CN105485014B - A kind of screw rotor of uniform pitch Varied pole piece - Google Patents

Abstract

The invention discloses a kind of screw rotor of uniform pitch Varied pole piece, belong to dry type Twin-screw vacuum pump field；From the low pressure end face I I of screw rotor to high pressure end face VI VI, the pitch (P of screw rotor₁、P₂、P₃、P₄) keep constant, and the facewidth of screw rotor, including topland width (M₁、M₂、M₃) and bottom width (N₁、N₂、N₃) but gradually increase；In any axial positions, the axial cross section molded line of screw rotor all includes 5 sections of curves, is followed successively by：Circle involute AB, addendum circle arc BC, cycloid CD, tooth root circular arc DE, cycloid EA, wherein tooth root circular arc DE, circle involute AB are smoothly connected with cycloid EA；The screw rotor for being proposed increased operating on low voltage chamber volume, reduce high-pressure working chamber volume, increased interior volume specific ratio, reduce spiro rod length, with higher-strength and good sealing property, improve the final vacuum and pumping speed of Twin-screw vacuum pump.

Description

A kind of screw rotor of uniform pitch Varied pole piece

Technical field

The present invention relates to dry type Twin-screw vacuum pump, more particularly to suitable for a kind of uniform pitch of dry type Twin-screw vacuum pump The screw rotor of Varied pole piece.

Background technology

Dry type Twin-screw vacuum pump is a kind of positive-displacement vacuum pump, is by 2 screw rotors that can realize engagement Synchronous incorgruous dual AC power motion, forms multiple periodically variable working chamber volumes between 2 screw rotors and pump housing inner chamber, Suction, supercharging and the discharge of gas are realized, vacuum is formed at the import of pump；Working chamber is by 2 intermeshing screw rods Formed between rotor and pump housing inner chamber, the sealing between each working chamber is realized by the engagement between 2 screw rotors , therefore screw rotor is the most key parts, the sealing property of screw rotor, efficiency, area utilization factor, direct shadow Ring appearance and size, pumping speed and the final vacuum of Twin-screw vacuum pump.

Screw rotor is to make axial screw along circular helix by the axial cross section molded line of screw rotor to launch generation；Often Screw rotor is the screw rotor of the facewidth such as uniform pitch, is characterized in the low pressure end face from screw rotor to high pressure end face, The pitch of screw rotor is constant, the facewidth of screw rotor, including topland width and tooth bottom width are also constant；By The working chamber volume that the screw rotor of the facewidth such as uniform pitch is formed is constant, and interior volume specific ratio is equal to 1, i.e. high-pressure working chamber to be held Product is equal to operating on low voltage chamber volume；Gas in the facewidth size influence high and low pressure working chamber of screw rotor by crest top land and The leakage in bottom of the tooth face, while influenceing the intensity of screw rotor, rigidity and axial dimension.

In the working chamber that screw rotor is formed, because gas pressure is relatively low in the working chamber at low pressure end face I-I, And gas pressure is higher in the working chamber at the place of high pressure end face VI-VI；According to this feature, the work that the screw rotor of optimization is formed Making the Changing Pattern of chamber volume and the facewidth should be：High-pressure working chamber volume is smaller, and operating on low voltage chamber volume is larger；High pressure work The screw rod facewidth made at chamber is larger, and the screw rod facewidth at operating on low voltage chamber is smaller.

The content of the invention

The present invention proposes a kind of screw rotor of uniform pitch Varied pole piece, from the low pressure end face I-I of screw rotor to high pressure End face VI-VI, the pitch (P of screw rotor₁、P₂、P₃、P₄) keep constant, and the facewidth of screw rotor, including topland width (M₁、M₂、M₃) and bottom width (N₁、N₂、N₃) but gradually increase；Thus the working chamber that screw rotor is formed, its high pressure work Make chamber volume smaller, and operating on low voltage chamber volume is larger, the facewidth of screw rotor is larger at high-pressure working chamber, in operating on low voltage The facewidth of screw rotor is smaller at chamber.

