Vacuum pump rotary vane and vacuum pump
Through the innovative design of the parent rotary plate and the child rotary plate, the hinge and torsion spring are connected to the child rotary plate to achieve independent suction, compression and exhaust process, which solves the problem of gas reflux of the single-stage rotary plate vacuum pump, improves the pumping efficiency and ultimate vacuum degree, and reduces costs.
Patent Information
- Application Number
- CN202510499728.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-21
- Publication Date
- 2025-07-08
AI Technical Summary
The existing single-stage rotary vacuum pump has serious gas reflux, resulting in low pumping efficiency, difficulty in further improving the limit vacuum, and the cost of double-stage rotary pump is relatively high.
The structural design of the parent rotary plate and the child rotary plate is adopted. The rotary plate is rotatable through the hinge connection and the torsion spring. A rotary plate suction hole and valve plate are installed on the child rotary plate. The child rotary plate is opened and closed by centrifugal force, forming an independent suction, compression and exhaust process to reduce gas reflux.
It improves the pumping efficiency of the vacuum pump, reduces gas reflux, improves the ultimate vacuum degree, and reduces costs.
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Figure CN120273904A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of vane devices of rotary vane vacuum pumps, and specifically, to a vane for a vacuum pump and a vacuum pump. Background Art
[0002] A rotary vane vacuum pump is a variable-volume gas transfer vacuum pump and is one of the most basic vacuum acquisition devices in vacuum technology. A rotary vane pump generally consists of a pump body, a rotor, vanes, end covers, etc. The rotor is eccentrically installed in the pump body and its outer circle is tangent to the inner surface of the pump body (this is an ideal state, and generally there is a very small gap between the two). Slots are provided on the rotor, and the vanes are installed in the slots. When the rotor rotates, the vanes always keep their tips in contact with the inner wall of the pump body by the action of centrifugal force and slide along the inner wall of the pump body. The mainstream rotary vane vacuum pump products on the market have two vanes and three vanes. Taking a two-vane vacuum pump as an example, the vanes divide the crescent space formed by the rotor, the pump body, and the end cover into three parts: A, B, and C. When the rotor rotates, the A space close to the suction port increases from small to large, and the expansion of the space causes the pressure to decrease, and the gas is sucked in through the pump inlet, and it is in the suction process; the volume of the B space in the middle decreases, the pressure increases, and the exhaust valve opens and it is in the compression process; the volume of the C space close to the exhaust port further decreases, the pressure increases, and when the pressure exceeds the set pressure of the exhaust valve piece, the gas is compressed and discharged, and it is in the exhaust process; when the A space is isolated from the suction port, it becomes the B space. During the continuous operation of the pump, the processes of suction, compression, and exhaust are continuously carried out, so as to achieve the purpose of continuous air extraction.
[0003] There is no absolutely sealed vacuum container. Among the gases pumped out by the vacuum pump during operation, the main gases pumped out are these four types: the gas inside the container itself; the desorption of the gas adsorbed on the inner surface of the container; the gas reflux from the vacuum pump into the container; and the gas that penetrates into the container from the atmosphere. If the container is sealed, after the vacuum pump operates for a period of time, the pumped-out gas will form an equilibrium with the gas generated inside the container, and the measured vacuum degree of the container at this time is the ultimate vacuum degree that the vacuum pump can reach.
[0004] If the gas discharged by the rotary vane pump enters another rotary vane pump and is compressed by it and then discharged into the atmosphere. Through the compression of the second rotary vane pump, the ultimate vacuum degree of the required environment can be further reduced. This method of connecting two single-stage rotary vane pumps in series is called a two-stage rotary vane vacuum pump. A two-stage pump can obtain a higher vacuum degree. Now, partitions are mostly used to separate the pump cavities to achieve the structure of a two-stage rotary vane vacuum pump. Even so, its cost is much higher than that of a single-stage rotary vane pump. Summary of the Invention
[0005] To solve at least one aspect of the above problems, the present invention provides a rotary vane for a vacuum pump, comprising: a mother vane, on one side of which a hinge is provided; a son vane, the son vane includes a first son vane and a second son vane, at least one of the first son vane and the second son vane is rotatably connected to the mother vane through the hinge, one side of the first son vane and the second son vane is rotatably connected through the hinge, and a vane suction hole is provided on the first son vane.
