Cubic curve type screw rotor of double-screw vacuum pump and design method of cubic curve type screw rotor

Abstract

The invention discloses a cubic curve type screw rotor of a double-screw vacuum pump and a design method of the cubic curve type screw rotor, the screw rotor comprises a left screw rotor and a right screw rotor, the left section molded line of the left screw rotor is composed of a left cubic curve, a conjugate curve of the left cubic curve, a left tooth top arc, a left first cycloid, a left tooth bottom arc and a left second cycloid; the shape and composition curve of the right section molded line of the right screw rotor are completely the same as those of the left section molded line of the left screw rotor; in the working process, the left screw rotor and the right screw rotor can be correctly meshed; the screw rotor has a large arc central angle, a large compression ratio can be achieved, leakage between the rotors is reduced through line-line meshing of a cubic curve and a conjugate curve of the cubic curve, the sealing performance of the screw vacuum pump is improved, and the ultimate vacuum degree and the working efficiency are improved.

Description

Technical Field

[0001] This invention relates to twin-screw vacuum pumps, and particularly to a cubic curve-shaped screw rotor suitable for a twin-screw vacuum pump and its design method. Background Technology

[0002] A twin-screw vacuum pump is a rotary positive displacement pump whose core consists of two parallel, meshing screw rotors. It offers advantages such as dry, oil-free operation, smooth running, low vibration and noise, few vulnerable parts, and adaptability to various complex operating conditions. Its performance is highly dependent on the cross-sectional profile design of the screw rotors. Currently, it is widely used in aerospace, electronics and semiconductors, petrochemicals, nuclear industry, and other fields with stringent requirements for cleanliness and stability, making it a key piece of equipment in modern industrial vacuum systems.

[0003] Currently, the cross-sectional profile of commonly used screw rotors consists of four curve segments, including the tooth root arc, tooth tip arc, cycloid, and circular involute. The central angle of the arc in the cross-sectional profile of this screw rotor is relatively small, making it difficult to manufacture small-pitch screws and limiting the internal volume ratio. Patent CN202210628074 proposes a twin-screw vacuum pump rotor profile, in which the tooth back is connected by two cycloid segments to the tooth root arc and the tooth tip arc, resulting in a larger central angle. However, it extensively uses cycloid meshing with points, leading to poor sealing performance. Summary of the Invention

[0004] Based on the above problems, a cubic curve type screw rotor is proposed. It uses cycloids, cubic curves, and conjugate curves of cubic curves to connect the tooth tip arc and the tooth root arc, which has a large arc center angle, making the convex surface of the screw rotor more three-dimensional, reducing the machining difficulty of the small pitch section. Moreover, the meshing of cubic curves and conjugate curves of cubic curves improves the problem of large leakage between cycloid and point meshing rotors, and improves the ultimate vacuum degree and working efficiency.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A cubic curve type screw rotor for a twin-screw vacuum pump includes a left screw rotor and a right screw rotor. The left section profile of the left screw rotor is composed of six curve segments, arranged counterclockwise as follows: left cubic curve AB, the conjugate curve BC of the left cubic curve, left tooth tip arc CD, left first cycloid DE, left tooth root arc EF, and left second cycloid FA. The central angle ∠COD of the left tooth tip arc ranges from 168° to 172°. Points C and D on the left tooth tip arc CD are cusps, and the remaining parts are smoothly connected.

[0007] The right section profile (201) of the right screw rotor (2) consists of 6 curve segments, which are arranged in counterclockwise order as follows: right cubic curve ab, right cubic curve conjugate curve bc, right tooth tip arc cd, right first cycloid de, right tooth root arc ef, and right second cycloid fa. The central angle ∠cod of the right tooth tip arc ranges from 168° to 172°. Points c and d on the right tooth tip arc cd are cusps, and the rest are smoothly connected. The shape and composition curves of the left section profile are exactly the same as those of the right section profile.

[0008] During the synchronous and opposite double-rotation motion, the meshing relationships of the curves on the left and right cross-section profiles are as follows: the left cubic curve AB meshes with the conjugate curve bc of the right cubic curve; the conjugate curve BC of the left cubic curve meshes with the right cubic curve ab; the left tooth tip arc CD meshes with the right tooth root arc ef; the left tooth root arc EF meshes with the right tooth tip arc cd; the left first cycloid DE meshes with point c; the left second cycloid FA meshes with point d; point C meshes with the right first cycloid de; and point D meshes with the right second cycloid fa.

