CN106528974A - Profile coupling design method for tooth angle of star wheel and groove bottom angle of screw rod - Google Patents
Profile coupling design method for tooth angle of star wheel and groove bottom angle of screw rod Download PDFInfo
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- CN106528974A CN106528974A CN201610933595.5A CN201610933595A CN106528974A CN 106528974 A CN106528974 A CN 106528974A CN 201610933595 A CN201610933595 A CN 201610933595A CN 106528974 A CN106528974 A CN 106528974A
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- screw rod
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- teeth groove
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
Abstract
The invention discloses a profile coupling design method for a tooth angle of a star wheel and a groove bottom angle of a screw rod. The method comprises the steps of 1) forming a transitional circular arc of a bottom angle of a tooth groove according to a principle of selecting a value greater than the radius of a ball end of a milling cutter as the radius of an enveloping circular arc; and 2) forming a variable-diameter round angle of a tooth of a star wheel with the variable-diameter round angle at the tooth angle of the star wheel. According to the method, the joint (called the groove bottom angle) between the bottom surface and the side surface of the tooth groove of the screw rod adopts circular arc transition, and the tooth angle of the star wheel adopts corresponding circular arc or elliptic arc transition; and the tooth groove of the screw rod, designed with the method, is convenient for machining of a numerical control milling machine, and can ensure a design gap between the tooth angle of the star wheel and the groove bottom angle of the screw rod, and meet a seal requirement of a compressor/expander in a working process.
Description
Technical field
The invention belongs to Machine Design processing and manufacturing field, is related to a kind of single screw compressor/decompressor culminant star wheel tooth angle
With screw slot base angle type face coupling design method.
Background technology
Single screw compressor/decompressor has preferable dynamic balance, and single-machine capacity is big, vibrates little, the low technology of noise
Advantage, which is widely used in the every field such as chemical industry, iron and steel, refrigeration, air force.
Single screw compressor/decompressor mainly engages to realize its course of work with the accurate of star-wheel by screw rod,
Meshing Pair is the heart of single screw compressor/decompressor, and machining accuracy and the Profile Design of Meshing Pair directly influence machine
Performance.With the application of the Novel wires such as cylindrical envelope, multi-column envelope and curve molded line, single screw compressor star-wheel, screw rod
Processing also becomes more complicated.Using Five-axis numerical control milling machine process Dan Luoganyasuoji decompressors screw rod and star-wheel into
For a kind of trend.
The design of traditional star-wheel, screw meshing pair is as shown in Figure 1.Star-wheel tooth angle is star-wheel outer rim and star-wheel flank side
The angle of cut, is close to right angle；And screw rod teeth groove base angle is then matched, it is the star-wheel flank arm of angle for being close to right angle in screw rod region envelope
Molding.In theory, during bottom land angle such using CNC milling machine processing, diameter is needed to be close to the milling cutter of " 0 ".This clearly can not
Can.
The content of the invention
It is an object of the invention to provide a kind of star-wheel tooth angle and screw slot base angle type face coupling design method, solve star
Wheel, the NC milling problems faced of screw meshing pair.
