plane θ LjWith axial plane θ LkNext draws envelope surface With axial plane θ LjIntersection l Ij, axial plane θ LjWith axial plane θ LkIntersection l Jk, axial plane θ LkAnd envelope surface
Figure DEST_PATH_RE-GSB00000584207000021
Intersection l KiThe 3rd draws three intersection l Ij, l JkAnd l KiIntersect the intersection point d that produces Ijk, envelope surface family (i=1,2 ..., n) with intersection l JkN intersection point arranged; At last according to intersection point d IjkArrive the distance at the center of I space | d Ijk| value determine intersection point d for minimum principle Ijk min
Analytic method is to utilize envelope surface
Figure DEST_PATH_RE-GSB00000584207000023
Axial plane θ LjWith radial plane u kConstruct n * m * w and organize set of equation; Find the solution the intersection point d of these set of equation IjkCoordinate figure; Find intersection d then IjkDistance to axis L | d Ijk|; Again according to intersection point d IjkDistance to axis L | d Ijk| value determine intersection point d for minimum principle Ijk minPerhaps use envelope surface
Figure DEST_PATH_RE-GSB00000584207000024
Axial plane θ LjWith axial plane θ LkConstruct n * m * w and organize set of equation; Find the solution the intersection point d of these set of equation IjkCoordinate figure; Find intersection d then IjkDistance to I space central point | d Ijk|; According to intersection point d IjkArrive the distance at the center of I space | d Ijk| value determine intersection point d for minimum principle Ijk min
(3), the secondary enveloping surface of structure space conjugation engagement pair
Figure DEST_PATH_RE-GSB00000584207000025
Choose envelope surface
Figure DEST_PATH_RE-GSB00000584207000026
Axial plane θ LjWith radial plane u kOr envelope surface
Figure DEST_PATH_RE-GSB00000584207000027
Axial plane θ LjWith another axial plane θ LkIn any one face, as axial plane θ Lj, link axial plane θ in order with smoothed curve LjIn all intersection point d Ijk min(k=1,2 ..., w), connection shaft is to family of planes θ again Lj(j=1,2 ..., m) the middle described smoothed curve of m bar namely constructs the secondary enveloping surface of space conjugation engagement pair
Figure DEST_PATH_RE-GSB00000584207000028
The star-wheel of the single screw compressor of three concurrent structured approach structures of a kind of usefulness, the star-wheel tooth comprises leading flank, trailing flank and Topland, it is characterized in that: the secondary enveloping surface of star-wheel
Figure DEST_PATH_RE-GSB00000584207000029
Be divided into the front side envelope surface
Figure DEST_PATH_RE-GSB000005842070000210
The rear side envelope surface
Figure DEST_PATH_RE-GSB000005842070000211
And addendum envelope Use the front side envelope surface
Figure DEST_PATH_RE-GSB000005842070000213
Axial plane θ LjWith radial plane u kThe leading flank of structure star-wheel is used the rear side envelope surface
Figure DEST_PATH_RE-GSB000005842070000214
Axial plane θ LjWith radial plane u kThe trailing flank of structure star-wheel is used addendum envelope
Figure DEST_PATH_RE-GSB000005842070000215
Axial plane θ LjWith axial plane θ LkThe Topland of structure star-wheel.
Marginal data
1, Fig. 1 is single screw compressor star-wheel and star-wheel tooth sectional drawing
In Fig. 1 a, 1 is star-wheel, and 2 is the leading flank of star-wheel tooth, and 3 is star-wheel tooth Topland, and 4 is the trailing flank of star-wheel tooth.Left side figure among Fig. 1 b is the drawing in side sectional elevation of star-wheel tooth, 5 is the conjugation contact sealed working face of leading flank among the figure, 6 is the instantaneous surface of contact of compression-side, 7 is the instantaneous surface of contact of back pressure side, 10 is the conjugation contact sealed working face of trailing flank, and 11 is the instantaneous surface of contact of compression-side, and 12 is the instantaneous surface of contact of back pressure side, 8 is the compression face of star-wheel tooth, and 9 is the back pressure face of star-wheel tooth.Right side figure among Fig. 1 b is the sectional arrangement drawing of star-wheel tooth, and 13 are tooth top conjugation contact sealed working face among the figure, and 14 is the instantaneous surface of contact of tooth top compression-side, and 15 is the instantaneous surface of contact of tooth top back pressure side.
