CN110005609A - A kind of smooth molded lines of rotor of Twin-screw vacuum pump and its design method - Google Patents

A kind of smooth molded lines of rotor of Twin-screw vacuum pump and its design method Download PDF

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CN110005609A
CN110005609A CN201910051620.0A CN201910051620A CN110005609A CN 110005609 A CN110005609 A CN 110005609A CN 201910051620 A CN201910051620 A CN 201910051620A CN 110005609 A CN110005609 A CN 110005609A
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circular arc
rotor
parabola
line
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CN110005609B (en
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耿茂飞
王乐
毛京兵
邢志胜
张成彦
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Hefei General Machinery Research Institute Co Ltd
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Hefei General Machinery Research Institute Co Ltd
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04C—ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT PUMPS
    • F04C18/00—Rotary-piston pumps specially adapted for elastic fluids
    • F04C18/08—Rotary-piston pumps specially adapted for elastic fluids of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing
    • F04C18/12—Rotary-piston pumps specially adapted for elastic fluids of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing of other than internal-axis type
    • F04C18/14—Rotary-piston pumps specially adapted for elastic fluids of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing of other than internal-axis type with toothed rotary pistons
    • F04C18/16—Rotary-piston pumps specially adapted for elastic fluids of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing of other than internal-axis type with toothed rotary pistons with helical teeth, e.g. chevron-shaped, screw type
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04C—ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT PUMPS
    • F04C25/00—Adaptations of pumps for special use of pumps for elastic fluids
    • F04C25/02—Adaptations of pumps for special use of pumps for elastic fluids for producing high vacuum
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04C—ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT PUMPS
    • F04C29/00—Component parts, details or accessories of pumps or pumping installations, not provided for in groups F04C18/00 - F04C28/00
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04C—ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT PUMPS
    • F04C2240/00—Components
    • F04C2240/20—Rotors
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04C—ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT PUMPS
    • F04C2250/00—Geometry
    • F04C2250/20—Geometry of the rotor

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Rotary Pumps (AREA)

Abstract

The present invention relates to a kind of smooth molded lines of rotor of Twin-screw vacuum pump and its design methods.The smooth rotor end-face molded line of the Twin-screw vacuum pump is made of the sequentially connected class circular arc conjugate line a1b1 of head and the tail, class circular arc b1c1, addendum circle arc c1d1, class parabola d1e1, class parabola conjugate line e1f1 and tooth root circular arc f1a1.The present invention smooth no cusp of rotor generated, a pair of meshing rotor that the molded lines of rotor generates equal total conjugated of molded line and smooth on axial section and end face, meshing performance is good, and leakage area is small, can reach very low ultimate vacuum；Molded lines of rotor smooth simultaneously is that the design of rotor cutter provides a great convenience, and reduces the processing cost of rotor.

Description

一种双螺杆真空泵光滑转子型线及其设计方法A kind of smooth rotor profile of twin-screw vacuum pump and its design method

技术领域technical field

本发明属于机械工程设计领域，具体是涉及一种双螺杆真空泵光滑转子型线及其设计方法。The invention belongs to the field of mechanical engineering design, in particular to a smooth rotor profile of a twin-screw vacuum pump and a design method thereof.

背景技术Background technique

双螺杆干式真空泵具有单级压比高、输送介质平稳、压力脉动小、机械振动小、结构简单紧凑、效率高、工作可靠及寿命长等特点，广泛应用于核科学、电子器械、食品工业、石油化工和医药制造等领域。The twin-screw dry vacuum pump has the characteristics of high single-stage pressure ratio, stable conveying medium, small pressure pulsation, small mechanical vibration, simple and compact structure, high efficiency, reliable operation and long life. It is widely used in nuclear science, electronic equipment, food industry. , petrochemical and pharmaceutical manufacturing fields.

转子型线作为双螺杆干式真空泵的核心技术，决定了真空泵的抽速和极限真空等性能，是双螺杆真空泵设计和优化的关键技术，而目前已公开的双螺杆真空泵型线中较多的存在的问题有：As the core technology of the twin-screw dry vacuum pump, the rotor profile determines the pumping speed and ultimate vacuum performance of the vacuum pump, and is the key technology for the design and optimization of the twin-screw vacuum pump. The problems that exist are:

1、转子型线不能完全共轭，一对转子的啮合性能差，泄露面积大，不能达到很低的极限真空。1. The rotor profile cannot be completely conjugated, the meshing performance of a pair of rotors is poor, the leakage area is large, and a very low ultimate vacuum cannot be achieved.

