CN110259682A - A kind of bias involute roots rotor and its design method - Google Patents

A kind of bias involute roots rotor and its design method Download PDF

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Publication number
CN110259682A
CN110259682A CN201910671467.1A CN201910671467A CN110259682A CN 110259682 A CN110259682 A CN 110259682A CN 201910671467 A CN201910671467 A CN 201910671467A CN 110259682 A CN110259682 A CN 110259682A
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China
Prior art keywords
involute
molded line
side molded
roots rotor
eccentric
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CN110259682B (en
Inventor
王君
许超
李祥艳
赵胜
奚周瑾
杨舒然
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China University of Petroleum East China
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China University of Petroleum East China
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04C—ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT PUMPS
    • F04C18/00—Rotary-piston pumps specially adapted for elastic fluids
    • F04C18/08—Rotary-piston pumps specially adapted for elastic fluids of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing
    • F04C18/12—Rotary-piston pumps specially adapted for elastic fluids of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing of other than internal-axis type
    • F04C18/126—Rotary-piston pumps specially adapted for elastic fluids of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing of other than internal-axis type with radially from the rotor body extending elements, not necessarily co-operating with corresponding recesses in the other rotor, e.g. lobes, Roots type
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04C—ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT PUMPS
    • F04C25/00—Adaptations of pumps for special use of pumps for elastic fluids
    • F04C25/02—Adaptations of pumps for special use of pumps for elastic fluids for producing high vacuum
    • 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
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04C—ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT PUMPS
    • F04C2240/00—Components
    • F04C2240/20—Rotors

Abstract

The invention discloses a kind of eccentric involute roots rotor and its design methods, including left roots rotor (1), right roots rotor (2), the left side molded line (101) of left roots rotor (1) and the right side molded line (201) of right roots rotor (2) be not identical；The left side molded line (101) of left roots rotor (1) is made of 2 sections of circular arcs and 4 sections of involutes, and is smoothly transitted between each section of adjacent curve；The right side molded line (201) of right roots rotor (2) is made of 2 sections of circular arcs, 4 sections of involute envelopes, and is smoothly transitted between each section of adjacent curve；During the work time, left roots rotor (1) and right roots rotor (2) can be realized correct engagement.The present invention is smoothly connected by eccentric involute and its envelope with tooth root, addendum circle arc, solves the problems, such as that the circular arc central angle of conventional involute-type roots rotor profile is limited by rotor pitch circle, exradius, and composition molded line is simple, is convenient for optimization design.

