CN111794962A - Tooth-type rotor profile sharp point correction method and tooth-type rotor - Google Patents

Tooth-type rotor profile sharp point correction method and tooth-type rotor Download PDF

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CN111794962A
CN111794962A CN202010682767.2A CN202010682767A CN111794962A CN 111794962 A CN111794962 A CN 111794962A CN 202010682767 A CN202010682767 A CN 202010682767A CN 111794962 A CN111794962 A CN 111794962A
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rotor
arc
tooth
correction
point
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CN111794962B (en
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高秀峰
朱珍昱
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Xi'an Tianrong Industrial Technology Co ltd
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Xi'an Tianrong Industrial Technology 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
    • F04C18/18—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 similar tooth forms
    • 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
    • F04C18/082—Details specially related to intermeshing engagement type pumps
    • F04C18/084—Toothed wheels
    • 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 tooth type rotor profile cusp correction method and a tooth type rotor, wherein the correction method comprises cusp correction of a female rotor and cusp correction of a male rotor, and the cusp correction of the female rotor comprises correction of a female rotor correction circular arc ab and correction of a female rotor correction cycloid bc corresponding to a cycloid meshed with an original cusp of the female rotor; the correction of the cusp of the male rotor comprises the correction of a male rotor correction arc BC and a male rotor correction cycloid AB corresponding to a cycloid meshed with the original cusp of the male rotor; the female rotor correction arc ab is tangent to the original profile at the cusp of the female rotor profile at a point a and is tangent to a point b with the female rotor correction cycloid bc; the male rotor correction arc BC is tangent to the original molded line at the sharp point of the molded line of the male rotor at a point C, and is tangent to the point B with the corrected cycloid AB of the male rotor. The invention can improve the spraying effect of the rotor surface, reduce the precision requirement in milling, reduce noise, reduce local leakage amount and avoid increasing the leakage clearance between the tooth rotor and the inner wall of the cylinder.

Description

Tooth-type rotor profile sharp point correction method and tooth-type rotor
Technical Field
The invention belongs to the technical field of compressors and vacuum pumps, and relates to a tooth type rotor profile cusp correction method and a tooth type rotor.
Background
The tooth-type rotor compressor is a rotary positive displacement compressor, has very good application prospect in the field of oil-free air compressors, and particularly has great development potential in high-rotating-speed, small-volume and oil-free occasions for vehicles and food. The tooth-type rotor compressor is composed of a pair of tooth-type rotors which are always meshed, an infinity-shaped cylinder, end plates on two axial sides, a pair of synchronous counter gears and the like.
The early tooth type rotor compressor mostly adopts a single tooth structure, and two rotors have eccentricity of different degrees, so that the balance of the rotation inertia force is often realized by a certain means. Rotors of the double-tooth, three-tooth and multi-tooth rotor compressors are symmetrical about the center of the axes of the rotors, so that self-balance of rotation inertia force can be realized. Regardless of the number of teeth of the rotor, the profile of the rotor tends to have sharp points at the tooth tips, which causes the following four problems for the compressor:
(1) the surface of the rotor sharp point is difficult to spray, and even if the spraying is good, the spraying material at the sharp point can also fall off quickly when the rotor works;
(2) the rotor is usually milled, the theoretical 'sharp point' has extremely high precision required on the milling cutter, and the sharp point is inevitably machined into a tiny round angle no matter how high-precision machine tools are adopted in practice;
(3) when the machine is processed, the rotor sharp point is replaced by milling of a small arc, and obvious leakage gaps appear when the small arc is milled to participate in meshing, so that the leakage amount at the sharp point is greatly increased, and the heat efficiency of the compressor is reduced;
(4) the current 'high rotation speed' becomes the development direction of the rotary compressor, and the local noise of the rotor with the sharp point at the working sharp point is increased.
Disclosure of Invention
The invention aims to provide a tooth type rotor profile cusp correction method and a tooth type rotor.
