CN112377407A - Three-section type double-screw compressor rotor and design method of molded line thereof - Google Patents

Three-section type double-screw compressor rotor and design method of molded line thereof Download PDF

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Publication number
CN112377407A
CN112377407A CN202011072802.5A CN202011072802A CN112377407A CN 112377407 A CN112377407 A CN 112377407A CN 202011072802 A CN202011072802 A CN 202011072802A CN 112377407 A CN112377407 A CN 112377407A
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circular arc
envelope
rotor
coordinate
coordinate system
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CN112377407B (en
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耿茂飞
王乐
陈德祥
邢志胜
毛京兵
张成彦
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Hefei General Machinery Research Institute Co Ltd
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Hefei General Machinery Research Institute Co Ltd
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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
    • F04C18/14—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 toothed rotary pistons
    • F04C18/16—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 toothed rotary pistons with helical teeth, e.g. chevron-shaped, screw 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
    • F04C29/00—Component parts, details or accessories of pumps or pumping installations, not provided for in groups F04C18/00 - F04C28/00
    • 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
    • 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
    • F04C2250/00—Geometry
    • F04C2250/20—Geometry of the rotor

Abstract

The invention belongs to the technical field of double-screw compressors, and particularly relates to a three-section double-screw compressor rotor which comprises a male rotor and a female rotor and is characterized in that the end surface profile of the male rotor is formed by a plurality of sections of curves and comprises a polynomial curve envelope ab, an arc bc and an arc envelope cd which are connected in a smooth transition mode in sequence; the end face molded line of the female rotor is composed of a plurality of sections of curves and comprises a polynomial curve AB, an arc envelope curve BC and an arc CD which are connected in sequence.

Description

Three-section type double-screw compressor rotor and design method of molded line thereof
Technical Field
The invention belongs to the technical field, and particularly relates to a three-section type double-screw compressor rotor and a design method of a molded line thereof.
Background
The double-screw compressor has the advantages of high reliability, convenient operation and maintenance, good power balance, strong adaptability, multiphase mixed transportation and the like, and is widely applied to the fields of mines, chemical industry, power, food, medicine, refrigeration and the like.
The rotor profile is used as a core technology of the double-screw compressor, determines the performance of the double-screw compressor, is a key technology for designing and optimizing the double-screw compressor, and along with the development of scientific technology, in the rotor profile which is disclosed at present, the rotor profile is developed by three generations: the symmetrical arc rotor profile in the first generation of rotor profile is simple in design, but the leakage triangle area is large; in the second generation, asymmetric rotor molded lines adopt molded lines such as points, straight lines, cycloid and the like, so that the leakage triangle is reduced, but the asymmetric rotor molded lines are sensitive to the formed points of the cycloid, and the sealing effect of the formed lines is poor; the third generation, also the latest generation, of asymmetric rotor profiles adopts curves such as circular arcs, ellipses, parabolas and the like, and the 'line' sealing is improved to 'band' sealing, so that the sealing effect is obviously improved, but the design is generally realized by 'splicing' multiple sections of curves, and the curves are of multiple types and have high design difficulty.
Disclosure of Invention
The invention aims to provide a three-section type double-screw compressor rotor, wherein a male rotor and a female rotor are completely meshed, the male rotor and the female rotor are respectively formed by only three sections of curves, the molded lines are simple in structure and easy to design and modify, circular arcs, polynomial curves and conjugate envelope lines thereof are adopted, the tooth surfaces of the rotors are improved from line sealing to belt sealing, and meanwhile, the highest point of the contact line of the molded lines of the rotors is close to the intersection line of a cylinder hole, so that a smaller leakage triangle is formed, and a better sealing effect is achieved.
