CN102979731B - Rotor profile of double-screw vacuum pump, and designing method of rotor profile - Google Patents

Abstract

The invention discloses a rotor profile of a double-screw vacuum pump, and a designing method of the rotor profile. The tooth profile of the double-screw vacuum pump consists of a point gearing cycloid, a point meshing epicycloid, an arc-arc envelope curve, a like Archimedean spiral and a conjugated envelope curve of the like Archimedean spiral, the range and cycloid range of the like Archimedean spiral and the conjugated envelope curve of the like Archimedean spiral are defined through positions of upper and lower bottoms of an axial trapezoid on the basis of a common trapezoid, the like Archimedean spiral is continuously determined through a first-order derivative of an arc, the conjugated envelope curve of the like Archimedean spiral is added, and equations of the point gearing cycloid and the point gearing epicycloid are finally determined by a sealed meshing line, thereby completing the design of the profile. The tooth profile of the double-screw vacuum pump can completely meet the meshing theorem, the sealed meshing line and the continuous contact line are designed, the areas of through holes are small, and the volume efficiency is high. The designed double-screw rotor profiles are the same, so that the processing cost of a rotor can be well lowered.

Description

A kind of Twin-screw vacuum pump molded lines of rotor and design method thereof

Technical field

The invention belongs to Mechanical Engineering Design field, particularly a kind of Twin-screw vacuum pump molded lines of rotor and design method thereof.

Background technique

Dry vacuum pump due in the middle of working procedure without any liquid working media and sealing medium, have a wide range of applications in modern industry.Such as in semiconductor fabrication without the vacuum drawn of backflowing, the extraction of coercibility steam or etchant gas in petrochemical industry.It inherits screw rod mechanism and forces the feature such as gas transmission, compact structure, reliability is high, the life-span is long, dynamical balancing performance is good, multi-phase mixed delivering, and there is lower and stable power consumption and the nonstaining property to cooling water, the focus becoming vacuum pump research and manufacture.

Core component in Twin-screw vacuum pump is exactly the contrary rotor of the rotation direction that is meshed for a pair, the design of molded lines of rotor directly has influence on pump performance, molded lines of rotor research is the basis of Twin-screw vacuum pump thermodynamic property research, is also optimized model line design, improves the key of overall performance.As trade secret, in actual available screw molded lines document abroad, report seldom.

Traditional screw vacuum pump is divided into two kinds, generally all requires that two molded lines of rotor are identical, is beneficial to processing:

1. rectangular teeth and stepped tooth

The distinguishing feature of this Twin-screw vacuum pump is axial cross section is rectangle or trapezoidal.This kind of vacuum pump does not meet meshing condition, and radial direction has larger open-work, and tightness is poor.

2. cycloid-Archimedes spiral tooth

This Twin-screw vacuum pump is made up of point gearing cycloid, tooth root circular arc, Archimedes spiral (or claiming involute) and tooth top circular arc.Its tightness compares rectangular teeth and stepped tooth has had very large improvement.By adjustment Archimedes spiral section parameter, the Archimedes spiral of negative and positive rotor can be made to contact with each other, but do not meet engagement theorem, and there is open-work equally in rotor radial.

The design of Novel wire is wished to meet: 1) negative and positive two rotor meets engagement theorem completely, and line of contact is closed, Line of contact is continuous; 2) two molded lines of rotor compositions are identical, to cut down finished cost 3) open-work area is little.

Summary of the invention

The object of the present invention is to provide a kind of Twin-screw vacuum pump molded lines of rotor and design method thereof, the Twin-screw vacuum pump molded lines of rotor total conjugated adopting this design method to obtain and two molded lines of rotor composition identical, open-work area is little.This molded line has good tightness, and the profile formed processing is simple, and processing cost is low.