2, Fig. 2 is the schematic diagram of three concurrent structured approaches
O-XYZ is the space coordinates of star-wheel, and Fig. 2 a mean camber A1-A2-A3-A4 is front side envelope surface or rear side envelope surface, and plane B1-B2-B3-B4 was that the structural plane of axis X or the X that parallels to the axis is axial plane θ Lj, the structural plane that plane C1-C2-C3-C4 is perpendicular to axis X is radial plane u kAmong Fig. 2 b, curved surface A1-A2-A3-A4 is addendum envelope, and plane B1-B2-B3-B4 was that the structural plane of axis X or the X that parallels to the axis is axial plane θ Lj, plane D1-D2-D3-D4 was that the structural plane of axis Y is axial plane θ Lk
3, Fig. 3 is the space conjugation engagement pair with three concurrent structured approach designs
1 is star-wheel among the figure, and 16 is screw rod, and 17 is screw axis, and 18 is spider gear shaft, and 19 is worm gear, and 20 is worm screw.Wherein Fig. 3 a is the single helical-lobe compressor intermeshing pair of screw axis and spider gear shaft square crossing, Fig. 3 b single helical-lobe compressor intermeshing pair that to be screw axis tilt to intersect with spider gear shaft, and Fig. 3 c is anchor ring worm and gear engagement pair.
4, Fig. 4 is the single screw compressor with three concurrent structured approach designs
1 is star-wheel, and 16 is screw rod, and 17 is screw axis, and 21,22 is end cap, and 23 is casing, and 24 is the star-wheel support.The profile of star-wheel uses three concurrent structured approaches to generate.
Embodiment
Understand the present invention for clear, further be illustrated with an embodiment:
1, the structure first enveloped curved surface B of cylndrical surface on screw rod.
In the single screw compressor system that three spaces 0, I, II represent, reference space or the static space of 0 representative are bodies, and the space of I representative is star-wheel, and the space of II representative is screw rod.Do the tooth that generating surface replaces star-wheel with a cylndrical surface, star-wheel is pressed with respect to casing
Figure DEST_PATH_RE-GSB00000584207000031
Motion, screw rod is done with respect to casing
Figure DEST_PATH_RE-GSB00000584207000032
Motion, The cylinder generating surface goes out first enveloped face B at the screw rod coenvelope, and the vector function of first enveloped face B is
Figure DEST_PATH_RE-GSB00000584207000034
Satisfy the mesh equation NV=0 of first enveloped, N is any the normal vector on the first enveloped face B, and V is the speed of related movement that first enveloped face B goes up same point.