2、转子型线不光滑，真空泵转子在加工、安装和运行过程中，尖点易磨损，降低啮合性能。同时，由于型线不光滑，转子加工刀具的设计难度大大增加。2. The rotor profile is not smooth, and the cusp of the vacuum pump rotor is easy to wear during processing, installation and operation, which reduces the meshing performance. At the same time, because the profile line is not smooth, the design difficulty of the rotor machining tool is greatly increased.

发明内容SUMMARY OF THE INVENTION

为了解决上述技术问题，本发明提供一种双螺杆真空泵光滑转子型线。In order to solve the above technical problems, the present invention provides a smooth rotor profile of a twin-screw vacuum pump.

为了实现本发明的目的，本发明采用了以下技术方案：In order to realize the purpose of the present invention, the present invention adopts the following technical solutions:

一种双螺杆真空泵光滑转子型线，该双螺杆真空泵光滑转子端面型线由首尾依次连接的类圆弧共轭线a1b1、类圆弧b1c1、齿顶圆弧c1d1、类抛物线d1e1、类抛物线共轭线e1f1以及齿根圆弧f1a1组成；A smooth rotor profile of a twin-screw vacuum pump, the end profile of the smooth rotor of the twin-screw vacuum pump consists of arc-like conjugate line a1b1, circular arc b1c1, tooth top arc c1d1, parabolic-like d1e1, and parabolic-like common The yoke line e1f1 and the tooth root arc f1a1 are composed;

所述类圆弧b1c1在转子轴向剖面上为一段圆弧BC，所述圆弧BC经坐标变换得到转子端面型线中所述类圆弧b1c1，所述类圆弧b1c1分别与齿顶圆弧c1d1和类圆弧共轭线a1b1相切；The circular arc b1c1 is a segment of circular arc BC on the axial section of the rotor, and the circular arc BC is obtained by coordinate transformation to obtain the circular arc b1c1 in the rotor end face profile. The arc c1d1 is tangent to the arc-like conjugate line a1b1;

所述类圆弧b1c1的坐标方程由以下公式得到：The coordinate equation of the arc-like arc b1c1 is obtained by the following formula:

其中，xb1c1为类圆弧b1c1的X坐标，yb1c1为类圆弧b1c1的Y坐标，zBC为所述圆弧BC的Z坐标，yBC为所述圆弧BC的Y坐标，T为转子导程；Wherein, x b1c1 is the X coordinate of the circular arc b1c1, y b1c1 is the Y coordinate of the circular arc b1c1, z BC is the Z coordinate of the circular arc BC, y BC is the Y coordinate of the circular arc BC, and T is the rotor lead;

所述类圆弧共轭线a1b1由所述类圆弧b1c1的共轭包络线经坐标变换得到，所述类圆弧共轭线a1b1分别与齿根圆弧f1a1和类圆弧b1c1相切；The arc-like conjugate line a1b1 is obtained by coordinate transformation of the conjugate envelope of the arc-like arc b1c1, and the arc-like conjugate line a1b1 is respectively tangent to the tooth root arc f1a1 and the arc-like arc b1c1 ;

所述类圆弧共轭线a1b1的坐标方程由以下公式得到：The coordinate equation of the arc-like conjugate line a1b1 is obtained by the following formula:

其中，xa1b1为类圆弧共轭线a1b1的X坐标，ya1b1为类圆弧共轭线a1b1的Y坐标，φ1为转子型线位置参数且为中间参量，A表示中心距即为齿顶圆弧c1d1和齿根圆弧f1a1半径之和，t1表示类圆弧共轭线a1b1相对圆心旋转的角度；由上述方程消去φ1，得到xa1b1和ya1b1关于参量t1的坐标方程，由此得到类圆弧共轭线a1b1坐标方程；Among them, x a1b1 is the X coordinate of the arc-like conjugate line a1b1, y a1b1 is the Y coordinate of the arc-like conjugate line a1b1, φ 1 is the rotor profile position parameter and is an intermediate parameter, A indicates the center distance is the tooth The sum of the radius of the top arc c1d1 and the root arc f1a1, t 1 represents the rotation angle of the arc-like conjugate line a1b1 relative to the center of the circle; eliminate φ 1 from the above equation, and obtain the coordinate equation of x a1b1 and y a1b1 about the parameter t 1 , the coordinate equation of the arc-like conjugate line a1b1 is obtained;

