A low leakage Roots rotor profile with a larger form factor

Abstract

The invention discloses a low-leakage Roots rotor profile with a larger shape coefficient, which is composed of half-leaf profiles symmetrically adjacent to the pitch circle of twice the number of blades, wherein the half-leaf profile is sequentially composed of four parts, namely, a peak concentric arc outside the pitch circle, a peak conjugate profile, a valley transition curve inside the pitch circle, and a valley concentric arc, which are connected end to end, and the corresponding endpoints and connection points are sequentially a peak point, a vertex, a midpoint, a root point located on the peak symmetry axis, and a valley point located on the valley symmetry axis. The invention has a larger shape coefficient and volume utilization coefficient; has a smaller radial leakage rate and a conjugate leakage rate, and thus has a higher volumetric efficiency and a better lightweight effect.

Description

Technical Field

[0001] The invention belongs to the technical field of Roots pumps, and in particular relates to a low-leakage profile structure of a Roots rotor with a larger shape coefficient. Background Art

[0002] Roots pump is a type of vacuum positive displacement pump that uses the inlet vacuum suction generated by two identical Roots rotors (referred to as rotors) during conjugate rotation to transport gaseous media to the outlet. The number of rotor blades is usually 2 to 4. The volumetric efficiency of this type of pump "≈ volumetric utilization coefficient × (100% - internal leakage rate)" directly determines its lightweight degree. The higher the volumetric efficiency, the better the lightweight degree. Among them, the volumetric utilization coefficient = "partial blade slot volume used for extruding medium in the volume of the rotor top cylinder / volume of the rotor top cylinder" ∝ "1-1 / square of the rotor shape coefficient", and the internal leakage rate ≈ radial leakage rate + axial leakage rate + conjugate leakage rate. Therefore, in the construction of the rotor profile, it is always hoped to obtain higher volumetric efficiency by adopting a larger shape coefficient and a smaller internal leakage rate.

[0003] For ordinary rotors whose shape coefficient is completely determined by the conjugate profile, the conjugate profiles with the maximum shape coefficient are arcs and involutes. The maximum shape coefficients of 1.6699, 1.4770, 1.3680 and 1.6177, 1.4638, 1.3655 can be obtained for 2-blade, 3-blade, and 4-blade rotors, respectively. The conjugate profile consists of two parts: the peak conjugate profile outside the pitch circle and the valley conjugate profile inside the pitch circle.

[0004] Although the axial leakage rate is slightly affected by the rotor profile structure, the radial leakage and conjugate leakage can be effectively controlled by the equal gap seal with the inner surface of the pump housing and the profile improvement of the conjugate zone multi-point seal, thereby achieving a minimized radial leakage rate and conjugate leakage rate. Among them, the closed space caused by the conjugate zone multi-point seal will cause pressure shock to the medium inside, but for the Roots rotor pair using gas medium and having a non-contact gap, the impact of this pressure shock is relatively small. Summary of the invention

[0005] Aiming at the high volumetric efficiency expected in the background art of Roots pumps, the present invention provides a low-leakage rotor profile with a larger shape coefficient, radial equal gaps and multi-point sealing in the conjugate area by shrinking the valley conjugate profile to gather on the pitch circle (i.e., a valley-free conjugate profile) in a special geometric relationship.

[0006] To achieve the above purpose, the technical solution of the present invention is as follows:

[0007] A low-leakage Roots rotor profile with a larger shape coefficient is composed of half-leaf profiles that are circumferentially symmetrically adjacent to the pitch circle with twice the number of blades, and is characterized in that the half-leaf profile is composed of four parts, which are connected end to end, in sequence: a peak concentric arc outside the pitch circle, a peak conjugate profile, a valley transition curve inside the pitch circle, and a valley concentric arc, and the corresponding endpoints and connection points are, in sequence, a peak point, a vertex, a midpoint, a root point on the peak symmetry axis, and a valley point on the valley symmetry axis.

[0008] The peak symmetry axis and the valley symmetry axis are the boundary lines of the half-leaf contour, the intersection of the two is the center of the rotor and the center of the above-mentioned concentric arcs, the angle between the two is the center angle of the half-leaf contour uniquely determined by the number of leaves, the intersection of the two with the pitch circle is the peak node and the valley node respectively, the pitch arc between the two is the half-leaf pitch arc, the midpoint of the midpoint is the vertex node, the intersection of the normal line of the peak conjugate contour at the vertex and the pitch circle is the apex node, the pitch arc from the apex node to the midpoint is the conjugate pitch arc, the center angle of the pitch arc from the apex node to the peak node is the multi-point sealing angle, any point on the conjugate pitch arc is an instantaneous node, the normal line segment from the instantaneous node to the peak conjugate contour is the instantaneous diameter line, and the point where the instantaneous diameter line is located on the peak conjugate contour is the instantaneous contour point.