The technical scheme adopted by the invention is as follows:
the tooth type rotor profile cusp correction method comprises cusp correction of a female rotor and cusp correction of a male rotor. The cusp correction of the female rotor comprises the correction of a female rotor correction circular arc ab and a female rotor correction cycloid bc corresponding to a cycloid meshed with the original cusp of the female rotor; the correction of the cusp of the male rotor comprises correction of a male rotor correction arc BC and correction of a male rotor correction cycloid AB corresponding to a cycloid meshed with the original cusp of the male rotor;
the female rotor correction arc ab is tangent to the original profile at the cusp of the female rotor profile at a point a and is tangent to a point b with the female rotor correction cycloid bc; the male rotor correction arc BC is tangent to the original molded line at the sharp point of the molded line of the male rotor at a point C, and is tangent to the point B with the corrected cycloid AB of the male rotor.
Since the tooth-type rotor profile correction method provided by the invention is applicable to any tooth-type rotor profile, the tooth-type rotor profile with a cusp correction is combined for explanation.
Preferably, the tooth rotor profile with cusp correction comprises a profile of a female rotor and a profile of a male rotor, the female rotor and the male rotor are always meshed, the female rotor and the male rotor have the same number of teeth, and the profile of the female rotor and the profile of the male rotor are obtained by respectively and basically meshing curves through a centrosymmetric array; the basic meshing curve of the female rotor comprises a female rotor correction circular arc ab, a female rotor correction cycloid bc, a tooth bottom circular arc cd, a line segment de, a pin tooth circular arc ef and an addendum circular arc fg which are connected in sequence; the basic meshing curve of the male rotor comprises a male rotor correction cycloid AB, a male rotor correction arc BC, an addendum arc CD, a straight line conjugate curve segment DE, a pin tooth arc EF and a tooth bottom arc FG.
Preferably, the coordinate system referenced by the female rotor profile is O1X1Y1The coordinate system of the male rotor profile reference is O2X2Y2In which O is1And O2Center of the female and male rotors, respectively, O1X1Shaft and O2X2Collinear axes, O1Y1Shaft and O2Y2The axes are parallel;
the front tangent of the rotor correction arc ab is O1The addendum arc with the circle center and the radius rh is at the point a, the posterior tangent female rotor corrects the cycloid bc at the point b, and the female rotor corrects the arc abThe radius is r0, the center of the female rotor correction circular arc AB is on the O1X1 axis, and the female rotor correction circular arc AB is conjugated with the male rotor correction cycloid AB on the male rotor; the negative rotor correction cycloid BC is formed by forward cutting a negative rotor correction arc ab at a point b, backward cutting a tooth bottom arc cd at a point c and conjugating with a positive rotor correction arc BC on a positive rotor; the radius of the tooth bottom arc cd is rw, and the circle center is O1Point, the front tangent negative rotor corrects the cycloid bc at the point c, the back tangent line de is at the point d, and the tooth bottom arc CD is conjugated with the tooth top arc CD on the positive rotor; the line DE is conjugated with a straight conjugate curve segment DE on the male rotor; the front tangent line de of the pin tooth circular arc ef is at the point e, the rear tangent takes rh as the radius, O1The tooth crest arc as the center of circle is at point f, the circle center of the pin tooth arc ef is at radius of rt and O1Circle of pitch and straight line O as center of circle1f, the pin tooth arc EF is conjugated with the pin tooth arc EF on the male rotor; the addendum arc fg is represented by O1Taking the circle center as well as rh as the radius, cutting the tooth arc ed at the point f before cutting the tooth arc FG of the pin, and correcting the arc at the point g by the upper and lower male rotors of the rear cutting female rotor, and conjugating with the tooth bottom arc FG of the male rotor;