所述类抛物线d1e1在转子轴向剖面上为一段抛物线DE，该抛物线DE经坐标变换得到转子端面型线中所述类抛物线d1e1，所述类抛物线d1e1分别与齿顶圆弧c1d1和类抛物线共轭线e1f1相切；The parabola-like d1e1 is a section of parabola DE on the axial section of the rotor, and the parabola DE is transformed into the parabola-like d1e1 in the rotor end face profile through coordinate transformation. The yoke line e1f1 is tangent;

所述类抛物线d1e1的坐标方程由以下公式得到：The coordinate equation of the parabola-like d1e1 is obtained by the following formula:

其中，xd1e1为类抛物线d1e1的X坐标，yd1e1为类抛物线d1e1的Y坐标，zDE为抛物线DE的Z坐标，yDE为抛物线DE的Y坐标，T为转子导程；Among them, x d1e1 is the X coordinate of the parabola d1e1, y d1e1 is the Y coordinate of the parabola d1e1, z DE is the Z coordinate of the parabola DE, y DE is the Y coordinate of the parabola DE, and T is the rotor lead;

所述类抛物线共轭线e1f1由所述类抛物线d1e1的共轭包络线经坐标变换得到，所述类抛物线共轭线e1f1分别与齿根圆弧f1a1和类抛物线d1e1相切；The parabola-like conjugate line e1f1 is obtained by coordinate transformation of the conjugate envelope of the parabola-like line d1e1, and the parabola-like conjugate line e1f1 is respectively tangent to the tooth root arc f1a1 and the parabola-like line d1e1;

所述类抛物线共轭线e1f1的坐标方程由以下公式得到：The coordinate equation of the parabolic-like conjugate line e1f1 is obtained by the following formula:

其中，xe1f1为类抛物线共轭线X坐标，ye1f1为类抛物线共轭线Y坐标，φ2为转子型线位置参数且为中间参量，A表示中心距即为齿顶圆弧c1d1和齿根圆弧f1a1半径之和，t2表示类抛物线共轭线e1f1相对圆心旋转的角度；由上述方程消去φ2，得到xe1f1和ye1f1关于参量t2的坐标方程，由此得到类抛物线共轭线e1f1坐标方程。Among them, x e1f1 is the X coordinate of the parabola-like conjugate line, y e1f1 is the Y-coordinate of the parabola-like conjugate line, φ 2 is the rotor profile position parameter and is an intermediate parameter, A represents the center distance, which is the tooth tip arc c1d1 and the tooth The sum of the radii of the root arc f1a1, t 2 represents the rotation angle of the parabolic-like conjugate line e1f1 relative to the center of the circle; from the above equation, eliminate φ 2 to obtain the coordinate equations of x e1f1 and y e1f1 about the parameter t 2 , thus obtaining the parabolic-like common Yoke line e1f1 coordinate equation.

进一步的技术方案：所述转子型线生成的一对啮合转子端面型线完全相同且互相共轭。A further technical solution: a pair of meshing rotor end face profiles generated by the rotor profile lines are completely identical and mutually conjugated.