The present invention proposes a kind of Twin-screw vacuum pump, it is characterized in that：Use uniform pitch Varied pole piece proposed by the invention Screw rotor.

The present invention proposes a kind of double-screw compressor, it is characterized in that：Use uniform pitch Varied pole piece proposed by the invention Screw rotor.

The present invention proposes a kind of twin-screw expander, it is characterized in that：Use uniform pitch Varied pole piece proposed by the invention Screw rotor.

To achieve these goals, the present invention is adopted the following technical scheme that：

Determine axial cross section molded line of the screw rotor at axially different position, that is, determine the curve of axial cross section molded line Cluster；The axial cross section molded line of screw rotor refers to the plane with screw rotor axis perpendicular with one, in different axial positions The place of putting goes to cut screw rotor, the contour curve for being intercepted.

The screw rotor of uniform pitch Varied pole piece proposed by the invention, at axially different position, the axial direction of screw rotor Section molded line is different from, but the type of its constituent curve is identical；In any axial positions, the axial cross section type of screw rotor Line all includes 5 sections of curves and 2 points, is followed successively by：Circle involute AB, point B, addendum circle arc BC, point C, cycloid CD, tooth root circular arc DE, cycloid EA, wherein tooth root circular arc DE, circle involute AB are smoothly connected with cycloid EA, and addendum circle arc BC central angle ∠ The central angle ∠ DOE of BOC and tooth root circular arc DE are equal, as central angle θ；In different axial positions, the axle of screw rotor It is different to section molded line, is changed with the difference of place axial location, from the low pressure end face I-I of screw rotor to high-pressure side Face VI-VI, the axial cross section molded line of screw rotor is with the Changing Pattern of axial location：The base radius R of circle involute AB_bBy Cumulative big, the generation angle α of circle involute AB is gradually reduced, and the central angle θ of addendum circle arc BC and tooth root circular arc DE gradually increases.

Twin-screw vacuum pump includes intermeshing two screw rotors, i.e. left-hand screw rotor (301) and right handed screw Rotor (302)；Left-handed, dextrorotation regulation is：Left-handed is that rotation direction meets lefft-hand rule, and the direction indication of left hand thumb is from spiral shell The low pressure end face I-I of bar rotor arrives the axial movement direction of high pressure end face VI-VI, i.e. circular helix, remaining four direction for referring to It is the rotation direction of circular helix；Dextrorotation is that rotation direction meets right-hand rule, and the direction indication of right hand thumb is to turn from screw rod To the axial movement direction of high pressure end face VI-VI, i.e. circular helix, remaining four direction for referring to is round to the low pressure end face I-I of son The rotation direction of post helix.

Intermeshing 2 screw rotors：Left-hand screw rotor (301) and right-hand screw rotor (302), all including 5 The flank of tooth and 2 circular helixes, the composition flank of tooth and circular helix of right-hand screw rotor (302) are followed successively by：The cycloid flank of tooth (1), pitch face (2), circular helix (3), crest top land (4), circular helix (5), concave tooth face (6), root face (7), and tiltedly The flank of tooth (2), root face (7) are all smoothly connected with the cycloid flank of tooth (1)；The composition flank of tooth and cylinder spiral shell of left-hand screw rotor (301) Spin line is followed successively by：The cycloid flank of tooth (1 ＇), pitch face (2 ＇), circular helix (3 ＇), crest top land (4 ＇), circular helix (5 ＇), Concave tooth face (6 ＇), root face (7 ＇), and pitch face (2 ＇), root face (7 ＇) be all smoothly connected with the cycloid flank of tooth (1 ＇)；In synchronization In the course of work of incorgruous dual AC power motion, the cycloid flank of tooth (1) of right-hand screw rotor (302), pitch face (2), cylindrical screw Line (3), crest top land (4), circular helix (5), concave tooth face (6), root face (7), respectively with the circle of left-hand screw rotor (301) Post helix (3 ＇), pitch face (2 ＇), the cycloid flank of tooth (1 ＇), root face (7 ＇), concave tooth face (6 ＇), circular helix (5 ＇), tooth Top surface (4 ＇) can realize correct engagement；In any axial positions, left-hand screw rotor (301) and right-hand screw rotor (302) axial cross section molded line is identical, and circle involute AB in the axial cross section molded line (201) of left-hand screw rotor (301), Point B, addendum circle arc BC, point C, cycloid CD, tooth root circular arc DE and cycloid EA, respectively with the axial direction section of right-hand screw rotor (302) Circle involute ba, cycloid ae, tooth root circular arc ed in face molded line (202), cycloid dc, point c, addendum circle arc cb, point b can be realized Correct engagement.

