WO2023092525A1 - 一种双螺杆转子型线综合性能判断及优化设计方法 - Google Patents

一种双螺杆转子型线综合性能判断及优化设计方法 Download PDF

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WO2023092525A1
WO2023092525A1 PCT/CN2021/133834 CN2021133834W WO2023092525A1 WO 2023092525 A1 WO2023092525 A1 WO 2023092525A1 CN 2021133834 W CN2021133834 W CN 2021133834W WO 2023092525 A1 WO2023092525 A1 WO 2023092525A1
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rotor
line
twin
point
male
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PCT/CN2021/133834
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English (en)
French (fr)
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何雪明
胡蓉
于嘉川
闫俊霞
宋健忠
孙维杰
范海港
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江南大学
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Publication of WO2023092525A1 publication Critical patent/WO2023092525A1/zh
Priority to US18/220,908 priority Critical patent/US20230349383A1/en

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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
    • 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
    • F04C18/082—Details specially related to intermeshing engagement type pumps
    • F04C18/084—Toothed wheels
    • 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
    • F04C28/00—Control of, monitoring of, or safety arrangements for, pumps or pumping installations specially adapted for elastic fluids
    • F04C28/28—Safety arrangements; Monitoring
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Definitions

  • the invention relates to a comprehensive performance judgment and optimal design method of twin-screw rotor profiles, belonging to the field of compressor design and manufacture.
  • the twin-screw compressor is a kind of volumetric rotary mechanical equipment, which consists of a pair of screw rotors (also known as male and female rotors), a pair of end covers and a shell.
  • twin-screw compressors are widely used in various industrial sectors such as power and refrigeration due to their own structure and performance characteristics.
  • the twin-screw compressor also has good adaptability, so it gradually replaces other types of compressors such as sliding vane compressors.
  • the screw rotor (yin and yang rotor) is the core component of the screw compressor. Its design directly determines the performance of the screw compressor, and the rotor profile is the research basis for many issues such as the processing performance of the screw rotor and the comprehensive performance of the equipment.
  • the rotor profile is the section line of the axial end face of the screw rotor), that is, the performance of the rotor profile directly affects the overall performance of the twin-screw compressor, so the research and design personnel of the screw rotor conduct research on the parameters that affect the performance of the rotor profile, Including contact line length, leakage triangle area and area utilization coefficient, etc.; From the perspective of sealing, examine the impact of rotor profile changes on performance parameters, summarize the change rules of performance parameters, and optimize the rotor profile based on the meshing line method in the future Design provides certain theoretical guidance.
  • the pros and cons of screw rotor profile design are mainly judged by examining whether the inter-tooth volume has excellent sealing.
  • the screw compressor performance especially the evaluation of the performance parameters of the rotor shape line, it is extended on the basis of the meshing line equation.
  • the design principle of the screw rotor profile is to form a short and continuous contact line, a small leakage triangle and a large area utilization factor.
  • the performance parameters of the compressor's contact line length, leakage triangle area, and area utilization coefficient have different influence directions on the performance of the compressor. Therefore, it is not possible to judge whether the design of the rotor profile is good or bad according to one of the parameters, which leads to low design efficiency.
  • the invention provides a rotor type of twin-screw rotor
  • the line comprehensive performance judgment and optimal design method by providing a comprehensive performance index K to determine the rotor profile performance of the twin-screw rotor, and then divide the meshing line into eight sections, and determine the adjustment direction and distance of each section through the comprehensive performance index K, Further, a high-performance rotor profile is obtained, and a high-performance compressor is subsequently produced according to the obtained high-performance rotor profile.
  • a method for judging the comprehensive performance of a twin-screw rotor profile comprising:
  • the relevant parameters of the male and female rotors of the twin-screw rotor the length of the contact line L, the area of the leakage triangle S, the number of teeth of the male and female rotors and the radius of the addendum circle;
  • a, b and c are coefficients that unify the contact line length L and the area utilization coefficient C ⁇ to the order of magnitude of the leakage triangle area S;
  • the area utilization coefficient C ⁇ is calculated according to the number of teeth of the male and female rotors and the radius of the addendum circle, including:
  • the inter-tooth area refers to the volume of the relatively closed element formed between the helical tooth surfaces of the two rotors and the casing when the male and female rotors rotate and engage on the rotor end surface The area of the projection;
  • D 1 is the diameter of the addendum circle of the male rotor
  • z 1 is the number of teeth of the male rotor.
  • the method when the method obtains the length L of the contact line, it includes:
  • the direction pointing to the axis center of the female rotor is the X axis
  • the axial direction is the Z axis
  • the Y axis is perpendicular to the XOZ plane to establish a three-dimensional coordinate system
  • the contact line is discretized into m points, and the length L of the contact line is calculated according to formula (1):
  • the method obtains the leakage triangle area S, it includes:
  • Point A is the intersection point of the intersection line WW between the tooth surface of the male rotor and the inner wall of the casing
  • point B is the intersection point of the intersection line WW between the tooth surface of the female rotor and the inner wall surface of the casing
  • point C is the highest point of the contact line of the twin-screw rotor
  • the contact line is a curve formed in space by the contact parts of the two helical tooth surfaces when the male and female rotors mesh
  • the present invention also provides a twin-screw rotor profile optimization design method, the method comprising:
  • A' is the intersection point of the tooth top circle of the female rotor and the tooth bottom circle of the male rotor
  • point B' is the intersection point of the pitch circle of the male and female rotors
  • C' The point is the bottom dead center of the meshing line
  • the point D' is the intersection point of the tooth top circle of the male rotor and the tooth bottom circle of the female rotor; then respectively take the lowest point P' of the arc A'B' section and the highest point N of the arc D'B' section ' and the highest point M' of arc B'A' are bounded, and arc A'B', arc D'B', and arc B'A' are divided into left and right sections;
  • the meshing line of each section is adjusted "inside” and “outside”, and the adjustment direction and distance of each section are determined by calculating the comprehensive performance index K of the twin-screw rotor profile before and after adjustment. Among them, the area enclosed by the meshing line is reduced. Modify the direction to be “inside”, otherwise "outside”;
  • the twin-screw rotor profile that minimizes the comprehensive performance index K of the twin-screw rotor profile is determined, which is the optimized twin-screw rotor profile.