本发明的另一个目的是提供一种所述双螺杆真空泵光滑转子型线的设计方法，该方法包括以下步骤：Another object of the present invention is to provide a design method for the smooth rotor profile of the twin-screw vacuum pump, the method comprising the following steps:

步骤1，在转子轴向剖面上，设计连接齿顶圆与节圆的圆弧BC，且所述圆弧BC与齿顶圆光滑连接，将所述圆弧BC经空间坐标变换得到转子端面上的类圆弧b1c1，并求得转子端面上连接齿根圆与节圆的类圆弧共轭线a1b1，其中节圆半径为齿顶圆与齿根圆半径之和的一半；Step 1, on the axial section of the rotor, design an arc BC connecting the addendum circle and the pitch circle, and the arc BC and the addendum circle are smoothly connected, and transform the arc BC through the spatial coordinate to obtain the rotor end surface. The arc-like arc b1c1 is obtained, and the arc-like conjugate line a1b1 connecting the root circle and the pitch circle on the end face of the rotor is obtained, where the pitch circle radius is half of the sum of the addendum circle and the root circle radius;

步骤2，在转子轴向剖面上，设计连接齿顶圆与节圆的抛物线DE，且所述抛物线DE与齿顶圆光滑连接，将所述抛物线DE经空间坐标变换得到转子端面上的类抛物线d1e1，并求得转子端面上连接齿根圆与节圆的类抛物线共轭线e1f1；Step 2: On the axial section of the rotor, a parabola DE connecting the addendum circle and the pitch circle is designed, and the parabola DE and the addendum circle are smoothly connected, and the parabola-like curve on the end face of the rotor is obtained by transforming the parabola DE through the space coordinates d1e1, and obtain the parabolic-like conjugate line e1f1 connecting the root circle and the pitch circle on the rotor end face;

步骤3，在转子端面上添加齿顶圆弧c1d1和齿根圆弧f1a1连接上述曲线，形成封闭的转子端面型线。Step 3: Add the tip arc c1d1 and the root arc f1a1 on the rotor end face to connect the above curves to form a closed rotor end face profile.

本发明的有益效果在于：The beneficial effects of the present invention are:

(1)本发明所生成的转子光滑无尖点，所述转子型线生成的一对啮合转子在轴向剖面和端面上型线均完全共轭且光滑，啮合性能良好，泄露面积小，能够达到很低的极限真空；同时光滑的转子型线为转子刀具的设计提供了极大的便利，降低了转子的加工成本。(1) The rotors produced by the present invention are smooth and without sharp points, and a pair of meshing rotors generated by the rotor profile lines are completely conjugated and smooth in both the axial section and the end face profiles, with good meshing performance and small leakage area. A very low ultimate vacuum is achieved; at the same time, the smooth rotor profile provides great convenience for the design of the rotor tool and reduces the processing cost of the rotor.

(2)传统的转子型线设计局限于端面型线设计，没有从轴向剖面上进行型线设计。本发明在设计方法上，不同于传统的端面型线设计方法，本发明采用了轴向型线设计和端面型线设计相结合的方式，从而实现将更多的曲线形式应用到型线设计中。(2) The traditional rotor profile design is limited to the end profile design, and the profile design is not carried out from the axial section. In the design method of the present invention, different from the traditional end profile design method, the present invention adopts the combination of the axial profile design and the end profile design, so as to realize the application of more curve forms to the profile design. .

附图说明Description of drawings

图1为本发明所述转子端面型线视图；1 is a profile view of the rotor end face according to the present invention;

图2为本发明所述转子轴面型线视图；Fig. 2 is the rotor axial profile view of the present invention;

图3为本发明所述转子型线生成的一对啮合转子的轴向剖面视图；3 is an axial cross-sectional view of a pair of meshing rotors generated by the rotor profile of the present invention;

图4为本发明所述转子型线生成的一对啮合转子的三维模型图。4 is a three-dimensional model diagram of a pair of meshing rotors generated by the rotor profile of the present invention.

具体实施方式Detailed ways

下面结合实施例对本发明技术方案做出更为具体的说明：Below in conjunction with the embodiment, the technical scheme of the present invention is described in more detail:

如图1所示：本发明双螺杆真空泵光滑转子端面型线由首尾依次连接的类圆弧共轭线a1b1、类圆弧b1c1、齿顶圆弧c1d1、类抛物线d1e1、类抛物线共轭线e1f1以及齿根圆弧f1a1组成；As shown in Fig. 1: The profile line of the smooth rotor of the twin-screw vacuum pump of the present invention consists of the arc-like conjugate line a1b1, the arc-like arc b1c1, the tooth tip arc c1d1, the parabola-like d1e1, and the parabola-like conjugate line e1f1 which are connected in turn. and the tooth root arc f1a1;