In order to achieve the purpose, the invention adopts the following technical scheme: a three-section type double-screw compressor rotor comprises a male rotor and a female rotor, wherein the end surface profile of the male rotor is formed by a plurality of sections of curves and comprises a polynomial curve envelope ab, an arc bc and an arc envelope cd which are connected in a smooth transition mode in sequence; the end face molded line of the female rotor is composed of a plurality of sections of curves and comprises a polynomial curve AB, an arc envelope BC and an arc CD which are connected in sequence;
the polynomial curve envelope AB in the end face tooth profile of the male rotor is a conjugate envelope of the polynomial curve AB in the end face molded line of the female rotor, and the head and the tail of the polynomial curve envelope AB are respectively tangent with a pitch circle of the male rotor and a tip circle of the male rotor;
the head and the tail of an arc bc in the end surface tooth shape of the male rotor are respectively tangent with the addendum circle of the male rotor and an arc envelope cd;
the end face tooth shape middle circular arc envelope line CD of the male rotor is a conjugate envelope line of the end face tooth shape middle circular arc CD of the female rotor, the tangent end of the circular arc envelope line CD and the circular arc section bc is a head end, and the tail end of the circular arc envelope line CD is tangent to a pitch circle of the male rotor;
the head and the tail of a polynomial curve AB in the end face tooth profile of the female rotor are respectively tangent with a female rotor pitch circle and a female rotor tooth root circle;
the end face tooth shape middle circular arc envelope line BC of the female rotor is a conjugate envelope line of a circular arc BC in the end face tooth shape of the male rotor, the end, connected with the circular arc CD, of the circular arc envelope line BC is a tail end, and the head end of the circular arc envelope line BC is tangent to a tooth root circle of the female rotor;
the end face tooth-shaped middle circular arc CD of the female rotor is connected with the circular arc envelope line BC to form a head end, and the tail end of the circular arc CD is tangent to the pitch circle of the female rotor.
Preferably, at the center point O of the male rotor1Central point O of female rotor2Establishing a coordinate system for the origin of coordinates;
the coordinate equation of a polynomial curve AB in the end face tooth form of the female rotor is as follows:
Figure BDA0002715665710000021
wherein x isABIs a polynomial curve AB in the end face tooth form of the female rotor2X-coordinate, y in a coordinate systemABIs a polynomial curve AB in the end face tooth form of the female rotor2In a coordinate systemY coordinate, b2Is the root radius of the female rotor, d2Is the pitch diameter of the female rotor, t1Is O2Angular coordinate in a coordinate system, theta1Is a polynomial curve AB in the end face tooth form of the female rotor2The angle occupied in the coordinate system;
the coordinate equation of the circular arc CD in the face tooth shape of the female rotor is as follows:
Figure BDA0002715665710000031
wherein x isCDIs a circular arc CD is at O2X-coordinate, y in a coordinate systemCDIs a circular arc CD is at O2Y coordinate, r, in a coordinate system1Radius of the circular arc CD, t3Is a circular arc CD is at O2Angular coordinate in a coordinate system, xrThe center of the circular arc CD is O2X-coordinate, y in a coordinate systemrThe center of the circular arc CD is O2Y-coordinate of the coordinate system, theta2Is a circular arc envelope line BC at O2Polar angle, θ, in the coordinate system3Is a circular arc CD is at O2Polar angle in coordinate system, center of circular arc CD is located at O2D is connected with the wire.