  • the adjustment direction and distance of each segment are determined, including:
  • the adjusted comprehensive performance index K value of the twin-screw rotor profile is less than the value before adjustment, then continue to adjust towards the current direction; until the comprehensive performance index K value appears an inflection point;
  • the adjusted comprehensive performance index K value of the twin-screw rotor profile is greater than the value before adjustment, adjust in the opposite direction until the comprehensive performance index K value shows an inflection point.
  • the meshing line is a projection of the contact line on the axial end surface of the rotor.
  • the area surrounded by the meshing line refers to the area of the enclosed area surrounded by the meshing line.
  • the relationship between the contact line length, the leakage triangle and the area utilization coefficient of the compressor rotor profile can be determined, so that the design of the compressor rotor profile can be judged according to this method Find out the advantages and disadvantages of the performance of the designed compressor rotor profile, and then improve the design efficiency of the compressor rotor profile, and provide high-performance rotor profiles for the production of high-performance compressors.
  • Figure 1A is a diagram of the screw rotor profile and its elements; 1 is the profile of the male rotor, 2 is the profile of the female rotor, 3 is the closed volume, 4 is the meshing line, 6 is the volume between the teeth of the male rotor, and 7 is the section of the male rotor Circle, 8 is the pitch circle of the female rotor, 9 is the volume between the teeth of the female rotor, 11 is the inner wall of the casing, and W is the projection point of the intersection line of the cylindrical surface of the inner wall of the casing.
  • Figure 1B is an enlarged view of the enclosed volume and engagement line of the screw rotor.
  • Figure 1C is an axial view of the screw rotor leakage triangle and contact line, where 5 is the leakage triangle and 10 is the contact line.
  • Fig. 2A is a schematic diagram of the relationship between the compressor rotor contact line and meshing line.
  • Figure 2B is a compressor rotor engagement line diagram.
  • Fig. 3 is a schematic diagram of the spatial position of the leakage triangle.
  • Figure 4 is a schematic diagram of the leakage triangle calculation.
  • Figure 5 is the diagram of Fusheng meshing line after segmentation.
  • Fig. 6A is a diagram of the meshing line A'M' moving inward.
  • Fig. 6B is a view of the meshing line A'M' moving outward.
  • Fig. 7A is a view of the meshing line M'B' moving inward.
  • Fig. 7B is a view of the meshing line M'B' moving outward.
  • Fig. 8A is a view of the meshing line B'C' moving inward.
  • Fig. 8B is a view of the B'C' section of the meshing line moving outward.
  • Fig. 9A is a view of the segment C'D' of the meshing line moving inward.
  • Fig. 9B is a diagram showing the movement of the segment C'D' of the meshing line to the outside.
  • Fig. 10A is a diagram of the meshing line D'N' moving to the inside.
  • Fig. 10B is a diagram of the meshing line D'N' moving outward.
  • Fig. 11A is a view of the meshing line N'B' moving inward.
  • Fig. 11B is a diagram showing the movement of the meshing line N'B' to the outside.
  • Fig. 12A is a view of the meshing line B'P' moving inward.
  • Fig. 12B is a view of the meshing line B'P' moving outward.
  • Fig. 13A is a view of the meshing line P'A' moving inward.
  • Fig. 13B is a view of the meshing line P'A' moving outward.
  • Figure 14 is the optimized direction diagram of each segment of the meshing line.
  • Engagement line The projection of the contact line on the axial end face of the rotor is called the engagement line.
  • Leakage triangle The curved side triangle formed by the intersection of the cylindrical surface of the inner wall of the casing and the tooth surface of the male and female rotors is called a leakage triangle.
  • Elementary volume When the male and female rotors rotate and mesh, the relatively closed volumes formed between the helical tooth surfaces of the two rotors and the casing are called elementary volumes.
  • Inter-tooth area When the male and female rotors rotate and mesh, the projected area of the relatively closed primitive volume formed between the helical tooth surfaces of the two rotors and the casing on the rotor end surface is called the inter-tooth area.
  • Closed volume When the male and female rotors are rotating, the volume formed by the tooth profiles of the two rotors in the space is called the closed volume.
  • Addendum circle the intersection line between the cylindrical surface of the addendum and the end plane of the male and female rotors.
  • Rotor profile The projection of the tooth profile of the male and female rotors on its end face is called the rotor profile.
  • Fusheng rotor profile Yin-Yang rotor gear ratio is 6:5, the rotor profile is asymmetric profile, composed of 4 sections of curves, male rotor consists of 1 section of circular arc envelope, 1 section of elliptical arc and 2 sections of circular arc Composition; the female rotor is composed of 1 section of arc, 1 section of elliptical arc envelope and 2 sections of arc envelope.
  • Hitachi rotor profile the gear ratio of the male and female rotors is 6:5, the rotor profile is asymmetrical and consists of 6 sections of curves, the female rotor consists of 4 sections of arc, 1 section of pin tooth arc and 1 section of addendum arc Composition; the male rotor is composed of 4 sections of arc envelope, 1 section of pin tooth arc envelope and 1 section of tooth root arc.
  • This embodiment provides a method for judging the comprehensive performance of twin-screw rotor profiles, the method comprising:
  • Step 1 Determine the calculation formula of the parameters related to the comprehensive performance of the rotor profile, the contact length L, the leakage triangle area S and the area utilization coefficient M of the parameters related to the rotor profile performance;
  • the tooth curve of the Fusheng profile consists of 4 sections
  • the female rotor includes 2 sections of circular arc envelope, 1 section of elliptical envelope and 1 section of circular arc
  • the male rotor includes 2 sections of circular arc, 1 section of ellipse And 1 arc envelope.
  • the Fusheng meshing line is also composed of 4 tooth curves, and the segmented Fusheng meshing line is shown in Figure 5.
  • Figure 1A shows the rotor profile, meshing line, inter-tooth area and closed volume
  • Figure 1B shows the closed volume of the screw rotor and the enlarged view of the meshing line, the leakage triangle and the axial view of the contact line are shown in Figure 1C.
