CN1499183A - Calculation method for leakage flow of leakage tester - Google Patents

Abstract

The leak air flow rate Q1 is calculated according to the equations shown in formulas 17 and 18, wherein P<SB>T</SB>is test pressure, V<SB>m0</SB>is the initial capacity of a standard container, k<SB>s</SB>is the coefficient of a differential pressure sensor, P<SB>a</SB>is atomspheric pressure, V<SB>e</SB>is the equivalent capacity of a measuring container, and V<SB>w0</SB>is the initial capacity of the measuring container.

Description

The computing method of the leakage flow of leak tester

Technical field

The present invention relates to calculate the method for the leakage flow that spills from pneumatic cylinder etc. with leak tester.

Background technology

For the structural detail of the positive displacement of pneumatic cylinder etc., sealing is one of most important index about product property.Utilize differential pressure pickup to measure and have the pressure reduction between the tested container (Work container) of leakage to change the leakage flow that calculates tested container at leak free volumetric standard (benchmark) under the identical original pressure condition.This measuring method has measurement mechanism simple, easy acquisition testing signal, easy to operate a plurality of advantages.Traditional measurement model that utilizes pressure reduction comparison principle measurement leakage air as shown in Figure 1.In Fig. 1, on the pipeline of pneumatic supply with 1 of volumetric standard, on the pipeline of pneumatic supply with 2 of tested containers, dispose cut-off valve V1 and cut-off valve V2 respectively.Differential pressure pickup 3 is configured on the pipeline that is communicated with volumetric standard 1 and tested container 2.

As previously mentioned, volumetric standard 1 is the container that does not have leakage, and tested container 2 is the containers that have minute quantity to leak.When detecting, open cut-off valve V1 and V2, pressurized air flows in two containers simultaneously.Air pressure in two containers reaches closes two cut-off valve V1 and V2 in stable.Because in tested container 2 leakage is arranged, internal pressure descends continuously.So the pressure reduction between two containers increases continuously.Leakage flow is many more, and the variation of pressure reduction is fast more.Use this method, determine the leakage flow of tested container 2 according to computing method described later.

The computing method of traditional leakage flow are that the variation of supposition pressure reduction is linear, have ignored the influence of continuous decline to leaking of interior pressure.Utilize following formula (1) simply must calculate leakage flow.

$Q_l=\frac{V_e}{P_a}\&CenterDot;\frac{{\mathrm{\&Delta;P}}_t}{\mathrm{\&Delta;t}}---\left(1\right)$

In addition, according to the practical experience relevant with measuring condition, Measuring Time Δ t is by given in advance.Δ Pt/ Δ t is the variable quantity of pressure reduction.

Although the variation of classic method supposition pressure reduction is linear, is non-linear actually, exist suitable error between the leakage of measured value and reality.

Summary of the invention

The present invention is first problem with the method (theoretical formula) of seeking the high precision computation leakage flow, is second problem with the error of calculating leakage flow.

At first, the symbol that is used for the present invention's calculating is described.

K _s: the coefficient t of differential pressure pickup _ζ: the initial detecting time (the unknown during detection)

L: the length V of leak _e: the volume of equal value of measured container

M: the quality V of air _l: the volume of leakage air

N: the data number V of trial target _m: the volume of volumetric standard

P _a: atmospheric pressure V _M0: the original volume of volumetric standard

P _m: the air pressure V in the volumetric standard _S: the internal volume of differential pressure pickup

P _T: test pressure V _W: the volume of measured container

P _W: the air pressure V in the measured container _W0: the original volume of measured container

Q _l: the leakage flow Δ P under the atmospheric pressure _t: the variable quantity of the interior pressure reduction of Δ t detection time

R: air constant Δ P: pressure reduction

R: the radius Δ t of leak: Measuring Time

T: air themperature μ: the kinematic viscosity coefficient of air

T: time

Computing method of the present invention are carried out in order to measure the leakage of air flow.Based on the principle of the air flow of leak (supposition aperture is arranged), can obtain containing the theoretical formula of the leakage flow of unknown parameter in periphery.According to the parsing of statistics aspect, the unknown parameter in the mathematical model of pressure reduction, in other words the unknown parameter in the theoretical formula of leakage flow can be calculated out by the test of pressure reduction.Thus, can calculate leakage flow, equally also can extrapolate the error of leakage flow.

The shortcoming of classic method is: the variable quantity of pressure reduction is affected along with the variation of the Measuring Time that begins from initial detecting.In addition, under the actual detection condition, it not is linear that the pressure of measured container changes.Think that in theory mobile leakage air is an isothermal flow.Based on the Hagen-Poiseuille rule, leakage flow is represented with following theoretical formula.

