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

Abstract

The invention discloses a screw rotor with equal pitch and variable tooth width, which belongs to the field of dry twin _- screw vacuum pumps _; P ₃ , P ₄ ) remain unchanged, while the tooth width of the screw rotor, including the tooth top width (M ₁ , M ₂ , M ₃ ) and tooth root width (N ₁ , N ₂ , N ₃ ) gradually increases Large; at any axial position, the axial section profile of the screw rotor includes 5 curves, which are: circular involute AB, addendum arc BC, cycloid CD, dedendum arc DE, cycloid EA, in which the dedendum arc DE and the circular involute AB are smoothly connected with the cycloid EA; the proposed screw rotor increases the volume of the low-pressure working chamber, reduces the volume of the high-pressure working chamber, increases the internal volume ratio, reduces The length of the screw is increased, with high strength and good sealing performance, which improves the ultimate vacuum and pumping speed of the twin-screw vacuum pump.

Description

A screw rotor with equal pitch and variable tooth width

technical field

The invention relates to a dry twin-screw vacuum pump, in particular to a screw rotor with equal pitch and variable tooth width suitable for the dry twin-screw vacuum pump.

Background technique

The dry twin-screw vacuum pump is a positive displacement vacuum pump, which forms multiple periodically changing working chambers between the two screw rotors and the inner cavity of the pump through the synchronous counter-rotating double-rotation motion of two screw rotors that can be meshed. Volume, realize the suction, pressurization and discharge of gas, and form a vacuum at the inlet of the pump; the working chamber is formed between two intermeshing screw rotors and the inner cavity of the pump, and the seal between each working chamber is through 2 The meshing between two screw rotors is realized, so the screw rotor is the most critical component. The sealing performance, efficiency and area utilization coefficient of the screw rotor directly affect the overall size, pumping speed and ultimate vacuum degree of the twin-screw vacuum pump.

The screw rotor is generated by the axial cross-sectional profile of the screw rotor along the cylindrical helix for axial helical expansion; the commonly used screw rotor is a screw rotor with equal pitch and equal tooth width. , the pitch of the screw rotor is constant, and the tooth width of the screw rotor, including the width of the tooth top surface and the width of the tooth bottom surface, is also constant; the volume of the working chamber formed by the screw rotor with equal pitch and equal tooth width is constant. The internal volume ratio is equal to 1, that is, the volume of the high-pressure working chamber is equal to the volume of the low-pressure working chamber; the tooth width of the screw rotor affects the leakage of gas in the high-pressure and low-pressure working chambers through the top and bottom surfaces of the teeth, and at the same time affects the strength and stiffness of the screw rotor and axial dimensions.

In the working chamber formed by the screw rotor, the gas pressure in the working chamber at the low-pressure end surface I-I is low, while the gas pressure in the working chamber at the high-pressure end surface VI-VI is relatively high; according to this characteristic, the optimized The volume of the working chamber formed by the screw rotor and the change rule of the tooth width should be: the volume of the high-pressure working chamber is small, and the volume of the low-pressure working chamber is large; the screw tooth width at the high-pressure working chamber is large, and the screw tooth at the low-pressure working chamber The width is smaller.

Contents of the invention

The present invention proposes a screw rotor with equal pitch and variable tooth width. From the low-pressure end surface I-I of the screw rotor to the high-pressure end surface VI-VI, the pitches (P ₁ , P ₂ , P ₃ , P ₄ ) of the screw rotor remain constant. However, the tooth width of the screw rotor, including the tooth top width (M ₁ , M ₂ , M ₃ ) and the dedendum width (N ₁ , N ₂ , N ₃ ), increases gradually; thus the screw rotor forms The high-pressure working chamber has a small volume, while the low-pressure working chamber has a large volume. The tooth width of the screw rotor at the high-pressure working chamber is large, and the tooth width of the screw rotor at the low-pressure working chamber is small.

The invention proposes a twin-screw vacuum pump, which is characterized in that: the screw rotor with equal pitch and variable tooth width proposed by the invention is used.

The present invention proposes a twin-screw compressor, which is characterized in that: the screw rotor with equal pitch and variable tooth width proposed by the present invention is used.