To achieve these goals, the present invention is adopted the following technical scheme that：
Star-wheel tooth angle and screw slot base angle type face coupling design method, comprise the following steps：
One) according to the principle that the value chosen more than milling cutter Probe-radius is envelope arc radius, the angle transition of molding gear bottom land
Circular arc；
Set up comprehensive coordinate system：S1、S2、S3、S4；Position fixing system S1, S3 represent respectively star-wheel tooth, screw rod teeth groove it is initial
Position, Z1 and star-wheel overlapping of axles, Z3 and screw rod overlapping of axles, O1O3For the perpendicular bisector of two axles；The original position and S1 of moving coordinate system S2
It is identical, it is consolidated in star-wheel；The original position of moving coordinate system S4 is identical with S3, is consolidated in screw rod；Moving coordinate system S2 and S4 distinguish table
Show the dynamic position of star-wheel tooth and screw rod teeth groove；Rotating ratio between star-wheel tooth and screw rod teeth groove is：
Wherein φswRepresent star-wheel tooth corner, φsrRepresent screw rod corner, ωswRepresent the angular velocity of star-wheel, ωsrRepresent spiral shell
The angular velocity of bar, P are the gear ratio of star-wheel and screw rod；
In coordinate system S2, when star-wheel tooth corner is φswWhen, X of the corresponding screw rod tooth in moving coordinate system S22Y2Plane
The equation of the section line of section inner screw bottom land and the section line of teeth groove side is：
The section line equation of screw rod bottom land：
The section line equation of screw rod teeth groove side：
Wherein, φswFor the corner of the star-wheel tooth of the section correspondence engagement, t is to represent meshing point position on star-wheel tooth
The theory of engagement and molded line parameter that parameter, specific equation and parameter are designed by designer is determined；
After the section line equation of bottom land section line and teeth groove side is obtained, transition of the radius for r between two lines is determined
Arc position, the circular arc keep tangent, its center of circle position with the section line of the section line of screw rod bottom land and screw rod teeth groove side
Put and be expressed as,
(xc2(φsw),yc2(φsw)) (4)
To ensure milling success, Probe-radius of the transition arc radius r more than milling cutter；
In engagement range, with the rotation of star-wheel, corner φswGradually change, by the center of circle equation (4) for obtaining by coordinate
The deferent that screw rod moving coordinate system S4 obtains screw rod teeth groove base angle transition arc is converted into, with the arc surface that the track is formed is
Teeth groove base angle transition circle arc shaped surface；
Two) in the star-wheel tooth angle fillet of falling reducing star-wheel tooth reducing fillet.
Further, step 2) in from star-wheel upper surface location to star-wheel lower surface position, the diameter of circular arc gradually becomes
It is little.
Further, step 2) specifically include：
1) the arc radius span positioned at star-wheel upper and lower surface is 0.1r-2.5r, wherein r be by bottom land section line and
Between the radius star-wheel upper and lower surface of the transition arc that the section line equation of teeth groove side determines, arc radius are according to circular arc distance
Upper surface apart from linear change；
2) in the middle of the reducing arc surface, along star-wheel upper surface to the direction of star-wheel lower surface, several are evenly arranged
Coupling point, and obtain the coordinate of these Coupling points；
3) according to star-wheel and the movement relation of screw rod, one by one by these Coupling point Coordinate Conversion to screw rod moving coordinate system S4
In, and calculate different star-wheel tooth angle position φswWhen, between these Coupling points and screw rod bottom land, base angle circular arc and side
Distance；
4) all Coupling points are optimized：When the Coupling point is interfered with screw rod teeth groove, increase the position star
The diameter of gear teeth chamfering circular arc, when the minimum range between the Coupling point and teeth groove is more than design gaps, reduces the position
The diameter of star-wheel tooth chamfering circular arc, until the minimum range between the Coupling point and teeth groove is in the positive and negative 0.01mm scopes of design gaps
Shi Jilu chamfering circular arc diameters this moment；
5) the arc radius linear transitions between each Coupling point, the star-wheel tooth reducing fillet after being optimized.
Further, step 2) specifically include：
1) ellipse long and short shaft ratio is between 1.0-1.5；Positioned at the elliptic arc major semiaxis span of star-wheel upper and lower surface
For 0.1r-2.5r, wherein r is determined by the section line equation of bottom land section line and teeth groove side, major semiaxis between the two
According to circular arc apart from upper surface apart from linear change；
2) in the middle of the reducing arc surface, along star-wheel upper surface to the direction of star-wheel lower surface, several are evenly arranged
Coupling point, and obtain the coordinate of these Coupling points；
3) according to star-wheel and the movement relation of screw rod, one by one by these Coupling point Coordinate Conversion to screw rod moving coordinate system S4
In, and calculate different star-wheel tooth angle position φswWhen, between these Coupling points and screw rod bottom land, base angle circular arc and side
Distance；
4) when the Coupling point is interfered with teeth groove, increase the semiaxis of the position star-wheel tooth chamfering ellipse circular arc, when
When minimum range between the Coupling point and teeth groove is more than design gaps, reduce the half of the position star-wheel tooth chamfering ellipse circular arc
Axle, when the minimum range between the Coupling point and teeth groove is in design gaps positive and negative 0.01mm scopes, record chamfering this moment is ellipse
Circle arc size；
5) the oval circular arc linear transitions between each Coupling point, the star-wheel tooth reducing fillet after being optimized.