$Q_l=\frac{{\mathrm{\&pi;<figure-callout\; id="4"\; label="r"\; filenames="A03152645.400111.png"\; state="\{\{state\}\}">r</figure-callout>}}^4}{16\mathrm{\&mu;l}}\&CenterDot;\frac{P_w^2-P_a^2}{P_a}---\left(2\right)$

Exploration also confirms that the position of leak is difficult, and same measurement parameter r and 1 also is difficult, so, calculate the invariant parameter r and 1 in the aforesaid equation in the following method.

The equation of state of the certain air capacity in the container can be expressed with following formula.

PV＝mRT (3)

Think that the air themperature that is spilling is certain.

Behind formula (3) differential, the equation below deriving.

Volumetric standard one side:

$P_m\frac{{\mathrm{dV}}_m}{\mathrm{dt}}+V_m\frac{{\mathrm{dP}}_m}{\mathrm{dt}}=0---\left(4\right)$

Measured container one side

$P_w\frac{{\mathrm{dV}}_w}{\mathrm{dt}}+V_w\frac{{\mathrm{dP}}_w}{\mathrm{dt}}=-P_a\frac{{\mathrm{<figure-callout\; id="1"\; label="dV"\; filenames="A03152645.400101.png"\; state="\{\{state\}\}">dV</figure-callout>}}_1}{\mathrm{dt}}---\left(5\right)$

The equation of the pressure reduction between two containers can followingly be represented.

ΔP＝P _m-P _w (6)

The differential equation that produces the volume-variation when leaking is as follows.

$\frac{{\mathrm{dV}}_s}{\mathrm{dt}}=\frac{{\mathrm{dV}}_m}{\mathrm{dt}}=-\frac{{\mathrm{dV}}_w}{\mathrm{dt}}=k_s\frac{{\mathrm{dP}}_w-d{P}_m}{\mathrm{dt}}---\left(7\right)$

After formula (2), can write out the equation of following leakage flow.

$\frac{{\mathrm{<figure-callout\; id="1"\; label="dV"\; filenames="A03152645.400101.png"\; state="\{\{state\}\}">dV</figure-callout>}}_1}{\mathrm{dt}}=Q_l=\frac{{\mathrm{\&pi;<figure-callout\; id="4"\; label="r"\; filenames="A03152645.400111.png"\; state="\{\{state\}\}">r</figure-callout>}}^4}{16\mathrm{\&mu;l}}\&CenterDot;\frac{P_w^2-P_a^2}{P_a}---\left(8\right)$

Because be small leakage, can carry out following supposition during calculating.

P _m=P _T, P _W=P _T, V _m=V _M0, V _W=V _W0With above-mentioned differential equation from initial detecting time t _ζ

Behind the beginning integration, it is as follows to obtain pressure differential deltap P.

$\mathrm{\&Delta;p}=\frac{V_{\mathrm{<figure-callout\; id="0"\; label="m"\; filenames="A03152645.400111.png"\; state="\{\{state\}\}">m</figure-callout>}0}\&CenterDot;[P_T-P_a-\frac{2\frac{P_T-P_a}{P_T+P_a}{e}^{-c(t-\mathrm{t\&zeta;})}}{1-\frac{P_T-P_a}{P_T+P_a}{e}^{-c(t-\mathrm{t\&zeta;})}}\&CenterDot;P_a]}{k_s{P}_T+V_{m0}}---\left(9\right)$

Here,

$C=\frac{P_a\&CenterDot;\frac{{\mathrm{\&pi;<figure-callout\; id="4"\; label="r"\; filenames="A03152645.400111.png"\; state="\{\{state\}\}">r</figure-callout>}}^4}{8\mathrm{\&mu;<figure-callout\; id="0"\; label="l\; V\; m"\; filenames="A03152645.400111.png"\; state="\{\{state\}\}">l</figure-callout>}}}{V_m}---\left(10\right)$

Measure pressure differential deltap P along detection time, be suitable for the principle of LSD (least significant difference LeastSignificant Difference).Parametric t _ζWith C be unknown.For easy wushu (a 9) displacement accepted way of doing sth (11).

y＝a+C _t (11)

Here,

$y=\ln \frac{P_T+P_a-(l+\frac{k_s{P}_T}{V_m})\mathrm{\&Delta;P}}{P_T-P_a-(l+\frac{k_s{P}_T}{V_m})\mathrm{\&Delta;P}}---\left(12\right)$

$a=\ln \frac{P_T+P_a}{P_T-P_a}-C_{\mathrm{t\&zeta;}}---\left(13\right)$

Utilize the simple regression analysis method, can from formula (14) and formula (15), extrapolate unknown parameter t _ζAnd C.

