A roots pump with an elliptical rotor waist line and a design method thereof

Abstract

The application discloses a Roots pump with an elliptical line as a rotor waist line and a design method thereof. The Roots pump has the following features: a curve inside a pitch circle of a rotor line is an elliptical line, which is referred to as a waist elliptical line; and a curve outside the pitch circle is a conjugate curve of the waist elliptical line. Compared with a rotor line with an elliptical line at a top part, the rotor line with the elliptical line at the waist part has the characteristics of high volume utilization rate, and the volume utilization rate can reach more than 55%, which is more than 10% higher than that of the rotor line with the elliptical line at the top part.

Description

Technical Field

[0001] This invention relates to the field of Roots pump design technology, specifically to a Roots pump with an elliptical rotor waist profile and its design method. Background Technology

[0002] Roots pumps are mainly used in industries such as semiconductors, petrochemicals, papermaking, food processing, and electronics. Currently, the rotor profiles of Roots pumps on the market are mainly involute, cycloidal, and circular arc, collectively known as standard profiles. Standard profile rotors are easy to design and manufacture, but they have lower technical parameters such as effective pumping speed, compression ratio, and ultimate vacuum, and are also noisier. Researchers have designed the top (outside the pitch circle) curve of the rotor profile as an ellipse, but the volumetric utilization rate of this type of rotor is no more than 50%, which is lower than that of the standard profile. Summary of the Invention

[0003] In view of this, the present invention provides a Roots pump with an elliptical rotor waist profile, which can effectively improve the volume utilization rate of the Roots pump rotor.

[0004] The Roots pump of the present invention has an elliptical rotor waist profile. The curve of the rotor profile located inside the pitch circle is an elliptical line, referred to as the waist elliptical line; the curve located outside the pitch circle is the conjugate curve of the waist elliptical line.

[0005] Preferably, the waist ellipse line lies on an ellipse T, and the center Ot of the ellipse T lies on the O1y1 axis of the rotor pitch circle, at a distance from the center O1 of the rotor pitch circle. d The major axis of ellipse T is a, the minor axis is b, and the rotor pitch circle radius is R1; take the curve AF of ellipse T located in the first quadrant as 1 / 4 of the waist ellipse line;

[0006] The conjugate curve AG of the waist ellipse is calculated according to formula (9):

[0007] (9)

[0008] in, The engagement angle is the angle between the line O1B connecting the intersection point B and the pitch circle center O1 and the O1y1 axis; the intersection point B is the intersection of the normal of any point C(x1, y1) on the waist ellipse and the pitch circle.

[0009] A better approach is to adjust the parameter d. 、 a, b, and R1 are used to optimize the rotor profile volume utilization rate, and then the rotor profile is finally determined.

[0010] The better one is based on formula (2).

[0011] (2)

[0012] Adjusting parameter d 、 b and R1, optimizing the rotor profile volume utilization, and finally determining the rotor profile.

[0013] The application also provides a rotor profile design method of the Roots pump with the above-mentioned rotor waist profile being an elliptic line, comprising the following steps:

[0014] Step 1, determining an independent variable parameter, which is the distance between the center O t of the ellipse T and the center O1 of the rotor pitch circle d ; the major axis a and the minor axis b of the ellipse T; the rotor pitch circle radius R1;

[0015] Step 2, determining the ellipse T as:

[0016]

[0017] Taking the curve AF of the ellipse T located in the first quadrant part as the 1 / 4 waist elliptic line;

[0018] Step 3, determining the meshing angle :

[0019] The meshing angle is the included angle between the line O1B connecting the intersection point B and the center O1 of the pitch circle and the O1y1 axis, the intersection point B is the intersection point of the normal line of any point C (x1, y1) on the curve AF and the pitch circle, is:

[0020]

[0021] wherein, is the included angle between the line O1C connecting the point C and the center O1 of the pitch circle and the O1x1 axis, ; is the included angle between O1B and BC, ; is the included angle between O1C and BC, ; is the included angle between the horizontal line CE of the point C and the tangent of the point C, ;

[0022] Step 4, determining the conjugate curve AG of the 1 / 4 waist elliptic line according to formula (9):

[0023] (9)

[0024] determining whether the conjugate curve AG is a smooth curve, if yes, executing step 5, if not, returning to step 1 to re-determine the value of the independent variable parameter;

[0025] Step 5, determining the rotor profile of the Roots pump: mirroring the AF and AG along the O1x1 axis and the O1y1 axis to obtain the profile of the entire rotor.

