A design method of roots pump rotor profile based on pin-tooth circular arc

Abstract

This application relates to the field of Roots pump design technology, specifically to a method for designing the rotor profile of a Roots pump based on pin tooth arcs. The method includes: Step 1: Designing a basic rotor profile based on pin tooth arcs; Step 2: Dividing the basic profile into four segments; Step 3: Improving the top pin tooth arc with the rotor center as the center and the highest point of the rotor as the radius to form a sealing arc; Step 4: Improving the waist pin tooth arc with the rotor center as the center and the apex of the rotor as the radius; Step 5: Completing the design of the Roots pump rotor profile. The improved Roots pump rotor pin tooth arcs mesh only at the moment of perpendicular meeting during rotation, with the meshing occurring at other times achieved by quadratic curves and conjugate curves. By improving the rotor profile of the Roots pump, the effective pumping speed, compression ratio, and ultimate vacuum of the Roots pump are further improved, noise is reduced, and the overall technical specifications of the product are enhanced.

Description

Technical Field

[0001] This application relates to the field of Roots pump design technology, and more specifically, to a method for designing the rotor profile of a Roots pump based on the circular arc of the pin teeth. Background Technology

[0002] Roots pumps are mainly used in semiconductor, petrochemical, papermaking, food, and electronics industries.

[0003] Currently, the main profiles of Roots pump rotors on the market are involute, cycloid, and circular arc, which are collectively referred to as standard profiles. Rotors with standard profiles are easier to design and manufacture, but they have lower technical parameters such as effective pumping speed, compression ratio, and ultimate vacuum, and are also noisier.

[0004] Based on this, in order to further improve the technical indicators of the Roots pump, such as effective pumping speed, compression ratio and ultimate vacuum, and reduce noise, it is necessary to improve the design of the Roots pump rotor profile. Therefore, a Roots pump rotor profile design based on pin tooth arc is proposed. Summary of the Invention

[0005] This application provides a method for designing the rotor profile of a Roots pump based on the circular arc of the pin teeth, which can improve the technical parameters of the Roots pump such as effective pumping speed, compression ratio and ultimate vacuum, and reduce noise.

[0006] To achieve the above objectives, this application provides a method for designing the rotor profile of a Roots pump based on pin tooth arcs, comprising the following steps: Step 1: Designing the basic profile of the Roots pump rotor based on pin tooth arcs; Step 2: Dividing the basic profile into four segments, including a top pin tooth arc, a quadratic curve, a conjugate curve, and a waist pin tooth arc; Step 3: Improving the top pin tooth arc with the rotor center as the center and the highest point of the rotor as the radius to form a sealing arc; Step 4: Improving the waist pin tooth arc with the rotor center as the center and the apex of the rotor as the radius; Step 5: Completing the design of the Roots pump rotor profile. The improved Roots pump rotor pin tooth arcs mesh only at the moment of perpendicularity during rotation, and the meshing at other times is achieved by the quadratic curve and the conjugate curve.

[0007] Furthermore, in step 1, the rotor profile of the Roots pump is an axisymmetric figure.

[0008] Furthermore, in step 2, the basic profile is located in the first quadrant of the coordinate system.

[0009] Furthermore, the improved design increased the clearance between the top of the rotor and the housing of the Roots pump.

[0010] Furthermore, after the improvement, the backflow resistance formed between the rotor and the casing wall of the Roots pump increases.

[0011] The present invention provides a method for designing the rotor profile of a Roots pump based on the circular arc of pin teeth, which has the following beneficial effects:

[0012] This application improves the effective pumping speed, compression ratio, and ultimate vacuum of the Roots pump by modifying the rotor profile, thereby reducing noise and improving the overall technical specifications of the product. Attached Figure Description

[0013] The accompanying drawings, which form part of this application, are used to provide a further understanding of the application and to make other features, objects, and advantages of the application more apparent. The illustrative embodiments and descriptions of this application are used to explain the application and do not constitute an undue limitation of the application. In the drawings:

[0014] Figure 1 This is the first schematic diagram of the basic profile design of the Roots pump rotor profile based on the pin tooth arc;

[0015] Figure 2 This is a second schematic diagram of the basic profile design of the Roots pump rotor profile based on the pin tooth arc;

[0016] Figure 3 This is a schematic diagram of the overall design of the rotor profile of a Roots pump based on the circular arc of the pin teeth;

[0017] Figure 4 This is a schematic diagram of the rotor profile after the improvement of the Roots pump rotor profile based on the pin tooth arc.

[0018] Figure 5 This is a schematic diagram of the rotor after the improvement of the rotor profile of the Roots pump based on the pin tooth arc.

[0019] Figure 6 This is a magnified view of the clearance between the rotor and the wall of the Roots pump before the improvement.