[0006] Preferably, the first son vane and the second son vane are respectively rotatably connected to the mother vane through hinges.
[0007] Preferably, a torsion spring is further included, the spring portion of the torsion spring is sleeved on the hinge, and two ends of the torsion spring respectively abut against adjacent side surfaces of the first son vane and the second son vane.
[0008] Preferably, a limiting end face is provided on one side of the first son vane close to the hinge, and when adjacent side surfaces of the first son vane and the second son vane are attached, the included angle between the limiting end face and the side surface of the mother vane is an acute angle.
[0009] Preferably, a valve plate is provided on the first son vane, the valve plate is arranged on the side adjacent to the second son vane of the first son vane, one side of the valve plate is fixedly connected to the first son vane, and the other side of the valve plate covers the vane suction hole.
[0010] Preferably, balance small holes are provided on the valve plate, and the positions of the balance small holes correspond to those of the vane suction holes.
[0011] Preferably, chamfered cutting surfaces are provided on the sides of the first son vane and the second son vane far from the mother vane.
[0012] On the other hand, a vacuum pump is provided, comprising: a pump body, on which an air inlet and an air outlet are provided; a rotor, there is an air outlet gap with a preset width between the outer wall of the rotor and the inner wall of the pump body at the air outlet of the pump body, a vane slot is provided on the rotor, a vane is arranged in the vane slot, the vane adopts any one of the previous vacuum pump vanes, and when the rotor rotates, the first son vane of the vane is behind the second son vane.
[0013] Preferably, three vane slots are provided on the rotor, and the central angles of any two adjacent vane slots among the three vane slots are equal.
[0014] Preferably, the width of the vane slot gradually increases in the direction away from the axis of the rotor.
[0015] The rotary vane of the vacuum pump and the vacuum pump according to the embodiments of the present invention have the following beneficial effects: Compared with the conventional single-stage rotary vane vacuum pump, the gas backflow of the vacuum pump can be reduced to improve the pumping efficiency and optimize its ultimate vacuum degree to solve the problems mentioned in the above background technology. While ensuring the normal progress of the suction, compression, and exhaust processes of the rotary vane vacuum pump itself, the rotary vane itself is also undergoing independent suction, compression, and exhaust processes to further reduce the amount of backflow gas, so as to achieve the purpose of improving the pumping efficiency and the ultimate vacuum degree of the product. BRIEF DESCRIPTION OF THE DRAWINGS
[0016] In order to better understand the above and other objects, features, advantages, and functions of the present invention, reference may be made to the embodiments shown in the drawings. The same reference numerals in the drawings refer to the same components. Those skilled in the art should understand that the drawings are intended to schematically illustrate the preferred embodiments of the present invention and have no restrictive effect on the scope of the present invention. The components in the drawings are not drawn to scale.
[0017] Figure 1 FIG. shows a schematic structural view of a rotary vane of a vacuum pump according to an embodiment of the present invention;
[0018] Figure 2 FIG. shows a schematic structural view of the rotary vane of the vacuum pump according to an embodiment of the present invention from another perspective;
[0019] Figure 3 FIG. shows a schematic structural view of a first sub-rotary vane of the rotary vane of the vacuum pump according to an embodiment of the present invention;
[0020] Figure 4 FIG. shows a schematic structural view of a vacuum pump according to an embodiment of the present invention;
[0021] Figure 5 FIG. shows a schematic structural view of the vacuum pump according to an embodiment of the present invention from another perspective.
[0022] REFERENCE NUMERALS:
[0023] 1, mother rotary vane; 11, mounting groove; 2, first sub-rotary vane; 3, second sub-rotary vane; 4, hinge pin; 41, hinge sleeve; 5, torsion spring; 6, valve plate; 7, fastening countersunk bolt; 8, right-angled triangular prism; 9, rotary vane suction hole; 10, rotor; 11, pump body; 12, combined rotary vane; 13, air inlet; 14, air outlet. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0024] Exemplary embodiments of the present disclosure will be described below with reference to the accompanying drawings. Various details of the embodiments of the present disclosure are included to facilitate understanding, and they should be considered merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present disclosure. Similarly, descriptions of well-known functions and structures are omitted below for clarity and conciseness.
