CN104182635A - Accelerated-storage test method for on-missile sealing pieces - Google Patents

Abstract

The invention discloses an accelerated-storage test method for on-missile sealing pieces. The accelerated-storage test method includes the steps of 1), making an accelerated-storage test plan for sealing piece materials, implementing the accelerated-storage test for the sealing piece materials, and evaluating activation energy of the sealing piece materials; 2), optimizing the accelerated-storage test plane for sealing piece products, implementing the accelerated-storage test for the sealing piece products, and evaluating storage life of the sealing piece products. In the method, the test is divided into to steps, namely the accelerated-storage test of the materials and the accelerated-storage test of the products, so that shortcomings of high risk and inaccurate evaluation of accelerated-storage test of the products can be directly reduced. Data statistics of the accelerated-storage tests for the on-missile sealing pieces are performed, matching of the performance degradation process of the sealing pieces is performed by the adoption of multiple models, and the models with the highest matching accuracy are selected to be calculated, so that the material activation energy obtained can be more conforms to actual products.

Description

A kind of accelerated storage test method of seal on bullet

Technical field

The present invention relates to accelerated storage technical field.More specifically, relate to the accelerated storage test method of seal on a kind of bullet.

Background technology

Accelerated storage test technology is to improve the gordian technique of reliable Long Life Products storage life assessment.Can adopt accelerated storage test technology to predict product storage life at engineering development stage, expose weak link, carry out design improvement, improve the storage reliability of product; Disposing operational phase, can adopt accelerated storage test technology to carry out Fast Evaluation to the residual life that is stored to longevity product, carry out the work of lengthening the life foundation is provided for formulating the scheme of lengthening the life.A lot of airborne equipments need to be used sealed product, and seal is restricting the storage life of guided missile, how to carry out the accelerated storage test of seal on bullet and are current guided missile storage life appraisals and the task of top priority in the field of lengthening the life according to its storage life of test assessment.

Main acceleration (hot air aging) test and the assessment that adopts GJB 92 " hot air aging method mensuration vulcanized rubber shelf characteric directive/guide " Part I testing regulations and Part II statistical method to carry out vulcanized rubber series products in engineering at present.This army is designated as promulgation in 1986, and along with the development of accelerated test technology, in the testing regulations that GJB92 provides and statistical method, mathematical model exists inapplicable situation.In testing regulations, adopt material sample to test, and assay intervals under each stress is not described, for seal on bullet, material, shape, size, frock etc. are different, only carry out test with sample, can not well simulate the actual applying working condition of seal product, therefore, need one first to carry out material test, estimate material activation energy, carry out again product testing, " two steps " test method(s) of assessment life of product.In statistical method, recommend adoption exponential model is to the matching of performance degradation process, and the situation that the data acquisition obtaining in actual tests exists related-coefficient test not pass through during with exponential model.

Summary of the invention

The technical problem to be solved in the present invention is to provide the accelerated storage test method of seal on a kind of bullet, the method adopts multiple model to carry out matching to degraded data, select the highest model of fitting precision to performance degradation process model building, and then carry out parameter estimation and life appraisal.

For solving the problems of the technologies described above, the present invention adopts following technical proposals:

An accelerated storage test method for seal on bullet, comprises the following steps:

The first step is formulated the accelerated storage test scheme of sealing member material, implements the accelerated storage test of sealing member material, estimates the activation energy of sealing member material;

Accelerated storage test scheme comprises following key element: assay intervals and detect number of times, experimental test project under sample size, each stress under proof stress, acceleration model, acceleration stress level number, stress intensity, each stress.Definite method of each key element is as follows:

Proof stress: cylinder bullet is under inflated with nitrogen sealed type storage condition, and the environmental stress that affects seal storage life on bullet is temperature, and therefore selecting temperature is proof stress.

