A variable pitch multi-stage Roots vacuum pump and its rotor design method

Abstract

A variable pitch multi-stage Roots vacuum pump and its rotor design method. The variable pitch multi-stage Roots vacuum pump has a female rotor and a male rotor that mesh with each other. Both the female rotor and the male rotor include multi-stage Roots rotors with different pitches. The different-stage Roots rotors are obtained by stretching and lofting the rotor end face profile along the axial spiral guide line. The first-stage Roots rotor is a straight blade Roots rotor, and the pitches of the Roots rotors decrease sequentially from the first stage to the last stage. The thicknesses of each stage of the rotors along the axis of the rotating shaft, that is, the axial lengths, also decrease sequentially. Each stage of the rotors of the female rotor and the male rotor adopts a rotor profile with the same curve structure. One side curve of the single tooth profile of one rotor is a parabola A1B1 and its envelope line B1C1, and the other side curve is the symmetric curve of the curve A1B1C1 about the x-axis. The single tooth profile is rotationally symmetrically combined multiple times along the center O1 of the rotor pitch circle to form a complete tooth profile. The present invention can optimize the overall performance of the rotor, improve the ultimate vacuum degree, and reduce the energy consumption.

Description

Technical Field

[0001] The invention belongs to the technical field of multi-stage Roots vacuum pumps, and particularly relates to a variable-pitch multi-stage Roots vacuum pump and a rotor design method thereof. Background Art

[0002] Multi-stage Roots vacuum pumps have the advantages of a wide working pressure range, direct exhaust to the atmosphere, low maintenance cost, and high pumping speed, and are widely used in the fields of semiconductors, pharmaceuticals, metallurgy, petrochemicals, aerospace, etc. A multi-stage Roots vacuum pump can be regarded as each stage of Roots pump operating simultaneously, and multi-stage compression is achieved through an isochoric compression process to realize air extraction and vacuum.

[0003] In the case of relatively high pressures, the gas particle collisions between the rotors are intense, and the vibration noise is large, which has a greater impact on the performance of the vacuum pump. The straight-lobe Roots pump has problems of high energy consumption and high noise, while the twisted-lobe Roots can reduce the operating noise of the vacuum pump to a certain extent, thereby improving the performance of the Roots pump. In the case of relatively low pressures, the leakage between the rotors directly affects the ultimate pumping performance of the compressor. Under the same profile and geometric dimensions, the volume between the rotor teeth is the same, but the contact line of the twisted-lobe Roots rotor is longer than that of the straight-lobe Roots rotor, and the contact line length directly affects the rotor leakage amount, thereby affecting the performance of the vacuum pump. At present, the commonly used constant-pitch twisted-lobe multi-stage Roots vacuum pumps and all-straight-lobe multi-stage Roots vacuum pumps cannot optimize the overall performance of the rotor. Summary of the Invention

[0004] The purpose of the present invention is to address the problem that the overall performance of the rotor cannot be optimized when the same-pitch rotors are used on the high-pressure and low-pressure sides of the multi-stage Roots vacuum pump in the above-mentioned prior art, and to provide a variable-pitch multi-stage Roots vacuum pump and a rotor design method thereof, which combines the different advantages of straight-lobe and twisted-lobe Roots to reduce the rotor operating noise and the leakage between the rotors, and improve the overall performance of the multi-stage Roots vacuum pump.

[0005] To achieve the above purpose, the present invention has the following technical solutions:

[0006] A variable-pitch multi-stage Roots vacuum pump has a female rotor and a male rotor that mesh with each other. Both the female rotor and the male rotor include multi-stage Roots rotors with different pitches. The different-stage Roots rotors are obtained by stretching and lofting the rotor end face profile along the axial spiral guide line; the first-stage Roots rotor is a straight-lobe Roots rotor, and the pitch decreases sequentially from the first-stage Roots rotor to the last-stage Roots rotor, and the thickness of each stage of the rotor along the axis of rotation, that is, the axial length, also decreases sequentially; each stage of the rotor of the female rotor and the male rotor adopts the same curve structure of the rotor profile. One side curve of the single-tooth profile of one rotor is a parabola A1B1 and its envelope B1C1, and the other side curve is the symmetric curve of the curve A1B1C1 about the x-axis. The single-tooth profile is rotationally symmetric multiple times along the center O1 of the rotor pitch circle to form a complete tooth profile.

