The present disclosure belongs to the technical field of compressors, and particularly relates to a method for modifying performance of a rotor profile by adjusting meshing line segments.
From the beginning of development of screw rotor profiles, scholars have been exploring new design methods and calculation methods thereof. The design methods are generally divided into two types according to different initial design objects: forward design and reverse design. In the decades after the advent of screw compressors, the forward design method was basically adopted, that is, the profile of another screw rotor was derived from the known data of one screw rotor profile. The forward design theory is very mature at present. However, the working performance of the compressor cannot be directly predicted by the rotor profile, and must be judged by the meshing line of male and female rotors. It usually needs repeated revision and verification to obtain a complete screw rotor profile with better performance, so the entire design process is very complicated. A good rotor profile should have a large flow cross-sectional area, a short space contact line and a small leak triangle, and the changes in these geometric performance parameters can be intuitively observed by adjusting the meshing line. At present, the design and optimization of rotor profiles are mostly limited to simple curves such as points, straight lines and quadratic curves. The generated screw rotor profile is not good, resulting in a large aerodynamic loss during the operation of the compressor. Moreover, it is unlikely to adjust the local curve in the forward or reverse design to achieve the purpose of optimizing the curve. The conventional screw rotor profile design method still focuses on the forward design, the reverse design process is seldom explored, and systematically dividing the meshing line to study the influence of the local change of the meshing line on the change rule of the rotor profile is not carried out.
In order to solve the existing technical problems, the present disclosure provides a method for modifying performance of a rotor profile by adjusting meshing line segments. In the present disclosure, the meshing line is locally adjusted in the reverse design process of a screw rotor profile according to the design requirements to observe the size changes in flow cross-sectional area, spatial contact lines and leak triangle in real time, so as to optimize the design of the rotor profile.
The objective of the present disclosure is achieved by the following technical solution: a method for modifying performance of a rotor profile by adjusting meshing line segments, comprising the following steps:
step 1, dividing a meshing line of a bilateral profile into eight functional segments;
step 2, constructing each functional segment by using a cubic NURBS curve; and
step 3, locally adjusting the functional segments of the meshing line by adjusting control points or weight factors of the NURBS curve, and observing corresponding changes of the rotor profile so as to adjust corresponding geometrical parameters;
where the rotor profile is the intersecting line between the helical surface of the screw rotor and the section perpendicular to the rotor shaft.
Further, the eight functional segments comprises af, fo0, o0b, bc, cd, do0, o0e and ea, where point a is the rightmost intersection of the meshing line and the x0 axis, i.e., the tangent point of the tip circle a female rotor and the root circle of a male rotor, point b is the lowest point of the meshing line in the III quadrant, point c is a point farthest from the coordinate origin O0 in the horizontal direction on the meshing line, i.e., the tangential point of the tip circle of the male rotor and the root circle of the female rotor, point d is the highest point of the meshing line in the II quadrant, point e is the lowest point of the meshing line in the IV quadrant, and point f is the highest point of the meshing line in the I quadrant.
Further, step 2 specifically comprises the following steps:
step 2.1, establishing reverse design coordinates, and establishing a conversion relation between male and female rotor coordinates and meshing line static coordinates;
step 2.2, establishing a meshing condition relation according to a tooth profile normal method, and establishing a one-to-one mapping relation between rotor rotation angles and design parameters, i.e., an envelope condition formula:
where R1 is the radius of the pitch circle of a male rotor; φ1 is an initial rotation angle of a male rotor, referred to as a rotation angle parameter; φ0 is a constant, an integral result of the end point of the previous curve segment, and a starting angle of meshing for the first curve segment of the meshing line, φ0=0;
step 2.3, designing a cubic NURBS spline curve segment of the meshing line, the parameter equation thereof being obtained by derivatives and interpolation at a specified data point and two end points, and a parameter equation for a NURBS curve segment of the meshing line being set as follows:
where
k is the degree of curves; Pi is a control point, having the number of n+1; wi is a weight factor of the control point Pi, determining the extent to which the control point deviates from the curve, and all wi>0 Ni,k(u) is a k-degree B spline basis function defined on an aperiodic and non-uniform node vector U={a, . . . , a, uk+1, . . . , um-p-1, b, . . . , b}, having the number of m+1, wherein the number of a and b is k+1, and m=n+k+1, a=0, b=1;
substituting the parametric equation into the envelope condition formula to obtain the following formula:
substituting the numerical integration result of any point on the meshing line into the meshing condition relation to obtain a one-to-one mapping relation between rotor rotation angles and design parameters; and
step 2.4, obtaining a male and female rotor profile equation corresponding to the meshing line of the NURBS spline curve segment using the meshing condition relation and the conversion relation between male and female rotor coordinates and meshing line static coordinates simultaneously.
