A rotor profile design method for three-leaf Roots pump

Abstract

The present invention discloses a rotor profile design method for a three-lobe Roots pump, the steps comprising: determining the design parameters of the rotor profile based on the traditional three-lobe involute profile; designing a 1 / 6 segment rotor profile based on the design parameters; obtaining a complete rotor profile by symmetric and rotating the 1 / 6 segment rotor profile. The three-lobe rotor profile design method provided by the present invention can expand the range of the diameter-to-pitch ratio, which can cover the diameter-to-pitch ratio of a two-lobe rotor to a greater extent, and can realize the replacement of a two-lobe rotor. In addition, the rotor designed by the design method can obtain a larger area utilization factor and a more stable and uniform rotor gap through parameter adjustment.

Description

Technical Field

[0001] The invention relates to the field of fluid machinery, and in particular to a rotor profile design method for a three-leaf Roots pump. Background Art

[0002] Roots pumps are widely used in petrochemical, vacuum, electric power and fuel cell hydrogen circulation. With the improvement of environmental protection and quality of life, the requirements for equipment vibration and noise performance are further improved, especially when used in vehicle fuel cell hydrogen circulation system. The dynamic characteristics of three-blade rotors are obviously better than two-blade rotors. Therefore, with the improvement of processing level, three-blade rotors will gradually replace two-blade rotors.

[0003] Due to the limitation of the processing level in the early stage of manufacturing, there are still a large number of two-lobe pumps working in different fields. According to the conventional three-lobe rotor, in order to replace the two-lobe rotor, the shell needs to be further processed or replaced, which is costly. The diameter-to-pitch ratio of the conventional three-lobe rotor is up to 1.46, and the diameter-to-pitch ratio of the two-lobe rotor is usually 1.5, which can be appropriately increased to a maximum of 1.6. There is no intersection between the two parameters, so the traditional three-lobe rotor cannot completely replace the two-lobe. The replacement process requires changing the overall size, which is costly. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a novel method for designing a three-blade rotor profile of a Roots blower. The method is improved on the basis of the traditional three-blade involute profile, retaining the original involute part, and can realize the design of a three-blade rotor with uniform meshing clearance under different diameter-to-pitch ratios to replace different types of two-blade rotors, and can be quickly generated through MATLAB software.

[0005] To achieve the above object, the present invention provides a rotor profile design method for a three-leaf Roots pump, the steps comprising:

[0006] Based on the traditional three-blade involute profile, determine the design parameters of the rotor profile;

[0007] Based on the design parameters, a 1 / 6 segment rotor profile is designed;

[0008] The complete rotor profile is obtained by symmetric and rotating the 1 / 6 segment of the rotor profile.

[0009] Preferably, the designed 1 / 6 segment rotor profile includes 5 segments of profiles, namely: a tooth top arc, a first gradient arc, an involute, a second gradient arc and a tooth root arc.

[0010] Preferably, the tooth tip arc is used to determine the outer diameter of the final rotor profile, and the calculation method includes:

[0011]

[0012] In the formula, α 1 It is the angle of the tooth tip circle of the AB segment, and the range can be adjusted according to the actual situation; R 1 Indicates the radius of the arc; R m Indicates the theoretical outer circle radius; x 1 It represents the horizontal coordinate of the tooth top arc in the plane rectangular coordinate system; 1 It represents the ordinate corresponding to the abscissa of the tooth top arc in the plane rectangular coordinate system; δ represents half of the design clearance.

[0013] Preferably, the method for calculating the tooth root arc includes:

[0014]

[0015] In the formula, α 2 Indicates the root round angle of the EF segment; R 2 Indicates the radius of the arc; x 2 It represents the horizontal coordinate of the tooth root arc in the plane rectangular coordinate system; 2 It represents the ordinate corresponding to the abscissa of the tooth root arc in the plane rectangular coordinate system.