[0025] As used herein, the term "comprising" and its variations mean open inclusion, i.e., "including but not limited to". Unless otherwise specified, the term "or" means "and / or". The term "based on" means "at least partially based on". The terms "an exemplary embodiment" and "an embodiment" mean "at least one exemplary embodiment". The term "another embodiment" means "at least one additional embodiment". The terms "first", "second", etc. may refer to different or the same objects. Other explicit and implicit definitions may also be included below.
[0026] To at least partially solve one or more of the above problems and other potential problems, an embodiment of the present disclosure provides a rotary vane for a vacuum pump, comprising: a mother vane 1 and a child vane. A hinge is provided on one side of the mother vane 1. The child vane includes a first child vane 2 and a second child vane 3. At least one of the first child vane 2 and the second child vane 3 is rotatably connected to the mother vane 1 through the hinge. One side of the first child vane 2 and the second child vane 3 is rotatably connected through the hinge. A vane suction hole 9 is provided on the first child vane 2.
[0027] Specifically, the mother vane 1 and the child vane adopt a flat plate structure, and a hinge is provided on the side of the mother vane 1 close to the child vane. The connection between the child vane and the mother vane 1 is realized by rotatably connecting at least one of the first child vane 2 and the second child vane 3 to the mother vane 1. The change in the angle between the first child vane 2 and the second child vane 3 is realized by the rotatable connection on one side of the first child vane 2 and the second child vane 3. By providing the vane suction hole 9 on the first child vane 2, suction can be achieved from the side of the first child vane 2 away from the second child vane 3 when the angle between the first child vane 2 and the second child vane 3 gradually increases.
[0028] In some embodiments, the first child vane 2 is rotatably connected to the mother vane 1 through a hinge, the second child vane 3 is fixedly connected to the mother vane 1, and the first child vane 2 is rotatably connected to the mother vane 1 through a hinge at the connection between the second child vane 3 and the mother vane 1. In other embodiments, the second child vane 3 and the mother vane 1 adopt an integrally formed structure, and the hinge is provided at the boundary between the second child vane 3 and the mother vane 1. The first child vane 2 is rotatably connected to the mother vane 1 and the second child vane 3 through a hinge. In still other embodiments, the first child vane 2 and the second child vane 3 are respectively rotatably connected to the mother vane 1 through a hinge.
[0029] In some embodiments, the sum of the thicknesses of the first sub-vane 2 and the second sub-vane 3 is equal to the thickness of the mother vane 1. When the first sub-vane 2 and the second sub-vane 3 are in contact with each other, the upper surface of the first sub-vane and the lower surface of the second sub-vane are coplanar with the upper surface and the lower surface of the mother vane 1 respectively.
[0030] In some embodiments, a plurality of mounting grooves 11 are formed on one side of the mother vane 1 close to the sub-vane. The hinge includes a hinge pin 4 and a hinge sleeve 41. The hinge sleeves 41 are respectively arranged in the plurality of mounting grooves 11, and the hinge pin 4 sequentially passes through the plurality of mounting grooves 11 and the hinge sleeves arranged therein. The first sub-vane 2 and the second sub-vane 3 are respectively fixedly connected to at least one hinge sleeve 41.
[0031] In some embodiments, a torsion spring 5 is further included. The spring portion of the torsion spring 5 is sleeved on the hinge, and the two ends of the torsion spring 5 respectively abut against the adjacent side surfaces of the first sub-vane 2 and the second sub-vane 3.
[0032] Specifically, to ensure that when the rotary vane vacuum pump is in operation, after the rotary vane is thrown out under the action of centrifugal force, the first sub-vane 2 and the second sub-vane 3 can be effectively separated, a torsion spring 5 is added in the middle of the hinge connecting the rotary vanes to ensure that the sub-vane can open.
[0033] During use, the rotary vane is installed in the rotary vane vacuum pump. Under the action of centrifugal force, the rotary vane is thrown out. Under the elastic force of the torsion spring 5, the first sub-vane 2 and the second sub-vane 3 open. The enclosed space formed between the two sub-vanes and the mother vane 1 has a volume that increases from small to large, and the pressure decreases, generating a negative pressure to produce suction, and sucking air from the adjacent chamber through the rotary vane suction hole 9.