Description

A kind of bias involute roots rotor and its design method
Technical field
The present invention relates to a kind of positive displacement drum pump, especially a kind of eccentric involute roots rotor and its design method.
Background technique
A kind of bias involute roots rotor, main includes including left roots rotor (1) and right roots rotor (2), work As principle be left roots rotor (1) and right roots rotor (2) is intermeshing two roots rotors rotor, passes through two roots rotors Incorgruous dual AC power movement is synchronized, realizes the cyclically-varying of working chamber, to complete the sucking of gas, transport and discharge.Sieve Thatch vacuum pump has the characteristics that dry type is oil-free, starts fast, reliable for operation, few easy workout part.It is mainly used in petroleum, chemical industry, partly leads Body industry.
The profile design of roots rotor has a significant impact the working performance of Roots vaccum pump；Common roots rotor Section molded line be made of circular arc, involute, circular arc central angle is limited by rotor outer circle radius, pitch radius；Publication No. The patent of CN103195704B proposes a kind of constant flow rate rotor of cam pump Profile Design method, the face type of rotor of cam pump Line includes 2 sections of circular arcs, 2 sections of involutes and 2 sections of high order curve compositions, passes through the smooth mistake of high order curve between involute and circular arc It crosses, eliminating rotor end-face molded line has cusp；But it introduces high order curve and causes molded lines of rotor complicated composition and turn The difficult problem of son processing and manufacturing.Existing roots rotor there are the problem of: molded lines of rotor complicated composition.
Summary of the invention
For the circular arc central angle in the profile of the above conventional involute-type roots rotor by rotor pitch radius, outer The problem of radius of circle limitation, rotor end-face molded line complicated composition, the invention proposes a kind of eccentric involute roots rotors.In sieve On the profile of thatch rotor, by translating, rotating by involute, realization is smoothly connected with tooth root circular arc, to obtain a left side The left side molded line of roots rotor solves to obtain the envelope of eccentric involute further according to flank profil engagement basic principle, thus To the right side molded line with the intermeshing right roots rotor of the left side molded line of left roots rotor.The present invention can guarantee it is left, Right roots rotor realizes correct engagement during the work time, and the profile composition of roots rotor profile is simple, each section Adjacent curve is smoothly connected, and is convenient for optimization design, is enriched roots rotor molded line type, is had to the development for promoting Roots vaccum pump There is important meaning.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of bias involute roots rotor, including left roots rotor, right roots rotor；The left side type of left roots rotor Line is made of 2 sections of circular arcs and 4 sections of eccentric involutes, counterclockwise successively are as follows: the first tooth root circular arc AB, the first bias are gradually opened Line BC, the second eccentric involute CD, the second tooth root circular arc DE, third bias involute EF, the 4th eccentric involute FA；Left Roots It is all smoothly connected between each constituent curve in the left side molded line of rotor, and symmetrical about x-axis, y-axis；
The right side molded line of right roots rotor is made of 2 sections of circular arcs and 4 sections of eccentric involute envelopes, in the direction of the clock Successively are as follows: the first addendum circle arc ab, the first eccentric involute envelope bc, the second eccentric involute envelope cd, the second tooth top Circular arc de, third bias involute envelope ef, the 4th eccentric involute envelope fa；It is each in the profile of right roots rotor It is all smoothly connected between constituent curve, and symmetrical about x-axis, y-axis；
The first tooth root circular arc AB in the left side molded line of left roots rotor and the right side molded line of right roots rotor, second Tooth root circular arc DE, the first addendum circle arc ab, the radius of the second addendum circle arc de are all the same, and centre point is on pitch circle, circular arc circle Heart angle is all the same；
In the course of work for synchronizing the movement of incorgruous dual AC power, the left side molded line of left roots rotor and right roots rotor Right side molded line can be realized correct engagement, meshing relation are as follows: the first tooth root circular arc AB of left roots rotor, the first bias are gradually Burst at the seams BC, the second eccentric involute CD, the second tooth root circular arc DE, third bias involute EF, the 4th bias involute FA difference The first addendum circle arc ab, the first eccentric involute envelope bc with right roots rotor (2), the second eccentric involute envelope Cd, the second addendum circle arc de, third bias involute envelope ef, the 4th bias involute envelope fa realize correct engagement.
A kind of design method of the left side molded line of the left roots rotor of the eccentric involute roots rotor, including with Lower step:
1) with basic circle centre point O1Two-dimensional coordinate system is established for origin, gives roots rotor exradius R1, pitch radius R2, half central angle θ of circular arc；
2) the first tooth root circular arc AB of left side molded line, equation are determined by following equation are as follows:
3) the second tooth root circular arc DE of left side molded line, equation are determined by following equation are as follows:
More than: t-angle parameter, rad；
4) the base radius R of the first eccentric involute BC of the left side molded line of left roots rotor is determinedb, first it is eccentric gradually Burst at the seams the basic circle centre point O of BCbCoordinate, the value range of angle parameter t, the first eccentric involute BC generation angle α；
1. the base radius R of the first eccentric involute BCbAre as follows:
2. the basic circle centre point O of the first eccentric involute BCbCoordinate (xOb, yOb) are as follows:
3. angle parameter t value range are as follows:
t∈[t1, t1+ pi/2+θ], wherein
4. the generation angle α of the first eccentric involute BC are as follows:
5) equation of the first eccentric involute BC of left side molded line is determined, are as follows:
6) the first bias involute BC of left side molded line is symmetrically obtained to a left side for left roots rotor respectively about x-axis, y-axis The equation of each section of constituent curve in profile:
1. the equation of the eccentric involute CD of the second of left side molded line are as follows:
2. the equation of the third bias involute EF of left side molded line are as follows:
3. the equation of the eccentric involute FA of the 4th of left side molded line are as follows:
More than: t-angle parameter, rad.
A kind of design method of the right side molded line of the right roots rotor of the eccentric involute roots rotor, including with Lower step:
1) with basic circle centre point O2Two-dimensional coordinate system is established for origin, giving roots rotor exradius is R1, pitch radius For R2, half central angle of circular arc is θ；
2) the first addendum circle arc ab of right side molded line, equation are determined by following equation are as follows:
3) the second addendum circle arc de of right side molded line, equation are determined by following equation are as follows:
4) equation of the first eccentric involute envelope bc of right side molded line is determined, are as follows:
In formula:- intermediate parameters,