[0009] The peak conjugate profile is uniquely determined by its instantaneous radial length and orientation.

[0010] The length of the instantaneous diameter line and the symmetric relationship between the azimuth of the straight line segment from the instantaneous node to the mid-node about the tangent line of the pitch circle at the instantaneous node are uniquely determined, and the multi-point sealing angle and the half-top sealing angle are determined thereby.

[0011] The half top sealing angle is the center angle of the concentric arc of the half leaf peak.

[0012] The shape coefficient - 1 = length from peak point to peak node / pitch circle radius = length from peak node to mid node / pitch circle radius, which is 1.7654, 1.5176, and 1.3902 for 2 blades, 3 blades, and 4 blades, which are larger than the maximum shape coefficients of existing ordinary rotors of 1.6699, 1.4770, and 1.3680, so it is a larger shape coefficient.

[0013] The valley transition curve is a rotation avoidance trajectory line generated by the vertices on the paired rotors on the rotors, during which the conjugate rotation angle of the rotor pair is also the multi-point sealing angle.

[0014] In this way, when the rotor auxiliary rotation angle is in the interval of [0, half-top sealing angle), there will be 5 sealing points, when the rotor auxiliary rotation angle = half-top sealing angle, there will be 4 sealing points; in the interval of (half-top sealing angle, multi-point sealing angle), there will be 3 sealing points, when the rotor auxiliary rotation angle = multi-point sealing angle, there will be 2 sealing points; there is 1 sealing point in the interval of (multi-point sealing angle, half-leaf center angle / 2). Compared with an ordinary rotor with only one sealing point throughout the entire process, the present invention will achieve a smaller conjugate leakage rate. In addition, due to the radial equal-gap seal of the leaf 2×half-top sealing angle, the present invention achieves a smaller radial leakage rate.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] The low-leakage Roots rotor profile with a larger shape coefficient of the present invention has a larger shape coefficient and volume utilization coefficient; and a smaller radial leakage rate and conjugate leakage rate, so it has higher volumetric efficiency and better lightweight effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Other features, objectives and advantages of the present invention will become more apparent from a reading of the detailed description of non-limiting embodiments made with reference to the following accompanying drawings.

[0018] Figure 1 Schematic diagram of the half-blade profile structure of the Roots rotor with a larger shape factor and low leakage effect.

[0019] Figure 2 The middle is a schematic diagram of the generation of the valley transition curve.

[0020] Figure 3 Schematic diagram of the number of sealing points in different intervals.

[0021] Among them: O, rotor center, 0, peak point, 1, vertex, 2, midpoint, 3, root point, 4, valley point, 5, peak node, 6, valley node, 7, instantaneous node, 77', pitch circle tangent, 8, instantaneous contour point, 9, top node, O50, peak symmetry axis, O46, valley symmetry axis, 01, peak concentric arc, 12, peak conjugate contour, 23, valley transition curve, 34, valley concentric arc, 72, straight line segment, 78, instantaneous diameter line, r, pitch circle radius, ε, shape coefficient, φ, half blade contour center angle, σ, half top sealing angle, β, rotor auxiliary rotation angle, β * , multi-point sealing angle, O', matching rotor center. DETAILED DESCRIPTION

[0022] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0023] like Figures 1 to 3As shown, a low-leakage Roots rotor profile with a larger shape coefficient is composed of half-lobe profiles that are circumferentially symmetrically adjacent to the pitch circle with twice the number of blades. The half-lobe profile is composed of four parts, which are connected end to end, in sequence: a peak concentric arc 01 outside the pitch circle, a peak conjugate profile 12, a valley transition curve 23 inside the pitch circle, and a valley concentric arc 34. The corresponding endpoints and connection points are peak point 0, vertex 1, midpoint 2, root point 3 on the peak symmetry axis O50 and valley point 4 on the valley symmetry axis O46. Among them, the peak symmetry axis and the valley symmetry axis are the boundary lines of the half-leaf contour, the intersection of the two is the rotor center O and the center of the peak concentric arc 01 and the valley concentric arc 34, the angle between the two is the half-leaf contour center angle φ uniquely determined by the number of leaves, the intersection of the two with the pitch circle is the peak node 5 and the valley node 6 respectively, and the pitch arc between the two is the half-leaf pitch arc; the midpoint of the half-leaf pitch arc is the midpoint 2, the intersection of the normal of the peak conjugate contour at the vertex 1 and the pitch circle is the top node 9, the pitch arc from the top node 9 to the midpoint 2 is the conjugate pitch arc, and the center angle of the pitch arc from the top node 9 to the peak node 5 is the multi-point sealing angle β * , any point on the conjugate nodal arc is the instantaneous node 7, the normal line segment from the instantaneous node 7 to the peak conjugate contour 12 is the instantaneous diameter line 78, the point where the instantaneous diameter line 78 is located at the peak conjugate contour 12 is the instantaneous contour point 8, 77' is the pitch circle tangent at the instantaneous node 7, r is the pitch circle radius, ε is the shape coefficient, N is the number of rotor blades, and λ is the volume utilization coefficient.