The present invention proposes a twin-screw expander, which is characterized in that: the screw rotor with equal pitch and variable tooth width proposed by the present invention is used.

In order to achieve the above object, the present invention adopts the following technical solutions:

Determine the axial section profile line of the screw rotor at different axial positions, that is, determine the curve cluster of the axial section profile line; the axial section profile line of the screw rotor refers to a plane perpendicular to the axis of the screw rotor, in different The contour curve obtained by cutting the screw rotor at the axial position.

In the screw rotor with equal pitch and variable tooth width proposed by the present invention, the axial section profiles of the screw rotor are different at different axial positions, but the types of the composition curves are the same; at any axial position, the screw rotor The axial cross-section profile includes 5 curves and 2 points, which are: circular involute AB, point B, addendum arc BC, point C, cycloid CD, dedendum arc DE, cycloid EA , where the dedendum arc DE and the circular involute AB are smoothly connected with the cycloid EA, and the central angle ∠BOC of the dedendum arc BC is equal to the central angle ∠DOE of the dedendum arc DE, which is the central angle θ ; At different axial positions, the axial cross-sectional profile of the screw rotor is different, and varies with the axial position. From the low-pressure end surface Ⅰ-I of the screw rotor to the high-pressure end surface VI-VI, the screw rotor The changing law of the axial section shape line with the axial position is: the radius R _b of the base circle of the circular involute AB gradually increases, the occurrence angle α of the circular involute AB gradually decreases, the addendum arc BC and the dedendum The central angle θ of the arc DE gradually increases.

The twin-screw vacuum pump includes two screw rotors meshing with each other, that is, a left-handed screw rotor (301) and a right-handed screw rotor (302); From the low-pressure end surface Ⅰ-Ⅰ of the screw rotor to the high-pressure end surface Ⅵ-Ⅵ, that is, the axial movement direction of the cylindrical helix, the direction of the other four fingers is the rotation direction of the cylindrical helix; The indication direction of the thumb is from the low-pressure end surface I-I of the screw rotor to the high-pressure end surface VI-VI, that is, the axial movement direction of the cylindrical helix, and the direction of the other four fingers is the rotation direction of the cylindrical helix.

Two screw rotors meshing with each other: a left-handed screw rotor (301) and a right-handed screw rotor (302), both including 5 tooth surfaces and 2 cylindrical helical lines, and a right-handed screw rotor (302) consists of a tooth surface and a cylindrical The helixes are: cycloid tooth surface (1), helical tooth surface (2), cylindrical helix (3), tooth top surface (4), cylindrical helix (5), concave tooth surface (6), dedendum surface (7), and the helical tooth surface (2) and the tooth root surface (7) are smoothly connected with the cycloidal tooth surface (1); the left-handed screw rotor (301) consists of the tooth surface and the cylindrical helix in turn: cycloidal Tooth surface (1'), helical tooth surface (2'), cylindrical helix (3'), tooth top surface (4'), cylindrical helix (5'), concave tooth surface (6'), tooth root surface (7'), and the helical tooth surface (2') and tooth root surface (7') are smoothly connected with the cycloidal tooth surface (1'); (302) cycloid tooth surface (1), helical tooth surface (2), cylindrical helix (3), tooth top surface (4), cylindrical helix (5), concave tooth surface (6), dedendum surface (7), respectively with the cylindrical helix (3'), helical tooth surface (2'), cycloidal tooth surface (1'), dedendum surface (7'), concave tooth surface ( 6'), cylindrical helix (5'), tooth top surface (4') can achieve correct meshing; at any axial position, the axial section of left-handed screw rotor (301) and right-handed screw rotor (302) The profiles are the same, and the circular involute AB, point B, addendum arc BC, point C, cycloid CD, dedendum arc DE and The cycloid EA is respectively connected with the circular involute ba, cycloid ae, dedendum arc ed, cycloid dc, point c, and addendum circle in the axial section profile (202) of the right-handed screw rotor (302). Arc cb, point b enables correct meshing.

