A spiral twisted-lobe Roots rotor, compressor and expander

Abstract

A spiral twisted lobe Roots rotor, compressor and expander. The rotor includes a female rotor and a male rotor with the same profile structure. The tooth profile of a single tooth of one rotor is composed of a spiral envelope line segment A1B1, a spiral line segment B1C1, a spiral line segment C1D1 and a spiral envelope line segment D1E1 connected in sequence. During the reverse rotation of the two rotors, continuous and correct meshing can be achieved. The complete rotor profile is formed by rotating the single-tooth profile around the origin of the rotor profile by #imgabs0# and then connecting the head and tail of the single-tooth profile. This is repeated z times, where z represents the number of teeth of the rotor. The profile structure of the rotor of the present invention has multiple adjustable profile parameters, and single-tooth symmetric and asymmetric profiles can be obtained according to different values of the order of the single-tooth spiral line segment profile equation, and there is a greater optimization space in terms of profile design and adaptability. Compared with other conventional pump types, the compressor and expander using the spiral twisted lobe Roots rotor of the present invention have the advantages of fewer wearing parts, forced suction and exhaust, high pumping speed, no surging, low vibration and noise, etc.

Description

Technical Field

[0001] The present invention belongs to the field of rotary machinery processing, and particularly relates to a spiral-shaped twisted lobe Roots rotor, a compressor, and an expander. Background Art

[0002] The twisted lobe Roots compressor and expander are a widely used rotary compressor and expander, which can be used to obtain the transportation and compression of fluid working media under medium and low pressure conditions. It has the characteristics of long service life of rotary machinery, continuous and reliable operation, low vibration and noise, and stable operation. At the same time, it also has the characteristics of no valve structure, forced suction and exhaust, simple processing, and few wearing parts, and plays an important role in machinery such as air compressors for fuel cell systems and semiconductor vacuum pumps.

[0003] The twisted lobe Roots compressor and expander rely on the pushing action of a pair of lobe-shaped rotors rotating synchronously and reversely in the rotor cavity to achieve gas transportation. Its rotor determines the overall performance of the compressor and expander. The optimal design of the rotor is also a key technical field for manufacturing high-performance twisted lobe Roots compressors and expanders. However, at present, the rotor profile design parameters of the widely used twisted lobe Roots compressors and expanders are few, and the utilization coefficient of the tooth space area is affected by the design parameters. The optimization space of the rotor structure is limited under different operating conditions, so the rotor performance cannot reach the optimal under different operating conditions. Summary of the Invention

[0004] The purpose of the present invention is to provide a spiral-shaped twisted lobe Roots rotor, a compressor, and an expander aiming at the problem of insufficient rotor profile design parameters in the above-mentioned prior art, which can provide more profile design parameters, effectively suppress the leakage between working chambers under different operating conditions, improve the utilization coefficient of the rotor area, and thus improve the overall performance of the twisted lobe Roots rotary machinery.

[0005] In order to achieve the above purpose, the present invention has the following technical solutions:

[0006] A spiral-shaped twisted lobe Roots rotor includes a female rotor and a male rotor with the same profile structure. The tooth profile A1B1C1D1E1 of a single tooth of one rotor is composed of a spiral envelope segment A1B1, a spiral segment B1C1, a spiral segment C1D1, and a spiral envelope segment D1E1 connected in sequence. The two rotors can achieve continuous and correct meshing during the reverse rotation process. The spiral envelope segment A1B1 of one rotor meshes with the spiral segment A2B2 of the other rotor, the spiral segment B1C1 meshes with the spiral envelope segment B2C2 of the other rotor, the spiral segment C1D1 meshes with the spiral envelope segment C2D2 of the other rotor, and the spiral envelope segment D1E1 meshes with the spiral segment D2E2 of the other rotor. The complete rotor profile is formed by rotating the single tooth profile A1B1C1D1E1 around the origin of the rotor profile Then connect the single-tooth profile A1B1C1D1E1 end to end, and repeat this process z times, where z represents the number of rotor teeth; the origin of the rotor profile of one rotor is O1, and the origin of the rotor profile of the other rotor is O2.

[0007] As a preferred solution, the spiral-shaped twisted lobe Roots rotor of the present invention is divided into a symmetric spiral rotor profile and an asymmetric spiral rotor profile according to whether the spiral line segment B1C1 and the spiral line segment C1D1 are of the same order of spiral, and the order of the spiral is represented by n.

