CN112746987A - Fibonacci spiral impeller - Google Patents

Fibonacci spiral impeller Download PDF

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Publication number
CN112746987A
CN112746987A CN202110167768.8A CN202110167768A CN112746987A CN 112746987 A CN112746987 A CN 112746987A CN 202110167768 A CN202110167768 A CN 202110167768A CN 112746987 A CN112746987 A CN 112746987A
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China
Prior art keywords
impeller
theta
flow channel
formula
base
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Chinese (zh)
Inventor
王健
丁剑
夏永忠
赵振江
宋向前
李杨
万浩
周银
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Taizhou University
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Taizhou University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/18—Rotors
    • F04D29/22—Rotors specially for centrifugal pumps
    • F04D29/2205—Conventional flow pattern
    • F04D29/2216—Shape, geometry
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04D—NON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00—Details, component parts, or accessories
    • F04D29/66—Combating cavitation, whirls, noise, vibration or the like; Balancing
    • F04D29/669—Combating cavitation, whirls, noise, vibration or the like; Balancing especially adapted for liquid pumps

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Structures Of Non-Positive Displacement Pumps (AREA)

Abstract

The invention discloses a Fibonacci spiral impeller which comprises an impeller main body, wherein the impeller main body comprises a base, blades are arranged on one side of the base, and a through hole connected with an output shaft of a motor is formed in the center of the base; the blades are enveloped to form a space flow channel, the starting point of the space flow channel is arranged on the outer side of the through hole, the end point of the space flow channel is arranged on the outer edge of the base, the section of the space flow channel is groove-shaped, and the bottom of the space flow channel protrudes to the other side away from the blades; the shape of the base is the same as that of the frame at 360 degrees on the outermost side of the blade; the wrap angle of the blades is 720-1440 degrees, and the locus curve of the space flow channel is { f (theta, r (theta), H (theta)) }. The Fibonacci series impeller can reduce the radial force borne by the impeller, improve the lift pulsation and reduce the dynamic load of a shaft system, thereby playing the roles of inhibiting the vibration of a pump, improving the running stability of the whole machine and prolonging the service life.

