WO2019119503A1 - 一种调节啮合线段修改转子型线性能的方法 - Google Patents

一种调节啮合线段修改转子型线性能的方法 Download PDF

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Publication number
WO2019119503A1
WO2019119503A1 PCT/CN2017/119422 CN2017119422W WO2019119503A1 WO 2019119503 A1 WO2019119503 A1 WO 2019119503A1 CN 2017119422 W CN2017119422 W CN 2017119422W WO 2019119503 A1 WO2019119503 A1 WO 2019119503A1
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Prior art keywords
meshing
line
rotor
point
profile
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English (en)
French (fr)
Inventor
何雪明
施国江
黄涛涛
黄海楠
陈小飞
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Jiangnan University
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Jiangnan University
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Priority to US16/234,914 priority Critical patent/US10883496B2/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
    • F04C2/00—Rotary-piston machines or pumps
    • F04C2/08—Rotary-piston machines or pumps of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing
    • F04C2/12—Rotary-piston machines or pumps of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing of other than internal-axis type
    • F04C2/14—Rotary-piston machines or pumps 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
    • F04C2/16—Rotary-piston machines or pumps 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
    • F04C2/165—Rotary-piston machines or pumps 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 having more than two rotary pistons with parallel axes
    • 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
    • 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
    • F04C18/12—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
    • F04C18/165—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 having more than two rotary pistons with parallel axes
    • 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
    • F04C2/00—Rotary-piston machines or pumps
    • F04C2/08—Rotary-piston machines or pumps of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing
    • F04C2/082—Details specially related to intermeshing engagement type machines or pumps
    • 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
    • F04C2/00—Rotary-piston machines or pumps
    • F04C2/08—Rotary-piston machines or pumps of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing
    • F04C2/12—Rotary-piston machines or pumps of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing of other than internal-axis type
    • F04C2/14—Rotary-piston machines or pumps 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
    • F04C2/16—Rotary-piston machines or pumps 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
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • 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
    • F04C2230/00—Manufacture
    • F04C2230/90—Improving properties of machine parts
    • 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

Definitions

  • the invention belongs to the technical field of compressors, and in particular relates to a method for adjusting the meshing line segment to modify the performance of a rotor profile.
  • a good rotor profile should have a large flow cross-sectional area, a short space contact line and a small leakage triangle, and these geometric performance parameters can be visually observed by adjusting the mesh line.
  • the design and optimization of the rotor profile are mostly limited to simple curves such as points, straight lines and quadratic curves.
  • the resulting screw rotor streamline type is not good, resulting in a large aerodynamic loss in the compressor during operation, and in positive and negative It is not easy to adjust the local curve in the design to achieve the purpose of optimizing the curve.
  • the existing screw rotor profile design method still focuses on the forward design. There are few explorations for the reverse design process.
  • the meshing line is not systematically divided, and the influence of the local variation of the meshing line on the variation law of the rotor profile is studied. .
  • the present invention proposes a method for adjusting the meshing line segment to modify the performance of the rotor profile.
  • the invention adjusts the meshing line locally in the reverse design process of the screw rotor profile to observe the change of the flow cross-sectional area, the space contact line and the leakage triangle in real time, so as to optimize the design of the rotor profile.
  • a method of adjusting the meshing line segment to modify the performance of the rotor profile comprising the steps of:
  • Step 1 Divide the mesh line of the bilateral profile into 8 functional segments
  • Step 2 Each functional segment is constructed using three NURBS curves
  • Step 3 Adjust the meshing line functional section by adjusting the control point or weight factor of the NURBS curve, observe the corresponding rotor profile change, and adjust the corresponding geometric parameters.
  • the eight functional segments include af, fo 0 , o 0 b, bc, cd, do 0 , o 0 e, ea, where point a is the intersection of the mesh line and the x 0 axis at the rightmost side, ie The point of tangency between the top of the female rotor and the root of the male rotor, point b is the lowest point of the mesh line in the third quadrant, and point c is the point on the meshing line that is farthest from the coordinate origin o 0 in the horizontal direction, ie The tip of the male rotor is tangent to the root of the female rotor.
  • the point d is the highest point of the meshing line in the II quadrant
  • the point e is the lowest point of the meshing line in the IV quadrant
  • the point f is the meshing line in the first quadrant. The highest point.
  • step 2 specifically includes the following steps:
  • Step 2.1 Establish a reverse design coordinate system, and establish a conversion relationship between the yin and yang rotor coordinate system and the meshing coordinate system;
  • Step 2.2 According to the tooth profile normal method, establish the relationship condition of the meshing condition, and establish a one-to-one mapping relationship between the rotor angle and the design parameter, that is, the envelope condition type:
  • R 1 is the radius of the anode rotor pitch;
  • the angle at which the male rotor is initially rotated is called the corner parameter;
  • Step 2.3 Design the three-NURBS spline curve segment of the meshing line, and the parameter equation is obtained by interpolation of the specified type value point and the position of the two ends; the parameter equation of the NURBS curve segment of a piece of meshing line is:
  • Step 2.4 the joint meshing condition relationship formula and the conversion relationship between the yin and yang rotor rotating coordinate system and the meshing line static coordinate system, thereby obtaining the female and male rotor profile equations corresponding to the NURBS spline curve segment meshing line.
