CN112989652B - Method for predicting leakage rate of flange connection - Google Patents
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Abstract
The invention relates to a method for predicting the leakage rate of flange connection, which utilizes a uniform compression gasket leakage test to obtain gasket stress, leakage rate, gasket thickness and gasket compression deformation data and determine the correlation between the basic leakage rate and the relative compression deformation of the gasket; establishing a finite element analysis model for flange connection of the non-uniformly compressed non-metallic gasket, and acquiring the compression deformation distribution of the gasket under the operating condition; and obtaining the compression deformation of the gasket at any radius position from the compression deformation distribution of the gasket, introducing the conductance, respectively integrating the conductance with the radius r along the radial direction and the annular direction to obtain the conductance of the unevenly compressed gasket, and calculating the leakage rate. The method introduces a 'flow guide' concept, considers the condition of uneven compression of the gasket and solves the problem of prediction of leakage rate under the condition of uneven compression deformation of the gasket through flow guide integration.
Description
Technical Field
The invention relates to the field of process industrial equipment and pipeline flange connection sealing, in particular to prediction of flange connection leakage rate.
Background
The leakage rate of flange connection is related to the performance of the gasket, the rigidity of the flange, the size and the uniformity of pretightening force, the operating pressure, the temperature and the like. Non-metallic gaskets and non-metallic and metallic combination gaskets are typically treated as porous media to predict the leakage rate of a flange connection based on gasket stress. However, the gasket stress depends on the preload load and the operating pressure, the same gasket stress obtained under different preload loads and operating pressures does not have the same leakage rate, the gasket stress and the leakage rate do not have a one-to-one correspondence relationship, and the gasket stress in the operating state cannot be directly utilized to predict the leakage rate.
Therefore, the invention provides a method for predicting the leakage rate of the flange connection based on the relative compression deformation of the gasket, introduces the concept of 'conductance', and solves the problem of predicting the leakage rate under the condition of uneven compression deformation of the gasket.
Disclosure of Invention
The invention aims to solve the problem of predicting the leakage rate of flange connection of a non-uniformly compressed gasket, provides a method for predicting the leakage rate of flange connection based on the relative compression deformation of the gasket, introduces the concept of 'conductance', considers the condition of non-uniform compression of the gasket, and solves the problem of predicting the leakage rate of the gasket under the condition of non-uniform compression deformation through the integral of conductance.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for predicting the leakage rate of flange connection comprises the following steps;
let the radius r of the leakage path of the gasket itselfjAnd the number k of leakage passages and the amount of relative compressive deformation of the gasket
The radius of the leakage channel and the quantity of the leakage channel are respectively expressed by a function related to the relative compression deformation of the gasket, and the basic leakage rate is expressed in a form related to the relative compression deformation of the gasket, so that a basic leakage rate prediction model of an equation (6) is obtained:
wherein h is the dynamic viscosity of the medium; p is a radical ofi、poThe inlet and outlet pressures of the capillary tube; p is a radical ofmThe average pressure of the inlet and the outlet of the capillary is; ls represents the base leak rate; alpha and n are undetermined constants and are obtained through test fitting; di、doRespectively compressing the inner diameter and the outer diameter by a gasket, wherein l is the compressing width of the gasket; deltaaIs the amount of compression deformation of the gasket, TaIs the thickness of the gasket;
performing a gasket cyclic compression rebound test, recording the gasket leakage rate, the gasket compression deformation, the gasket stress and the gasket thickness, solving the relative compression deformation of the gasket, and obtaining a relation curve between the gasket stress and the gasket compression deformation and a corresponding relation between the leakage rate and the relative compression deformation of the gasket;
determining the values of undetermined constants alpha and n in a formula (6) according to the corresponding relation between the leakage rate and the relative compression deformation of the gasket obtained by the test, and further determining an expression of a basic leakage rate prediction model;
establishing a three-dimensional finite element model according to the flange connection structure and the symmetry of the load, fully considering the contact between a nut and a flange and the contact between a flange pressing surface and a gasket in the model, and calculating the pre-tightening and operating conditions by adopting gasket stress and gasket compression deformation data obtained by the gasket cyclic compression rebound test for gasket performance so as to obtain the gasket compression deformation distribution under the operating conditions;