Left-hand screw rotor (301) is justified along left-handed uniform pitch by a series of axial cross section molded line (201) of screw rotors Post helix makees spiral and launches and generate；Right-hand screw rotor (302) is by a series of axial cross section molded line of screw rotors (202) make spiral expansion along dextrorotation uniform pitch circular helix and generate；Left-handed uniform pitch circular helix and dextrorotation uniform pitch The rotation direction of circular helix is different；

The equation of left-handed uniform pitch circular helix is：

The equation of dextrorotation uniform pitch circular helix is：

In formula：τ is the spiral angle of spread, rad；R is helix base radius, mm；N is spiral number of turns, n >=2；P is screw rod The pitch of rotor, mm.

In any axial positions, the axial cross section molded line of screw rotor all includes 5 sections of curves：Circle involute AB, tooth top Circular arc BC, cycloid CD, tooth root circular arc DE, cycloid EA；In different axial locations, that is, correspond to different spiral angle of spread τ, each song The set of curves equation of line is as follows：

1. the set of curves equation of circle involute AB is：

In formula：T is angle parameter, rad；R_b(τ) is the base radius of circle involute AB at axially different position；α (τ) is The generation angle of circle involute AB at axially different position；R_b(τ) and α (τ) are determined by equation below：

In formula：K is coefficient；R_bs、R_beRespectively the axial direction of the screw rotor of low pressure end face I-I and high pressure end face VI-VI is cut The base radius of the circle involute AB in the molded line of face, mm；

2. the set of curves equation of addendum circle arc BC is：

In formula：R₁It is addendum circle arc radius, mm；

3. the set of curves equation of cycloid CD is：

In formula：R₂It is pitch radius, mm；

4. the set of curves equation of tooth root circular arc DE is：

In formula：R₃It is fillet radius, mm；

5. the set of curves equation of cycloid EA is：

In formula：θ (τ) is the central angle of addendum circle arc BC and tooth root circular arc DE at axially different position, true by equation below It is fixed：

Beneficial effects of the present invention are：

The screw rotor of a kind of uniform pitch Varied pole piece for being proposed, from the low pressure end face I-I of screw rotor to high pressure end face VI-VI, the pitch (P of screw rotor₁、P₂、P₃、P₄) keep constant, and the facewidth of screw rotor, including topland width (M₁、 M₂、M₃) and bottom width (N₁、N₂、N₃) but gradually increase；The low pressure end face I-I of screw rotor can be used as Twin-screw vacuum pump Suction end, high pressure end face VI-VI can be used as the exhaust end of Twin-screw vacuum pump；Thereby increase aspirated volume, the row of reducing Air space, interior volume specific ratio is increased, realize Changing Pattern of the working chamber volume from suction end to exhaust end with gas in working chamber The Changing Pattern of body pressurization is consistent, i.e., suction muffler volume is big, and discharge chamber volume is small；Simultaneously the exhaust end screw rod facewidth compared with Greatly, it is smaller in the suction end screw rod facewidth, reduce the gas between each working chamber by crest top land and leak, realize screw rotor Changing Pattern of the facewidth from suction end to exhaust end it is consistent with the Changing Pattern of gas pressure in working chamber；Therefore the screw rod Rotor has the advantages that compact conformation, intensity are high, rigidity is high, good seal performance, improves the end vacuum of Twin-screw vacuum pump Degree and pumping speed.