Relative to prior art, the invention has the advantages that：
A kind of star-wheel tooth angle of the present invention and screw slot base angle type face coupling design method, screw rod bottom land and side it
Between junction (referred to as bottom land angle) adopt arc transition, star-wheel tooth angle then adopts corresponding circular arc or elliptic arc transition；Using
The screw rod teeth groove of the inventive method design is easy to CNC milling machine to process, and can guarantee that between star-wheel tooth angle and screw slot base angle
Design gaps, meet compressor/decompressor seal request in the course of the work.
Description of the drawings
Fig. 1 is single screw compressor/decompressor screw rod star-wheel Meshing Pair and star-wheel tooth angle, screw slot base angle position description
Figure；
Fig. 2 is the coordinate system setting figure that the movement relation of screw rod star-wheel Meshing Pair and the present invention are adopted；
Fig. 3 is the key element explanatory diagram of implementation culminant star gear teeth reducing fillet design of the present invention.
Specific embodiment
The method of present embodiment is that the junction (referred to as bottom land angle) between screw rod bottom land and side adopts circle
Arc transition, star-wheel tooth angle is then using the coupling method for designing profile of corresponding arc transition.Arc transition is adopted with star-wheel tooth angle
Illustrate as embodiment.
Embodiment one
A kind of star-wheel tooth angle and screw slot base angle type face coupling design method, comprise the following steps：
One) according to the principle that the value chosen more than milling cutter Probe-radius is envelope arc radius, the angle transition of molding gear bottom land
Circular arc.
Star-wheel is with the movement relation of screw rod as shown in Fig. 2 setting up comprehensive coordinate system：S1、S2、S3、S4.Position fixing system S1,
S3 represents star-wheel tooth, the initial position of screw rod teeth groove, Z1 and star-wheel overlapping of axles, Z3 and screw rod overlapping of axles, O respectively1O3For two axles
Perpendicular bisector；The original position of moving coordinate system S2 is identical with S1, is consolidated in star-wheel；The original position of moving coordinate system S4 is identical with S3,
It is consolidated in screw rod；Moving coordinate system S2 and S4 represent the dynamic position of star-wheel tooth and screw rod teeth groove respectively.Star-wheel tooth and screw rod teeth groove
Between rotating ratio be：
Wherein φswRepresent star-wheel tooth corner, φsrRepresent screw rod corner, ωswRepresent the angular velocity of star-wheel, ωsrRepresent spiral shell
The angular velocity of bar, P is the gear ratio of star-wheel and screw rod, generally 11/6.
When star-wheel tooth corner is φswWhen, X of the corresponding screw rod tooth in moving coordinate system S22Y2The section of plane such as Fig. 2 institutes
Show.No matter which kind of molded line is adopted, such as：Lines enveloping, cylindrical envelope, multi-column envelope etc., can obtain the spiral shell in the section
The equation of the section line of bar bottom land and the section line of teeth groove side, and represent in coordinate system S2.
The section line equation of screw rod bottom land：
The section line equation of screw rod teeth groove side,
Wherein, φswFor the corner of the star-wheel tooth of the section correspondence engagement, t is to represent meshing point position on star-wheel tooth
The theory of engagement and molded line type that parameter, specific equation and parameter are designed by designer is determined.
After the section line equation of bottom land section line and teeth groove side is obtained, it is easy to determine that radius is r between two lines
Transition arc position, the circular arc and aforementioned two section lines keep tangent, and its home position is expressed as,
(xc2(φsw),yc2(φsw)) (4)
To ensure milling success, Probe-radius of the transition arc radius r more than milling cutter.
In engagement range, with the rotation of star-wheel, corner φswGradually change, by the center of circle equation (4) for obtaining by coordinate
The deferent that screw rod moving coordinate system S4 is obtained with screw rod teeth groove base angle transition arc is converted into, with the circle that the track is formed
Cambered surface transition circle arc shaped surface then for base angle.
Two) in the star-wheel tooth angle fillet of falling reducing, it is characterized in from star-wheel upper surface location to star-wheel lower surface position, circular arc
Diameter taper into.