Description

Fibonacci spiral impeller
Technical Field
The invention relates to the technical field of centrifugal pump impeller design, in particular to a Fibonacci spiral impeller.
Background
The runner type impeller is an impeller structure commonly adopted by a sewage pump, has more excellent winding resistance and anti-blocking performance compared with a closed impeller, and has higher wear resistance. The conventional blade molded lines at the present stage mainly include Archimedes spiral lines, constant-angle spiral lines, logarithmic spiral lines, involute lines, composite molded lines and the like. However, when the profile equations solve the problem of a large blade wrap angle, the profile of the blade is easy to form an S shape, and a scanning fluid channel is easy to generate a wrinkled surface, so that the particle size of the particles passing through the impeller channel is influenced, and the change of the placement angle is not monotonous, so that the gradient change of the blade load is large, and further, the fluid is easy to flow off the blade. The two factors can reduce the passing performance of the sewage pump, reduce the efficiency, induce the sewage pump to generate obvious vibration noise and seriously affect the operation stability of the sewage pump.
Disclosure of Invention
It is an object of the present invention to provide a fibonacci spiral impeller which addresses the problems of the prior art described above.
In order to achieve the purpose, the invention provides the following scheme: the invention provides a Fibonacci spiral impeller which comprises an impeller main body, wherein the impeller main body comprises a base, blades are arranged on one side of the base, and a through hole connected with an output shaft of a motor is formed in the center of the base; the blades are enveloped to form a space flow channel, the starting point of the space flow channel is arranged on the outer side of the through hole, the end point of the space flow channel is arranged on the outer edge of the base, the cross section of the space flow channel is groove-shaped, and the bottom of the space flow channel protrudes to the other side away from the blades; the shape of the base is the same as that of a 360-degree frame at the outermost side of the blade; the wrap angle of the blade is 720 degrees to 1440 degrees; the trajectory curve of the space flow channel is { f (theta, r (theta), H (theta)) }, wherein r (theta) is shown as formula 1, and H (theta) is shown as formula 2:
Figure BDA0002938044170000021
Figure BDA0002938044170000022
in the formula, theta is a variable of a track curve, and theta is a polar angle of the curve; r (θ) is a radius function of the trajectory curve; α is a radius function parameter; b is a fibonacci number;
Figure BDA0002938044170000023
is the maximum polar angle of the trajectory curve; h (theta) is a distance function of the trajectory curve in the axial direction; l is the maximum distance of the trajectory curve in the axial direction; h is a distance function parameter.
Preferably, the outlet diameter of the impeller is D2，D2As shown in equation 3:
Figure BDA0002938044170000024
in the formula, n is the rotating speed; hdThe lift is the design working condition; qdThe flow rate under the design working condition is adopted; psidFor the lift coefficient, psi, under design conditionsdAs shown in equation 4:
Figure BDA0002938044170000025
in the formula, nsIs a specific number of revolutions, ns，Ref＝1,nsAs shown in equation 5:
Figure BDA0002938044170000026
preferably, the outlet width of the impeller is b2，b2As shown in equation 6:
b2＝kb2dk…………………………………6
in the formula (d)kIs the maximum particle diameter through which the impeller can pass, kb2Is a coefficient, kb2The value range of (A) is 1.05-1.1.
Preferably, the thickness of the blade (2) is δ, which is represented by formula 7:
Figure BDA0002938044170000031
in the formula u2Is the peripheral speed of the outlet of the impeller blade (2).
Preferably, the outlet of the blade (2) is placed at an angle beta2，β2As shown in equation 8:
Figure BDA0002938044170000032
preferably, the maximum polar angle of the trajectory curve
Figure BDA0002938044170000033
Figure BDA0002938044170000034
As shown in equation 9:
Figure BDA0002938044170000035
preferably, the maximum distance of the trajectory curve in the axial direction is L, where L is represented by formula 10:
L＝D2×(b-1)-2b2×b…………………………………10
the invention discloses the following technical effects: the Fibonacci series impeller can reduce the radial force borne by the impeller, improve the lift pulsation and reduce the dynamic load of a shaft system, thereby playing the roles of inhibiting the vibration of a pump, improving the running stability of the whole machine and prolonging the service life.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic view of a conventional impeller structure;
FIG. 2 is an isometric view of an impeller of the present invention;
FIG. 3 is a rear view of the impeller of the present invention;
FIG. 4 is a schematic view of the impeller structure of the present invention;
FIG. 5 is a front view of the impeller of the present invention;
FIG. 6 is a cross-sectional view of the impeller of the present invention;
FIG. 7 is a Lissajous diagram of the radial force of a conventional impeller and a novel impeller of the present invention;
FIG. 8 is a radial force pulsation graph of a conventional impeller and the novel impeller of the present invention;
fig. 9 is a head pulsation diagram of a conventional impeller and the novel impeller of the present invention.
