A vacuum pump rotor profile and design method thereof

Abstract

The present application discloses a vacuum pump rotor profile and a design method thereof, comprising a first curved segment, a second curved segment, a third curved segment and a fourth curved segment which are closed and connected in sequence around the rotation axis of the rotor, and any two adjacent curved segments are axially symmetrically arranged; the first curved segment comprises a tooth top arc, a first arc, a second arc, an envelope arc, a third arc and a tooth root arc which are smoothly connected in sequence; along the radial direction of the rotor, the third arc is concave inwardly, and the radius of the first arc is equal to that of the third arc; the offset angles of the centers of the first arc and the third arc relative to the rotation axis of the rotor are equal; the centers of the tooth top arc and the tooth root arc coincide with the rotation axis of the rotor; compared with the prior art, the rotor profile described in the present application can effectively solve the defect of triangular gap in rotor meshing in the prior art, the gap between the rotors is uniform and plastic, and gapless meshing can also be achieved to meet the different working conditions of customers.

Description

Technical Field

[0001] The present application relates to the technical field of fluid conveying equipment, and in particular to a vacuum pump rotor profile and a design method thereof. Background Art

[0002] The vacuum pump mainly changes the volume of different chambers by rotating the rotor, thereby realizing the extraction and discharge of fluid, and the change of the chamber volume is mainly achieved by changing the rotor profile, that is, the rotor profile is not a regular shape such as a circle; there are various rotor profiles in the prior art, but when the two rotors rotate in meshing directions, a triangular gap will appear at the transition point between the pin peak top curve and the adjacent curve and at the transition point between the peak bottom curve and the adjacent curve, thereby causing a gap between the two rotors that are tangentially meshed. This gap will increase the internal leakage of the vacuum pump and reduce the vacuum pumping performance of the vacuum pump. Summary of the invention

[0003] The main purpose of the present application is to provide a vacuum pump rotor profile and a design method thereof, aiming to solve the defect of triangular gaps appearing when the rotors are meshed in the prior art.

[0004] This application achieves the above objectives through the following technical solutions:

[0005] A vacuum pump rotor profile, comprising a first curve, a second curve segment, a third curve segment and a fourth curve segment, around the rotation axis of the rotor, the first curve segment, the second curve segment, the third curve segment and the fourth curve segment are closed and connected in sequence; any two adjacent curve segments are axially symmetrically arranged;

[0006] The first curved segment includes a tooth top arc, a first arc, a second arc, an envelope arc, a third arc and a tooth root arc that are smoothly connected in sequence; along the radial direction of the rotor, the third arc is concave inward, and the radii of the first arc and the third arc are equal; the offset angles of the centers of the first arc and the third arc relative to the rotation axis of the rotor are equal; the centers of the tooth top arc and the tooth root arc coincide with the rotation axis of the rotor.

[0007] Accordingly, the present application also discloses a design method for the above-mentioned profile line, comprising the following steps:

[0008] Determine basic parameters according to the actual working condition of the rotor, wherein the basic parameters include the center distance A of two mutually meshing rotors, the number of teeth N, the maximum outer radius RX of two mutually meshing envelope arcs, and the radius RM of the tooth top arc;

[0009] Constructing a calculation coordinate system, wherein the calculation coordinate system includes a first symmetry axis and a second symmetry axis that are perpendicular to each other, and the origin of the calculation coordinate system is the rotation center of the profile;

[0010] Taking the rotation center as the center of the circle, and drawing analytical equations of the tooth addendum arc and the tooth root arc in the calculation coordinate system according to the tooth addendum arc radius RM and the center distance A respectively;

[0011] Determine analytical equations of the second arc and the envelope arc in the calculation coordinate system according to the maximum outer circle radius RX and the center distance A;

[0012] The analytical equations of the first arc and the third arc in the calculation coordinate system are determined respectively according to the maximum outer circle radius RX and the center distance A.