  • 1 is the profile line of the male rotor
  • 2 is the profile line of the female rotor
  • 3 is the closed volume
  • 4 is the meshing line
  • 5 is the leakage triangle
  • 6 is the volume between the teeth of the male rotor
  • 7 is the pitch circle of the male rotor
  • 8 is the pitch circle of the female rotor
  • 9 is the volume between the teeth of the female rotor
  • 10 is the contact line
  • 11 is the inner wall of the casing
  • W is the projection point of the intersection line of the cylindrical surface of the inner wall of the casing on the end surface.
  • the contact line divides the volume between the teeth of the male and female rotors into two parts, one of which is The medium on one side is in a compressed state, while the medium on the other side is in a suction state, so there is a certain pressure difference in the working chamber on both sides of the contact line, one side is called the high pressure side, and the other side is called the low pressure side, so the contact line It is also the dividing line between the high-voltage side and the low-pressure side of the cell volume, as shown in Figure 1B.
  • the volume flow rate decreases and the volume efficiency decreases, so it is necessary to improve the sealing effect of the contact line on the volume of the cells on both sides.
  • the volumetric flow rate mentioned above refers to the gas volume discharged by the compressor per unit time under the required discharge pressure.
  • Volumetric efficiency refers to the ratio of the actual volume flow of the compressor to the theoretical volume flow of the working chamber.
  • the calculation process of the contact line length is to first discretize the contact line into a series of points, and then sum the distances between two adjacent points to obtain the contact line length. When the number of discrete points is large enough, the calculation accuracy can be guaranteed, and Easy to realize by programming algorithm.
  • the calculation process of the contact line length is as follows:
  • n is the subscript of each discrete point
  • m is the number of discrete points
  • x n , y n , z n are the three-dimensional coordinates of each discrete point.
  • the rotor meshing line derived from the male and female rotor profiles is an important consideration for judging the performance of the rotor profile, and the meshing line is the trajectory of the meshing point of the rotor profile. It can be seen from this that the meshing line is the contact line on the axial end surface of the rotor. Projection, the relationship between the meshing line and the contact line is shown in Figure 2A, and Figure 2B is a schematic diagram of the meshing line.
  • the leakage triangle is also a channel connecting the volumes of two adjacent units, and the gas on the high-pressure side will leak to the low-pressure side through the leakage triangle, which is an internal axial leakage.
  • the right figure in Fig. 3 is an enlarged view of the circled part I in the left figure.
  • the area of the leakage triangle is the size of the area of the space curved triangle ⁇ ABC.
  • the curves AC and BC are discretized into p points and q points respectively. The more the discrete points are, the more accurate the calculation result is.
  • Mi and F j be the discrete points on the curves AC and BC respectively, and the distance from the intersection line The distances of WW are and Then you can get:
  • the area of the leaky triangle can be expressed as:
  • the inter-tooth area is the projection of the element volume on the rotor end face.
  • the shaded parts 6 and 9 in Fig. 1 represent the inter-tooth area of the male rotor and the female rotor respectively, and their size directly reflects the size of the element volume.
  • the area utilization coefficient C ⁇ characterizes the degree of utilization within the range of the addendum circle of the twin-screw rotor.
  • the inter-tooth area refers to the volume of the relatively closed element formed between the helical tooth surfaces of the two rotors and the casing when the male and female rotors rotate and engage on the rotor end surface The area of the projection;
  • D 1 is the diameter of the addendum circle of the male rotor
  • z 1 is the number of teeth of the male rotor.
  • the center of the male rotor Take the center of the male rotor as the origin O, the direction from the center of the female rotor to the center of the male rotor is the U-axis, and the U-axis rotates 90° counterclockwise on the end face to establish a two-dimensional coordinate system as the V-axis;
  • Tooth curve refers to a section of contour curve corresponding to the male and female rotor profiles
  • the rotor profile is composed of g-segment tooth curves. According to the number of rotor teeth and the radius of the addendum circle of the yin and yang rotors, the inter-tooth area corresponding to each tooth curve of the yin and yang rotors is calculated respectively, and then accumulated and summed to obtain the complete yin and yang The area between rotor teeth A 02 and A 01 ;
  • z is the number of rotor teeth
  • R is the radius of the addendum circle
  • g is the number of tooth curves
  • the subscripts 2 and 1 represent the female and male rotors respectively
  • u and v are the variables on the tooth curve equation
  • u' and v' are The first-order derivative
  • t s and t e are the value range of the parameter t.
  • Step 2 Adjust the segmented rotor meshing line, and calculate the value of each performance parameter of the adjusted rotor profile.
  • the performance parameters include contact line length L, leakage triangle area S and area utilization coefficient C ⁇ .
  • each point on the meshing line of the twin-screw rotor is determined in a clockwise direction, and the meshing line is divided into eight segments through each point: A' is the intersection point of the tooth top circle of the female rotor and the tooth bottom circle of the male rotor, B' Point is the intersection point of the pitch circles of the male and female rotors, point C' is the bottom dead center of the meshing line, point D' is the intersection point of the tooth top circle of the male rotor and the tooth bottom circle of the female rotor; then the lowest points P', The highest point N' of the arc D'B' section and the highest point M' of the arc B'A' section are bounded, and the arc A'B', the arc D'B', and the arc B'A' are divided into left and right sections.
  • the meshing line is a " ⁇ "-shaped figure, the size of the circles on the left and right sides is quite different. Therefore, the left side of Figure 5 is the overall picture of the meshing line, and the right side of Figure 5 is framed by a box in the left side. A magnified view of a portion of .
  • the calculation can be performed directly, or by using the TSPD program, or by using an excel sheet to record the values of the parameters before and after adjustment; for the introduction of the TSPD program, please refer to "Shi Guojiang, He Xueming, & Zhang Rong. (2016). Development and research on the design system of male and female rotor profiles of twin-screw compressors. Compressor Technology, (5), 6-13.”.