所述类圆弧b1c1在转子轴向剖面上为一段圆弧BC，所述圆弧BC经坐标变换得到转子端面型线中所述类圆弧b1c1，所述类圆弧b1c1分别与齿顶圆弧c1d1和类圆弧共轭线a1b1相切；The circular arc b1c1 is a segment of circular arc BC on the axial section of the rotor, and the circular arc BC is obtained by coordinate transformation to obtain the circular arc b1c1 in the rotor end face profile. The arc c1d1 is tangent to the arc-like conjugate line a1b1;

所述类圆弧b1c1的坐标方程由以下公式得到：The coordinate equation of the arc-like arc b1c1 is obtained by the following formula:

其中，xb1c1为类圆弧b1c1的X坐标，yb1c1为类圆弧b1c1的Y坐标，zBC为所述圆弧BC的Z坐标，yBC为所述圆弧BC的Y坐标，T为转子导程；Wherein, x b1c1 is the X coordinate of the circular arc b1c1, y b1c1 is the Y coordinate of the circular arc b1c1, z BC is the Z coordinate of the circular arc BC, y BC is the Y coordinate of the circular arc BC, and T is the rotor lead;

所述类圆弧共轭线a1b1由所述类圆弧b1c1的共轭包络线经坐标变换得到，所述类圆弧共轭线a1b1分别与齿根圆弧f1a1和类圆弧b1c1相切；The arc-like conjugate line a1b1 is obtained by coordinate transformation of the conjugate envelope of the arc-like arc b1c1, and the arc-like conjugate line a1b1 is respectively tangent to the tooth root arc f1a1 and the arc-like arc b1c1 ;

所述类圆弧共轭线a1b1的坐标方程由以下公式得到：The coordinate equation of the arc-like conjugate line a1b1 is obtained by the following formula:

其中，xa1b1为类圆弧共轭线a1b1的X坐标，ya1b1为类圆弧共轭线a1b1的Y坐标，φ1为转子型线位置参数且为中间参量，A表示中心距即为齿顶圆弧c1d1和齿根圆弧f1a1半径之和，t1表示类圆弧共轭线a1b1相对圆心旋转的角度；由上述方程消去φ1，得到xa1b1和ya1b1关于参量t1的坐标方程，由此得到类圆弧共轭线a1b1坐标方程；Among them, x a1b1 is the X coordinate of the arc-like conjugate line a1b1, y a1b1 is the Y coordinate of the arc-like conjugate line a1b1, φ 1 is the rotor profile position parameter and is an intermediate parameter, A indicates the center distance is the tooth The sum of the radius of the top arc c1d1 and the root arc f1a1, t 1 represents the rotation angle of the arc-like conjugate line a1b1 relative to the center of the circle; eliminate φ 1 from the above equation, and obtain the coordinate equation of x a1b1 and y a1b1 about the parameter t 1 , the coordinate equation of the arc-like conjugate line a1b1 is obtained;

所述类抛物线d1e1在转子轴向剖面上为一段抛物线DE，该抛物线DE经坐标变换得到转子端面型线中所述类抛物线d1e1，所述类抛物线d1e1分别与齿顶圆弧c1d1和类抛物线共轭线e1f1相切；The parabola-like d1e1 is a section of parabola DE on the axial section of the rotor, and the parabola DE is transformed into the parabola-like d1e1 in the rotor end face profile through coordinate transformation. The yoke line e1f1 is tangent;

所述类抛物线d1e1的坐标方程由以下公式得到：The coordinate equation of the parabola-like d1e1 is obtained by the following formula:

其中，xd1e1为类抛物线d1e1的X坐标，yd1e1为类抛物线d1e1的Y坐标，zDE为抛物线DE的Z坐标，yDE为抛物线DE的Y坐标，T为转子导程；Among them, x d1e1 is the X coordinate of the parabola d1e1, y d1e1 is the Y coordinate of the parabola d1e1, z DE is the Z coordinate of the parabola DE, y DE is the Y coordinate of the parabola DE, and T is the rotor lead;