The coordinate equation of the circular arc bc in the face tooth shape of the male rotor is as follows:
Figure BDA0002715665710000032
wherein x isbcIs arc bc at O1X-coordinate, y in a coordinate systembcIs arc bc at O1Y coordinate, r, in a coordinate system0Is the radius, ξ, of the circular arc bc2Is O1Polar angle, t, occupied by arc bc under coordinate system2Arc bc at O1Angle coordinate in coordinate system, the center of arc bc is located at O1O2On the connecting line of (2);
the polynomial curve envelope ab in the end face tooth profile of the male rotor has the following equation:
Figure BDA0002715665710000033
wherein x isabFor the polynomial curve envelope ab in the face tooth profile of the male rotor at O1X-coordinate, y in a coordinate systemabFor the polynomial curve envelope ab in the face tooth profile of the male rotor at O1Y coordinate in coordinate system, A represents O1O2I is the transmission ratio, R1tIs the pitch radius of the male rotor, R2tIs the pitch radius of the female rotor1For the position parameter of the polynomial curve envelope AB, the elimination of phi from the coordinate equation of the polynomial curve AB and the above-mentioned equation system for the polynomial curve envelope AB1To obtain xabAnd yabWith respect to parameter t1From the equation of coordinates of (a) to (b) to obtain the polynomial curve envelope ab at O in the face tooth profile of the male rotor1A coordinate equation in a coordinate system;
the end face tooth shape middle circular arc envelope line BC of the female rotor has the following equation:
Figure BDA0002715665710000041
wherein x isBCIs a circular arc envelope line BC at O2X-coordinate, y in a coordinate systemBCIs a circular arc envelope line BC at O2Y-coordinate in a coordinate system, phi2For the position parameter of the circular arc envelope BC, the coordinate equation of the circular arc BC and the above equation set for the circular arc envelope BC are eliminated2To obtain xBCAnd yBCWith respect to parameter t2From the envelope BC of the circular arc in the face tooth profile of the female rotor at O2Coordinates in a coordinate system;
the end face tooth shape middle circular arc envelope cd of the male rotor has the following equation:
Figure BDA0002715665710000042
wherein x iscdIs a circular arc envelope cd at O1X-coordinate, y in a coordinate systemcdIs a circular arc envelope cd at O1Y-coordinate in a coordinate system, phi3For the position parameter of the circular arc envelope CD, phi is eliminated from the coordinate equation of the circular arc CD and the above equation set for the circular arc envelope CD3To obtain xcdAnd ycdWith respect to parameter t3From the equation of coordinates of (c), the envelope cd of the circular arc in the face tooth profile of the male rotor is obtained at O1Coordinate equations in a coordinate system.
Preferably, in O1In a coordinate system, a polynomial curve envelope ab, an arc bc and an arc envelope cd in the end face tooth profile of the male rotor are arranged along a circle center O1Repeating the steps for a plurality of times in sequence to obtain a complete male rotor end face profile;
at O2In a coordinate system, a polynomial curve AB, an arc envelope BC and an arc CD in the end face tooth profile of the female rotor are arranged along the center O of a circle2And repeating the steps for a plurality of times to obtain a complete female rotor end face molded line.
Preferably, the ratio of the teeth of the male rotor to the teeth of the female rotor is 5: 6.
Preferably, the male rotor end face profile is completely conjugated with the male rotor end face profile.
The invention further aims to provide a three-section type double-screw compressor rotor profile design method, different high-order polynomials, arcs and envelope lines of the arcs are selected, and the design method is more flexible and simpler.
In order to achieve the purpose, the invention adopts the following technical scheme: a three-section type double-screw compressor rotor profile design method comprises the following steps:
s1 at O2Under a coordinate system, a polynomial curve AB in the end face tooth profile of the female rotor is established by utilizing a coordinate equation of the polynomial curve AB, and the head and the tail of the polynomial curve AB are respectively tangent with a tooth root circle and a pitch circle of the female rotor;
s2, deriving the polynomial curve AB based on the equation1An envelope ab of a polynomial curve in an end face tooth form of the lower male rotor in a coordinate system;
S3、at O1Under a coordinate system, establishing an arc bc by using a coordinate equation of the arc bc, wherein the center of the arc bc is positioned at O1O2And the arc bc is tangent to the addendum circle of the male rotor;
s4, deriving the equation on the basis of the circular arc bc2An end surface tooth-shaped middle arc envelope line BC of the lower female rotor in a coordinate system;
s5 at O2Establishing a circular arc CD by using a coordinate equation of the circular arc CD under a coordinate system, wherein the center of the circular arc CD is positioned at O2D, connecting the line, wherein one end of the circular arc CD is tangent to the pitch circle of the female rotor, and the other end of the circular arc CD is connected with the circular arc envelope line BC;
s6, deriving the data on O on the basis of the circular arc CD1The end face tooth shape middle arc envelope cd of the male rotor under the coordinate system completes the design of single teeth in the male rotor and single teeth in the female rotor;
s7 at O1In a coordinate system, a polynomial curve envelope ab, an arc bc and an arc envelope cd which form a single tooth in the male rotor are arranged along a circle center O1Repeating the steps for a plurality of times in sequence to obtain a complete male rotor end face profile;
in an O2 coordinate system, a polynomial curve AB, an arc envelope BC and an arc CD which form a single tooth in a female rotor are arranged along a center O2And repeating the steps for a plurality of times to obtain a complete female rotor end face molded line.
