A Roots rotor profile with higher volumetric efficiency and internal direct conjugation

Abstract

The invention relates to a Roots rotor profile with higher volumetric efficiency and inner straight conjugation, comprising 4, 6, and 8 half-lobe profiles circumferentially symmetrically adjacent to each other under 2, 3, and 4 blades. The half-lobe profile is composed of six parts, namely, a peak concentric arc outside the pitch circle, a peak transition curve, a peak conjugated profile, and an inner straight conjugated profile, a valley transition curve, and a valley concentric arc inside the pitch circle, which are connected end to end. The corresponding endpoints and connection points are, in sequence, a peak point, a vertex, an outer starting point, a mid-node, an inner starting point, a root point located on a peak symmetry axis, and a valley point located on a valley symmetry axis. The low-leakage Roots rotor profile with a larger shape coefficient of the invention has a larger shape coefficient and a volume utilization coefficient, and a smaller radial leakage rate and a conjugate leakage rate, so it 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 contour structure of a Roots rotor with high volumetric efficiency and conjugate straight line segments within a pitch circle. 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 (generally composed of two parts: the peak conjugate profile outside the pitch circle and the valley conjugate profile inside the pitch circle), the conjugate profiles with the largest shape coefficient are currently arcs and involutes, which are 1.6699, 1.4770, 1.3680 and 1.6177, 1.4638, 1.3655 for 2-blade, 3-blade, and 4-blade respectively. However, the involute belongs to the full convex-convex conjugate mode, and the arc belongs to the partial convex-convex conjugate mode, which cannot effectively suppress conjugate leakage.

[0004] Although the axial leakage rate is slightly affected by the rotor profile structure, the radial equal gap seal with the inner surface of the pump housing and the conjugate zone multi-point seal with a convex-flat conjugate mode profile improvement can effectively control radial leakage and conjugate leakage. Of course, the confined space surrounded by the conjugate zone multi-point seal will cause pressure shock to the medium inside, but for non-contact Roots rotor pairs using gas media and with large gaps, the impact of this pressure shock is relatively small. Summary of the invention

[0005] Aiming at the higher volumetric efficiency expected in the background art of Roots pumps, the present invention provides a low leakage rotor profile with a larger shape factor, radial equal gaps and multi-point sealing in the conjugate area based on the special geometric relationship of the chord height line of the half-blade pitch arc adopted in the valley conjugate profile.

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

[0007] A Roots rotor profile with higher volumetric efficiency and internal straight conjugation includes a half-lobe profile, characterized in that the half-lobe profile is composed of six parts, namely, a peak concentric arc outside the pitch circle, a peak transition curve, a peak conjugate profile, and an internal straight conjugate profile, a valley transition curve, and a valley concentric arc inside the pitch circle, which are connected end to end, and the corresponding endpoints and connection points are, in sequence, a peak point, a vertex, an outer starting point, a midpoint, an inner starting point, a root point on the peak symmetry axis, and a valley point on the valley symmetry axis.

[0008] The half-lobe profile is a half-lobe profile with 4 pitch circles circumferentially symmetrically adjacent under 2 lobe, a half-lobe profile with 6 pitch circles circumferentially symmetrically adjacent under 3 lobe, and a half-lobe profile with 8 pitch circles circumferentially symmetrically adjacent under 4 lobe. The peak concentric arc takes the rotor center as the circle center, and the half-lobe top sealing angle is the circle center angle. The radius of the peak concentric arc is determined by the shape coefficient and the pitch circle radius. Specifically, the radius size of the peak concentric arc numerically satisfies "the radius of the peak concentric arc = the shape coefficient × the pitch circle radius".

[0009] The valley concentric arc is an arc with the rotor center as the center and the half-leaf top sealing angle as the central angle. The radius of the valley concentric arc is determined by the shape coefficient and the pitch circle radius. Specifically, the radius of the valley concentric arc numerically satisfies "valley concentric arc radius = (2-shape coefficient) × pitch circle radius".

[0010] The inner straight conjugate profile is a chord height line of a known pitch arc between the peak symmetry axis and the valley symmetry axis.

[0011] The peak conjugate profile is a trajectory of symmetric points about the tangent line of the pitch circle at the conjugate instantaneous node at any point on the inner straight conjugate profile; the conjugate instantaneous node is the intersection of the normal line at any point on the inner straight conjugate profile and one side of the near-peak symmetry axis of the pitch circle.