  • Step 4 According to step 1 to step 3, determine the relational expression of the comprehensive performance index K of compressor rotor performance; according to the coefficient of each parameter in step 3, draw the relational expression of comprehensive performance index K as:
  • the adjustment methods of each section that will make the overall performance of the molded line better are: A'M' outward, M'B' outward, B'C' outward, C'D' inward, D'N 'outward, N'B' outward, B'P' unchanged, P'A' outward, as shown in Figure 14 below, and the left figure of Figure 14 shows the adjustment direction of each segment on the left circle of the meshing line , The figure on the right side of Figure 14 shows the adjustment direction of each segment on the circle on the right side of the meshing line.
  • Each segment can be optimized separately, and then integrated into a complete meshing line, and an optimized profile can be generated based on the meshing line.
  • the various performance parameters of this optimized line are shown in Table 4 below. Compared with the original profile, the length of the contact line of the optimized profile is slightly increased, only 0.6306mm, a relative increase of 0.3%; the area of the leakage triangle area is reduced by 0.3317mm 2 , a relative decrease of 7.8%; the area utilization factor The relative increase of 0.0325 is 7.2%; the comprehensive performance index K value is relatively reduced by 13.66%, that is, the sealing performance of the rotor profile is optimized by 13.66%.
  • twin-screw rotor profile optimization design method provided in this application, the design efficiency of the twin-screw rotor profile is greatly improved, and the subsequent twin-screw rotor produced according to the optimized rotor profile can make the performance of the compressor better.
  • Part of the steps in the embodiments of the present invention can be realized by software, and the corresponding software program can be stored in a readable storage medium, such as an optical disk or a hard disk.

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  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Applications Or Details Of Rotary Compressors (AREA)
  • Rotary Pumps (AREA)

Abstract

一种双螺杆转子型线综合性能判断及优化设计方法，属于压缩机设计制造领域。所述方法通过建立压缩机转子型线性能的综合性能指标的表达式，确定压缩机转子型线的接触线长度、泄漏三角形和面积利用系数之间的关系，使得在设计压缩机转子型线时能够根据该方法判断出设计出的压缩机转子型线的性能的优劣，进而为优化设计转子型线提供参考指标，提高压缩机转子型线的设计效率，为生产出高性能的压缩机提供高性能的转子型线。

Description

一种双螺杆转子型线综合性能判断及优化设计方法
Method for judging and optimizing the comprehensive performance of twin-screw rotor profile
技术领域
本发明涉及一种双螺杆转子型线综合性能判断及优化设计方法，属于压缩机设计制造领域。
背景技术
双螺杆压缩机属于容积式回转机械设备的一种，由一对螺杆转子(也称阴阳转子)、一对端盖和一个壳体组成。双螺杆压缩机作为一种通用机械，由于自身结构和性能的特点，被广泛应用在动力、制冷等各个工业部门。同时双螺杆压缩机还具有较好的适应能力，因而逐渐代替了滑片压缩机等其他种类的压缩机。