Conjugation envelope (ef) and the tooth top circular arc (fa) of the point gearing cycloid (ab) that this Twin-screw vacuum pump molded lines of rotor is connected successively by head and the tail, point gearing epicycloid (bc), tooth root circular arc (cd), class Archimedes spiral (de), class Archimedes spiral form, and the molded line of female rotor is identical with the molded line of male rotor.The curve connecting tooth top circular arc (fa) and tooth root circular arc (cd) is two sections, is respectively the conjugation envelope of class Archimedes spiral and this section of class Archimedes spiral.Two molded lines of rotor of Twin-screw vacuum pump can be made identical by this design, effectively reduce processing cost.

The right angled coordinates parametric equation of described class Archimedes spiral (de) is:

$\left\{\begin{array}{c}{x}_{\mathrm{de}}=-(\mathrm{\α}\×f\left(t\right)+\mathrm{\β})\×\sin \left(t\right)\\ y_{\mathrm{de}}=(\mathrm{\α}\×f\left(t\right)+\mathrm{\β})\×\cos \left(t\right)\end{array}\right.$

X in equation _dethe X-coordinate of representation class Archimedes spiral, y _dethe Y-coordinate of representation class Archimedes spiral, f (t) represents the function replacing angle parameter in Archimedes spiral, t denotation coordination parameter, and equation ρ (t)=α × f (t)+β meets t _d, t _fthe initial sum end of a period angle of representation class Archimedes spiral and conjugation envelope (def) thereof respectively, and ρ (t _d)=d/2, ρ (t _f)=D/2, d represents root diameter, and D represents tip diameter, can solve constant α thus, the condition of β and f (t) demand fulfillment, and the conjugation envelope of class Archimedes spiral is rotated by the conjugate curve translation of class Archimedes spiral and obtains.

The conjugation envelope (ef) of described class Archimedes spiral is determined by following right angled coordinates parametric equation:

$\left\{\begin{array}{c}{x}_{\mathrm{ef}}=X_2\×\cos \mathrm{\θ}-Y_2\×\sin \mathrm{\θ}\\ y_{\mathrm{ef}}=X_2\×\sin \mathrm{\θ}+Y_2\×\cos \mathrm{\θ}\end{array}\right.$

θ is the polar angle difference under the conjugate curve starting point of class Archimedes spiral terminal and class Archimedes spiral is converted into polar coordinates;

Wherein k=i+1, i represent velocity ratio, are taken as 1, represent molded lines of rotor location parameter (being obtained by above-mentioned solution of equation), A represents the centre distance of negative and positive two rotor, being determined by rotation direction during yin, yang two working rotor, male rotor dextrorotation to Shi Qu –, otherwise is+.

Described point gearing cycloid and the epicycloidal length of point gearing are determined by the line of contact of molded line and Line of contact, need ensure the line of contact of molded line close and Line of contact continuous.

The right angled coordinates parametric equation of described point gearing cycloid (ab) is:

$\left\{\begin{array}{c}{x}_{\mathrm{ab}}=A\×\sin (t+t_1)-1/4\×(d+D)\×\sin (2\×t+t_1)\\ y_{\mathrm{ab}}=A\×\cos (t+t_1)-1/4\×(d+D)\×\cos (2\×t+t_1)\end{array}\right.$

The right angled coordinates parametric equation of point gearing epicycloid (bc) is:

$\left\{\begin{array}{c}{x}_{\mathrm{bc}}=-A\×\sin (t+t_2)-1/2\×D\×\sin (2\×t+t_2)\\ y_{\mathrm{bc}}=A\×\cos (t+t_2)-1/2\×D\×\cos (2\×t+t_2)\end{array}\right.$

X in equation _abrepresent the X-coordinate of point gearing cycloid, y _abrepresent the Y-coordinate of point gearing cycloid, x _bcrepresent the epicycloidal X-coordinate of point gearing, y _bcrepresent the epicycloidal Y-coordinate of point gearing, A represents the centre distance of negative and positive two rotor, and d represents root diameter, and D represents tip diameter, t ₁represent the start angle of point gearing cycloid, t ₂represent the epicycloidal start angle of point gearing, t denotation coordination parameter.

