Self-balancing screw vacuum pump rotor structure and design method thereof

Abstract

A self-balancing screw vacuum pump rotor structure and a design method thereof, wherein a pitch law curve of the rotor is determined by coordinate positions of points A, B, C, D, E and F and a curve slope at the point B; a coordinate system is established with a rotor rotation angle as an abscissa and a pitch as an ordinate, the abscissas of the points A, B, C, D, E and F are 0°, 180°, 360°, 540°, 720° and N*360° respectively, N is a natural number greater than 2; the ordinates of the points A, E and F are all P1, the ordinates of the points B and D are all P0, the ordinate of the point C is P2, P2=nP1; and the pitch law of the rotor is determined by a minimum pitch P1, a maximum minimum pitch ratio n, a curve slope parameter k and a rotor stage number N. The screw vacuum pump rotor structure with natural dynamic and static balance characteristics can be constructed, and the design space of the self-balancing rotor structure is expanded.

Description

Technical Field

[0001] This invention belongs to the technical field of dry screw vacuum pumps, specifically relating to a self-balancing screw vacuum pump rotor structure and its design method. Background Technology

[0002] Dry screw vacuum pumps are positive displacement rotary machines with forced suction and exhaust functions. Due to their high pumping speed, high efficiency, high cleanliness and high reliability, they are widely used in obtaining medium and high vacuum environments.

[0003] The core component of a dry screw vacuum pump is a pair of meshing rotors. Due to the need for high rotor structural sealing, the rotor profile often adopts an asymmetrical single-tooth profile, which results in a high dynamic imbalance in conventional constant pitch and variable pitch rotor structures. This requires a long dynamic balancing process. At the same time, the large dynamic imbalance results in a large amount of weight removal from the rotor tooth tips, which in turn seriously reduces the rotor's sealing performance.

[0004] Designing the screw pitch to achieve theoretical dynamic balance is an effective way to solve the above problems. However, existing self-balancing screw pitch design methods have poor adjustability, which means that the internal volume ratio of the screw is directly determined by the number of screw stages, making it impossible to further optimize for different operating conditions. Summary of the Invention

[0005] The purpose of this invention is to address the problems in the prior art by providing a self-balancing screw vacuum pump rotor structure and its design method. The invention uses cubic spline curves to construct the pitch law of the screw rotor, thereby constructing a screw vacuum pump rotor structure with natural dynamic and static balance characteristics. The structure can be designed using cubic spline curves, thus expanding the design space of the internal volume ratio of the self-balancing rotor structure.

[0006] To achieve the above objectives, the present invention provides the following technical solution: Firstly, a self-balancing screw vacuum pump rotor structure is provided, wherein the rotor pitch curve is derived from a point... A ,point B ,point C ,point D ,point E ,point F coordinates and points B The slope of the curve at that point is determined by the angle of rotation; establishing a coordinate system with the rotor angle as the abscissa and the pitch as the ordinate, then the point... A ,point B ,point C ,point D ,point E ,point F The x-coordinates are 0°, 180°, 360°, 540°, 720° andN ×360°, N A natural number greater than 2; point A ,point E With point F The ordinates are all P 1. Pitch, point B ,point D The ordinates are all P 0 pitch, point C The ordinate is P 2 pitch, P 2= nP 1; The pitch law of the rotor is based on the minimum pitch P 1. Maximum and minimum pitch ratio n Curve slope parameter k and the number of rotor stages N The decision was made.

[0007] As a preferred solution, the P 0 pitch and P 1. Pitch and P The following relationship exists between the two pitches: .

[0008] As a preferred option, the rotor pitch curve at point B The slope is k At point A If the slope is 0, then the curve AB Calculated using the following generating equation:

[0009] In the formula, P ( φ The ) indicates the pitch variation pattern. φ For angular parameters; The polynomial coefficients can be solved using the following expression:

[0010] curve BC , CD , DE and EF The calculations are performed using the following generating equations:

[0011] In the formula, φ total This indicates the total rotation angle of the rotor.

[0012] As a preferred option, the rotor adopts a single-tooth profile, and the face-centered coordinates are ( x c ,y c The distance between the face center and the axis is... r c The geometric condition for the screw rotor to achieve static balance is:

[0013] In the formula, ω d represents the rotational angular velocity. m Indicates the mass of the rotor element; The geometric conditions for achieving dynamic balance of the screw rotor are:

[0014] In the formula, L ( φ The symbol ) represents the relationship between the screw length and the rotation angle.