[0007] As a preferred solution, a Cartesian two-dimensional rectangular coordinate system O1X1Y1 and O2X2Y2 of the two rotors are established with the center O1 and O2 of the rotor pitch circle as the origin respectively for the female rotor and the male rotor. Then, the relationship of the coordinate change between the female rotor and the male rotor conforms to the following expression:

[0008]

[0009] In the formula, M rot,1 、M rot,2 、M stat,1,2 respectively represent the coordinate transformation matrix of the O1X1Y1 coordinate system rotating around the origin, the coordinate transformation matrix of the O2X2Y2 coordinate system rotating around the origin, and the transformation matrix from the O1X1Y1 coordinate system to the O2X2Y2 coordinate system. In the formula, i and A respectively represent the rotation angle of the coordinate system, the transmission ratio, and the distance between the centers of the rotors; the transmission ratio i satisfies the following relational expression:

[0010]

[0011] In the formula, z2 and z1 respectively represent the number of teeth of the two rotors.

[0012] As a preferred solution, the parabola A1B1 is expressed in the Cartesian two-dimensional rectangular coordinate system O1X1Y1 with the center O1 of the rotor pitch circle as the center and the x-axis direction as the starting direction as:

[0013]

[0014] Among them, N is the tooth profile coefficient, a is the tip radius, and P 1a is the coordinate parameter matrix of the parabola A1B1 profile, and the superscript semicolon represents the matrix transpose.

[0015] As a preferred solution, by simultaneously changing the tooth profile coefficient and the tip radius, the continuous meshing of the rotor profile and the change of the rotor profile shape are realized, and the following equation is satisfied:

[0016]

[0017] The above formula establishes a Cartesian two-dimensional rectangular coordinate system with the center of the rotor pitch circle as the coordinate origin. In the formula, y' represents the curve slope, and y represents the ordinate value of the curve in the rotor coordinate system.

[0018] As a preferred solution, the parabola A1B1 and the parabola A2B2 can complete correct meshing. According to the meshing theorem, the parabola A2B2 is expressed in the rectangular coordinate system with the center O1 of the rotor pitch circle as the origin as the following formula:

[0019] P 2a =M stat,1,2 'Mrot,2 M stat,1,2 M rot,1 P 1a

[0020] In the formula, P 1a is the line coordinate parameter matrix of type A1B1, and P 2a is the line coordinate parameter matrix of type A2B2. M stat,1,2 ' is the inverse matrix of M stat,1,2 , and it is the transformation matrix for realizing the transformation from the O2X2Y2 coordinate system to the O1X1Y1 coordinate system.

[0021] According to the planar meshing theorem, substituting the following meshing envelope condition expression into the expression of the line coordinate parameter matrix of type A2B2, P 2a can be solved, thereby obtaining the line of type A2B2:

[0022]

[0023] In the formula, D is the differential operator, θ is the meshing angle of the rotor curve, and x, y are the 2a two-dimensional position parameters.

[0024] The parametric equation of the envelope line B1C1 of the parabola A1B1 can be solved through the following expression:

[0025]

[0026] P 1b = M stat,1,2 M rot,1,p P 2a

[0027] In the formula, M rot,1,p represents the coordinate transformation matrix for the O1X1Y1 coordinate system to rotate by a specific angle around the origin.

[0028] Similarly, through the above method, the parametric equation of the envelope line B2C2 can be obtained from the parabola A2B2.

[0029] As a preferred solution, through the line coordinate parameter matrices P 1a , P 1b , P 2a , P 2b of each curve segment A1B1, B1C1, A2B2, B2C2 of the rotor end face profile, rotating periodically around the center of the pitch circle of their respective rotors, the complete rotor end face profiles of the two rotors are obtained.