[0020] Figure 7 It is the improved clearance between the rotor and the wall of the Roots pump. Figure 5 A magnified view of a portion of the image;

[0021] In the diagram: 1-top pin tooth arc, 2-secondary curve, 3-conjugate curve, 4-waist pin tooth arc, 5-rotor, 6-shell. Detailed Implementation

[0022] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of the present application.

[0023] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this application described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0024] In this application, the terms "upper," "lower," "left," "right," "front," "rear," "top," "bottom," "inner," "outer," "middle," "vertical," "horizontal," "lateral," and "longitudinal" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are primarily for the purpose of better describing this application and its embodiments, and are not intended to limit the indicated device, element, or component to having a specific orientation, or to be constructed and operated in a specific orientation.

[0025] Furthermore, in addition to indicating location or positional relationship, some of the aforementioned terms may also have other meanings. For example, the term "above" may also be used in some cases to indicate a certain dependency or connection relationship. Those skilled in the art can understand the specific meaning of these terms in this application based on the specific circumstances.

[0026] In addition, the term "multiple" should mean two or more.

[0027] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0028] like Figure 3As shown, this application provides a method for designing the rotor profile of a Roots pump based on pin tooth arcs, including the following steps: Step 1: Designing the basic profile of the Roots pump rotor based on pin tooth arcs; Step 2: Dividing the basic profile into 4 segments, including a top pin tooth arc 1, a quadratic curve 2, a conjugate curve 3, and a waist pin tooth arc 4; Step 3: Improving the top pin tooth arc 1 with the rotor center as the center and the highest point of the rotor as the radius to form a sealing arc; Step 4: Improving the waist pin tooth arc 4 with the rotor center as the center and the vertex of the rotor as the radius; Step 5: Completing the design of the Roots pump rotor profile. The improved Roots pump rotor pin tooth arcs mesh only at the moment of perpendicularity during rotation, and the meshing at other times is achieved by the quadratic curve and the conjugate curve.

[0029] Furthermore, in step 1, the rotor profile of the Roots pump is an axisymmetric figure.

[0030] Furthermore, in step 2, the basic profile is located in the first quadrant of the coordinate system.

[0031] Furthermore, the improved design increases the clearance between the top of the rotor 5 and the housing 6 of the Roots pump.

[0032] Furthermore, after the improvement, the backflow resistance formed between the rotor 5 and the wall of the casing 6 of the Roots pump increases.

[0033] Specifically, the Roots pump rotor profile design method based on pin tooth arc provided in this application mainly improves the design of the top pin tooth arc and the waist pin tooth arc on the basis of the existing standard profile design of the Roots pump rotor, so that the gap between the Roots pump rotor and the wall surface forms a sealed arc, thereby improving the effective pumping speed, compression ratio and ultimate vacuum of the Roots pump.

[0034] More specifically, in the embodiments of this application, the rotor profile of the Roots pump is an axisymmetric figure. Therefore, in the improvement process, only 1 / 4 of its profile needs to be analyzed. In practice, the portion of the profile located in the first quadrant is usually analyzed. Figure 1 As shown in the figure, the basic profile of the Roots pump rotor is shown. Section AB is the top pin tooth arc, section BC is a quadratic curve, section CD is a conjugate curve, and section DE is the waist pin tooth arc.

[0035] In the design process, assuming the radius of the pitch circle is R1, the equation of the pitch circle corresponding to the coordinate system is:

[0036]

[0037] Let the equation of the conic section be the parabola BC:

[0038]

[0039] The equation for the arc of the top pin tooth is:

[0040]

[0041] The arc AB is tangent to the parabola BC at point B; therefore, the slopes of the arc and the parabola are equal at point B.

[0042]

[0043] Obtain the x-coordinate of point B Substituting into equations (2) and (3), we get

[0044]

[0045] The y-coordinates of point B in equation (5) 1b Equal, we get:

[0046]

[0047] Based on the characteristics of the rotor profile, the coordinates of point C are: Substituting into the parabola equation (2), we get:

[0048]

[0049] CD is the conjugate curve of BC. Solving for CD requires determining the meshing angle. like Figure 2 As shown, suppose there is any point M(x1, y1) on the parabola BC, and the slope of the tangent line to the parabola at that point is:

[0050] tan(-γ)=-2ax1 (8)

[0051] Draw the normal MP to the parabola through point M. Point P is the intersection of the normal and the pitch circle. Connect O1P. The angle between O1P and the y1 axis is the meshing angle φ. Draw a line O1L perpendicular to MP. In RTΔO1LP, the length of line segment O1L is:

[0052]

[0053] At the same time, the coordinates O1L of point M can also be expressed as:

[0054] O1L=-x1cosγ+y1sinγ (10)