[0026] Step 6, determining rotor profile volume utilization ratio :

[0027] (10)

[0028] wherein, A is the area of rotor profile section, is the rotor top circle radius, ;

[0029] Step 7, designing rotor length is:

[0030] (11)

[0031] wherein, n is the rotor speed, is the Roots pump geometric suction speed.

[0032] Preferably, the ratio of rotor length and rotor top circle radius is 1.0-2.5.

[0033] Beneficial effects:

[0034] The waist part of the rotor profile of the present application is an elliptic line, which has the characteristic of high volume utilization ratio compared with the rotor profile with the top part of an elliptic line, and the volume utilization ratio can reach more than 55%, which is more than 10% better than the rotor profile with the top part of an elliptic line. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 is the waist part elliptic line rotor profile analysis diagram.

[0036] Figure 2 is the waist part elliptic line conjugate curve analysis diagram.

[0037] Figure 3 is the parameter R 1=34, b =31, take d =49 and d =45, the rotor profile design diagram, the geometric suction speed is 70L / s.

[0038] Figure 4 is the parameter R 1=34, d =45, take b =27 and b =31, the rotor profile design diagram, the geometric suction speed is 70L / s. DETAILED DESCRIPTION

[0039] The present application will be described in detail below in combination with the drawings and examples.

[0040] The present application provides a Roots pump with an elliptical rotor profile, which can significantly increase the volume utilization rate of the elliptical rotor profile of the Roots pump. The Roots pump mainly comprises two parts: (1) the curve of the rotor profile inside the pitch circle is an elliptical line; and (2) the curve of the rotor profile outside the pitch circle is a conjugate curve of the waist elliptical line.

[0041] Since the rotor profile of the Roots pump is an axisymmetric figure, only the part in the first quadrant is analyzed in the actual analysis and solution, and then the entire rotor profile is obtained by symmetry.

[0042] (1) Elliptical line part

[0043] As shown in Figure 1 , an x1O1y1 coordinate system S1 and an elliptical line are established; wherein the coordinate system S1 is fixed on the rotor 1, the origin O1 is the center of the rotor 1, O1x1 is the horizontal coordinate, O1y1 is the vertical coordinate, and the elliptical equation can be expressed as:

[0044] (1)

[0045] In formula (1), a is the length of the major axis of the ellipse, b is the length of the minor axis of the ellipse, d is the distance from the center O t of the ellipse to the coordinate center O1.

[0046] If the pitch circle radius is , according to the characteristics of the rotor profile of the Roots pump, the connecting point of the inner and outer profiles of the pitch circle is point A , , therefore, the A point is on the ellipse, and the value range of x1 in the elliptical equation is (0, ), and the A point is substituted into formula (1) to obtain:

[0047] (2)

[0048] Therefore, the elliptical equation determined by formula (2) has three independent variable parameters, such as the pitch circle radius , the minor axis of the ellipse b , and the distance from the center of the ellipse to the center of the rotor , which are three independent variable parameters.

[0049] (2) Conjugate curve part

[0050] According to the characteristics of the conjugate curve, the meshing angle needs to be solved first: as Figure 1As shown, the engagement angle is: the intersection point B of the normal line of any point C (x1, y1) on the elliptic line and the pitch circle, the angle between the line O1B connecting the intersection point B and the center O1 of the rotor and the y1 axis .