[0008] As a preferred solution, the spiral curve equation is as follows:

[0009]

[0010] In the formula, n i represents the specific order of the spiral curve, and a e , b e are adjustable geometric parameters of the curve.

[0011] As a preferred solution, the parametric equation of the spiral line segment B1C1 is:

[0012]

[0013]

[0014] In the formula, r p , r m , n, P 1b respectively represent the rotor pitch circle radius, the rotor addendum circle radius, the rotor spiral order and the coordinate parameter matrix of the curve B1C1; the superscript semicolon represents the matrix transpose, is the central angle of the rotor spiral line segment B1C1.

[0015] Furthermore, is solved according to the following equation:

[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 slope of the curve, and y represents the ordinate value of the curve in the rotor coordinate system. The solution is obtained as:

[0018]

[0019] And so on, the central angles of the curve corresponding to each spiral line segment and the spiral envelope line segments A1B1, B1C1, C1D1, and D1E1 are obtained respectively Thus, the complete parametric equation of the spiral line segment is obtained.

[0020] As a preferred solution, taking the center points O1 and O2 of the pitch circles of the female rotor and the male rotor as the origins respectively, two Cartesian two-dimensional rectangular coordinate systems O1X1Y1 and O2X2Y2 of the two rotors are established. Thus, the relationship of the coordinate changes between the rotors conforms to the following formula:

[0021]

[0022]

[0023]

[0024] In the above 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 the distance between the rotor center points, and respectively satisfy the following relational expressions:

[0025]

[0026] In the formula, z2 and z1 respectively represent the number of teeth of the two rotors, respectively represent the rotor center angles corresponding to the rotor profile line segments A1B1, B1C1, C1D1, and D1E1.

[0027] As a preferred solution, the profile coordinate parameter matrix P 2b of the spiral envelope line segment B2C2 is obtained by the following transformation:

[0028]

[0029] In the formula, P 1b is the profile coordinate parameter matrix of the profile line B1C1, P 2b is the profile coordinate parameter matrix of the profile line B2C2, 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.

[0030] According to the plane meshing theorem, the above formula is solved through the following equations to obtain the profile parameter equation of the spiral envelope line segment B2C2:

[0031]

[0032] In the formula, D is the differential operator, θ is the meshing angle of the rotor curve, is the coordinate system rotation angle parameter variable, x, y are the two-dimensional position parameter variables of P 2b ;

[0033] And so on, through the profile parameter matrices P 2a , P 1b , P 1c , P 2d of the tip involute rotor profiles A2B2, B1C1, C1D1, D2E2, the profile parameter matrices P 1a , P 2b , P 2c , P 1d of the root involute envelope rotor profiles A1B1, B2C2, C2D2, D1E1 are obtained. The complete profile parameter matrices P1 and P2 of the two rotors are as follows:

[0034]

[0035] A twisted-lobe Roots compressor and a twisted-lobe Roots expander are also proposed, which have the above-mentioned involute-type twisted-lobe Roots rotors.

[0036] A design method for the above-mentioned involute-type twisted-lobe Roots rotor includes the following steps:

[0037] Select the center distance O1O2 between the rotors, the number of teeth z of the rotor, and the tip circle radius r according to the volume size and the pumping rate m ;

[0038] The profile tooth profiles of the involutes of different orders have different meshing lines and force characteristics. In the actual application process, optimize and select the order n i of the involute segment B1C1 and the involute segment C1D1 according to the sealing requirement and the force performance requirement of the specific usage scenario;

[0039] Use the above-selected parameters to construct the profile of the involute-type twisted-lobe Roots rotor.

[0040] Compared with the prior art, the present invention has at least the following beneficial effects:

[0041] The profile structure of the twisted lobe Roots rotor of the present invention has five adjustable profile parameters, including the spiral order, the number of rotor teeth, the rotor center distance, and two profile geometric parameters, providing a greater optimization space in terms of profile design and adaptability. The profile can obtain single-tooth symmetric and asymmetric profiles according to different values of the order of the single-tooth spiral segment profile equation. The two rotor profiles have a short contact line, which can effectively improve the overall performance of the twisted lobe Roots compressor and expander. In addition, the present invention can also flexibly adjust the shape of the rotor profile according to the design conditions, improving the volumetric efficiency, energy-saving performance, and power characteristics of the optimized twisted lobe Roots compressor and expander. Compared with other conventional pump types, the compressor and expander using the spiral twisted lobe Roots rotor of the present invention have the advantages of fewer wearing parts, forced suction and exhaust, high pumping speed, no surging, and low vibration and noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Schematic diagrams of complete spiral profiles of different orders of the spiral twisted lobe Roots rotor of the present invention, n = 1, 2, 3, 4, 5,