Further, the ƒ(u) is solved using the following Romberg quadrature formula:
where
I=∫abƒ(u)dx, and the interval [a, b] is equally divided into 2k portions;
the specific steps are as follows:
A, determining a corresponding integrand ƒ(u) on the meshing line segment according to the NURBS curve parameter equation, setting a=0 and b=u, and setting the solution precision ε;
B, setting the initial step size
and initializing k=1;
C, calculating an iterative formula and using the formula to calculate:
then calculating:
D, judging whether the precision requirement is met by judging whether a difference between the previous and late iteration results is smaller than a precision value, i.e., |Tm(0)−Tm-1(0)|<ε; if the requirement is met, stopping the calculation and outputting Tk(0); if the requirement is not met, setting
and then returning to step C;
wherein if the point on the meshing line segment is on the x axis, Cy(u0)=0, and the point is the first type of discontinuity point of the function ƒ(u); according to the design requirement of the meshing line, the point passing through the x axis on the meshing line must satisfy Cx(u0)=0 or C′x(u0)=0, and the function value at this point is substituted with a limit value for solving; and it can be obtained using the L'Hospital's rule:
Further, step 3 is specifically: adjusting the control vertexes of the eight functional segments af, fo0, o0b, bc, cd, do0, o0e and ea of the meshing line respectively to observe corresponding changes of the rotor profile, or slightly adjusting the weight factor wi of the control point of the NURBS curve of each functional segment to control the local curve variation of the meshing line, thereby adjusting the rotor profile and observing the changes in leak triangle, contact line length, inter-tooth area and area utilization coefficient.
Starting from the reverse design method of the rotor profile, the meshing line of the bilateral profile is divided into eight functional segments, the NURBS curve is used to construct meshing line segments, corresponding changes of the rotor profile are modified by locally adjusting the meshing line segments, and therefore the profile meeting the performance requirements is designed according to the design needs. The design means is flexible and convenient, the change of the profile is controlled by adjusting the free curve, and the meshing line is locally adjusted in combination with the corresponding relationship between the meshing line and the rotor profile to observe the corresponding change trends, particularly the changes in leak triangle, contact line length, inter-tooth area and area utilization coefficient, of the male and female rotor profile, so that the design efficiency of the rotor profile of a twin-rotor screw compressor is improved, and the defect in the prior art that the rotor profile cannot be locally modified is avoided.
A clear and complete description will be made to the technical solutions in the embodiments of the present disclosure below in combination with the accompanying drawings in the embodiments of the present disclosure. Apparently, the embodiments described are only part of the embodiments of the present disclosure, not all of them. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present disclosure without creative efforts shall fall within the protection scope of the present disclosure.
Referring to
The present disclosure proposes a method for modifying performance of a rotor profile by adjusting meshing line segments, including the following steps:
Step 1, dividing a meshing line of a bilateral profile into eight functional segments, wherein the eight functional segments includes af, fo0, o0b, bc, cd, do0, o0e and ea, point a is the rightmost intersection of the meshing line and the x0 axis, i.e., the tangent point of the tip circle of the female rotor and the root circle of the male rotor, point b is the lowest point of the meshing line in the III quadrant, point c is a point farthest from the coordinate origin O0 in the horizontal direction on the meshing line, i.e., the tangential point of the tip circle of the male rotor and the root circle of the female rotor, point d is the highest point of the meshing line in the II quadrant, point e is the lowest point of the meshing line in the IV quadrant, and point f is the highest point of the meshing line in the I quadrant. When a meshing line of a unilateral profile is studied, point a coincides with the origin of the coordinate system. The meshing line of the unilateral profile exists only in the second and third quadrants of the static coordinates of the meshing line, whereas the meshing line of the bilateral profile is distributed in the four quadrants of the static coordinates.