所述类抛物线共轭线e1f1由所述类抛物线d1e1的共轭包络线经坐标变换得到，所述类抛物线共轭线e1f1分别与齿根圆弧f1a1和类抛物线d1e1相切；The parabola-like conjugate line e1f1 is obtained by coordinate transformation of the conjugate envelope of the parabola-like line d1e1, and the parabola-like conjugate line e1f1 is respectively tangent to the tooth root arc f1a1 and the parabola-like line d1e1;

所述类抛物线共轭线e1f1的坐标方程由以下公式得到：The coordinate equation of the parabolic-like conjugate line e1f1 is obtained by the following formula:

其中，xe1f1为类抛物线共轭线X坐标，ye1f1为类抛物线共轭线Y坐标，φ2为转子型线位置参数且为中间参量，A表示中心距即为齿顶圆弧c1d1和齿根圆弧f1a1半径之和，t2表示类抛物线共轭线e1f1相对圆心旋转的角度；由上述方程消去φ2，得到xe1f1和ye1f1关于参量t2的坐标方程，由此得到类抛物线共轭线e1f1坐标方程。Among them, x e1f1 is the X coordinate of the quasi-parabolic conjugate line, y e1f1 is the Y coordinate of the quasi-parabolic conjugate line, φ 2 is the position parameter of the rotor profile and is an intermediate parameter, A indicates the center distance is the tip arc c1d1 and the tooth The sum of the radii of the root arc f1a1, t 2 represents the angle of rotation of the parabolic-like conjugate line e1f1 relative to the center of the circle; by eliminating φ 2 from the above equation, the coordinate equations of x e1f1 and y e1f1 about the parameter t 2 are obtained, and the parabolic-like common Yoke line e1f1 coordinate equation.

本发明所述双螺杆真空泵光滑转子型线的设计方法，包括以下步骤：The design method of the smooth rotor profile of the twin-screw vacuum pump according to the present invention includes the following steps:

步骤1，在转子轴向剖面上，设计连接齿顶圆与节圆的圆弧BC，且所述圆弧BC与齿顶圆光滑连接，将所述圆弧BC经空间坐标变换得到转子端面上的类圆弧b1c1，并求得转子端面上连接齿根圆与节圆的类圆弧共轭线a1b1，其中节圆半径为齿顶圆与齿根圆半径之和的一半；Step 1, on the axial section of the rotor, design an arc BC connecting the addendum circle and the pitch circle, and the arc BC and the addendum circle are smoothly connected, and transform the arc BC through the spatial coordinate to obtain the rotor end surface. The arc-like arc b1c1 is obtained, and the arc-like conjugate line a1b1 connecting the root circle and the pitch circle on the end face of the rotor is obtained, where the pitch circle radius is half of the sum of the addendum circle and the root circle radius;

步骤2，在转子轴向剖面上，设计连接齿顶圆与节圆的抛物线DE，且所述抛物线DE与齿顶圆光滑连接，将所述抛物线DE经空间坐标变换得到转子端面上的类抛物线d1e1，并求得转子端面上连接齿根圆与节圆的类抛物线共轭线e1f1；Step 2: On the axial section of the rotor, a parabola DE connecting the addendum circle and the pitch circle is designed, and the parabola DE and the addendum circle are smoothly connected, and the parabola-like curve on the end face of the rotor is obtained by transforming the parabola DE through the space coordinates d1e1, and obtain the parabolic-like conjugate line e1f1 connecting the root circle and the pitch circle on the rotor end face;

步骤3，在转子端面上添加齿顶圆弧c1d1和齿根圆弧f1a1连接上述曲线，形成封闭的转子端面型线。Step 3: Add the tip arc c1d1 and the root arc f1a1 on the rotor end face to connect the above curves to form a closed rotor end face profile.

图2中转子轴面型线中各线段与图1中转子端面型线中各线段呈一一对应关系，其中圆弧共轭线AB对应类圆弧共轭线a1b1，圆弧BC对应类圆弧b1c1，直线CD对应齿顶圆弧c1d1，抛物线DE对应类抛物线d1e1，抛物线共轭线EF对应类抛物线共轭线e1f1，直线FG对应齿根圆弧f1a1。Each line segment in the rotor axial profile in Fig. 2 has a one-to-one correspondence with each line segment in the rotor end profile in Fig. 1, in which the circular arc conjugate line AB corresponds to the circular arc conjugate line a1b1, and the circular arc BC corresponds to the circular circular segment The arc b1c1, the straight line CD corresponds to the tooth tip arc c1d1, the parabola DE corresponds to the parabola d1e1, the parabola conjugate EF corresponds to the parabola conjugate e1f1, and the straight line FG corresponds to the root arc f1a1.