Compared with the screw rotor of the facewidth such as existing uniform pitch, a kind of screw rotor of the uniform pitch Varied pole piece for being proposed Have the following advantages that：1. larger operating on low voltage chamber volume, less high-pressure working chamber volume can be formed, therefore with larger Content ratio, be conducive to improve vavuum pump final vacuum and pumping speed；2. at pressure working chamber higher, screw rotor The facewidth is larger, with blocking capability is leaked between stronger level, can make leakage of the reduction gas between each working chamber；3. it is strong Degree is high, rigidity is high.

Brief description of the drawings

Fig. 1 is the axial cross section molded lines of uniform pitch Varied pole piece screw rotor.

Fig. 2 is the engagement figure between intermeshing 2 screw rotors axial cross section molded line.

Fig. 3 is the screw rotor figure of uniform pitch Varied pole piece.

Fig. 4 is 2 engagement figures of the screw rotor of uniform pitch Varied pole piece.

In figure：R₁- radius of addendum；R₂- pitch radius；R₃- root radius；R_bThe basic circle of-circle involute half Footpath；The generation angle of α-circle involute；The central angle of θ-addendum circle arc BC and tooth root circular arc DE；201st, 202-screw rotor axle To section molded line；301-left-hand screw rotor；302-right-hand screw rotor；1st, 1 ＇-cycloid flank of tooth；2nd, 2 ＇-pitch face；3、 3 ＇, 5,5 ＇-circular helix；4th, 4 ＇-crest top land；6th, 6 ＇-concave tooth face；7th, 7 ＇-root face；P₁、P₂、P₃、P₄- screw rod turns The pitch of son；M₁、M₂、M₃The topland width of-screw rotor；N₁、N₂、N₃The bottom width of-screw rotor.

Specific embodiment

The invention will be further described with embodiment below in conjunction with the accompanying drawings.

As shown in figure 1, be the axial cross section molded lines of uniform pitch Varied pole piece screw rotor, in any axial positions, spiral shell The axial cross section molded line of bar rotor all includes 5 sections of curves and 2 points, is followed successively by：Circle involute AB, point B, addendum circle arc BC, point C, cycloid CD, tooth root circular arc DE, cycloid EA；Wherein tooth root circular arc DE, circle involute AB are smoothly connected with cycloid EA, and tooth top The central angle ∠ DOE of the central angle ∠ BOC and tooth root circular arc DE of circular arc BC are equal, as central angle θ.

As shown in Fig. 2 be the engagement figure between intermeshing 2 screw rotors axial cross section molded line, in same axial direction At position, left-hand screw rotor (301) is identical with the axial cross section molded line of right-hand screw rotor (302), and left-hand screw rotor (301) the circle involute AB in axial cross section molded line (201), point B, addendum circle arc BC, point C, cycloid CD, tooth root circular arc DE and Cycloid EA, respectively with the axial cross section molded line (202) of right-hand screw rotor (302) in circle involute ba, cycloid ae, root circle Arc ed, cycloid dc, point c, addendum circle arc cb, point b can realize correct engagement.

As shown in figure 3, being the screw rotor figure of uniform pitch Varied pole piece, Twin-screw vacuum pump includes 2 screw rotors：It is left-handed Screw rotor (301) and right-hand screw rotor (302)；Left-hand screw rotor (301) is cut by a series of axial direction of screw rotors Face molded line (201) is made spiral expansion and is generated along left-handed uniform pitch circular helix；Right-hand screw rotor (302) is by a series of The axial cross section molded line (202) of screw rotor is made spiral expansion and is generated along dextrorotation uniform pitch circular helix；Left-handed uniform pitch Circular helix is different from the rotation direction of dextrorotation uniform pitch circular helix.