then introducing a 'conductance' concept, expressing the conductance as a formula related to relative compression deformation of the gasket, obtaining the conductance of the uneven compression gasket by respectively integrating along the radial direction and the annular direction according to the obtained compression deformation distribution of the gasket under the operating condition, and multiplying the conductance of the uneven compression gasket by the pressure difference between an inlet and an outlet of a capillary tube to obtain a prediction model of the connection leakage rate of the uneven compression flange;
according to the prediction model of the non-uniform compression flange connection leakage rate, the non-uniform compression gasket flange connection leakage rate can be obtained under the condition that the relative compression deformation is known.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a method for predicting the connection leakage rate of an uneven compression flange based on the relative compression deformation of a gasket. The method requires that firstly, a cyclic loading relation between gasket stress and gasket deformation in a uniform compression state is obtained through a gasket leakage test, a relational expression between a leakage rate and a gasket relative compression deformation is fitted, and a basic leakage rate model (the basic leakage rate refers to the leakage rate in the uniform compression state) is established; then according to the characteristics of the structure and the load, the symmetry is fully considered, a flange connection three-dimensional finite element model is established, the pre-tightening and the operation working conditions are analyzed, and the compression deformation distribution rule of the gasket under the operation working conditions is obtained (the flange rigidity, the gasket form, the number of bolts, the pre-tightening force, the operation pressure and the pipe system bending moment load are different, the uneven compression conditions are different, the distribution rule of uneven compression can be given out through finite element calculation, and the integral calculation can be carried out by using the concept of flow guidance according to the distribution rule); according to the distribution rule of the compression deformation of the gasket, introducing a 'conductance' concept, respectively performing conductance integration along the radial direction and the circumferential direction, performing integration according to a formula (12) at the same circumferential position, and performing integration according to a formula (13) at different circumferential positions; and finally, establishing a non-uniform compression flange connection leakage rate prediction model according to the formula (14), and obtaining the non-uniform compression gasket flange connection leakage rate according to the formula (14).
The invention grasps the physical essence that the leakage rate corresponds to the relative compression deformation meaning of the gasket, establishes the prediction model of the leakage rate of the non-uniform compression flange connection, has clear physical meaning, realizes the direct calculation of the leakage rate of the non-uniform compression flange connection, and can be used for determining the allowable load of the flange connection and designing the flange connection when the load and the allowable leakage rate are known.
Drawings
To more clearly illustrate the objects of the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. The drawings in the following description are merely exemplary and exemplary of the present invention, and it will be apparent to those skilled in the art that other drawings can be obtained from the methods and drawings provided without inventive effort. In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 all other embodiments obtained by a person of ordinary skill in the art without any creative work belong to the scope of protection of the present invention.
The invention will now be described by way of example and with reference to the accompanying drawings.
FIG. 1 shows the gasket stress σ in the embodiment of the present applicationeAmount of deformation delta from the gasketaA schematic diagram of the relationship of (1);
FIG. 2 shows the basic leakage rate Ls and the gasket stress σ in the embodiment of the present applicationeA schematic diagram of the relationship of (1);
FIG. 3 shows the basic leakage rate Ls and the relative compressive deformation of the gasket in the embodiment of the present application
A relationship and fit diagram;
FIG. 4 is a schematic diagram of a three-dimensional finite element model according to an embodiment of the present application;
FIG. 5 is a schematic diagram of a finite element mesh subdivision in an embodiment of the present application;
FIG. 6 is a stress cloud of a gasket under a pre-tightening condition in an embodiment of the present application;
FIG. 7 is a cloud chart of the compression amount of the gasket under the pre-tightening condition in the embodiment of the application;
FIG. 8 is a stress cloud plot of a gasket under operation in an embodiment of the present application;
FIG. 9 is a cloud graph of the amount of compression of the gasket under the operation conditions in the embodiment of the present application;
FIG. 10 is a graph of the allowable pipe bending moment determination in an embodiment of the present application.