[0051] Let Figure 1 the angle between the line connecting any point C on the ellipse and the center of the rotor and the O1x1 axis be , then can be expressed as:

[0052] (3)

[0053] Figure 1 In , the angle between the horizontal line CE and the tangent line at point C is , which can be expressed as:

[0054] (4)

[0055] Figure 1 In , the angle between O1C and BC is , which can be expressed as:

[0056] (5)

[0057] Figure 1 In , the angle between O1B and BC is , in which the sine theorem is applied, which can be expressed as:

[0058] (6)

[0059] In summary, Figure 1 the engagement angle can be expressed as:

[0060] (7)

[0061] In order to obtain the conjugate curve, a coordinate system S2 as shown in Figure 2 is established, which is fixed on the rotor 2, with the origin O2 being the center of the rotor 2, O2x2 being the horizontal coordinate, and O2y2 being the vertical coordinate; during the rotation of the rotor 1 and the rotor 2, the coordinate systems S1 and S2 also rotate, in which the waist elliptic line represented by formula (1) is AF, located in the coordinate system S1, and according to the engagement relationship, the conjugate curve thereof located in the coordinate system S2 can be expressed as:

[0062] (8)

[0063] Obviously, due to the symmetry of the rotor profile, it can be seen that the rotor located in coordinate system S2... It is completely consistent with AG located in coordinate system S1, therefore it is necessary to... Translate to coordinate system S1 and rotate counterclockwise. Then the curve AG can be represented as:

[0064] (9)

[0065] (x1, y1) in formulas (8) and (9) are determined by formula (1).

[0066] The volume utilization rate of the rotor profile is an important evaluation index for rotor profile design, which can be expressed as:

[0067] (10)

[0068] In formula (10), A The area of ​​the rotor cross-section enclosed by the rotor profile is called the rotor cross-section. The radius of the rotor tip circle is, for example Figure 1 As shown, .

[0069] The length of the rotor is designed to be:

[0070] (11)

[0071] In formula (11), n The rotor speed is (r / min). To design the geometric pumping speed (L / s) of the Roots pump.

[0072] Based on the above analysis, the steps for solving the rotor profile where the waist curve is an ellipse are as follows:

[0073] ① Determine independent variable parameters: First, select three independent variable parameter values, such as: pitch circle radius. ellipse semi-axis b and the distance from the center of the ellipse to the center of the rotor (like Figure 1 (As shown).

[0074] ② Determine the ellipse line: Obtain the semi-major axis of the ellipse using formula (2). Substituting it and the known parameters into formula (1) yields the equation of the ellipse. And take the curve AF located in the first quadrant as the rotor section profile (e.g. Figure 1 (As shown).

[0075] ③ Determine the meshing angle: Based on the obtained waist ellipse AF located inside the pitch circle, calculate the corresponding conjugate curve meshing angle. (likeFigure 1 are as follows:

[0076] (a) According to the coordinate (x1, y1) value of the ellipse AF, solve by formula (3) , solve by formula (4) ;

[0077] (b) Substitute and and related parameters into formulas (5), (6) and (7) to solve the meshing angle (as shown in Figure 1 ).

[0078] 4. Determine the conjugate curve: according to the coordinate (x1, y1) value of the waist ellipse AF, the meshing angle , and the pitch circle radius , substitute into formula (9) to obtain the conjugate curve AG (as shown in Figure 2 ), the conjugate curve AG must be a smooth curve, if AG obtained by calculation is a non-smooth curve, the independent variable parameter value needs to be reselected and adjusted.

[0079] 5. Determine the 1 / 4 profile of the Roots pump rotor: as shown in Figure 2 , the part of the rotor profile in the first quadrant is obtained from AF and AG.

[0080] 6. Determine the Roots pump rotor profile: mirror the 1 / 4 rotor profile along the horizontal and vertical coordinate axes to obtain the entire rotor profile, as shown in Figure 2 .

[0081] 7. Determine the volume utilization rate of the rotor profile: calculate the volume utilization rate of the rotor by formula (10) to evaluate the rotor profile.

[0082] 8. Determine the design rotor length: calculate the length of the rotor by formula (11) with related parameters, generally the ratio of the length of the rotor to the top circle radius is required to be 1.0~2.5.