[0024] Under the premise of given pitch circle radius r and number of rotor blades N, peak symmetry axis O50, peak node 5, mid-node 2, valley node 6, half-blade profile center angle φ, and valley symmetry axis O46 are all uniquely determined:

[0025] In the first step, the peak conjugate profile 12 is uniquely constructed by the symmetry of the instantaneous diameter line 78 and the straight line segment 72 about the pitch circle tangent line 77' and the construction relationship of "shape coefficient - 1 = length from peak point to peak node / pitch circle radius = length from peak node to mid-node / pitch circle radius", which is:

[0026]

[0027] The second step is to deduce from the trigonometric relationship in △1O9 and the calculation of the volume utilization coefficient:

[0028]

[0029] The maximum shape factor ε of the involute rotor j and its volume utilization coefficient λ j of

[0030]

[0031] In comparison, the shape coefficient ε of the rotor of the present invention is increased by 9.13% under 2 blades, 3.68% under 3 blades and 1.81% under 4 blades, and the volume utilization coefficient λ is increased by 8.06% under 2 blades, 5.38% under 3 blades and 3.72% under 4 blades.

[0032] The third step is to construct the peak concentric arc 01 (with a radius of r×ε) and the valley concentric arc 34 (with a radius of r×(2-ε)) based on the known r and the obtained ε and σ;

[0033] The fourth step is to obtain β * The valley transition curve 23 is constructed by the rotation avoidance trajectory line generated by the vertex on the paired rotor on the rotor.

[0034] Then there will be 5 sealing points in [0, σ), (σ, β * ) has 3 sealing points, (β * , φ / 2) has one sealing point. Compared with the common rotor with only one sealing point in (0, φ / 2), the multi-point sealing ratio of the present invention is 2β * / φ>50%, thereby achieving a minimized conjugate leakage rate, coupled with the radial equal gap sealing of the leaf's 2×σ large central angle, the present invention achieves a minimized radial leakage rate.

[0035] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention.

Claims

1. A low leakage Roots rotor with a larger shape factor, comprising a rotor profile consisting of half-lobe profiles symmetrically adjacent to each other in the circumferential direction of a pitch circle twice the number of lobes, characterized in that: The half-leaf contour is composed of four parts, namely, the peak concentric arc outside the pitch circle, the peak conjugate contour, the valley transition curve and the valley concentric arc inside the pitch circle, which are connected end to end. The corresponding endpoints and connection points are, in sequence, the peak point, the vertex, the midpoint, the root point on the peak symmetry axis and the valley point on the valley symmetry axis. The peak symmetry axis and the valley symmetry axis are the boundary lines of the half-leaf contour. The intersection of the two is the rotor center, the center of the peak concentric arc and the center of the valley concentric arc. The angle between the peak symmetry axis and the valley symmetry axis is the center angle of the half-leaf contour uniquely determined by the number of leaves. The intersection of the two with the pitch circle is the peak node and the valley node respectively. The pitch arc between the two is the half-leaf pitch arc, and the midpoint is the midpoint. The peak at the vertex is The intersection of the normal line of the conjugate profile and the pitch circle is the vertex node, the pitch circle arc from the vertex node to the mid-node is the conjugate pitch circle arc, the center angle of the pitch circle arc from the vertex node to the peak node is the multi-point sealing angle, any point on the conjugate pitch circle arc is the instantaneous node, the normal line segment from the instantaneous node to the peak conjugate profile is the instantaneous diameter line, the point where the instantaneous diameter line is located on the peak conjugate profile is the instantaneous profile point, the peak conjugate profile is uniquely determined by the length and orientation of its instantaneous diameter line, the valley transition curve is the rotation avoidance trajectory line generated by the vertex on the paired rotor on the rotor, the conjugate rotation angle of the rotor pair during this period is the multi-point sealing angle, and the shape coefficient -1 = the length from the peak point to the peak node / the pitch circle radius = the length from the peak node to the mid-node / the pitch circle radius.

2. A low leakage Roots rotor with a larger shape factor as claimed in claim 1, characterized in that: The length of the instantaneous diameter line and the symmetric relationship between the azimuth of the straight line segment from the instantaneous node to the mid-node about the tangent line of the pitch circle at the instantaneous node are uniquely determined, and the multi-point sealing angle and the half-top sealing angle are determined thereby.

3. A low leakage Roots rotor with a larger shape factor as claimed in claim 2, characterized in that: The half top sealing angle is the center angle of the concentric arc of the half leaf peak.

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