螺杆转子(阴阳转子)作为螺杆压缩机的核心零部件，其设计优劣直接决定了螺杆压缩机的性能如何，而转子型线又是螺杆转子加工性能和设备运转综合性能等诸多问题的研究基础(转子型线即螺杆转子轴向端面截线)，也即，转子型线的性能直接影响到双螺杆压缩机整体性能，因而螺杆转子的研究设计人员针对影响转子型线性能的参数展开研究，包括接触线长度、泄漏三角形面积和面积利用系数等；从密封性角度出发，考查转子型线变化对性能参数的影响，总结性能参数的变化规律，为日后基于啮合线法对转子型线进行优化设计提供一定的理论指导。
对于螺杆转子型线设计的优劣，主要是通过考察其齿间容积是否具备出色的封闭性来进行判断。而对于螺杆压缩机性能，特别是转子型线性能参数的评判都是以啮合线方程为基础延伸的。针对主要的性能参数，螺杆转子型线的设计原则是形成长度较短且连续的接触线、较小的泄漏三角形和较大的面积利用系数。而压缩机的接触线长度、泄漏三角形面积和面积利用系数各性能参数对压缩机性能的影响方向不一致，比如在减小泄漏三角形面积大小的同时，可能会导致阴阳转子型线接触线长度增加，因此不能根据其中某一个参数来评判转子型线的设计是否优劣，从而导致其设计效率低下。
发明内容
解决螺杆压缩机各性能参数对压缩机性能影响方向不一致，无法根据其中某一个参数来判断转子齿形的设计是否优劣从而导致设计效率低下的问题，本发明提供一种双螺杆转子的转子型线综合性能判断及优化设计方法，通过提供一种综合性能指标K确定双螺杆转子的转子型线性能，进而将啮合线分为八段，通过综合性能指标K确定各段的调整方向及距离，进而得到高性能的转子型线，后续根据所得到的高性能的转子型线生产出高性能的压缩机。
一种双螺杆转子型线综合性能判断方法，所述方法包括：
获取双螺杆转子的阴阳转子的相关参数：接触线长度L、泄漏三角形面积S、阴阳转子的转子齿数及齿顶圆半径；
根据阴阳转子的转子齿数及齿顶圆半径计算出面积利用系数C α；
根据公式(10)计算综合性能指标K；
K＝aL*bS/(cC α)      (10)
其中，a、b和c为将接触线长度L和面积利用系数C α统一至泄漏三角形面积S的数量级的系数；
根据计算出的综合性能指标K的取值判断双螺杆转子型线的性能；
可选的，接触线长度L、阴阳转子的转子齿数及齿顶圆半径的单位为毫米、泄漏三角形面积S的单位为平方毫米时，a、b和c取值分别为：
a＝0.01，b＝1，c＝10。
可选的，所述根据阴阳转子的转子齿数及齿顶圆半径计算出面积利用系数C α，包括：
分别计算阴、阳转子齿间面积A 02和A 01；所述齿间面积指阴阳转子旋转啮合时，两转子的螺旋齿面与机壳之间形成的相对封闭的基元容积在转子端面上的投影的面积；
根据公式(9)计算面积利用系数C α：
Figure PCTCN2021133834-appb-000001
其中，D 1为阳转子齿顶圆直径，z 1为阳转子齿数。
可选的，所述方法在获取接触线长度L时，包括：
以阳转子端面轴心为原点O，以指向阴转子轴心方向为X轴，轴向为Z轴，Y轴垂直于XOZ平面建立三维坐标系；
将接触线离散成m个点，根据公式(1)计算接触线长度L：
Figure PCTCN2021133834-appb-000002
式中，n为各个离散点的下标；n＝1,2,……,m；x n、y n、z n为各离散点的三维坐标。
可选的，所述方法在获取泄漏三角形面积S时，包括：
设A点为阳转子齿面与机壳内壁面交线WW的交点，B点为阴转子齿面与机壳内壁面交线WW的交点，C点是双螺杆转子的接触线的最高点；所述接触线为阴阳转子啮合时，两螺旋齿面的接触部位在空间上形成的曲线；
将曲线AC和BC分别离散成p个点和q个点；
设点M i和F j分别为曲线AC和BC上离散点，且点M i和F j距离交线WW的距离分别为
Figure PCTCN2021133834-appb-000003
和
Figure PCTCN2021133834-appb-000004
则可得到：
Figure PCTCN2021133834-appb-000005
Figure PCTCN2021133834-appb-000006
则泄漏三角形面积S为：
Figure PCTCN2021133834-appb-000007
其中，
Figure PCTCN2021133834-appb-000008
为空间曲边泄漏三角形的曲边AB投影到交线WW上的边，
Figure PCTCN2021133834-appb-000009
为接触线的最高点在交线WW投影点到B点的距离。
本发明还提供一种双螺杆转子型线优化设计方法，所述方法包括：
根据权利要求1-5任一所述的方法获取待优化的双螺杆转子型线的综合性能指标K；
以顺时针方向确定双螺杆转子的啮合线上各点将啮合线分为八段：A'为阴转子齿顶圆和阳转子齿底圆交点，B'点为阴阳转子节圆交点，C'点为啮合线下止点，D'点为阳转子齿顶圆和阴转子齿底圆交点；再分别以弧A'B'段的最低点P'、弧D'B'段的最高点N'及弧B'A'段最高点M'为界，将弧A'B'、弧D'B'、弧B'A'分为左右两段；
对各段啮合线分别进行“内”“外”调整，通过计算调整前后双螺杆转子型线的综合性能指标K，确定各段的调整方向和距离，其中，使啮合线所围面积减小的修改方向为“内”，否则为“外”；
综合各段的调整方向和距离确定使得双螺杆转子型线的综合性能指标K最小的双螺杆转子型线，即为优化后的双螺杆转子型线。
可选的，所述通过计算调整前后双螺杆转子型线的综合性能指标K，确定各段的调整方向和距离，包括：
若调整后的双螺杆转子型线的综合性能指标K值小于调整前的值，则继续朝当前方向进 行调整；直至综合性能指标K值出现拐点；
若调整后的双螺杆转子型线的综合性能指标K值大于调整前的值，则朝反方向调整，直至综合性能指标K值出现拐点。
可选的，所述啮合线为接触线在转子轴向端面上的投影。
可选的，所述啮合线所围面积指啮合线围成的封闭区域的面积。
本发明有益效果是：
通过建立压缩机转子型线综合性能指标的表达式，确定压缩机转子型线的接触线长度、泄漏三角形和面积利用系数之间的关系，使得在设计压缩机转子型线时能够根据该方法判断出设计出的压缩机转子型线的性能的优劣，进而提高压缩机转子型线的设计效率，为生产出高性能的压缩机提供高性能的转子型线。
附图说明
为了更清楚地说明本发明实施例中的技术方案，下面将对实施例描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1A为螺杆转子型线及其要素图；其中1是阳转子型线，2是阴转子型线，3是封闭容积，4是啮合线，6是阳转子齿间容积，7是阳转子节圆，8是阴转子节圆，9是阴转子齿间容积，11是机壳内壁，W是机壳内壁圆柱面交线的投影点。