[0015] As a preferred embodiment, the rotor micro-element mass d m The calculation is performed using the following expression:

[0016] In the formula, ρ d represents the density of a material. V Represents the volume of a infinitesimal element. S profile d represents the cross-sectional area of ​​the profile. L This indicates the length of the rotor element; the relationship between screw length and rotation angle. L (φ) and rotor element length d L The calculation is performed using the following expression:

[0017] .

[0018] As a preferred approach, considering that the material density is constant at different cross-sectional locations, and taking into account the rotor micro-element mass d... m Substituting the calculation expressions, we obtain the geometric conditions for the screw rotor to achieve static balance and dynamic balance as follows:

[0019] .

[0020] As a preferred option, the curve BC , CD , DE and EF Substituting the generating equation into the geometric conditions for static balance of the screw rotor, we obtain the following expression:

[0021] The pitch curve defined by the above pitch variation formula enables the screw rotor to automatically meet the static balance condition.

[0022] As a preferred solution, the dynamic imbalance of the screw rotor is solved using the following expression:

[0023] To ensure that the dynamic imbalance of the screw rotor is zero, the dynamic imbalance of the screw rotor must conform to the following relationship:

[0024] In the formula, m un This represents the dynamic imbalance mass of the screw rotor; to ensure the screw rotor meets the dynamic balance condition, the pitch variation depends on adjusting the maximum and minimum pitch ratio. n Curve slope parameter k and the number of rotor stages N A specific relationship needs to be satisfied.

[0025] Secondly, a design method for the rotor structure of the self-balancing screw vacuum pump described above is provided: The rotor pitch follows the law of minimum pitch. P 1. Maximum and minimum pitch ratio n Curve slope parameter k and the number of rotor stages N Determined by the number of rotor stages; N and maximum and minimum pitch ratio n Next, perform curve slope parameter analysis. k The parameters are solved to satisfy the dynamic and static balance characteristics of the screw vacuum pump rotor, and then based on the defined and solved parameters... n , k , N Solving for the polynomial coefficients of the pitch law curve allows for the construction of the pitch variation law of the self-balancing screw rotor; based on the constructed pitch variation law of the self-balancing screw rotor, different rotor stages are generated. N Self-balancing screw vacuum pump rotors with different volume ratios.

[0026] As a preferred embodiment, the design method includes: Select the initial screw pitch based on the rotor's exhaust volume and sealing requirements. P 0 and rotor stage number N ; Based on the vacuum application requirements of the vacuum pump, select the design range of the internal volume ratio of the screw rotor and determine the maximum and minimum pitch ratio. n ; Select the corresponding curve slope parameter kThis ensures that the screw rotor meets the dynamic and static balance conditions; Based on parameters n , k , N Solve for the polynomial coefficients of the pitch law curve to construct the pitch variation law of the self-balancing screw rotor. Based on the pitch variation law of the self-balancing screw rotor, different rotor stages are generated. N Self-balancing screw vacuum pump rotors with different volume ratios.

[0027] Compared with the prior art, the present invention has at least the following beneficial effects: The dynamic and static balance characteristics of the screw vacuum pump rotor can be achieved without dynamic balancing. The pitch law of the self-balancing screw vacuum pump rotor structure of this invention is based on the minimum pitch... P 1. Maximum and minimum pitch ratio n Curve slope parameter k and the number of rotor stages N The number of rotor stages determines the outcome. N and maximum and minimum pitch ratio n Under these conditions, the curve slope parameter can be determined. k The solution is to satisfy the dynamic and static balance characteristics of the screw vacuum pump rotor, and thus, based on the parameters... n , k , N The polynomial coefficients of the pitch variation curve are solved to construct the pitch variation law of the self-balancing screw rotor. The self-balancing screw vacuum pump rotor structure proposed in this invention significantly reduces the dynamic balancing process time and minimizes the impact of the dynamic balancing holes on the rotor's sealing performance because the rotor meets the self-balancing condition. The rotor pitch variation law has a large adjustable range, allowing for flexible adjustment of the internal volume ratio based on existing screw structures, thus enabling the acquisition of the optimal internal volume ratio design to meet different requirements. Attached Figure Description