实施例Example

本发明提供的各段型线坐标方程如下：The coordinate equations of each segment profile provided by the present invention are as follows:

取齿顶圆弧直径D＝40mm、齿根圆弧直径d＝20mm，转子导程T＝40mm。Take the tip arc diameter D=40mm, the tooth root arc diameter d=20mm, and the rotor lead T=40mm.

所述圆弧BC在轴向剖面上的参数方程如下：The parametric equation of the arc BC on the axial section is as follows:

将圆弧BC的轴向参数方程带入类圆弧b1c1公式，得到所述类圆弧b1c1在端面上的坐标方程为：Bringing the axial parameter equation of the arc BC into the formula of the quasi-circle arc b1c1, the coordinate equation of the quasi-circle b1c1 on the end face is obtained as:

所述类圆弧共轭线a1b1的坐标方程为：The coordinate equation of the arc-like conjugate line a1b1 is:

由上述方程通过数值方法消去中间参量φ1，得到xa1b1和ya1b1关于参量t1的坐标方程，即为类圆弧共轭线a1b1的坐标方程。By eliminating the intermediate parameter φ 1 numerically from the above equation, the coordinate equation of x a1b1 and y a1b1 about the parameter t 1 is obtained, which is the coordinate equation of the arc-like conjugate line a1b1.

所述抛物线DE在轴向剖面上的参数方程如下：The parametric equation of the parabola DE on the axial section is as follows:

将抛物线DE的轴向参数方程带入类抛物线d1e1公式，得到所述类抛物线d1e1在端面上的坐标方程为：The axial parameter equation of the parabola DE is brought into the parabola-like d1e1 formula, and the coordinate equation of the parabola-like d1e1 on the end surface is obtained as:

所述类抛物线共轭线e1f1的坐标方程为：The coordinate equation of the parabolic-like conjugate line e1f1 is:

由上述方程通过数值方法消去中间参量φ2，得到xe1f1和ye1f1关于参量t2的坐标方程，即为类抛物线共轭线e1f1的方程。By eliminating the intermediate parameter φ 2 numerically from the above equation, the coordinate equations of x e1f1 and y e1f1 about the parameter t 2 are obtained, which is the equation of the parabolic-like conjugate line e1f1.

补充直径分别为40mm和20mm的齿顶圆弧和齿根圆弧。Supplementary tip and root arcs with diameters of 40mm and 20mm, respectively.

将各段曲线围绕圆心调整角度，构成首尾相接的封闭曲线，即可得到本发明所述的型线。The angle of each segment of the curve is adjusted around the center of the circle to form an end-to-end closed curve, and then the profile line of the present invention can be obtained.

上述角度参数均采用弧度制表示。The above angle parameters are expressed in radians.

由图3、图4所示：本发明设计的转子型线生成的一对啮合转子在轴向剖面和端面上型线均完全共轭且光滑。As shown in FIG. 3 and FIG. 4 , a pair of meshing rotors generated by the rotor profile designed by the present invention are completely conjugated and smooth on the axial section and the profile line on the end face.

Claims (3)