the corrected cycloid AB of the male rotor is anterior tangent with rw as radius and O2The circular arc at the tooth bottom which is the circle center is positioned at the point A, the circular arc BC at the point B is corrected by cutting the male rotor, and the corrected cycloid AB of the male rotor is conjugated with the corrected circular arc AB of the female rotor; the radius of the correction arc BC of the male rotor is r0, the front tangent male rotor corrects a cycloid AB at a point B, the rear tangent tooth top arc CD is at a point C, and the correction arc BC of the male rotor is conjugated with the cycloid BC on the female rotor; the addendum arc CD is O2Taking the circle center and rh as the radius, the front cutting male rotor corrects the arc BC at the point C, the rear cutting straight line conjugate curve section DE at the point D, and the tooth top arc CD is conjugated with the tooth bottom arc CD on the female rotor; the straight conjugate curve section DE is conjugated with the upper line section DE of the female rotor; the conjugate curve section DE of the front cutting straight line of the pin tooth circular arc EF is at the point E, the circular arc FG of the back cutting tooth bottom is at the point F, and the circle center of the pin tooth circular arc EF takes rt as the radius and O2Circle of pitch and straight line O as center of circle2F, pin tooth arc EF and the female rotorThe arc ef of the pin tooth is conjugated; the tooth bottom arc FG is equal to O2The center of the circle is, rw is the radius, the front cutting pin tooth arc EF is at the point F, the tooth bottom arc FG and the upper and lower male rotors of the male rotor are corrected cycloids, then the tooth bottom arc FG is cut at the point G, and the tooth bottom arc FG and the upper and lower male rotors of the male rotor are conjugated with the tooth top arc FG of the female rotor.
Preferably, the coordinate system referenced by the female rotor profile is O1X1Y1The coordinate system of the male rotor profile reference is O2X2Y2The parameter equation of the corrected circular arc ab of the female rotor is as follows:
Figure BDA0002586453350000031
the male rotor correction cycloid AB parameter equation conjugated with the female rotor correction arc AB is as follows:
Figure BDA0002586453350000041
wherein (m, l) represents the center coordinates of the correction arc ab,
Figure BDA0002586453350000042
preferably, the parameter equation of the male rotor correction arc BC is as follows:
Figure BDA0002586453350000043
the negative rotor modified cycloid BC parameter equation conjugated with the positive rotor modified arc BC is:
Figure BDA0002586453350000044
wherein (p, q) represents the center coordinates of the modified arc BC,
Figure BDA0002586453350000045
preferably, the parameter equation of the tooth bottom arc cd is as follows:
Figure BDA0002586453350000046
the crest arc CD parametric equation conjugated with the tooth bottom arc CD is:
Figure BDA0002586453350000047
preferably, the parametric equation of the straight line de section is as follows:
Figure BDA0002586453350000048
the parametric equation for the straight conjugate curve segment DE, which is conjugate to the straight segment DE, is:
Figure BDA0002586453350000049
wherein the content of the first and second substances,
Figure BDA00025864533500000410
preferably, the parameter equation of the pin tooth circular arc ef is as follows:
Figure BDA00025864533500000411
the parameter equation of the pin tooth arc EF conjugate to the pin tooth arc EF is:
Figure BDA0002586453350000051
wherein a is the central angle camber value corresponding to the tooth bottom arc cd, b is the central angle camber value corresponding to the pin tooth arc ef,
Figure BDA0002586453350000052
further preferably, the parameter equation of the addendum arc fg is as follows:
Figure BDA0002586453350000053
the parametric equation for the tooth bottom arc FG conjugate to the tooth top arc FG is:
Figure BDA0002586453350000054
in the above parametric equation: t-reference variable; rt-pitch radius, mm; rw-radius of circular arc at tooth bottom, mm; rh-radius of addendum arc, rh 2rt-rw, mm; a-the camber value, rad, of the tooth bottom arc cd. Given the values of rt, rw, a profile equation is obtained.
