A helical gear

Abstract

The present application discloses a helical gear, and the web portion of the helical gear includes a first web, a second web, and a plurality of connecting columns; the first web and the second web are arranged axially; the first web is in an annular shape; the second web includes a body and a connecting body, the body is in an annular shape, and its inner edge is connected to a shaft connecting portion; the connecting body is used to connect the body and the helical tooth portion, and two line segments formed by two surfaces of the connecting body facing away from each other in a cross-section passing through the rotation axis of the helical gear are parallel to each other and both inclined relative to the rotation axis; the connecting columns extend axially and are evenly distributed circumferentially around the rotation axis, and the connecting columns are used to connect two surfaces of the first web and the body facing each other and are close to the connecting body in position. The above-mentioned helical gear has an innovative configuration and realizes lightweight under the premise of ensuring that the stress requirements are met.

Description

Technical Field

[0001] The present application relates to a helical gear. Background Art

[0002] The transmission system is one of the three key moving components of a helicopter and is an essential power transmission component for the power output of a turboshaft engine. Its performance largely determines the overall performance of the helicopter. As the core component of the transmission system, gears / gear trains have always attracted the attention of researchers. In terms of gear design optimization, domestic and foreign scholars have carried out preliminary research. These studies mainly focus on the size optimization of conventional solid configuration gears, and most of them are carried out under simple working conditions and single-discipline conditions, and the weight reduction potential of advanced optimization design techniques has not been fully explored. In particular, with the significant increase in the demand for the transmission power of the reducer in the transmission system, the loads borne by the gears are becoming larger and more complex, the self-structure size is larger and the weight is heavier, the dynamic problems are more prominent, and the lightweight design requirements under complex working conditions are more urgent. Summary of the Invention

[0003] The purpose of the present application is to overcome the above-mentioned defects or problems in the background art and provide a helical gear with an innovative configuration that can achieve lightweight while meeting the stress requirements.

[0004] To achieve the above purpose, the following technical solutions are adopted:

[0005] A helical gear, which sequentially includes an axially connecting portion, a web portion, and a helical tooth portion that are integrally connected to each other from the inside to the outside in the radial direction. Among them, the web portion includes a first web, a second web, and a plurality of connecting columns; the web portion includes a first web, a second web, and a plurality of connecting columns; the first web and the second web are arranged along the rotation axis direction of the helical gear, and the first web is closer to the tooth top surface of the helical tooth portion; the first web is circular, its inner edge is connected to the axially connecting portion, and its outer edge is connected to the helical tooth portion; the first web has two surfaces perpendicular to the rotation axis; the second web includes a body and a connecting body that are integrally connected to each other, the body is circular, its inner edge is connected to the axially connecting portion, and its outer edge is connected to the connecting body, the body has two surfaces perpendicular to the rotation axis, the connecting body is used to connect the body and the helical tooth portion, and two surfaces of the connecting body facing away from each other form two line segments that are parallel to each other and inclined relative to the rotation axis in a cross-section passing through the rotation axis; the connecting columns extend axially and are evenly distributed in the circumferential direction around the rotation axis, and the connecting columns are used to connect two opposite surfaces of the first web and the body and are located close to the connecting body.

[0006] Further, a plurality of first holes are circumferentially and uniformly distributed on the first web plate around the rotation axis. The number of the first holes is the same as that of the connecting columns. The first holes penetrate through two surfaces of the first web plate in the direction of the rotation axis, and their openings are at the outer edge of the first web plate.

[0007] Further, the projection of the first hole on the projection plane perpendicular to the rotation axis includes a first straight line segment, a second straight line segment and a first arc segment. The first straight line segment and the second straight line segment are both connected to the outer edge of the first web plate and are both located on the straight line passing through the projection of the rotation axis on the projection plane. The first arc segment connects the first straight line segment and the second straight line segment.

[0008] Further, the connecting body includes a plurality of connecting sub-bodies circumferentially and uniformly distributed around the rotation axis. The number of the connecting sub-bodies is the same as that of the connecting columns; the intervals between the connecting sub-bodies form second holes.

[0009] Further, the projection of the second hole on the projection plane is successively composed of a second arc segment, a third arc segment, a fourth arc segment, a third straight line segment and a fifth arc segment. The second arc segment is connected to the inner edge of the helical tooth portion. The fourth arc segment is located on the projection of the outer edge of the body. The third arc segment connects the second arc segment and the fourth arc segment. The fifth arc segment is connected to the inner edge of the helical tooth portion. The third straight line segment connects the fourth arc segment and the fifth arc segment.