Detailed Description
In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the present invention is described with reference to the following examples.
The invention discloses a method for predicting the leakage rate of flange connection, which comprises the following steps:
firstly, finishing a gasket performance test (namely a gasket cyclic compression rebound test) by referring to JIS B2490, and obtaining loading and unloading curves of the gasket under different stress levels, namely a relation curve between gasket stress and gasket compression deformation and a relation curve between leakage rate and gasket stress. In order to improve the leak rate prediction accuracy, the number of stress levels may be increased as appropriate. And (4) according to the gasket compression deformation and the gasket thickness recorded in the test, calculating the relative compression deformation of the gasket, and further obtaining the leakage rate and the relative compression deformation data of the gasket.
Second step, determination of basic leak rate leak model
Considering that the non-metal gasket is a porous medium, the flow of the gas medium through the porous medium of the gasket has laminar flow and molecular flow, the leakage flow is the sum of the laminar flow and the molecular flow, and the original leakage model is written as
In the formula ImIs the average length of the capillary; k is the number of leak paths, i.e. capillaries; r isjIs the leak path radius, i.e., the radius of the jth capillary; h is the dynamic viscosity of the medium; c is the capillary bending coefficient; p is a radical ofi、poThe inlet and outlet pressures of the capillary tube; p is a radical ofmThe average pressure of the inlet and the outlet of the capillary is; r isjIs the radius of the leakage path; t is the Kelvin temperature; m is the gas molar mass. p is a radical ofiThe subscript i of (a) represents an internal imide, poSubscript o of (a) represents outer outside. L represents a leak rate (Leakage rate).
Suppose the leakage path radius r of the gasket itselfjAnd the number k of leakage paths and the relative compression of the gasket
Have a negative exponential relationship between
In the formula ofaThe average value of the compression amount of the gasket represents the condition of uniform compression; t isaIs the average value of the thickness of the gasket, f1,f2And m 'and n' are undetermined constants.
The original leakage model is rewritten as
In the formula, l is the gasket pressing width; alpha, beta and n are undetermined constants.
In the formula (d)i、doThe gasket compresses the inner diameter and the outer diameter respectively.
When the gasket stress is low and the pressure of the sealed medium is high, the molecular flow can be ignored, so that
Obtaining a model of the base leak rate of
And according to the performance test data of the gasket, obtaining undetermined constants alpha and n by least square fitting. Equation (6) represents the gasket leak rate model for a uniformly compressed state.
Thirdly, calculating the compression deformation of the non-uniform compression gasket
A three-dimensional finite element model is established according to the symmetry of a flange connection structure and loads, the contact between a nut and a flange and the contact between a flange pressing surface and a gasket are fully considered in the model, the gasket performance adopts the cyclic compression gasket stress and gasket compression deformation data (cyclic compression rebound test) obtained by the test, pre-tightening and operation condition calculation are carried out, and then the gasket compression deformation distribution is obtained, the compression deformation is different, the radius and the number of porous medium leakage channels are different, and the leakage rate is different.
Fourth, calculating the leakage rate of the non-uniform compression gasket
And (4) carrying out flow guide calculation according to the uneven compression deformation distribution, and determining the leakage rate of the uneven compression gasket.
In the case of the gasket test device, since the rigidity of the gasket pressing device is sufficiently large, it can be considered that the gasket is uniformly pressed, and the compressive deformation amount δ of the gasket in the state considered to be uniformly pressedaIs a constant.
Introduction of the concept of 'conductance', uniform compaction of leakage rate LaCan be expressed as
Where C is conductance, which represents the ability of the leak path to pass gas, in liters per second (m)3In steady state, conductance is equal to the leakage path flow divided by the pressure difference across the leakage path.