The left-handed screw rotor (301) is produced by helically expanding the axial cross-sectional profile (201) of a series of screw rotors along the left-handed cylindrical helix with equal pitch; the right-handed screw rotor (302) is formed by the axial The section profile (202) is generated by helically expanding along a right-handed cylindrical helix with equal pitch; the helical direction of the left-handed cylindrical helix with equal pitch is different from that of the right-handed cylindrical helix with equal pitch;

The equation for a left-handed equi-pitch cylindrical helix is:

The equation for a right-handed equi-pitch cylindrical helix is:

In the formula: τ is the helix expansion angle, rad; R is the radius of the base circle of the helix, mm; n is the number of helix turns, n≥2; P is the pitch of the screw rotor, mm.

At any axial position, the axial section profile of the screw rotor includes 5 curves: circular involute AB, addendum arc BC, cycloid CD, dedendum arc DE, cycloid EA; in different The axial position, that is, corresponding to different helical expansion angles τ, the curve cluster equation of each curve is as follows:

① The curve family equation of circular involute AB is:

In the formula: t is the angle parameter, rad; R _b (τ) is the radius of the base circle of the circular involute AB at different axial positions; α(τ) is the occurrence angle of the circular involute AB at different axial positions; R _b (τ) and α(τ) are determined by the following formulas:

In the formula: k is a coefficient; R _bs and R _be are the base circle radius of the circular involute AB in the axial section profile of the screw rotor on the low-pressure end face Ⅰ-I and the high-pressure end face Ⅵ-Ⅵ respectively, mm;

②The curve cluster equation of addendum arc BC is:

In the formula: R ₁ is the radius of the addendum arc, mm;

③The curve family equation of cycloid CD is:

In the formula: R ₂ is pitch circle radius, mm;

④ The curve cluster equation of the dedendum arc DE is:

In the formula: R ₃ is the root arc radius, mm;

⑤ The curve cluster equation of cycloid EA is:

In the formula: θ(τ) is the central angle of the addendum arc BC and the dedendum arc DE at different axial positions, which is determined by the following formula:

The beneficial effects of the present invention are:

A screw rotor with equal pitch and variable tooth width is proposed. From the low-pressure end surface I-I of the screw rotor to the high-pressure end surface VI-VI, the pitch (P ₁ , P ₂ , P ₃ , P ₄ ) of the screw rotor remains unchanged. , while the tooth width of the screw rotor, including the tooth top width (M ₁ , M ₂ , M ₃ ) and dedendum width (N ₁ , N ₂ , N ₃ ), gradually increases; the low-pressure end surface of the screw rotor Ⅰ- Ⅰ can be used as the suction end of the twin-screw vacuum pump, and the high-pressure end face Ⅵ-Ⅵ can be used as the exhaust end of the twin-screw vacuum pump; thus, the suction volume is increased, the exhaust volume is reduced, and the internal volume ratio is increased. The change law of the chamber volume from the suction end to the exhaust end is consistent with the change law of the gas pressurization process in the working chamber, that is, the volume of the suction chamber is large, and the volume of the exhaust chamber is small; at the same time, the tooth width of the screw at the exhaust end is large, The tooth width of the screw at the suction end is small, which reduces the gas leakage through the tooth top surface between the working chambers, and realizes the change law of the tooth width of the screw rotor from the suction end to the exhaust end and the gas pressure in the working chamber. The change rules are consistent; therefore, the screw rotor has the advantages of compact structure, high strength, high rigidity and good sealing performance, which improves the ultimate vacuum degree and pumping speed of the twin-screw vacuum pump.

Compared with the existing screw rotors with equal pitch and equal tooth width, the proposed screw rotor with variable tooth width and equal pitch has the following advantages: ①It can form a larger volume of low-pressure working chamber and a smaller volume of high-pressure working chamber , so it has a larger content ratio, which is beneficial to improve the ultimate vacuum degree and pumping speed of the vacuum pump; ②In the working chamber with higher pressure, the tooth width of the screw rotor is larger, which has a stronger interstage leakage blocking ability, which can To reduce the leakage of gas between each working chamber; ③High strength and high rigidity.

Description of drawings

Figure 1 is an axial cross-sectional line diagram of a constant-pitch variable-tooth-width screw rotor.

