CN102494992A - Accelerated degradation testing method for nitrile rubber O-shaped sealing ring based on step stress - Google Patents

Abstract

The invention discloses an accelerated degradation testing method for a nitrile rubber O-shaped sealing ring based on step stress, which includes the concrete steps: firstly, preliminarily testing the nitrile rubber O-shaped sealing ring; secondly, determining an accelerated simulation model and the stress level of a formal test; thirdly, testing step-stress accelerated degradation of the nitrile rubber O-shaped sealing ring; fourthly, arranging degradation data; and fifthly, building an accelerated degradation model for predicting the reliable life of the sealing ring. By means of applying the step stress, testing cost and testing time can be greatly reduced, and an example verification failure mechanism is unchanged. Evaluation of the degradation data is based on a plurality of degradation paths of a plurality of test specimens, errors caused by difference among the specimens can be greatly reduced, and the reliability of evaluation results is higher than that of aging life prediction.

Description

Accelerated degradation test method based on the nitrile rubber O RunddichtringO of stepstress

Technical field

The present invention is a kind of accelerated degradation test method of the nitrile rubber O RunddichtringO based on stepstress, belongs to the accelerated degradation test technical field.

Background technology

Research to accelerated degradation test at present mainly concentrates on the reliability assessment of electronic products such as light emitting diode, laser instrument, logical integrated circuit, power supply, insulator, medicine; Degeneration research to this material type product of rubber mainly is the method for accelerated aging test, seldom sees and adopts the method for accelerated degradation test that it is studied.It is constant that the test method stress of accelerated deterioration applies mode; Test period is long; And the model of assessing its aging life-span is based on the single aging track under each constant stress, and this does not consider the bigger error that the otherness between the sample is brought, and assessment models is also fairly simple.The advantage of quickening the test assessment method of degeneration is to quicken the test figure of the foundation of degradation model based on a plurality of test samples; This has just significantly reduced the influence that the difference between the sample causes assessment result, thereby effectively improves the credibility of life of product assessment.And the mode that applies of quickening stress is divided into three kinds: promptly constant stress, stepstress and preface are advanced stress.The mode that applies that preface is advanced stress is complicated; The difficult control of process; Generally seldom adopt; The mode that applies that adopts stepstress can be to a great extent than constant stress saving test period and cost, also be the exploration of a success so adopt the accelerated degradation test method of stepstress that it is studied to rubber seal.

Summary of the invention

The objective of the invention is shortening test period largely; Reduce cost; Improve the reliability of rubber seal life appraisal, propose a kind of accelerated degradation test method of the nitrile rubber O RunddichtringO based on stepstress, specifically be with nitrile rubber O RunddichtringO compression deformation rate as amount of degradation; As quickening stress, adopt the mode that applies of stepstress that it is carried out accelerated degradation test with temperature.The test degraded data is adopted the reliability estimation method based on Brownian Motion with Drift, and the bound rubber self character has defined the notion of using failure threshold, product is used in difference carry out the Q-percentile life prediction under failure threshold and the different temperatures.

The accelerated degradation test method of a kind of nitrile rubber O RunddichtringO based on stepstress of the present invention, concrete steps are:

The trial test of step 1, nitrile rubber O RunddichtringO;

Step 2, confirm the stress level of degeneration model of fit and official test;

Step 3, nitrile rubber O RunddichtringO stepstress accelerated degradation test;

Step 4, arrangement degraded data;

Step 5, foundation are quickened degradation model O-ring seal are carried out the Q-percentile life prediction.

The invention has the advantages that:

(1) accelerated aging test that in the past was directed against rubber seal is based on steady temperature stress, and the present invention adopts the mode that applies of stepstress can practice thrift experimentation cost and test period widely, and the case verification failure mechanism can not change;

(2) life prediction of the accelerated aging test of rubber ring in the past is based on an aging track of a plurality of samples under each steady temperature stress; This has ignored the difference between the rubber ring itself; Error is bigger, and it is not accurate enough to predict the outcome, and the assessment of degraded data is based on many degeneration tracks of a plurality of test samples; Can reduce the error that difference caused between the sample greatly, and assessment result has higher fiduciary level than the aging life-span prediction;

(3) propose the notion that rubber ring uses failure threshold, obtain the fiduciary level in the life-span under different failure threshold and the different temperatures, make analysis result more comprehensive, can more effectively analyze the influence of O-ring seal system.