[0010] Further, the helical gear further includes a transition portion. The transition portion is integrally connected with the helical tooth portion and the first web plate, and is used for connecting the inner edge of the helical tooth portion and the surface of the first web plate facing away from the second web plate. The transition portion has a sixth arc segment in the cross section passing through the rotation axis, and the sixth arc segment bends towards the direction close to the first web plate.

[0011] Further, the number of the connecting columns is 12.

[0012] Further, the distance between two surfaces of the first web plate is greater than the distance between two surfaces of the body, and is also greater than the distance between two surfaces of the connecting body; the area of the second hole on the projection plane is greater than the area of the first hole on the projection plane.

[0013] Further, when the tangential component of the meshing force on the tooth of the helical gear is less than or equal to 81000 N, the axial component of the meshing force on the tooth is less than or equal to 23000 N, the radial component of the meshing force on the tooth is less than or equal to 53000 N, and the rotational speed is less than or equal to 323 rpm, if the total mass of the helical part is less than or equal to 20 kg, the yield strength of the material used for the web part is greater than or equal to 700 Mpa and the material density is less than or equal to 7.86 g / cm 3 , then when 113 ≤ R0 ≤ 120 and 176.85 ≤ R1 ≤ 201.4, the following parameters of the helical gear are: R2 ≥ R1 - 32.055; R3 ≤ R1 - 46.4; R4 ≥ 173.585; r1 ≥ 8; r2 ≤ 15; r3 ≤ 7.5; r4 ≤ 7.5; r5 ≥ 1.7; w0 ≥ 51.5; w3 ≥ 8; where, R0 is the radius of the inner edge of the web part, in mm; R1 is the radius of the outer edge of the web part, in mm; R2 is the radius of the outer edge of the body, in mm; R3 is the distance between the center of the projection of the connecting column on the projection plane and the rotation axis, in mm; R4 is the distance between the center of the first arc segment and the rotation axis, in mm; r1 is the radius of the connecting column on the projection plane, in mm; r2 is the radius of the first arc segment, in mm; r3 is the radius of the third arc segment, in mm; r4 is the radius of the fifth arc segment, in mm; r5 is the radius of the sixth arc segment, in mm; w0 is the distance between the surface of the first web away from the body and the surface of the body away from the first web, in mm; w1 is the distance between the two surfaces of the first web, in mm; w2 is the distance between the two surfaces of the body, in mm; w3 is the distance between the two surfaces of the connecting body, in mm.

[0014] Further, the parameters of the helical gear are as follows: ∝ = 153.33°; ∠O1OO2 = 5.35°; ∠O1OA = 3.37°; ∠OAB = 3.37°; ∠BOC = 17.9°; ∠OCG = 154.2°; where ∝ is the angle between the intersection line of the surface of the connecting body in the cross-section passing through the rotation axis and the intersection line of the surface of the body in the cross-section passing through the rotation axis; ∠O1OO2 is the angle between the perpendicular line from the center of the projection of the connecting column on the projection plane to the rotation axis and the perpendicular line from the center of the first arc segment to the rotation axis; ∠O1OA is the angle between the perpendicular line from the center of the projection of the connecting column on the projection plane to the rotation axis and the perpendicular line from the intersection point of the extension line of the third straight line segment and the inner edge of the helical tooth part to the rotation axis; ∠OAB is the angle between the perpendicular line from the intersection point of the extension line of the third straight line segment and the inner edge of the helical tooth part to the rotation axis and the third straight line segment; ∠BOC is the angle between the perpendicular line from the intersection point of the third straight line segment and the outer edge of the body to the rotation axis and the perpendicular line from the intersection point of the arc extension line of the second arc segment and the outer edge of the body to the rotation axis; ∠OCG is the angle between the perpendicular line from the intersection point of the arc extension line of the second arc segment and the outer edge of the body to the rotation axis and the tangent line of the second arc segment passing through this intersection point.