[0030] As a preferred solution, the axial spiral guiding line is solved by the following equation:

[0031]

[0032] Among them, I j represents the number of stages of the multi-stage Roots vacuum pump, and α j is the correction coefficient, L j is the pitch of the spiral guiding line, R j is the radius of the spiral guiding line, and ρ M is the distance between any point on the profile curve of the rotor end face and the center of the rotor pitch circle.

[0033] A rotor design method for the variable pitch multi-stage Roots vacuum pump described above includes the following steps:

[0034] Select the profile curve coefficient N and the tip radius a of the first-stage Roots rotor according to the pumping speed requirement;

[0035] Select the number of stages of the rotor of the multi-stage Roots vacuum pump, the axial length of each stage, and the pitch L of each stage according to the internal compression degree requirement j ;

[0036] Using the parameters selected above, construct the profile curve of the rotor end face of the variable pitch multi-stage Roots vacuum pump, and then stretch and loft along the axial spiral guiding line from the profile curve of the rotor end face to obtain the overall rotor structure of the variable pitch multi-stage Roots vacuum pump.

[0037] Compared with the prior art, the present invention has at least the following beneficial effects:

[0038] The multi-stage Roots vacuum pump of the present invention uses multi-stage Roots rotors with different pitches. The multi-stage Roots rotors of different stages are obtained by stretching and lofting the profile curve of the rotor end face along the axial spiral guiding line. Among them, the first-stage Roots rotor uses a rotor with an infinite pitch, that is, a straight vane Roots rotor, and the last-stage Roots rotor uses a rotor with a smaller pitch. The pitch decreases sequentially from the first-stage Roots rotor to the last-stage Roots rotor, and the thickness of each stage rotor along the axis direction, that is, the axial length, also decreases sequentially. The higher the number of stages, the smaller the rotor pitch and the larger the twist angle. Combining the beneficial gain effects of the straight vane Roots and the twisted vane Roots, it avoids the problem of increased leakage caused by the long contact line on the low-pressure side of the twisted vane Roots rotor and the problem of relatively large noise on the high-pressure side of the straight vane Roots rotor, thereby improving the overall performance of the rotor, enabling the overall performance of the rotor to reach the optimal, improving the ultimate vacuum degree of the multi-stage Roots vacuum pump, and reducing the energy consumption of the multi-stage Roots vacuum pump. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of the rotor structure of the variable pitch multi-stage Roots vacuum pump according to the embodiment of the present invention;

[0040] Figure 2 Schematic diagram of the profile curve of the rotor end face of the variable pitch multi-stage Roots vacuum pump according to the embodiment of the present invention;

[0041] Figure 3Schematic diagram of the contact line between straight blades and twisted blades. Specific implementation manner

[0042] The present invention will be further described in detail below with reference to the accompanying drawings.

[0043] Under low-pressure conditions, the leakage between rotors directly affects the ultimate pumping performance of the compressor. Under the same profile and geometric dimensions, the inter-tooth volume of the rotors is the same, but the contact line of the twisted-lobe Roots rotor is longer than that of the straight-lobe Roots rotor. The length of the contact line directly affects the rotor leakage, thereby affecting the performance of the vacuum pump. Therefore, the commonly used equal-pitch multi-stage twisted-lobe Roots vacuum pumps and all-straight-lobe multi-stage Roots vacuum pumps at present cannot optimize the overall performance of the rotors.

[0044] See Figure 1 , the variable-pitch multi-stage Roots vacuum pump of the present invention has a female rotor and a male rotor that mesh with each other. Both the female rotor and the male rotor include multi-stage Roots rotors with different pitches. The different-stage Roots rotors are obtained by stretching and lofting the rotor end face profile along the axial spiral guide line; the first-stage Roots rotor uses an infinitely large pitch rotor, that is, a straight-lobe Roots rotor, and the last-stage Roots rotor uses a smaller pitch rotor. The pitch decreases sequentially from the first-stage Roots rotor to the last-stage Roots rotor, and the thickness of each stage of the rotor along the axis of rotation, that is, the axial length, also decreases sequentially.