The invention has the beneficial effects that:
1) the rotor profile of the double-screw compressor avoids the splicing of multiple curves through the polynomial curve and the envelope curve thereof, and has the advantages of small-leakage triangle and belt-type sealing of the third-generation rotor profile, so that the rotor profile with simple curve structure and excellent performance is obtained.
2) The three-section type double-screw compressor rotor profile design method provided by the invention can select different high-order polynomials, arcs and envelope lines thereof, and is more flexible and simpler.
Drawings
FIG. 1 is a schematic end view of a rotor profile of the present invention;
fig. 2 is a three-dimensional model diagram of a rotor generated by the rotor profile of the present invention.
Detailed Description
For the purposes of understanding, the invention will be further described in its specific structure and mode of operation with reference to the accompanying drawings in which:
a three-section type double-screw compressor rotor comprises a male rotor and a female rotor, wherein the end surface profile of the male rotor is formed by a plurality of sections of curves and comprises a polynomial curve envelope ab, an arc bc and an arc envelope cd which are connected in a smooth transition mode in sequence; the end face molded line of the female rotor is composed of a plurality of sections of curves and comprises a polynomial curve AB, an arc envelope BC and an arc CD which are connected in sequence;
the polynomial curve envelope AB in the end face tooth profile of the male rotor is a conjugate envelope of the polynomial curve AB in the end face molded line of the female rotor, and the head and the tail of the polynomial curve envelope AB are respectively tangent with a pitch circle of the male rotor and a tip circle of the male rotor;
the head and the tail of an arc bc in the end surface tooth shape of the male rotor are respectively tangent with the addendum circle of the male rotor and an arc envelope cd;
the end face tooth shape middle circular arc envelope line CD of the male rotor is a conjugate envelope line of the end face tooth shape middle circular arc CD of the female rotor, the tangent end of the circular arc envelope line CD and the circular arc section bc is a head end, and the tail end of the circular arc envelope line CD is tangent to a pitch circle of the male rotor;
the head and the tail of a polynomial curve AB in the end face tooth profile of the female rotor are respectively tangent with a female rotor pitch circle and a female rotor tooth root circle;
the end face tooth shape middle circular arc envelope line BC of the female rotor is a conjugate envelope line of a circular arc BC in the end face tooth shape of the male rotor, the end, connected with the circular arc CD, of the circular arc envelope line BC is a tail end, and the head end of the circular arc envelope line BC is tangent to a tooth root circle of the female rotor;
the end face tooth-shaped middle circular arc CD of the female rotor is connected with the circular arc envelope line BC to form a head end, and the tail end of the circular arc CD is tangent to the pitch circle of the female rotor.
According to the double-screw compressor rotor molded line formed by the invention, the male rotor and the female rotor are completely meshed, the male rotor and the female rotor are respectively formed by only three sections of curves, the molded line is simple in structure and easy to design and modify, points, straight lines and cycloid do not exist in the molded line, circular arcs, polynomial curves and conjugate envelope lines of the polynomial curves are adopted, the rotor tooth surface is improved from 'line' sealing to 'belt' sealing, and the sealing effect is greatly improved; meanwhile, the highest point of the contact line of the rotor profile formed by the invention is close to the intersection line of the cylinder holes, so that the rotor profile has a smaller leakage triangle, and further achieves a better sealing effect.