[0034] In some embodiments, a limiting end face is formed on one side of the first sub-vane 2 close to the hinge. When the adjacent side surfaces of the first sub-vane 2 and the second sub-vane 3 are in contact, the included angle between the limiting end face and the side surface of the mother vane 1 is an acute angle.
[0035] Specifically, considering that if the opening angle of the sub-vane is too large, it cannot be retracted and is easily stuck, a limiting end face is provided at the hinge connection position of the sub-vane. For example, for the limiting end face of the first sub-vane 2: the included angle between the limiting end face and the upper surface of the first sub-vane is an obtuse angle (for example, 150°), and the included angle between the limiting end face and the lower surface of the first sub-vane is an acute angle (for example, 180° - 150°). For the limiting end face of the second sub-vane 3: the included angle between the limiting end face and the lower surface of the second sub-vane is an obtuse angle (for example, 150°), and the included angle between the limiting end face and the upper surface of the second sub-vane is an acute angle (for example, 180° - 150°).
[0036] In another embodiment, the limiting end face is a right triangular prism 8 provided on the sides of the first sub-vane 2 and the second sub-vane 3. Specifically, both the first sub-vane 2 and the second sub-vane 3 are flat structures with sides perpendicular to the upper and lower surfaces. One side of the right triangular prism 8 is attached to the side of the first sub-vane 2, and one side is coplanar with the lower surface of the first sub-vane 2. Then, the other side of the right triangular prism 8 is the limiting end face. One side of the right triangular prism 8 is attached to the side of the second sub-vane 3, and one side is coplanar with the upper surface of the second sub-vane 3. Then, the other side of the triangular prism is the limiting end face. By adding the limiting end face of the right triangular prism 8, the maximum opening angle between the two sub-vanes is restricted. In some embodiments, by setting the angle between the sides of the triangular prism, the maximum opening angle between the two sub-vanes does not exceed 60°, that is, the angle range between the adjacent sides of the first sub-vane 2 and the second sub-vane 3 is 0° to 60°.
[0037] In some embodiments, a valve plate 6 is provided on the first sub-vane 2. The valve plate 6 is provided on the side of the first sub-vane 2 adjacent to the second sub-vane 3. One side of the valve plate 6 is fixedly connected to the first sub-vane 2, and the other side of the valve plate 6 covers the vane suction hole 9.
[0038] Specifically, to ensure that the vane can suck air, a vane suction hole 9 needs to be opened on the sub-vane on the opposite side of the rotation direction. And we need the space formed by the mother vane 1 and the two sub-vanes to suck air during the opening process and compress during the closing process until it is discharged from the exhaust port 14. Also, it is necessary to ensure that the space formed by the mother vane 1 and the sub-vanes is relatively airtight during the compression process. Therefore, an air suction metal valve plate 6 is installed on the first sub-vane 2 where the vane suction hole 9 is opened. During the opening process of the two sub-vanes, the metal valve plate 6 opens under the action of the pressure difference and sucks air from the adjacent space through the vane suction hole 9. During the closing and compression process of the first sub-vane 2 and the second sub-vane 3, the metal valve plate 6 is airtight, forming an airtight space to ensure vane compression and exhaust.
[0039] In some embodiments, balance small holes are opened on the valve plate 6, and the positions of the balance small holes correspond to the vane suction hole 9.
[0040] Specifically, balance small holes are opened on the metal valve plate 6 to prevent the valve plate 6 from being sucked and unable to open.
[0041] In some embodiments, chamfered cut surfaces are provided on the sides of the first sub-vane 2 and the second sub-vane 3 away from the mother vane 1.
[0042] Specifically, by providing the chamfered cut surfaces on the sides of the first sub-vane 2 and the second sub-vane 3, the contact area between the sub-vanes and the inner wall of the pump body can be increased, and the airtightness of the space can be increased.