Acceleration model: Arrhenius model has reflected the chemical reaction rate of interiors of products material under temperature stress, therefore selects Arrhenius model, and model is as follows:

d(S _l)＝exp[a+b/S _l] (1)

In formula, S _lfor absolute temperature; A, b are model parameter, and a is constant, a>0, b=-E _a/ (kS ₀); E _afor material activation energy, unit: electron-volt, ev; K is Boltzmann constant, k=8.617 × 10 ^-5ev/ DEG C; D (S _l) expression temperature stress S _lthe performance degradation rate of lower product.

Accelerate stress level and count L: stress level is counted L and generally got 3～5, l=1 ..., L.

Stress intensity S _l: respectively accelerate stress level S _linefficacy (degeneration) mechanism of lower product should be in the horizontal S of normal stress ₀inefficacy (degeneration) mechanism of lower product is identical.According to the thermogravimetric analysis of sealing member material, quality of materials occurs that the temperature before obvious downtrending is defined as high stress level S _l.Minimum acceleration stress level S ₁extrapolation accuracy should be considered and acceleration effect is selected.Determine after the highest and minimum stress level, intermediate stress level in engineering generally according to value uniformly-spaced.

Assay intervals Δ t under each stress _lwith detection number of times m _l: heavily stressed lower assay intervals is less than assay intervals under low stress, detects number of times m under each stress _lall be not less than 10.

Sample size n under each stress _l: heavily stressed lower sample size is generally less than sample size under low stress, and under each stress, sample size is all no less than 5.

Experimental test project: seal generally adopts elastomeric material, test event conventional in accelerated test comprises: tensile property, compression set rate, hardness, elastic modulus etc.Select the compression set rate that can reflect seal life of product feature as test event, i.e. compression set rate is the performance degradation parameter y (t) of sealing member material test.

The computing formula of compression set rate is as follows:

$\mathrm{CS}=\frac{H_0-H_t}{H_0-d}\×100\%---\left(2\right)$

In formula: H ₀---the rubbery sample original height after physics is lax, unit: mm;

H _t---after the aging t time, be down to room temperature and recover the height after 1h, unit: mm;

D---the height of fixture limiter, unit: mm.

Determine according to the method described above the accelerated storage test scheme of sealing member material.

Adopt constant stress to apply mode, the testing program of formulating according to the first step is carried out test, records each test data y (t), carries out Fitting Analysis by multiple mathematical model, sets up y (t) the degenerative process model of t in time.

Sealing member material performance parameter degenerative process in time, chooses four kinds of conventional models: (1) linear model: y (t)=at+b, (2) power index model: y (t)=at ^b, (3) exponential model: y (t)=ae ^bt, (4) logarithmic model: y (t)=alnt+b carries out regretional analysis to degenerative process respectively, and wherein exponential model is the statistical model that GJB92 recommends.By regretional analysis, obtain the parameter analysis under different model of fit.The quality of models fitting is judged by the fitting precision parameter under more different models.Fitting precision parameter comprises error sum of squares SSE, root mean square RMSE, coefficient of determination R-square.SSE and RMSE, more close to 0, illustrate that models fitting is better, and data prediction is also more successful, or judges by R-square, and the normal span of R-square is [0,1], and its value, more close to 1, illustrates that models fitting effect is better.

After preference pattern, to nonlinear model, should be the linear forms of Y (x)=Ax+B by model transferring.Mapping mode is in table 1:

Table 1 non-linear behaviour degradation model

After sealing member material Performance Degradation Data y (t) and measurement time t distortion, degradation model all can be expressed as:

Y(x)＝Ax+B (3)

A, B are undetermined parameter.Wherein, the performance degradation curve journey monotone increasing of product in the time of A>0; In the time of A<0, the performance degradation curve journey monotone decreasing of product.A represents the performance degradation speed of product, i.e. d (s)=A.

Degraded data under each stress is carried out to matching, obtain degradation ratio d (s under each stress _l)=A _l, according to formula (1), a+b/S _l=ln A _l, adopt least square fitting, try to achieve parameter a and b, and then try to achieve the activation energy E of normal stress lower seal material _a=-bk.