Preferably, at the center point O of the male rotor1Central point O of female rotor2Establishing a coordinate system for the origin of coordinates;
the coordinate equation of a polynomial curve AB in the end face tooth form of the female rotor is as follows:
Figure BDA0002715665710000071
wherein x isABIs a polynomial curve AB in the end face tooth form of the female rotor2X-coordinate, y in a coordinate systemABIs a polynomial curve AB in the end face tooth form of the female rotor2Y coordinate in a coordinate system, b2Is the root radius of the female rotor, d2Is the pitch diameter of the female rotor, t1Is O2Angular coordinate in a coordinate system, theta1Is a polynomial curve AB in the end face tooth form of the female rotor2The angle occupied in the coordinate system;
the coordinate equation of the circular arc CD in the face tooth shape of the female rotor is as follows:
Figure BDA0002715665710000072
wherein x isCDIs a circular arc CD is at O2X-coordinate, y in a coordinate systemCDIs a circular arc CD is at O2Y coordinate, r, in a coordinate system1Radius of the circular arc CD, t3Is a circular arc CD is at O2Angular coordinate in a coordinate system, xrThe center of the circular arc CD is O2X-coordinate, y in a coordinate systemrThe center of the circular arc CD is O2Y-coordinate of the coordinate system, theta2Is a circular arc envelope line BC atO2Polar angle, θ, in the coordinate system3Is a circular arc CD is at O2Polar angle in coordinate system, center of circular arc CD is located at O2D is connected with the wire.
The coordinate equation of the circular arc bc in the face tooth shape of the male rotor is as follows:
Figure BDA0002715665710000073
wherein x isbcIs arc bc at O1X-coordinate, y in a coordinate systembcIs arc bc at O1Y coordinate, r, in a coordinate system0Is the radius, ξ, of the circular arc bc2Is O1Polar angle, t, occupied by arc bc under coordinate system2Arc bc at O1Angle coordinate in coordinate system, the center of arc bc is located at O1O2On the connecting line of (2);
the polynomial curve envelope ab in the end face tooth profile of the male rotor has the following equation:
Figure BDA0002715665710000081
wherein x isabFor the polynomial curve envelope ab in the face tooth profile of the male rotor at O1X-coordinate, y in a coordinate systemabFor the polynomial curve envelope ab in the face tooth profile of the male rotor at O1Y coordinate in coordinate system, A represents O1O2I is the transmission ratio, R1tIs the pitch radius of the male rotor, R2tIs the pitch radius of the female rotor1For the position parameter of the polynomial curve envelope AB, the elimination of phi from the coordinate equation of the polynomial curve AB and the above-mentioned equation system for the polynomial curve envelope AB1To obtain xabAnd yabWith respect to parameter t1From the equation of coordinates of (a) to (b) to obtain the polynomial curve envelope ab at O in the face tooth profile of the male rotor1A coordinate equation in a coordinate system;
the end face tooth shape middle circular arc envelope line BC of the female rotor has the following equation:
Figure BDA0002715665710000082
wherein x isBCIs a circular arc envelope line BC at O2X-coordinate, y in a coordinate systemBCIs a circular arc envelope line BC at O2Y-coordinate in a coordinate system, phi2For the position parameter of the circular arc envelope BC, the coordinate equation of the circular arc BC and the above equation set for the circular arc envelope BC are eliminated2To obtain xBCAnd yBCWith respect to parameter t2From the envelope BC of the circular arc in the face tooth profile of the female rotor at O2Coordinates in a coordinate system;
the end face tooth shape middle circular arc envelope cd of the male rotor has the following equation:
Figure BDA0002715665710000091
wherein x iscdIs a circular arc envelope cd at O1X-coordinate, y in a coordinate systemcdIs a circular arc envelope cd at O1Y-coordinate in a coordinate system, phi3For the position parameter of the circular arc envelope CD, phi is eliminated from the coordinate equation of the circular arc CD and the above equation set for the circular arc envelope CD3To obtain xcdAnd ycdWith respect to parameter t3From the equation of coordinates of (c), the envelope cd of the circular arc in the face tooth profile of the male rotor is obtained at O1Coordinate equations in a coordinate system.