[0083] Design parameters of the Roots pump rotor profile:

[0084] The parameters of the designed Roots pump with a geometric pumping speed of 70 L / s and a rotational speed of 3000 r / min are as follows:

[0085] 1. Pitch circle radius ;

[0086] 2. Ellipse short semi-axis mm;

[0087] 3. Ellipse center to rotor center inner distance mm;

[0088] 4. Top circle radius ;

[0089] 5. Elliptic long semi-axis mm;

[0090] 6. Rotor volume utilization rate %;

[0091] 7. Rotor length mm.

[0092] The volume utilization rate of the rotor of the application can reach more than 55%, and relative to the rotor profile with the top elliptical line, the volume utilization rate is more than 10% higher, which plays an important role in improving the effective pumping speed, compression ratio and limit vacuum of the Roots pump.

[0093] To sum up, the above is only a preferred embodiment of the application, and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A lobe pump having an elliptical rotor waist profile, characterized in that, The curve inside the pitch circle of the rotor profile is an ellipse, which is called a waist ellipse. The waist ellipse line is located on the ellipse T, the center of the ellipse T is Ot located on the O1y1 axis of the rotor pitch circle, and the distance from the center of the rotor pitch circle O1 is d ; the long axis of the ellipse T is a, the short axis is b, and the rotor pitch circle radius is R1; take the curve AF of the first quadrant part of the ellipse T as 1 / 4 waist ellipse line; The conjugate curve AG of the waist ellipse is calculated according to formula (9): （9） wherein is the engagement angle, is the angle between the line O1B and the O1y1 axis of the center of the pitch circle O1 and the intersection point B; the intersection point B is the intersection point of the normal line of any point C (x1, y1) on the waist ellipse line and the pitch circle.

2. The lobe pump of claim 1, wherein the rotor waist profile is an elliptical line. By adjusting parameter d 、 a, b and R1, optimizing the rotor profile volume utilization, and finally determining the rotor profile.

3. The lobe pump of claim 2, wherein the rotor waist line is an elliptical line. Based on formula (2) （2） By adjusting parameter d 、 b and R1, optimizing the rotor profile volume utilization, and finally determining the rotor profile.

4. A method of designing a rotor profile of a lobe pump according to any one of claims 1 to 3, wherein the rotor waist line is an elliptic line, characterized in that, Comprising the following steps: Step 1, determining the independent variable parameter, which is the distance between the center of the ellipse T Ot and the center of the rotor pitch circle O1 d ; the major axis a, the minor axis b of the ellipse T; the rotor pitch circle radius R1; Step 2, determine the ellipse T as: Take the curve AF of the ellipse T in the first quadrant as a 1 / 4 waist ellipse; Step 3, determining the angle of engagement : said engagement angle is the angle between the line O1B and the O1y1 axis, said line O1B being the line joining the intersection point B of the normal to the curve AF at a point C (x1, y1) and the centre O1 of the pitch circle, said intersection point B being the intersection point of the normal to the curve AF at a point C (x1, y1) and the centre O1 of the pitch circle; is: wherein, is the angle between the line O1C connecting point C and the center of the pitch circle O1 and the O1x1 axis, ; is the angle between O1B and BC, ; is the angle between O1C and BC, ; is the angle between the horizontal line CE of point C and the tangent line of point C, ; Step 4, determine the conjugate curve AG of the 1 / 4 waist ellipse according to formula (9): （9） Determine whether the conjugate curve AG is a smooth curve, if yes, execute step 5, if not, return to step 1 and re-determine the independent variable parameter value; Step 5, determine the rotor profile of the Roots pump: mirror the curve AF in the first quadrant and the conjugate curve AG along the O1x1 axis and the O1y1 axis to obtain the profile of the entire rotor; Step 6, determining rotor profile volume utilization : （10） wherein A is the area of the rotor cross-section enclosed by the rotor profile, is the rotor tip circle radius, ; Step 7, Designing the length of the rotor is: （11） wherein, n is the rotor speed, is the Roots pump geometric suction speed.

5. The method of claim 4, wherein, The ratio of the length of the rotor to the radius of the rotor top circle is 1.0-2.5.

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