Second step is optimized the accelerated storage test scheme of seal product, implements the accelerated storage test of seal product, the storage life of assessment seal product

Obtained by the first step after the parameter such as activation energy of material, can be optimized the accelerated storage test scheme of seal product, improve test efficiency.According to scheme, implement the accelerated test of seal product, analyzing and processing test figure, the storage life of assessment seal product.

According to the activation energy parameter of sealing member material etc., formulate the accelerated storage test scheme of seal product.The accelerated storage test scheme of seal product need to be determined equally under proof stress, acceleration model, acceleration stress level number, stress intensity, each stress under sample size, each stress assay intervals and detect the key elements such as number of times, experimental test project.Wherein proof stress, acceleration model and experimental test project are identical with the accelerated storage test of material, and stress level number is generally taken as 3, and under stress intensity, each stress, sample size, assay intervals and detection number of times obtain by optimal design.Testing program optimization method can be referring to patent 201010033998.7 " optimization design method of step-stress accelerated degradation test ", and process is as follows:

Seal properties of product degenerative process adopts Brownian Motion with Drift model modeling, and model is as follows:

Y _l(t)＝σB(t)+d(S _l)·t+y ₀ (4)

In formula, Y _l(t) be S _lthe performance degradation curve of lower product, σ is coefficient of diffusion, does not change with stress level, and B (t) is standard Brownian movement, and t is the time, y ₀for performance initial value.

Obtained by formula (1) and formula (4):

Y _l(t)＝σB(t)+exp［a-E _a/(k·S _l)］·t+y ₀ (5)

Model parameter is θ={ a, E _a, σ }, wherein parameter a and E _adetermine initial value by second step.σ has portrayed the impact of enchancement factor on properties of product such as measurement capability and measuring error and process of the test peripheral noise of inconsistency and instability in process of producing product, measuring equipment, and the initial value that makes σ is 0.01.

Reliability Function is:

$R\left(t\right)=\mathrm{\&Phi;}\left[\frac{c-y_0-d\left(S\right)\&CenterDot;t}{\mathrm{\&sigma;}\sqrt{t}}\right]-\exp \left(\frac{2d\left(S\right)\&CenterDot;(c-y_0)}{{\mathrm{\&sigma;}}^2}\right)\mathrm{\&Phi;}[-\frac{c-y_0+d\left(S\right)\&CenterDot;t}{\mathrm{\&sigma;}\sqrt{t}}]---\left(6\right)$

In formula, c is properties of product degradation failure threshold value.

Log-likelihood function is:

$\ln L\&Proportional;-\frac{1}{2}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n_L}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m_L}{\mathrm{\&Sigma;}}}\left\{\right[\ln \left(2\mathrm{\&pi;\&Delta;t}\right)+\ln \left({\mathrm{\&sigma;}}^2\right)]+\frac{{[x_{\mathrm{lij}}-d\left(S\right)\&CenterDot;\mathrm{\&Delta;}t]}^2}{{\mathrm{\&sigma;}}^2\mathrm{\&Delta;}t}\}\left(7\right)$

In formula, x _lij=y _{li (j+1)}-y _lij, represent interval of delta t detection time _lon performance increment.

Choose the fiduciary level R (t that p divides a life estimation value _p) asymptotic variance minimum as objective function.

min AsVar(R(t _p)) (8)

In formula, t _pit is the estimated value that product p under normal operation divides a life-span.