[0015] Compared with the prior art, the above solution has the following beneficial effects:

[0016] For the helical gear involved in this application, its web part is composed of a first web, a second web and several connecting columns, which is lighter in weight and meets the requirements of stress and deformation. Compared with the webs in the prior art, lightweighting is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments, the following briefly introduces the drawings to be used:

[0018] Figure 1 It is the front view of the helical gear in the embodiment;

[0019] Figure 2 It is the rear view of the helical gear in the embodiment;

[0020] Figure 3 is Figure 1 the X-X cross-sectional view of;

[0021] Figure 4 For Figure 3 the partial enlarged view of part E of;

[0022] Figure 5 For Figure 3 the Y-Y cross-sectional view of;

[0023] Figure 6 is Figure 5 Partial enlarged view of part F;

[0024] Figure 7 is Figure 2 Partial enlarged view of part P;

[0025] Description of main reference numerals in part:

[0026] Helical gear 1; shaft connection part 2; web part 3; helical tooth part 4; first web 5; second web 6, connecting column 7; transition part 8; body 9; connecting sub-body 10; first hole 11; second hole 12. Detailed implementation manners

[0027] In the claims and the description, unless otherwise defined, the terms "first", "second", "third", etc. are used to distinguish different objects, rather than to describe a specific order.

[0028] In the claims and the description, unless otherwise defined, the terms "center", "lateral", "longitudinal", "horizontal", "vertical", "top", "bottom", "inner", "outer", "upper", "lower", "front", "rear", "left", "right", "clockwise", "counterclockwise", etc. indicate the orientation or positional relationship based on the orientation and positional relationship shown in the drawings, and are only for the convenience of simplified description, rather than implying that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation.

[0029] In the claims and the description, unless otherwise defined, the term "fixed connection" or "fixedly connected" shall be understood in a broad sense, that is, any connection method without displacement relationship and relative rotation relationship between the two, that is, including non-detachable fixed connection, detachable fixed connection, being integrally connected, and being fixedly connected through other devices or elements.

[0030] In the claims and the description, unless otherwise defined, the terms "comprising", "having" and their variants mean "including but not limited to".

[0031] Next, the technical solutions in the embodiments will be described clearly and completely with reference to the drawings.

[0032] Refer to Figure 1 、 Figure 2 and Figure 3 , as shown in the figure, the helical gear 1 in this embodiment sequentially includes a shaft connection part 2, a web part 3, a helical tooth part 4 and a transition part that are integrally connected to each other from the inside to the outside in the radial direction. Among them, the shaft connection part 2 and the helical tooth part 4 belong to the prior art and are not improved in this application, so they will not be elaborated here.

[0033] The web part 3 includes a first web 5, a second web 6 and a plurality of connecting columns 7.

[0034] The first web plate 5 and the second web plate 6 are arranged along the rotation axis O of the helical gear 1, and the first web plate 5 is closer to the tooth top surface of the helical tooth portion 4.

[0035] As Figure 1 shown, the first web plate 5 is annular, its inner edge is connected to the shaft connection portion 2, and its outer edge is connected to the helical tooth portion 4. As Figure 3 and Figure 4 shown, the first web plate 5 has two surfaces perpendicular to the rotation axis O of the helical gear 1.

[0036] As Figure 5 and Figure 6 shown, in this embodiment, a plurality of first holes 11 are evenly distributed along the circumferential direction of the first web plate 5. The number of the first holes 11 is the same as the number of the connecting columns 7, both being 12. The first holes 11 penetrate through the two surfaces of the first web plate 5 in the rotation axis direction, and their openings are at the outer edge of the first web plate 5. Specifically, the projection of the first hole 11 on the projection plane perpendicular to the rotation axis includes a first straight line segment KL, a second straight line segment NM, and a first arc segment LM. The first straight line segment KL and the second straight line segment NM are both connected to the outer edge of the first web plate 5 and are both located on the straight line passing through the projection of the rotation axis on the projection plane. The first arc segment LM connects the first straight line segment KL and the second straight line segment NM.

[0037] As Figure 2 , Figure 3 , Figure 4 and Figure 7 shown, the second web plate 6 includes an integrated body 9 and a connecting body. The body 9 is annular, its inner edge is connected to the shaft connection portion 2, and its outer edge is connected to the connecting body. The body 9 has two surfaces perpendicular to the rotation axis of the helical gear 1. The connecting body is used to connect the body 9 and the helical tooth portion 4. The two surfaces of the connecting body facing away from each other form two line segments that are parallel to each other and are both inclined with respect to the rotation axis of the helical gear 1 in the cross-section passing through the rotation axis of the helical gear 1.