The arc diameter of star-wheel tooth reducing fillet determines method：1) positioned at the arc radius span of star-wheel upper and lower surface
For 0.1r-2.5r, wherein r is the radius star-wheel of the transition arc determined by the section line equation of bottom land section line and teeth groove side
Between upper and lower surface arc radius according to circular arc apart from upper surface apart from linear change；2) as shown in figure 3, in the reducing circular arc
In the middle of face, along star-wheel upper surface to the direction of star-wheel lower surface, several Coupling points are evenly arranged, and obtain these Coupling points
Coordinate；3) according to the movement relation of star-wheel and screw rod, one by one by these Coupling point Coordinate Conversion to screw rod moving coordinate system S4,
And calculate different star-wheel tooth angle position φswWhen, between these Coupling points and screw rod bottom land, base angle circular arc and side away from
From；4) all Coupling points are optimized：When the Coupling point is interfered with screw rod teeth groove, increase the position star-wheel tooth and fall
The diameter of angle circular arc, when the minimum range between the Coupling point and teeth groove is more than design gaps, reduces the position star-wheel tooth
The diameter of chamfering circular arc, records when the minimum range between the Coupling point and teeth groove is in design gaps positive and negative 0.01mm scopes
Chamfering circular arc diameter this moment；5) the arc radius linear transitions between each Coupling point, the star-wheel tooth reducing after being optimized
Fillet.
Star-wheel tooth reducing fillet after completing to optimize is as shown in Figure 3.
The screw rod teeth groove designed using the inventive method is easy to CNC milling machine to process, and can guarantee that in star-wheel tooth angle and screw rod
Design gaps between bottom land angle, meet compressor/decompressor seal request in the course of the work.
Embodiment two
The method that the present embodiment is provided is that the junction (referred to as bottom land angle) between screw rod bottom land and side adopts
Arc transition, star-wheel tooth angle is then using corresponding reducing ellipse arc transition.
A kind of star-wheel tooth angle and screw slot base angle type face coupling design method, comprise the following steps：
One) according to the principle that the value chosen more than milling cutter Probe-radius is envelope arc radius, the angle transition of molding gear bottom land
Circular arc.
Star-wheel is with the movement relation of screw rod as shown in Fig. 2 setting up comprehensive coordinate system：S1、S2、S3、S4.Position fixing system S1,
S3 represents star-wheel tooth, the initial position of screw rod teeth groove, Z1 and star-wheel overlapping of axles, Z3 and screw rod overlapping of axles, O respectively1O3For two axles
Perpendicular bisector；The original position of moving coordinate system S2 is identical with S1, is consolidated in star-wheel；The original position of moving coordinate system S4 is identical with S3,
It is consolidated in screw rod；Moving coordinate system S2 and S4 represent the dynamic position of star-wheel tooth and screw rod teeth groove respectively.
When star-wheel tooth corner is φswWhen, X of the corresponding screw rod tooth in moving coordinate system S22Y2The section of plane such as Fig. 2 institutes
Show.No matter which kind of molded line is adopted, such as：Lines enveloping, cylindrical envelope, multi-column envelope etc., can obtain the spiral shell in the section
The equation of the section line of bar bottom land and the section line of teeth groove side, and represent in coordinate system S2.
Obtain bottom land section line equation (2) and teeth groove side section line equation (3) after, it is easy to determine two lines it
Between radius for r transition arc position.
To ensure milling success, Probe-radius of the transition arc radius r more than milling cutter.
In engagement range, gradually change φsw, by the center of circle equation (4) for obtaining by coordinate transform to screw rod coordinate system
S4 is obtained with the deferent of screw rod teeth groove base angle transition arc, with the transition then as base angle of the arc surface of track formation
Arc profile.
Two) in the star-wheel tooth angle fillet of falling reducing, it is characterized in using ellipse arc into knuckle, from star-wheel upper surface position
Star-wheel lower surface position is put, the diameter of axle of transition ellipse circular arc is tapered into.