As shown in figure 4, being 2 engagement figures of the screw rotor of uniform pitch Varied pole piece, intermeshing 2 screw rotors： Left-hand screw rotor (301) and right-hand screw rotor (302), all including 5 flank of tooth and 2 circular helixes, right handed screw turns The composition flank of tooth and circular helix of sub (302) are followed successively by：The cycloid flank of tooth (1), pitch face (2), circular helix (3), tooth top Face (4), circular helix (5), concave tooth face (6), root face (7), and pitch face (2), root face (7) all with the cycloid flank of tooth (1) It is smoothly connected；The composition flank of tooth and circular helix of left-hand screw rotor (301) are followed successively by：The cycloid flank of tooth (1 ＇), pitch face (2 ＇), circular helix (3 ＇), crest top land (4 ＇), circular helix (5 ＇), concave tooth face (6 ＇), root face (7 ＇), and pitch face (2 ＇), root face (7 ＇) are all smoothly connected with the cycloid flank of tooth (1 ＇)；In the course of work of synchronous incorgruous dual AC power motion, dextrorotation It is the cycloid flank of tooth (1) of screw rotor (302), pitch face (2), circular helix (3), crest top land (4), circular helix (5), recessed The flank of tooth (6), root face (7), circular helix (3 ＇) respectively with left-hand screw rotor (301), pitch face (2 ＇), the cycloid flank of tooth (1 ＇), root face (7 ＇), concave tooth face (6 ＇), circular helix (5 ＇), crest top land (4 ＇) can realize correct engagement；Any The axial cross section molded line of axial positions, left-hand screw rotor (301) and right-hand screw rotor (302) is all identical.

The spiral number of turns of intermeshing 2 screw rotors, left-hand screw rotor (301) and right-hand screw rotor (302) Both greater than 2.

As shown in figure 4, be 2 engagement figures of the screw rotor of uniform pitch Varied pole piece, the pitch of screw rotor is from low-pressure end Face I-I keeps constant, i.e. P to high pressure end face VI-VI₁=P₂=P₃=P₄, but crest top land and root face width from low pressure end face I-I gradually increases to high pressure end face VI-VI, i.e. M₁＜ M₂＜ M₃、N₁＜ N₂＜ N₃；Sectional view I-I, II-II, III-III, IV-IV, V-V, VI-VI, when being that spiral angle of spread τ is respectively 0,2 π, 3 π, 4 π, 6 π, 8 π, the axial cross section molded line of screw rotor is nibbled Close figure；In any axial positions, the axial cross section molded line of screw rotor all includes 5 sections of curves：Circle involute AB, addendum circle arc BC, cycloid CD, tooth root circular arc DE, cycloid EA；Low pressure end face I-I from screw rotor to high pressure end face VI-VI, screw rotor Axial cross section molded line is with the Changing Pattern of axial location：The base radius R of circle involute AB_bGradually increase, circle involute AB Generation angle α be gradually reduced, the central angle θ of addendum circle arc BC and tooth root circular arc DE gradually increases.Thus screw rotor is formed Working chamber, its high-pressure working chamber volume is smaller, and operating on low voltage chamber volume is larger, the tooth of screw rotor at high-pressure working chamber Wide larger, the facewidth of screw rotor is smaller at operating on low voltage chamber.

Although above-mentioned be described with reference to accompanying drawing to specific embodiment of the invention, not to present invention protection model The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not Need the various modifications made by paying creative work or deformation still within protection scope of the present invention.

Claims (7)

1. a kind of screw rotor of uniform pitch Varied pole piece, it is characterized in that：From the low pressure end face I-I of screw rotor to high pressure end face VI-VI, the pitch (P of screw rotor₁、P₂、P₃、P₄) keep constant, and the facewidth of screw rotor, including topland width (M₁、 M₂、M₃) and bottom width (N₁、N₂、N₃) but gradually increase；Thus the working chamber that screw rotor is formed, its high-pressure working chamber Volume is smaller, and operating on low voltage chamber volume is larger, and the facewidth of screw rotor is larger at high-pressure working chamber, at operating on low voltage chamber The facewidth of screw rotor is smaller.