Fig. 2 is the meshing diagram between the axial section profiles of two screw rotors meshing with each other.

Figure 3 is a diagram of a screw rotor with equal pitch and variable tooth width.

Figure 4 is the meshing diagram of two screw rotors with equal pitch and variable tooth width.

In the figure: R ₁ — radius of addendum circle; R ₂ — radius of pitch circle; R ₃ — radius of root circle; R _b — radius of base circle of circular involute; α — occurrence angle of circular involute; θ — Central angle of addendum arc BC and dedendum arc DE; 201, 202—axial section profile of screw rotor; 301—left-handed screw rotor; 302—right-handed screw rotor; 1, 1’—cycloid tooth surface; 2, 2'—helical tooth surface; 3,3',5,5'—cylindrical helix; 4,4'—tooth top surface; 6,6'—concave tooth surface; 7,7'—dedendum surface; P ₁ , P ₂ , P ₃ , P ₄ —the pitch of the screw rotor; M ₁ , M ₂ , M ₃ —the width of the top surface of the screw rotor; N ₁ , N ₂ , N ₃ —the width of the root surface of the screw rotor .

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

As shown in Figure 1, it is the axial section profile diagram of the screw rotor with equal pitch and variable tooth width. At any axial position, the axial section profile line of the screw rotor includes 5 curves and 2 points, in order: Circular involute AB, point B, addendum arc BC, point C, cycloid CD, dedendum arc DE, cycloid EA; among them, dedendum arc DE, circular involute AB are smooth with cycloid EA connected, and the central angle ∠BOC of the addendum arc BC is equal to the central angle ∠DOE of the dedendum arc DE, which is the central angle θ.

As shown in Figure 2, it is the meshing diagram between the axial section profiles of two screw rotors meshing with each other. At the same axial position, the axial sections of the left-handed screw rotor (301) and the right-handed screw rotor (302) The profiles are the same, and the circular involute AB, point B, addendum arc BC, point C, cycloid CD, dedendum arc DE and The cycloid EA is respectively connected with the circular involute ba, cycloid ae, dedendum arc ed, cycloid dc, point c, and addendum circle in the axial section profile (202) of the right-handed screw rotor (302). Arc cb, point b enables correct meshing.

As shown in Figure 3, it is a screw rotor diagram with equal pitch and variable tooth width. The twin-screw vacuum pump includes two screw rotors: a left-handed screw rotor (301) and a right-handed screw rotor (302); the left-handed screw rotor (301) is composed of a The axial section profile (201) of a series of screw rotors is helically expanded along a left-handed equal-pitch cylindrical helix; the right-handed screw rotor (302) is formed by a series of axial section profiles (202) of a screw rotor Cylindrical helixes of equal pitch are generated by helical expansion; left-handed cylindrical helixes of equal pitch are different from right-handed cylindrical helices of equal pitch.

As shown in Figure 4, it is the meshing diagram of two screw rotors with equal pitch and variable tooth width. The two screw rotors meshing with each other: left-handed screw rotor (301) and right-handed screw rotor (302), both include 5 tooth surfaces . Surface (4), cylindrical helix (5), concave tooth surface (6), tooth root surface (7), and helical tooth surface (2), tooth root surface (7) are smooth with cycloidal tooth surface (1) connection; left-handed screw rotor (301) consists of tooth surface and cylindrical helix in order: cycloidal tooth surface (1'), helical tooth surface (2'), cylindrical helix (3'), tooth top surface (4' ), cylindrical helix (5'), concave tooth surface (6'), dedendum surface (7'), and helical tooth surface (2'), dedendum surface (7') and cycloidal tooth surface (1 ’) smooth connection; during the working process of synchronous and opposite double-rotational motion, the cycloidal tooth surface (1), helical tooth surface (2), cylindrical helix (3), tooth top surface of the right-handed screw rotor (302) (4), cylindrical helix (5), concave tooth surface (6), dedendum surface (7), respectively with the cylindrical helix (3 '), helical tooth surface (2 '), Cycloid tooth surface (1'), dedendum surface (7'), concave tooth surface (6'), cylindrical helix (5'), and tooth top surface (4') can achieve correct meshing; in any axial direction position, the axial section profiles of the left-handed screw rotor (301) and the right-handed screw rotor (302) are the same.