Congruence and the asymptotic normality estimated according to maximum likelihood, in the time of n → ∞, R (t _p) obey average be variance is h ^tf ^-1(θ) asymptotic normality of h distributes., asymptotic variance AsVar (R (t _p)) be

AsVar(R(t _p))＝h ^TF ^-1(θ)h (9)

In formula,

θ＝(a,E _a,σ ²) (10)

$h^T=(\frac{\&PartialD;R\left(t_p\right)}{\&PartialD;a},\frac{\&PartialD;R\left(t_p\right)}{\&PartialD;E_a},\frac{\&PartialD;R\left(t_p\right)}{\&PartialD;{\mathrm{\&sigma;}}^2})---\left(11\right)$

$F\left(\mathrm{\&theta;}\right)=\left[\begin{array}{ccc}E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;a^2})& E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;a\&PartialD;E_a})& E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;a\&PartialD;{\mathrm{\&sigma;}}^2})\\ & E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;{E_a}^2})& E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;E_a\&PartialD;{\mathrm{\&alpha;}}^2})\\ \mathrm{symmetrical}& & E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;{\left({\mathrm{\&sigma;}}^2\right)}^2})\end{array}\right]---\left(12\right)$

The Fisher information matrix that F (θ) is θ is three rank Positive Definite Square Matrices.

Buying seal product test specimen, makes test tool according to actual condition situation.The accelerated storage test of seal product adopts stepstress mode, and test sample amount and test period are definite according to project funds, and ordinary test sample size is no less than 5, and under low stress, test period is longer than heavily stressed lower test period.Under each stress level and each stress, the constraint condition of assay intervals, detection number of times is:

S ₀<S ₁<S ₂<…<S _L≤S _max

Δt ₁>Δt ₂>…>Δt _L

m _l≥10(l＝1,2,…,L) (13)

Optimization aim and constraint condition form Optimized model:

min AsVar(R(t _p))

s.t.S ₀<S ₁<S ₂<…<S _L≤S _max

Δt ₁>Δt ₂>…>Δt _L

m _l≥10(l＝1,2,…,L) (14)

Solve formula (14) and obtain each test variable, thereby obtain the accelerated storage test scheme of seal product.

Implement the accelerated storage test of seal product, obtain the performance detection data of product under each stress level, by estimation of test data model parameter θ={ a, E _a, σ }, parameter a and E that the first step is obtained _aand the initial value of σ is revised adjustment.Model parameter estimation value substitution formula (6) is obtained to the storage Q-percentile life of normal stress lower seal product.Method for parameter estimation is as follows:

A and E _aestimate according to second step method.

σ adopts maximum likelihood to estimate to solve, as follows:

${\widehat{\mathrm{\&sigma;}}}^2=\frac{1}{n\&CenterDot;(m-L)}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n_l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m_l-1}{\mathrm{\&Sigma;}}}\frac{{[x_{\mathrm{lij}}-\exp (\hat{a}-{\hat{E}}_a/\left({\mathrm{kS}}_l\right))\&CenterDot;\mathrm{\&Delta;}{t}_{\mathrm{lij}}]}^2}{\mathrm{\&Delta;}{t}_{\mathrm{lij}}}---\left(15\right)$

Will with substitution formula (6) is storage life and the reliability of measurable seal product under normal stress level.

So far, realized " two steps " accelerated storage test method of seal on a kind of bullet.

Beneficial effect of the present invention is as follows:

(1), for seal accelerated storage test on bullet, test is divided into the accelerated storage test of material and the accelerated storage test of product two steps.Can reduce directly carry out product accelerated storage test risk high, assess coarse shortcoming;

(2) for the accelerated storage test data statistics of seal on bullet, the present invention adopts multiple model to carry out matching to property of sealing piece degenerative process, selects the highest model of fitting precision to calculate, and the material activation energy obtaining more meets product reality;

(3) adopt Brownian Motion with Drift model to the modeling of seal properties of product degenerative process, testing program is optimized, make test more effective, obtain the storage Q-percentile life of normal stress lower seal product, GJB92 obtains under normal stress relatively, mean value and the lower limit of different period of storage properties of product change indicators, have more practical significance.

Brief description of the drawings

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.