The joint first derivative of the joint of described class Archimedes spiral and tooth root circular arc and the conjugation envelope of class Archimedes spiral and tooth top circular arc is continuous, is and is smoothly connected.Its conjugate rotors (female rotor) is similarly and is smoothly connected.

The right angled coordinates parametric equation of described tooth root circular arc (cd) is:

$\left\{\begin{array}{c}{x}_{\mathrm{cd}}=-d\×\sin \left(t\right)/2\\ y_{\mathrm{cd}}=d\×\cos \left(t\right)/2\end{array}\right.$

The right angled coordinates parametric equation of described tooth top circular arc (fa) is:

$\left\{\begin{array}{c}{x}_{\mathrm{fa}}=-D\×\sin \left(t\right)/2\\ y_{\mathrm{fa}}=D\×\cos \left(t\right)/2\end{array}\right.$

X in equation _cdrepresent the X-coordinate of tooth root circular arc, y _cdrepresent the Y-coordinate of tooth root circular arc, x _farepresent the X-coordinate of tooth top circular arc, y _farepresent the Y-coordinate of tooth top circular arc, D represents tip diameter, and d represents root diameter, t denotation coordination parameter.

The design method of above-mentioned Twin-screw vacuum pump molded lines of rotor, comprises the following steps:

1) to trapezoidal rotor to the radial molded line carrying out radial cuts and obtain Twin-screw vacuum pump flute profile, in male rotor molded line, fa section is tooth top circular arc, and ac section is Archimedes spiral, cd section is tooth root circular arc, df section is Archimedes spiral, and the molded line of female rotor is identical with male rotor, in female rotor molded line, f'a' section is tooth top circular arc, a'c' section is Archimedes spiral, and c'd' section is tooth root circular arc, and d'f' section is Archimedes spiral;

2) the ac section Archimedes spiral of male rotor is substituted with the point gearing epicycloid of female rotor a' point;

3) df section Archimedes spiral is replaced with the class Archimedes spiral that equation under the coordinate of footpath, pole is ρ=α × f (t)+β, f (t) represents the function replacing former Archimedes spiral angle parameter, this function meets in two end points places and tooth top circular arc and root circle arc smooth transition, namely at two end points places $\frac{\mathrm{d\ρ}}{\mathrm{dt}}=0;$

4) be two sections by class Archimedes spiral in the punishment of e point, and retain wherein one section, suppose to remain de section, ask for the conjugate curve e'f' of de section, the contact points that wherein e point is corresponding is the contact points that e', d point is corresponding is f', e'f' and de section is connected by rotating translation;

5) on point gearing epicycloid, get the intersection point with pitch circle, and ask for point gearing cycloid corresponding to this intersection point.

The present invention designs the Twin-screw vacuum pump profile of tooth that produces by point gearing cycloid, point gearing epicycloid, circular arc-arc envelope line, class Archimedes spiral and conjugation envelope composition thereof, the present invention is on common stepped tooth basis, scope and the cycloid scope of class Archimedes spiral and conjugation envelope thereof are defined in position of going to the bottom on axially trapezoidal by this, class Archimedes spiral is determined continuously by the first derivative with circular arc, and add the conjugation envelope of class Archimedes spiral, finally with the line of contact determination point gearing cycloid closed and point gearing epicycloid equation, thus complete Profile Design, the molded line of Twin-screw vacuum pump flute profile of the present invention meets engagement theorem completely, has closed line of contact and continuous print Line of contact, thus has good performance, meanwhile, the molded line adopting this kind of design method to produce can make the molded lines of rotor of two screw rods identical, thus can reduce rotor machining cost preferably.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of Twin-screw vacuum pump molded lines of rotor of the present invention;

Fig. 2 is the radial molded line of traditional trapezoidal screw vacuum pump;

Fig. 3 engages the molded line after cycloid to the radial molded line adjusting point of traditional trapezoidal screw vacuum pump;

Fig. 4 is the axial cross section of Twin-screw vacuum pump rotor of the present invention;

Fig. 5 is molded lines of rotor of the present invention and pitch curve thereof the projection drawing at radial end face;

Fig. 6 is the instantaneous contact line of rotor of the present invention;

Fig. 7 is the molded line shown in Fig. 3 and line of contact thereof;

Fig. 8 is the molded line after the adjusting point of molded line shown in Fig. 7 engagement cycloid and line of contact.