[0043] Embodiment
[0044] A rotary vane of a vacuum pump according to this embodiment, its sub-vane can cycle between opening and closing to perform suction and exhaust, reducing the reflux gas in the pump chamber. As Figure 1 shown, the mother vane 1 is connected to the first sub-vane 2 and the second sub-vane 3 through hinge holes. To ensure that the sub-vane can open freely, a vane torsion spring 5 is inserted at the hinge hole position on the mother vane 1 to provide the tension for the sub-vane to open. The vane hinge pin 4 passes through the mother vane 1, the first sub-vane 2, the second sub-vane 3, and the vane torsion spring 5 to connect these four parts together. The metal valve plate 6 is fixed to the inner side of the first sub-vane 2 by a fastening countersunk bolt 7 to block the suction port of the sub-vane with a suction port.
[0045] On the end faces at the hinge hole positions of the first sub-vane 2 and the second sub-vane 3, there are two limiting right-angled triangular prisms 8. The purpose is to ensure that the maximum opening angle of the first sub-vane 2 and the second sub-vane 3 does not exceed 60°, to prevent the sub-vane from being unable to close. Through the vane torsion spring 5 and the limiting right-angled triangular prism 8, it is ensured that during the operation of the vane pump, the first sub-vane 2 and the second sub-vane 3 can cycle between opening and closing.
[0046] On the other hand, a vacuum pump is provided, including: a pump body 11 and a rotor 10. An air inlet 13 and an air outlet 14 are provided on the pump body 11; there is a preset-width air outlet gap between the outer wall of the rotor 10 and the inner wall of the pump body 11 at the air outlet 14 of the pump body 11. A vane groove is provided on the rotor 10, and a vane is slidably arranged in the vane groove. The vane adopts the rotary vane of any of the previous vacuum pumps. When the rotor 10 rotates, the first sub-vane 2 of the vane is behind the second sub-vane 3.
[0047] Specifically, the pump body 11 of the vacuum pump has a cylindrical cavity, in which the rotor 10 is arranged. The rotor 10 is installed on the inner wall of the pump body 11 and is tangent to the inner wall of the pump body 11. The preset width of its air outlet gap is between 0.04 - 0.08 mm, near the air outlet 14 of the pump body 11. At least one combined vane 12 composed of a mother vane 1, a first sub-vane 2, and a second sub-vane 3 is arranged in the vane groove of the rotor 10. The length of the combined vane 12 is determined according to the diameters of the rotor 10 and the inner wall of the pump body 11. When the rotor 10 rotates, the first sub-vane 2 is behind the second sub-vane 3.
[0048] In some embodiments, three vane grooves are provided on the rotor 10, and the central angles of any two adjacent vane grooves among the three vane grooves are equal.
[0049] Specifically, for a single-stage vane vacuum pump with three vane grooves, there are three vane grooves on the rotor 10, and each vane groove contains a combined vane 12. The structural dimensions of the three combined vanes 12 are exactly the same. During the installation process, the side with the hole of the sub-vane is placed on the side opposite to the rotation direction.
[0050] In some embodiments, the width of the vane slot gradually increases in a direction away from the axis of the rotor 10.
[0051] Specifically, to ensure that the sub-vane can gradually open, a chamfer is provided on the cross-section of the vane slot of the rotor 10, which can ensure that the combined vane 12 can gradually open after spinning out from the tangent point of the rotor 10 and the pump body 11.
[0052] Embodiment
[0053] In the single-stage vane vacuum pump described in the present invention, three combined vanes 12 are evenly distributed in three vane slots of the rotor 10, and the first sub-vane 2 of the combined vane 12 is installed on the side opposite to the direction of rotation of the rotor 10. The rotor 10 is installed on the inner wall of the pump body 11 and is tangent to the inner wall of the pump body 11 (with a gap of 0.04 - 0.08 mm), near the exhaust port 14 of the pump body 11.
[0054] After one of the combined vanes 12 spins out from the tangent point of the rotor 10 and the pump body 11, the sub-vanes are in contact with each other, and the combined vane 12 is completely thrown out as a whole, adheres to the pump body 11, and slides along the inner wall of the pump body 11. The crescent space formed by the combined vane 12, the rotor 10, and the pump body 11 increases from small to large, forming a negative pressure to suck air from the suction port. The combined vane 12 continues to rotate, and the second sub-vane 3 of the first sub-vane 2 gradually opens under the action of the inclined angle of the rotor 10 slot, forming a negative pressure to suck air from the crescent space formed by the combined vane 12, the rotor 10, and the pump body 11. This crescent space is connected to the intake port 13, and part of the originally reflux gas is sucked into the vane, reducing the reflux gas.