  • the f(u) is solved by using the Longberg quadrature formula, and the Longberg quadrature formula is:
  • step D Determine whether the accuracy requirement is met, and judge whether the difference between the before and after iteration results is less than the precision value by comparison, that is, If the requirements are met, stop the calculation and output If the requirements are not met, then Then return to step C;
  • the step 3 is specifically: adjusting a control vertex of a total of eight meshing line functional segments of af, fo 0 , o 0 b, bc, cd, do 0 , o 0 e, ea to observe the corresponding rotor profile Change, or fine-tune the weighting factor w i of each functional segment NURBS curve control point to control the amount of local curve change of the meshing line, thereby adjusting the rotor profile and observing the leakage triangle, the length of the contact line, the area between the teeth, and the variation of the area utilization coefficient.
  • the invention starts from the reverse design method of the rotor type line, divides the meshing line of the double-sided line into eight functional segments, selects the NURBS curve structure meshing line segment, and modifies the corresponding rotor type line change by locally adjusting the meshing line segment, by this means According to the design needs, the design meets the performance requirements.
  • the design method is flexible and convenient. By adjusting the free curve to control the change of the profile line, combined with the corresponding relationship between the meshing line and the rotor profile, the change trend of the yin and yang rotor profile corresponding to the meshing line observation is partially adjusted, especially the leakage triangle, the length of the contact line, and the tooth.
  • the change of the area and the area utilization factor improves the design efficiency of the rotor profile of the twin-screw compressor, and avoids the drawback that the rotor profile design cannot partially modify the profile.
  • Figure 1 is a coordinate conversion relationship diagram in the reverse design method
  • Figure 2 (a) is a segmentation diagram of the meshing line
  • Figure 2 (b) is a rotor tooth profile corresponding to the meshing segment segment diagram
  • Figure 3 is a view showing the shape of the meshing line before and after the movement of the meshing line segment af, where 1 represents before moving and 2 represents after moving;
  • FIG. 4 is a view showing a change of a rotor profile line before and after the meshing line segment af moves, where 1 represents before moving and 2 represents after moving;
  • Figure 5 is a yin and yang rotor profile of the Fusheng line
  • Figure 6 is the meshing line of the refill type line
  • Figure 7 is the curvature comb of the different mesh NURBS architecture of the meshing line A 0 B 0 of the resurfacing type line, where (a) is a cubic NURBS curve, (b) is a four-time NURBS curve, (c) For the five-time NURBS curve, (d) is a six-time NURBS curve;
  • Figure 8 is the curvature comb of the meshing line A 0 B 0 of the replenishing type line plus the segmentation point;
  • Figure 9 is a diagram showing the distribution of control points of the NURBS curve structure resurfacing mesh line
  • Figure 10 is an overall curvature comb of the NURBS curve structure resurfacing mesh line
  • Figure 11 is the final rendering of the NURBS curve reverse design resurfacing line, where (a) is the meshing line and (b) is the generated male and female rotor profile;
  • Figure 12 is a comparison diagram of control points before and after the improvement of the meshing line
  • Figure 13 is a comparison of before and after the improvement of the profile.
  • Figure 1 is a coordinate transformation relationship diagram in the reverse design method, where O 0 x 0 y 0 is the meshing line stationary coordinate system, and O 1 x 1 y 1 is the male rotor rotating coordinate system, O 2 x 2 y 2 is the rotation coordinate system of the female rotor, O 1 X 1 Y 1 is the static coordinate system of the male rotor, and O 2 X 2 Y 2 is the static coordinate system of the female rotor.
  • R 2 and R 1 are the yin and yang rotor pitch radius
  • R a1 is the anode rotor tip circle radius
  • the invention provides a method for adjusting the meshing line segment to modify the performance of the rotor profile, comprising the following steps:
  • Step 1 Divide the mesh line of the double-sided line into eight functional segments; the eight functional segments include af, fo 0 , o 0 b, bc, cd, do 0 , o 0 e, ea, where point a is The meshing line and the x 0 axis are at the rightmost intersection point, that is, the tangent point of the female rotor tip circle and the male rotor root circle, point b is the lowest point of the mesh line in the third quadrant, and point c is the meshing line at the horizontal point.
  • the d point is the highest point of the mesh line in the II quadrant
  • the e point is the mesh line in the IV quadrant
  • point f is the highest point of the mesh line in the first quadrant.
  • Step 2 Each functional segment is constructed by using three NURBS curves; the step 2 specifically includes the following steps:
  • Step 2.1 Establish a reverse design coordinate system, and establish a conversion relationship between the yin and yang rotor coordinate system and the meshing coordinate system; and the meshed stationary coordinate system O 0 x 0 y 0 of Fig. 1 is converted to the anode rotor rotation coordinate system.