5) the first bias involute envelope bc of right side molded line right Roots is symmetrically obtained respectively about x-axis, y-axis to turn The equation of each section of constituent curve in the right side molded line of son:
1. the equation of the eccentric involute envelope cd of the second of right side molded line are as follows:
2. the equation of the third bias involute envelope ef of right side molded line are as follows:
3. the equation of the eccentric involute envelope fa of the 4th of right side molded line are as follows:
More than: t-angle parameter, rad.
A kind of Roots vaccum pump uses the left roots rotor and right roots rotor.
The invention has the benefit that
1. passing through eccentric involute envelope and addendum circle arc by being smoothly connected for eccentric involute and tooth root circular arc Be smoothly connected, make in the design process of roots rotor addendum circle arc, tooth root circular arc central angle no longer by rotor pitch circle half The limitation of diameter, exradius designs more flexible；
2. the constituent curve of the profile of roots rotor is simple, it is convenient for optimization design；
3. enriching the molded line type of roots rotor.
Detailed description of the invention
Fig. 1 is eccentric involute and tooth root circular arc connection figure.
Fig. 2 is the envelope and addendum circle arc connection figure of eccentric involute.
Fig. 3 is the left side molded line (101) of left roots rotor and engaging for right side molded line (201) of right roots rotor Figure.
Fig. 4 is eccentric involute roots rotor left side molded line (101) figure.
Fig. 5 is eccentric involute roots rotor right side molded line (201) figure.
Fig. 6 is eccentric involute roots rotor profile (301) figure.
In figure: R1- roots rotor exradius, mm；R2- roots rotor pitch radius, mm；θ-roots rotor face type Half central angle of circular arc, rad in line；ObThe basic circle center of circle of-the first eccentric involute BC；RbThe basic circle of-the first eccentric involute BC Radius；The generation angle of the eccentric involute BC of α-first, rad.
Specific embodiment
The invention will be further described with embodiment with reference to the accompanying drawing.
As shown in Figure 1, for eccentric involute and tooth root circular arc connection figure, by the basic circle center of circle of involute by coordinate origin O It is moved to point Ob, then by involute with ObCentered on be rotated in the counterclockwise direction α degree, be just able to achieve tooth root circular arc with bias gradually open Linear light slip.
As shown in Fig. 2, the envelope and addendum circle arc connection figure of eccentric involute, acquire bias by the theory of engagement and gradually open The envelope of line, is just able to achieve addendum circle arc and the envelope of eccentric involute is smoothly connected.
As shown in figure 3, being the left side molded line 101 of left roots rotor and nibbling for the right side molded line 201 of right roots rotor Close figure, a kind of profile of asymmetry roots rotor, left side molded line 101 and right roots rotor 2 including left roots rotor 1 Right side molded line 201 it is not identical；The left side molded line 101 of left roots rotor 1 includes 2 sections of circular arcs, 4 sections of involutes, by the inverse time Needle direction is successively are as follows: the first tooth root circular arc AB, the first eccentric involute BC, the second eccentric involute CD, the second tooth root circular arc DE, Third bias involute EF, the 4th eccentric involute FA；It is complete between each constituent curve in the profile 101 of left roots rotor 1 Portion is smoothly connected, and symmetrical about x-axis, y-axis；The right side molded line 201 of right roots rotor 2 includes 2 sections of circular arcs, 4 sections of involutes Envelope, in the direction of the clock successively are as follows: the first addendum circle arc ab, the first eccentric involute envelope bc, the second bias are gradually opened Line envelope cd, the second addendum circle arc de, third bias involute envelope ef, the 4th eccentric involute envelope fa；Right sieve It is all smoothly connected between each constituent curve in the profile 201 of thatch rotor 2, and symmetrical about x-axis, y-axis.
As shown in figure 4, for 101 figure of eccentric involute roots rotor left side molded line, the design method of left side molded line 101 It is as follows:
1) with basic circle centre point O1Two-dimensional coordinate system is established for origin, gives roots rotor exradius R1, pitch radius R2, half central angle θ of circular arc；
2) the first tooth root circular arc AB of left side molded line 101, equation are determined by following equation are as follows:
3) the second tooth root circular arc DE of left side molded line 101, equation are determined by following equation are as follows:
More than: t-angle parameter, rad；
4) the base radius R of the first eccentric involute BC of the left side molded line 101 of left roots rotor 1 is determinedb, first partially The basic circle centre point O of heart involute BCbCoordinate, the value range of angle parameter t, the first eccentric involute BC generation angle α；
1. the base radius R of the first eccentric involute BCbAre as follows:
2. the basic circle centre point O of the first eccentric involute BCbCoordinate (xOb, yOb) are as follows:
3. angle parameter t value range are as follows:
t∈[t1, t1+ pi/2+θ], wherein
4. the generation angle α of the first eccentric involute BC are as follows:
5) equation of the first eccentric involute BC of left side molded line 101 is determined, are as follows:
6) the first bias involute BC of left side molded line 101 is symmetrically obtained into left roots rotor 1 respectively about x-axis, y-axis Left side molded line 101 in each section of constituent curve equation:
1. the equation of the eccentric involute CD of the second of left side molded line 101 are as follows:
2. the equation of the third bias involute EF of left side molded line 101 are as follows:
3. the equation of the eccentric involute FA of the 4th of left side molded line 101 are as follows:
More than: t-angle parameter, rad.
As shown in figure 5, for 201 figure of eccentric involute roots rotor right side molded line, the design method of right side molded line 201 It is as follows:
1) with basic circle centre point O2Two-dimensional coordinate system is established for origin, giving roots rotor exradius is R1, pitch radius For R2, half central angle of circular arc is θ；
2) the first addendum circle arc ab of right side molded line 201, equation are determined by following equation are as follows:
3) the second addendum circle arc de of right side molded line 201, equation are determined by following equation are as follows:
4) equation of the first eccentric involute envelope bc of right side molded line 201 is determined, are as follows:
In formula:- intermediate parameters,
5) the first bias involute envelope bc of right side molded line 201 is symmetrically obtained into right sieve respectively about x-axis, y-axis The equation of each section of constituent curve in the right side molded line 201 of thatch rotor 2:
1. the equation of the eccentric involute envelope cd of the second of right side molded line 201 are as follows:
2. the equation of the third bias involute envelope ef of right side molded line 201 are as follows:
3. the equation of the eccentric involute envelope fa of the 4th of right side molded line 201 are as follows:
More than: t-angle parameter, rad.
As shown in fig. 6, eccentric involute is along expansion counterclockwise for eccentric 301 figure of involute roots rotor profile.
Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not protects model to the present invention The limitation enclosed, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art are not Need to make the creative labor the various modifications or changes that can be made still within protection scope of the present invention.