[0055] When the combined vane 12 rotates 120°, at this time another combined vane 12 starts to be thrown out. After the combined vane 12 rotates 180°, the sub-vanes are completely opened, further absorbing the reflux gas in this crescent space. The combined vane 12 continues to rotate, and the space inside the vane decreases for gas compression. After the combined vane 12 rotates 240°, a closed space is formed with another combined vane 12, the rotor 10, and the pump body 11, and this space stops sucking air from the suction port and enters the compression stage. The combined vane 12 continues to rotate to the exhaust port 14, and the compressed gas in the combined vane 12 is discharged. Then, the gas compression and discharge in the closed space formed by the combined vane 12, another combined vane 12, the rotor 10, and the pump body 11 occur. The combined vane 12 continues to rotate and enters the next cycle. In this process, the suction, compression, and exhaust processes of the single-stage vane pump itself proceed normally. During the rotation process, the hinge is always in the vane slot. In the limit state, the sub-vane is in close contact with the vane slot on the rotor 10 for sealing, avoiding the influence of the hinge gap on the vane seal inside the pump body 11. At the same time, the vane is also performing an independent suction, compression, and exhaust process to further reduce the amount of reflux gas, so as to achieve the purpose of improving the pumping efficiency and the ultimate vacuum degree of the product.
[0056] The embodiments of the present disclosure have been described above. The above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The choice of terms used herein is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the market, or to enable other ordinary skilled persons in the art to understand this text.
Claims
1. A rotary vane for a vacuum pump, characterized in that, Comprising: A mother vane, on one side of which a hinge is provided; A son vane, the son vane includes a first son vane and a second son vane, at least one of the first son vane and the second son vane is rotatably connected to the mother vane through the hinge, one side of the first son vane and the second son vane is rotatably connected through the hinge, and a vane suction hole is provided on the first son vane.
2. The rotary vane of the vacuum pump according to claim 1, wherein, The first son vane and the second son vane are respectively rotatably connected to the mother vane through a hinge.
3. The rotary vane of the vacuum pump according to claim 2, characterized in that, It further includes a torsion spring, the spring part of the torsion spring is sleeved on the hinge, and the two ends of the torsion spring respectively abut against the adjacent side surfaces of the first son vane and the second son vane.
4. The rotary vane of the vacuum pump according to claim 3, characterized in that, A limiting end face is provided on one side of the first son vane close to the hinge. When the adjacent side surfaces of the first son vane and the second son vane are attached, the included angle between the limiting end face and the side surface of the mother vane is an acute angle.
5. The rotary vane of the vacuum pump according to claim 4, characterized in that, A valve plate is provided on the first son vane, the valve plate is arranged on the adjacent side surface of the first son vane and the second son vane, one side of the valve plate is fixedly connected to the first son vane, and the other side of the valve plate covers the vane suction hole.
6. The rotary vane of the vacuum pump according to claim 5, wherein, A balance small hole is provided on the valve plate, and the position of the balance small hole corresponds to that of the vane suction hole.
7. The rotary vane of the vacuum pump according to claim 1, characterized in that, Chamfered cut surfaces are provided on the side surfaces of the first son vane and the second son vane away from the mother vane.
8. A vacuum pump, characterized in that, Comprising: A pump body, on which an air inlet and an air outlet are provided; A rotor, there is an air outlet gap with a preset width between the outer wall of the rotor and the inner wall of the pump body at the air outlet of the pump body. A vane is arranged in the vane slot, and the vane adopts the vacuum pump vane as described in any one of claims 1-7. When the rotor rotates, the first son vane of the vane is behind the second son vane.
9. The vacuum pump according to claim 8, characterized in that, Three vane slots are provided on the rotor, and the central angles of any two adjacent vane slots among the three vane slots are equal.
10. The vacuum pump according to claim 9, characterized in that, The width of the vane slot gradually increases along the direction away from the axis of the rotor.