2, with three concurrent structured approach structure secondary enveloping surfaces
Do generating surface with the first enveloped face B on the screw rod again, press φ with respect to body 2Motion, star-wheel is φ with respect to body 1Motion,
Figure DEST_PATH_RE-GSB00000584207000036
First enveloped face B goes out secondary enveloping surface at the star-wheel coenvelope
Figure DEST_PATH_RE-GSB00000584207000037
Secondary enveloping surface
Figure DEST_PATH_RE-GSB00000584207000038
Function be Obviously use secondary enveloping surface Function
Figure DEST_PATH_RE-GSB000005842070000311
The profile that directly generates secondary enveloping surface in computer system is difficult.Therefore, use Fig. 2 a and described three the concurrent structured approaches of Fig. 2 b in the coordinate space of star-wheel, constructed fuction
Figure DEST_PATH_RE-GSB00000584207000041
Profile
Figure DEST_PATH_RE-GSB00000584207000042
According to Fig. 1 a, the engagement profile of star-wheel tooth is divided into leading flank, trailing flank and Topland, is specifically related to the envelope surface of leading flank, trailing flank and Topland
Figure DEST_PATH_RE-GSB00000584207000043
Shi Ze is the front side envelope surface
Figure DEST_PATH_RE-GSB00000584207000044
The rear side envelope surface And addendum envelope
Figure DEST_PATH_RE-GSB00000584207000046
At first construct leading flank and the trailing flank of star-wheel teeth with three concurrent structured approaches:
(1), structure front side envelope surface
Figure DEST_PATH_RE-GSB00000584207000047
Or rear side envelope surface
Figure DEST_PATH_RE-GSB00000584207000048
Get
Figure DEST_PATH_RE-GSB00000584207000049
(i=1,2 ..., n), by secondary enveloping surface
Figure DEST_PATH_RE-GSB000005842070000410
Vector function In the star-wheel space, generate and use vector function family
Figure DEST_PATH_RE-GSB000005842070000412
(i=1,2 ..., n) Biao Shi a n envelope surface, wherein the i envelope surface is called for short the front side envelope surface Or rear side envelope surface Be the curved surface A1-A2-A3-A4 among Fig. 2 a.
(2), structure axial plane θ Lj: with the line (a) at the center of described star-wheel and screw rod or be parallel to star-wheel and the straight line of the line at screw rod center (b) is axis L and is done coaxial plane family, be r with vector function for sake of convenience j=θ (θ Lj) (j=1,2 ..., m) expression, θ LjBe family of planes r j=θ (θ Lj) (j=1,2 ..., m) in the characteristic angle on j plane, θ LjValue by selected reference level and j determines that wherein axial plane θ is called for short on the j plane LjBe the plane B1-B2-B3-B4 among Fig. 2 a.
(3), structure radial plane u k: making the family of planes perpendicular to axis L, is r with vector function for sake of convenience k=u (u k) (k=1,2 ..., w) expression, u kBe family of planes r k=u (u k) (k=1,2 ..., w) in the intersection point of k plane and axis L along axis L to star-wheel or the distance of screw rod coordinate plane, wherein radial plane u is called for short on the k plane kBe the plane C1-C2-C2-C4 among Fig. 2 a.
(4), structure envelope surface
Figure DEST_PATH_RE-GSB000005842070000415
Axial plane θ LjWith radial plane u kIntersection point d Ijk min: the intersection point d that constructs described leading flank Ijk minUse the front side envelope surface
Figure DEST_PATH_RE-GSB000005842070000416
Axial plane θ LjWith radial plane u k, construct the intersection point d of described trailing flank Ijk minUse the rear side envelope surface
Figure DEST_PATH_RE-GSB000005842070000417
Axial plane θ LjWith radial plane u kStructure intersection point d Ijk minTwo kinds of methods are arranged, i.e. graphical solution and analytic method.
Graphical solution: with the intersection point d of the leading flank of structure star-wheel tooth Ijk minBe example, at first in computer system, construct the front side envelope surface
Figure DEST_PATH_RE-GSB000005842070000418
Or rear side envelope surface
Figure DEST_PATH_RE-GSB000005842070000419
Axial plane θ LjWith radial plane u kNext draws the front side envelope surface
Figure DEST_PATH_RE-GSB000005842070000420
Or rear side envelope surface
Figure DEST_PATH_RE-GSB000005842070000421
With axial plane θ LjIntersection l Ij, axial plane θ LjWith radial plane u kIntersection l Jk, radial plane u kWith the front side envelope surface
Figure DEST_PATH_RE-GSB000005842070000422
Or rear side envelope surface Intersection l KiThe 3rd draws three intersection l Ij, l JkAnd l KiThe intersection point d that intersects Ijk, envelope surface
Figure DEST_PATH_RE-GSB000005842070000424
Family (i=1,2 ..., n) with intersection l JkN intersection point arranged; At last according to along intersection l JkDistance to axis L | d Ijk| value determine intersection point d for minimum principle Ijk min, this point is secondary enveloping surface
Figure DEST_PATH_RE-GSB000005842070000425
On the point of being asked, such intersection point has m * w.