  • O 1 x 1 y 1
  • Step 2.2 According to the tooth profile normal method, establish the relationship of the meshing condition, and establish a one-to-one mapping relationship between the rotor angle and the design parameters, that is, the envelope condition:
  • R 1 is the radius of the anode rotor pitch;
  • the angle at which the male rotor is initially rotated is called the corner parameter;
  • Step 2.3 Design the three-NURBS spline curve segment of the meshing line, and the parameter equation is obtained by interpolation of the specified type value point and the position of the two ends; the parameter equation of the NURBS curve segment of a piece of meshing line is:
  • the f(u) is solved by the Longberg quadrature formula, and the Longberg quadrature formula is:
  • step D Determine whether the accuracy requirement is met, and judge whether the difference between the before and after iteration results is less than the precision value by comparison, that is, If the requirements are met, stop the calculation and output If the requirements are not met, then Then return to step C;
  • Step 2.4 the joint meshing condition relationship formula and the conversion relationship between the yin and yang rotor rotating coordinate system and the meshing line static coordinate system, thereby obtaining the female and male rotor profile equations corresponding to the NURBS spline curve segment meshing line.
  • Step 3 Adjust the meshing line functional section by adjusting the control point or weight factor of the NURBS curve, observe the corresponding rotor profile change, and adjust the corresponding geometric parameters.
  • the step 3 is specifically: adjusting a control vertex of a total of eight meshing line functional segments of af, fo 0 , o 0 b, bc, cd, do 0 , o 0 e, ea to observe corresponding rotor profile changes, or Fine-tune the weighting factor w i of each functional segment NURBS curve control point to control the amount of local curve change of the meshing line, thereby adjusting the rotor profile and observing the change of the leakage triangle, the length of the contact line, the area between the teeth, and the area utilization coefficient.
  • FIG. 2 is a meshing line segment and its corresponding rotor type line, wherein (a) is a meshing line segmentation diagram, and the meshing lines are respectively composed of six control points a, b, c, d, e, and f and a coordinate origin. It is divided into 8 functional segments, and (b) is a rotor tooth profile corresponding to the meshing line. Based on the above-mentioned NURBS rotor meshing line expression, the meshing NURBS is used to express each meshing line functional segment, and then the shape of each meshing wire can be adjusted separately to observe the corresponding rotor tooth profile change.
  • Figure 3 is a view of the shape of the meshing line before and after the movement of the meshing line segment af, where 1 represents before moving and 2 represents after moving.
  • Figure 4 shows the change of the rotor profile before and after the movement of the meshing segment af, where 1 represents before moving and 2 represents after moving. It can be found that when the af segment of the meshing line is moved to the upper right for a distance, the high-pressure side profile near the inner wall of the casing of the female rotor will change in the direction of increasing the thickness of the tooth tip, and the curvature of the tooth profile will increase. Large, the area between the teeth is reduced.
  • adjusting the weighting factor of the NURBS meshing line control point can also change the adjustment direction of the meshing line, reduce the size of the weighting factor, the direction of change of the meshing line at the control point is inward, increase the size of the weighting factor, and the meshing line is under control.
  • the direction of change at the point is outward, and the law of changing the weight factor to adjust the rotor performance parameters is similar to the above table.
  • Figure 5 shows the existing Fusheng type line
  • Figure 6 shows the meshing line corresponding to the Fusheng type line
  • Table 2 shows the design data related to the Fusheng type line.
  • Table 2 shows the design data related to Fusheng line
  • the meshing line of the resurfacing line is a double-sided line.
  • the meshing line is on both sides of the pitch circle, and the right side area is small, so the curvature of the meshing line changes very much. It is violent, so many control points are needed to meet the requirements of high-precision fitting.
  • the curvature combs from three to six times although the curvature gradually becomes gentle with the increase of the number of times, the change is still obvious. Fluctuation, so the meshing line needs to be added with several segmentation points to make the curvature transition more gradual.
  • the resulting curve is shown in Figure 11, where (a) is the mesh line of the NURBS architecture, and (b) the male and female rotor profile corresponding to the figure. It can be found that the rotor profile is different from the angle of Figure 5 because of the different relationship between the starting and the meshing points defined in the forward and reverse design methods.
  • the starting point in the forward direction is at the root circle of the female rotor, and the reverse direction is On the root circle of the male rotor, the male rotors of the two are different by 24°, that is, the female rotors are different by 20°.
  • the meshing line is composed of a NURBS curve
  • the local modification of the NURBS curve and the method for adjusting the performance of the rotor profile by adjusting the meshing line segment proposed by the present invention the local shape of the meshing line can be easily modified to achieve an optimized type.
  • the purpose of line performance Without changing the original rotor structure, such as the size of the tooth top arc and the gear ratio of the male and female rotors, the profile line is optimized to reduce the area of the leakage triangle and increase the area utilization coefficient.
  • the shape of the meshing line is changed by moving the position of the control point, and the front and rear meshing lines are improved as shown in Fig.