[0043] Figure 2 Schematic diagram of the profile structure of the symmetric spiral rotor in the embodiment of the present invention:

[0044]

[0045]

[0046] Figure 3 Schematic diagram of the profile structure of the asymmetric spiral rotor in the embodiment of the present invention: z1 = z2 = 3, n1 = 2, n2 = 6,

[0047] Figure 4 Schematic diagram of the envelope line clusters of the profile of the asymmetric spiral rotor in the embodiment of the present invention: z1 = z2 = 3, n1 = 2, n2 = 6,

[0048] Figure 5 Schematic diagram of the three-dimensional structure of the asymmetric spiral rotor in the embodiment of the present invention: z1 = z2 = 3, n1 = 2, n2 = 6, DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] The present invention will be further described in detail below with reference to the accompanying drawings.

[0050] At present, for the widely used twisted lobe Roots compressors and expanders, due to the small number of rotor profile design parameters, the utilization coefficient of the area between teeth is affected by the design parameters, and the optimization space of the rotor structure is limited under different operating conditions. Therefore, it is impossible to optimize the rotor performance under different operating conditions. To solve this problem, the present invention proposes a spiral twisted lobe Roots rotor, including a female rotor and a male rotor with the same profile structure. The tooth profile A1B1C1D1E1 of a single tooth of one rotor profile is composed of a spiral envelope line segment A1B1, a spiral line segment B1C1, a spiral line segment C1D1, and a spiral envelope line segment D1E1 connected in sequence.

[0051] During the reverse rotation process of the two rotors, continuous and correct meshing can be achieved. The spiral envelope line segment A1B1 of one rotor meshes with the spiral line segment A2B2 of the other rotor, the spiral line segment B1C1 meshes with the spiral envelope line segment B2C2 of the other rotor, the spiral line segment C1D1 meshes with the spiral envelope line segment C2D2 of the other rotor, and the spiral envelope line segment D1E1 meshes with the spiral line segment D2E2 of the other rotor.

[0052] The complete rotor profile is formed by rotating the single tooth profile A1B1C1D1E1 around the origin of the rotor profile and then connecting the head and tail with the single tooth profile A1B1C1D1E1. This is repeated z times, where z represents the number of rotor teeth; the origin of the rotor profile of one rotor is O1, and the origin of the rotor profile of the other rotor is O2.

[0053] Furthermore, according to whether the spiral line segments B1C1 and C1D1 are of the same order spiral, it is divided into a symmetric spiral rotor profile and an asymmetric spiral rotor profile. The spiral order is represented by n, and generally an integer is taken.

[0054] In a possible implementation manner, the profile equation of the spiral is as follows:

[0055]

[0056] In the formula, n i represents the specific spiral profile order, and a e , b e are adjustable geometric parameters of the profile.

[0057] Further, the parametric equation of the spiral line segment B1C1 is:

[0058]

[0059]

[0060] In the formula, r p , r m , n, P 1brespectively represent the pitch radius of the rotor, the addendum radius of the rotor, the order of the rotor spiral curve, and the coordinate parameter matrix of the profile line B1C1; the superscript semicolon represents the matrix transpose, is the central angle of the rotor spiral curve segment B1C1.

[0061] Furthermore, is solved according to the following equations:

[0062]

[0063] The above equation establishes a Cartesian two-dimensional rectangular coordinate system with the center of the rotor pitch circle as the coordinate origin. In the equation, y' represents the curve slope, and y represents the ordinate value of the curve in the rotor coordinate system. The solution is obtained as:

[0064]

[0065] And so on, the profile line central angles corresponding to each spiral curve segment and the spiral curve envelope segments A1B1, B1C1, C1D1, and D1E1 are obtained respectively Thus, the parametric equation of the complete spiral curve segment is obtained.

[0066] Taking the centers O1 and O2 of the rotor pitch circles of the female rotor and the male rotor as the origins respectively, two Cartesian two-dimensional rectangular coordinate systems O1X1Y1 and O2X2Y2 of the rotors are established. Thus, the relationship between the coordinate changes between the rotors conforms to the following formula:

[0067]

[0068]

[0069]

[0070] In the above 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, and respectively satisfy the following relational expressions:

[0071]

[0072] In the formula, z2 and z1 respectively represent the number of teeth of the two rotors, respectively represent the rotor central angles corresponding to the rotor profile line segments A1B1, B1C1, C1D1, and D1E1.