The invention also provides the tooth-type rotor obtained based on the tooth-type rotor profile cusp correction method.
The invention has the following beneficial effects:
according to the tooth type rotor profile sharp point correction method, arcs (namely a female rotor correction arc ab and a male rotor correction arc BC) are used as substitution curves of tooth type rotor profile sharp points, the substitution curves are simple, the rotor surface spraying effect can be greatly improved, and meanwhile, the precision requirement during milling is reduced; the correction cycloid of the male rotor is determined by the correction circular arc of the female rotor, the correction cycloid of the female rotor is determined by the correction circular arc of the male rotor, the selection range of the radius of the correction circular arc is wide, the meshing relation of the tooth-type rotors can be ensured all the time, and the noise can be reduced; the meshing relation of the cusps and the cycloid of the original molded line is changed into the meshing relation of the modified arc and the modified cycloid, so that the sealing performance of the cusps and the cycloid on the original molded line can be improved, and the local leakage amount is reduced; the modified arc is adopted to replace a sharp point, so that the leakage clearance between the tooth-type rotor and the inner wall of the cylinder cannot be increased when the compressor actually works.
Drawings
Fig. 1 is a line drawing of a double-tooth rotor with cusp correction according to the present invention.
Fig. 2 is a sectional view of a three-tooth rotor with cusp correction according to the present invention.
Fig. 3 is a diagram of the exhaust hole of the double-tooth compressor according to the present invention.
FIG. 4 is a discharge hole diagram of a three-tooth compressor according to the present invention.
Fig. 5(a) to 5(f) are views showing the operation of the double-tooth compressor according to the present invention.
Fig. 6(a) to 6(f) are views illustrating an operation process of the three-tooth compressor according to the present invention.
In the figure, 1 is a female rotor, and 2 is a male rotor.
Detailed Description
The invention is further described with reference to the following figures and examples.
As shown in figure 1, the double-tooth rotor profile with cusp correction of the invention comprises a female rotor 1 and a male rotor 2, wherein the female rotor 1 and the male rotor 2 are both in a centrosymmetric structure, and the symmetric centers are O respectively1And O2(ii) a The basic meshing curve of the female rotor 1 comprises a female rotor correction circular arc ab, a female rotor correction cycloid bc, a tooth bottom circular arc cd, a line segment de, a pin tooth circular arc ef segment and an addendum circular arc fg which are connected in sequence, and the coordinate system of the basic meshing curve is O1X1Y1A rectangular coordinate system; the basic meshing curve of the male rotor 2 comprises a male rotor correction cycloid AB, a male rotor correction arc BC, an addendum arc CD, a straight line conjugate curve segment DE, a pin tooth arc EF and a tooth bottom arc FG which are connected in sequence, and the coordinate system of the basic meshing curve is O2X2Y2Rectangular coordinate system, wherein O1X1Y1Rectangular coordinate system and O2X2Y2Coplanar rectangular coordinate systems, O1X1Shaft and O2X2Collinear axes, O1Y1Shaft and O2Y2The axes are parallel.
