CN109460581B - Spherical pump displacement calculation method - Google Patents

Spherical pump displacement calculation method Download PDF

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CN109460581B
CN109460581B CN201811198495.8A CN201811198495A CN109460581B CN 109460581 B CN109460581 B CN 109460581B CN 201811198495 A CN201811198495 A CN 201811198495A CN 109460581 B CN109460581 B CN 109460581B
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spherical pump
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杨楠
李竞
宗轶奇
沈辉
龚俊杰
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Yangzhou University
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Abstract

The invention provides a spherical pump bankThe quantity calculation method comprises the following steps of firstly establishing a spherical pump model: establishing a right-hand rectangular coordinate system by taking the middle of a spherical pump piston and a rotary table connecting shaft as an original point, the axial direction of the connecting shaft as an X axis and the axial direction of a rotary shaft of the spherical pump piston as a Z axis; then, the volume of the liquid inlet cavity is equal to that of the liquid outlet cavity, and the volume of the liquid outlet cavity is calculated: the liquid inlet cavity and the liquid outlet cavity are spherical wedge-shaped cavities with central angle of 2 alpha, wherein alpha is the spherical pump piston angle and the volume is V 1 (ii) a The volume of the part with the central angle of 2 alpha corresponding to the rotating pair between the piston and the rotating disc is V 2 Then the volume of the liquid discharge cavity V' = V 1 ‑V 2 (ii) a And finally, calculating the displacement of the spherical pump: calculating the displacement of the spherical pump according to the fact that the central angle occupied by the actual displacement of the spherical pump is 4 alpha; the method for calculating the displacement of the spherical pump can accurately calculate the specific numerical relationship between the displacement of the spherical pump and the piston angle, the radius of the piston and the outer diameter of the rotary pair, and provides theoretical guidance for the design of the spherical pump.

Description

Spherical pump displacement calculation method
Technical Field
The invention belongs to the field of design of displacement of a spherical pump, and particularly relates to a displacement calculation method of the spherical pump.
Background
The spherical pump is a novel hydraulic pump and has the advantages of simple and compact structure, low vibration noise and the like. Different structural parameters, such as piston diameter, piston angle, central pin shaft outer diameter and the like all affect the discharge capacity of the spherical pump. The size of the displacement also affects the use occasion of the spherical pump, power consumption and other parameters. Therefore, a simple and feasible method for calculating the displacement of the spherical pump needs to be developed to meet the engineering design requirements of the spherical pump.
However, the design theory of the spherical pump is relatively deficient at present, and although the documents Guan D, wu J H, sting L, et al, kinematic modeling, analysis and test on a theoretical pump [ J ]. Journal of Sound & simulation, 2016, 383.
Disclosure of Invention
The invention aims to provide a displacement calculation method of a spherical pump so as to guide the design of the spherical pump.
The technical solution for realizing the purpose of the invention is as follows:
a spherical pump displacement calculation method comprising the steps of:
step 1, establishing a spherical pump model:
establishing a right-hand rectangular coordinate system by taking the middle of a spherical pump piston and a rotary table connecting shaft as an original point, the axial direction of the connecting shaft as an X axis and the axial direction of a rotary shaft of the spherical pump piston as a Z axis;
step 2, setting the volume of the liquid inlet cavity to be the same as that of the liquid discharge cavity, and calculating the volume of the liquid discharge cavity: the liquid inlet cavity and the liquid outlet cavity are spherical wedge-shaped cavities with a central angle of 2 alpha, wherein alpha is a spherical pump piston angle; calculating the total volume of the spherical wedge as V 1 The volume of the rotary pair between the piston and the rotary disc is V 2 Then the volume of the drain cavity V' = V 1 -V 2 ；
Step 3, calculating the displacement of the spherical pump: and calculating the displacement of the spherical pump according to the fact that the central angle occupied by the actual displacement of the spherical pump is 4 alpha.
Compared with the prior art, the invention has the following remarkable advantages:
the method for calculating the displacement of the spherical pump can accurately calculate the specific numerical relationship between the displacement of the spherical pump and the piston angle, the radius of the piston and the outer diameter of the rotary pair, and provides theoretical guidance for the design of the spherical pump.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a flow chart of a method of calculating displacement for a spherical pump according to the present invention.
Fig. 2 (a) - (b) are schematic views of a spherical pump piston and rotary disk connection model.
Fig. 3 is a schematic structural view of a spherical wedge with a central angle of 2 α.
FIG. 4 is a schematic diagram of a cylindrical coordinate system used to calculate the revolute pair volume between the piston and the turntable.
Fig. 5 (a) - (b) are graphs showing displacement of the spherical pump as a function of piston radius and piston angle, respectively.
Detailed Description
For the purpose of illustrating the technical solutions and technical objects of the present invention, the present invention will be further described with reference to the accompanying drawings and specific embodiments.
Referring to fig. 1, the displacement calculation method of a spherical pump of the present invention includes the following steps:
step 1, establishing a spherical pump model:
and establishing a right-hand rectangular coordinate system by taking the middle of the spherical pump piston and the turntable connecting shaft as an original point, the axial direction of the connecting shaft as an X axis and the axial direction of the rotating shaft of the spherical pump piston as a Z axis.
Step 2, setting the volume of the liquid inlet cavity to be the same as that of the liquid discharge cavity, and calculating the volume of the liquid discharge cavity:
the liquid inlet cavity and the liquid outlet cavity are both spherical wedge-shaped cavities with a central angle of 2 alpha, as shown in fig. 2 (a) and fig. 3, wherein alpha is a spherical pump piston angle. The total volume of the spherical wedge is V 1 The volume of the rotary pair between the piston and the rotary disc is V 2 Then the volume of the drain cavity V' = V 1 -V 2 。
2.1, calculating the total volume of the spherical wedge as V 1 ：
Obtaining V by using spherical coordinate equation 1 ：
Figure GDA0003948539340000021
Wherein R is the piston radius; omega 1 Is the total volume V of the spherical wedge 1 The integration area of (1); f (x, y, z) is an integral function in rectangular coordinates; dv is the integral volume microcell;
Figure GDA0003948539340000022
the integral function is under a spherical coordinate system by taking the center of the rotating pair as the center; r is the radial distance of any point in the integration area; theta is productAn included angle between any point in the subarea and the positive direction of the X axis;
Figure GDA0003948539340000031
an included angle between any point in the integral area and the positive direction of the Z axis is formed; alpha is the piston angle.
2.2 calculating the volume V of the revolute pair between the piston and the turntable 2 ：
The cylindrical equation yields:
Figure GDA0003948539340000032
wherein r is 0 The outer diameter of the rotating pair between the piston and the rotating disc, namely the inner radius of the working chamber, is shown in fig. 3. Omega 2 Is volume V 2 The integration area of (1); dv is the integral volume microcell; theta is an included angle between the cylindrical surface coordinate and the positive direction of the X axis; rho is the radial radius of any point in the integral area under the cylindrical coordinate;
Figure GDA0003948539340000033
and
Figure GDA0003948539340000034
respectively represent the lower surface and the upper surface of the connecting shaft;
2.3, calculating the volume V' of the liquid discharge cavity:
Figure GDA0003948539340000035
step 3, calculating the discharge volume V of the spherical pump:
the volume V' of the working chamber obtained above is the same as the volumes of the liquid inlet chamber and the liquid outlet chamber, i.e., the central angle is 2 α. And actually the central angle occupied by the displacement of the spherical pump is 4 α as shown in (b) of fig. 2, the displacement of the spherical pump is calculated by the formula:
Figure GDA0003948539340000036
with reference to fig. 5, the variation law of the displacement V of the spherical pump with different structural parameters, such as the radius R of the piston and the angle α of the piston, can be obtained. In FIG. 5 (a), when the spherical pump piston angle α and the radius r inside the working chamber are set to 0 At some point, it can be seen that the displacement V of a spherical pump increases non-linearly with increasing piston radius R. In FIG. 5 (b), when the piston radius R and the working chamber inside radius R are equal 0 At a certain time, it can be seen that the displacement V of the spherical pump increases in a nearly linear manner with the piston angle of the spherical pump. The displacement V of the spherical pump, the piston angle alpha, the piston radius R and the outer diameter R of the rotary pair can be obtained by the displacement calculation method of the spherical pump 0 The specific numerical relationship of (a).