For uniformly compressed gasket conductance CaIs composed of
In the formula
For non-uniform compression gaskets, the range of d theta (theta is a circumferential angle) considers that the compression amount of the gasket is uniformly distributed along the circumferential direction and is only non-uniformly distributed along the radial direction, and the position with the radius r defines the flow conductance c as
In the formula, rmIn the form of an average radius,
δrthe amount of compressive deformation of the gasket at the position of radius r, at which is deltaaCompression of gasket in d theta rangeAverage value of deformation amount.
The inverse of the conductance of the d θ range pad is equation (12), equation (12) is the integration in the radial direction
Then multiplying the conductance obtained by the formula (12) by rmIntegration in the circumferential direction (i.e., integration over the circumferential angle θ) yields a conductance C of the non-uniform compression pad of
The non-uniform compression flange connection then has a leakage rate L of
In this formula, the relative compressive deformation amount of the gasket
Is the average value of the compressive deformation of the gasket in the range of d theta/the average value of the thickness of the gasket in the range of d theta, deltaaCan be regarded as a function of the circumferential angle theta, and for convenience of calculation, the average value of the compression deformation of the gasket in the angle range, T, can be takenaThe shim thickness is an average measurement that can be taken at a fixed value throughout the calculation.
According to the invention, because the rigidity of the flange is limited, the number of bolts is limited, the flange can deflect and warp under the action of internal pressure, the gasket can not be uniformly compressed, and the phenomenon of non-uniformity occurs, the non-uniform compression flange connection leakage rate prediction model provided by the invention can be directly used for the non-uniform compression flange connection leakage rate, namely the formula (14), according to the formula, under the condition that the compression deformation amount of the gasket at each constant and any radius position is known, the non-uniform compression flange connection leakage rate under different working conditions can be directly and simply obtained.
Examples
A flange connection of a certain pipeline adopts a welding flange with a neck, the nominal pressure is PN16, the nominal diameter is DN50, the medium is octafluorocyclobutane, the working pressure P is 0.2MPa, the design temperature is 20 ℃, the concave-convex surface is sealed, and the material is S30408. A polytetrafluoroethylene gasket is adopted, and the thickness of the gasket is 1.6 mm. The pipe has the size phi 57x3.5, the material is S30408, and the pipe system load bending moment M is 1x106N.mm, fastener material a2-70, the leak rate of the flange connection was predicted.
Firstly, a leakage rate test is carried out on a polytetrafluoroethylene gasket according to JIS B2490, the test pressure is 2MPa, the test temperature is 20 ℃, the test medium is helium, and the gasket thickness T isa1.6mm, 49mm of the inner diameter of the gasket and 90mm of the outer diameter of the gasket. Obtaining shim stress sigmaeAmount of compression deformation delta from gasketaRelationship between (FIG. 1), basic leak rate LsAnd gasket stress sigmaeRelationship between (FIG. 2) and the basic leak rate LsAmount of compression deformation δ relative to gasketa/TaThe relationship between (fig. 3).
Second, the basic leakage rate L obtained according to the testsAmount of compression deformation δ relative to gasketa/TaPerforming parameter fitting on the data to obtain the undetermined constant in the formula (6), wherein the fitting formula is the formula (15)
The relation between the basic leakage rate and the relative compression deformation of the gasket obtained after deformation according to the formula (15) is shown as a formula (16)
Helium viscosity at 20 ℃ of 1.89x10-5Pa.s, test pressure 2MPa, pi-po＝2MPa，pmWhen the absolute pressure was 1.1MPa, α in formula (6) was 1.9387x10-23。
Substituting the determinations alpha and n into equation (6) to obtain the current basic leak rate prediction model of
Thirdly, calculating the compression deformation of the non-uniform compression gasket
1. Material properties
The performance of the flange and fastener materials can be found from GB/T150-2014 Steel pressure vessel, the elastic modulus of the material at the design temperature is 195GPa, and the Poisson ratio is 0.3. The gasket compression resilience performance data is shown in figure 1. The specific gasket pressure y is 20.7MPa, and the gasket coefficient m is 3.
2. Finite element model
Since the influence of the bending moment on the sealing performance needs to be considered, 1/2 models (11 in fig. 4 represents a local cylindrical coordinate system number in data processing) are established, wherein bolts are arranged across the center.