More specifically, the parameter equation of the female rotor correction arc ab is as follows:
Figure BDA0002586453350000061
the male rotor correction cycloid AB parameter equation conjugated with the female rotor correction arc AB is as follows:
Figure BDA0002586453350000062
wherein, (m, l) represents the center coordinates of the female rotor correction arc ab, m is rh-r0, l is 0,
Figure BDA0002586453350000063
Figure BDA0002586453350000064
the value range of t in the equation is [ -pi, 0]。
The parameter equation of the rotor arc BC is as follows:
Figure BDA0002586453350000071
the negative rotor modified cycloid BC parameter equation conjugated with the positive rotor modified arc BC is:
Figure BDA0002586453350000072
wherein, (p, q) represents the center coordinates of the male rotor correction arc BC, the center coordinates are determined by a common tangent point B, C and a radius r0,
Figure BDA0002586453350000073
the value range of t in the equation is [0, pi ]]。
The parameter equation of the tooth bottom arc cd is as follows:
Figure BDA0002586453350000074
the crest arc CD parametric equation conjugated with the tooth bottom arc CD is:
Figure BDA0002586453350000075
t has a value in the range of [0, -a]Wherein a is the camber value corresponding to the tooth bottom arc cd,
Figure BDA0002586453350000076
the parameter equation of the line segment de is as follows:
Figure BDA0002586453350000077
the parametric equation for the straight conjugate curve segment DE conjugated with the segment DE is:
Figure BDA0002586453350000078
wherein the content of the first and second substances,
Figure BDA0002586453350000079
t has a value of [0, rt × sinb ]]。
The parameter equation of the pin tooth circular arc ef is as follows:
Figure BDA00025864533500000710
the parameter equation of the pin tooth arc EF conjugate to the pin tooth arc EF is:
Figure BDA00025864533500000711
wherein a is the central angle camber value corresponding to the tooth bottom arc cd, b is the central angle camber value corresponding to the pin tooth arc ef,
Figure BDA0002586453350000081
t has a value range of [0, b]。
The parameter equation of the addendum arc fg is as follows:
Figure BDA0002586453350000082
the parametric equation for the tooth bottom arc FG conjugate to the tooth top arc FG is:
Figure BDA0002586453350000083
t has a value range of
Figure BDA0002586453350000084
n is the number of teeth of the tooth compressor, and n is 2 for the double tooth compressor, namely t is in the range of [ -pi, -a-b]。
Specifically, the above-described double-tooth compressor requires given values of: rt-pitch radius, mm; rw-radius of circular arc at tooth bottom, mm; a-the camber value, rad, of the tooth bottom arc fg; the number of teeth of the n-double-tooth compressor is 2. And the other rhs are the radius of the addendum arc, and the rhs is 2rt-rw and mm.
As shown in FIG. 2, the three-tooth rotor profile with cusp correction according to the present invention comprises a female rotor 1 and a male rotor 2, wherein the female rotor 1 and the male rotor 2 are both of a centrosymmetric structure, and the symmetric centers are O1And O2(ii) a The basic meshing curve of the female rotor 1 comprises a female rotor correction circular arc ab, a female rotor correction cycloid bc, a tooth bottom circular arc cd, a line segment de, a pin tooth circular arc ef segment and an addendum circular arc fg which are connected in sequence, and the coordinate system of the basic meshing curve is O1X1Y1A rectangular coordinate system; the basic meshing curve of the male rotor 2 comprises a male rotor correction cycloid AB, a male rotor correction arc BC, an addendum arc CD, a straight line conjugate curve segment DE, a pin tooth arc EF and a tooth bottom arc FG which are connected in sequence, and the coordinate system of the basic meshing curve is O2X2Y2Rectangular coordinate system, wherein O1X1Y1Rectangular coordinate system and O2X2Y2Coplanar rectangular coordinate systems, O1X1Shaft and O2X2Collinear axes, O1Y1Shaft and O2Y2The axes are parallel.
Specifically, the three-tooth rotor profile construction process with the cusp correction is the same as that of the two-tooth compressor rotor profile construction process, except that the number n of teeth of the three-tooth compressor rotor is 3.
As shown in fig. 3, in the exhaust hole diagram of the double-tooth compressor according to the present invention, the outline of the exhaust hole IJK includes an addendum arc IJ, a dedendum arc IK, and a bottom edge line JK. The determination method of the vent hole IJk comprises the following steps: determined by the closed areas S1 and S2 according to the set internal volume ratioDetermining an exhaust closing area S3, and further determining the relative position of the female rotor and the male rotor when exhaust starts; the bottom edge line and the center of the circle of the male rotor are O1The intersection point of the addendum arcs with the radius of rh is a J point; the bottom edge line and the center of the circle of the male rotor are O2The intersection point of the circular arc at the tooth bottom with the radius rw is a point K; the male rotor bottom edge line between points J, K is the bottom edge line JK.