$C=\frac{S_{\mathrm{ty}}}{S_t}=\frac{\underset{i=l}{\overset{n}{\mathrm{\&Sigma;}}}(t_i-\stackrel{\_}{t})(y_i-\stackrel{\_}{y})}{\underset{i=l}{\overset{n}{\mathrm{\&Sigma;}}}{(t_i-\stackrel{\_}{t})}^2}---\left(14\right)$

$\ln \frac{P_T+P_a}{P_T-P_a}-C_{\mathrm{t\&zeta;}}=\frac{l}{n}\underset{i=l}{\overset{n}{\mathrm{\&Sigma;}}}\frac{P_T+P_a-(l+\frac{k_s{P}_T}{V_m})\mathrm{\&Delta;}{P}_i}{P_T-P_a-(l+\frac{k_s{P}_T}{V_m})\mathrm{\&Delta;}{P}_i}-\frac{S_{\mathrm{ty}}}{S_t}\&CenterDot;\frac{l}{n}\underset{i=l}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i---\left(15\right)$

In addition, in formula (14), in (15), t _iBe n data t ₁, t ₂..., t _i..., t _nIn a certain data, y _iBe n data y ₁, y ₂..., y _i..., y _nIn a certain data.

Based on above-mentioned analysis, in actual measurement, the leakage flow of container reduces with the continuous reduction of the internal pressure of measured container., under a certain test pressure, the leakage flow of container is used as the air mass flow that flows to external container in the container usually and considers.So the calculating formula of leakage flow can be write as following form.

$Q_l=\frac{\mathrm{d\&Delta;P}}{\mathrm{dt}}{|}_{\mathrm{\&Delta;P}=0}\&CenterDot;\frac{V_e}{P_a}---\left(16\right)$

In formula (14) substitution formula (16).

$Q_l=\frac{V_{m0}}{k_s{P}_T+{\mathrm{<figure-callout\; id="0"\; label="V\; m"\; filenames="A03152645.400111.png"\; state="\{\{state\}\}">V</figure-callout>}}_m}\&CenterDot;\frac{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A03152645.400101.png,A03152645.400111.png"\; state="\{\{state\}\}">C</figure-callout>}}{2}\&CenterDot;\frac{P_T^2-P_a^2}{P_a}\&CenterDot;\frac{V_e}{P_a}---\left(17\right)$

Here,

$V_e={\mathrm{<figure-callout\; id="0"\; label="V\; w"\; filenames="A03152645.400111.png"\; state="\{\{state\}\}">V</figure-callout>}}_w+\frac{k_s{P}_T{V}_{m0}}{k_s{P}_T+V_{m0}}---\left(18\right)$

Formula (17) is the real leakage air flow that spills from container under a certain test pressure.Draw from formula (17), the systematic error of this method is determined by formula (19).

$\frac{\&PartialD;Q_l}{Q_l}=\sqrt{{\left(\frac{{2P}_T\&CenterDot;\mathrm{\&delta;}{P}_T}{P_T^2-P_u^2}\right)}^2+{\left(\frac{k_s{P}_T\&CenterDot;\mathrm{\&delta;}{V}_{m0}}{V_{m0}}\right)}^2+{\left(\frac{{\mathrm{\&delta;}V}_{w0}}{{\mathrm{<figure-callout\; id="0"\; label="V\; w"\; filenames="A03152645.400111.png"\; state="\{\{state\}\}">V</figure-callout>}}_w+\frac{k_s{P}_T{V}_{m0}}{k_s{P}_T+V_{m0}}}\right)}^2+{\left(\frac{\mathrm{\&delta;C}}{C}\right)}^2}---\left(19\right)$

The error that is formed by the systematic error delta P of pressure transducer approximately is ± 0.0112MPa.Think the error delta V that the volume measurements of measured container and volumetric standard causes _W0With δ V _M0Be ± 2 cubic centimetres.δ C is the statistical error of calculation of unknown parameter C, and δ C represents with following formula.

$\mathrm{\&delta;C}=\&PlusMinus;t({\mathrm{\&phi;}}_e,0.01)\sqrt{V_e/S_t}---\left(20\right)$

In addition, ζ C is approximately equal to 0.After amounting to above-mentioned error, systematic error is approximately 8.2% (P _T=0.5MPa).

The computing method of the leakage flow of the described leak tester of claim 1 are the computing method of high precision leakage flow.Can calculate the error of leakage flow with the described computing method of claim 2.

Description of drawings

Fig. 1 is the key diagram that shows the measurement model of traditional leak tester.