The connecting pipe, the flange and the bolt and nut are all made of SOLID185 units of ANSYS software, the gasket is made of INTER95 units, the bolt is pre-tightened by PRETS179 units, and TARGE170 and CONTA174 units are adopted for the nut-flange contact pair and the flange-gasket contact pair. The mesh generation is shown in fig. 5.
3. Load and restraint
Symmetrical constraint is applied to the symmetrical surface, and axial and circumferential constraint is applied to the end face of the lower connecting pipe.
Pre-tightening force F of each bolt calculated according to GB/T150-2014boltIs 1.53x104N, applied to two bolts in the model. A medium pressure P of 0.2MPa is applied to the inner surface of the structure, and an axial balance surface load P is applied to the end surface of the upper connecting pipeend，PendCalculated as equation (18).
Where K is the diameter ratio of the connecting pipe and K is 1.14, P is calculatedend＝0.668MPa。
The bending moment is applied thereto in the form of a surface loadPartial pipe end, face load gradient SgradIs composed of
Wherein I is the sectional axial moment of inertia.
In the formula Do、DiRespectively the outer diameter and the inner diameter of the connecting pipe.
For this example, Sgrad＝4.73MPa/mm。
4. Calculation results
The stress cloud picture of the gasket under the pre-tightening working condition is shown in fig. 6, and the compression deformation cloud picture of the gasket is shown in fig. 7, and the stress cloud picture and the compression deformation cloud picture can be used for checking whether the pre-tightening calculation result is correct or not. The stress cloud picture of the gasket under the action of the internal pressure and the bending moment is shown in figure 8, and the compression deformation cloud picture of the gasket is shown in figure 9. And further obtain the distribution of the compression deformation of the gasket under the corresponding working condition.
Fourth, calculating the leakage rate of the non-uniform compression gasket
According to the compression deformation cloud chart of the gasket shown in fig. 9, it can be seen that the compression deformation amounts of the gaskets at different positions (i.e., at different radius positions of the gasket) are different, the conduction capacities of the fluids are different, the compression deformation amount of the gasket at any radius position can be obtained from the compression deformation amount distribution of the gasket, and the relative compression deformation amount of the gasket is the ratio of the compression deformation amount of the gasket to the thickness of the gasket; and (3) calculating the leakage rate of the unevenly pressed gasket by using an equation (14) according to the relative compression deformation of the gasket at different positions, wherein the average value of the compression deformation of the gasket in the range of d theta is introduced as an intermediate variable for convenience of expression of the equation. The bending moment M obtained according to the formula (14) is 1.2x106Leak rate at N.mm, wherein octafluorocyclopropane viscosity is 1.2x10-5Pa.s. Calculated leak rate of 1.812x10-2Pa.m3S, i.e. 1.812x10-2MPa.mL/s。
Calculation of the different bending moments and leakage rate using equation (14) is required to obtain figure 10,
the magnitude of the bending moment is changed to obtain the corresponding distribution of the compression deformation of the gasket under different bending moments, and then the leakage rate under the action of different piping system loads can be obtained through a formula (14). From the allowable leak rates, the allowable bending moment loads at the flange connection locations can be determined (fig. 10). For example, when the allowable leakage rate is 0.02MPa · mL/s, the allowable bending moment M is 1.2 × 10 at the set working pressure P of 0.2MPa6N·mm。
And similarly, the working pressure P and the bending moment M are changed to obtain the corresponding compression deformation distribution of the gasket under different working pressures and bending moments, and then the leakage rate under the action of different bending moments under different working pressures can be obtained through a formula (14), and further the allowable bending moment under the allowable leakage rate under different working pressures can be obtained.