[0016] Preferably, the angle range of the first gradual arc includes:

[0017] α 3 ∈[α 1 , α 1 +α e ]

[0018] Among them, α 3 is the angle range of the first gradient arc; α 1 is the tooth tip circle angle of segment AB; α e is the angle between the end point of the involute and the horizontal axis;

[0019] The angle range of the second gradient arc α 4 include:

[0020] α 4 ∈[α b ,π / 3-α 2 ]

[0021] Among them, α 4 is the angle range of the second gradient arc; α 2 Indicates the root fillet angle of the EF segment; α b It is the angle between the starting point of the involute and the horizontal axis.

[0022] Preferably, the method for calculating the involute includes:

[0023]

[0024] In the formula, R 0 is the radius of the involute base circle; α i is the pressure angle at the starting point of the involute; α j is the pressure angle at the end point of the involute; α p is the involute pitch pressure angle; Z is the number of rotor blades; m 1 is the diameter-to-pitch ratio of the involute part, which is independent of the diameter-to-pitch ratio m and is used to adjust the involute shape; x 3 Represents the horizontal coordinate of the involute in the plane rectangular coordinate system; y 3 It represents the ordinate corresponding to the involute and the abscissa in the plane rectangular coordinate system; τ represents the angle between the starting radius of the involute on the base circle and the X-axis; θ represents the sum of the pressure angle and the development angle of the involute.

[0025] Preferably, based on the tooth addendum arc, the involute and the tooth root arc, the first gradual arc and the second gradual arc are designed in a segmented manner.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] The three-blade rotor profile design method provided by the present invention can expand the range of the diameter-pitch ratio (the ratio of the rotor diameter to the rotor center distance), which can cover the diameter-pitch ratio of the two-blade rotor to a greater extent, and can realize the replacement of the two-blade rotor. In addition, the rotor designed by the design method can obtain a larger area utilization factor and a more stable and uniform rotor clearance through parameter adjustment. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0029] Figure 1 A schematic diagram of a novel rotor profile according to an embodiment of the present invention;

[0030] Figure 2 It is a schematic diagram of various parameters of the involute part of an embodiment of the present invention;

[0031] Figure 3 This is a schematic diagram of a 1 / 6 segment novel rotor according to an embodiment of the present invention;

[0032] Figure 4 Schematic diagram of the distribution change of the number of points of the type line in an embodiment of the present invention; wherein, Figure 4 (a) shows the distribution of points of the BC segment type line; Figure 4 (b) represents the distribution of the number of points of the DE segment type line;

[0033] Figure 5 Schematic diagram of the change of the BC segment profile under different parameters of an embodiment of the present invention;

[0034] Figure 6 Schematic diagram of rotor meshing under different diameter-to-pitch ratios according to an embodiment of the present invention; wherein, Figure 6 (a) indicates when m = 1.5; Figure 6 (b) indicates when m = 1.55;

[0035] Figure 7 Schematic diagram of the distribution of rotor meshing point positions under different diameter-to-pitch ratios according to an embodiment of the present invention; wherein: Figure 7 (a) indicates when m = 1.5; Figure 7 (b) indicates when m = 1.55;

[0036] Figure 8 It is a schematic diagram of the change of meshing clearance of the rotor under different diameter-to-pitch ratios in an embodiment of the present invention; wherein, Figure 8 (a) indicates when m = 1.5; Figure 8 (b) indicates when m = 1.55;

[0037] Fig. 9 This is a comparison chart of the new type of wire and the traditional type of wire at the same center distance; Fig. 9 (a) A comparison of the area utilization factor and outer contour of the new wire at different diameter-to-span ratios; Fig. 9 (b) shows the comparison between the new type of line with m=1.5 and the involute type line. Fig. 9 (c) shows the comparison between the new type of line with m = 1.5 and the cycloid type line; Fig. 9 (d) is a comparison diagram between the new type wire with m=1.55 and the arc-shaped wire. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] Before describing, the meanings of the characters in the drawings of the present invention are first introduced:

[0041] Rp-pitch circle radius; R b - Radius of the involute starting point; R e - radius of the involute end point; Rm -Rotor outer radius; R 1 -Actual radius of the tooth tip arc; R 2 - Actual radius of tooth root arc; α 1 -AB segment tooth tip circle angle; α 2 -EF segment tooth root fillet angle; α b -The angle between the starting point of the involute and the horizontal axis; α e -Angle between the end point of the involute and the horizontal axis; AB-tooth top arc; BC-first gradient arc; CD-involute; DE-second gradient arc; EF-tooth root arc; R 0 - Involute base circle radius; α i -pressure angle at the involute starting point; α j - pressure angle at the end of the involute; α p -Involute pitch circle pressure angle; P-BC segment line normal intersection point; Q-DE segment line normal intersection point; r 1 - gradient semi-diameter PB length; r 2 - PC length of gradient radius, m-diameter-to-pitch ratio, λ-area utilization.

[0042] like Figure 1 The figure shows a schematic diagram of the new rotor profile. As shown in the figure, the rotor is highly symmetrical. Only the profile segment AF needs to be designed to obtain the entire profile through symmetry and rotation. Therefore, it is sufficient to describe the design idea of ​​the 1 / 6 segment profile. The AF segment profile includes 5 segments, namely AB-tooth top arc; BC-first gradient arc; CD-involute; DE-second gradient arc; EF-tooth root arc.

[0043] Rotor outer diameter R m Determined by the rotor center distance 2a and the diameter-to-pitch ratio m, the calculation formula is as follows:

[0044] R m =a×m

[0045] Among them, the diameter-to-spacing ratio m has a wider range of values ​​than the traditional three-blade profile, which can realize the replacement of traditional two-blade rotors.

[0046] Among them, the tooth top arc profile AB is used to determine the outer diameter of the final rotor profile, with point G as the center point and radius R 1 , the formula is:

[0047]

[0048] In the formula, α 1 It is the angle of the tooth tip circle of the AB segment, and the range can be adjusted according to the actual situation; R 1 Indicates the radius of the arc; R m Indicates the theoretical outer circle radius; x 1It represents the horizontal coordinate of the tooth top arc in the plane rectangular coordinate system; 1 It represents the ordinate corresponding to the abscissa of the tooth top arc in the plane rectangular coordinate system; δ represents half of the design clearance.

[0049] The tooth root arc line EF has point H as the center point and a radius of R. 2 , the formula is:

[0050]

[0051] In the formula, α 2 is the tooth root radius angle of segment EF, and the range can be adjusted according to actual conditions. The arc radius R 2 Compared with the theoretical outer radius R m Expanded the design gap by half; x 2 It represents the horizontal coordinate of the tooth root arc in the plane rectangular coordinate system; 2 It represents the ordinate corresponding to the abscissa of the tooth root arc in the plane rectangular coordinate system.

[0052] The first gradient arc-BC angle range α 3 for:

[0053] α 3 ∈[α 1 , α 1 +α e ]

[0054] Among them, α e is the angle between the end point of the involute and the horizontal axis.

[0055] The second gradient arc-DE angle range α 4 for:

[0056] α 4 ∈[α b ,π / 3-α 2 ]

[0057] Among them, α b It is the angle between the starting point of the involute and the horizontal axis.

[0058] like Figure 2 As shown, it is a schematic diagram of the parameters of the involute part. The formula of the involute part of the CD segment is:

[0059]

[0060] In the formula, R 0 is the radius of the involute base circle; α i is the pressure angle at the starting point of the involute; α j is the pressure angle at the end point of the involute; α p is the involute pitch pressure angle; Z is the number of rotor blades; m1 is the diameter-to-pitch ratio of the involute part, which is independent of the diameter-to-pitch ratio m and is used to adjust the involute shape; x 3 Represents the horizontal coordinate of the involute in the plane rectangular coordinate system; y 3 It represents the ordinate corresponding to the involute and the abscissa in the plane rectangular coordinate system; τ represents the angle between the starting radius of the involute on the base circle and the X-axis; θ represents the sum of the pressure angle and the development angle of the involute.