Specifically execute mode

Below in conjunction with accompanying drawing, the invention will be further described.As shown in Figure 1, it consists of point gearing cycloid, circular arc to screw vacuum pump molded line of the present invention---arc envelope line and class Archimedes spiral and conjugation envelope composition thereof.Male rotor is specifically formed: point gearing cycloid (a ₁b ₁), point gearing epicycloid (b ₁c ₁), tooth root circular arc (c ₁d ₁), class Archimedes spiral (d ₁e ₁), the conjugation envelope (e of class Archimedes spiral ₁f ₁), tooth top circular arc (f ₁a ₁).Female rotor molded line is made up of the conjugate curve that male rotor is corresponding, can be identical with male rotor molded line.Female rotor is specifically formed: point gearing cycloid (a ₂b ₂), point gearing epicycloid (b ₂c ₂), tooth root circular arc (c ₂d ₂), class Archimedes spiral (d ₂e ₂), the conjugation envelope (e of class Archimedes spiral ₂f ₂), tooth top circular arc (f ₂a ₂).Subscript 1 represents male rotor, and subscript 2 represents female rotor, yin, yang two rotor can be made identical by adjustment parameter.

The present invention proposes a kind of improvement curve of Archimedes spiral, it is called class Archimedes spiral.If the class Archimedes spiral Archimedes spiral generally adopted in the middle of current screw vacuum pump design is replaced by the present invention and engagement envelope thereof, the rotor curve obtained connects smooth, negative and positive two rotor meets engagement theorem completely, and negative and positive two rotor is identical, achieve the conjugation of same profile of tooth negative and positive rotor.

Fig. 4 is the axial cross section of the design, and each section of curve is corresponding with profile.Can see that tooth top section is wider than section at the bottom of tooth, be conducive to the design of rotor machining cutter.

Fig. 5 is the projection drawing of the design's rotor pitch curve at radial end face.

Fig. 6 is the instantaneous contact line of the design's rotor, and as can be seen from the figure, the Line of contact of the design is completely continuous, and rotor has good tightness.

Each section of constituent curve of the present invention equation under cartesian coordinate system is as follows:

The parametric equation of described point gearing cycloid (ab) is:

$\left\{\begin{array}{c}{x}_{\mathrm{ab}}=A\×\sin (t+t_1)-1/4\×(d+D)\×\sin (2\×t+t_1)\\ y_{\mathrm{ab}}=A\×\cos (t+t_1)-1/4\×(d+D)\×\cos (2\×t+t_1)\end{array}\right.$

The parametric equation of described point gearing epicycloid (bc) is:

$\left\{\begin{array}{c}{x}_{\mathrm{bc}}=-A\×\sin (t+t_2)-1/2\×D\×\sin (2\×t+t_2)\\ y_{\mathrm{bc}}=A\×\cos (t+t_2)-1/2\×D\×\cos (2\×t+t_2)\end{array}\right.$

The parametric equation of described tooth root circular arc (cd) is:

$\left\{\begin{array}{c}{x}_{\mathrm{cd}}=-d\×\sin \left(t\right)/2\\ y_{\mathrm{cd}}=d\×\cos \left(t\right)/2\end{array}\right.$

The parametric equation of described class Archimedes spiral (de) is:

$\left\{\begin{array}{c}{x}_{\mathrm{de}}=-(\mathrm{\α}\×f\left(t\right)+\mathrm{\β})\×\sin \left(t\right)\\ y_{\mathrm{de}}=(\mathrm{\α}\×f\left(t\right)+\mathrm{\β})\×\cos \left(t\right)\end{array}\right.$

The conjugation envelope (ef) of described class Archimedes spiral is rotated by the conjugate curve translation of de section and obtains:

The conjugate curve e'f' of de is asked for by following equation, and by required conjugate curve by X ₂o ₂y ₂system of coordinates is converted at X ₁o ₁y ₁system of coordinates:

Wherein being determined by rotation direction during two working rotors, male rotor dextrorotation to Shi Qu –, otherwise is+.

