CN102779112A - Method for generating groove-shaped line of dry gas seal fitted curve - Google Patents

Method for generating groove-shaped line of dry gas seal fitted curve Download PDF

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Publication number
CN102779112A
CN102779112A CN2012101759284A CN201210175928A CN102779112A CN 102779112 A CN102779112 A CN 102779112A CN 2012101759284 A CN2012101759284 A CN 2012101759284A CN 201210175928 A CN201210175928 A CN 201210175928A CN 102779112 A CN102779112 A CN 102779112A
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Prior art keywords
equation
dry gas
matched curve
pressure
generation method
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Inventor
黄义仿
丁雪兴
张伟政
郑劲
俞树荣
赵芳
苏虹
张海舟
韩明君
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Lanzhou University of Technology
Lanzhou Petrochemical College of Vocational Technology
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Lanzhou University of Technology
Lanzhou Petrochemical College of Vocational Technology
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Abstract

The invention relates to a method for generating a groove-shaped line of a dry gas seal fitted curve, which comprises the following steps: (1) a nonlinear Reynolds equation of a dry gas seal micro-scale flow field between two smooth plates is deduced; (2) the circumferential speed and the radial speed of gas under the non-slip boundary condition are determined; (3) the nonlinear Reynolds equation is approximately solved to obtain the approximate analysis formula of gas film pressure; and (4) a streamline equation under a polar coordinate and the approximate analysis formula of the gas film pressure are solved through Maple software to obtain the fitted curve.