The oval circular arc of reducing fillet determines that method is：1) ellipse long and short shaft ratio is between 1.0-1.5；2) positioned at star-wheel
The elliptic arc major semiaxis span of upper and lower surface is 0.1r-2.5r, and wherein r is by the section of bottom land section line and teeth groove side
What line equation determined, major semiaxis between the two is according to circular arc apart from upper surface apart from linear change；3) as shown in figure 3,
In the middle of the reducing arc surface, along star-wheel upper surface to the direction of star-wheel lower surface, several Coupling points are evenly arranged, and are obtained
The coordinate of these Coupling points；4) according to star-wheel and the movement relation of screw rod, one by one these Coupling point Coordinate Conversion are moved to screw rod
In coordinate system S4, and calculate different star-wheel tooth angle position φswWhen, these Coupling points and screw rod bottom land, base angle circular arc and
The distance between side；5) when the Coupling point is interfered with teeth groove, increase the position star-wheel tooth chamfering ellipse circular arc
Semiaxis, when the minimum range between the Coupling point and teeth groove is more than design gaps, reduces the position star-wheel tooth chamfering oval
The semiaxis of circular arc, records this moment when the minimum range between the Coupling point and teeth groove is in design gaps positive and negative 0.01mm scopes
Chamfering ellipse arc size；6) the oval circular arc linear transitions between each Coupling point, the star-wheel tooth reducing after being optimized
Fillet.
The screw rod teeth groove designed using the inventive method is easy to CNC milling machine to process, and can guarantee that in star-wheel tooth angle and screw rod
Design gaps between bottom land angle, meet compressor/decompressor seal request in the course of the work.
Claims (4)
1. star-wheel tooth angle and screw slot base angle type face coupling design method, it is characterised in that comprise the following steps：
One) according to the principle that the value chosen more than milling cutter Probe-radius is envelope arc radius, molding gear bottom land angle transition arc；
Set up comprehensive coordinate system：S1、S2、S3、S4；Position fixing system S1, S3 represent star-wheel tooth, the initial bit of screw rod teeth groove respectively
Put, Z1 and star-wheel overlapping of axles, Z3 and screw rod overlapping of axles, O1O3For the perpendicular bisector of two axles；The original position of moving coordinate system S2 and S1 phases
Together, it is consolidated in star-wheel；The original position of moving coordinate system S4 is identical with S3, is consolidated in screw rod；Moving coordinate system S2 and S4 are represented respectively
The dynamic position of star-wheel tooth and screw rod teeth groove；Rotating ratio between star-wheel tooth and screw rod teeth groove is：
Wherein φswRepresent star-wheel tooth corner, φsrRepresent screw rod corner, ωswRepresent the angular velocity of star-wheel, ωsrRepresent screw rod
Angular velocity, P are the gear ratio of star-wheel and screw rod；
In coordinate system S2, when star-wheel tooth corner is φswWhen, X of the corresponding screw rod tooth in moving coordinate system S22Y2The section of plane
The equation of the section line of inner screw bottom land and the section line of teeth groove side is：
The section line equation of screw rod bottom land：
The section line equation of screw rod teeth groove side：
Wherein, φswFor the corner of the star-wheel tooth of the section correspondence engagement, t is the parameter for representing meshing point position on star-wheel tooth；
After the section line equation of bottom land section line and teeth groove side is obtained, transition arc of the radius for r between two lines is determined
Position, the circular arc keep tangent, its home position table with the section line of the section line of screw rod bottom land and screw rod teeth groove side
It is shown as,
(xc2(φsw),yc2(φsw)) (4)
To ensure milling success, Probe-radius of the transition arc radius r more than milling cutter；
In engagement range, with the rotation of star-wheel, corner φswGradually change, by the center of circle equation (4) for obtaining by coordinate transform
The deferent of screw rod teeth groove base angle transition arc is obtained to screw rod moving coordinate system S4, the arc surface with track formation is as teeth groove
Base angle transition circle arc shaped surface；
Two) in the star-wheel tooth angle fillet of falling reducing star-wheel tooth reducing fillet.
2. star-wheel tooth angle according to claim 1 and screw slot base angle type face coupling design method, it is characterised in that include
Following steps：Step 2) in from star-wheel upper surface location to star-wheel lower surface position, the diameter of circular arc is tapered into.