[0045] See Figure 2 , each stage of the rotor of the female rotor and the male rotor respectively adopts a rotor profile with the same curve structure. One side curve of the single-tooth profile of one rotor is a parabola A1B1 and its envelope B1C1, and the other side curve is the symmetric curve of the curve A1B1C1 about the x-axis. The single-tooth profile is rotated symmetrically multiple times along the center O1 of the rotor pitch circle to form a complete tooth profile.

[0046] In a possible implementation manner, the female rotor and the male rotor respectively establish two Cartesian two-dimensional rectangular coordinate systems O1X1Y1 and O2X2Y2 with the center O1 and O2 of the rotor pitch circle as the origin. Then the relationship between the coordinate changes between the female rotor and the male rotor conforms to the following expression:

[0047]

[0048] In the formula, M rot,1 、M rot,2 、M stat,1,2 respectively represent the coordinate transformation matrix of the O1X1Y1 coordinate system rotating around the origin, the coordinate transformation matrix of the O2X2Y2 coordinate system rotating around the origin, and the transformation matrix from the O1X1Y1 coordinate system to the O2X2Y2 coordinate system. In the formula, i, A respectively represent the coordinate system rotation angle, transmission ratio, and rotor center distance; the transmission ratio i satisfies the following relationship:

[0049]

[0050] In the formula, z2 and z1 respectively represent the number of teeth of the two rotors.

[0051] Furthermore, the parabola A1B1 is represented in the Cartesian two-dimensional rectangular coordinate system O1X1Y1 with the center O1 of the rotor pitch circle as the center and the x-axis direction as the starting direction as:

[0052]

[0053] Where N is the tooth profile curve coefficient, a is the addendum radius, and P 1a is the coordinate parameter matrix of the parabola A1B1 curve, and the superscript semicolon represents the matrix transpose.

[0054] By simultaneously changing the tooth profile curve coefficient and the addendum radius, continuous meshing of the rotor curve and changing the shape of the rotor curve can be achieved, and the following equation is satisfied:

[0055]

[0056] The above formula establishes a Cartesian two-dimensional rectangular coordinate system with the center of the rotor pitch circle as the coordinate origin. In the formula, y' represents the curve slope, and y represents the ordinate value of the curve in the rotor coordinate system.

[0057] In a possible implementation manner, the parabola A1B1 and the parabola A2B2 can achieve correct meshing. According to the meshing theorem, the parabola A2B2 is represented by the following formula in the rectangular coordinate system with the center O1 of the rotor pitch circle as the origin:

[0058] P 2a = M stat,1,2 'M rot,2 M stat,1,2 M rot,1 P 1a

[0059] In the formula, P 1a is the coordinate parameter matrix of the A1B1 curve, P 2a is the coordinate parameter matrix of the A2B2 curve, M stat,1,2 ' is the inverse matrix of M stat,1,2 and is the transformation matrix for realizing the transformation from the O2X2Y2 coordinate system to the O1X1Y1 coordinate system.

[0060] According to the planar meshing theorem, substituting the following meshing envelope condition expression into the A2B2 curve coordinate parameter matrix expression can solve for P 2a and thus obtain the A2B2 curve:

[0061]

[0062] Where D is the differential operator, θ is the meshing angle of the rotor curve, and x and y are the 2a two-dimensional position parameter variables.

[0063] The parametric equation of the envelope line B1C1 of the parabola A1B1 can be solved through the following expressions:

[0064]

[0065] P 1b = M stat,1,2 M rot,1,p P 2a

[0066] Where M rot,1,p represents the coordinate transformation matrix for the O1X1Y1 coordinate system to rotate by a specific angle around the origin of the coordinate transformation matrix.

[0067] Similarly, through the above method, the parametric equation of the envelope line B2C2 can be obtained from the parabola A2B2.