Fig. 1 is the process flow diagram of seal on a kind of bullet of the present invention " two steps " accelerated storage test method;

Fig. 2 is the embodiment of the present invention 1 sealing member material test figure figure.

Embodiment

In order to be illustrated more clearly in the present invention, below in conjunction with preferred embodiments and drawings, the present invention is described further.Parts similar in accompanying drawing represent with identical Reference numeral.It will be appreciated by those skilled in the art that specifically described content is illustrative and nonrestrictive below, should not limit the scope of the invention with this.

Embodiment 1

On a kind of bullet, the concrete steps of " two steps " accelerated storage test method of seal are:

The first step is formulated the accelerated storage test scheme of sealing member material, implements the accelerated storage test of sealing member material, estimates the activation energy of sealing member material

Alternative costs are low, the sealing member material of easy processing is formulated accelerated storage test scheme, carry out test; To test figure, adopt multiple model to carry out regretional analysis, estimate the activation energy of sealing member material.

Accelerated storage test scheme comprises following key element: assay intervals and detect number of times, experimental test project under sample size, each stress under proof stress, acceleration model, acceleration stress level number, stress intensity, each stress.Each key element is determined as follows:

Proof stress: cylinder bullet is under inflated with nitrogen sealed type storage condition, and the environmental stress that affects seal storage life on bullet is temperature, and therefore selecting temperature is proof stress.

Acceleration model: Arrhenius model has reflected the chemical reaction rate of interiors of products material under temperature stress, therefore selects Arrhenius model, and model is as follows:

d(S _l)＝exp[a+b/S _l] (1)

In formula, S _lfor absolute temperature; A, b are model parameter, and a is constant, a>0, b=-E _a/ k; E _afor material activation energy, unit: electron-volt, ev; K is Boltzmann constant, k=8.617 × 10 ^-5ev/ DEG C; D (S _l) expression temperature stress S _lthe performance degradation rate of lower product.

Accelerate stress level and count L: stress level is counted L and is generally no less than 4, l=1 ..., L.

Stress intensity S _l: respectively accelerate stress level S _linefficacy (degeneration) mechanism of lower product should be in the horizontal S of normal stress ₀inefficacy (degeneration) mechanism of lower product is identical.According to the thermogravimetric analysis of sealing member material, quality of materials occurs that the temperature before obvious downtrending is defined as high stress level S _l.Minimum acceleration stress level S ₁extrapolation accuracy should be considered and acceleration effect is selected.Determine after the highest and minimum stress level, intermediate stress level in engineering generally according to value uniformly-spaced.

Assay intervals Δ t under each stress _lwith detection number of times m _l: heavily stressed lower assay intervals is less than assay intervals under low stress, detects number of times m under each stress _lall be not less than 10.

Sample size n under each stress _l: heavily stressed lower sample size is generally less than sample size under low stress, and under each stress, sample size is all no less than 5.

Experimental test project: seal generally adopts elastomeric material, test event conventional in accelerated test comprises: tensile property, compression set rate, hardness, elastic modulus etc.Select the compression set rate that can reflect seal life of product feature as test event, i.e. compression set rate is the performance degradation parameter y (t) of sealing member material test.

The computing formula of compression set rate is as follows:

$\mathrm{CS}=\frac{H_0-H_t}{H_0-d}\&times;100\%---\left(2\right)$

In formula: H ₀---the rubbery sample original height after physics is lax, unit: mm

H _t---after the aging t time, be down to room temperature and recover the height after 1h, unit: mm

D---the height of fixture limiter, unit: mm

Determine according to the method described above the accelerated storage test scheme of sealing member material.

Adopt constant stress to apply mode, the testing program of formulating according to the first step is carried out test, records each test data y (t), carries out Fitting Analysis by multiple mathematical model, sets up y (t) the degenerative process model of t in time.