Preferably, in O1In a coordinate system, a polynomial curve envelope ab, an arc bc and an arc envelope cd in the end face tooth profile of the male rotor are arranged along a circle center O1Repeating the steps for a plurality of times in sequence to obtain a complete male rotor end face profile;
at O2In a coordinate system, a polynomial curve AB, an arc envelope BC and an arc CD in the end face tooth profile of the female rotor are arranged along the center O of a circle2And repeating the steps for a plurality of times to obtain a complete female rotor end face molded line.
Preferably, the ratio of the teeth of the male rotor to the teeth of the female rotor is 5: 6.
Preferably, the male rotor end face profile is completely conjugated with the male rotor end face profile.
A three-section type double-screw compressor rotor profile design method comprises the following steps:
s1 at O2Under a coordinate system, a polynomial curve AB in the end face tooth profile of the female rotor is established by utilizing a coordinate equation of the polynomial curve AB, and the head and the tail of the polynomial curve AB are respectively tangent with a tooth root circle and a pitch circle of the female rotor;
s2, deriving the polynomial curve AB based on the equation1An envelope ab of a polynomial curve in an end face tooth form of the lower male rotor in a coordinate system;
s3 at O1Under a coordinate system, establishing an arc bc by using a coordinate equation of the arc bc, wherein the center of the arc bc is positioned at O1O2And the arc bc is tangent to the addendum circle of the male rotor;
s4, deriving the equation on the basis of the circular arc bc2An end surface tooth-shaped middle arc envelope line BC of the lower female rotor in a coordinate system;
s5 at O2Establishing a circular arc CD by using a coordinate equation of the circular arc CD under a coordinate system, wherein the center of the circular arc CD is positioned at O2D, connecting the line, wherein one end of the circular arc CD is tangent to the pitch circle of the female rotor, and the other end of the circular arc CD is connected with the circular arc envelope line BC;
s6, deriving the data on O on the basis of the circular arc CD1The end face tooth shape middle arc envelope cd of the male rotor under the coordinate system completes the design of single teeth in the male rotor and single teeth in the female rotor;
s7 at O1In a coordinate system, a polynomial curve envelope ab, an arc bc and an arc envelope cd which form a single tooth in the male rotor are arranged along a circle center O1Repeating the steps for a plurality of times in sequence to obtain a complete male rotor end face profile;
in an O2 coordinate system, a polynomial curve AB, an arc envelope BC and an arc CD which form a single tooth in a female rotor are arranged along a center O2And repeating the steps for a plurality of times to obtain a complete female rotor end face molded line.
The method for designing the profile of the three-section type double-screw compressor rotor can select different high-order polynomials, arcs and envelope lines thereof, and is more flexible and simpler.

Claims (6)

1. A three-section double-screw compressor rotor comprises a male rotor and a female rotor, and is characterized in that the end surface profile of the male rotor is formed by a plurality of sections of curves and comprises a polynomial curve envelope ab, an arc bc and an arc envelope cd which are connected in sequence in a smooth transition manner; the end face molded line of the female rotor is composed of a plurality of sections of curves and comprises a polynomial curve AB, an arc envelope BC and an arc CD which are connected in sequence;
the polynomial curve envelope AB in the end face tooth profile of the male rotor is a conjugate envelope of the polynomial curve AB in the end face molded line of the female rotor, and the head and the tail of the polynomial curve envelope AB are respectively tangent with a pitch circle of the male rotor and a tip circle of the male rotor;
the head and the tail of an arc bc in the end surface tooth shape of the male rotor are respectively tangent with the addendum circle of the male rotor and an arc envelope cd;
the end face tooth shape middle circular arc envelope line CD of the male rotor is a conjugate envelope line of the end face tooth shape middle circular arc CD of the female rotor, the tangent end of the circular arc envelope line CD and the circular arc section bc is a head end, and the tail end of the circular arc envelope line CD is tangent to a pitch circle of the male rotor;
the head and the tail of a polynomial curve AB in the end face tooth profile of the female rotor are respectively tangent with a female rotor pitch circle and a female rotor tooth root circle;
the end face tooth shape middle circular arc envelope line BC of the female rotor is a conjugate envelope line of a circular arc BC in the end face tooth shape of the male rotor, the end, connected with the circular arc CD, of the circular arc envelope line BC is a tail end, and the head end of the circular arc envelope line BC is tangent to a tooth root circle of the female rotor;
the end face tooth-shaped middle circular arc CD of the female rotor is connected with the circular arc envelope line BC to form a head end, and the tail end of the circular arc CD is tangent to the pitch circle of the female rotor.