Analytic method: use the front side envelope surface
Figure DEST_PATH_GSB000005842070000426
Or rear side envelope surface
Figure DEST_PATH_GSB000005842070000427
Axial plane θ LjWith radial plane u kConstruct n * m * w and organize set of equation; Find the solution these set of equation and obtain intersection point d in star-wheel IjkCoordinate figure; Find intersection d then IjkDistance to axis L | d Ijk|; Basis again | d Ijk| for the principle of minimum value is determined intersection point d Ijk min, intersection point d Ijk minBe the point of being asked, such intersection point has m * w.
(5), the secondary enveloping surface of structure star-wheel tooth
Figure BSA00000265930100071
Leading flank with structure star-wheel tooth is example equally, chooses the front side envelope surface
Figure BSA00000265930100072
Axial plane θ LjWith radial plane u kIn any one face, as axial plane θ Lj, link axial plane θ in order with smoothed curve LjIn all intersection point d Ijk min(k=1,2 ..., w), connection shaft is to family of planes θ again Lj(j=1,2 ..., m) the middle described smoothed curve of m bar namely constructs secondary enveloping surface A.
Secondly construct the Topland of star-wheel teeth with three concurrent structured approaches:
(1), structure star-wheel addendum envelope
Figure BSA00000265930100073
Get (i=1,2 ..., n), by secondary enveloping surface
Figure BSA00000265930100075
Vector function
Figure BSA00000265930100076
In the star-wheel space, generate and use vector function family (i=1,2 ..., n) Biao Shi a n envelope surface, wherein the i envelope surface is called for short envelope surface
Figure BSA00000265930100078
Be the curved surface A1-A2-A3-A4 among Fig. 2 b.
(2), structure axial plane θ Lj: with the line (a) at the center of described star-wheel and screw rod or be parallel to star-wheel and the straight line of the line at screw rod center (b) is axis L and is done coaxial plane family, be r with vector function for sake of convenience j=θ (θ Lj) (j=1,2 ..., m) expression, θ LjBe family of planes r j=θ (θ Lj) (j=1,2 ..., m) in the characteristic angle on j plane, θ LjValue by selected reference level and j determines that wherein axial plane θ is called for short on the j plane LjBe the B1-B2-B3-B4 among Fig. 2 b.
(3), construct another axial plane θ Lk: in the central plane of star-wheel, making the straight line l perpendicular to described axis L, do the family of planes that axis was made described axis l with straight line l, is r with vector function for sake of convenience k=θ (θ Lk) (k=1,2 ..., w) expression, θ LkBe family of planes r k=θ (θ Lk) (j=1,2 ..., m) in the characteristic angle on k plane, θ LkValue by selected reference level and k determines that wherein axial plane θ is called for short on the k plane LkBe the D1-D2-D3-D4 among Fig. 2 b.The central plane of described star-wheel was the central point of star-wheel and perpendicular to the plane of spider gear shaft.
(4), structure envelope surface Axial plane θ LjWith another axial plane θ LkIntersection point d Ijk min: structure intersection point d Ijk minTwo kinds of methods are arranged, i.e. graphical solution and analytic method.