[0012] The peak transition curve is a trajectory line of symmetric points of the inner starting point about the tangent of the pitch circle at the transition instant node, and the transition instant node is any point on the pitch circle arc between the top node and the peak node; the peak node is the intersection of the peak symmetry axis and the pitch circle, and the top node is the intersection of the normal of the peak transition profile at the vertex and the pitch circle, and the position of the top node is controlled by the central angle of the pitch circle arc between it and the peak node, that is, the multi-point sealing angle.

[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] According to the structural relationship of "shape coefficient - 1 = length from peak point to peak node / pitch circle radius = length from peak node to inner starting point / pitch circle radius", the shape coefficient is 1.7071, 1.500, and 1.3827 for 2 leaves, 3 leaves, and 4 leaves, which is larger than the existing largest values ​​of 1.6699, 1.4770, and 1.3680, so it is a larger shape coefficient. The multi-point sealing angle and the half-leaf top sealing angle are uniquely determined by the specific geometric relationship of the inner straight conjugate profile as the chord height line and the obtained shape coefficient. The multi-point sealing angle is 10.8985°, 13.8060°, and 14.7474° for 2 leaves, 3 leaves, and 4 leaves, and the half-leaf top sealing angle is 9.1605°, 9.7505°, and 9.1074° for 2 leaves, 3 leaves, and 4 leaves.

[0015] In this way, when the rotor pair conjugate rotation angle is in the interval of [0, half-leaf top sealing angle), there will be 5 sealing points, in the interval of (half-leaf top sealing angle, multi-point sealing angle), there will be 3 sealing points, and in the interval of (multi-point sealing angle, half-leaf center angle / 2), there will be 1 sealing point. Compared with the ordinary rotor with only 1 sealing point in the entire range of (0, half-leaf center angle / 2), the present invention achieves a smaller conjugate leakage rate; coupled with the radial equal gap sealing of the leaf 2×half-leaf top sealing angle, the present invention achieves a smaller radial leakage rate.

[0016] Compared with the prior art, the present invention has the following beneficial effects:

[0017] 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

[0018] 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.

[0019] Figure 1 Schematic diagram of the half-leaf profile structure of the Roots rotor with higher volumetric efficiency.

[0020] Figure 2 The middle is a schematic diagram of the generation of the valley transition curve.

[0021] Figure 3 Schematic diagram of the number of sealing points in different intervals.

[0022] In the figure: O, rotor center, 0, peak point, 1, vertex, 2, outer starting point, 3, middle node, 4, inner starting point, 5, root point, 6, valley point, 7, peak node, 8, valley node, 9, conjugate instantaneous node, 9', transition instantaneous node, 01, peak concentric arc, 12, peak transition curve, 23, peak conjugate contour, 34, inner straight conjugate contour and chord height line, 45, valley transition curve, 56, valley concentric arc, O70, peak symmetry axis, O68, valley symmetry axis, a, any point on the inner straight conjugate contour, b, symmetric point of a, b', symmetric point of inner starting point 4; c, top node, r, pitch circle radius, ε, shape coefficient, Half blade center angle, σ, half blade top sealing angle, β, rotor auxiliary rotation angle, β * , multi-point sealing angle, O', matching rotor center. DETAILED DESCRIPTION

[0023] 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.

[0024] like Figure 1 , 2 As shown in FIG. 3 , a Roots rotor profile with higher volumetric efficiency and inner straight conjugation, wherein the half-blade profile is composed of six parts connected end to end, in sequence, the peak concentric arc 01 outside the pitch circle, the peak transition curve 12, the peak conjugated profile 23, the inner straight conjugated profile 34 inside the pitch circle, the valley transition curve 45, and the valley concentric arc 56, and the corresponding endpoints and connection points are, in sequence, the peak point 0 located on the peak symmetry axis, the vertex 1, the outer starting point 2, the midpoint 3, the inner starting point 4, the root point 5, and the valley point 6 located on the valley symmetry axis; is the half-leaf center angle, σ is the half-leaf top sealing angle, β* is the multi-point sealing angle, 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.

[0025] Under the premise of given pitch circle radius r and leaf number N, the peak symmetry axis, peak node 7, mid node 3, valley node 8, half leaf center angle The chord height line 34 and the valley symmetry axis are both uniquely determined.

[0026] The first step is to use the construction relationship of "ε-1 = 07 length / r = 74 length / pitch circle radius r" to obtain

[0027]

[0028] The second step is to use the obtained ε and c1 length = c4 length, and the trigonometric relationship between △1Oc and △7O4 to obtain

[0029]

[0030] In the third step, with the rotor center O as the center, the radii are ε×r and (2-ε)×r respectively, and the central angle is σ, to construct the peak concentric arc 01 and the valley concentric arc 56 respectively.