2. A three-stage twin-screw compressor rotor according to claim 1, characterised in that the male rotor centre point O is taken1Central point O of female rotor2Establishing a coordinate system for the origin of coordinates;
the coordinate equation of a polynomial curve AB in the end face tooth form of the female rotor is as follows:
Figure FDA0002715665700000011
wherein x isABIs a polynomial curve AB in the end face tooth form of the female rotor2X-coordinate, y in a coordinate systemABIs a polynomial curve AB in the end face tooth form of the female rotor2Y coordinate in a coordinate system, b2Is the root radius of the female rotor, d2Is the pitch diameter of the female rotor, t1Is O2Angular coordinate in a coordinate system, theta1Is a polynomial curve AB in the end face tooth form of the female rotor2The angle occupied in the coordinate system;
the coordinate equation of the circular arc CD in the face tooth shape of the female rotor is as follows:
Figure FDA0002715665700000021
wherein x isCDIs a circular arc CD is at O2X-coordinate, y in a coordinate systemCDIs a circular arc CD is at O2Y coordinate, r, in a coordinate system1Radius of the circular arc CD, t3Is a circular arc CD is at O2Angular coordinate in a coordinate system, xrThe center of the circular arc CD is O2X-coordinate, y in a coordinate systemrThe center of the circular arc CD is O2Y-coordinate of the coordinate system, theta2Is a circular arc envelope line BC at O2Polar angle, θ, in the coordinate system3Is a circular arc CD is at O2Polar angle in coordinate system, center of circular arc CD is located at O2D is connected with the wire.
The coordinate equation of the circular arc bc in the face tooth shape of the male rotor is as follows:
Figure FDA0002715665700000022
wherein x isbcIs arc bc at O1X-coordinate, y in a coordinate systembcIs arc bc at O1Y coordinate, r, in a coordinate system0Is the radius, ξ, of the circular arc bc2Is O1Polar angle, t, occupied by arc bc under coordinate system2Is arc bc at O1Angle coordinate in coordinate system, the center of arc bc is located at O1O2On the connecting line of (2);
the polynomial curve envelope ab in the end face tooth profile of the male rotor has the following equation:
Figure FDA0002715665700000023
wherein x isabFor the polynomial curve envelope ab in the face tooth profile of the male rotor at O1X-coordinate, y in a coordinate systemabFor the polynomial curve envelope ab in the face tooth profile of the male rotor at O1Y coordinate in coordinate system, A represents O1O2I is the transmission ratio, R1tIs the pitch radius of the male rotor, R2tIs the pitch radius of the female rotor1For the position parameter of the polynomial curve envelope AB, the elimination of phi from the coordinate equation of the polynomial curve AB and the above-mentioned equation system for the polynomial curve envelope AB1To obtain xabAnd yabWith respect to parameter t1From the equation of coordinates of (a) to (b) to obtain the polynomial curve envelope ab at O in the face tooth profile of the male rotor1A coordinate equation in a coordinate system;
the end face tooth shape middle circular arc envelope line BC of the female rotor has the following equation:
Figure FDA0002715665700000031
wherein x isBCIs a circular arc envelope line BC at O2X-coordinate, y in a coordinate systemBCIs a circular arc envelope line BC at O2Y-coordinate in a coordinate system, phi2For the position parameter of the circular arc envelope BC, the coordinate equation of the circular arc BC and the above equation set for the circular arc envelope BC are eliminated2To obtain xBCAnd yBCWith respect to parameter t2From the envelope BC of the circular arc in the face tooth profile of the female rotor at O2Coordinates in a coordinate system;
the end face tooth shape middle circular arc envelope cd of the male rotor has the following equation:
Figure FDA0002715665700000032
wherein x iscdIs a circular arc envelope cd at O1X-coordinate, y in a coordinate systemcdIs a circular arc envelope cd at O1Y-coordinate in a coordinate system, phi3For the position parameter of the circular arc envelope CD, phi is eliminated from the coordinate equation of the circular arc CD and the above equation set for the circular arc envelope CD3To obtain xcdAnd ycdWith respect to parameter t3From the equation of coordinates of (c), the envelope cd of the circular arc in the face tooth profile of the male rotor is obtained at O1Coordinate equations in a coordinate system.