1. a kind of smooth molded lines of rotor of Twin-screw vacuum pump, it is characterised in that: the smooth rotor end-face molded line of the Twin-screw vacuum pump By the sequentially connected class circular arc conjugate line a1b1 of head and the tail, class circular arc b1c1, addendum circle arc c1d1, class parabola d1e1, class parabolic Line conjugate line e1f1 and tooth root circular arc f1a1 composition；
The class circular arc b1c1 obtains rotor-end through coordinate transform for one section of circular arc BC, the circular arc BC on rotor axial section Class circular arc b1c1 described in the molded line of face, the class circular arc b1c1 respectively with addendum circle arc c1d1 and class circular arc conjugate line a1b1 phase It cuts；
The equation in coordinates of the class circular arc b1c1 is obtained by the following formula:
Wherein, xb1c1For the X-coordinate of class circular arc b1c1, yb1c1For the Y-coordinate of class circular arc b1c1, zBCIt is sat for the Z of the circular arc BC Mark, yBCFor the Y-coordinate of the circular arc BC, T is rotor lead；
The class circular arc conjugate line a1b1 is obtained by the conjugation envelope of the class circular arc b1c1 through coordinate transform, the class circular arc Conjugate line a1b1 is tangent with tooth root circular arc f1a1 and class circular arc b1c1 respectively；
The equation in coordinates of the class circular arc conjugate line a1b1 is obtained by the following formula:
Wherein, xa1b1For the X-coordinate of class circular arc conjugate line a1b1, ya1b1For the Y-coordinate of class circular arc conjugate line a1b1, φ1For rotor Molded line location parameter and be intermediate parameter, A indicate center away from the sum of as addendum circle arc c1d1 and tooth root circular arc f1a1 radius, t1 Indicate the angle that class circular arc conjugate line a1b1 is rotated relative to the center of circle；φ is eliminated by above-mentioned equation1, obtain xa1b1And ya1b1About ginseng Measure t1Equation in coordinates, thus obtain class circular arc conjugate line a1b1 equation in coordinates；
The class parabola d1e1 is one section of parabola DE on rotor axial section, and parabola DE is turned through coordinate transform Class parabola d1e1 described in sub- profile, the class parabola d1e1 are conjugated with addendum circle arc c1d1 and class parabola respectively Line e1f1 is tangent；
The equation in coordinates of the class parabola d1e1 is obtained by the following formula:
Wherein, xd1e1For the X-coordinate of class parabola d1e1, yd1e1For the Y-coordinate of class parabola d1e1, zDEIt is sat for the Z of parabola DE Mark, yDEFor the Y-coordinate of parabola DE, T is rotor lead；
The class parabola conjugate line e1f1 is obtained by the conjugation envelope of the class parabola d1e1 through coordinate transform, the class Parabola conjugate line e1f1 is tangent with tooth root circular arc f1a1 and class parabola d1e1 respectively；
The equation in coordinates of the class parabola conjugate line e1f1 is obtained by the following formula:
Wherein, xe1f1For class parabola conjugate line X-coordinate, ye1f1For class parabola conjugate line Y-coordinate, φ2For molded lines of rotor position Parameter and be intermediate parameter, A indicate center away from the sum of as addendum circle arc c1d1 and tooth root circular arc f1a1 radius, t2Indicate that class is thrown The angle that object line conjugate line e1f1 is rotated relative to the center of circle；φ is eliminated by above-mentioned equation2, obtain xe1f1And ye1f1About parameter t2's Thus equation in coordinates obtains class parabola conjugate line e1f1 equation in coordinates.
2. the smooth molded lines of rotor of Twin-screw vacuum pump as described in claim 1, it is characterised in that: what the molded lines of rotor generated A pair of meshing rotor end-face molded line is identical and mutual phase conjugate.
3. a kind of design method of the smooth molded lines of rotor of Twin-screw vacuum pump as claimed in claim 1 or 2, it is characterised in that: packet Include following steps:
Step 1, on rotor axial section, the circular arc BC of design connection outside circle and pitch circle, and the circular arc BC and outside circle It is smoothly connected, the circular arc BC is obtained into the class circular arc b1c1 on rotor end-face through space coordinate transformation, and acquire rotor end-face The class circular arc conjugate line a1b1 of upper connection root circle and pitch circle, wherein pitch radius is the one of the sum of outside circle and root radius Half；
Step 2, on rotor axial section, the parabola DE of design connection outside circle and pitch circle, and the parabola DE and tooth Tip circle is smoothly connected, and the parabola DE is obtained the class parabola d1e1 on rotor end-face through space coordinate transformation, and acquire The class parabola conjugate line e1f1 of root circle and pitch circle is connected on rotor end-face；
Step 3, addendum circle arc c1d1 is added on rotor end-face and connect above-mentioned curve with tooth root circular arc f1a1, form closed turn Sub- profile.
CN201910051620.0A 2019-01-21 2019-01-21 A kind of smooth rotor profile of twin-screw vacuum pump and its design method Active CN110005609B (en)

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