[0068] And so on, through the profile coordinate parameter matrices P 1a 、P 1b 、P 2a 、P 2b of each curve segment A1B1, B1C1, A2B2, B2C2 of the rotor end face profile, perform periodic rotation around the center of the respective rotor pitch circle to obtain the complete rotor end face profile of the two rotors.

[0069] In a possible implementation, the axial spiral guide line is solved through the following equation:

[0070]

[0071] Where I j represents the number of stages of the multi-stage Roots vacuum pump, α j is the correction coefficient, L j is the pitch of the spiral guide line, R j is the radius of the spiral guide line, and ρ M is the distance between any point on the rotor end face profile and the center of the rotor pitch circle.

[0072] Another embodiment of the present invention also proposes a rotor design method for the variable pitch multi-stage Roots vacuum pump, including the following steps:

[0073] Select the profile coefficient N of the first-stage Roots rotor and the tip radius a according to the pumping speed requirement;

[0074] Select the number of stages of the rotor of the multi-stage Roots vacuum pump, the axial length of each stage, and the pitch L of each stage according to the internal compression degree requirement j ;

[0075] Using the parameters selected above, construct the rotor end face profile of the variable pitch multi-stage Roots vacuum pump, and then stretch and loft along the axial spiral guiding line according to the rotor end face profile to obtain the overall rotor structure of the variable pitch multi-stage Roots vacuum pump.

[0076] In the embodiment, when the pitch L of each stage is [∞, 1800, 1500, 1200, 900] mm, the profile parameter A = 200 mm, N = 7, and z1 = z2 = 3, the obtained rotor profile is as Figure 2 shown, and the obtained multi-stage Roots rotor is as Figure 1 shown.

[0077] Set the first-stage Roots rotor of the multi-stage Roots vacuum pump as a straight blade Roots. The higher the number of stages, the smaller the rotor pitch and the larger the twist angle. Refer to Figure 3 . The variable pitch multi-stage Roots vacuum pump of the present invention combines the beneficial gain effects of the straight blade Roots and the twisted blade Roots, avoiding the problem of increased leakage caused by the long contact line on the low-pressure side of the twisted blade Roots rotor and the problem of relatively high noise on the high-pressure side of the straight blade Roots rotor, thereby improving the overall performance of the rotor, enhancing the ultimate vacuum degree and reducing energy consumption.

[0078] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A variable pitch multi-stage Roots vacuum pump, characterized in that: It has a female rotor and a male rotor that mesh with each other. Both the female rotor and the male rotor include multi-stage Roots rotors with different pitches. The different-stage Roots rotors are obtained by stretching and lofting the rotor end face profile along the axial spiral guide line. The first-stage Roots rotor is a straight-blade Roots rotor. The pitch decreases sequentially from the first-stage Roots rotor to the last-stage Roots rotor, and the thickness of each stage of the rotor in the direction of the rotating shaft decreases sequentially. Each stage of the rotor of the female rotor and the male rotor adopts a rotor profile with the same curve structure. One side curve of the single-tooth tooth profile of one rotor is the parabola A1B1 and its envelope B1C1, and the other side curve is the symmetric curve of the curve A1B1C1 about the x-axis. The single-tooth tooth profile is rotationally symmetric multiple times along the rotor pitch circle center O1 to form a complete tooth profile. The axial spiral guide line is solved by the following equation: Among them, I j represents the number of stages of the multi-stage Roots vacuum pump, α j is the correction coefficient, L j is the pitch of the spiral guiding line, R j is the radius of the spiral guiding line, ρ M is the distance between any point on the profile curve of the rotor end face and the center of the rotor pitch circle.