3. A three-stage twin-screw compressor rotor according to claim 2, characterised in that O is1In a coordinate system, a polynomial curve envelope ab, an arc bc and an arc envelope cd in the end face tooth profile of the male rotor are arranged along a circle center O1Repeating the steps for a plurality of times in sequence to obtain a complete male rotor end face profile;
at O2In a coordinate system, a polynomial curve AB, an arc envelope BC and an arc CD in the end face tooth profile of the female rotor are arranged along the center O of a circle2And repeating the steps for a plurality of times to obtain a complete female rotor end face molded line.
4. A three-stage twin-screw compressor rotor according to claim 3, characterised in that the ratio of the number of teeth of the male rotor to the female rotor is 5: 6.
5. A three-stage twin screw compressor rotor as claimed in claim 3, characterised in that the male rotor end profile is fully conjugate to the male rotor end profile.
6. A profile design method for a three-stage double-screw compressor rotor according to claims 1-5, characterized by comprising the following steps:
s1 at O2Under a coordinate system, a polynomial curve AB in the end face tooth profile of the female rotor is established by utilizing a coordinate equation of the polynomial curve AB, and the head and the tail of the polynomial curve AB are respectively tangent with a tooth root circle and a pitch circle of the female rotor;
s2, deriving the polynomial curve AB based on the equation1An envelope ab of a polynomial curve in an end face tooth form of the lower male rotor in a coordinate system;
s3 at O1Under a coordinate system, establishing an arc bc by using a coordinate equation of the arc bc, wherein the center of the arc bc is positioned at O1O2And the arc bc is tangent to the addendum circle of the male rotor;
s4, deriving the equation on the basis of the circular arc bc2An end surface tooth-shaped middle arc envelope line BC of the lower female rotor in a coordinate system;
s5 at O2Establishing a circular arc CD by using a coordinate equation of the circular arc CD under a coordinate system, wherein the center of the circular arc CD is positioned at O2D, connecting the line, wherein one end of the circular arc CD is tangent to the pitch circle of the female rotor, and the other end of the circular arc CD is connected with the circular arc envelope line BC;
s6, deriving the data on O on the basis of the circular arc CD1The end face tooth shape middle arc envelope cd of the male rotor under the coordinate system completes the design of single teeth in the male rotor and single teeth in the female rotor;
s7 at O1In a coordinate system, a polynomial curve envelope ab, an arc bc and an arc envelope cd which form a single tooth in the male rotor are arranged along a circle center O1Repeating the steps for a plurality of times in sequence to obtain a complete male rotor end face profile;
at O2In the coordinate system, a polynomial curve of a single tooth in the female rotor is formedAB. The arc envelope BC and the arc CD are along the center O2And repeating the steps for a plurality of times to obtain a complete female rotor end face molded line.
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