Fig. 2 is the key diagram of experimental provision that is used for the air leakage flow of measuring vessel.

Fig. 3 be presented under a certain condition about the experimental data of leakage flow and pressure reduction and the chart of simulation.

Fig. 4 be presented under other conditions about the test data of leakage flow and pressure reduction and the chart of simulation.

Fig. 5 shows the experimental result of the precision be used to confirm computing method of the present invention, Fig. 5 (a) is presented at the test result under the test pressure 0.2MPa, Fig. 5 (b) is presented at the test result under the test pressure 0.5MPa, and Fig. 5 (c) is presented at the experimental result of a certain leak.

Preferred embodiment

Be used for measuring vessel the air leakage flow experimental provision as shown in Figure 2, this is to be used for the device that compares with the result that computing method of the present invention obtain.In Fig. 2, the pressurized air that comes from pneumatic supply is by pressure regulator valve 11 pressure regulation, and the pressurized air after the pressure regulation is measured by tensimeter 12, is input in the A/D converter.In addition, the pressurized air after the pressure regulation may pass through reversal valve 13, and switch valve 15 flows in the volumetric standard 17, also may flow in the measured container 18 by switch valve 16 simultaneously.Differential pressure pickup 19 is configured on the pipeline that is communicated with volumetric standard 17 and measured container 18, and the output signal of differential pressure pickup 19 is imported in the A/D converter 14.Measure the leakage flow that spills from measured container 18 with flowmeter 20, leakage flow is released in the atmosphere by pettiness flow breakout box 21.The output signal of flowmeter 20 is input in the A/D converter 14.

Think that jumbo flowmeter is an inside caliper.Computing machine 22 and A/D converter are used to measure test pressure, pressure reduction between two containers and pettiness leakage flow.The original volume of volumetric standard 17 and tested container 18 is respectively 310.3 cubic centimetres and 376.8 cubic centimetres.

Use experimental provision shown in Figure 2, under same pressure (0.5MPa), test.From experimental data and with its corresponding simulating result, obtain Fig. 3 and Fig. 4.Learn that Simulation result and experimental data based on computing method of the present invention meet very much.

At different leaks, carry out the precision that computing method of the present invention are confirmed in considerable test under the condition of different test pressures.Measurement result as shown in Figure 5.From this table as can be known, computing method of the present invention are than traditional method precision height.

Utilize pressure reduction comparative method for measuring leakage of air flow, proved that it is non-linear that pressure reduction changes.Thus, traditional as can be known computing method are not enough as the measuring method accuracy of air leakage flow.

Adopt actual pettiness flow equation formula and statistical method to propose to be used to measure the computing method of the present invention of air leakage flow.Between the leakage flow of computing method of the present invention and reality, more unanimity is arranged.Compare with traditional computing method, improved the measuring accuracy of air leakage flow.

Claims (2)

1. the computing method of the leakage flow of leak tester are P at test pressure _TPressurized air flow in volumetric standard and the tested container and on the pipeline that is communicated with volumetric standard and tested container and dispose in the leak tester of differential pressure pickup, it is characterized in that: when the original volume of volumetric standard is V _M0, the coefficient of differential pressure pickup is Ks, and atmospheric pressure is Pa, and the volume of equal value of measured container is Ve, and the original volume of measured container is V _W0The time, leakage air flow Q _lBy following formula (17), calculate (18).

$Q_l=\frac{V_{m0}}{k_s{P}_T+V_{m0}}\&CenterDot;\frac{C}{2}\&CenterDot;\frac{P_T^2-P_a^2}{P_a}\&CenterDot;\frac{V_e}{P_a}---\left(17\right)$

$V_e=V_{w0}+\frac{k_s{P}_T{V}_{m0}}{k_s{P}_T+V_{m0}}---\left(18\right)$

2. the computing method of the leakage flow of leak tester according to claim 1 is characterized in that: when the volume of measured container is V _WThe time, the error of leakage flow is calculated by following formula (19).

$\frac{\&PartialD;Q_l}{Q_l}=\sqrt{{\left(\frac{{2P}_T\&CenterDot;{\mathrm{\&delta;P}}_T}{P_T^2-P_u^2}\right)}^2+{\left(\frac{k_s{P}_T\&CenterDot;{\mathrm{\&delta;V}}_{m0}}{V_{m0}}\right)}^2+{\left(\frac{{\mathrm{\&delta;V}}_{w0}}{V_{w0}+\frac{k_s{P}_T{V}_{m0}}{k_s{P}_T+V_{m0}}}\right)}^2+{\left(\frac{\mathrm{\&delta;C}}{C}\right)}^2}---\left(19\right)$

Images