[0038] As Figure 2 and Figure 7As shown, in this embodiment, the connecting body includes a number of connecting sub-bodies 10 that are circumferentially distributed around the rotation axis of the helical gear 1. The number of connecting sub-bodies 10 is the same as the number of connecting columns 7, both being 12. The intervals between the connecting sub-bodies 10 form the second holes 12. The projection of the second holes 12 on the projection plane is successively composed of a second arc segment DH, a third arc segment HI, a fourth arc segment IB, a third straight segment BJ, and a fifth arc segment JK. Among them, the second arc segment DH is connected to the inner edge of the helical tooth part 4, the fourth arc segment IB is located on the projection of the outer edge of the body 9, and the third arc segment HI connects the second arc segment DH and the fourth arc segment IB. The fifth arc segment KJ is connected to the inner edge of the helical gear 1, and the third straight segment JB connects the fourth arc segment IB and the fifth arc segment KJ.

[0039] As Figure 3 and Figure 4 shown, the connecting columns 7 extend axially. The connecting columns 7 are circumferentially distributed around the rotation axis of the helical gear 1, and the number of them is 12. The connecting columns 7 are used to connect two opposite surfaces of the first web 5 and the body 9 and are located close to the connecting body.

[0040] As Figure 4 shown, the transition part 8 is integrally connected with the helical tooth part 4 and the first web 5, and is used to connect the inner edge of the helical tooth part 4 and the surface of the first web 5 facing away from the second web 6. The transition part 8 has a sixth arc segment in the cross-section passing through the rotation axis, and the sixth arc segment bends towards the direction close to the first web 5.

[0041] The above technical solution provides an innovative configuration for those skilled in the art to design a helical gear web. Compared with the traditional web structure, this configuration realizes lightweight and can meet the stress requirements. As a more specific design guidance, when adopting this configuration and the number of connecting columns 7 can be 12, the distance between the two surfaces of the first web 5 is greater than the distance between the two surfaces of the body 9, and also greater than the distance between the two surfaces of the connecting body; the area of the second holes 12 on the projection plane is greater than the area of the first holes 11 on the projection plane.

[0042] As a more specific design guidance, refer to Figure 4 , Figure 6 and Figure 7 , when the working conditions of the helical gear 1 are that the tangential component of the meshing force received is less than or equal to 81000N, the axial component of the tooth meshing force received is less than or equal to 23000N, the radial component of the tooth meshing force received is less than or equal to 53000N, and the rotational speed is less than or equal to 323 rpm. If the total mass of the helical tooth part 4 is less than or equal to 20 kg, the yield strength of the material used for the web part 3 is greater than or equal to 700 Mpa, and the material density is less than or equal to 7.86 g / cm 3, when 113 ≤ R0 ≤ 120 and 176.85 ≤ R1 ≤ 201.4; then the following parameters of the helical gear 1 are: R2 ≥ R1 - 32.055; R3 = 1 - 46.4; R4 ≥ 173.585; r1 ≥ 8; r2 ≤ 15; r3 ≤ 7.5; r4 ≤ 7.5; r5 ≥ 1.7; w0 ≥ 51.5; w3 ≥ 8; where, R0 is the radius of the inner edge of the web portion 3, in mm; R1 is the radius of the outer edge of the web portion 3, in mm; R2 is the radius of the outer edge of the body 9, in mm; R3 is the distance between the center of the projection of the connecting column 7 on the projection plane and the rotation axis, in mm; R4 is the distance between the center of the first arc segment LM and the rotation axis, in mm; r1 is the radius of the connecting column 7 on the projection plane, in mm; r2 is the radius of the first arc segment LM, in mm; r3 is the radius of the third arc segment HI, in mm; r4 is the radius of the fifth arc segment KJ, in mm; r5 is the radius of the sixth arc segment, in mm; w0 is the distance between the surface of the first web 5 away from the body 9 and the surface of the body 9 away from the first web 5, in mm; w1 is the distance between the two surfaces of the first web 5, in mm; w2 is the distance between the two surfaces of the body 9, in mm; w3 is the distance between the two surfaces of the connecting body, in mm.