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Abstract

一种调节啮合线段修改转子型线性能的方法，包括以下步骤：步骤1、将双边型线的啮合线分成8个功能段；步骤2、每个功能段利用三次NURBS曲线进行架构；步骤3、通过调整NURBS曲线的控制点或权因子来局部调整啮合线功能段，观测相应的转子型线变化，从而调整相应的几何参数。该方法设计手段灵活方便，通过调节自由曲线来控制型线变化，结合啮合线与转子型线的对应关系，局部调整啮合线观测对应的阴阳转子型线变化趋势，特别是泄漏三角形、接触线长度、齿间面积以及面积利用系数的变化情况，提升双螺杆压缩机转子型线的设计效率，避免了以往转子型线设计不能局部修改型线的弊端。

Description

一种调节啮合线段修改转子型线性能的方法 技术领域
本发明属于压缩机技术领域，特别是涉及一种调节啮合线段修改转子型线性能的方法。
背景技术
螺杆转子型线从发展之初，就有学者一直在探索其新的设计方法和计算方式。就设计方法而言，根据初始设计对象的不同一般可分两种：正向设计和反向设计。在螺杆式压缩机出现之后的几十年里，人们基本上采用的都是正向设计方法，即从一个螺杆转子型线的已知数据，推导计算出另一个螺杆转子的型线。正向设计理论目前已经很成熟，但是压缩机的工作性能无法直接通过转子型线预知，必须通过阴阳转子的啮合线才能判断，若要获得一条完整的性能较好的螺杆转子型线通常需要经历反复修改与验证，整个设计过程十分繁杂。良好的转子型线应具备较大的流动横截面积、较短的空间接触线和较小的泄漏三角形，而这些几何性能参数可以通过调整啮合线来直观地观测其大小变化。目前转子型线的设计和优化大都局限于采用点、直线和二次曲线等简单曲线，生成的螺杆转子流线型不好，造成压缩机在运转过程中出现较大的气动损失，而且在正、反向设计中不易于调整局部曲线来达到优化曲线的目的。现有的螺杆转子型线设计方法仍然集中于正向设计，对于反向设计过程的探索很少，没能将啮合线进行系统的划分，研究啮合线的局部变化对转子型线变化规律的影响。
发明内容
本发明为了解决现有的技术问题，提出一种调节啮合线段修改转子型线性能的方法。本发明根据设计要求在螺杆转子型线反向设计过程中局部调整啮合线来实时观测流动横截面积、空间接触线和泄漏三角形的大小变化，以便对转子型线进行优化设计。
本发明的目的通过以下技术方案实现：一种调节啮合线段修改转子型线性能的方法，包括以下步骤：
步骤1、将双边型线的啮合线分成8个功能段；
步骤2、每个功能段利用三次NURBS曲线进行架构；
步骤3、通过调整NURBS曲线的控制点或权因子来局部调整啮合线功能段，观测相应的转子型线变化，从而调整相应的几何参数。
进一步地，所述8个功能段包括af、fo 0、o 0b、bc、cd、do 0、o 0e、ea，其中，a点为啮合线与x 0轴在最右侧交点，即阴转子齿顶圆与阳转子齿根圆的相切点，b点为啮合线在 第Ⅲ象限的最低点，c点为啮合线上在水平方向上距离坐标原点o 0最远的点，即阳转子齿顶圆与阴转子齿根圆相切点，d点为啮合线在第Ⅱ象限的最高点，e点为啮合线在第Ⅳ象限的最低点，f点为啮合线在第Ⅰ象限的最高点。
进一步地，所述步骤2具体包括以下步骤：
步骤2.1、建立反向设计坐标系，确立阴阳转子坐标系与啮合线静坐标系之间的转换关系式；
步骤2.2、根据齿廓法线法，确立啮合条件关系式，建立转子转角与设计参数之间的一一映射关系，即包络条件式：
Figure PCTCN2017119422-appb-000001
式中，R 1为阳转子节园半径；
Figure PCTCN2017119422-appb-000002
为阳转子初始转过的角度，称为转角参数；
Figure PCTCN2017119422-appb-000003
为常数，是上一段曲线终点的积分结果，对于啮合线的第一段曲线，是啮合的起始角度，取
Figure PCTCN2017119422-appb-000004
步骤2.3、设计啮合线三次NURBS样条曲线段，其参数方程通过指定的型值点和两端点处的导矢插值得到；设定一段啮合线的NURBS曲线段的参数方程为：
Figure PCTCN2017119422-appb-000005
其中，
Figure PCTCN2017119422-appb-000006
k是曲线次数；P i为控制点，数量为n+1个；w i是控制点P i的权因子，决定了控制点偏离曲线的程度，且所有w i＞0；N i,k(u)是定义在非周期且非均匀节点矢量U＝{a,…,a,u k+1,…,u m-p-1,b,…,b}上的k次B样条基函数，数量为m+1个，其中a、b的个数为k+1个，且m＝n+k+1；取a＝0，b＝1；
将参数方程代入包络条件式中可以得到如下式子：
Figure PCTCN2017119422-appb-000007
令
Figure PCTCN2017119422-appb-000008
则：
Figure PCTCN2017119422-appb-000009