2. a kind of screw rotor of uniform pitch Varied pole piece as claimed in claim 1, it is characterized in that：In any axial positions, The axial cross section molded line of screw rotor all includes 5 sections of curves and 2 points, is followed successively by：Circle involute AB, point B, addendum circle arc BC, Point C, cycloid CD, tooth root circular arc DE, cycloid EA, wherein tooth root circular arc DE, circle involute AB are smoothly connected with cycloid EA, and tooth The central angle ∠ DOE of the central angle ∠ BOC and tooth root circular arc DE of tip circle arc BC are equal, as central angle θ；In different axial positions Place is put, the axial cross section molded line of screw rotor is different from, and changed with the difference of place axial location, from screw rotor Low pressure end face I-I arrives high pressure end face VI-VI, and the axial cross section molded line of screw rotor is with the Changing Pattern of axial location：Circle is gradually Burst at the seams the base radius R of AB_bGradually increase, the generation angle α of circle involute AB is gradually reduced, addendum circle arc BC and tooth root circular arc DE Central angle θ gradually increase.

3. a kind of screw rotor of uniform pitch Varied pole piece as claimed in claim 1, it is characterized in that：Screw rotor includes 5 teeth Face and 2 circular helixes, are followed successively by：The cycloid flank of tooth (1), pitch face (2), circular helix (3), crest top land (4), cylinder Helix (5), concave tooth face (6), root face (7), and pitch face (2), root face (7) be all smoothly connected with the cycloid flank of tooth (1)； In the course of work of synchronous incorgruous dual AC power motion, the cycloid flank of tooth (1) of right-hand screw rotor (302), pitch face (2), cylinder Helix (3), crest top land (4), circular helix (5), concave tooth face (6), root face (7), respectively with left-hand screw rotor (301) Circular helix (3 ＇), pitch face (2 ＇), the cycloid flank of tooth (1 ＇), root face (7 ＇), concave tooth face (6 ＇), circular helix (5 ＇), crest top land (4 ＇) can realize correct engagement；In any axial positions, left-hand screw rotor (301) and dextrorotation spiral shell The axial cross section molded line of bar rotor (302) is identical, and the circle in the axial cross section molded line (201) of left-hand screw rotor (301) is gradually opened Line AB, point B, addendum circle arc BC, point C, cycloid CD, tooth root circular arc DE and cycloid EA, respectively with the axle of right-hand screw rotor (302) To the circle involute ba in section molded line (202), cycloid ae, tooth root circular arc ed, cycloid dc, point c, addendum circle arc cb, point b can Realize correct engagement.

4. as described in claim 1 a kind of screw rotor of uniform pitch Varied pole piece, left-hand screw rotor (301) is to be by one The axial cross section molded line (201) of row screw rotor is made spiral expansion and is generated along left-handed uniform pitch circular helix；Right handed screw Rotor (302) is to make spiral exhibition along dextrorotation uniform pitch circular helix by a series of axial cross section molded line (202) of screw rotors Open and generate；Left-handed uniform pitch circular helix is different from the rotation direction of dextrorotation uniform pitch circular helix；Left-handed uniform pitch cylinder The equation of helix is：

$\left\{\begin{array}{c}x\left(\mathrm{\τ}\right)=Rcos\left(\mathrm{\τ}\right)\\ y\left(\mathrm{\τ}\right)=-Rsin\left(\mathrm{\τ}\right),\mathrm{\τ}\∈\[0,2n\mathrm{\π}\]\\ z\left(\mathrm{\τ}\right)=\frac{P}{2\mathrm{\π}}\mathrm{\τ}\end{array}\right.$

The equation of dextrorotation uniform pitch circular helix is：

$\left\{\begin{array}{c}x\left(\mathrm{\τ}\right)=Rcos\left(\mathrm{\τ}\right)\\ y\left(\mathrm{\τ}\right)=Rsin\left(\mathrm{\τ}\right),\mathrm{\τ}\∈\[0,2n\mathrm{\π}\]\\ z\left(\mathrm{\τ}\right)=\frac{P}{2\mathrm{\π}}\mathrm{\τ}\end{array}\right.$

In formula：τ is the spiral angle of spread, rad；R is helix base radius, mm；N is spiral number of turns, n >=2；P is screw rotor Pitch, mm；