[0043] Specifically in this embodiment, the helical gear 1 is made of 9310 steel with a density of 7.86 g / cm 3 and the material yield strength is greater than or equal to 940 Mpa. The input loads are all taken as the maximum, that is, the tangential component of the meshing force is equal to 81000 N, the axial component of the meshing force on the tooth is equal to 23000 N, the radial component of the meshing force on the tooth is equal to 53000 N and the rotational speed is equal to 323 rpm. R0 is taken as 113 mm, R1 is taken as 201.4 mm, R2 is taken as 169.345 mm, R3 is taken as 155 mm, w1 is 10 mm, w2 is 8 mm, and w3 is 8 mm.

[0044] Other main parameters of the helical gear 1 in the embodiment include: ∝ = 153.33°; ∠O1OO2 = 5.35°; ∠O1OA = 3.37°; ∠OAB = 3.37°; ∠BOC = 17.9°; ∠OCG = 154.2°. Among them, ∝ is the angle between the intersection line of the surface of the connecting body in the cross-section passing through the rotation axis and the intersection line of the surface of the body 9 in the cross-section passing through the rotation axis; ∠O1OO2 is the angle between the perpendicular line from the center of the projection of the connecting column 7 on the projection plane to the rotation axis and the perpendicular line from the center of the first arc segment LM to the rotation axis; ∠O1OA is the angle between the perpendicular line from the center of the projection of the connecting column 7 on the projection plane to the rotation axis and the perpendicular line from the intersection point of the extension line of the third straight line segment BJ and the inner edge of the helical tooth part 4 to the rotation axis; ∠OAB is the angle between the perpendicular line from the intersection point of the extension line of the third straight line segment BJ and the inner edge of the helical tooth part 4 to the rotation axis and the third straight line segment BJ; ∠BOC is the angle between the perpendicular line from the intersection point of the third straight line segment BJ and the outer edge of the body 9 to the rotation axis and the perpendicular line from the intersection point of the arc extension line of the second arc segment DH and the outer edge of the body 9 to the rotation axis; ∠OCG is the angle between the perpendicular line from the intersection point of the arc extension line of the second arc segment and the outer edge of the body to the rotation axis and the tangent line of the second arc segment passing through this intersection point.

[0045] If the web part 3 of the helical gear 1 for the same environment is solid, its volume is 4.489*10 6 mm 3 , and the mass is 35.287 kg. The volume of the helical gear 1 in this embodiment is 1.331*10 6 mm 3 , and the mass is 10.458 kg. Compared with the known web, the volume is smaller and the mass is lighter. The mass can be reduced by 70.363%, achieving a good lightweight effect.

[0046] Perform a static analysis on the above helical gear 1. The mesh division size is 2 mm, and the number of network elements is 1,044,250. The equivalent stress (von-Mises stress) of its web part 3 is between 477.46 Mpa and 592.09 Mpa, and the stress is much smaller than the material yield strength. Therefore, reliable operation can be ensured.

[0047] The above description of the specification and the embodiment is used to explain the protection scope of the present application, but does not constitute a limitation on the protection scope of the present application.

Claims

1. A helical gear, which sequentially includes an axially connecting portion, a web portion, and a helical tooth portion that are integrally connected to each other from inside to outside in the radial direction, and is characterized in that: The web portion includes a first web, a second web, and a plurality of connecting columns; the first web and the second web are arranged along the rotation axis direction of the helical gear, and the first web is closer to the tooth top surface of the helical tooth portion; The first web is in a circular ring shape, its inner edge is connected to the axially connecting portion, and its outer edge is connected to the helical tooth portion; the first web has two surfaces perpendicular to the rotation axis; The second web includes a body and a connecting body that are integrally connected to each other. The body is in a circular ring shape, its inner edge is connected to the axially connecting portion, and its outer edge is connected to the connecting body. The body has two surfaces perpendicular to the rotation axis. The connecting body is used to connect the body and the helical tooth portion. Two surfaces of the connecting body facing away from each other form two line segments that are parallel to each other and inclined relative to the rotation axis in a cross-section passing through the rotation axis; The connecting columns extend axially and are circumferentially evenly distributed around the rotation axis. The connecting columns are used to connect two surfaces of the first web and the body facing each other, and their positions are close to the connecting body; A plurality of first holes are circumferentially evenly distributed on the first web around the rotation axis. The number of the first holes is the same as the number of the connecting columns. The first holes penetrate through two surfaces of the first web in the rotation axis direction and open at the outer edge of the first web; The projection of the first hole on a projection plane perpendicular to the rotation axis includes a first straight line segment, a second straight line segment, and a first arc segment. The first straight line segment and the second straight line segment are both connected to the outer edge of the first web and are both located on a straight line passing through the projection of the rotation axis on the projection plane. The first arc segment connects the first straight line segment and the second straight line segment; The connecting body includes a plurality of connecting sub-bodies that are circumferentially evenly distributed around the rotation axis. The number of the connecting sub-bodies is the same as the number of the connecting columns; intervals between the connecting sub-bodies form second holes; The projection of the second hole on the projection plane is sequentially composed of a second arc segment, a third arc segment, a fourth arc segment, a third straight line segment, and a fifth arc segment. The second arc segment is connected to the inner edge of the helical tooth portion. The fourth arc segment is located on the projection of the outer edge of the body. The third arc segment connects the second arc segment and the fourth arc segment. The fifth arc segment is connected to the inner edge of the helical tooth portion. The third straight line segment connects the fourth arc segment and the fifth arc segment.