Description

The generation method of dry gas seals matched curve grooved line
Technical field
[0001] the present invention relates to dry gas seals rotating ring end face groove molded lines generation technique.
Background technology
Dry gas seals is utilized the principle of dynamics of fluid; Realize the noncontact operation of seal face through on sealing surface, offering the dynamic pressure groove; Be state-of-the-art in present rotating machinery (as: compressor, the centrifugal pump) shaft end seal, a kind of preferably packoff of sealing effectiveness.The research of dry gas seals mechanism mainly concentrates on the technical matters of hydrodynamic effect, and key for design is how to design the geometric configuration and the geometric parameter of sealing surface fluting, and this directly has influence on sealing reliability of operation and stability.At present in known grooved curve dynamic pressure effect and sealing property the best be spiral yarn shaped.Yet the spiral fluted performance study has only been considered its structural parameters, does not consider concrete operating mode.Therefore in engineering practice, the helicla flute dry gas seals is used unsatisfactory, the dry gas seals failure phenomenon especially when low speed, low pressure, usually occurs: big like wearing and tearing, leakage rate.
Summary of the invention
The generation method that the purpose of this invention is to provide a kind of dry gas seals matched curve grooved line.
The generation method of dry gas seals matched curve grooved line the steps include:
(1) the non-linear Reynolds equation of dry gas seals microscale field of flow between derivation two smooth plates;
(2) circumferential speed and the radial velocity of gas under definite no slip boundary condition;
(3), obtain the approximate analysis formula of gas film pressure to non-linear Reynolds equation approximate solution;
(4) find the solution streamline equation and the approximate analysis formula of gas film pressure under the polar coordinates through Maple software, obtain matched curve.
The present invention compares with background technology, and the useful effect that has is: when air-film thickness is 3～5 μ m, under three kinds of operating modes: high-voltage high-speed, middle pressure middling speed, low pressure low speed, and the dynamic pressure effect of matched curve groove is better than helicla flute, and leakage rate is littler than helicla flute.
Description of drawings
Fig. 1 is a matched curve groove dry gas seals rotating ring end face two dimensional model synoptic diagram of the present invention;
Fig. 2 is that matched curve of the present invention and helix compare synoptic diagram.
Embodiment
1. the derivation of non-linear Reynolds equation
The general expression of N-S equation:
Figure 346745DEST_PATH_IMAGE001
In the formula:
Figure 870130DEST_PATH_IMAGE002
: gas density;
Figure 237658DEST_PATH_IMAGE003
: gas general speed in the lubricating layer;
Figure 213704DEST_PATH_IMAGE004
: air film thrust;
Figure 754407DEST_PATH_IMAGE005
: Laplace operator;
Figure 335561DEST_PATH_IMAGE006
: the pressure in the lubricating layer,
Figure 670727DEST_PATH_IMAGE007
: the kinetic viscosity of gas;
For gas; Ignore external force item F, then:
Figure 337332DEST_PATH_IMAGE008
;
The supposition of gas flow mechanical model is as follows between two sheet separations:
(1) gas is isothermal flow;
(2) flowing in the gap is laminar flow;
(3) the inertial force item is compared much for a short time with the pressure slope item, and promptly the formula left side can be ignored;
(4) main viscous force only is ;
Figure 866455DEST_PATH_IMAGE010
item, other can be ignored;
(5) ZThe speed w of direction can ignore, and promptly the gap thickness directional pressure is certain.
By above hypothesis, N-S equation in the rectangular coordinate system that can simplify:
Figure 372523DEST_PATH_IMAGE011
（1）
Figure 526424DEST_PATH_IMAGE012
（2）
U=u when considering no slip boundary condition z=0 0, v=0 (3)
U=0 during z=h, v=0 (4)
In the formula:
Figure 408929DEST_PATH_IMAGE013
;
Figure 699096DEST_PATH_IMAGE014
: the rotating speed of axle;
Figure 641645DEST_PATH_IMAGE015
: sealing ring internal diameter;
Figure 17262DEST_PATH_IMAGE016
: sealant thickness;
Figure 437879DEST_PATH_IMAGE017
: circumferential speed,
Figure 910449DEST_PATH_IMAGE018
: radial velocity;
Continuity equation:
Figure 696002DEST_PATH_IMAGE019
Stable state:
Figure 621233DEST_PATH_IMAGE020
;
Figure 783224DEST_PATH_IMAGE021
;
Figure 110300DEST_PATH_IMAGE022
In the formula: : axial velocity;
Figure 744861DEST_PATH_IMAGE024
; P: dimensionless pressure;
Figure 507281DEST_PATH_IMAGE025
: environmental pressure
Integration type:
Figure 561300DEST_PATH_IMAGE026
(5)
The equation of gas state:
Figure 16552DEST_PATH_IMAGE027
(6)
In the formula: T: gas temperature, R: gas law constant,
Obtain by formula (1)～(4) u, V:
Figure 854058DEST_PATH_IMAGE028
(7)
Figure 420168DEST_PATH_IMAGE029
（8）
Again with its substitution (5), and (6) formula of utilization gets Reynolds equation:
Figure 393941DEST_PATH_IMAGE030
(9)
Streamline equation under the polar coordinates is:
Figure 20094DEST_PATH_IMAGE031
(10)
In the formula: r: the radius of sealing ring,
With (9) formula nondimensionalization then be:
（11）
X is that radius does R i The circular arc coordinate, yUtmost point footpath for vertical circular arc;
In the formula:
Figure 449118DEST_PATH_IMAGE033
;
Figure 605293DEST_PATH_IMAGE034
;
Figure 340031DEST_PATH_IMAGE035
: dimensionless utmost point footpath;
Figure 948867DEST_PATH_IMAGE036
: compressibility coefficient under the no slip boundary condition
,
Figure 70724DEST_PATH_IMAGE038
: compressibility coefficient:
Figure 976363DEST_PATH_IMAGE039
Figure 72495DEST_PATH_IMAGE040
: air-film thickness;
Boundary condition:
Figure 456203DEST_PATH_IMAGE041
,
Figure 586970DEST_PATH_IMAGE042
(12)
In the formula:
Figure 725827DEST_PATH_IMAGE043
: pressure medium,
Figure 249868DEST_PATH_IMAGE044
: sealing ring external diameter;
2.PH linearization technique:
Order:
Figure 499584DEST_PATH_IMAGE045
, then (11) formula turns to:
Functional
Figure 422540DEST_PATH_IMAGE046
(13)
Newton-strange the method for Kan Toro dimension of broad sense is applied to equation (13), the available following sequence of function:
Figure 732299DEST_PATH_IMAGE047
(14)
Differential on the research point can be confirmed by following formula:
Figure 740706DEST_PATH_IMAGE048
(15)
(13) formula is carried out differential, then
Figure 794113DEST_PATH_IMAGE049
(16)
Make equation (14) ;
Figure 52236DEST_PATH_IMAGE051
;
Figure 344677DEST_PATH_IMAGE052
is used for equation (14) then with operator (16):
Figure 139458DEST_PATH_IMAGE053
（17）
Consider
Figure 833744DEST_PATH_IMAGE054
, expression formula (13) and (16) during utilization
Figure 422989DEST_PATH_IMAGE051
Figure 468305DEST_PATH_IMAGE055
(18)
Can get the linear Reynolds equation of first approximation PH:
Figure 801197DEST_PATH_IMAGE056
(19)
Corresponding boundary condition
Figure 349990DEST_PATH_IMAGE057
,
Figure 375715DEST_PATH_IMAGE058
(20)
In the formula: : PH dimensionless function, H: sealant dimensionless thickness;
3. introduce the complex function abbreviation:
Make
Figure 576069DEST_PATH_IMAGE060
;
Figure DEST_PATH_IMAGE061
Then (19), (20) become
Figure 179702DEST_PATH_IMAGE062
(21)
Figure 376328DEST_PATH_IMAGE063
,
Figure 865078DEST_PATH_IMAGE064
(22)
Calculate for ease, separating with plural form of (21), (22) represented, study following complex function for this reason
Boundary value problem
Figure 805352DEST_PATH_IMAGE065
(23)
The corresponding function of a complex variable of y is K
Figure 328737DEST_PATH_IMAGE066
,
Figure 430685DEST_PATH_IMAGE067
(24)
Separating of boundary value problem (23), (24) has following form
Figure 672311DEST_PATH_IMAGE068
(25)
Substitution (23) formula gets:
Figure 150697DEST_PATH_IMAGE069
(26)
Figure 528588DEST_PATH_IMAGE070
,
Figure 129334DEST_PATH_IMAGE071
(27)
In the formula:
Figure 530360DEST_PATH_IMAGE072
;
Figure 874753DEST_PATH_IMAGE073
,
Figure 310414DEST_PATH_IMAGE074
;
4. solution by iterative method:
Figure 816481DEST_PATH_IMAGE075
（28）
With (28) formula substitution (26)
Figure 970382DEST_PATH_IMAGE076
,
Figure 852888DEST_PATH_IMAGE077
(29)
Order: ; is small parameter, and
Figure 249169DEST_PATH_IMAGE080
is real constant;
Then (29) formula is
Figure DEST_PATH_IMAGE081
,
Figure 873049DEST_PATH_IMAGE082
(30)
Its approximate solution is:
Figure 17722DEST_PATH_IMAGE083
(32)
Figure 131172DEST_PATH_IMAGE084
（33）
Each time homogeneous power of (31) formula substitution (30) and collection
Figure 994085DEST_PATH_IMAGE085
is got:
Zero-order approximation: ;
Figure 483153DEST_PATH_IMAGE087
Corresponding boundary condition: ;
Figure 914451DEST_PATH_IMAGE089
;
Figure 880133DEST_PATH_IMAGE090
;
Figure 61716DEST_PATH_IMAGE091
Solve:
Figure 454651DEST_PATH_IMAGE092
;
In the formula:
Figure 858267DEST_PATH_IMAGE094
;
Figure 894356DEST_PATH_IMAGE095
Figure 455263DEST_PATH_IMAGE096
，
Figure 576803DEST_PATH_IMAGE097
，
First approximation:
Figure 884288DEST_PATH_IMAGE098
;
Figure 40462DEST_PATH_IMAGE099
Boundary condition:
Figure 837517DEST_PATH_IMAGE100
;
Figure 384036DEST_PATH_IMAGE101
;
Figure 291949DEST_PATH_IMAGE102
;
Figure 240314DEST_PATH_IMAGE103
Solve:
Figure 208270DEST_PATH_IMAGE104
,
Figure 304402DEST_PATH_IMAGE105
，
In the formula: ,
Figure 84456DEST_PATH_IMAGE107
，
Figure 160996DEST_PATH_IMAGE108
，
Figure 478845DEST_PATH_IMAGE109
，
Figure 994140DEST_PATH_IMAGE110
?，
Figure 917097DEST_PATH_IMAGE111
，
Figure 226855DEST_PATH_IMAGE112
， ；
First-order approximation is separated:
Figure 23090DEST_PATH_IMAGE114
Figure 862870DEST_PATH_IMAGE115
，
In the formula
Figure 284143DEST_PATH_IMAGE116
;
Figure 842163DEST_PATH_IMAGE117
;
Figure 371365DEST_PATH_IMAGE118
; : integral constant
; ;
Figure 95421DEST_PATH_IMAGE122
;
Figure 847476DEST_PATH_IMAGE123
: integral constant
Figure 669939DEST_PATH_IMAGE124
;
Figure 936972DEST_PATH_IMAGE125
; ;
Figure 742434DEST_PATH_IMAGE127
: integral constant
5. the dynamic pressure approximate function is separated:
Figure 673481DEST_PATH_IMAGE128
，
Figure 427810DEST_PATH_IMAGE129
，
First approximation:
Figure 430402DEST_PATH_IMAGE130
,
Figure 891470DEST_PATH_IMAGE131
（34）
6. the grooved line of matched curve design:
Figure 55735DEST_PATH_IMAGE132
，
Figure 235044DEST_PATH_IMAGE133
，
Streamline equation: .
Utilization Maple software is found the solution streamline equation and pressure equation, and to obtain matched curve as shown in Figure 1.
7. the performance verification of matched curve groove
Utilization fluent software carries out numerical simulation to the matched curve groove that air-film thickness is respectively 3 μ m, 4 μ m, 5 μ m; And compare (as shown in Figure 2) with the helicla flute under the identical operating mode; Result of study shows: the dynamic pressure effect of matched curve groove is better than helicla flute, and leakage rate is littler than helicla flute.
Experimental gas is an air, and operational factor is: inside radius R i =58.42mm, external radius R 0 =77.78mm, root radius R g =69mm, the channel mould number n=12, dielectric viscosity μ=1.8 * 10 -5Pas, helix angle α=15 °, environmental pressure p i =0.10325MPa, groove depth 2E=7 μ m.Following three kinds of operating modes are studied matched curve groove, spiral fluted dynamic pressure effect and leakage rate respectively.(1) low pressure low speed: pressure medium p 0 =0.3MPa, rotating speed n r =200 r/min; (2) press middling speed in: pressure medium p 0 =0.5MPa, rotating speed n r =1500 r/min; (3) high-voltage high-speed: pressure medium p 0 =3MPa, rotating speed n r =10100 r/min.