Step 2, constructing each functional segment by using a cubic NURBS curve. Step 2 specifically includes the following steps:
step 2.1, establishing reverse design coordinates, and establishing a conversion relation between male and female rotor coordinates and meshing line static coordinates; it can be seen from the
meshing line static coordinates O0x0y0 are converted to female rotor rotating coordinates O2x2y2:
step 2.2, establishing a meshing condition relation according to a tooth profile normal method, and establishing a one-to-one mapping relation between rotor rotation angles and design parameters, i.e., an envelope condition formula:
where R1 is the radius of the pitch circle of a male rotor; φ1 is an initial rotation angle of a male rotor, referred to as a rotation angle parameter; φ0 is a constant, an integral result of the end point of the previous curve segment, and a starting angle of meshing for the first curve segment of the meshing line, φ0=0;
step 2.3, designing a cubic NURBS spline curve segment of the meshing line, the parameter equation thereof being obtained by derivatives and interpolation at a specified data point and two end points, and a parameter equation for a NURBS curve segment of the meshing line being set as follows:
where
k is the degree of curves; Pi is a control point, having the number of n+1; wi is a weight factor of the control point Pi, determining the extent to which the control point deviates from the curve, and all wi>0; Ni,k(u) is a k-degree B spline basis function defined on an aperiodic and non-uniform node vector U={a, . . . , a, uk+1, . . . , um-p-1, b, . . . , b}, having the number of m+1, wherein the number of a and b is k+1, and m=n+k+1; a=0, b=1;
substituting the parametric equation into the envelope condition formula to obtain the following formula:
substituting the numerical integration result of any point on the meshing line into the meshing condition relation to obtain a one-to-one mapping relation between rotor rotation angles and design parameters; and
solving the ƒ(u) using the Romberg quadrature formula:
where
and the interval [a, b] is equally divided into 2k portions;
The specific steps are as follows:
A, determining a corresponding integrand ƒ(u) on the meshing line segment according to the NURBS curve parameter equation, setting a=0 and b=u, and setting the solution precision ε;
B, setting the initial step size
and initializing k=1;
C, calculating an iterative formula and using the formula to calculate:
then calculating:
D, judging whether the precision requirement is met by judging whether a difference between the previous and late iteration results is smaller than a precision value, i.e., |Tm(0)−Tm-1(0)|<ε; if the requirement is met, stopping the calculation and outputting Tk(0); if the requirement is not met, setting
and then returning to step C;
wherein if the point on the meshing line segment is on the x axis, Cy(u0)=0, and the point is the first type of discontinuity point of the function ƒ(u); according to the design requirement of the meshing line, the point passing through the x axis on the meshing line must satisfy Cx(u0)=0 or C′x(u0)=0, and the function value at this point is substituted with a limit value for solving; and it can be obtained using the L'Hospital's rule:
and
step 2.4, obtaining a male and female rotor profile equation corresponding to the meshing line of the NURBS spline curve segment using the meshing condition relation and the conversion relation between male and female rotor coordinates and meshing line static coordinates simultaneously.
Step 3: locally adjusting the functional segments of the meshing line by adjusting control points or weight factors of the NURBS curve, and observing corresponding changes of the rotor profile so as to adjust corresponding geometrical parameters. Step 3 is specifically: adjusting the control vertexes of the eight functional segments af, fo0, o0b, bc, cd, do0, o0e and ea of the meshing line respectively to observe corresponding changes of the rotor profile, or slightly adjusting the weight factor wi of the control point of the NURBS curve of each functional segment to control the local curve variation of the meshing line, thereby adjusting the rotor profile and observing the changes in leak triangle, contact line length, inter-tooth area and area utilization coefficient.
Similarly, the remaining seven segments can be studied using the same method. If the increasing direction of the area surrounded by the adjusted meshing line is defined as “outside”, the opposite direction is “inside”. Finally, the influence of each meshing line segment on the performance parameters of the rotor profile is shown in Table 1.
Similarly, the adjustment direction of the meshing line can also be changed by adjusting the weight factors of the control point of the NURBS meshing line, the change direction of the meshing line at the control point is inward by reducing the weight factors and the change direction of the meshing line at the control point is outward by increasing the weight factors, so that the law of changing the weight factors to adjust the performance parameters of the rotor is similar to that of the above table.
Referring to
Now a cubic NURBS curve is used to reversely construct the Fusheng profile. The meshing line of the Fusheng profile is a bilateral profile, the meshing line thereof is on two sides of the pitch circle, and the right area is small, so that the curvature of the meshing line changes dramatically, and a lot of control points are needed to meet the requirement of high-precision fitting. Taking the A0B0 segment as an example, as shown in
The finally generated curve is shown in
Since the meshing line consists of a NURBS curve, the local shape of the meshing line can be conveniently modified by the local modification of the NURBS curve and the method for modifying the performance of the rotor profile by adjusting the meshing line segments according to the present disclosure, so as to achieve the purpose of optimizing the performance of the profile. The profile is optimized mainly to reduce the area of the leak triangle and increase the area utilization coefficient without changing the original rotor structure, such as the size of the tooth crest arc and the tooth ratio of the male and female rotors. The shape of the meshing line can be directly changed by moving the positions of the control points. The meshing lines before and after the improvement are shown in
Number | Date | Country | Kind |
---|---|---|---|
2017 1 1371154 | Dec 2017 | CN | national |
Number | Name | Date | Kind |
---|---|---|---|
20070273688 | Chen | Nov 2007 | A1 |
20110020162 | Izawa et al. | Jan 2011 | A1 |
Number | Date | Country |
---|---|---|
102352846 | Feb 2012 | CN |
102828954 | Dec 2012 | CN |
106194717 | Dec 2016 | CN |
107023480 | Aug 2017 | CN |
Entry |
---|
Xueming He et al., Design and Numerical Simulation for Double-Screw Compressor Rotor Profile, Journal of Mechanical Strength, China, Dec. 31, 2016, No. 2, vol. 38, ISSN:1001-966, line 8 of left column of p. 289-line 39 of right column of p. 292. |
Number | Date | Country | |
---|---|---|---|
20190186487 A1 | Jun 2019 | US |
Number | Date | Country | |
---|---|---|---|
Parent | PCT/CN2017/119422 | Dec 2017 | US |
Child | 16234914 | US |