Graphical solution: at first in computer system, construct addendum envelope
Figure BSA000002659301000710
Axial plane θ LjWith another axial plane θ LkNext draws envelope surface
Figure BSA000002659301000711
With axial plane θ LjIntersection l Ij, axial plane θ LjWith another axial plane θ LkIntersection l Jk, axial plane θ LkAnd envelope surface
Figure BSA000002659301000712
Intersection l KiThe 3rd draws three intersection l Ij, l JkAnd l KiIntersect and produce intersection point d Ijk, envelope surface family (i=1,2 ..., n) with intersection l JkN intersection point arranged; At last according to along intersection l JkDistance to the star-wheel center | d Ijk| value determine intersection point d for minimum principle Ijk min, this point is secondary enveloping surface
Figure BSA000002659301000714
On the point of being asked, such intersection point has m * w.
Analytic method: same, use addendum envelope
Figure BSA00000265930100081
Axial plane θ LjWith with another axial plane θ LkConstruct n * m * w and organize set of equation; Find the solution these set of equation and obtain intersection point d in star-wheel IjkCoordinate figure; Find intersection d then IjkDistance to the star-wheel center | d Ijk|; More definite again | d Ijk| be the intersection point d of minimum value Ijk min, intersection point d Ijk minBe the point of being asked, such intersection point has m * w.
(5), the secondary enveloping surface of structure star-wheel tooth
Figure BSA00000265930100082
Choose addendum envelope
Figure BSA00000265930100083
Axial plane θ LjWith another axial plane θ LkIn any one face, as axial plane θ Lj, link axial plane θ in order with smoothed curve LjIn all intersection point d Ijk min(k=1,2 ..., w), link axial plane θ again LjFamily (j=1,2 ..., m) the middle described smoothed curve of m bar namely constructs secondary enveloping surface
At last, utilize leading flank, trailing flank and the Topland of the star-wheel tooth of above step structure, applying three-dimensional software is drawn out the mockup of star-wheel.
Use star-wheel or the worm gear of three concurrent structured approach design space conjugation engagement pair, can once generate the conjugation contact sealed working face 5 of leading flank among Fig. 1 a, the instantaneous surface of contact 6 of compression-side and the instantaneous surface of contact 7 of back pressure side, the conjugation contact sealed working face 10 of trailing flank, the instantaneous surface of contact 11 of compression-side and the instantaneous surface of contact 12 of back pressure side, the conjugation contact sealed working face 13 of Topland, the instantaneous surface of contact 14 of compression-side and the instantaneous surface of contact 15 of back pressure side, the threaded profile of the profile of star-wheel tooth is the total conjugated engagement, overcome the precision problem that the special plane envelope is brought by machine error, adopt 4-coordinate or five-coordinate linkage machine tooling, its precision is fully controlled at micron order.Reduced difficulty of processing, improved manufacturing efficiency, reduced cost of production, be suitable for producing in enormous quantities.
Essence of the present invention is to intersect the generation intersection point by constructing two auxiliary planes with three of secondary enveloping surfaces, and utilize the minimum range principle to determine that intersection point is on the twice-enveloping profile of space conjugation engagement pair, the method not only is used for the star-wheel of structure single screw compressor, it has applicability widely, can be applied to cutter, grinding tool, emery wheel in Machine Design or the machine-building; Crowded wheel in the material forming, roll, mould; Cam in the mechanical transmission, gear, worm and gear and anchor ring worm and gear; Single screw compressor in the fluid machinery, single-screw expander, helical-lobe compressor and pump class; The mechanism of precision instrumentation, conjugation engagement and other need industry-by-industry and the fields such as device of conjugation engagement.