The number of helical turns of the two screw rotors engaged with each other, the left-handed screw rotor (301) and the right-handed screw rotor (302), are both larger than 2.

As shown in Figure 4, it is the meshing diagram of two screw rotors with equal pitch and variable tooth width. The pitch of the screw rotor remains unchanged from the low-pressure end surface I-I to the high-pressure end surface VI-VI, that is, P ₁ =P ₂ =P ₃ ＝P ₄ , but the width of tooth top surface and tooth root surface gradually increases from low pressure end surface I-I to high pressure end surface VI-VI, that is, M ₁ <M ₂ <M ₃ , N ₁ <N ₂ <N ₃ ; sectional view Ⅰ-Ⅰ, Ⅱ-Ⅱ, Ⅲ-Ⅲ, Ⅳ-Ⅳ, Ⅴ-Ⅴ, Ⅵ-Ⅵ, are the axial sections of the screw rotor when the helical expansion angle τ is 0, 2π, 3π, 4π, 6π, 8π respectively The meshing diagram of the profile; at any axial position, the axial section profile of the screw rotor includes 5 curves: circular involute AB, addendum arc BC, cycloid CD, dedendum arc DE, pendulum Line EA; from the low-pressure end surface Ⅰ-Ⅰ of the screw rotor to the high-pressure end surface Ⅵ-Ⅵ, the change law of the axial section profile line of the screw rotor with the axial position is: the radius R _b of the base circle of the circular involute AB gradually increases , the occurrence angle α of the circular involute AB gradually decreases, and the central angle θ of the addendum arc BC and the dedendum arc DE gradually increases. The working chamber formed by the screw rotor has a small volume of the high-pressure working chamber and a large volume of the low-pressure working chamber. The tooth width of the screw rotor is larger in the high-pressure working chamber and wider in the low-pressure working chamber. small.

Although the specific implementation of the present invention has been described above in conjunction with the accompanying drawings, it does not limit the protection scope of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, those skilled in the art do not need to pay creative work Various modifications or variations that can be made are still within the protection scope of the present invention.

Claims (7)