Claims (1)

1. A method of calculating displacement of a spherical pump, comprising the steps of:
step 1, establishing a spherical pump model:
establishing a right-hand rectangular coordinate system by taking the middle of a spherical pump piston and a rotary table connecting shaft as an original point, the axial direction of the connecting shaft as an X axis and the axial direction of a rotary shaft of the spherical pump piston as a Z axis;
step 2, setting the volume of the liquid inlet cavity to be the same as that of the liquid discharge cavity, and calculating the volume of the liquid discharge cavity: the liquid inlet cavity and the liquid outlet cavity are spherical wedge-shaped cavities with a central angle of 2 alpha, wherein alpha is a spherical pump piston angle; calculating the total volume of the spherical wedge as V 1 The volume of the rotating pair between the piston and the rotating disc is V 2 Then the volume of the liquid discharge cavity V' = V 1 -V 2 The specific calculation steps are as follows,
2.1, calculating the total volume of the spherical wedge as V 1 ：
V can be obtained by adopting spherical coordinate equation 1 ：
Figure FDA0003948539330000011
Wherein R is the piston radius; omega 1 Is the total volume V of the spherical wedge 1 The integration area of (2); f (x, y, z) is an integral function in rectangular coordinates; dv is integral volumeA micro-accumulation unit;
Figure FDA0003948539330000012
is an integral function under a spherical coordinate system; r is the radial distance of any point in the integration region; theta is an included angle between any point in the integral area and the positive direction of the X axis;
Figure FDA0003948539330000013
an included angle between any point in the integral area and the positive direction of the Z axis is formed;
2.2 calculating the volume V of the revolute pair between the piston and the turntable 2 ：
The cylindrical equation is used to obtain:
Figure FDA0003948539330000014
wherein r is 0 Is the outer diameter of a rotating pair between a piston and a rotating disc, omega 2 Is volume V 2 The integration area of (2); rho is the radial radius of any point in the integration area under the cylindrical coordinate;
Figure FDA0003948539330000021
and
Figure FDA0003948539330000022
respectively represent the lower surface and the upper surface of the connecting shaft;
2.3, calculating the volume V' of the liquid discharge cavity:
Figure FDA0003948539330000023
step 3, calculating the discharge capacity of the spherical pump: calculating the displacement V of the spherical pump according to the central angle of 4 alpha occupied by the actual displacement of the spherical pump,
Figure FDA0003948539330000024
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090123319A1 (en) * 2004-08-05 2009-05-14 Boerger Alois "rotary piston pump comprising a pump housing and two double bladed rotary pistons"
CN105626516A (en) * 2016-03-10 2016-06-01 无锡博泰微流体技术有限公司 Combined type spherical pump

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090123319A1 (en) * 2004-08-05 2009-05-14 Boerger Alois "rotary piston pump comprising a pump housing and two double bladed rotary pistons"
CN105626516A (en) * 2016-03-10 2016-06-01 无锡博泰微流体技术有限公司 Combined type spherical pump

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
球形叶片液压泵流量特性;俞亚新 等;《中国机械工程》;20180423;第29卷(第8期);第930-936页 *

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