Wherein, 1 is the base, 2 is the blade, 3 is the through-hole, 4 is the space runner.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Referring to fig. 1-9, the invention provides a fibonacci spiral impeller, which comprises an impeller main body, wherein the impeller main body comprises a base 1, one side of the base 1 is provided with a blade 2, and the center of the base 1 is provided with a through hole 3 connected with an output shaft of a motor; the blades 2 are enveloped to form a space flow channel 4, the starting point of the space flow channel 4 is arranged on the outer side of the through hole 3, the end point of the space flow channel 4 is arranged on the outer edge of the base 1, the section of the space flow channel 4 is an arc-shaped groove, the bottom of the space flow channel 4 protrudes to the other side away from the blades 2, namely the arc-shaped bottom of the space flow channel 4 is arranged on one side of the base 1 away from the blades; the shape of the base 1 is the same as that of the outermost 360-degree frame of the blade 2, namely the outermost ring frame of the blade is the same as that of the base; the wrap angle of the blade 2 is 720-1440 degrees, the track curve of the space flow channel 4 is a Fibonacci spiral line and is determined by { f (theta, r (theta), H (theta)) }, wherein r (theta) is shown as formula (1), and H (theta) is shown as formula (2):
Figure BDA0002938044170000051
Figure BDA0002938044170000052
in the formula, theta is a variable of a track curve, and theta is a polar angle of the curve; r (θ) is a radius function of the trajectory curve; alpha is a radius function parameter, and alpha is b/2; b is the Fibonacci number, the Fibonacci number being the "golden ratio",
Figure BDA0002938044170000053
Figure BDA0002938044170000054
is the maximum polar angle of the trajectory curve; h (theta) is a distance function of the trajectory curve in the axial direction; l is the maximum distance of the trajectory curve in the axial direction; h is a distance function parameter, and h is 2.5 lnb.
The outlet diameter of the impeller is D2，D2As shown in equation 3:
Figure BDA0002938044170000055
in the formula, n is the rotating speed; hdThe lift is the design working condition; qdThe flow rate under the design working condition is adopted; psidFor the lift coefficient, psi, under design conditionsdAs shown in equation 4:
Figure BDA0002938044170000056
in the formula, nsIs a specific number of revolutions, ns，Ref＝1,nsAs shown in equation 5:
Figure BDA0002938044170000057
outlet width of impeller is b2，b2As shown in equation 6:
b2＝kb2dk…………………………………6
in the formula, kb2Is a coefficient, kb2The value range of (A) is 1.05-1.1; dkThe design of a single-channel impeller for the maximum particle diameter through which the impeller can pass depends to a large extent on the maximum particle diameter d through which the impeller can passkAnd the enterprise can generally pass the maximum particle size dkThe method is one of important parameters for product model selection of the single-channel centrifugal pump.
The thickness of the blade 2 is delta, and delta is shown as a formula 7; the minimum thickness of the blades of the multi-blade centrifugal pump is generally 3 mm-6 mm, and the inlet of each blade is thinner. The sewage pump impeller comprises a single-flow-channel impeller, a double-flow-channel impeller and a three-flow-channel impeller, but the thickness of the blade inlet of the sewage pump impeller is increased so as to prevent plastic, long fiber and the like from being attached to the edge of the blade inlet.
Figure BDA0002938044170000061
In the formula u2Is the circumference of the outlet of the impeller blade 2Speed.
Outlet setting angle beta of blade 22，β2As shown in equation 8:
Figure BDA0002938044170000062
maximum polar angle of trajectory curve
Figure BDA0002938044170000063
Figure BDA0002938044170000064
As shown in equation 9:
Figure BDA0002938044170000065
the maximum distance of the trajectory curve in the axial direction is L, which is shown in formula 10:
L＝D2×(b-1)-2b2×b…………………………………10。
the radial force Lissajous of the conventional impeller and the novel impeller of the application is shown in figure 7, and the pulsation of the radial force is shown in figure 8. As can be seen from the Lissajous figure, the radial force distribution of the traditional impeller has large fluctuation and irregularity, and is far away from the axis, so that the radial vibration displacement of the rotor is large, the vibration level of the whole machine is increased, and the bearing is easy to damage after long-term operation. The novel impeller provided by the invention has the advantages that the bionic technology is adopted, so that the impeller bears very small radial force, the radial force pulsation of the novel impeller is very regular and has small numerical value, the deviation distance from the axis is short, the static load and the dynamic load borne by the rotor and the bearing are small, the vibration is favorably inhibited, the running stability of the whole machine is improved, and the service life is prolonged.
The head pulsation of the conventional impeller and the novel impeller of the present application is shown in fig. 9. As can be seen from fig. 9, the lift pulsation of the conventional impeller is large and the variation is irregular, so that the mechanical parts bear the dynamic load which is changed frequently, and the material is easy to be damaged by fatigue. The lift pulsation of the novel impeller is small, which indicates that the dynamic load of the novel impeller is small, and the impeller-shaft system is stable.
The Fibonacci series impeller can reduce the radial force borne by the impeller, improve the lift pulsation and reduce the dynamic load of a shaft system, thereby playing the roles of inhibiting the vibration of a pump, improving the running stability of the whole machine and prolonging the service life.
In the description of the present invention, it is to be understood that the terms "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, are merely for convenience of description of the present invention, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention.
The above-described embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solutions of the present invention can be made by those skilled in the art without departing from the spirit of the present invention, and the technical solutions of the present invention are within the scope of the present invention defined by the claims.