[0028] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 A schematic diagram of the rotor pitch curve in an embodiment of the present invention; Figure 2 A schematic diagram illustrating the calculation principle of achieving dynamic and static balance of the screw rotor in an embodiment of the present invention; Figure 3 A schematic diagram of parameter values ​​for constructing the pitch variation law of a self-balancing screw rotor according to an embodiment of the present invention; Figure 4 A schematic diagram illustrating the variation of rotor pitch under different parameters in an embodiment of the present invention; Figure 5 A schematic diagram of the self-balancing screw vacuum pump rotor structure generated in this embodiment of the invention: (a) k =3, n =4.364515, N =6; (b) k =2.85, n =4.2905, N =8. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, those skilled in the art can obtain other embodiments without creative effort.

[0031] It should be noted that in the description of the embodiments of the present invention, the terms "upper", "lower", "left", "right", "inner", "outer", "front end", "rear end", "head", "tail", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the present invention.

[0032] Please see Figure 1 and Figure 2 This invention proposes a self-balancing screw vacuum pump rotor structure. The screw pitch law of the screw rotor is constructed by using cubic spline curves, thereby constructing a screw vacuum pump rotor structure with natural dynamic and static balance characteristics. The cubic spline curve structure can be used for design, thereby expanding the design space of the internal volume ratio of the self-balancing rotor structure.

[0033] In the self-balancing screw vacuum pump rotor structure of this embodiment of the invention, the rotor pitch curve is from point... A ,point B ,point C ,point D ,point E ,point F coordinates and points B The slope of the curve at that point is determined by the angle of rotation. Establish a coordinate system with the rotor angle as the x-axis and the pitch as the y-axis, then the point... A ,point B ,point C ,pointD ,point E ,point F The x-coordinates are 0°, 180°, 360°, 540°, 720° and N ×360°, N It is a natural number greater than 2. (Point) A ,point E With point F The ordinates are all P 1. Pitch, point B ,point D The ordinates are all P 0 pitch, point C The ordinate is P 2 pitch, P 2= nP 1. The rotor pitch follows the law of minimum pitch. P 1. Maximum and minimum pitch ratio n Curve slope parameter k and the number of rotor stages N The decision was made.

[0034] In one possible implementation, P 0 pitch and P 1. Pitch and P The following relationship exists between the two pitches:

[0035] In one possible implementation, the rotor pitch curve is at point... B The slope is k At point A If the slope is 0, then the curve AB Calculated using the following generating equation:

[0036] In the formula, P ( φ The ) indicates the pitch variation pattern. φ For angular parameters; The polynomial coefficients can be solved using the following expression:

[0037] curve BC , CD , DE and EF The calculations are performed using the following generating equations:

[0038] In the formula, φ total This indicates the total rotation angle of the rotor.

[0039] like Figure 2 As shown, the rotor profile of the screw vacuum pump is a single-tooth profile, and its face center is not located on the axis. The coordinates of the face center are ( x c , y c The distance between the face center and the axis is... r c The geometric condition for the screw rotor to achieve static balance is:

[0040] In the formula, ω d represents the rotational angular velocity. m Indicates the mass of the rotor element; The geometric conditions for achieving dynamic balance of the screw rotor are:

[0041] In the formula, L ( φ The symbol ) represents the relationship between the screw length and the rotation angle.

[0042] Furthermore, the rotor micro-element mass d m The calculation is performed using the following expression:

[0043] In the formula, ρ d represents the density of a material. V Represents the volume of a infinitesimal element. S profile d represents the cross-sectional area of ​​the profile. L This indicates the length of the rotor element; the relationship between screw length and rotation angle. L (φ) and rotor element length d L The calculation is performed using the following expression:

[0044]

[0045] Considering that the material density is constant at different cross-sectional locations, and taking into account the rotor element mass d... m Substituting the calculation expressions, we obtain the geometric conditions for the screw rotor to achieve static balance and dynamic balance as follows:

[0046] .

[0047] curve BC , CD , DE and EF Substituting the generating equation into the geometric conditions for static balance of the screw rotor, we get:

[0048] The pitch curve defined by the above pitch variation formula enables the screw rotor to automatically meet the static balance condition.