[0061] In this embodiment, when Z=3, the involute part of the designed profile is obtained.

[0062] After the AB, CD, and EF segment profiles are determined, the BC and DE segment profiles are designed based on the existing profiles.

[0063] Figure 3 This is a schematic diagram of a 1 / 6 segment new rotor. Both BC and DE segments are gradient arc lines. Taking the BC segment line as an example, first calculate the normals PB and PC near point B and point C based on AB and CD segments. The formula is as follows:

[0064] PC:

[0065] PB: in, The product of the slope of the straight line PC and the slope of the normal line of the CD segment at point C is -1. The product of the slope of the straight line PB and the slope of the normal line of the AB segment at point B is -1; PC Represents the horizontal coordinate of the straight line PC in the plane rectangular coordinate system; y PC Indicates the ordinate corresponding to the horizontal coordinate of the straight line PC in the plane rectangular coordinate system; x C Indicates the horizontal coordinate of point C; y C Indicates the ordinate of point C; x PB represents the horizontal coordinate of the line PB in the plane rectangular coordinate system; y PB Indicates the ordinate corresponding to the horizontal coordinate of the straight line PC in the plane rectangular coordinate system; x B Indicates the horizontal coordinate of point B; y B Indicates the ordinate of point B.

[0066] The calculation method of the first gradient arc includes:

[0067] The coordinates of the intersection point P are obtained as (x P ,y P ), BC is an arc with the intersection point P as the center and a gradually changing radius. From B to C, the radius changes from BP (r 1 ) to PC(r 2 ) gradually transitions, the formula is:

[0068]

[0069] Among them, x BC Represents the horizontal coordinate of the first gradient arc in the plane rectangular coordinate system; y BC represents the ordinate corresponding to the abscissa of the first gradient arc in the plane rectangular coordinate system; r represents the radius of the gradient arc r∈[r 1 , r 2 ]; x p Indicates the horizontal coordinate of the intersection point P; y p Represents the ordinate of the intersection point P.

[0070] By segmenting, the point distribution of the BC segment from C to B is controlled. The arc from B to C is divided into 10 parts, one part each near the two end points, and 8 parts in the middle. By adjusting the values ​​of b and c, the point distribution in each area is controlled to change the shape of the BC segment line to obtain the best running clearance change.

[0071] like Figure 4 As shown in the figure, by adjusting the values ​​of b and c, the BC segment profile will present different shapes, which will affect the change of the gap during the operation of the entire profile. The larger the values ​​of b and c, the more the BC segment profile will shrink to avoid interference. However, if the values ​​are too large, the smoothness will decrease, which needs to be considered comprehensively.

[0072] The parameter formula of the second gradient arc of 1 / 6 segment is:

[0073] QD:

[0074] QE:

[0075] The coordinates of the intersection point Q are obtained as (x Q ,y Q ), the subsequent design of the DE segment profile is the same as the BC segment profile, controlling the two parameters d and e:

[0076]

[0077] In the formula, α 2 is the root fillet angle of segment EF, α b It is the angle between the starting point of the involute and the horizontal axis.

[0078] like Figure 5 The figure shows the change of the BC segment profile under different parameters.

[0079] Figure 6 Schematic diagram of rotor meshing under different diameter-to-pitch ratios. Figure 7 is the distribution of rotor meshing point positions under different diameter-to-pitch ratios, Figure 8The figure is a schematic diagram of the change of meshing clearance when the rotor runs one circle under different pitch ratios, taking pitch ratios of 1.5 and 1.55 as examples. Good meshing characteristics are achieved under different pitch ratios. By adjusting the values ​​of b, c, d, and e, taking a gap of 0.3mm as an example, when m=1.5, the gap difference after one circle is 0.019mm, and when m=1.55, the gap difference after one circle is 0.041mm, and both can run smoothly.