The explanation of accompanying drawing table

Fig. 1 is a method flow diagram of the present invention;

Fig. 2 is the degradation trend figure of the trial test of the embodiment of the invention;

Fig. 3 is the different model fitting results of the 1# O-ring seal of the embodiment of the invention;

Fig. 4 is the different model fitting results of the 2# O-ring seal of the embodiment of the invention;

Fig. 5 is the different model fitting results of the 3# O-ring seal of the embodiment of the invention;

Fig. 6 is the different model fitting results of the 4# O-ring seal of the embodiment of the invention;

Fig. 7 is the different model fitting results of the 5# O-ring seal of the embodiment of the invention;

Fig. 8 is the different model fitting results of the 6# O-ring seal of the embodiment of the invention;

Fig. 9 is whole sample degradation trend figure under the stepstress;

Figure 10 is that degraded data is handled back degeneration trend map;

It is the fiduciary level curve under 60% the different temperatures that Figure 11 is to use failure threshold;

It is the fiduciary level curve under 55% the different temperatures that Figure 12 is to use failure threshold;

Embodiment

To combine accompanying drawing and embodiment that the present invention is done further detailed description below.

The present invention is a kind of accelerated degradation test method of the nitrile rubber O RunddichtringO based on stepstress, and flow process is as shown in Figure 1, comprises following step:

The trial test of step 1, nitrile rubber O RunddichtringO;

For the maximum temperature that can bear of confirming to be tried the nitrile rubber O-ring seal, temperature stress apply value and method and performance degradation model of fit, so need carry out trial test to rubber seal, sample size is at least 3.

According to the rubber ring material behavior, choose a temperature and quicken stress, to drop into rubber ring and carry out steady temperature stress accelerated test, the performance test time is survey in a day.Specifically the test implementation step to rubber seal is:

1) sample pretreatment.Sample is compressed to the compression deformation rate of appointment through anchor clamps; Under standard temperature (23 ± 2 ℃), park and remove stress (being the pressure of anchor clamps) after 24 hours O-ring seal, let sample under free state, park 1h; Measure sample and park the thickness that recover the back, as the sample original depth before the test;

2) surveying instrument.The sample original depth is measured in rubber thicknessmeter zeroing (through the rotation dial plate, making its pointer aligned at zero scale mark), promptly measures the axial width of four distributed points on the circumference, gets its mean value;

3) with between disposable each pressing plate of putting into anchor clamps of sample, sample and limiter must not contact with each other, and guarantee that compression back sample does not contact mutually with limiter; The anchor clamps of sample of will packing into compress, and pressing plate is closely contacted with limiter, and fastening nut guarantees that in this process sample must not reverse;

The anchor clamps that 4) will install sample are parked 30min under laboratory temperature after, put into the incubator that arrives set point of temperature, and pick up counting;

5) from incubator, take out anchor clamps after the arrival stipulated time, open anchor clamps fast, take out sample, under free state, park 1h with tweezers;

6) measure the thickness after sample recovers height with the rubber thicknessmeter, concrete measuring method and the 2nd) go on foot identical, record data.

Step 2, confirm the stress level of degeneration model of fit and official test;

Data result to trial test is analyzed, and its degradation trend is carried out the match of mathematical model, chooses optimum model of fit.

Temperature stress with trial test is reference, confirms the stress level that official test applies.Concrete grammar is following:

1) the stress highest level should not surpass the working limit of product;

2) the primary stress level should be as far as possible near actual work temperature, and this is in order to improve the credibility of assessment, primary stress is not provided with simultaneously yet too high, in case product produces new failure mechanism, so want the initial temperature stress value is set at comprehensive these 2;

3) the temperature stress adjacent spaces is greater than and equals 10 ℃.

Step 3, nitrile rubber O RunddichtringO stepstress accelerated degradation test;

Drop into a plurality of samples and carry out official test, accelerated degradation test test sample quantity is many more, and assessment result is accurate more, minimumly must not be less than 7.

Be specially:

1) respectively goes on foot confirming of stress test time

Test period under the low stress should be higher than the test period under heavily stressed, and this is because performance degradation is slower under low stress, prolongs test period and can improve the precision of extrapolation; And product degradation is very fast under heavily stressed; In order to save test period, suitable shortening, so both can save time; Can reduce experimentation cost again, promptly stress of per step applies test period and reduces with the rising of temperature.