将啮合线上任意一点的数值积分结果代入到啮合条件关系式即可得到转子转角与设计参 数之间的一一映射关系；
步骤2.4、联立啮合条件关系式和阴阳转子转动坐标系与啮合线静坐标系之间转换关系式，从而得到NURBS样条曲线段啮合线对应的阴、阳转子型线方程。
进一步地，所述f(u)利用龙贝格求积公式进行求解，龙贝格求积公式为：
Figure PCTCN2017119422-appb-000010
式中，
Figure PCTCN2017119422-appb-000011
Figure PCTCN2017119422-appb-000012
将区间[a,b]分成2 k等分；
具体步骤如下：
A.根据NURBS曲线参数方程确定啮合线段上相应的被积函数f(u)，并令a＝0和b＝u，以及设置求解精度ε；
B.设置初始步长h＝b-a，
Figure PCTCN2017119422-appb-000013
并初始化k＝1；
C.计算迭代公式，利用公式计算：
Figure PCTCN2017119422-appb-000014
然后再依次计算：
Figure PCTCN2017119422-appb-000015
D.判断是否达到精度要求，通过比较判断前后迭代结果差值是否小于精度值，即
Figure PCTCN2017119422-appb-000016
若满足要求，则停止计算，输出
Figure PCTCN2017119422-appb-000017
若不满足要求，则令
Figure PCTCN2017119422-appb-000018
然后返回第C步；
若啮合线段上的点在x轴上，则C y(u 0)＝0，该点为函数f(u)的第一类间断点；根据啮合线设计要求，啮合线上经过x轴的点必须满足C x(u 0)＝0或者C' x(u 0)＝0，在该点的函数值采用极限值代替进行求解；利用洛必达法则可得：
Figure PCTCN2017119422-appb-000019
进一步地，所述步骤3具体为：分别调节af、fo 0、o 0b、bc、cd、do 0、o 0e、ea共8 个啮合线功能段的控制顶点来观测相应的转子型线变化，或微调每个功能段NURBS曲线控制点的权因子w i来控制啮合线局部曲线变化量，从而调节转子型线并观测泄漏三角形、接触线长度、齿间面积以及面积利用系数的变化情况。
本发明从转子型线反向设计方法入手，将双边型线的啮合线分成8个功能段，并选择NURBS曲线架构啮合线段，通过局部调整啮合线段来修改相应的转子型线变化，通过此手段，根据设计需要进而设计出满足性能要求的型线。设计手段灵活方便，通过调节自由曲线来控制型线变化，结合啮合线与转子型线的对应关系，局部调整啮合线观测对应的阴阳转子型线变化趋势，特别是泄漏三角形、接触线长度、齿间面积以及面积利用系数的变化情况，提升双螺杆压缩机转子型线的设计效率，避免了以往转子型线设计不能局部修改型线的弊端。
附图说明
图1为反向设计方法中的坐标转换关系图；
图2(a)为啮合线分段图；
图2(b)为啮合线分段图对应的转子齿形图；
图3为啮合线段af移动前后的啮合线形状图，其中1代表移动前，2代表移动后；
图4为啮合线段af移动前后对应的转子型线变化情况图，其中1代表移动前，2代表移动后；
图5为复盛型线的阴阳转子型线；
图6为复盛型线的啮合线；
图7为复盛型线的啮合线A 0B 0段用不同阶数的NURBS架构的曲率梳，其中(a)图为三次NURBS曲线，(b)图为四次NURBS曲线，(c)图为五次NURBS曲线，(d)图为六次NURBS曲线；
图8为复盛型线的啮合线A 0B 0加分段点后的曲率梳；
图9为NURBS曲线架构复盛啮合线的控制点分布效果图；
图10为NURBS曲线架构复盛啮合线的整体曲率梳图；
图11为NURBS曲线反向设计复盛型线的最终效果图，其中(a)图为啮合线，(b)图为生成的阴阳转子型线；
图12为啮合线改进优化前后的控制点对比图；
图13为型线改进优化前后的对比图。
具体实施方式
下面将结合本发明实施例中的附图对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
实施例1
结合图1-图4，图1为反向设计方法中的坐标转换关系图，其中O 0x 0y 0为啮合线静止坐标系，O 1x 1y 1为阳转子转动坐标系，O 2x 2y 2为阴转子转动坐标系，O 1X 1Y 1为阳转子静止坐标系，O 2X 2Y 2为阴转子静止坐标系，
Figure PCTCN2017119422-appb-000020
分别为阴阳转子转动坐标系O 2x 2y 2、O 1x 1y 1相对于阴阳转子静止坐标系O 2X 2Y 2、O 1X 1Y 1的转动量，ω 2、ω 1分别为阴阳转子转速，R 2、R 1分别为阴阳转子节园半径，R a1是阳转子齿顶圆半径，R f2是阴转子齿根圆半径，满足R a1+R f2＝H。
本发明提出一种调节啮合线段修改转子型线性能的方法，包括以下步骤：