[0013] Optionally, the analytical equation expression of the tooth addendum arc in the calculation coordinate system is:

[0014] x=RMcost; y=RMsint; where x and y are the coordinates of any point on the curve in the plane rectangular coordinate system; t is the variable that relates the relationship between x and y, called the parameter, or parameter for short, and its range is 0≤t<2π; RM is the radius of the tooth top arc.

[0015] Optionally, the analytical equation of the root arc in the calculation coordinate system is expressed as: x=RNcost; y=RNsint; wherein RN is the radius of the root arc, and its expression is RN=A-RM; x, y are the coordinates of any point on the curve in the plane rectangular coordinate system; t is the variable that relates x and y, called the parameter, abbreviated as parameter, and its range is 0≤t<2π.

[0016] Optionally, determining analytical equations of the second arc and the enveloping arc in the calculation coordinate system according to the maximum outer circle radius RX and the center distance A respectively comprises the following steps:

[0017] Calculate the tangent angle M between the envelope arc and the second arc according to the number of teeth N;

[0018] Calculate the second arc radius R1 according to the maximum outer circle radius RX, the center distance A and the tangent angle M;

[0019] Calculate the distance B from the center of the second arc to the center of the tooth root arc according to the maximum outer circle radius RX, the center distance A and the tangent angle M;

[0020] Calculate the analytical equation of the second arc in the calculation coordinate system according to the second arc radius R1 and the distance B;

[0021] Calculate the analytical equation of the envelope arc in the calculation coordinate system according to the second arc radius R1 and the center distance A;

[0022] Optionally, the analytical equation expression of the second arc in the calculation coordinate system is x=R1cost; y=B+R1sint; the analytical equation expression of the envelope arc in the calculation coordinate system is Among them, x and y are the coordinates of any point on the curve in the plane rectangular coordinate system; t is the variable that relates x and y, called the parameter, and its range is 0≤t<2π.

[0023] Optionally, the calculation expression of the tangent angle is M=360° / 4N; the calculation expression of the second arc radius R1 is The calculation expression of the distance B is:

[0025] Optionally, determining analytical equations of the first arc and the third arc in the calculation coordinate system according to the maximum outer circle radius RX and the center distance A respectively includes the following steps:

[0026] Calculate the first arc radius R2 and the distance R4 between the first arc and the tooth root arc according to the tooth top arc radius RM and the tooth root arc radius RN;

[0027] Calculate an offset angle α of the first circular arc relative to the rotor rotation axis according to the distance R4, the distance B and the first circular arc radius R2;

[0028] Calculate an analytical equation of the first arc in the calculation coordinate system according to the first arc radius R2, the distance R4 between the first arc and the tooth root arc circle, and the offset angle α;

[0029] The analytical equation of the third arc in the calculation coordinate system is calculated according to the first arc radius R2, the tooth root arc radius and the offset angle β of the third arc relative to the rotor rotation axis.

[0030] Optionally, the analytical equation of the first arc in the calculation coordinate system is expressed as x=R4sinα+R2cost; y=R4cosα+R2sint; the analytical equation of the third arc in the calculation coordinate system is expressed as x=(RN+R3)cosβ+R3cost; y=(RN+R3)sinβ+R3sint; wherein R3=R2, β=α, x, y are the coordinates of any point on the curve in the plane rectangular coordinate system; t is the variable that relates x and y, called the parameter, abbreviated as parameter, and its range is 0≤t<2π.

[0031] Optionally, the calculation expression of the first arc radius R2 is: The calculation expression of the distance R4 between the first arc and the tooth root arc circle is: The calculation expression of the offset angle α of the first arc relative to the rotor rotation axis is:

[0032] Compared with the prior art, this application has the following beneficial effects:

[0033] The rotor profile of the present application includes a first curved segment, a second curved segment, a third curved segment and a fourth curved segment which are closed and connected in sequence around the rotation axis of the rotor, and any two adjacent curved segments are axially symmetrically arranged; the first curved segment includes a tooth top arc, a first arc, a second arc, an envelope arc, a third arc and a tooth root arc which are smoothly connected in sequence; along the radial direction of the rotor, the third arc is concave inwardly, and the radius of the first arc is equal to that of the third arc; the center of the first arc and the third arc has an equal offset angle relative to the rotation axis of the rotor; the center of the tooth top arc and the tooth root arc is angularly aligned with the rotor; The rotation axis coincides; accordingly, the present application also discloses a design method for the above-mentioned profile line, firstly determining the basic parameters and establishing a calculation coordinate system, then taking the rotation center as the center of the circle, drawing the analytical equations of the tooth top arc and the tooth root arc in the calculation coordinate system according to the tooth top arc radius RM and the center distance A respectively; then determining the analytical equations of the second arc and the envelope arc in the calculation coordinate system according to the maximum outer circle radius RX and the center distance A respectively, and finally determining the analytical equations of the first arc and the third arc in the calculation coordinate system according to the maximum outer circle radius RX and the center distance A respectively.

[0034] When two rotors with the same profile as described in the present application are meshed with each other, the mirror image line segments of the tooth top arc and the tooth root arc are meshed and tangent, the mirror image line segments of the first arc and the third arc are meshed and tangent, the second arc and the mirror image line segment of the envelope arc are meshed and tangent, the envelope arc and the mirror image line segment of the second arc are meshed and tangent, the third arc and the mirror image line segment of the first arc are meshed and tangent, and the tooth root arc and the mirror image line segment of the tooth top arc are meshed and tangent; similarly, when two rotors with the same Roots rotor profile are meshed with each other and run in different directions, the two Roots rotor profiles are meshed and tangent; so that the two rotors are in a gap-free state when they rotate in meshing, thereby preventing leakage from increasing inside the vacuum pump and improving the vacuum pumping performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A schematic structural diagram of a vacuum pump rotor profile provided in Embodiment 1 of the present application;

[0036] Figure 2 It is a schematic diagram of the meshing of two rotors;

[0037] Figure 3 A flowchart of a design method provided for implementation mode 2 of the present application;

[0038] Figure 4 A schematic diagram of the design method provided for implementation mode 2 of this application;

[0039] Figure numerals: 1 - first curve, 2 - second curve, 3 - third curve, 4 - fourth curve, 101 - tooth top arc, 102 - first arc, 103 - second arc, 104 - envelope arc, 105 - third arc, 106 - tooth root arc.

[0040] The purpose, features and advantages of this application will be further described in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0043] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0044] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, the meaning of "and / or" appearing in the full text includes three parallel schemes. Taking "A and / or B" as an example, it includes scheme A, or scheme B, or a scheme that satisfies both A and B. In addition, the technical solutions between the various embodiments can be combined with each other, but it must be based on the ability of ordinary technicians in the field to implement. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0045] Implementation Method 1

[0046] Reference Figure 1 This embodiment is an optional embodiment of the present application, which discloses a vacuum pump rotor profile. To facilitate the description of the rotor profile, a first symmetry axis and a second symmetry axis perpendicular to each other are marked on the rotor profile;

[0047] The rotor profile includes a first curve 1 end, a second curve 2 segment, a third curve 3 segment and a fourth curve 4 segment. Around the rotation axis of the rotor, the first curve 1 segment, the second curve 2 segment, the third curve 3 segment and the fourth curve 4 segment are closed and connected in sequence; any two adjacent curve segments are axially symmetrically arranged;

[0048] For example, in a clockwise direction, the first curve segment 1, the second curve segment 2, the third curve segment 3 and the fourth curve segment 4 are connected in sequence, and the first curve segment 1 is also connected to the fourth curve segment 4;

[0049] The first curve segment 1 is symmetrical with the second curve segment 2 about the first symmetry axis, the second curve segment 2 is symmetrical with the third curve segment 3 about the second symmetry axis, the third curve segment 3 is symmetrical with the fourth curve segment 4 about the first symmetry axis, and the fourth curve segment 4 is symmetrical with the first curve segment 1 about the first symmetry axis;

[0050] The first curve segment 1 includes a tooth top arc 101, a first arc 102, a second arc 103, an envelope arc 104, a third arc 105 and a tooth root arc 106 which are smoothly connected in sequence; along the radial direction of the rotor, the third arc 105 is concave inward, and the radii of the first arc 102 and the third arc 105 are equal; the offset angles of the centers of the first arc 102 and the third arc 105 relative to the rotation axis of the rotor are equal; the centers of the tooth top arc 101 and the tooth root arc 106 coincide with the rotation axis of the rotor.