Claims (4)

1. a kind of bias involute roots rotor, including left roots rotor (1), right roots rotor (2)；It is characterized in that: left Roots The left side molded line (101) of rotor (1) is made of 2 sections of circular arcs and 4 sections of eccentric involutes, counterclockwise successively are as follows: first Tooth root circular arc AB, the first eccentric involute BC, the second eccentric involute CD, the second tooth root circular arc DE, third bias involute EF, 4th eccentric involute FA；It is all smoothly connected between each constituent curve in the left side molded line (101) of left roots rotor (1), And it is symmetrical about x-axis, y-axis；
The right side molded line (201) of right roots rotor (2) is made of 2 sections of circular arcs and 4 sections of eccentric involute envelopes, by clockwise Direction is successively are as follows: the first addendum circle arc ab, the first eccentric involute envelope bc, the second eccentric involute envelope cd, second Addendum circle arc de, third bias involute envelope ef, the 4th eccentric involute envelope fa；The end face of right roots rotor (2) It is all smoothly connected between each constituent curve in molded line (201), and symmetrical about x-axis, y-axis；
The first tooth in the left side molded line (101) of left roots rotor (1) and the right side molded line (201) of right roots rotor (2) Root circular arc AB, the second tooth root circular arc DE, the first addendum circle arc ab, the radius of the second addendum circle arc de are all the same, and centre point exists On pitch circle, circular arc central angle is all the same；
In the course of work for synchronizing incorgruous dual AC power movement, the left side molded line (101) of left roots rotor (1) and right Roots turn The right side molded line (201) of sub (2) can be realized correct engagement, meshing relation are as follows: the first root circle of left roots rotor (1) Arc AB, the first eccentric involute BC, the second eccentric involute CD, the second tooth root circular arc DE, third bias involute EF, the 4th are partially For heart involute FA respectively with the first addendum circle arc ab of right roots rotor (2), the first eccentric involute envelope bc, second is eccentric Involute envelope cd, the second addendum circle arc de, third bias involute envelope ef, the 4th eccentric involute envelope fa are real Existing correct engagement.
2. a kind of left side molded line (101) of the left roots rotor (1) of eccentric involute roots rotor as described in claim 1 Design method, it is characterized in that: the following steps are included:
1) with basic circle centre point O1Two-dimensional coordinate system is established for origin, gives roots rotor exradius R1, pitch radius R2, circle Half central angle θ of arc；
2) the first tooth root circular arc AB of left side molded line (101), equation are determined by following equation are as follows:
3) the second tooth root circular arc DE of left side molded line (101), equation are determined by following equation are as follows:
More than: t-angle parameter, rad；
4) the base radius R of the first eccentric involute BC of the left side molded line (101) of left roots rotor (1) is determinedb, first partially The basic circle centre point O of heart involute BCbCoordinate, the value range of angle parameter t, the first eccentric involute BC generation angle α；
1. the base radius R of the first eccentric involute BCbAre as follows:
2. the basic circle centre point O of the first eccentric involute BCbCoordinate (xOb, yOb) are as follows:
3. angle parameter t value range are as follows:
t∈[t1, t1+ pi/2+θ], wherein
4. the generation angle α of the first eccentric involute BC are as follows:
5) equation of the first eccentric involute BC of left side molded line (101) is determined, are as follows:
6) the first bias involute BC of left side molded line (101) is symmetrically obtained into left roots rotor (1) respectively about x-axis, y-axis Left side molded line (101) in each section of constituent curve equation:
1. the equation of the eccentric involute CD of the second of left side molded line (101) are as follows:
2. the equation of the third bias involute EF of left side molded line (101) are as follows:
3. the equation of the eccentric involute FA of the 4th of left side molded line (101) are as follows:
More than: t-angle parameter, rad.
3. a kind of right side molded line (201) of the right roots rotor (2) of eccentric involute roots rotor as described in claim 1 Design method, it is characterized in that: the following steps are included:
1) with basic circle centre point O2Two-dimensional coordinate system is established for origin, giving roots rotor exradius is R1, pitch radius be R2, half central angle of circular arc is θ；
2) the first addendum circle arc ab of right side molded line (201), equation are determined by following equation are as follows:
3) the second addendum circle arc de of right side molded line (201), equation are determined by following equation are as follows:
4) equation of the first eccentric involute envelope bc of right side molded line (201) is determined, are as follows:
In formula:- intermediate parameters,
5) the first bias involute envelope bc of right side molded line (201) is symmetrically obtained into right Roots respectively about x-axis, y-axis The equation of each section of constituent curve in the right side molded line (201) of rotor (2):
1. the equation of the eccentric involute envelope cd of the second of right side molded line (201) are as follows:
2. the equation of the third bias involute envelope ef of right side molded line (201) are as follows:
3. the equation of the eccentric involute envelope fa of the 4th of right side molded line (201) are as follows:
More than: t-angle parameter, rad.
4. a kind of Roots vaccum pump, it is characterized in that: using left roots rotor (1) described in claim 1 and right roots rotor (2)。
CN201910671467.1A 2019-07-24 2019-07-24 Eccentric involute Roots rotor and design method thereof Active CN110259682B (en)