Sealing member material performance parameter degenerative process in time, chooses four kinds of conventional models: (1) linear model: y (t)=at+b, (2) power index model: y (t)=at ^b, (3) exponential model: y (t)=ae ^bt, (4) logarithmic model: y (t)=alnt+b carries out regretional analysis to degenerative process respectively, and wherein exponential model is the statistical model that GJB 92 recommends.By regretional analysis, obtain the parameter analysis under different model of fit.The quality of models fitting is judged by the fitting precision parameter under more different models.Fitting precision parameter comprises error sum of squares SSE, root mean square RMSE, coefficient of determination R-square.SSE and RMSE, more close to 0, illustrate that models fitting is better, and data prediction is also more successful, or judges by R-square, and the normal span of R-square is [0,1], and its value, more close to 1, illustrates that models fitting effect is better.

After preference pattern, to nonlinear model, should be the linear forms of Y (x)=Ax+B by model transferring.Mapping mode is in table 1:

Table 2 non-linear behaviour degradation model

After sealing member material Performance Degradation Data y (t) and measurement time t distortion, degradation model all can be expressed as:

Y(x)＝Ax+B (3)

A, B are undetermined parameter.Wherein, the performance degradation curve journey monotone increasing of product in the time of A>0; In the time of A<0, the performance degradation curve journey monotone decreasing of product.A represents the performance degradation speed of product, i.e. d (s)=A.

Degraded data under each stress is carried out to matching, obtain degradation ratio d (s under each stress _l)=A _l, according to formula (1), a+b/S _l=ln A _l, adopt least square fitting, try to achieve parameter a and b, and then try to achieve the activation energy E of normal stress lower seal material _a=-bk.

In present case, stress level number gets 4, i.e. L=4.Sealing member material is carried out to thermogravimetric analysis, find that obvious downtrending appears in quality of materials after 100 DEG C, for the purpose of conservative, determine high stress level S _l=373 (100 DEG C), consider extrapolation accuracy and acceleration effect, determine minimum acceleration stress level S ₁=333 (60 DEG C), intermediate stress is S according to value uniformly-spaced ₂=346 (73 DEG C), S ₃=359 (86 DEG C).Under each stress, detect number of times m _l=10; Under each stress, assay intervals is Δ t ₁=7, Δ t ₂=5, Δ t ₃=3, Δ t ₄=2, unit: day.When each test of sealing member material, get 3 test samples and average, test rear sample at every turn and do not put back in chamber, therefore, under each stress, sample size is n _l=30.

The accelerated storage test of implementing sealing member material, under each stress level, the compression set rate test data (mean values of 3 samples) of material as shown in Figure 2.Test figure is carried out to different models fitting analyses, in the fitting precision parameter under different models in table 2. comparison sheet, can find out power index model fitting effect the best under four temperature stresses, therefore choose power index model.

Degraded data under each stress is carried out to matching, obtain degradation ratio under each stress, adopt least square fitting, try to achieve acceleration model parameter estimation: a=10.2; B=-5016.6, and then try to achieve the activation energy E of normal stress lower seal material _a=0.43.

Parameter analysis under the different model of fit of table 2 seal

Second step is optimized the accelerated storage test scheme of seal product, implements the accelerated storage test of seal product, the storage life of assessment seal product

Obtained by the first step after the parameter such as activation energy of material, can be optimized the accelerated storage test scheme of seal product, improve test efficiency.According to scheme, implement the accelerated test of seal product, analyzing and processing test figure, the storage life of assessment seal product.