[0073] In a possible implementation, the profile coordinate parameter matrix P of the spiral envelope line segment B2C2 2b is obtained by transformation from the following formula:

[0074]

[0075] In the formula, P 1b is the profile coordinate parameter matrix of the profile B1C1, and P 2b is the profile coordinate parameter matrix of the profile B2C2. 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.

[0076] According to the plane meshing theorem, substituting the following meshing envelope condition expression into the profile coordinate parameter matrix expression of the B2C2 profile, P 2b can be solved to obtain the B2C2 profile:

[0077]

[0078] In the formula, D is the differential operator, θ is the meshing angle of the rotor curve, is the coordinate system rotation angle parameter variable, and x and y are the P 2b two-dimensional position parameter variables;

[0079] And so on, through the profile parameter matrices P 2a , P 1b , P 1c , P 2d of the tip spiral rotor profiles A2B2, B1C1, C1D1, D2E2, the profile parameter matrices P 1a , P 2b , P 2c , P 1d of the root spiral envelope rotor profiles A1B1, B2C2, C2D2, D1E1 are obtained. The complete profile parameter matrices P1 and P2 of the two rotors are as follows:

[0080]

[0081] In the embodiment of the present invention, the profile parameters of the twisted-lobe Roots compressor rotor take z1 = z2 = n1 = n2 = 2, 3, 4, 5, Figure 2 and the obtained symmetric rotor profiles are as shown in Figure 2 (a) to (d) of

[0082] In the embodiment of the present invention, the profile parameters of the twisted-lobe Roots compressor rotor take z1 = z2 = 3, n1 = 2, n2 = 6, and the obtained asymmetric rotor profiles, envelope line clusters and three-dimensional structures are respectively as shown in Figure 3 ,Figure 4 , Figure 5 as shown

[0083] Another embodiment of the present invention further provides a twisted-lobe Roots compressor having the spiral twisted-lobe Roots rotor described above.

[0084] Another embodiment of the present invention further provides a twisted-lobe Roots expander having the spiral twisted-lobe Roots rotor described above.

[0085] A design method for the spiral twisted-lobe Roots rotor described above includes the following steps:

[0086] Select the center distance O1O2 of the rotor, the number of rotor teeth z, and the tip circle radius r according to the volume size and pumping rate m ;

[0087] The tooth profiles of the spiral lines of different orders have different meshing lines and force characteristics. In the actual application process, according to the sealing requirements and force performance requirements of the specific usage scenario, optimize and select the order n of the spiral line segment B1C1 and the spiral line segment C1D1 i ;

[0088] Using the parameters selected above, construct the tooth profile of the spiral twisted-lobe Roots rotor.

[0089] The tooth profile of the spiral twisted-lobe Roots rotor proposed by the present invention is entirely composed of spiral lines and their envelopes. Compared with the prior art, the tooth profile has five adjustable tooth profile parameters, including the spiral order, the center distance of the rotor, the number of rotor teeth, and two geometric tooth profile parameters, and has a greater optimization space in tooth profile design and adaptability; the tooth profile can obtain single-tooth symmetric and asymmetric tooth profiles according to different values of the order of the single-tooth spiral line segment equation; the tooth profile has a shorter contact line, which can effectively improve the overall performance of the twisted-lobe Roots compressor. In addition, the present invention can also flexibly adjust the shape of the rotor tooth profile according to the design working conditions, and the volumetric efficiency, energy-saving performance, and dynamic characteristics of the optimized twisted-lobe Roots compressor are improved.