Claims (6)

1. three concurrent structured approaches of the worm gear of the star-wheel of a single screw compressor or single-screw expander and anchor ring worm and gear, the mechanical system that comprises three spaces 0, I, II, wherein 0 representative is with reference to space or static space, and I, II represent space, is r at the vector function of I space 1(u, generating surface A v) presses with reference to the space with respect to 0=A
Figure FSB00001061711800011
Motion, the II space is done with reference to the space with respect to 0 Motion,
Figure FSB00001061711800013
Generating surface A envelope in the II space generates first enveloped face B, and the vector function of first enveloped face B is
Figure FSB00001061711800014
Comprise the II space of making generating surface of first enveloped face B, press φ with respect to 0 with reference to the space 2Motion, the I space is φ with respect to 0 with reference to the space 1Motion,
Figure FSB00001061711800015
First enveloped face B envelope in the I space goes out secondary enveloping surface
Figure FSB00001061711800016
Secondary enveloping surface
Figure FSB00001061711800017
Vector function be
It is characterized in that: by constructing two crossing auxiliary planes, its intersection l JkRun through vector function
Figure FSB00001061711800019
The secondary enveloping surface family that generates produces intersection point, and utilizes the minimum range principle to be determined to the shortest common intersection d of a certain reference range IjkminThe twice-enveloping profile of structure space conjugation engagement pair;
Appliance computer is designed the three-dimensional entity model of the twice-enveloping profile that comprises space conjugation engagement pair;
The mockup that process equipments such as application turnning and milling Compositions of metal-working machines, 4-coordinate or five coordinate lathes will comprise the twice-enveloping profile of space conjugation engagement pair is processed into entity component.
2. three concurrent structured approaches of the worm gear of the star-wheel of single screw compressor according to claim 1 or single-screw expander and anchor ring worm and gear is characterized in that:
(1) three faces of structure:
The structure envelope surface
Figure FSB000010617118000110
According to secondary enveloping surface
Figure FSB000010617118000111
Vector function
Figure FSB000010617118000112
Get (i=1,2 ..., n), obtain secondary enveloping surface
Figure FSB000010617118000114
Vector function family (i=1,2 ..., n) Biao Shi a n envelope surface, wherein the i envelope surface is called for short envelope surface
Figure FSB000010617118000116
Structure axial plane θ Lj: with the line (a) at the center of described I space and II space or be parallel to the I space and the straight line of the line at II space center (b) is axis L and is done coaxial plane family, be r with vector function for sake of convenience j=θ (θ Lj) (j=1,2 ..., m) expression, θ LjBe family of planes r j=θ (θ Lj) (j=1,2 ..., m) in the characteristic angle on j plane, θ LjValue by selected reference level and j determines that wherein axial plane θ is called for short on the j plane Lj
Structure radial plane u kOr construct another axial plane θ Lk: making the family of planes perpendicular to described axis L, is r with vector function for sake of convenience k=u (u k) (k=1,2 ..., w) expression, u kBe family of planes r k=u (u k) (k=1,2 ..., w) in the intersection point of k plane and axis L along axis L to the I space or the distance of II space coordinate plane, wherein radial plane u is called for short on the k plane k
Perhaps in the central plane of I space, making the straight line l perpendicular to described axis L, do the family of planes that axis was made described axis l with straight line l, is r with vector function for sake of convenience k=θ (θ Lk) (k=1,2 ..., w) expression, θ LkBe family of planes r k=θ (θ Lk) (k=1,2 ..., w) in the characteristic angle on k plane, θ LkValue by selected reference level and k determines that wherein axial plane θ is called for short on the k plane LkThe central plane of described I space was the central point of I space and perpendicular to the plane of the axis of I space;
(2) the common intersection d of three faces of structure Ijkmin:
Utilize envelope surface
Figure FSB00001061711800021
Axial plane θ LjWith radial plane u kThe common intersection d of these three faces of structure Ijk, according to common intersection d IjkDistance to axis L | d Ijk| value determine common intersection d for minimum principle IjkminPerhaps utilize envelope surface
Figure FSB00001061711800022