图1B为螺杆转子封闭容积和啮合线放大图。
图1C为螺杆转子泄漏三角形和接触线轴向图，其中5是泄漏三角形，10是接触线。
图2A为压缩机转子接触线与啮合线关系示意图。
图2B为压缩机转子啮合线图。
图3为泄漏三角形空间位置示意图。
图4为泄漏三角形计算示意图。
图5为分段后的复盛啮合线图。
图6A为啮合线A′M′段向内侧移动图。
图6B为啮合线A′M′段向外侧移动图。
图7A为啮合线M′B′段向内侧移动图。
图7B为啮合线M′B′段向外侧移动图。
图8A为啮合线B′C′段向内侧移动图。
图8B为啮合线B′C′段向外侧移动图。
图9A为啮合线C′D′段向内侧移动图。
图9B为啮合线C′D′段向外侧移动图。
图10A为啮合线D′N′段向内侧移动图。
图10B为啮合线D′N′段向外侧移动图。
图11A为啮合线N′B′段向内侧移动图。
图11B为啮合线N′B′段向外侧移动图。
图12A为啮合线B′P′段向内侧移动图。
图12B为啮合线B′P′段向外侧移动图。
图13A为啮合线P′A′段向内侧移动图。
图13B为啮合线P′A′段向外侧移动图。
图14为啮合线各段优化方向图。
具体实施方式
为使本发明的目的、技术方案和优点更加清楚，下面将结合附图对本发明实施方式作进一步地详细描述。
接触线：阴阳转子啮合时，两螺旋齿面的接触部位在空间上形成的曲线称为接触线。
啮合线：接触线在转子轴向端面上的投影称为啮合线。
泄漏三角形：机壳内壁圆柱面交线和阴阳转子齿面构成的曲边三角形称为泄漏三角形。
基元容积：阴阳转子旋转啮合时，两转子的螺旋齿面与机壳之间形成的一个个相对封闭的体积称为基元容积。
齿间面积：阴阳转子旋转啮合时，两转子的螺旋齿面与机壳之间形成的相对封闭的基元容积在转子端面上的投影的面积称为齿间面积。
封闭容积：阴阳转子在旋转时，两转子的齿廓在空间形成的一个体积称为封闭容积。
齿顶圆：阴阳转子齿顶圆柱面与端平面的交线。
转子型线：阴阳转子的齿面轮廓在其端面的投影称为转子型线。
常见的转子型线中复盛转子型线、日立转子型线的特点如下：
复盛转子型线：阴阳转子齿数比为6：5，转子型线为不对称型线，由4段曲线构成，阳转子由1段圆弧包络线、1段椭圆弧和2段圆弧组成；阴转子由1段圆弧、1段椭圆弧包络线和2段圆弧包络线组成。
日立转子型线：阴阳转子齿数比为6：5，转子型线为不对称型线，由6段曲线构成，阴转子由4段圆弧，1段销齿圆弧和1段齿顶圆弧组成；阳转子由4段圆弧包络线，1段销齿圆弧包络线和1段齿根圆弧组成。
实施例一：
本实施例提供一种双螺杆转子型线综合性能判断方法，所述方法包括：
步骤一：确定与转子型线综合性能优劣有关的参数的计算公式，与转子型线性能优劣有关的参数接触长度L、泄漏三角形面积S和面积利用系数M；
压缩机转子有多种型线，本实施例以一条6次NURBS拟合的复盛啮合线为例进行说明。
如上所述，复盛型线的齿曲线由4段构成，阴转子包括2段圆弧包络线、1段椭圆包络线和1段圆弧；阳转子包括2段圆弧、1段椭圆和1段圆弧包络线。复盛啮合线也由4段齿曲线构成，分段后的复盛啮合线如图5所示。
如图1A、图1B和图1C所示，为螺杆转子型线及其要素示意图，图1A中显示了转子型线、啮合线、齿间面积和封闭容积，图1B中显示了螺杆转子封闭容积和啮合线放大图，图1C中显示了泄漏三角形和接触线轴向图。
图1A和图1C中，1是阳转子型线，2是阴转子型线，3是封闭容积，4是啮合线，5是泄漏三角形，6是阳转子齿间容积，7是阳转子节圆，8是阴转子节圆，9是阴转子齿间容积，10是接触线，11是机壳内壁，W是机壳内壁圆柱面交线在端面的投影点。
当双螺杆转子的齿相互啮合时，两螺旋齿面的接触部位在空间上形成了一条形状特殊的曲线，称之为接触线，接触线将阴阳转子的齿间容积分为两部分，其中一侧的介质处于压缩状态，而另一侧的介质处于吸气状态，所以接触线两侧的工作腔内存在一定的压力差，一侧称为高压侧，一侧称为低压侧，因此接触线也是基元容积高压侧与低压侧的分界线，如图1B所示。由于阴阳转子在运行过程中受热载荷和压力作用的影响，如果紧密接触则会产生微小变形，为避免转子啮合时发生干涉，保护转子不被损坏，因此阳转子齿顶与阴转子齿底之间会预留一定的间隙，因此理论中的接触线实际上是一条接触线间隙带，高压侧的气体受压力作用通过这条间隙带流向低压侧，这种内部横向泄漏将导致双螺杆压缩机的容积流量降低和容积效率下降，因此提高接触线对其两侧基元容积的密封效果十分必要。在保证阴阳转子之间留有适当间隙以避免运动干涉的前提下，减小接触线长度是一个行之有效的方法。上 述提到的容积流量是指在所要求的排气压力下，压缩机单位时间内排出的气体容积。容积效率是指压缩机实际的容积流量与工作腔的理论容积流量之比。
接触线长度的计算过程是先将接触线离散成一系列点，再将两相邻点之间的距离累加求和即可得到接触线长度，当离散点的数量足够多时就可以保证计算精度，且易于通过编程算法实现。接触线长度的计算过程如下：
首先建立一个三维坐标系，以阳转子端面轴心为原点O，以指向阴转子轴心方向为X轴，轴向为Z轴，Y轴垂直于XOZ平面，则公式如下：
Figure PCTCN2021133834-appb-000010
式中，n为各个离散点的下标；m为离散点的数量；x n、y n、z n为各离散点的三维坐标。
由阴阳转子型线衍生的转子啮合线对于转子型线性能判断的重要考量，而啮合线是转子型线啮合点的轨迹，由此可以看出，啮合线就是接触线在转子轴向端面上的投影，啮合线与接触线的关系如图2A所示，图2B即啮合线示意图。
通常双螺杆压缩机阴阳转子接触线的最高点(如图3中C点所示)位置并不能到达机壳内壁圆柱面交线(WW)上，因此机壳内壁圆柱面交线与阴、阳转子齿面将构成一个空间曲边三角形泄漏区域，称之为泄漏三角形，如图3中△ABC所示，其中A点是阳转子齿面与机壳内壁面交线WW的交点，B点是阴转子齿面与机壳内壁面交线WW的交点，C点是接触线的最高点。泄漏三角形同样是连通两个相邻基元容积的通道，高压侧气体会通过泄漏三角形向低压侧泄漏，为内部轴向泄漏。图3中右侧图为左侧图中圈出部分I的放大图。
从转子端面上看去，通常近似认为啮合线最高点C距离机壳内壁面交线端点W越远，则泄漏三角形面积越大，内部轴向泄漏越严重。泄漏三角形面积的大小就是该空间曲边三角形△ABC的面积大小。经过机壳内壁圆柱面交线WW和啮合线最高点C做一平面，并将曲边三角形△ABC投影到该平面上，如下图4所示，则泄漏三角形的面积可以表示为：