步骤1、将双边型线的啮合线分成8个功能段；所述8个功能段包括af、fo 0、o 0b、bc、cd、do 0、o 0e、ea，其中，a点为啮合线与x 0轴在最右侧交点，即阴转子齿顶圆与阳转子齿根圆的相切点，b点为啮合线在第Ⅲ象限的最低点，c点为啮合线上在水平方向上距离坐标原点o 0最远的点，即阳转子齿顶圆与阴转子齿根圆相切点，d点为啮合线在第Ⅱ象限的最高点，e点为啮合线在第Ⅳ象限的最低点，f点为啮合线在第Ⅰ象限的最高点。当研究的是单边型线的啮合线时，a点将与坐标系原点重合。单边型线的啮合线只存在于啮合线静坐标系的第二、三象限，而双边型线的啮合线在静坐标系的四个象限均有分布。
步骤2、每个功能段利用三次NURBS曲线进行架构；所述步骤2具体包括以下步骤：
步骤2.1、建立反向设计坐标系，确立阴阳转子坐标系与啮合线静坐标系之间的转换关系式；由图1得啮合线静止坐标系O 0x 0y 0转换到阳转子转动坐标系O 1x 1y 1：
Figure PCTCN2017119422-appb-000021
从啮合线静止坐标系O 0x 0y 0转换到阴转子转动坐标系O 2x 2y 2：
Figure PCTCN2017119422-appb-000022
步骤2.2、根据齿廓法线法，确立啮合条件关系式，建立转子转角与设计参数之间的一一 映射关系，即包络条件式：
Figure PCTCN2017119422-appb-000023
式中，R 1为阳转子节园半径；
Figure PCTCN2017119422-appb-000024
为阳转子初始转过的角度，称为转角参数；
Figure PCTCN2017119422-appb-000025
为常数，是上一段曲线终点的积分结果，对于啮合线的第一段曲线，是啮合的起始角度，取
Figure PCTCN2017119422-appb-000026
步骤2.3、设计啮合线三次NURBS样条曲线段，其参数方程通过指定的型值点和两端点处的导矢插值得到；设定一段啮合线的NURBS曲线段的参数方程为：
Figure PCTCN2017119422-appb-000027
其中，
Figure PCTCN2017119422-appb-000028
k是曲线次数；P i为控制点，数量为n+1个；w i是控制点P i的权因子，决定了控制点偏离曲线的程度，且所有w i＞0；N i,k(u)是定义在非周期且非均匀节点矢量U＝{a,…,a,u k+1,…,u m-p-1,b,…,b}上的k次B样条基函数，数量为m+1个，其中a、b的个数为k+1个，且m＝n+k+1；取a＝0，b＝1；
将参数方程代入包络条件式中可以得到如下式子：
Figure PCTCN2017119422-appb-000029
令
Figure PCTCN2017119422-appb-000030
则：
Figure PCTCN2017119422-appb-000031
将啮合线上任意一点的数值积分结果代入到啮合条件关系式即可得到转子转角与设计参数之间的一一映射关系；
所述f(u)利用龙贝格求积公式进行求解，龙贝格求积公式为：
Figure PCTCN2017119422-appb-000032
式中，
Figure PCTCN2017119422-appb-000033
将区间[a,b]分成2 k等分；
具体步骤如下：
A.根据NURBS曲线参数方程确定啮合线段上相应的被积函数f(u)，并令a＝0和b＝u， 以及设置求解精度ε；
B.设置初始步长
Figure PCTCN2017119422-appb-000034
并初始化k＝1；
C.计算迭代公式，利用公式计算：
Figure PCTCN2017119422-appb-000035
然后再依次计算：
Figure PCTCN2017119422-appb-000036
D.判断是否达到精度要求，通过比较判断前后迭代结果差值是否小于精度值，即
Figure PCTCN2017119422-appb-000037
若满足要求，则停止计算，输出
Figure PCTCN2017119422-appb-000038
若不满足要求，则令
Figure PCTCN2017119422-appb-000039
然后返回第C步；
若啮合线段上的点在x轴上，则C y(u 0)＝0，该点为函数f(u)的第一类间断点；根据啮合线设计要求，啮合线上经过x轴的点必须满足C x(u 0)＝0或者C' x(u 0)＝0，在该点的函数值采用极限值代替进行求解；利用洛必达法则可得：
Figure PCTCN2017119422-appb-000040
步骤2.4、联立啮合条件关系式和阴阳转子转动坐标系与啮合线静坐标系之间转换关系式，从而得到NURBS样条曲线段啮合线对应的阴、阳转子型线方程。
步骤3、通过调整NURBS曲线的控制点或权因子来局部调整啮合线功能段，观测相应的转子型线变化，从而调整相应的几何参数。所述步骤3具体为：分别调节af、fo 0、o 0b、bc、cd、do 0、o 0e、ea共8个啮合线功能段的控制顶点来观测相应的转子型线变化，或微调每个功能段NURBS曲线控制点的权因子w i来控制啮合线局部曲线变化量，从而调节转子型线并观测泄漏三角形、接触线长度、齿间面积以及面积利用系数的变化情况。