2) metering system

Adopt continuous non-destroyed measurement mode, the sample after promptly measuring is proceeded test, the degeneration track that obtains each sample that so just can be complete;

Measuring intervals of TIME is pressed regular pattern composite measuring mode successively, and promptly the measurement number of times of each sample is identical with Measuring Time point, can make degraded data make things convenient for data statistics and processing like this, and operability is stronger.

Step 4, arrangement degraded data;

Comprise the pre-service and the data conversion of degraded data.

1) pre-service to degraded data mainly is to reject unreasonable sample data; This is because there are differences between same batch the sample; And possibly the inner existence of some rubber seal damage; So through to the analysis of all sample degeneration geometric locuses, promptly find out variation abnormality (comprise that the degradation trend fluctuation is big, amount of degradation becomes big, singular point suddenly etc.), reject the degraded data after irrational sample or the variation abnormality.

2) data conversion mainly is the degeneration model of fit that obtains to trial test, and degraded data is carried out conversion process, and whether the data trend after the analyzing and processing is normal then, further rejects.

Step 5, foundation are quickened degradation model O-ring seal are carried out the Q-percentile life prediction;

The degeneration model of fit that can be known rubber seal by trial test meets the double-log mathematical model, and promptly the linear fit model of i sample is:

ln(Y _i)＝A _i+B _iln?x (1)

In the formula, A _i, B _iBe unknown parameter, make y _i=ln (Y _i), t=ln x, then formula (1) becomes linear model, that is:

y _i＝A _i+B _it (2)

Employing is assessed O-ring seal performance degradation data based on the degradation model of Brownian Motion with Drift, supposes that promptly error term is a Brownian motion process, obtains the model based on the linear drift Brownian movement, that is:

Y(t)＝σB(t)+d(s)t+y ₀ (3)

In the formula, Y (t) is a performance of products; T is a time scale; y ₀Be the starting point of Brownian Motion with Drift, promptly properties of product are at initial time t ₀Value; B (t) is the standard Brownian movement, and B (t)～N (0, t); D (s) is a degradation ratio, is and the irrelevant only relevant determinacy function with stress of time t, so is acceleration model; σ is a coefficient of diffusion, and σ＞0 does not change with stress and time, is constant.

Because as stress, stress S representes with temperature T, so acceleration model is chosen the relation that the Arrhenius model comes temperature of reaction stress and rubber seal compression deformation rate deterioration velocity, that is: with temperature in test

$d\left(T\right)=\frac{\∂Y\left(t\right)}{\∂t}={\mathrm{Ae}}^{-E_a/\mathrm{kT}}---\left(4\right)$

In the formula, Y (t) expression product performance index value or amount of degradation; D (T) is reaction velocity or catagen speed; A is a constant; E _aRepresent the activation energy of degradation mechanism; K representes Boltzmann (Boltzmann) constant, is 8.6171 * 10-5eV/K; T is an absolute temperature, and unit is K.

Make B=E _a/ k, then formula (3) becomes:

y(t)＝σB(t)+Aexp(-B/T)t+y ₀ (5)

Parameter A is the multiplier appearance as whole algebraic expression in the Arrenhius model, is an adjustment coefficient that does not have dimension; Activation energy E _a(=Bk) is the potential barrier that rubber seal exists to the failure state transfer process from normal not failure state; Parameter σ is that the coefficient of diffusion of compression deformation rate degeneration stochastic process is the coefficient of diffusion of rubber seal, and its size has mainly characterized the inconsistency with batch products, and its value shows that more greatly consistency of product is poor more.

The performance degradation data of rubber seal are described with useable linear Brownian Motion with Drift behind double log transformation of corresponding time, because Brownian movement is a kind of normal process, are d (T) Δ t so the increment of y (t) in the time of Δ t obeyed average, and variance is σ ²The normal distribution of Δ t, that is:

Δy(t)～N(d(T)Δt，σ ²Δt) (6)

If given properties of product degeneration critical value C, then its life-span is obeyed contrary Gaussian distribution, and Reliability Function is so:

$R\left(t\right)=\mathrm{\&Phi;}\left[\frac{C-y_0-d\left(T\right)t}{\mathrm{\&sigma;}\sqrt{t}}\right]-\exp \left(\frac{2d\left(T\right)\&CenterDot;(C-y_0)}{{\mathrm{\&sigma;}}^2}\right)\mathrm{\&Phi;}[-\frac{C-{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA0000119603110000012.png,HDA0000119603110000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0+d\left(T\right)t}{\mathrm{\&sigma;}\sqrt{t}}]---\left(7\right)$

Thereby unknown parameter is A, B, σ, can obtain this three parameters according to test figure, and the substitution following formula can obtain the Q-percentile life curve of product.Next finding the solution of these three parameters be described.