The principle of the invention is as follows:
obtaining gasket stress, leakage rate, gasket thickness and gasket compression deformation data by using a uniform compression gasket leakage test, and determining a correlation formula of the basic leakage rate and the relative compression deformation of the gasket, namely a formula (17);
establishing a finite element analysis model for flange connection of the non-uniformly compressed non-metallic gasket, and acquiring the distribution of compression deformation of the gasket under the operating condition (the operating condition comprises different working pressures, different bending moment loads and different pre-tightening forces);
and obtaining the compressive deformation of the gasket at any radius position from the compressive deformation distribution of the gasket, introducing a 'conductance' concept, integrating the conductance with radius r in the circumferential angle range d theta in the radial direction and the circumferential direction respectively to obtain the conductance of the unevenly compacted gasket, and calculating the leakage rate.
The method for establishing the model and subdividing the mesh is common knowledge in the field.
The method is suitable for leakage prediction of flange connection of the non-uniformly-compressed non-metallic gasket.
Nothing in this specification is said to apply to the prior art.
Claims (3)
1. A method for predicting the leakage rate of flange connection comprises the following steps;
let the radius r of the leakage path of the gasket itselfjAnd the number k of leakage passages and the amount of relative compressive deformation of the gasket
The radius of the leakage channel and the quantity of the leakage channel are respectively expressed by a function related to the relative compression deformation of the gasket, and the basic leakage rate is expressed in a form related to the relative compression deformation of the gasket, so that a basic leakage rate prediction model of an equation (6) is obtained:
in the formula, eta is dynamic viscosity of the medium; p is a radical ofi、poThe inlet and outlet pressures of the capillary tube; p is a radical ofmThe average pressure of the inlet and the outlet of the capillary is; ls represents the base leak rate; alpha and n are undetermined constants and are obtained through test fitting; di、doRespectively compressing the inner diameter and the outer diameter by a gasket, wherein l is the compressing width of the gasket; deltaaIs the amount of compression deformation of the gasket, TaIs the thickness of the gasket;
guiding the uniformly compressed gasketaIs defined as
Respectively carrying out radial and circumferential integration on the flow conductance with the radius r in the circumferential angle d theta range to obtain the flow conductance of the uneven compression gasket, and multiplying the flow conductance of the uneven compression gasket by the pressure difference of an inlet and an outlet of a capillary tube to obtain a prediction model of the connection leakage rate of the uneven compression flange;
according to the prediction model of the non-uniform compression flange connection leakage rate, the non-uniform compression gasket flange connection leakage rate can be obtained under the condition that the gasket compression deformation amount at any radius position is known;
the expression of the prediction model of the leakage rate of the non-uniform compression flange connection is represented by formula (14):
where θ is the circumferential angle, L is the leak rate, C is the conductance of the non-uniform compression pad, and ri、roRespectively the inner and outer diameters, delta, of the leakage pathrThe compression deformation of the gasket at the position with the radius of r;
the radius of the leakage path and the number of the leakage paths are expressed by a function of the relative compressive deformation of the gasket, and the specific expression is formula (2)
In the formula f1,f2And m 'and n' are undetermined constants.
2. The prediction method of claim 1, wherein the data used for establishing the three-dimensional finite element model is obtained by a gasket cyclic compression rebound test, wherein in the gasket cyclic compression rebound test, a gasket leakage rate, a gasket compression deformation, a gasket stress and a gasket thickness are recorded, a gasket relative compression deformation is obtained, and a relationship curve between the gasket stress and the gasket compression deformation and a corresponding relationship between the leakage rate and the gasket relative compression deformation are obtained;
and (3) determining the values of undetermined constants alpha and n in the formula (6) according to the corresponding relation between the leakage rate obtained by the test and the relative compression deformation of the gasket.
3. The prediction method of claim 1, wherein the contact between the nut and the flange, and between the flange pressing surface and the gasket are fully considered in the establishment of the three-dimensional finite element model, and pre-tightening and operation condition calculation are performed to obtain the distribution of the compression deformation of the gasket under the operation condition.
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| 《基于温度场分析的安注管线止逆阀内漏监测方法研究》;董晓梅等;《核科学与工程》;20200831;全文 * |
| 《基于螺栓力的法兰连接泄漏率预测模型研究》;庄法坤等;《化工设备与管道》;20171231;全文 * |
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