图2为啮合线分段及其对应的转子型线，其中(a)图为啮合线分段图，啮合线分别由a、b、c、d、e、f这6个控制点和坐标原点分成8个功能段，(b)图为啮合线对应的转子齿形图。基于上述推导的NURBS转子啮合线表达式，用三次NURBS分别表达各啮合线功能段，然后可以分别调节每段啮合线的形状来观测对应的转子齿形变化。图3为啮合线段af移动前后 的啮合线形状，其中1代表移动前，2代表移动后。图4为啮合线段af移动前后对应的转子型线变化情况，其中1代表移动前，2代表移动后。可以发现，当啮合线af段向右上方移动一段距离后，阴转子齿顶附近靠近机壳内壁的高压侧型线将往增加其齿顶厚度的方向变化，同时这部分齿形的曲率将增大，其齿间面积减小。同样地，当啮合线af段向右上方移动一段距离后，阳转子齿槽底部的高压侧型线往增加其齿槽底部宽度的方向变化，对应阳转子齿形的曲率也将增大，同时其齿间面积得到增大。反之，如果啮合线af段往左下方移动，以上所述阴阳转子型线将往相反方向变化。
同理，可对其余7段采用同样的方法进行研究。若规定啮合线调整后使得其所围面积增大的趋势方向为向“外”，反之则为向“内”。最后得出各段啮合线对转子型线性能参数的影响如表1所示。
表1各段啮合线对转子型线性能参数的影响
Figure PCTCN2017119422-appb-000041
同样，调节NURBS啮合线控制点的权因子亦可以改变啮合线的调整方向，减小权因子的大小，啮合线在控制点处的变化方向为向内，增大权因子的大小，啮合线在控制点处的变化方向为向外，进而改变权因子大小调整转子性能参数的规律与上表类似。
实施例2
结合图5-图13，图5为现有的复盛型线，图6为复盛型线对应的啮合线，表2为复盛型 线相关的设计数据。
表2为复盛型线相关的设计数据
Figure PCTCN2017119422-appb-000042
现在以三次NURBS曲线反向架构复盛型线，复盛型线的啮合线为双边型线，其啮合线在节圆的两侧，而且右侧区域较小，所以导致啮合线的曲率变化很剧烈，所以需要很多的控制点才能使得满足高精度拟合的要求。以A 0B 0段为例，如图7所示，在相同的控制点数下，三次至六次的曲率梳，虽然随着次数的增加，曲率渐渐变得平缓，但其变化还是有明显的波动，所以啮合线拟合时需要增加几个分段点，让曲率过渡更加平缓，如图8所示，可以看出，加了一个分段点之后，A 0B 0段的曲率明显变得更加平滑。同理，在其他段曲率容易震荡变化的部分增加分段点，各段架构效果如图9所示，最终的拟合结果如图10所示，拟合精度如表3所示，精度较高，曲率变化也很平稳。
表3拟合精度
Figure PCTCN2017119422-appb-000043
最后生成的曲线如图11所示，其中(a)图为NURBS架构的啮合线，(b)图对应的阴阳转子型线。可以发现转子型线与图5相差了一个角度，这是由于正、反向设计方法中定义起始啮合点不同的关系，正向中的起始点在阴转子的齿根圆，而反向是在阳转子的齿根圆上，两者 的阳转子相差了24°，即阴转子相差了20°。
由于啮合线是由NURBS曲线组成，根据NURBS曲线的局部修改性和本发明提出的一种调节啮合线段修改转子型线性能的方法可以很方便地对啮合线的局部形状进行修改，从而达到优化型线性能的目的。在不改变原有转子结构的情况下，如阴阳转子的齿顶圆弧大小、齿数比等参数，主要以减小泄漏三角形的面积和增大面积利用系数为目标对型线进行优化，可以直接通过移动控制点的位置来改变啮合线的形状，改进前后的啮合线如图12所示(其中a 1、a 2、a 3、a 4、a 5、a 6、a' 5、a' 6，b 1、b 2、b 3、b 4、b 5、b 1'、b' 2、b 3'、b' 4，c 1、c 2、c 3、c 4、c 5、c 1'、c' 2、c' 3、c' 4、c' 5均为控制点)，及其对应的型线变化前后如图13所示，性能参数对比如表4所示。可以看出，优化后的型线增加了阴转子的厚度，同时增大了面积利用系数，减小了泄漏三角形的面积。
表4性能参数对比
Figure PCTCN2017119422-appb-000044
以上对本发明所提供的一种调节啮合线段修改转子型线性能的方法，进行了详细介绍，本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处，综上所述，本说明书内容不应理解为对本发明的限制。

Claims (7)

  1. 一种调节啮合线段修改转子型线性能的方法，其特征在于：包括以下步骤：
    步骤1、将双边型线的啮合线分成8个功能段；
    步骤2、每个功能段利用三次NURBS曲线进行架构；
    步骤3、通过调整NURBS曲线的控制点或权因子来局部调整啮合线功能段，观测相应的转子型线变化，从而调整相应的几何参数。
  2. 根据权利要求1所述的方法，其特征在于：所述8个功能段包括af、fo 0、o 0b、bc、cd、do 0、o 0e、ea，其中，a点为啮合线与x 0轴在最右侧交点，即阴转子齿顶圆与阳转子齿根圆的相切点，b点为啮合线在第Ⅲ象限的最低点，c点为啮合线上在水平方向上距离坐标原点O 0最远的点，即阳转子齿顶圆与阴转子齿根圆相切点，d点为啮合线在第Ⅱ象限的最高点，e点为啮合线在第Ⅳ象限的最低点，f点为啮合线在第Ⅰ象限的最高点。