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Cited By (3)

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Publication number Priority date Publication date Assignee Title
CN115076103A (en) * 2022-06-24 2022-09-20 宁波爱发科机械制造有限公司 Roots rotor molded lines
CN115076106A (en) * 2022-06-24 2022-09-20 宁波爱发科机械制造有限公司 Rotor profile of screw vacuum pump
CN115076104A (en) * 2022-06-24 2022-09-20 宁波爱发科真空技术有限公司 Roots vacuum pump rotor profile

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CN108757448A (en) * 2018-07-12 2018-11-06 中国石油大学(华东) Three leaf sectional circular camber roots rotors of one kind and its Profile Design method
CN108757447A (en) * 2018-07-12 2018-11-06 中国石油大学(华东) A kind of sectional circular camber roots rotor and its Profile Design method
CN210218105U (en) * 2019-07-24 2020-03-31 中国石油大学(华东) Eccentric involute Roots rotor

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WO2016197909A1 (en) * 2015-06-08 2016-12-15 中车戚墅堰机车车辆工艺研究所有限公司 Non-fully-symmetric involute gear and machining method therefor
CN106949053A (en) * 2017-05-24 2017-07-14 中国石油大学(华东) A kind of claw rotor for including elliptic arc
CN207879602U (en) * 2018-01-09 2018-09-18 中国石油大学(华东) A kind of asymmetry roots rotor
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115076103A (en) * 2022-06-24 2022-09-20 宁波爱发科机械制造有限公司 Roots rotor molded lines
CN115076106A (en) * 2022-06-24 2022-09-20 宁波爱发科机械制造有限公司 Rotor profile of screw vacuum pump
CN115076104A (en) * 2022-06-24 2022-09-20 宁波爱发科真空技术有限公司 Roots vacuum pump rotor profile
CN115076104B (en) * 2022-06-24 2023-10-20 宁波爱发科真空技术有限公司 Roots vacuum pump rotor
CN115076103B (en) * 2022-06-24 2023-10-20 宁波爱发科机械制造有限公司 Roots rotor
CN115076106B (en) * 2022-06-24 2023-12-08 宁波爱发科机械制造有限公司 Screw vacuum pump rotor

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