Figure PCTCN2021133834-appb-000011
为计算方便，将曲线AC和BC分别离散成p个点和q个点，离散点数量越多计算结果越精确，设点M i和F j分别为曲线AC和BC上离散点，距离交线W-W的距离分别为
Figure PCTCN2021133834-appb-000012
和
Figure PCTCN2021133834-appb-000013
则可得到：
Figure PCTCN2021133834-appb-000014
Figure PCTCN2021133834-appb-000015
由此，泄漏三角形的面积可表示为：
Figure PCTCN2021133834-appb-000016
齿间面积是基元容积在转子端面上的投影，图1中阴影部分6和9分别表示阳转子和阴转子的齿间面积，其大小直接反映给了基元容积的大小。
若已知转子型线中某一段齿曲线AB的参数方程：
Figure PCTCN2021133834-appb-000017
通常在进行转子型线的优化设计时，阳转子齿间面积的减小可能会导致增大阴转子齿间面积，因此为了更形象地描述和量化优化设计前后阴阳转子齿间面积的变化，引入面积利用系数C α来表征双螺杆转子齿顶圆范围内的利用程度。
计算面积利用系数C α过程如下：
分别计算阴、阳转子齿间面积A 02和A 01；所述齿间面积指阴阳转子旋转啮合时，两转子的螺旋齿面与机壳之间形成的相对封闭的基元容积在转子端面上的投影的面积；
计算得到阴、阳转子齿间面积A 02和A 01后，根据公式(9)计算面积利用系数C α：
Figure PCTCN2021133834-appb-000018
其中，D 1为阳转子齿顶圆直径，z 1为阳转子齿数。
在计算阴、阳转子齿间面积A 02和A 01时，可采用下述方法：
以阳转子中心为原点O，以阴转子中心指向阳转子中心的方向为U轴，U轴在端面上逆时针旋转90°为V轴建立二维坐标系；
获取转子型线中某一段齿曲线的参数方程：
Figure PCTCN2021133834-appb-000019
齿曲线指阴、阳转子型线对应的一段轮廓曲线；
转子型线由g段齿曲线组成，根据阴阳转子的转子齿数及齿顶圆半径分别计算出阴、阳转子的每一段齿曲线对应的齿间面积，再进行累加求和得到完整的阴、阳转子齿间面积A 02和A 01；
根据公式(7)和公式(8)计算阴、阳转子的齿间面积：
Figure PCTCN2021133834-appb-000020
Figure PCTCN2021133834-appb-000021
其中，z为转子齿数，R为齿顶圆半径，g为齿曲线的数量，下标2、1分别代表阴、阳转子，u、v为齿曲线方程上的变量，u’、v’为一阶导数，t s、t e为参数t的取值区间。
需要进行说明的是，上述仅列出了一种计算阴、阳转子的齿间面积的方法，采用其他已知方法亦可得到，本申请对此不做限定。
从上式(9)可以看出，当齿顶圆直径一定时，齿间面积越大，则面积利用系数越大，即该转子型线在齿顶圆范围内总的利用程度越高。下表1为常用转子型线面积利用系数C α值。
表1常用型线的面积利用系数
Figure PCTCN2021133834-appb-000022
步骤二：对分段后的转子啮合线进行调整，并计算调整后转子型线各性能参数的值，性能参数包括接触线长度L、泄漏三角形面积S和面积利用系数C α。
如图5所示，以顺时针方向确定双螺杆转子的啮合线上各点，通过各点将啮合线分为八段：A'为阴转子齿顶圆和阳转子齿底圆交点，B'点为阴阳转子节圆交点，C'点为啮合线下止点，D'点为阳转子齿顶圆和阴转子齿底圆交点；再分别以弧A'B'段的最低点P'、弧D'B'段的最高点N'及弧B'A'段最高点M'为界，将弧A'B'、弧D'B'、弧B'A'分为左右两段。
因为啮合线为一个“∞”形的图形，其左右侧的圆的大小相差较大，因此图5左侧图为啮合线的整体图，图5右侧图为左侧图中用方框框出的部分的放大图。
本申请中规定使啮合线所围面积减小的修改方向为“内”，否则为“外”，对各段啮合线分别进行“内”“外”调整，各段啮合线调整如图6-图13B所示，计算调整后转子型线各性能参数的值，如表2所示。
为便于计算表2中的各参数，可以直接进行计算，也可采用TSPD程序计算，也可采用excel表分别记录调整前后的各参数值；TSPD程序的介绍可参考“施国江,何雪明,&张荣.(2018).双螺杆压缩机阴阳转子型线设计系统的开发研究.压缩机技术,(5),6-13.”。
表2啮合线各段对转子性能参数的影响(↓表示减小，↑表示增大)
Figure PCTCN2021133834-appb-000023
Figure PCTCN2021133834-appb-000024
通过表2可以看出：
(1)当啮合线所围成的面积增大时，齿间面积利用系数增大，即阴阳转子齿间面积之和增大；
(2)啮合线对泄漏三角形面积产生影响的只有A′B′段、B′C′段和C′D′段，且均向原啮合线内部移动时，泄漏三角形面积是减小的，而此时面积利用系数也是减小的，形成了相互影响的关系；
(3)上述各性能参数对压缩机性能的影响方向不一致，不能根据其中某一个参数来决定转子型线的设计是否优劣。因此需要一个综合性能指标来对转子型线的优劣做一个合理的评价。建立评判压缩机转子性能的综合性能指标的关系式，关系式如下：
K＝aL*bS/(cM)      (10)
其中：
L——接触线长度，mm
S——泄漏三角形面积，mm 2
M——面积利用系数；
步骤三：确定综合性能指标关系式中各性能参数的系数；接触线长度在150mm左右，泄漏三角形面积在5mm 2左右，阳转子齿间面积在610mm 2左右，阴转子齿间面积在620mm 2左右，则面积利用系数在0.45左右，令a＝0.01，b＝1，c＝10，将L和M统一到S的数量级。
步骤四：根据步骤一至步骤三确定压缩机转子性能的综合性能指标K的关系式；根据步骤三中各参数的系数，得出综合性能指标K的关系式为：
K＝0.01L*S/(10*M)     (11)
根据双螺杆压缩机转子型线设计系统计算其接触线长度L＝148.146mm，泄漏三角形面积S＝4.2588mm 2，面积利用系数M＝0.4542，则综合性能指标K 原始＝1.3891。现对该6次NURBS拟合的复盛啮合线进行优化。
以同样的方法分别对各段进行调整，得到的转子型线性能参数及综合性能指标如表3所示。
表3啮合线对综合性能指标的影响