  3. 根据权利要求2所述的方法，其特征在于：所述步骤2具体包括以下步骤：
    步骤2.1、建立反向设计坐标系，确立阴阳转子坐标系与啮合线静坐标系之间的转换关系式；
    步骤2.2、根据齿廓法线法，确立啮合条件关系式，建立转子转角与设计参数之间的一一映射关系，即包络条件式：
    Figure PCTCN2017119422-appb-100001
    式中，R 1为阳转子节园半径；
    Figure PCTCN2017119422-appb-100002
    为阳转子初始转过的角度，称为转角参数；
    Figure PCTCN2017119422-appb-100003
    为常数，是上一段曲线终点的积分结果，对于啮合线的第一段曲线，是啮合的起始角度，取
    Figure PCTCN2017119422-appb-100004
    步骤2.3、设计啮合线三次NURBS样条曲线段，其参数方程通过指定的型值点和两端点处的导矢插值得到；设定一段啮合线的NURBS曲线段的参数方程为：
    Figure PCTCN2017119422-appb-100005
    其中，
    Figure PCTCN2017119422-appb-100006
    k是曲线次数；P i为控制点，数量为n+1个；w i是控制点P i的权因子，决定了控制点偏离曲线的程度，且所有w i＞0；N i,k(u)是定义在非周 期且非均匀节点矢量U＝{a,…,a,u k+1,…,u m-p-1,b,…,b}上的k次B样条基函数，数量为m+1个，其中a、b的个数为k+1个，且m＝n+k+1；取a＝0，b＝1；
    将参数方程代入包络条件式中可以得到如下式子：
    Figure PCTCN2017119422-appb-100007
    令
    Figure PCTCN2017119422-appb-100008
    则：
    Figure PCTCN2017119422-appb-100009
    将啮合线上任意一点的数值积分结果代入到啮合条件关系式即可得到转子转角与设计参数之间的一一映射关系；
    步骤2.4、联立啮合条件关系式和阴阳转子转动坐标系与啮合线静坐标系之间转换关系式，从而得到NURBS样条曲线段啮合线对应的阴、阳转子型线方程。
  4. 根据权利要求3所述的方法，其特征在于：所述f(u)利用龙贝格求积公式进行求解，龙贝格求积公式为：
    Figure PCTCN2017119422-appb-100010
    式中，
    Figure PCTCN2017119422-appb-100011
    将区间[a,b]分成2 k等分；
    具体步骤如下：
    A.根据NURBS曲线参数方程确定啮合线段上相应的被积函数f(u)，并令a＝0和b＝u，以及设置求解精度ε；
    B.设置初始步长h＝b-a，
    Figure PCTCN2017119422-appb-100012
    并初始化k＝1；
    C.计算迭代公式，利用公式计算：
    Figure PCTCN2017119422-appb-100013
    然后再依次计算：
    Figure PCTCN2017119422-appb-100014
    D.判断是否达到精度要求，通过比较判断前后迭代结果差值是否小于精度值，即
    Figure PCTCN2017119422-appb-100015
    若满足要求，则停止计算，输出
    Figure PCTCN2017119422-appb-100016
    若不满足要求，则令
    Figure PCTCN2017119422-appb-100017
    然后返回第C步；
    若啮合线段上的点在x轴上，则C y(u 0)＝0，该点为函数f(u)的第一类间断点；根据啮合线设计要求，啮合线上经过x轴的点必须满足C x(u 0)＝0或者C' x(u 0)＝0，在该点的函数值采用极限值代替进行求解；利用洛必达法则可得：
    Figure PCTCN2017119422-appb-100018
  5. 根据权利要求4所述的方法，其特征在于：所述步骤3具体为：分别调节af、fo 0、o 0b、bc、cd、do 0、o 0e、ea共8个啮合线功能段的控制顶点来观测相应的转子型线变化，或微调每个功能段NURBS曲线控制点的权因子wi来控制啮合线局部曲线变化量，从而调节转子型线并观测泄漏三角形、接触线长度、齿间面积以及面积利用系数的变化情况。
  6. 如权利要求1-5任一所述的一种调节啮合线段修改转子型线性能的方法的应用。
  7. 一种基于权利要求1-5任一所述的一种调节啮合线段修改转子型线性能的方法的设备。
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