[0051] Implementation Method 2

[0052] Reference Figure 2 and Figure 3 As another optional embodiment of the present application, this embodiment discloses a method for designing a vacuum pump rotor profile, comprising the following steps:

[0053] S1. Determine basic parameters according to the actual working condition of the rotor, wherein the basic parameters include the center distance A of two mutually meshing rotors, the number of teeth N, the maximum outer radius RX of two mutually meshing envelope arcs, and the radius RM of the tooth top arc;

[0054] Determine the basic parameters of the rotor according to the actual working condition of the rotor, wherein the basic parameters include the center distance A of two mutually meshing rotors, the number of teeth N, the maximum outer radius RX of two mutually meshing envelope arcs, and the radius RM of the tooth top arc;

[0055] S2. Constructing a calculation coordinate system, wherein the calculation coordinate system includes a first symmetry axis and a second symmetry axis that are perpendicular to each other, and the origin of the calculation coordinate system is the rotation center of the profile;

[0056] The cross section of the rotor's rotating shaft is used as the coordinate system plane, and the point formed by the cross section of the rotor's rotating shaft is used as the origin to construct a calculation coordinate system, wherein the X axis is the first symmetry axis and the Y axis is the second symmetry axis, thereby constructing a calculation coordinate system.

[0057] S3, taking the rotation center as the center of the circle, and drawing analytical equations of the tooth addendum arc and the tooth root arc in the calculation coordinate system according to the tooth addendum arc radius RM and the center distance A;

[0058] The analytical equation of the tooth top arc in the calculation coordinate system is calculated according to the tooth top arc radius RM and the center distance A. The specific expression of the analytical equation is x=RMcost; y=RMsint; wherein x, y are the coordinates of any point on the curve in the plane rectangular coordinate system; t is the variable that relates the relationship between x and y, called the parameter, referred to as parameter, and its range is 0≤t<2π; RM is the tooth top arc radius;

[0059] The tooth root arc radius RN is calculated according to the tooth top arc radius RM and the center distance A, and the expression of the tooth root arc RN is RN=A-RM;

[0060] Then, an analytical equation expression of the tooth root arc in the calculation coordinate system is constructed according to the tooth root arc radius. Specifically, the expression is x=RNcost, y=RNsint; x, y are the coordinates of any point on the curve in the plane rectangular coordinate system; t is a variable that relates the relationship between x and y, called a parameter, or parameter for short;

[0061] S4, determining analytical equations of the second arc and the envelope arc in the calculation coordinate system according to the maximum outer circle radius RX and the center distance A;

[0062] S41, calculating the tangent angle M between the envelope arc and the second arc according to the number of teeth N;

[0063] The calculation expression of the tangent angle is M=360° / 4N, which can be quickly calculated according to the set number of teeth N;

[0064] S42, calculating the second arc radius R1 according to the maximum outer circle radius RX, the center distance A and the tangent angle M;

[0065] The calculation expression of the second arc radius R1 is Substituting the tangent angle calculated in step S41, the maximum outer circle radius RX and the center distance A obtained in step S1 into the second arc radius R1 can be calculated;

[0066] S43, calculating the distance B from the center of the second arc to the center of the tooth root arc according to the maximum outer circle radius RX, the center distance A and the tangent angle M;

[0067] The calculation expression of the distance B from the center of the second arc to the center of the tooth root arc is: Substituting the tangent angle calculated in step S41, the maximum outer circle radius RX and the center distance A obtained in step S1 into the calculation result;

[0068] S44, calculating an analytical equation of the second arc in the calculation coordinate system according to the second arc radius R1 and the distance B;

[0069] The analytical equation of the second arc in the calculation coordinate system is expressed as x=R1cost, y=B+R1sint. Substituting the radius R1 and the distance B of the second arc calculated in step S43 into the analytical equation of the second arc in the calculation coordinate system can obtain the analytical equation of the second arc in the calculation coordinate system.