Claims (7)

1. A fibonacci spiral impeller characterized by: the impeller comprises an impeller main body, wherein the impeller main body comprises a base (1), one side of the base (1) is provided with a blade (2), and the center of the base (1) is provided with a through hole (3) connected with an output shaft of a motor; the blades (2) are enveloped to form a space flow channel (4), the starting point of the space flow channel (4) is arranged on the outer side of the through hole (3), the end point of the space flow channel (4) is arranged on the outer edge of the base (1), the cross section of the space flow channel (4) is groove-shaped, and the bottom of the space flow channel (4) protrudes to the other side away from the blades (2); the shape of the base (1) is the same as the shape of a 360-degree frame at the outermost side of the blade (2); the wrap angle of the blade (2) is 720-1440 degrees, the track curve of the space flow channel (4) is { f (theta, r (theta), H (theta)) }, wherein r (theta) is shown as formula 1, and H (theta) is shown as formula 2:
Figure FDA0002938044160000011
Figure FDA0002938044160000012
in the formula, theta is a variable of a track curve, and theta is a polar angle of the curve; r (θ) is a radius function of the trajectory curve; α is a radius function parameter; b is a fibonacci number;
Figure FDA0002938044160000013
is the maximum polar angle of the trajectory curve; h (theta) is a distance function of the trajectory curve in the axial direction; l is the maximum distance of the trajectory curve in the axial direction; h is a distance function parameter.
2. A fibonacci spiral impeller according to claim 1 wherein: the outlet diameter of the impeller is D2，D2As shown in equation 3:
Figure FDA0002938044160000014
in the formula, n is the rotating speed; hdThe lift is the design working condition; qdThe flow rate under the design working condition is adopted; psidFor the lift coefficient, psi, under design conditionsdAs shown in equation 4:
Figure FDA0002938044160000021
in the formula, nsIs a specific number of revolutions, ns，Ref＝1,nsAs shown in equation 5:
Figure FDA0002938044160000022
3. a fibonacci spiral impeller according to claim 2 wherein: outlet width of impeller is b2，b2As shown in equation 6:
b2＝kb2dk……………………………………6
in the formula (d)kIs the maximum particle diameter through which the impeller can pass, kb2Is a coefficient, kb2The value range of (A) is 1.05-1.1.
4. A fibonacci spiral impeller according to claim 2 wherein: the thickness of the blade (2) is delta, and delta is shown as a formula 7:
Figure FDA0002938044160000023
in the formula u2Is the peripheral speed of the outlet of the impeller blade (2).
5. A fibonacci spiral impeller according to claim 1 wherein: the outlet setting angle beta of the blade (2)2，β2As shown in equation 8:
Figure FDA0002938044160000024
6. a fibonacci spiral impeller according to claim 1 wherein: maximum polar angle of trajectory curve
Figure FDA0002938044160000025
As shown in equation 9:
Figure FDA0002938044160000026
7. a fibonacci spiral impeller according to claim 3 wherein: the maximum distance of the trajectory curve in the axial direction is L, which is shown in formula 10:
L＝D2×(b-1)-2b2×b…………………………………10。
CN202110167768.8A 2021-02-07 2021-02-07 Fibonacci spiral impeller Pending CN112746987A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2023149844A1 (en) * 2022-02-07 2023-08-10 Cleanfuture Energy Co., Ltd. Variable pitch propeller blades and associated propeller applications

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2023149844A1 (en) * 2022-02-07 2023-08-10 Cleanfuture Energy Co., Ltd. Variable pitch propeller blades and associated propeller applications

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