[0080] Fig. 9 This is a comparison chart of the new type of line and the traditional type of line at the same center distance. The new type of line is compared in two cases of diameter-to-pitch ratio of 1.5 and 1.55, and the new type of line diameter-to-pitch ratio is 1.5 (the diameter-to-pitch ratio of the two-blade rotor type line is usually 1.5) and different traditional types of lines (within the allowable range, the diameter-to-pitch ratio is the largest value). It can be found from the figure that the outer diameter of the traditional three-blade type line is significantly smaller than the improved new type of line. Therefore, when the traditional three-blade type line replaces the two-blade type line, the center distance and the gap size cannot be taken into account at the same time, and the entire set of parts can only be replaced as a whole. The improved type line solves this problem. In addition, the area utilization factor of the improved new line has increased by more than 6%, which means that the volumetric efficiency of the machine will increase by more than 6%, and better performance can be obtained.

[0081] The present invention can be implemented by quickly generating the wire diameters of different types through MATLAB software. Table 1 shows the comparison of the wire diameters of different types:

[0082] Table 1

[0083]

[0084] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "axial", "radial", "vertical", "horizontal", "inner", "outer" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0085] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0086] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0087] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A method for designing a rotor profile of a three-leaf Roots pump, characterized in that the steps include: Based on the traditional three-blade involute profile, determine the design parameters of the rotor profile; Based on the design parameters, a 1 / 6 segment rotor profile is designed; The designed 1 / 6 segment rotor profile includes 5 segments, namely: a tooth tip arc, a first gradient arc, an involute, a second gradient arc and a tooth root arc; the tooth tip arc is used to determine the outer diameter of the final rotor profile, and the calculation method includes: Where α1 is the tooth tip circle angle of segment AB; R1 is the tooth tip circle radius; R m represents the theoretical outer circle radius; x1 represents the horizontal coordinate of the tooth top arc in the plane rectangular coordinate system; y1 represents the vertical coordinate corresponding to the tooth top arc and the horizontal coordinate in the plane rectangular coordinate system; δ represents half of the design clearance; a represents half of the rotor center distance; The calculation method of the tooth root arc includes: Wherein, α2 represents the root round angle of the EF segment; R2 represents the radius of the root arc; x2 represents the horizontal coordinate of the root arc in the plane rectangular coordinate system; y2 represents the vertical coordinate corresponding to the horizontal coordinate of the root arc in the plane rectangular coordinate system; the calculation method of the involute includes: Where R0 is the radius of the involute base circle; α i is the pressure angle at the starting point of the involute; α j is the pressure angle at the end point of the involute; α p is the involute pitch circle pressure angle; Z is the number of rotor blades; m1 is the pitch ratio of the involute part, which is independent of the pitch ratio m and is used to adjust the shape of the involute; x3 represents the abscissa of the involute in the plane rectangular coordinate system; y3 represents the ordinate corresponding to the abscissa of the involute in the plane rectangular coordinate system; τ represents the angle between the starting radius of the involute on the base circle and the X-axis; θ represents the sum of the pressure angle and the spread angle of the involute; The complete rotor profile is obtained by symmetric and rotating the 1 / 6 segment of the rotor profile.

2. The rotor profile design method of a three-leaf Roots pump according to claim 1, characterized in that: The angle range of the first gradual arc includes: α3∈[α1，α1+α e ] Among them, α3 is the angle range of the first gradual arc; α1 is the angle of the tooth top circle of segment AB; α e is the angle between the end point of the involute and the horizontal axis; The angle range α4 of the second gradient arc includes: α4∈[α b ，π / 3-α2] Among them, α4 is the angle range of the second gradient arc; α2 represents the root round angle of the EF segment; α b It is the angle between the starting point of the involute and the horizontal axis.

3. The rotor profile design method of a three-leaf Roots pump according to claim 1, characterized in that: Based on the tooth addendum arc, the involute and the tooth root arc, the first gradual arc and the second gradual arc are designed in a segmented manner.

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