If total n rubber ring carries out the stepstress accelerated degradation test of K level; The time interval of in the test rubber ring being measured is Δ t, and is constant; Measurement number of times under each stress level is M ₁, detect M time altogether, have

Test period under each stress level then is M _lΔ t, total testing time are M Δ t; The time of at every turn monitoring is t _Ikj(i=1 ..., n; K=1 ..., K; J=1 ..., M), detected performance number is y _Ikj,

(1) estimation of unknown parameter A, B in the acceleration model

At first obtain the degradation ratio d (T) under each stress through the least square fitting degraded data;

Obtain A and B value through least square fitting d (T) and T value then.

(2) unknown parameter is σ

Parameter σ adopts maximum likelihood to estimate to obtain.Be specially: the increment Normal Distribution, its maximum likelihood function is:

$L\&Proportional;\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}\underset{j=1}{\overset{M_{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000119603110000021.png,HDA0000119603110000033.png"\; state="\{\{state\}\}">k</figure-callout>}}}{\mathrm{\&Pi;}}}\frac{1}{\sqrt{{2\mathrm{\&pi;\&sigma;}}^2\mathrm{\&Delta;t}}}\exp \{-\frac{{[(y_{\mathrm{ikj}}-y_{\mathrm{ik}(j-1)})-d\left(s_k\right)\mathrm{\&Delta;t}]}^2)}{{2\mathrm{\&sigma;}}^2\mathrm{\&Delta;t}}\}---\left(8\right)$

D (s in the formula (9) _k)=Aexp (B/T _k), so log-likelihood function is:

$\ln L\&Proportional;-\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{M_k}{\mathrm{\&Sigma;}}}\left\{\right[\ln \left(2\mathrm{\&pi;\&Delta;t}\right)+\ln \left({\mathrm{\&sigma;}}^2\right)]+\frac{{[(y_{\mathrm{ikj}}-y_{\mathrm{ik}(j-1)})-\mathrm{Aexp}(-B/T_k)\&CenterDot;\mathrm{\&Delta;t}]}^2}{{\mathrm{\&sigma;}}^2\mathrm{\&Delta;t}}\}---\left(9\right)$

Parameter σ in the formula (9) is asked partial derivative, make it equal zero, can obtain the maximum likelihood estimated value of σ.

Embodiment:

Nitrile rubber O RunddichtringO to using in certain type electricity liquid steering gear system is implemented the stepstress accelerated degradation test, and the trial test sample size is 6, and the official test sample size is 12; 4 temperature stress levels are 70 ℃, 80 ℃, 90 ℃, 100 ℃; Test period is 79 days, and measure dot number is 70 ℃ following 13,80 ℃ following 16; 90 ℃ following 17,100 ℃ following 14.By above-mentioned embodiment it is made an experiment.

The trial test of step 1, nitrile rubber O RunddichtringO;

Choose 90 ℃ as quickening stress, drop into six rubber rings and carry out the steady temperature accelerated test, survey the variation in thickness of a rubber every day.The degraded data of 6 samples that obtain is as shown in Figure 2.

Step 2, confirm the stress level of degeneration model of fit and official test;

With different data model the result of trial test is carried out match, it is best to choose fitting effect.Specifically like Fig. 3～shown in Figure 8 with shown in table 1～table 6.

Parameter analytical table under the different model of fit of table 11# O-ring seal

Parameter analytical table under the different model of fit of table 22# O-ring seal

Parameter analytical table under the different model of fit of table 33# O-ring seal

Parameter analytical table under the different model of fit of table 44# O-ring seal

Parameter analytical table under the different model of fit of table 55# O-ring seal

Parameter analytical table under the different model of fit of table 66# O-ring seal

Hence one can see that y=ax ^bThe variance and the degree of fitting of whole six samples of model all are superior to linear model y=ax+b, so this paper will choose y=ax ^bModel carries out the match of amount of degradation to rubber seal.To y=ax ^bTaking the logarithm simultaneously in both sides, can get:

lny＝lna+blnx (7)

In to certain type electricity liquid steering wheel investigation process, temperature can reach about 50 ℃ in the time of can knowing its work, and the highest withstand temperature of nitrile rubber is 120 ℃, and to sum up, choosing initial temperature stress is 70 ℃, and maximum temperature stress is 100 ℃, and step-length is 10 ℃.