1. A screw rotor with equal pitch and variable tooth width, characterized in that: from the low-pressure end surface I-I of the screw rotor to the high-pressure end surface VI-VI, the pitch of the screw rotor (P ₁ , P ₂ , P ₃ , P ₄ ) remains unchanged, but the tooth width of the screw rotor, including the width of the top surface (M ₁ , M ₂ , M ₃ ) and the width of the root surface (N ₁ , N ₂ , N ₃ ), increases gradually; thus the screw rotor In the formed working chamber, the volume of the high-pressure working chamber is small, while the volume of the low-pressure working chamber is large. The tooth width of the screw rotor in the high-pressure working chamber is larger, and the tooth width of the screw rotor in the low-pressure working chamber is smaller. 2. A screw rotor with equal pitch and variable tooth width as claimed in claim 1, characterized in that: at any axial position, the axial section profile of the screw rotor includes 5 sections of curves and 2 points, sequentially It is: circular involute AB, point B, addendum arc BC, point C, cycloid CD, dedendum arc DE, cycloid EA, in which dedendum arc DE, circular involute AB are all related to cycloid EA is smoothly connected, and the central angle ∠BOC of the addendum arc BC is equal to the central angle ∠DOE of the dedendum arc DE, which is the central angle θ; at different axial positions, the axial section profile of the screw rotor They are all different and vary with the axial position. From the low-pressure end surface I-I of the screw rotor to the high-pressure end surface VI-VI, the change law of the axial section profile of the screw rotor with the axial position is: circle gradually The radius R _b of the base circle of the open line AB gradually increases, the occurrence angle α of the circular involute AB gradually decreases, and the central angle θ of the addendum arc BC and the dedendum arc DE gradually increases. 3. A screw rotor with equal pitch and variable tooth width as claimed in claim 1, characterized in that: the screw rotor includes 5 tooth surfaces and 2 cylindrical helical lines, which are: cycloidal tooth surfaces (1), Helical tooth surface (2), cylindrical helix (3), tooth top surface (4), cylindrical helix (5), concave tooth surface (6), tooth root surface (7), and helical tooth surface (2), The tooth root surface (7) is smoothly connected with the cycloidal tooth surface (1); during the working process of synchronous counter-rotating double-rotational motion, the cycloidal tooth surface (1) and the helical tooth surface ( 2), cylindrical helix (3), tooth top surface (4), cylindrical helix (5), concave tooth surface (6), dedendum surface (7), and the cylindrical helix of the left-handed screw rotor (301) respectively (3'), helical tooth surface (2'), cycloid tooth surface (1'), dedendum surface (7'), concave tooth surface (6'), cylindrical helix (5'), tooth top surface ( 4') can achieve correct meshing; at any axial position, the axial section profiles of the left-handed screw rotor (301) and the right-handed screw rotor (302) are the same, and the axial section profiles of the left-handed screw rotor (301) The circular involute AB, point B, addendum arc BC, point C, cycloid CD, dedendum arc DE and cycloid EA in (201) are respectively related to the axial section of the right-handed screw rotor (302) The circular involute ba, cycloid ae, dedendum arc ed, cycloid dc, point c, addendum arc cb, and point b in the profile (202) can realize correct meshing. 4. A screw rotor with equal pitch and variable tooth width as claimed in claim 1, the left-handed screw rotor (301) is formed by a series of axial section profiles (201) of the screw rotor along the left-handed equal-pitch cylindrical helix. It is generated by helical expansion; the right-handed screw rotor (302) is generated by helically expanding the axial section profile (202) of a series of screw rotors along the right-handed equal-pitch cylindrical helix; the left-handed equal-pitch cylindrical helix and the right-handed Cylindrical helices of equal pitch differ in direction of hand; the equation for a left-handed cylindrical helix of equal pitch is: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; \&rsqb;</span>\\ \mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; \&tau;</span>}\end{array}\right.$ The equation for a right-handed equi-pitch cylindrical helix is: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; \&rsqb;</span>\\ \mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; \&tau;</span>}\end{array}\right.$ In the formula: τ is the helix expansion angle, rad; R is the radius of the base circle of the helix, mm; n is the number of helix turns, n≥2; P is the pitch of the screw rotor, mm; At any axial position, the axial section profile of the screw rotor includes 5 curves: circular involute AB, addendum arc BC, cycloid CD, dedendum arc DE, cycloid EA; in different The axial position, that is, corresponding to different helical expansion angles τ, the curve cluster equation of each curve is as follows: ① The curve family equation of circular involute AB is: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\end{array}\right.$ In the formula: t is the angle parameter, rad; R _b (τ) is the radius of the base circle of the circular involute AB at different axial positions; α(τ) is the occurrence angle of the circular involute AB at different axial positions; R _b (τ) and α(τ) are determined by the following formulas: ${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}$ $\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>$ In the formula: k is a coefficient; R _bs and R _be are the base circle radius of the circular involute AB in the axial section profile of the screw rotor of the low-pressure end face I-I and the high-pressure end face VI-VI respectively, mm; ②The curve cluster equation of addendum arc BC is: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; t</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right.$ In the formula: R ₁ is the radius of the addendum arc, mm; ③The curve family equation of cycloid CD is: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; t</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right.$ In the formula: R ₂ is pitch circle radius, mm; ④ The curve cluster equation of the dedendum arc DE is: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; t</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right.$ In the formula: R ₃ is the root arc radius, mm; ⑤ The curve cluster equation of cycloid EA is: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\end{array}\right.$ In the formula: θ(τ) is the central angle of the addendum arc BC and the dedendum arc DE at different axial positions, which is determined by the following formula: $\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>$ 5. A twin-screw vacuum pump, characterized in that: the screw rotor with equal pitch and variable tooth width as claimed in claim 1 is used. 6. A twin-screw compressor, characterized in that: the screw rotor with equal pitch and variable tooth width as claimed in claim 1 is used. 7. A twin-screw expander, characterized in that: the screw rotor with equal pitch and variable tooth width as claimed in claim 1 is used.