Claims (5)

1. the generation method of dry gas seals matched curve grooved line the steps include:
(1) the non-linear Reynolds equation of dry gas seals microscale field of flow between derivation two smooth plates;
(2) circumferential speed and the radial velocity of gas under definite no slip boundary condition;
(3), obtain the approximate analysis formula of gas film pressure to non-linear Reynolds equation approximate solution;
(4) find the solution streamline equation and the approximate analysis formula of gas film pressure under the polar coordinates through Maple software, obtain matched curve.
2. the generation method of dry gas seals matched curve grooved line according to claim 1 is characterized in that obtaining circumferential speed and radial velocity through N-S equation, no slip boundary condition:
Circumferential speed:
Figure 891373DEST_PATH_IMAGE001
Radial velocity:
Figure 104792DEST_PATH_IMAGE002
.
3. the generation method of dry gas seals matched curve grooved line according to claim 1 is characterized in that obtaining matched curve through the streamline equation under Maple program solution pressure equation and the polar coordinates:
Pressure equation:
Figure 363735DEST_PATH_IMAGE003
Streamline equation:
Figure 118065DEST_PATH_IMAGE004
.
4. the generation method of dry gas seals matched curve grooved line according to claim 1 is characterized in that obtaining Reynolds equation through the continuity equation and the equation of gas state.
5. the generation method of dry gas seals matched curve grooved line according to claim 3 is characterized in that pressure equation is the first-order approximation analytic expression of gas film pressure.
CN2012101759284A 2012-05-31 2012-05-31 Method for generating groove-shaped line of dry gas seal fitted curve Pending CN102779112A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105987175A (en) * 2016-08-05 2016-10-05 江西省科学院应用物理研究所 Mechanical sealing structure with combination of various holes and three-dimensional snowflake-shaped grooves
CN106104112A (en) * 2014-06-26 2016-11-09 伊格尔工业股份有限公司 Slide unit
CN110569518A (en) * 2019-03-29 2019-12-13 哈尔滨理工大学 Combined sealing oil film thickness solving method

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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106104112A (en) * 2014-06-26 2016-11-09 伊格尔工业股份有限公司 Slide unit
US9765892B2 (en) 2014-06-26 2017-09-19 Eagle Industry Co., Ltd. Sliding component
CN105987175A (en) * 2016-08-05 2016-10-05 江西省科学院应用物理研究所 Mechanical sealing structure with combination of various holes and three-dimensional snowflake-shaped grooves
CN110569518A (en) * 2019-03-29 2019-12-13 哈尔滨理工大学 Combined sealing oil film thickness solving method
CN110569518B (en) * 2019-03-29 2021-07-20 哈尔滨理工大学 Combined sealing oil film thickness solving method

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Application publication date: 20121114