Figure PCTCN2021133834-appb-000025
根据表3，会使型线综合性能变好的各段调整方式为：A′M′向外，M′B′向外，B′C′向外，C′D′向内，D′N′向外，N′B′向外，B′P′不变，P′A′向外，如下图14所示，图14左侧图示出了啮合线左侧圆上各段的调整方向，图14右侧图示出了啮合线右侧圆上各段的调整方向。
可将各段分别优化后，再整合成一条完整的啮合线，并根据该啮合线生成一条优化型线。现这条优化型线的各个性能参数如下表4所示。与原始型线相比，优化型线的接触线长度略有增加，仅增加0.6306mm，相对增加了0.3％；泄漏三角形区域面积减小了0.3317mm 2，相对减小了7.8％；面积利用系数增大了0.0325，相对增加了7.2％；综合性能指标K值相对降低了13.66％，即对转子型线的密封性能优化了13.66％。
表4原始型线与优化型线性能参数对比
Figure PCTCN2021133834-appb-000026
通过本申请提供的双螺杆转子型线优化设计方法，大大提高了双螺杆转子型线的设计效率，后续根据优化后的转子型线生产出的双螺杆转子可以使得压缩机性能更佳。
本发明实施例中的部分步骤，可以利用软件实现，相应的软件程序可以存储在可读取的存储介质中，如光盘或硬盘等。
以上所述仅为本发明的较佳实施例，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (9)

  1. 一种双螺杆转子型线综合性能判断方法，其特征在于，所述方法包括：
    获取双螺杆转子的阴阳转子的相关参数：接触线长度L、泄漏三角形面积S、阴阳转子的转子齿数及齿顶圆半径；
    根据阴阳转子的转子齿数及齿顶圆半径计算出面积利用系数C α；
    根据公式(10)计算综合性能指标K；
    K＝aL*bS/(cC α)  (10)
    其中，a、b和c为将接触线长度L和面积利用系数C α统一至泄漏三角形面积S的数量级的系数；
    根据计算出的综合性能指标K的取值判断双螺杆转子型线的性能优劣。
  2. 根据权利要求1所述的方法，其特征在于，接触线长度L、阴阳转子的转子齿数及齿顶圆半径的单位为毫米、泄漏三角形面积S的单位为平方毫米时，a、b和c取值分别为：
    a＝0.01，b＝1，c＝10。
  3. 根据权利要求1所述的方法，其特征在于，所述根据阴阳转子的转子齿数及齿顶圆半径计算出面积利用系数C α，包括：
    分别计算阴、阳转子齿间面积A 02和A 01；所述齿间面积指阴阳转子旋转啮合时，两转子的螺旋齿面与机壳之间形成的相对封闭的基元容积在转子端面上的投影的面积；
    根据公式(9)计算面积利用系数C α：
    Figure PCTCN2021133834-appb-100001
    其中，D 1为阳转子齿顶圆直径，z 1为阳转子齿数。
  4. 根据权利要求1所述的方法，其特征在于，所述方法在获取接触线长度L时，包括：
    以阳转子端面轴心为原点O，以指向阴转子轴心方向为X轴，轴向为Z轴，Y轴垂直于XOZ平面建立三维坐标系；
    将接触线离散成m个点，根据公式(1)计算接触线长度L：
    Figure PCTCN2021133834-appb-100002
    式中，n为各个离散点的下标；n＝1，2，……，m；x n、y n、z n为各离散点的三维坐标。
  5. 根据权利要求1所述的方法，其特征在于，所述方法在获取泄漏三角形面积S时， 包括：
    设A点为阳转子齿面与机壳内壁面交线WW的交点，B点为阴转子齿面与机壳内壁面交线WW的交点，C点是双螺杆转子的接触线的最高点；所述接触线为阴阳转子啮合时，两螺旋齿面的接触部位在空间上形成的曲线；
    将曲线AC和BC分别离散成p个点和q个点；
    设点M i和F j分别为曲线AC和BC上离散点，且点M i和F j距离交线WW的距离分别为
    Figure PCTCN2021133834-appb-100003
    和
    Figure PCTCN2021133834-appb-100004
    则可得到：
    Figure PCTCN2021133834-appb-100005
    Figure PCTCN2021133834-appb-100006
    则泄漏三角形面积S为：
    Figure PCTCN2021133834-appb-100007
    其中，
    Figure PCTCN2021133834-appb-100008
    为空间曲边泄漏三角形的曲边AB投影到交线WW上的边，
    Figure PCTCN2021133834-appb-100009
    为接触线的最高点在交线WW投影点到B点的距离。
  6. 一种双螺杆转子型线优化设计方法，其特征在于，所述方法包括：
    根据权利要求1-5任一所述的方法获取待优化的双螺杆转子型线的综合性能指标K；
    以顺时针方向确定双螺杆转子的啮合线上各点将啮合线分为八段：A'为阴转子齿顶圆和阳转子齿底圆交点，B'点为阴阳转子节圆交点，C'点为啮合线下止点，D'点为阳转子齿顶圆和阴转子齿底圆交点；再分别以弧A'B'段的最低点P'、弧D'B'段的最高点N'及弧B'A'段最高点M'为界，将弧A'B'、弧D'B'、弧B'A'分为左右两段；
    对各段啮合线分别进行“内”“外”调整，通过计算调整前后双螺杆转子型线的综合性能指标K，确定各段的调整方向和距离，其中，使啮合线所围面积减小的修改方向为“内”，否则为“外”；
    综合各段的调整方向和距离确定使得双螺杆转子型线的综合性能指标K最小的双螺杆转子型线，即为优化后的双螺杆转子型线。
  7. 根据权利要求6所述的方法，其特征在于，所述通过计算调整前后双螺杆转子型线的综合性能指标K，确定各段的调整方向和距离，包括：
    若调整后的双螺杆转子型线的综合性能指标K值小于调整前的值，则继续朝当前方向进行调整；直至综合性能指标K值出现拐点；
    若调整后的双螺杆转子型线的综合性能指标K值大于调整前的值，则朝反方向调整，直至综合性能指标K值出现拐点。
  8. 根据权利要求6所述的方法，其特征在于，所述啮合线为接触线在转子轴向端面上的投影。
  9. 根据权利要求6所述的方法，其特征在于，所述啮合线所围面积指啮合线围成的封闭区域的面积。
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