As shown in fig. 4, in the exhaust hole diagram of the three-tooth compressor according to the present invention, the outline of the exhaust hole IJK includes an addendum arc IJ, a dedendum arc IK, and a bottom edge line JK. The determination method of the three-tooth compressor exhaust hole IJK is completely the same as that of the double-tooth compressor exhaust hole.
Fig. 3 and 4 show that the molded line cusp correction method provided by the invention does not influence the exhaust hole opening of the tooth type rotor.
As shown in fig. 5(a) -5 (f), which are working process diagrams of the double-tooth compressor according to the present invention, the gas shown in fig. 5(a) enters the cavities S1 and S2 from the suction port, and the previous cavities are merged to form the effective cavity S3; as shown in fig. 5(b), the chambers S1, S2 gradually increase, the amount of inhaled air increases, and the effective chamber S3 gradually decreases; FIG. 5(c) shows the chambers S1, S2 as being at their maximum and both forming a closed volume, while the active chamber S3 continues to contract to its corresponding volume during venting, at which point the vent is about to open; the chambers S1, S2 shown in fig. 5(d) continue to be pushed but the volume does not change, while the active chamber S3 continues to shrink and a portion of the gas has been vented; the chambers S1, S2 shown in fig. 5(e) are further advanced, while chamber S3 is further contracted, and a part is discharged; as shown in fig. 5(f), the chamber S1 begins to shrink, the chamber S2 continues to advance and is about to merge with S1 to form a new effective chamber, and at the same time, the effective chamber S3 is about to shrink to 0, and the corresponding exhaust process is about to end.
As shown in fig. 6(a) to 6(f), the operation process of the three-tooth compressor according to the present invention is substantially the same as that of the two-tooth compressor, except that the cavities S1 and S2 formed at a certain number of revolutions of the three-tooth compressor have a small volume and a large number.
Fig. 5(a) -5 (f) and 6(a) -6 (f) show that the molded line cusp correction method proposed by the present invention does not affect the actual compression and exhaust processes of the tooth rotor compressor, and can ensure the permanent meshing of the female rotor and the male rotor.
The above-mentioned embodiments are only used for illustrating the implementation process of the invention, and do not limit the concept and scope of the invention, so long as the person skilled in the art can make various modifications and improvements within the scope of the design concept of the invention, and fall into the protection scope of the invention.

Claims (10)

1. A tooth type rotor profile cusp correction method is characterized by comprising cusp correction of a female rotor and cusp correction of a male rotor;
the cusp correction of the female rotor comprises the correction of a female rotor correction arc AB and a female rotor correction cycloid BC corresponding to a cycloid meshed with the original cusp of the female rotor, and the cusp correction of the male rotor comprises the correction of a male rotor correction arc BC and a male rotor correction cycloid AB corresponding to a cycloid meshed with the original cusp of the male rotor;
the female rotor correction arc ab is tangent to the original profile at the cusp of the female rotor profile at a point a and is tangent to a point b with the female rotor correction cycloid bc; the male rotor correction arc BC is tangent to the original molded line at the sharp point of the molded line of the male rotor at a point C, and is tangent to the point B with the corrected cycloid AB of the male rotor.
2. The tooth rotor profile cusp correction method according to claim 1, characterized in that the tooth rotor profiles with cusp correction comprise profiles of a female rotor and profiles of a male rotor, the female rotor and the male rotor are always meshed, the female rotor and the male rotor have the same number of teeth, and the profiles of the female rotor and the male rotor are both obtained by respectively passing through a centrosymmetric array by basic meshing curves; the basic meshing curve of the female rotor comprises a female rotor correction circular arc ab, a female rotor correction cycloid bc, a tooth bottom circular arc cd, a line segment de, a pin tooth circular arc ef and an addendum circular arc fg which are connected in sequence; the basic meshing curve of the male rotor comprises a male rotor correction cycloid AB, a male rotor correction arc BC, an addendum arc CD, a straight line conjugate curve segment DE, a pin tooth arc EF and a tooth bottom arc FG which are connected in sequence.