2. The helical gear according to claim 1, wherein The helical gear further includes a transition portion, which is integrally connected to the helical tooth portion and the first web, and is used to connect the inner edge of the helical tooth portion and the surface of the first web facing away from the second web. The transition portion has a sixth arc segment in a cross-section passing through the rotation axis, and the sixth arc segment bends towards the direction close to the first web.

3. A helical gear according to claim 2, characterized in that, The number of the connecting columns is 12.

4. A helical gear according to claim 3, characterized in that, The distance between the two surfaces of the first web is greater than the distance between the two surfaces of the body and also greater than the distance between the two surfaces of the connecting body; the area of the second hole on the projection plane is greater than the area of the first hole on the projection plane.

5. A helical gear according to claim 4, characterized in that, When the tangential component of the meshing force on the teeth of the helical gear is less than or equal to 81000 N, the axial component of the meshing force on the teeth is less than or equal to 23000 N, the radial component of the meshing force on the teeth is less than or equal to 53000 N, and the rotational speed is less than or equal to 323 rpm, if the total mass of the helical part is less than or equal to 20 kg, the yield strength of the material used for the web part is greater than or equal to 700 Mpa and the material density is less than or equal to 7.86 g / cm 3 , then When and then The following parameters of the helical gear are: ； ； ； ； ； ； ； ； ； ； ; ； Wherein, is the radius of the inner edge of the web portion, in mm; is the radius of the outer edge of the web portion, in mm; is the radius of the outer edge of the said body, with the unit of mm; It is the distance between the center of the projection of the connecting column on the projection plane and the rotation axis, with the unit of mm; is the distance between the center of the first arc segment and the rotation axis, with the unit of mm; is the radius of the connecting column on the projection plane, with the unit of mm; is the radius of the first circular arc segment, in mm; is the radius of the third arc segment, in mm; is the radius of the fifth arc segment, in mm; is the radius of the sixth arc segment, in mm; is the distance between the surface of the first web away from the body and the surface of the body away from the first web, with the unit of mm; is the distance between two surfaces of the first web plate, with the unit of mm; is the distance between two surfaces of the body, in mm; is the distance between two surfaces of the connecting body, with the unit of mm.

6. A helical gear according to claim 5, characterized in that: The parameters of the helical gear are as follows: ； ； ； ； ； ； Wherein, is the included angle between the intersection line of the surface of the connecting body in the cross-section passing through the rotation axis and the intersection line of the surface of the body in the cross-section passing through the rotation axis; The included angle between the perpendicular line from the center of the projection of the connecting column on the projection plane to the rotation axis and the perpendicular line from the center of the first arc segment to the rotation axis; is the included angle between the perpendicular line from the center of the projection of the connecting column on the projection plane to the rotation axis and the perpendicular line from the intersection point of the extension line of the third straight line segment and the inner edge of the helical tooth part to the rotation axis; The included angle between the perpendicular line from the intersection point of the extension line of the third straight line segment and the inner edge of the helical tooth part to the rotation axis and the third straight line segment; is the included angle between the perpendicular line from the intersection point between the third straight-line segment and the outer edge of the body to the rotation axis and the perpendicular line from the intersection point between the arc extension line of the second arc segment and the outer edge of the body to the rotation axis; It is the included angle between the perpendicular line from the intersection point between the arc extension line of the second arc segment and the outer edge of the body to the rotation axis and the tangent line of the second arc segment passing through this intersection point.

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