[0049] Furthermore, the dynamic imbalance of the screw rotor is solved using the following expression:

[0050] To ensure that the dynamic imbalance of the screw rotor is zero, the dynamic imbalance of the screw rotor must conform to the following relationship:

[0051] In the formula, m un This represents the dynamic imbalance mass of the screw rotor; to ensure the screw rotor meets the dynamic balance condition, the pitch variation depends on adjusting the maximum and minimum pitch ratio. n Curve slope parameter k and the number of rotor stages N A specific relationship needs to be satisfied.

[0052] Please see Figure 3 , Figure 3 Different rotor stages are given N Below, the dynamic imbalance mass of the screw rotor m un With curve slope parameter k and maximum and minimum pitch ratio n The changing curve, in which, m un When the parameter is 0 k , n The value lines are shown by the red line. It can be seen from the graph that the values ​​vary with different rotor stages. N Below, there is one parameter. k and n The corresponding curve ensures that the screw rotor meets the dynamic balance condition.

[0053] Please see Figure 4 , Figure 4 The number of rotor stages is given. N When it is 4, different k The pitch variation curve under the condition of satisfying dynamic balance shows that, compared with the traditional quadratic spline and cosine spline curves, the design method of the present invention has greater design flexibility, thus allowing for a larger adjustment space for the internal volume ratio of the screw rotor, thereby adapting to the screw rotor structure design under different working conditions.

[0054] Please see Figure 5 , Figure 5 (a) in the diagram shows the parameters. k =3, n =4.364515, N The self-balancing screw vacuum pump rotor structure generated by =6 has an internal volume ratio of 3.553. Figure 5 (b) shows the parameters k =2.85, n =4.2905, N The self-balancing screw vacuum pump rotor structure generated by =8 has an internal volume ratio of 4.

[0055] Another embodiment of the present invention also proposes a design method for the rotor structure of the self-balancing screw vacuum pump described above: The rotor pitch follows the law of minimum pitch. P 1. Maximum and minimum pitch ratio n Curve slope parameter k and the number of rotor stages N Determined by the number of rotor stages; N and maximum and minimum pitch ratio n Next, perform curve slope parameter analysis. k The parameters are solved to satisfy the dynamic and static balance characteristics of the screw vacuum pump rotor, and then based on the defined and solved parameters... n , k , N Solving for the polynomial coefficients of the pitch law curve allows for the construction of the pitch variation law of the self-balancing screw rotor; based on the constructed pitch variation law of the self-balancing screw rotor, different rotor stages are generated. N Self-balancing screw vacuum pump rotors with different volume ratios.

[0056] Specifically, the design method of this invention includes: 1. Select the initial screw pitch based on the rotor's exhaust volume and sealing requirements. P 0 and rotor stage number N ; 2. Based on the vacuum application requirements of the vacuum pump, select the design range of the internal volume ratio of the screw rotor and determine the maximum and minimum pitch ratio. n ; 3. Select the corresponding curve slope parameter k This ensures that the screw rotor meets the dynamic and static balance conditions; 4. Based on parameters n , k , N Solve for the polynomial coefficients of the pitch law curve to construct the pitch variation law of the self-balancing screw rotor. 5. Based on the pitch variation law of the constructed self-balancing screw rotor, generate different rotor stages. N Self-balancing screw vacuum pump rotors with different volume ratios.

[0057] The rotor designed in this embodiment of the invention satisfies the self-balancing condition, which can greatly reduce the dynamic balancing process time and reduce the impact of the dynamic balancing holes on the rotor's sealing performance. The rotor pitch variation law has a large adjustable space, which allows the internal volume ratio based on the existing screw structure to be flexibly adjusted, thereby obtaining the optimal internal volume ratio design to meet different needs.

[0058] It will be apparent to those skilled in the art that the present invention is not limited to the details described in the above embodiments, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of protection involved.