Step 3, nitrile rubber O RunddichtringO stepstress accelerated degradation test;

It is as shown in Figure 9 that whole samples carry out the degradation trend of accelerated degradation test under the stepstress.

Step 4, arrangement degraded data;

It is shown in figure 10 after four pairs of data are rejected and handled set by step.

Step 5, foundation are quickened degradation model O-ring seal are carried out the Q-percentile life prediction.

It is as shown in table 7 that rubber seal is carried out the known parameters of SSADT.

The list of values of table 7 official test known parameters

Parameter	n	T 1	T 2	T 3	T 4
						Value	12	70	80	90	100
Parameter	K	M 1	M 2	M 3	M 4
						Value	4	13	16	17	14

With each parameter substitution formula (5) in the table 7, can get the parameter estimation of model, as shown in table 8.

Table 8 model parameter estimation table

So 25 ℃ of following Reliability Function are:

$R\left(t\right)=\mathrm{\&Phi;}\left[\frac{C-1.0044-0.023\&CenterDot;t}{0.047121\sqrt{t}}\right]-\exp \left(\frac{2\&times;0.023\&CenterDot;(C-1.0044)}{{0.047121}^2}\right)\mathrm{\&Phi;}[-\frac{C-1.0044+0.023\&CenterDot;t}{0.047121\sqrt{t}}]---\left(9\right)$

50 ℃ of following Reliability Function are:

$R\left(t\right)=\mathrm{\&Phi;}\left[\frac{C-1.0044-0.0799\&CenterDot;t}{0.047121\sqrt{t}}\right]-\exp \left(\frac{2\&times;0.0799\&CenterDot;(C-1.0044)}{{0.047121}^2}\right)\mathrm{\&Phi;}[-\frac{C-1.0044+0.0799\&CenterDot;t}{0.047121\sqrt{t}}]$

$\left(10\right)$

That is: when 1) using failure threshold C=0.6, the fiduciary level curve under 25 ℃ is shown in Figure 11 (a), and the fiduciary level curve under 50 ℃ (working temperature) is shown in Figure 11 (b).Hence one can see that, and 25 ℃ following when the life-span of rubber seal is 10a, corresponding reliable degree R (t)=0.9821; Under 50 ℃, the median life t of rubber seal _0.5=407d, the reliability R the when life-span is 0.5a (t)=0.7286.

When 2) using failure threshold C=0.55, the fiduciary level curve under 25 ℃ is shown in Figure 12 (a).Fiduciary level curve under 50 ℃ is shown in Figure 12 (b).Hence one can see that, and 25 ℃ following when the life-span of rubber seal is 10a, and the corresponding reliable degree is R (t)=0.9233.Under 50 ℃, the median life t of rubber seal _0.5=137d, the life-span is the reliability R (t)=0.6305 of 0.25a (promptly 3 months).

(annotate: a---unit: year, d---unit: day)

Claims (5)

1. the accelerated degradation test method based on the nitrile rubber O RunddichtringO of stepstress is characterized in that, comprises following step:

The trial test of step 1, nitrile rubber O RunddichtringO;

Confirm the quantity of sample nitrile rubber O RunddichtringO, choose temperature and quicken stress, sample is compressed to the compression deformation rate of appointment, drop into rubber ring O RunddichtringO and carry out steady temperature stress accelerated test, the performance test time is survey in a day;

Step 2, confirm the stress level of degeneration model of fit and official test;

Data result to trial test is analyzed, and its degradation trend is carried out the match of mathematical model, chooses optimum model of fit;

Temperature stress with trial test is reference, confirms the stress level that official test applies, and concrete grammar is following:

1) the stress highest level should not surpass the working limit of product;

2) the primary stress level should be as far as possible near actual work temperature, and the while is not provided with primary stress too high yet, in case product produces new failure mechanism;

3) the temperature stress adjacent spaces is greater than and equals 10 ℃;

Step 3, nitrile rubber O RunddichtringO stepstress accelerated degradation test;

Drop into a plurality of samples and carry out the accelerated degradation test test, be specially:

1) respectively goes on foot confirming of stress test time

Test period under the low stress should be higher than the test period under heavily stressed, and promptly stress of per step applies test period and reduces with the rising of temperature;

2) metering system

Adopt continuous non-destroyed measurement mode, the sample after promptly measuring is proceeded test;

Measuring intervals of TIME is pressed regular pattern composite measuring mode successively, and promptly the measurement number of times of each sample is identical with Measuring Time point;

Step 4, arrangement degraded data;

Comprise the pre-service and the data conversion of degraded data;

1) pre-service of degraded data is: through all sample degeneration geometric locuses, promptly find out variation abnormality, comprise that degradation trend fluctuation is big, amount of degradation becomes big, singular point suddenly, reject the degraded data after irrational sample or the variation abnormality;

2) data conversion is: the degeneration model of fit to trial test obtains, degraded data is carried out conversion process, and whether the data trend after the analyzing and processing is normal then, and abnormal data are rejected;

Step 5, foundation are quickened degradation model O-ring seal are carried out the Q-percentile life prediction;

The degeneration model of fit that can be known rubber seal by trial test meets the double-log mathematical model, and promptly the linear fit model of i sample is:

ln(Y _i)＝A _i+B _iln?x (1)

In the formula, A _i, B _iBe unknown parameter, make y _i=ln (Y _i), t=ln x, then formula (1) becomes linear model, that is:

y _i＝A _i+B _it (2)

Employing is assessed O-ring seal performance degradation data based on the degradation model of Brownian Motion with Drift, supposes that promptly error term is a Brownian motion process, obtains the model based on the linear drift Brownian movement, that is:

Y(t)＝σB(t)+d(s)t+y ₀ (3)

In the formula, Y (t) is a performance of products; T is a time scale; y ₀Be the starting point of Brownian Motion with Drift, promptly properties of product are at initial time t ₀Value; B (t) is the standard Brownian movement, and B (t)～N (0, t); D (s) is a degradation ratio, is and the irrelevant only relevant determinacy function with stress of time t, so is acceleration model; σ is a coefficient of diffusion, and σ＞0 does not change with stress and time, is constant.

Because as stress, stress S representes with temperature T, so acceleration model is chosen the relation that the Arrhenius model comes temperature of reaction stress and rubber seal compression deformation rate deterioration velocity, that is: with temperature in test

$d\left(T\right)=\frac{\&PartialD;Y\left(t\right)}{\&PartialD;t}={\mathrm{Ae}}^{-E_a/\mathrm{kT}}---\left(4\right)$

In the formula, Y (t) expression product performance index value or amount of degradation; D (T) is reaction velocity or catagen speed; A is a constant; E _aRepresent the activation energy of degradation mechanism; K representes Boltzmann (Boltzmann) constant, is 8.6171 * 10-5eV/K; T is an absolute temperature, and unit is K.

Make B=E _a/ k, then formula (3) becomes:

y(t)＝σB(t)+Aexp(-B/T)t+y ₀ (5)

Parameter A is the multiplier appearance as whole algebraic expression in the Arrenhius model, is an adjustment coefficient that does not have dimension; Activation energy E _a(=Bk) is the potential barrier that rubber seal exists to the failure state transfer process from normal not failure state; Parameter σ is that the coefficient of diffusion of compression deformation rate degeneration stochastic process is the coefficient of diffusion of rubber seal, and its size has mainly characterized the inconsistency with batch products, and its value shows that more greatly consistency of product is poor more.

The performance degradation data of rubber seal are described with useable linear Brownian Motion with Drift behind double log transformation of corresponding time, because Brownian movement is a kind of normal process, are d (T) Δ t so the increment of y (t) in the time of Δ t obeyed average, and variance is σ ²The normal distribution of Δ t, that is:

Δy(t)～N(d(T)Δt，σ ²Δt) (6)

If given properties of product degeneration critical value C, then its life-span is obeyed contrary Gaussian distribution, and Reliability Function is so:

$R\left(t\right)=\mathrm{\&Phi;}\left[\frac{C-y_0-d\left(T\right)t}{\mathrm{\&sigma;}\sqrt{t}}\right]-\exp \left(\frac{2d\left(T\right)\&CenterDot;(C-y_0)}{{\mathrm{\&sigma;}}^2}\right)\mathrm{\&Phi;}[-\frac{C-y_0+d\left(T\right)t}{\mathrm{\&sigma;}\sqrt{t}}]---\left(7\right)$

Thereby unknown parameter is A, B, σ, can obtain this three parameters according to test figure, and the substitution following formula can obtain the Q-percentile life curve of product.Next finding the solution of these three parameters be described.