$\left\{\begin{array}{c}{x}_{\mathrm{ef}}=X_2\×\cos \mathrm{\θ}-Y_2\×\sin \mathrm{\θ}\\ y_{\mathrm{ef}}=X_2\×\sin \mathrm{\θ}+Y_2\×\cos \mathrm{\θ}\end{array}\right.$

θ is the polar angle difference under e and e ＇ is converted into polar coordinates.

The parametric equation of described tooth top circular arc (fa) is:

$\left\{\begin{array}{c}{x}_{\mathrm{fa}}=-D\×\sin \left(t\right)/2\\ y_{\mathrm{fa}}=D\×\cos \left(t\right)/2\end{array}\right.$

In formula: t---coordinate parameters, can be considered the polar angle value under polar coordinates

D---rotor tooth outside diameter circle

D---rotor tooth Root diameter

The centre distance of A---negative and positive two rotor

I---velocity ratio, is taken as 1

T ₁---the start angle of cycloid ab

T ₂---the start angle of cycloid bc

---molded lines of rotor location parameter

K---velocity ratio adds 1, is 2

F (t)---replace the function of angle parameter in Archimedes spiral

Female rotor molded line is made up of the conjugate curve that male rotor is corresponding, can try to achieve by envelope requirement relation.

Molded line due to the design can be improved by stepped tooth and obtain, therefore using the basis of stepped tooth as the design:

1. ask for traditional trapezoidal toothed

To trapezoidal screw rotor to the radial molded line carrying out radial cuts and obtain traditional trapezoidal screw vacuum pump flute profile as shown in Figure 2.

In Fig. 2, fa section is tooth top circular arc, and ac is Archimedes spiral, and cd is tooth root circular arc, and df is Archimedes spiral (involute).Female rotor is identical with male rotor, and corresponding acdf point changes a'c'd'f' into.

2. the epicycloidal correction of point gearing

By the ac section of male rotor in the point gearing epicycloid alternate figures 2 of female rotor a' point, the molded lines of rotor of formation is as Fig. 3.

3. class Archimedes spiral

The conjugate curve of df section Archimedes spiral have the phenomenon of intersecting with being separated with tooth top circular arc with tooth root circular arc.Cause the main cause of this phenomenon to be that Archimedes spiral (involute) ρ=α t+ β and tooth root circular arc and tooth top circular arc are discontinuous in the first derivative at tie point d, f place, molded lines of rotor is rough at d, f place, there is salient point and concave point, as Fig. 3.Can find by calculating, traditional Archimedes spiral (involute) is difficult to meet Profile Design requirement.

Archimedes spiral is amplified, replaces Archimedes spiral with the new curve that equation under the coordinate of footpath, pole is ρ=α × f (t)+β, be referred to as class Archimedes spiral.Class Archimedes spiral must with tooth top circular arc and tooth root circular arc continuously and first derivative is continuous, namely at two end points places the curve satisfied condition can be selected thus.Such as, ρ=α × sin (t)+β etc.

So far two rotors meeting meshing condition can be designed.

4. rotate the conjugate curve of class Archimedes spiral

For making negative and positive two molded lines of rotor identical and conjugation, be two sections by former class Archimedes spiral section in the punishment of e point, and retain wherein one section, suppose to remain de section, and ask for the conjugate curve e'f' of de section, wherein the contact points of e point correspondence is the corresponding f' point of e', d point.By rotating translation, e'f' and de is connected.So just obtain a molded line be made up of point gearing epicycloid, circular arc-arc envelope line and class Archimedes spiral and conjugation envelope thereof.Negative and positive two rotor of this kind of molded line composition meets conjugate condition, and negative and positive two rotor is identical.