Axial plane θ LjWith axial plane θ LkThe common intersection d of these three faces of structure Ijk, according to common intersection d IjkArrive the distance at the center of I space | d Ijk| value determine common intersection d for minimum principle Ijkmin
(3) secondary enveloping surface of structure space engagement pair
Figure FSB00001061711800023
Choose envelope surface
Figure FSB00001061711800024
Axial plane θ LjWith radial plane u kOr envelope surface
Figure FSB00001061711800025
Axial plane θ LjWith another axial plane θ LkIn any one face, as axial plane θ Lj, link axial plane θ in order with smoothed curve LjIn all intersection point d Ijkmin(k=1,2 ..., w), connection shaft is to family of planes θ again Lj(j=1,2 ..., m) the middle described smoothed curve of m bar namely constructs the secondary enveloping surface of space conjugation engagement pair
Figure FSB00001061711800026
3. three concurrent structured approaches of the worm gear of the star-wheel of single screw compressor according to claim 2 or single-screw expander and anchor ring worm and gear is characterized in that: with graphical solution or three crossing common intersection d of analytic method structure Ijkmin
4. three concurrent structured approaches of the worm gear of the star-wheel of single screw compressor according to claim 3 or single-screw expander and anchor ring worm and gear, it is characterized in that: graphical solution is to utilize three-dimensional software in computer:
At first construct envelope surface
Figure FSB00001061711800027
Axial plane θ LjWith radial plane u kNext draws envelope surface
Figure FSB00001061711800028
With axial plane θ LjIntersection l Ij, axial plane θ LjWith radial plane u kIntersection l Jk, radial plane u kAnd envelope surface Intersection l KiThe 3rd draws three intersection l Ij, l JkAnd l KiIntersect the common intersection d that produces Ijk, envelope surface family
Figure FSB000010617118000210
(i=1,2 ..., n) with intersection l JkN intersection point arranged; At last according to common intersection d IjkDistance to axis L | d Ijk| value determine common intersection d for minimum principle IjkminPerhaps at first construct envelope surface
Figure FSB000010617118000211
Axial plane θ LjWith axial plane θ LkNext draws envelope surface With axial plane θ LjIntersection l Ij, axial plane θ LjWith axial plane θ LkIntersection l Jk, axial plane θ LkAnd envelope surface
Figure FSB000010617118000213
Intersection l KiThe 3rd draws three intersection l Ij, l JkAnd l KiIntersect the common intersection d that produces Ijk, envelope surface family
Figure FSB000010617118000214
(i=1,2 ..., n) with intersection l JkN intersection point arranged; At last according to common intersection d IjkArrive the distance at the center of I space | d Ijk| value determine common intersection d for minimum principle Ijkmin
5. three concurrent structured approaches of the worm gear of the star-wheel of single screw compressor according to claim 3 or single-screw expander and anchor ring worm and gear, it is characterized in that: analytic method is to utilize envelope surface
Figure FSB000010617118000215
Axial plane θ LjWith radial plane u kConstruct n * m * w and organize set of equation; Find the solution the intersection point d of these set of equation IjkCoordinate figure; Find intersection d then IjkDistance to axis L | d Ijk|; Again according to intersection point d IjkDistance to axis L | d Ijk| value determine common intersection d for minimum principle IjkminPerhaps use envelope surface Axial plane θ LjWith axial plane θ LkConstruct n * m * w and organize set of equation; Find the solution the intersection point d of these set of equation IjkCoordinate figure; Find intersection d then IjkDistance to I space central point | d Ijk|; According to intersection point d IjkArrive the distance at the center of I space | d Ijk| value determine common intersection d for minimum principle Ijkmin
6. an application rights requires the star-wheel of single screw compressor of three concurrent structured approaches structures of the worm gear of the star-wheel of 1 described single screw compressor or single-screw expander and anchor ring worm and gear, be made of compression face, back pressure face, leading flank, trailing flank and Topland, it is characterized in that: leading flank, trailing flank and the Topland of the star-wheel tooth of this star-wheel all comprises a conjugation that seals and contacts sealed working face, an instantaneous surface of contact of compression-side and the instantaneous surface of contact of back pressure side.
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CN1619149A (en) * 2003-11-21 2005-05-25 邹汉华 Calculation of star wheel secondary enveloping surface and processing method
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