[0070] S45, calculating an analytical equation of the envelope arc in the calculation coordinate system according to the second arc radius R1 and the center distance A;

[0071] The analytical equation expression of the envelope arc in the calculation coordinate system is:

[0072]

[0073] Substituting the second arc radius R1 and distance B calculated in step S43 and the center distance A obtained in step S1 into the calculation result, the result can be obtained;

[0074] S5, determining analytical equations of the first arc and the third arc in the calculation coordinate system according to the maximum outer circle radius RX and the center distance A respectively;

[0075] S51, calculating the first arc radius R2 and the distance R4 between the first arc and the tooth root arc according to the tooth top arc radius RM and the tooth root arc radius RN;

[0076] The calculation expression of the first arc radius R2 is: Substitute the tooth top arc radius RM and tooth root arc radius RN to calculate;

[0077] The calculation expression of the distance R4 between the first arc and the tooth root arc circle is:

[0078] S52, calculating an offset angle α of the first circular arc relative to the rotor rotation axis according to the distance R4, the distance B and the first circular arc radius R2;

[0079] The calculation expression of the offset angle α of the first arc relative to the rotor rotation axis is:

[0081] Substitute the relevant parameters to calculate;

[0082] S53, calculating an analytical equation of the first arc in the calculation coordinate system according to the first arc radius R2, a distance R4 between the first arc and the tooth root arc, and an offset angle α;

[0083] The expression of the analytical equation of the first arc in the calculation coordinate system is x=R4sinα+R2cost; y=R4cosα+R2sint;

[0084] The analytical equation of the first arc in the calculation coordinate system can be calculated based on the parameters calculated in steps S51 and S52;

[0085] S54, calculating an analytical equation of the third arc in the calculation coordinate system according to the first arc radius R2, the tooth root arc radius and the offset angle β of the third arc relative to the rotor rotation axis.

[0086] The expression of the analytical equation of the third arc in the calculation coordinate system is x=(RN+R3)cosβ+R3cost;

[0087] Since the offset angle and radius of the third arc are equal to those of the first arc, the corresponding parameters of the third arc can be obtained according to steps S51 and S52, that is, R3=R2, β=α;

[0088] The above are only preferred embodiments of the present application, and are not intended to limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A vacuum pump rotor profile, characterized in that: It comprises a first curve (1), a second curve (2), a third curve (3) and a fourth curve (4), wherein the first curve (1), the second curve (2), the third curve (3) and the fourth curve (4) are sequentially closed and connected around the rotation axis of the rotor; any two adjacent curve segments are arranged axially symmetrically; The first curve (1) segment comprises a tooth top arc (101), a first arc (102), a second arc (103), an envelope arc (104), a third arc (105) and a tooth root arc (106) which are smoothly connected in sequence; along the radial direction of the rotor, the third arc (105) is concave inward, and the radii of the first arc (102) and the third arc (105) are equal; the offset angles of the centers of the first arc (102) and the third arc (105) relative to the rotation axis of the rotor are equal; and the centers of the tooth top arc (101) and the tooth root arc (106) coincide with the rotation axis of the rotor.

2. The design method of the profile according to claim 1, characterized in that: The following steps are involved: Determine basic parameters according to the actual working condition of the rotor, wherein the basic parameters include the center distance A of two mutually meshing rotors, the number of teeth N, the maximum outer radius RX of two mutually meshing envelope arcs, and the radius RM of the tooth top arc; Constructing a calculation coordinate system, wherein the calculation coordinate system includes a first symmetry axis and a second symmetry axis that are perpendicular to each other, and the origin of the calculation coordinate system is the rotation center of the profile; Taking the rotation center as the center of the circle, and drawing analytical equations of the tooth addendum arc and the tooth root arc in the calculation coordinate system according to the tooth addendum arc radius RM and the center distance A respectively; Determine analytical equations of the second arc and the envelope arc in the calculation coordinate system according to the maximum outer circle radius RX and the center distance A; The analytical equations of the first arc and the third arc in the calculation coordinate system are determined respectively according to the maximum outer circle radius RX and the center distance A.