Revise according to this, class Archimedes spiral should meet with tooth top, tooth root circular arc continuous, and first derivative meets $\frac{\mathrm{d\ρ}}{\mathrm{dt}}{|}_{t=t_d}=0$ .When $\frac{\mathrm{d\ρ}}{\mathrm{dt}}{|}_{t=t_e/2}=\frac{\mathrm{\π}}{4},$ Namely class Archimedes e point place slope is time, the curve that transition is smooth can be obtained.

4. carry out the epicycloidal correction of point gearing by line of contact

The line of contact of above-mentioned molded line as shown in Figure 7, do not close by Fig. 7 line of contact, is unfavorable for the gastight type of vacuum pump like this.Take up an official post at point gearing epicycloid and get a bit, and ask for the point gearing cycloid of its correspondence, after negative and positive two rotor operates equally, the engagement line chart shown in Fig. 8 can be obtained.

By changing the position of this adjusting point, engaging on epicycloidal path at initial point and being shifted to root circle, just can change the degree of closure of line of contact, finally reach closing of line of contact.As shown in Figure 4, molded line as shown in Figure 1 for the line of contact finally obtained.

Claims (6)

1. a Twin-screw vacuum pump molded lines of rotor, it is characterized in that: conjugation envelope and the tooth top circular arc of the point gearing cycloid that this Twin-screw vacuum pump molded lines of rotor is connected successively by head and the tail, point gearing epicycloid, tooth root circular arc, class Archimedes spiral, class Archimedes spiral form, and the molded line of female rotor is identical with the molded line of male rotor;

The right angled coordinates parametric equation of described class Archimedes spiral is:

$\left\{\begin{array}{c}{x}_{\mathrm{de}}=-(\mathrm{\α}\×f\left(t\right)+\mathrm{\β})\×\sin \left(t\right)\\ y_{\mathrm{de}}=(\mathrm{\α}\×f\left(t\right)+\mathrm{\β})\×\cos \left(t\right)\end{array}\right.$

X in equation _dethe X-coordinate of representation class Archimedes spiral, y _dethe Y-coordinate of representation class Archimedes spiral, f (t) represents the function replacing angle parameter in Archimedes spiral, t denotation coordination parameter, polar coordinate system parametric equation ρ (t)=α × f (the t)+β of class Archimedes spiral meets t _d, t _fthe initial sum end of a period angle of representation class Archimedes spiral and conjugation envelope thereof respectively, and ρ (t _d)=d/2, ρ (t _f)=D/2, d represents root diameter, and D represents tip diameter, can solve constant α thus, β;

The conjugation envelope of described class Archimedes spiral is determined by following right angled coordinates parametric equation:

$\left\{\begin{array}{c}{x}_{\mathrm{ef}}=X_2\×\cos \mathrm{\θ}-Y_2\×\sin \mathrm{\θ}\\ y_{\mathrm{ef}}=X_2\×\sin \mathrm{\θ}+Y_2\×\cos \mathrm{\θ}\end{array}\right.$

θ is the polar angle difference under the conjugate curve starting point of class Archimedes spiral terminal and class Archimedes spiral is converted into polar coordinates; x _efthe X-coordinate of the conjugation envelope of representation class Archimedes spiral, y _efthe Y-coordinate of the conjugation envelope of representation class Archimedes spiral;

Wherein k=i+1, i represent velocity ratio, are taken as 1, represent molded lines of rotor location parameter, A represents the centre distance of negative and positive two rotor, being determined by rotation direction during yin, yang two working rotor, male rotor dextrorotation to Shi Qu –, otherwise is+.

2. a kind of Twin-screw vacuum pump molded lines of rotor according to claim 1, is characterized in that: described point gearing cycloid and the epicycloidal length of point gearing are determined by the line of contact of molded line and Line of contact, need ensure the line of contact of molded line close and Line of contact continuous.