[0009] A design method for a cubic curve-shaped screw rotor, characterized by the following steps:

[0010] ①Given the following values: tooth tip radius R1, tooth root radius R3, tooth back central angle 2α, and second cycloidal central angle γ;

[0011] ②Establish a coordinate system with the rotation center O1 of the left screw rotor as the origin, and determine the left cubic curve AB, the conjugate curve BC of the left cubic curve, the left tooth tip arc CD, the left first cycloid DE, the left tooth root arc EF, and the left second cycloid FA of the left screw rotor according to the following equations.

[0012] The equation for the left tooth tip arc CD:

[0013]

[0014] In the formula: R1 is the radius of the tooth tip arc; t is the angle parameter;

[0015] The equation of the first cycloid DE on the left:

[0016]

[0017] In the formula: R3 is the radius of the tooth root arc;

[0018] The equation for the left tooth root arc EF is:

[0019]

[0020] The equation of the second cycloid FA on the left:

[0021]

[0022] The equation of the left cubic curve AB is:

[0023]

[0024] In the formula: C0, C1, C2, and C3 are constants, determined by the following equation:

[0025]

[0026] In the formula: λ is a constant used to adjust the curvature of point B to prevent root shear;

[0027] The equation of the conjugate curve BC of the left cubic curve is:

[0028]

[0029] In the formula, R2 is the pitch circle radius. As an intermediate variable, it is a function of the angle variable t and is determined by the following equation:

[0030]

[0031] ③ Based on the above steps, the left screw rotor is obtained. Since the left screw rotor is the same as the right screw rotor, the right screw rotor is obtained.

[0032] A twin-screw vacuum pump, characterized in that it uses a cubic curve-shaped screw rotor.

[0033] The beneficial effects of this invention are as follows:

[0034] ① The proposed screw rotor has a large circular arc center angle in its cross-sectional profile, which improves the problem of difficult machining of small-pitch screws, increases the internal volume ratio, and improves the ultimate vacuum degree and working efficiency.

[0035] ② The proposed screw rotor cross-sectional profile uses the meshing of cubic curves and conjugate curves of cubic curves instead of the meshing of cycloids and points, which reduces leakage between rotors and improves the sealing performance of the screw vacuum pump. Attached Figure Description

[0036] Figure 1 Figure 101 shows the left cross-sectional profile of the left screw rotor 1.

[0037] Figure 2 Figure 201 shows the right cross-sectional profile of the right screw rotor 2.

[0038] Figure 3 This is a diagram showing the meshing of the left section profile 101 and the right section profile 201.

[0039] Figure 4 This is the envelope diagram of the left section profile 101 and the right section profile 201.

[0040] Figure 5 This is a diagram showing the meshing of the left screw rotor 1 and the right screw rotor 2.

[0041] In the figure: 1—left screw rotor; 2—right screw rotor; 101—left section profile; 201—right section profile; R1—tooth tip radius; R2—pitch circle radius; R3—tooth root radius; central angle of the conjugate curve of the α cubic curve; central angle of the β cubic curve; central angle of the γ second cycloid. Detailed Implementation

[0042] The invention will now be further described with reference to the accompanying drawings.

[0043] like Figure 1 As shown, the left section profile 101 of the left screw rotor 1 consists of 6 curve segments, which, in counterclockwise order, are the left cubic curve AB, the conjugate curve BC of the left cubic curve, the left tooth tip arc CD, the left first cycloid DE, the left tooth root arc EF, and the left second cycloid FA. The generation method and curve equations are as follows:

[0044] ①Given the following values: tooth tip radius R1, tooth root radius R3, tooth back central angle 2α, and second cycloidal central angle γ;

[0045] ②Establish a coordinate system with the rotation center O1 of the left screw rotor 1 as the origin, and determine the left cubic curve AB, the conjugate curve BC of the left cubic curve, the left tooth tip arc CD, the left first cycloid DE, the left tooth root arc EF, and the left second cycloid FA of the left screw rotor 1 according to the following equations.

[0046] The equation for the left tooth tip arc CD:

[0047]

[0048] In the formula: R1 is the radius of the tooth tip arc; t is the angle parameter;

[0049] The equation of the first cycloid DE on the left:

[0050]

[0051] In the formula: R3 is the radius of the tooth root arc;

[0052] The equation for the left tooth root arc EF is:

[0053]

[0054] The equation of the second cycloid FA on the left:

[0055]

[0056] The equation of the left cubic curve AB is:

[0057]

[0058] In the formula: C0, C1, C2, and C3 are constants, determined by the following equation:

[0059]

[0060] In the formula: λ is a constant used to adjust the curvature of point B to prevent root shear;

[0061] The equation of the conjugate curve BC of the left cubic curve is:

[0062]

[0063] In the formula, R2 is the pitch circle radius. As an intermediate variable, it is a function of the angle variable t and is determined by the following equation:

[0064]

[0065] like Figure 2 As shown, the right section profile 201 of the right screw rotor 2 is shown. The left screw rotor 1 is the same as the right screw rotor 2.