3. star-wheel tooth angle according to claim 1 and screw slot base angle type face coupling design method, it is characterised in that step
Two) specifically include：
1) the arc radius span positioned at star-wheel upper and lower surface is 0.1r-2.5r, and wherein r is by bottom land section line and teeth groove
Between the radius star-wheel upper and lower surface of the transition arc that the section line equation of side determines arc radius according to circular arc apart from upper table
Face apart from linear change；
2) in the middle of the reducing arc surface, along star-wheel upper surface to the direction of star-wheel lower surface, several couplings are evenly arranged
Point, and obtain the coordinate of these Coupling points；
3) according to the movement relation of star-wheel and screw rod, one by one by these Coupling point Coordinate Conversion to screw rod moving coordinate system S4, and
Calculate different star-wheel tooth angle position φswWhen, between these Coupling points and screw rod bottom land, base angle circular arc and side away from
From；
4) all Coupling points are optimized：When the Coupling point is interfered with screw rod teeth groove, increase the position star-wheel tooth
The diameter of chamfering circular arc, when the minimum range between the Coupling point and teeth groove is more than design gaps, reduces the position star-wheel
The diameter of tooth chamfering circular arc, remembers when the minimum range between the Coupling point and teeth groove is in design gaps positive and negative 0.01mm scopes
Record chamfering circular arc diameter this moment；
5) the arc radius linear transitions between each Coupling point, the star-wheel tooth reducing fillet after being optimized.
4. star-wheel tooth angle according to claim 1 and screw slot base angle type face coupling design method, it is characterised in that step
Two) specifically include：
1) ellipse long and short shaft ratio is between 1.0-1.5；Elliptic arc major semiaxis span positioned at star-wheel upper and lower surface is
0.1r-2.5r, wherein r are to determine that major semiaxis between the two is pressed by the section line equation of bottom land section line and teeth groove side
According to circular arc apart from upper surface apart from linear change；
2) in the middle of the reducing arc surface, along star-wheel upper surface to the direction of star-wheel lower surface, several couplings are evenly arranged
Point, and obtain the coordinate of these Coupling points；
3) according to the movement relation of star-wheel and screw rod, one by one by these Coupling point Coordinate Conversion to screw rod moving coordinate system S4, and
Calculate different star-wheel tooth angle position φswWhen, between these Coupling points and screw rod bottom land, base angle circular arc and side away from
From；
4) when the Coupling point is interfered with teeth groove, increase the semiaxis of the position star-wheel tooth chamfering ellipse circular arc, when the coupling
When minimum range between chalaza and teeth groove is more than design gaps, reduce the semiaxis of the position star-wheel tooth chamfering ellipse circular arc,
When the minimum range between the Coupling point and teeth groove is in design gaps positive and negative 0.01mm scopes, record chamfering this moment is oval
Arc size；
5) the oval circular arc linear transitions between each Coupling point, the star-wheel tooth reducing fillet after being optimized.
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| CN201610933595.5A CN106528974B (en) | 2016-10-25 | 2016-10-25 | Star-wheel tooth angle and screw slot base angle type face coupling design method |
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| CN109555687A (en) * | 2019-01-07 | 2019-04-02 | 鑫磊压缩机股份有限公司 | A kind of forming method of single screw rod engaging mechanism and single screw rod cylindrical surface envelope molded line |
| CN111830908A (en) * | 2020-06-17 | 2020-10-27 | 上海烟草机械有限责任公司 | Cylindrical envelope tool path generation method, system, terminal and medium based on two-dimensional linear graph |
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| CN102338091A (en) * | 2011-10-17 | 2012-02-01 | 西安交通大学 | Enveloping tooth profile surface for meshing pair of single-screw compressor |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109555687A (en) * | 2019-01-07 | 2019-04-02 | 鑫磊压缩机股份有限公司 | A kind of forming method of single screw rod engaging mechanism and single screw rod cylindrical surface envelope molded line |
| CN109555687B (en) * | 2019-01-07 | 2024-03-19 | 鑫磊压缩机股份有限公司 | Single screw meshing mechanism and forming method of single screw cylindrical surface enveloping molded line |
| CN111830908A (en) * | 2020-06-17 | 2020-10-27 | 上海烟草机械有限责任公司 | Cylindrical envelope tool path generation method, system, terminal and medium based on two-dimensional linear graph |
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| CN106528974B (en) | 2019-04-12 |
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