In any axial positions, the axial cross section molded line of screw rotor all includes 5 sections of curves：Circle involute AB, addendum circle arc BC, cycloid CD, tooth root circular arc DE, cycloid EA；In different axial locations, that is, different spiral angle of spread τ are corresponded to, each curve Set of curves equation is as follows：

1. the set of curves equation of circle involute AB is：

$\left\{\begin{array}{c}x(t,\mathrm{\τ})=R_b\left(\mathrm{\τ}\right)(cos\left(t-\mathrm{\α}\left(\mathrm{\τ}\right)\right)+tsin\left(t-\mathrm{\α}\left(\mathrm{\τ}\right)\right))\\ y(t,\mathrm{\τ})=R_b\left(\mathrm{\τ}\right)(sin\left(t-\mathrm{\α}\left(\mathrm{\τ}\right)\right)-tcos\left(t-\mathrm{\α}\left(\mathrm{\τ}\right)\right))\end{array}\right.$

In formula：T is angle parameter, rad；R_b(τ) is the base radius of circle involute AB at axially different position；α (τ) is difference The generation angle of axial positions circle involute AB；R_b(τ) and α (τ) are determined by equation below：

$R_b\left(\mathrm{\τ}\right)=\frac{R_{be}-R_{bs}}{e^{2n\mathrm{\π}k}-1}(e^{k\mathrm{\τ}}-1)+R_{bs}$

$\mathrm{\α}\left(\mathrm{\τ}\right)=tan\left(\arccos \right(\frac{R_b\left(\mathrm{\τ}\right)}{R_2}\left)\right)-\arccos \left(\frac{R_b\left(\mathrm{\τ}\right)}{R_2}\right)$

In formula：K is coefficient；R_bs、R_beThe respectively screw rotor axial cross section molded line of low pressure end face I-I and high pressure end face VI-VI In circle involute AB base radius, mm；

2. the set of curves equation of addendum circle arc BC is：

$\left\{\begin{array}{c}x\left(t\right)=R_1\cos t\\ y\left(t\right)=R_1\sin t\end{array}\right.$

In formula：R₁It is addendum circle arc radius, mm；

3. the set of curves equation of cycloid CD is：

$\left\{\begin{array}{c}x\left(t\right)=2R_2\cos t+R_{1}cos2t\\ y\left(t\right)=2R_2\sin t+R_{1}sin2t\end{array}\right.$

In formula：R₂It is pitch radius, mm；

4. the set of curves equation of tooth root circular arc DE is：

$\left\{\begin{array}{c}x\left(t\right)=R_3\cos t\\ y\left(t\right)=R_3\sin t\end{array}\right.$

In formula：R₃It is fillet radius, mm；

5. the set of curves equation of cycloid EA is：

$\left\{\begin{array}{c}x(t,\mathrm{\τ})=2R_{2}cos(t+\mathrm{\θ}\left(\mathrm{\τ}\right))+R_1\cos (2t+\mathrm{\θ}\left(\mathrm{\τ}\right))\\ y(t,\mathrm{\τ})=2R_2\sin (t+\mathrm{\θ}\left(\mathrm{\τ}\right))+R_1\sin (2t+\mathrm{\θ}\left(\mathrm{\τ}\right))\end{array}\right.$

In formula：θ (τ) is the central angle of addendum circle arc BC and tooth root circular arc DE at axially different position, is determined by equation below：

$\mathrm{\θ}\left(\mathrm{\τ}\right)=\mathrm{\π}+\mathrm{\α}\left(\mathrm{\τ}\right)-\[tan\left(\arccos \right(\frac{R_b\left(\mathrm{\τ}\right)}{R_1}\left)\right)-\arccos \left(\frac{R_b\left(\mathrm{\τ}\right)}{R_1}\right)\]$

5. a kind of Twin-screw vacuum pump, it is characterized in that：Use the screw rotor of uniform pitch Varied pole piece as claimed in claim 1.

6. a kind of double-screw compressor, it is characterized in that：Use the screw rotor of uniform pitch Varied pole piece as claimed in claim 1.

7. a kind of twin-screw expander, it is characterized in that：Use the screw rotor of uniform pitch Varied pole piece as claimed in claim 1.