[0066] like Figure 3 As shown, the meshing diagram of the left section profile 101 and the right section profile 201 shows that the left section profile 101 and the right section profile 201 can achieve correct meshing.

[0067] like Figure 4 As shown, the envelope diagrams of the left cross-section profile 101 and the right cross-section profile 201 are shown. During the synchronous and opposite-directional double-rotation motion, the left cross-section profile 101 and the right cross-section profile 201 can achieve completely correct meshing: the left cubic curve AB meshes with the conjugate curve bc of the right cubic curve, the conjugate curve BC of the left cubic curve meshes with the right cubic curve ab, the left tooth tip arc CD meshes with the right tooth root arc ef, the left tooth root arc EF meshes with the right tooth tip arc cd, the left first cycloid DE meshes with point c, the left second cycloid FA meshes with point d, point C meshes with the right first cycloid de, and point D meshes with the right second cycloid fa.

[0068] like Figure 5 The diagram shows the meshing of the left screw rotor 1 and the right screw rotor 2. The left screw rotor 1 is formed by unfolding the left section profile 101 along the helical line, and the right screw rotor 2 is formed by unfolding the right section profile 201 along the helical line. When the two screw rotors perform synchronous and opposite double rotational motion, they can satisfy the correct meshing of the corresponding tooth surfaces.

[0069] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A cubic curve-shaped screw rotor for a twin-screw vacuum pump, comprising a left screw rotor (1) and a right screw rotor (2), characterized in that: The left section profile (101) of the left screw rotor (1) consists of 6 curve segments, which are arranged in counterclockwise order as follows: left cubic curve AB, conjugate curve BC of the left cubic curve, left tooth tip arc CD, left first cycloid DE, left tooth root arc EF, and left second cycloid FA. The central angle ∠COD of the left tooth tip arc ranges from 168° to 172°. Points C and D on the left tooth tip arc CD are cusps, and the rest are smoothly connected. The right section profile (201) of the right screw rotor (2) consists of 6 curve segments, which are arranged in counterclockwise order as follows: right cubic curve ab, right cubic curve conjugate curve bc, right tooth tip arc cd, right first cycloid de, right tooth root arc ef, and right second cycloid fa. The central angle ∠cod of the right tooth tip arc ranges from 168° to 172°. Points c and d on the right tooth tip arc cd are cusps, and the rest are smoothly connected. The shape and composition curves of the left section profile (101) are exactly the same as those of the right section profile (201). During the synchronous and opposite double-rotation motion, the meshing relationship of each curve segment on the left section profile (101) and the right section profile (201) is as follows: the left cubic curve AB meshes with the conjugate curve bc of the right cubic curve, the conjugate curve BC of the left cubic curve meshes with the right cubic curve ab, the left tooth tip arc CD meshes with the right tooth root arc ef, the left tooth root arc EF meshes with the right tooth tip arc cd, the left first cycloid DE meshes with point c, the left second cycloid FA meshes with point d, point C meshes with the right first cycloid de, and point D meshes with the right second cycloid fa.

2. The design method of a cubic curve-type screw rotor as described in claim 1, characterized in that: Includes the following steps: ①Given the following values: tooth tip radius R1, tooth root radius R3, tooth back central angle 2α, and second cycloidal central angle γ; ②Establish a coordinate system with the rotation center O1 of the left screw rotor (1) as the origin, and determine the left cubic curve AB, the conjugate curve BC of the left cubic curve, the left tooth tip arc CD, the left first cycloid DE, the left tooth root arc EF, and the left second cycloid FA of the left screw rotor (1) according to the following equations. The equation for the left tooth tip arc CD: In the formula: R1 is the radius of the tooth tip arc; t is the angle parameter; The equation of the first cycloid DE on the left: In the formula: R3 is the radius of the tooth root arc; The equation for the left tooth root arc EF is: The equation of the second cycloid FA on the left: The equation of the left cubic curve AB is: In the formula: C0, C1, C2, and C3 are constants, determined by the following equation: In the formula: λ is a constant used to adjust the curvature of point B to prevent root shear; The equation of the conjugate curve BC of the left cubic curve is: In the formula, R2 is the pitch circle radius. As an intermediate variable, it is a function of the angle variable t and is determined by the following equation: ③ Based on the above steps, the left screw rotor (1) is obtained. Since the left screw rotor (1) is the same as the right screw rotor (2), the right screw rotor (2) is obtained.

3. A twin-screw vacuum pump, characterized in that: The cubic curve screw rotor of the twin-screw vacuum pump as described in claim 1 is used.

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