[0059] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A self-balancing screw vacuum pump rotor structure, characterized in that, The rotor pitch curve starts from point A ,point B ,point C ,point D ,point E ,point F coordinates and points B The slope of the curve at that point is determined by the angle of rotation; establishing a coordinate system with the rotor angle as the abscissa and the pitch as the ordinate, then the point... A ,point B ,point C ,point D ,point E ,point F The x-coordinates are 0°, 180°, 360°, 540°, 720° and N ×360°, N A natural number greater than 2; point A ,point E With point F The ordinates are all P 1. Pitch, point B ,point D The ordinates are all P 0 pitch, point C The ordinate is P 2 pitch, P 2= nP 1; The rotor pitch follows the law of minimum pitch. P 1. Maximum and minimum pitch ratio n Curve slope parameter k and the number of rotor stages N The decision; The P 0 pitch and P 1. Pitch and P The following relationship exists between the two pitches: The rotor pitch curve at point B The slope is k At point A If the slope is 0, then the curve AB Calculated using the following generating equation: In the formula, P ( φ The ) indicates the pitch variation pattern. φ For angular parameters; The polynomial coefficients can be solved using the following expression: curve BC , CD , DE and EF The calculations are performed using the following generating equations: In the formula, φ total This indicates the total rotation angle of the rotor.

2. The self-balancing screw vacuum pump rotor structure according to claim 1, characterized in that, The rotor adopts a single tooth profile, and its face-centered coordinates are ( x c , y c The distance between the face center and the axis is... r c The geometric condition for the screw rotor to achieve static balance is: In the formula, ω d represents the rotational angular velocity. m Indicates the mass of the rotor element; The geometric conditions for achieving dynamic balance of the screw rotor are: In the formula, L ( φ The symbol ) represents the relationship between the screw length and the rotation angle.

3. The self-balancing screw vacuum pump rotor structure according to claim 2, characterized in that, The rotor micro-element mass d m The calculation is performed using the following expression: In the formula, ρ d represents the density of a material. V Represents the volume of a infinitesimal element. S profile d represents the cross-sectional area of ​​the profile. L Indicates the length of the rotor element; Relationship between screw length and rotation angle L (φ) and rotor element length d L The calculation is performed using the following expression: 。 4. The self-balancing screw vacuum pump rotor structure according to claim 3, characterized in that, Considering that the material density is constant at different cross-sectional locations, and taking into account the rotor element mass d... m Substituting the calculation expressions, we obtain the geometric conditions for the screw rotor to achieve static balance and dynamic balance, respectively: 。 5. The self-balancing screw vacuum pump rotor structure according to claim 4, characterized in that, curve BC , CD , DE and EF Substituting the generating equation into the geometric conditions for static balance of the screw rotor, we obtain the following expression: The pitch curve defined by the above pitch variation formula enables the screw rotor to automatically meet the static balance condition.

6. The self-balancing screw vacuum pump rotor structure according to claim 5, characterized in that, The dynamic imbalance of the screw rotor is solved by the following expression: To ensure that the dynamic imbalance of the screw rotor is zero, the dynamic imbalance of the screw rotor must conform to the following relationship: In the formula, m un This represents the dynamic imbalance mass of the screw rotor; to ensure the screw rotor meets the dynamic balance condition, the pitch variation depends on adjusting the maximum and minimum pitch ratio. n Curve slope parameter k and the number of rotor stages N A specific relationship needs to be satisfied.

7. A design method for a self-balancing screw vacuum pump rotor structure as described in any one of claims 1 to 6, characterized in that: The rotor pitch follows the law of minimum pitch. P 1. Maximum and minimum pitch ratio n Curve slope parameter k and the number of rotor stages N Determined by the number of rotor stages; N and maximum and minimum pitch ratio n Next, perform curve slope parameter analysis. k The parameters are solved to satisfy the dynamic and static balance characteristics of the screw vacuum pump rotor, and then based on the defined and solved parameters... n , k , N Solving for the polynomial coefficients of the pitch law curve allows for the construction of the pitch variation law of the self-balancing screw rotor; based on the constructed pitch variation law of the self-balancing screw rotor, different rotor stages are generated. N Self-balancing screw vacuum pump rotors with different volume ratios.

8. The design method according to claim 7, characterized in that, include: Select the initial screw pitch based on the rotor's exhaust volume and sealing requirements. P 0 and rotor stage number N ; Based on the vacuum application requirements of the vacuum pump, select the design range of the internal volume ratio of the screw rotor and determine the maximum and minimum pitch ratio. n ; Select the corresponding curve slope parameter k This ensures that the screw rotor meets the dynamic and static balance conditions; Based on parameters n , k , N Solve for the polynomial coefficients of the pitch law curve to construct the pitch variation law of the self-balancing screw rotor. Based on the pitch variation law of the self-balancing screw rotor, different rotor stages are generated. N Self-balancing screw vacuum pump rotors with different volume ratios.

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