3. A method for tooth rotor profile cusp correction according to claim 2, characterized in that said female rotor profile reference coordinate system is O1X1Y1The coordinate system of the male rotor profile reference is O2X2Y2In which O is1And O2Center of the female and male rotors, respectively, O1X1Shaft and O2X2Collinear axes, O1Y1Shaft and O2Y2The axes are parallel;
the front section of the corrected circular arc ab of the female rotor is cut by O1The addendum circular arc with the circle center and the radius rh is at the point a, the back tangent female rotor modified cycloid bc is at the point b, the radius of the female rotor modified circular arc ab is r0, and the circle center of the female rotor modified circular arc ab is O1X1On the shaft, a female rotor correction circular arc AB is conjugated with a male rotor correction cycloid AB on a male rotor; the negative rotor corrects the cycloid BC, cuts the negative rotor correction arc ab at the point b before, and the negative rotor corrects the cycloid BC, cuts the tooth bottom arc cd at the point c after, and is conjugated with the positive rotor correction arc BC on the positive rotor; the radius of the tooth bottom arc cd is rw, and the circle center is O1Point, the front tangent negative rotor corrects the cycloid bc at the point c, the back tangent line de is at the point d, and the tooth bottom arc CD is conjugated with the tooth top arc CD on the positive rotor; the line DE is conjugated with a straight conjugate curve segment DE on the male rotor; the front tangent line de of the pin tooth circular arc ef is at the point e, the rear tangent takes rh as the radius, O1The tooth crest arc as the center of circle is at point f, the circle center of the pin tooth arc ef is at radius of rt and O1Circle of pitch and straight line O as center of circle1f, the pin tooth arc EF is conjugated with the pin tooth arc EF on the male rotor; the addendum arc fg is represented by O1Taking the circle center as well as rh as the radius, cutting the tooth arc ed at the point f before cutting the tooth arc FG of the pin, and correcting the arc at the point g by the upper and lower male rotors of the rear cutting female rotor, and conjugating with the tooth bottom arc FG of the male rotor;
the corrected cycloid AB of the male rotor is anterior tangent with rw as radius and O2The circular arc of the tooth bottom as the center of a circle is positioned at the point A, and the post-cutting male rotor is repairedThe positive arc BC is at the point B, and the positive rotor modified cycloid AB is conjugated with the negative rotor modified arc AB on the negative rotor; the radius of the correction arc BC of the male rotor is r0, the front tangent male rotor corrects a cycloid AB at a point B, the rear tangent tooth top arc CD is at a point C, and the correction arc BC of the male rotor is conjugated with the cycloid BC on the female rotor; the addendum arc CD is O2Taking the circle center and rh as the radius, the front cutting male rotor corrects the arc BC at the point C, the rear cutting straight line conjugate curve section DE at the point D, and the tooth top arc CD is conjugated with the tooth bottom arc CD on the female rotor; the straight conjugate curve section DE is conjugated with the upper line section DE of the female rotor; the conjugate curve section DE of the front cutting straight line of the pin tooth circular arc EF is at the point E, the circular arc FG of the back cutting tooth bottom is at the point F, and the circle center of the pin tooth circular arc EF takes rt as the radius and O2Circle of pitch and straight line O as center of circle2F, the pin tooth arc EF is conjugated with the pin tooth arc EF on the female rotor at the intersection point; the tooth bottom arc FG is equal to O2The center of the circle is, rw is the radius, the front cutting pin tooth arc EF is at the point F, the tooth bottom arc FG and the upper and lower male rotors of the male rotor are corrected cycloids, then the tooth bottom arc FG is cut at the point G, and the tooth bottom arc FG and the upper and lower male rotors of the male rotor are conjugated with the tooth top arc FG of the female rotor.