If total n rubber ring carries out the stepstress accelerated degradation test of K level; The time interval of in the test rubber ring being measured is Δ t, and is constant; Measurement number of times under each stress level is M ₁, detect M time altogether, have

Test period under each stress level then is M _lΔ t, total testing time are M Δ t; The time of at every turn monitoring is t _Ikj(i=1 ..., n; K=1 ..., K; J=1 ..., M), detected performance number is y _Ikj,

(1) estimation of unknown parameter A, B in the acceleration model

At first obtain the degradation ratio d (T) under each stress through the least square fitting degraded data;

Obtain A and B value through least square fitting d (T) and T value then.

(2) unknown parameter is σ

Parameter σ adopts maximum likelihood to estimate to obtain.Be specially: the increment Normal Distribution, its maximum likelihood function is:

$L\&Proportional;\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}\underset{k=1}{\overset{K}{\mathrm{\&Pi;}}}\underset{j=1}{\overset{M_k}{\mathrm{\&Pi;}}}\frac{1}{\sqrt{{2\mathrm{\&pi;\&sigma;}}^2\mathrm{\&Delta;t}}}\exp \{-\frac{{[(y_{\mathrm{ikj}}-y_{\mathrm{ik}(j-1)})-d\left(s_k\right)\mathrm{\&Delta;t}]}^2)}{{2\mathrm{\&sigma;}}^2\mathrm{\&Delta;t}}\}---\left(8\right)$

D (s in the formula (9) _k)=Aexp (B/T _k), so log-likelihood function is:

$\ln L\&Proportional;-\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{M_k}{\mathrm{\&Sigma;}}}\left\{\right[\ln \left(2\mathrm{\&pi;\&Delta;t}\right)+\ln \left({\mathrm{\&sigma;}}^2\right)]+\frac{{[(y_{\mathrm{ikj}}-y_{\mathrm{ik}(j-1)})-\mathrm{Aexp}(-B/T_k)\&CenterDot;\mathrm{\&Delta;t}]}^2}{{\mathrm{\&sigma;}}^2\mathrm{\&Delta;t}}\}---\left(9\right)$

Parameter σ in the formula (9) is asked partial derivative, make it equal zero, can obtain the maximum likelihood estimated value of σ.

2. the accelerated degradation test method of a kind of nitrile rubber O RunddichtringO based on stepstress according to claim 1 is characterized in that described step 1 specifically comprises following step:

1) sample pretreatment; Sample is compressed to the compression deformation rate of appointment through anchor clamps; Under standard temperature; Park after 24 hours and remove stress, stress is the pressure of anchor clamps to nitrile rubber O RunddichtringO, lets sample under free state, park 1h; Measure sample and park the thickness that recover the back, as the sample original depth before the test;

2) surveying instrument; The zeroing of rubber thicknessmeter through the rotation dial plate, makes its pointer aligned at zero scale mark, measures the sample original depth, promptly measures the axial width of four distributed points on the circumference, gets its mean value;

3) with between disposable each pressing plate of putting into anchor clamps of sample, sample does not contact with limiter, and guarantees that compression back sample does not contact with limiter; The anchor clamps of sample of will packing into compress, and pressing plate is closely contacted with limiter, fastening nut, and sample must not reverse in this process;

The anchor clamps that 4) will install sample are parked 30min under laboratory temperature after, put into the incubator that arrives set point of temperature, and pick up counting;

5) from incubator, take out anchor clamps after the arrival stipulated time, open anchor clamps fast, take out sample, under free state, park 1h with tweezers;

6) measure the thickness after sample recovers height, record data with the rubber thicknessmeter.

3. the accelerated degradation test method of a kind of nitrile rubber O RunddichtringO based on stepstress according to claim 1 and 2 is characterized in that sample size is at least 3 in the described step 1.

4. the accelerated degradation test method of a kind of nitrile rubber O RunddichtringO based on stepstress according to claim 1 and 2 is characterized in that, is 23 ± 2 ℃ under the standard temperature in the described step 1.

5. the accelerated degradation test method of a kind of nitrile rubber O RunddichtringO based on stepstress according to claim 1 is characterized in that the described a plurality of samples of described step 3 must not be less than 7.

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