3. a kind of Twin-screw vacuum pump molded lines of rotor according to claim 1, is characterized in that: the right angled coordinates parametric equation of described point gearing cycloid is:

$\left\{\begin{array}{c}{x}_{\mathrm{ab}}=A\×\sin (t+t_1)-1/4\×(d+D)\×\sin (2\×t+t_1)\\ y_{\mathrm{ab}}=A\×\cos (t+t_1)-1/4\×(d+D)\×\cos (2\×t+t_1)\end{array}\right.$

The epicycloidal right angled coordinates parametric equation of point gearing is:

$\left\{\begin{array}{c}{x}_{\mathrm{bc}}=-A\×\sin (t+t_2)-1/2\×D\×\sin (2\×t+t_2)\\ y_{\mathrm{bc}}=A\×\cos (t+t_2)-1/2\×D\×\cos (2\×t+t_2)\end{array}\right.$

X in equation _abrepresent the X-coordinate of point gearing cycloid, y _abrepresent the Y-coordinate of point gearing cycloid, x _bcrepresent the epicycloidal X-coordinate of point gearing, y _bcrepresent the epicycloidal Y-coordinate of point gearing, A represents the centre distance of negative and positive two rotor, and d represents root diameter, and D represents tip diameter, t ₁represent the start angle of point gearing cycloid, t ₂represent the epicycloidal start angle of point gearing, t denotation coordination parameter.

4. a kind of Twin-screw vacuum pump molded lines of rotor according to claim 1, it is characterized in that: the joint first derivative of the joint of described class Archimedes spiral and tooth root circular arc and the conjugation envelope of class Archimedes spiral and tooth top circular arc is continuous, is and is smoothly connected.

5. a kind of Twin-screw vacuum pump molded lines of rotor according to claim 1, is characterized in that: the right angled coordinates parametric equation of described tooth root circular arc is:

$\left\{\begin{array}{c}{x}_{\mathrm{cd}}=-d\×\sin \left(t\right)/2\\ y_{\mathrm{cd}}=d\×\cos \left(t\right)/2\end{array}\right.$

The right angled coordinates parametric equation of described tooth top circular arc is:

$\left\{\begin{array}{c}{x}_{\mathrm{fa}}=-D\×\sin \left(t\right)/2\\ y_{\mathrm{fa}}=D\×\cos \left(t\right)/2\end{array}\right.$

X in equation _cdrepresent the X-coordinate of tooth root circular arc, y _cdrepresent the Y-coordinate of tooth root circular arc, x _farepresent the X-coordinate of tooth top circular arc, y _farepresent the Y-coordinate of tooth top circular arc, D represents tip diameter, and d represents root diameter, t denotation coordination parameter.

6. a design method for Twin-screw vacuum pump molded lines of rotor as claimed in claim 1, is characterized in that: comprise the following steps:

1) the radial molded line that radial cuts obtains Twin-screw vacuum pump flute profile is carried out to trapezoidal rotor, in male rotor molded line, fa section is tooth top circular arc, and ac section is Archimedes spiral, cd section is tooth root circular arc, df section is Archimedes spiral, and the molded line of female rotor is identical with male rotor, in female rotor molded line, f'a' section is tooth top circular arc, a'c' section is Archimedes spiral, and c'd' section is tooth root circular arc, and d'f' section is Archimedes spiral;

2) the ac section Archimedes spiral of male rotor is substituted with the point gearing epicycloid of female rotor a' point;

3) df section Archimedes spiral is replaced with the class Archimedes spiral that equation under the coordinate of footpath, pole is ρ=α × f (t)+β, f (t) represents and replaces the function of former Archimedes spiral angle parameter, and this function meets in two end points places and tooth top circular arc and root circle arc smooth transition;

4) be two sections by class Archimedes spiral in the punishment of e point, and retain wherein one section, suppose to remain de section, ask for the conjugate curve e'f' of de section, the contact points that wherein e point is corresponding is the contact points that e', d point is corresponding is f', e'f' and de section is connected by rotating translation;

5) on point gearing epicycloid, get the intersection point with pitch circle, and ask for point gearing cycloid corresponding to this intersection point.