[0055] From equations (9) and (10), the relationship between parameters γ and φ can be expressed as:

[0056]

[0057] Substituting the meshing angle φ and the coordinates (x1, y1) of the parabola equation into formula (12), we obtain the equation of the conjugate curve CD:

[0058]

[0059] The equation for the circular arc DE of the waist pin tooth is:

[0060]

[0061] In summary, it can be seen that the rotor profile composed of the quadratic parabola and the pin tooth arc has two independent variable parameters. Generally, the pitch circle radius R1 and the parabola parameter a are selected. Then, parameter b is determined by equation (7), and the pin tooth arc radius r is determined by equation (6). Then, 1 / 4 of the rotor profile is determined. The top pin tooth arc AB segment is determined by equation (3), the quadratic curve BC segment is determined by equation (2), the conjugate curve CD segment is determined by equation (12), and the waist pin tooth arc DE is determined by equation (13).

[0062] The obtained 1 / 4 profile is stacked along the horizontal and vertical axes to obtain the entire rotor profile, including the top pin tooth arc, the quadratic curve, the conjugate curve, and the waist pin tooth arc, as shown below. Figure 3 The rotor profile was then improved.

[0063] During the improvement process, the arc segment AB of the top pin tooth is divided into two parts, while part BF remains unchanged, as follows: Figure 4 As shown, where AF is the arc of a circle with center O1 and radius O1A = R1 + r, then the equation of AF is:

[0064]

[0065] At the same time, the symmetrical part of AF is modified accordingly;

[0066] Divide the arc segment DE of the waist pin tooth into two parts, while the DG part remains unchanged, as follows: Figure 4 As shown, where EG is an arc with center O2 and radius O2E = R1 + r, the equation of EG is:

[0067] (x1-2R1) 2 +y1 2 =(R1+r) 2 (15)

[0068] At the same time, the symmetrical part of EG is modified accordingly.

[0069] The effective pumping speed, compression ratio, ultimate vacuum of the Roots pump are related to the flow resistance of the rotor-wall gap, which is determined by formula (16):

[0070]

[0071] In the formula, R is the resistance to gas flow in the Roots pump, and η is a constant. Let l be the average velocity of gas molecules, l1 be the length of AF, and l be the length of the Roots pump rotor.

[0072] like Figure 5 As shown, when a Roots pump is working, gas enters from the top and exits from the bottom, resulting in a higher outlet pressure than inlet pressure. However, there is a gap between the rotor and the wall. Under the influence of the pressure difference, some gas flows from the outlet side through the gap to the inlet side. The flow rate is related to the resistance of the gap between the rotor and the wall. If the resistance is high, the backflow is low, the effective pumping speed is high, and the compression ratio is also increased. Figure 6 As shown, in the unmodified Roots pump rotor profile, the minimum clearance between the top of rotor 5 and housing 6 is only one point, as... Figure 7 As shown, in the improved rotor profile, the minimum gap between the top of rotor 5 and housing 6 is AF, and its length l1 is significantly increased. Therefore, the backflow resistance formed by the improved rotor 5 and the wall of housing 6 is increased, which reduces the backflow flow rate. The reduction in backflow flow rate will increase the effective pumping speed, compression ratio and ultimate vacuum of the Roots pump.

[0073] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for designing the rotor profile of a Roots pump based on the circular arc of pin teeth, characterized in that, Includes the following steps: Step 1: Design the basic profile of the Roots pump rotor based on the pin tooth arc; Step 2: Divide the basic profile into 4 segments, including the top pin tooth arc, the quadratic curve, the conjugate curve, and the waist pin tooth arc; Step 3: Using the rotor center as the center and the highest point of the rotor as the radius, improve the arc of the top pin tooth to form a sealing arc; Step 4: Improve the arc of the waist pin teeth with the rotor center as the center and the rotor vertex as the radius; Step 5: Complete the design of the rotor profile of the Roots pump. The improved Roots pump's two rotor pins mesh only at the moment when they meet perpendicularly during rotation. The meshing at other times is achieved by quadratic curves and conjugate curves.

2. The method for designing the rotor profile of a Roots pump based on pin tooth arcs according to claim 1, characterized in that, In step 1, the rotor profile of the Roots pump is an axisymmetric figure.

3. The Roots pump rotor profile design method based on pin tooth arc according to claim 2, characterized in that, In step 2, the basic profile is located in the first quadrant of the coordinate system.

4. According to the Roots pump rotor profile design method based on pin tooth arc as described in claim 1, after improvement, the gap between the top of the Roots pump rotor and the housing is increased.

5. According to the Roots pump rotor profile design method based on pin tooth arc as described in claim 1, after the improvement, the backflow resistance formed between the rotor of the Roots pump and the casing wall increases.

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