4. A tooth rotor profile cusp correction method according to claim 3, characterized in that the parametric equation for the female rotor correction arc ab is:
Figure FDA0002586453340000021
the male rotor correction cycloid AB parameter equation is as follows:
Figure FDA0002586453340000031
wherein (m, l) represents the center coordinates of the corrected circular arc ab of the female rotor,
Figure FDA0002586453340000032
t represents a parameter.
5. A tooth rotor profile cusp correction method according to claim 3, characterized in that the parametric equation for the male rotor correction arc BC is:
Figure FDA0002586453340000033
the negative rotor modified cycloid bc parameter equation is as follows:
Figure FDA0002586453340000034
wherein, (p, q) represents the center coordinates of the corrected circular arc BC of the male rotor,
Figure FDA0002586453340000035
t represents a parameter.
6. The method for correcting the tooth rotor profile cusp according to claim 3, wherein the parametric equation for the tooth bottom arc cd is:
Figure FDA0002586453340000036
the tooth crest circular arc CD parameter equation is as follows:
Figure FDA0002586453340000037
wherein t represents a parameter.
7. A tooth rotor profile cusp correction method according to claim 3, characterized in that the parametric equation for the segment de is:
Figure FDA0002586453340000038
the parameter equation of the straight conjugate curve segment DE is:
Figure FDA0002586453340000041
wherein the content of the first and second substances,
Figure FDA0002586453340000042
t represents a parameter.
8. A method for tooth rotor profile cusp correction according to claim 3, characterized in that the parametric equation for the pin tooth arc ef is:
Figure FDA0002586453340000043
the EF parameter equation of the circular arc of the pin tooth is as follows:
Figure FDA0002586453340000044
wherein a is the central angle camber value corresponding to the tooth bottom arc cd, b is the central angle camber value corresponding to the pin tooth arc ef,
Figure FDA0002586453340000045
t represents a parameter, rh-2 rt-rw.
9. A tooth rotor profile cusp correction method according to claim 3, characterized in that the parametric equation for the addendum arc fg is:
Figure FDA0002586453340000046
the parametric equation for the tooth bottom arc FG is:
Figure FDA0002586453340000047
wherein: t represents a parameter; (ii) a rw represents the tooth bottom arc radius; rh represents the radius of the addendum arc, rh-2 rt-rw.
10. A tooth rotor obtained based on the tooth rotor profile cusp correction method according to any one of claims 1 to 9.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115143107A (en) * 2022-07-04 2022-10-04 西安交通大学 Conical rotor and dry-type double-screw vacuum pump with same

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CN105317677A (en) * 2015-11-09 2016-02-10 中国石油大学(华东) Screw rotor without acute-angle cusp
CN206957921U (en) * 2017-06-08 2018-02-02 中国石油大学(华东) A kind of complete smooth screw rotor based on eccentric circle involute
CN108930650A (en) * 2018-07-02 2018-12-04 西安交通大学 A kind of double end claw pump rotor and its molded line

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CN105156323A (en) * 2015-09-10 2015-12-16 中国科学院等离子体物理研究所 Cold press rotor
CN105317677A (en) * 2015-11-09 2016-02-10 中国石油大学(华东) Screw rotor without acute-angle cusp
CN206957921U (en) * 2017-06-08 2018-02-02 中国石油大学(华东) A kind of complete smooth screw rotor based on eccentric circle involute
CN108930650A (en) * 2018-07-02 2018-12-04 西安交通大学 A kind of double end claw pump rotor and its molded line

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115143107A (en) * 2022-07-04 2022-10-04 西安交通大学 Conical rotor and dry-type double-screw vacuum pump with same

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