[0090] 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 described 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 spiral twisted lobe Roots rotor, characterized in that: It includes a female rotor and a male rotor with the same profile structure. The tooth profile of a single tooth of one rotor, A1B1C1D1E1, is composed of an involute envelope segment A1B1, an involute segment B1C1, an involute segment C1D1, and an involute envelope segment D1E1 connected in sequence. During the reverse rotation of the two rotors, continuous and correct meshing can be achieved. The involute envelope segment A1B1 of one rotor meshes with the involute segment A2B2 of the other rotor, the involute segment B1C1 meshes with the involute envelope segment B2C2 of the other rotor, the involute segment C1D1 meshes with the involute envelope segment C2D2 of the other rotor, and the involute envelope segment D1E1 meshes with the involute segment D2E2 of the other rotor. The complete rotor profile is formed by rotating the single-tooth profile A1B1C1D1E1 around the origin of the rotor profile and then connecting the head and tail with the single-tooth profile A1B1C1D1E1. This is repeated z times, where z represents the number of rotor teeth. The origin of the rotor profile of one rotor is O1, and the origin of the rotor profile of the other rotor is O2. According to whether the spiral line segment B1C1 and the spiral line segment C1D1 are spiral lines of the same order, it is divided into a symmetric spiral rotor profile and an asymmetric spiral rotor profile, and the spiral order is represented by n; The spiral profile equation is as follows: where n i represents the specific order of the spiral profile, and a e , b e are adjustable geometric parameters of the profile; The parametric equation of the spiral line segment B1C1 is: where r p , r m , n, and P 1b represent the rotor pitch radius, the rotor addendum radius, the rotor spiral order, and the coordinate parameter matrix of profile B1C1, respectively; the superscript semicolon represents matrix transpose, is the central angle of the rotor spiral segment B1C1.

2. The spiral twisted lobe Roots rotor according to claim 1, characterized in that, Solve according to the following equation: The above equation establishes a Cartesian two-dimensional rectangular coordinate system with the center of the rotor pitch circle as the coordinate origin. In the equation, y′ represents the curve slope, and y represents the ordinate value of the curve in the rotor coordinate system. The solution is obtained as follows: And so on, the involute center angles corresponding to each involute line segment and the involute envelope line segments A1B1, B1C1, C1D1, and D1E1 are obtained respectively. Thus, the parametric equation of the complete involute line segment is obtained.

3. The spiral twisted lobe Roots rotor according to claim 2, characterized in that, Taking the centers O1 and O2 of the rotor pitch circles of the female rotor and the male rotor as the origins respectively, two Cartesian two-dimensional coordinate systems O1X1Y1 and O2X2Y2 of the rotors are established. Thus, the relationship of the coordinate change between the rotors conforms to the following equation: The above formula M rot,1 , M rot,2 , M stat,1,2 respectively represent the coordinate transformation matrix of the rotation of the O1X1Y1 coordinate system around the origin, the coordinate transformation matrix of the rotation of the O2X2Y2 coordinate system 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 center distance of the rotor center, and respectively satisfy the following relational expressions: wherein, z2 and z1 respectively represent the number of teeth of two rotors, respectively represent the central angles of the rotor corresponding to the rotor profile line segments A1B1, B1C1, C1D1, and D1E1.

4. The spiral twisted lobe Roots rotor according to claim 3, characterized in that, Form line coordinate parameter matrix P of the spiral envelope line segment B2C2 2b Obtained by transformation from the following formula: Wherein, P 1b is the coordinate parameter matrix of the profile line B1C1, and P 2b is the coordinate parameter matrix of the profile line B2C2. 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; According to the plane meshing theorem, the above equation is solved through the following equation to obtain the parametric equation of the spiral envelope line segment B2C2 profile: where D is the differential operator, θ is the meshing angle of the rotor curve, is the coordinate system rotation angle parameter variable, and x, y are the P 2b two-dimensional position parameter variables; By analogy, the profile parameter matrix P of the rotor profile A2B2, B1C1, C1D1, and D2E2 is obtained. 2a , P 1b , P 1c , P 2d , and obtain the profile parameter matrix P of the tooth root spiral envelope rotor profile A1B1, B2C2, C2D2, D1E1 1a , P 2b , P 2c , P 1d ; The complete profile parameter matrices P1 and P2 of the two rotors are as follows:

5. A twisted-lobe Roots compressor, characterized in that, A spiral twisted-lobe Roots rotor as described in any one of claims 1-4.

6. A twisted-leaf Roots expander, characterized in that A spiral twisted-lobe Roots rotor as described in any one of claims 1-4.

7. A design method of a spiral twisted lobe Roots rotor as described in any one of claims 1-4, characterized in that, Including the following steps: Select the rotor center distance |O1O2|, the number of rotor teeth z, and the addendum circle radius r according to the volume and the pumping speed m ; The profiles of spirals of different orders have different meshing lines and force characteristics. In actual application, the order n of spiral segment B1C1 and spiral segment C1D1 is determined according to the sealing requirements and force performance requirements of specific usage scenarios. i Make optimal selections; Using the selected parameters above, construct the profile of the spiral twisted-lobe Roots rotor.

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