2. The variable pitch multi-stage Roots vacuum pump according to claim 1, characterized in that, Taking the rotor pitch circle centers O1 and O2 as the origins respectively, two Cartesian two-dimensional rectangular coordinate systems O1X1Y1 and O2X2Y2 of the two rotors are established for the female rotor and the male rotor. Then the relationship of the coordinate change between the female rotor and the male rotor conforms to the following expression: where M rot,1 , M rot,2 , M stat,1,2 respectively represent the coordinate transformation matrix of the O1X1Y1 coordinate system rotating around the origin, the coordinate transformation matrix of the O2X2Y2 coordinate system rotating around the origin, and the transformation matrix from the O1X1Y1 coordinate system to the O2X2Y2 coordinate system. In the formula, i, A respectively represent the rotation angle of the coordinate system, the transmission ratio, and the center distance of the rotor center; the transmission ratio i satisfies the following relationship: In the formula, z2 and z1 respectively represent the number of teeth of the two rotors.

3. The variable pitch multi-stage Roots vacuum pump according to claim 2, wherein, The parabola A1B1 is expressed in the Cartesian two-dimensional rectangular coordinate system O1X1Y1 with the rotor pitch circle center O1 as the center and the x-axis direction as the starting direction as: where N is the tooth profile curve coefficient, a is the addendum radius, and P 1a is the coordinate parameter matrix of the A1B1 curve type, and the superscript semicolon represents the matrix transpose.

4. The variable pitch multi-stage Roots vacuum pump according to claim 3, characterized in that, By simultaneously changing the tooth profile coefficient and the tip radius size, the continuous meshing of the rotor profile and the change of the rotor profile shape are realized, and the following equation is satisfied: The above formula establishes a Cartesian two-dimensional rectangular coordinate system with the rotor pitch circle center as the coordinate origin. In the formula, y' represents the curve slope, and y represents the ordinate value of the curve in the rotor coordinate system.

5. The variable pitch multi-stage Roots vacuum pump according to claim 3, characterized in that, The parabola A1B1 and the parabola A2B2 can complete correct meshing. According to the meshing theorem, the parabola A2B2 is expressed as the following formula in the rectangular coordinate system with the rotor pitch circle center O1 as the origin: P 2a = M stat,1,2 'M rot,2 M stat,1,2 M rot,1 P 1a Wherein, P 1a is the line coordinate parameter matrix of type A1B1, and P 2a is the line coordinate parameter matrix of type A2B2. M stat,1,2 ' is the inverse matrix of M stat,1,2 and is the transformation matrix for realizing the transformation from the O2X2Y2 coordinate system to the O1X1Y1 coordinate system.

6. The variable pitch multi-stage Roots vacuum pump according to claim 5, characterized in that: According to the planar meshing theorem, substitute the following meshing envelope condition expression into the line coordinate parameter matrix expression of the A2B2 type line for P 2a to solve and obtain the A2B2 type line: where D is the differential operator, θ is the meshing angle of the rotor curve, and x, y are the two-dimensional position parameter variables of P 2a parameters; The parametric equation of the envelope B1C1 of the parabola A1B1 is solved by the following expression: P 1b = M stat,1,2 M rot,1,p P 2a where M rot,1,p represents the coordinate transformation matrix for the rotation of the O1X1Y1 coordinate system by a specific angle around the origin ; Similarly, the parametric equation of the envelope B2C2 is obtained from the parabola A2B2.

7. The variable pitch multi-stage Roots vacuum pump according to claim 6, characterized in that: Through the profile coordinate parameter matrices P of each curve segment A1B1, B1C1, A2B2, B2C2 of the rotor end face profile 1a , P 1b , P 2a , P 2b , perform periodic rotation around the center of the respective rotor pitch circles to obtain the complete rotor end face profiles of the two rotors.

8. A rotor design method for a variable pitch multi-stage Roots vacuum pump according to any one of claims 1-7, characterized in that, It includes the following steps: Select the tooth profile coefficient N and the tip radius a of the first-stage Roots rotor according to the pumping rate requirement. Select the rotor stage number, the axial length of each stage, and the pitch L of each stage of the multi-stage Roots vacuum pump according to the requirement of internal compression degree j ; Using the selected parameters, construct the rotor end face profile of the variable-pitch multi-stage Roots vacuum pump, and then stretch and loft the rotor end face profile along the axial spiral guide line to obtain the overall rotor structure of the variable-pitch multi-stage Roots vacuum pump.

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