According to the activation energy parameter of sealing member material etc., formulate the accelerated storage test scheme of seal product.The accelerated storage test scheme of seal product need to be determined equally under proof stress, acceleration model, acceleration stress level number, stress intensity, each stress under sample size, each stress assay intervals and detect the key elements such as number of times, experimental test project.Wherein proof stress, acceleration model and experimental test project are identical with the accelerated storage test of material, and stress level number is generally taken as 3, and under stress intensity, each stress, sample size, assay intervals and detection number of times obtain by optimal design.Testing program optimization method can be referring to patent 201010033998.7 " optimization design method of step-stress accelerated degradation test ", and concise and to the point process is as follows:

Seal properties of product degenerative process adopts Brownian Motion with Drift model modeling, and model is as follows:

Y _l(t)＝σB(t)+d(S _l)·t+y ₀ (4)

In formula, Y _l(t) be S _lthe performance degradation curve of lower product, σ is coefficient of diffusion, does not change with stress level, and B (t) is standard Brownian movement, and t is the time, y ₀for performance initial value.

Obtained by formula (1) and formula (4):

Y _l(t)＝σB(t)+exp［a-E _a/(k·S _l)］·t+y ₀ (5)

Model parameter is θ={ a, E _a, σ }, wherein parameter a and E _adetermine initial value by second step.σ has portrayed the impact of enchancement factor on properties of product such as measurement capability and measuring error and process of the test peripheral noise of inconsistency and instability in process of producing product, measuring equipment, and the initial value that makes σ is 0.01.

Reliability Function is:

$R\left(t\right)=\mathrm{\&Phi;}\left[\frac{c-y_0-d\left(S\right)\&CenterDot;t}{\mathrm{\&sigma;}\sqrt{t}}\right]-\exp \left(\frac{2d\left(S\right)\&CenterDot;(c-y_0)}{{\mathrm{\&sigma;}}^2}\right)\mathrm{\&Phi;}[-\frac{c-y_0+d\left(S\right)\&CenterDot;t}{\mathrm{\&sigma;}\sqrt{t}}]---\left(6\right)$

In formula, c is properties of product degradation failure threshold value.

Log-likelihood function is:

$\ln L\&Proportional;-\frac{1}{2}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n_L}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m_L}{\mathrm{\&Sigma;}}}\left\{\right[\ln \left(2\mathrm{\&pi;\&Delta;t}\right)+\ln \left({\mathrm{\&sigma;}}^2\right)]+\frac{{[x_{\mathrm{lij}}-d\left(S\right)\&CenterDot;\mathrm{\&Delta;}t]}^2}{{\mathrm{\&sigma;}}^2\mathrm{\&Delta;}t}\}\left(7\right)$

In formula, x _lij=y _{li (j+1)}-y _lij, represent interval of delta t detection time _lon performance increment.

Choose the fiduciary level R (t that p divides a life estimation value _p) asymptotic variance minimum as objective function.

min AsVar(R(t _p)) (8)

In formula, t _pit is the estimated value that product p under normal operation divides a life-span.

Congruence and the asymptotic normality estimated according to maximum likelihood, in the time of n → ∞, R (t _p) obey average be variance is h ^tf ^-1(θ) asymptotic normality of h distributes., asymptotic variance AsVar (R (t _p)) be

AsVar(R(t _p))＝h ^TF ^-1(θ)h (9)

In formula,

θ＝(a,E _a,σ ²) (10)

$h^T=(\frac{\&PartialD;R\left(t_p\right)}{\&PartialD;a},\frac{\&PartialD;R\left(t_p\right)}{\&PartialD;E_a},\frac{\&PartialD;R\left(t_p\right)}{\&PartialD;{\mathrm{\&sigma;}}^2})---\left(11\right)$

$F\left(\mathrm{\&theta;}\right)=\left[\begin{array}{ccc}E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;a^2})& E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;a\&PartialD;E_a})& E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;a\&PartialD;{\mathrm{\&sigma;}}^2})\\ & E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;{E_a}^2})& E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;E_a\&PartialD;{\mathrm{\&alpha;}}^2})\\ \mathrm{symmetrical}& & E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;{\left({\mathrm{\&sigma;}}^2\right)}^2})\end{array}\right]---\left(12\right)$

The Fisher information matrix that F (θ) is θ is three rank Positive Definite Square Matrices.