[0031] The fourth step is to construct the peak conjugate profile 23 from the trajectory line of the symmetric point b of any point a on the inner straight conjugate profile 34 about the tangent line of the pitch circle at the conjugate instantaneous node 9.

[0032] The fifth step is to obtain the multi-point sealing angle β * The peak transition profile 12 is constructed by the trajectory line of the symmetric point b' of the internal starting point 4 about the tangent line of the pitch circle at the transition instant node 9'.

[0033] Step 6: The multi-point sealing angle β is obtained * The rotation avoidance trajectory line generated by the top point on the rotor in pair with O' is used to construct a valley transition curve 45.

[0034] Then there will be 5 sealing points in the interval [0, σ), (σ, β * ) There will be 3 sealing points in the interval, There is 1 sealing point in the interval, relative to Compared with an ordinary rotor with only one sealing point throughout the entire inner part, the present invention achieves a minimized conjugate leakage rate; coupled with the radial equal gap seal of the blade 2×half blade top sealing angle, the present invention achieves a minimized radial leakage rate.

[0035] Finally, by further derivation of the volume utilization coefficient calculation, we get

[0036]

[0037] The maximum shape coefficient εj and volume utilization coefficient λj of the involute rotor

[0038]

[0039] In comparison, the shape coefficient ε of the rotor of the present invention is increased by 5.53% under 2 blades, 2.47% under 3 blades and 1.26% under 4 blades, and the volume utilization coefficient λ is increased by 4.43% under 2 blades, 3.46% under 3 blades and 2.52% under 4 blades.

[0040] 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 Roots rotor with higher volumetric efficiency and inner direct conjugation, comprising a Roots rotor profile, wherein the Roots rotor profile comprises a half-lobe profile, characterized in that: The half-leaf contour is composed of six parts connected end to end, namely, the peak concentric arc outside the pitch circle, the peak transition curve, the peak conjugate contour, the inner straight conjugate contour, the valley transition curve, and the valley concentric arc inside the pitch circle. The corresponding endpoints and connection points are, in sequence, the peak point, the vertex, the outer starting point, the middle node, the inner starting point, the root point, and the valley point on the valley symmetry axis located on the peak symmetry axis; the peak concentric arc takes the rotor center as the center of the circle, and the half-leaf top sealing angle is the center angle. The radius of the peak concentric arc is determined by the pitch circle radius and the shape coefficient; the peak transition curve is the symmetric point trajectory line of the inner starting point about the pitch circle tangent at the transition instant node, and the transition instant node is any point on the vertex node and the peak node arc; the peak conjugate contour is the symmetric point trajectory line of any point on the inner straight conjugate contour about the pitch circle tangent at the conjugate instant node, and the conjugate instant node is the intersection of the normal at any point on the inner straight conjugate contour and the side of the pitch circle near the peak symmetry axis; The inner straight conjugate contour is the chord height line of the known pitch arc between the peak symmetry axis and the valley symmetry axis; the valley concentric arc has the rotor center as the center, the half-leaf top sealing angle as the center angle, and the radius of the valley concentric arc is determined by the shape coefficient and the pitch circle radius; the valley transition curve is the rotation avoidance trajectory line generated by the vertex on the paired rotor on the rotor, and the conjugate rotation angle of the rotor pair during this period is also the multi-point sealing angle.

2. A Roots rotor with higher volumetric efficiency and inner direct conjugation as claimed in claim 1, characterized in that: The half-leaf profile is a half-leaf profile with 4 adjacent pitch circles symmetrically in the circumferential direction under 2 leaves, a half-leaf profile with 6 adjacent pitch circles symmetrically in the circumferential direction under 3 leaves, and a half-leaf profile with 8 adjacent pitch circles symmetrically in the circumferential direction under 4 leaves.

3. A Roots rotor with higher volumetric efficiency and inner direct conjugation as claimed in claim 1, characterized in that: The peak node is the intersection of the peak symmetry axis and the pitch circle, and the vertex node is the intersection of the normal line of the peak transition profile at the vertex and the pitch circle.

4. A Roots rotor with higher volumetric efficiency and inner direct conjugation as claimed in claim 1, characterized in that: The half-leaf tip sealing angle is uniquely determined by the specific geometric relationship of the inner straight conjugate profile being the chord height line and the calculated shape coefficient.

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