3. The design method according to claim 2, characterized in that: The analytical equation expression of the tooth addendum arc in the calculation coordinate system is: x=RMcost; y=RMsint; where x and y are the coordinates of any point on the curve in the plane rectangular coordinate system; t is the variable that relates the relationship between x and y, called the parameter, or parameter for short, and its range is 0≤t<2π; RM is the radius of the tooth top arc.

4. The design method according to claim 2, characterized in that: The analytical equation of the root arc in the calculation coordinate system is expressed as: x=RNcost; y=RNsint; RN is the radius of the root arc, and its expression is RN=A-RM; x, y are the coordinates of any point on the curve in the plane rectangular coordinate system; t is the variable that relates x and y, called the parameter, and its range is 0≤t<2π.

5. The design method according to claim 2, characterized in that: The method of determining the analytical equations of the second arc and the envelope arc in the calculation coordinate system according to the maximum outer circle radius RX and the center distance A respectively comprises the following steps: Calculate the tangent angle M between the envelope arc and the second arc according to the number of teeth N; Calculate the second arc radius R1 according to the maximum outer circle radius RX, the center distance A and the tangent angle M; Calculate the distance B from the center of the second arc to the center of the tooth root arc according to the maximum outer circle radius RX, the center distance A and the tangent angle M; Calculate the analytical equation of the second arc in the calculation coordinate system according to the second arc radius R1 and the distance B; The analytical equation of the envelope arc in the calculation coordinate system is calculated according to the second arc radius R1 and the center distance A.

6. The design method according to claim 5, characterized in that: The analytical equation expression of the second arc in the calculation coordinate system is x=R1cost; y=B+R1sint; the analytical equation expression of the envelope arc in the calculation coordinate system is: Among them, x and y are the coordinates of any point on the curve in the plane rectangular coordinate system; t is the variable that relates x and y, called the parameter.

7. The design method according to claim 6, characterized in that: The calculation expression of the tangent angle is M=360° / 4N; the calculation expression of the second arc radius R1 is The calculation expression of the distance B is:

8. The design method according to claim 4, characterized in that: The step of respectively determining the analytical equations of the first arc and the third arc in the calculation coordinate system according to the maximum outer circle radius RX and the center distance A comprises the following steps: Calculate the first arc radius R2 and the distance R4 between the first arc and the tooth root arc according to the tooth top arc radius RM and the tooth root arc radius RN; Calculate an offset angle α of the first circular arc relative to the rotor rotation axis according to the distance R4, the distance B and the first circular arc radius R2; Calculate an analytical equation of the first arc in the calculation coordinate system according to the first arc radius R2, the distance R4 between the first arc and the tooth root arc circle, and the offset angle α; The analytical equation of the third arc in the calculation coordinate system is calculated according to the first arc radius R2, the tooth root arc radius and the offset angle β of the third arc relative to the rotor rotation axis.

9. The design method according to claim 8, characterized in that: The analytical equation of the first arc in the calculation coordinate system is expressed as x=R4sinα+R2cost; y=R4cosα+R2sint; the analytical equation of the third arc in the calculation coordinate system is expressed as x=(RN+R3)cosβ+R3cost; y=(RN+R3)sinβ+R3sint; wherein R3=R2, β=α, x, y are the coordinates of any point on the curve in the plane rectangular coordinate system; t is the variable that relates x and y, called the parameter, abbreviated as parameter, and its range is 0≤t<2π.

10. The design method according to claim 9, characterized in that: The calculation expression of the first arc radius R2 is: The calculation expression of the distance R4 between the first arc and the tooth root arc circle is: The calculation expression of the offset angle α of the first arc relative to the rotor rotation axis is:

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