Buying seal product test specimen, makes test tool according to actual condition situation.The accelerated storage test of seal product adopts stepstress mode, and test sample amount and test period are definite according to project funds, and ordinary test sample size is no less than 5, and under low stress, test period is longer than heavily stressed lower test period.Under each stress level and each stress, the constraint condition of assay intervals, detection number of times is:

S ₀<S ₁<S ₂<…<S _L≤S _max

Δt ₁>Δt ₂>…>Δt _L

m _l≥10(l＝1,2,…,L) (13)

Optimization aim and constraint condition form Optimized model:

min AsVar(R(t _p))

s.t.S ₀<S ₁<S ₂<…<S _L≤S _max

Δt ₁>Δt ₂>…>Δt _L

m _l≥10(l＝1,2,…,L) (14)

Solve formula (14) and obtain each test variable, thereby obtain the accelerated storage test scheme of seal product.

Implement the accelerated storage test of seal product, obtain the performance detection data of product under each stress level, by estimation of test data model parameter θ={ a, E _a, σ }, parameter a and E that the first step is obtained _aand the initial value of σ is revised adjustment.Model parameter estimation value substitution formula (6) is obtained to the storage Q-percentile life of normal stress lower seal product.Method for parameter estimation is as follows:

A and E _aestimate according to second step method.

σ adopts maximum likelihood to estimate to solve, as follows:

${\widehat{\mathrm{\&sigma;}}}^2=\frac{1}{n\&CenterDot;(m-L)}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n_l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m_l-1}{\mathrm{\&Sigma;}}}\frac{{[x_{\mathrm{lij}}-\exp (\hat{a}-{\hat{E}}_a/\left({\mathrm{kS}}_l\right))\&CenterDot;\mathrm{\&Delta;}{t}_{\mathrm{lij}}]}^2}{\mathrm{\&Delta;}{t}_{\mathrm{lij}}}---\left(15\right)$

Will with substitution formula (6) is storage life and the reliability of measurable seal product under normal stress level.

So far, realized " two steps " accelerated storage test method of seal on a kind of bullet.

In present case, model parameter is a=10.2; E _a=0.43, σ=0.01.Test sample amount is 5, and total testing time is 130 days, according to formula (14), solve and obtain,

S ₁＝338；S ₂＝353；S ₃＝373；

Δt ₁＝7；Δt ₂＝4；Δt ₃＝2；

m _l＝10.

Thereby obtain the accelerated storage test scheme of seal product.

According to testing program, implement the accelerated storage test of seal product, obtain the performance test data under each stress level, according to second step estimated parameter a and E _a, result is:

σ adopts maximum likelihood to estimate to solve,

Bring estimates of parameters into formula (6) and can draw Q-percentile life curve, on this bullet, the seal fiduciary level of 10 years is 0.98.

Obviously; the above embodiment of the present invention is only for example of the present invention is clearly described; and be not the restriction to embodiments of the present invention; for those of ordinary skill in the field; can also make other changes in different forms on the basis of the above description; here cannot give all embodiments exhaustively, everyly belong to apparent variation or the still row in protection scope of the present invention of variation that technical scheme of the present invention extends out.

Claims (4)

1. an accelerated storage test method for seal on bullet, is characterized in that, comprises the following steps:

The first step, taking temperature as proof stress, implements the accelerated storage test of sealing member material, obtains the activation energy of sealing member material; Specific as follows:

Sealing member material on test bullet

H ₀---the rubbery sample original height after physics is lax, unit: mm;

H _t---after the aging t time, be down to room temperature and recover the height after 1h, unit: mm;

D---the height of fixture limiter, unit: mm;

Press formula (2) and calculate compression set rate:

$\mathrm{CS}=\frac{H_0-H_t}{H_0-d}\&times;100\%---\left(2\right)$

Obtain the performance degradation parameter of sealing member material test

Adopt constant stress to apply mode, according to after sealing member material Performance Degradation Data y (t) and measurement time t distortion, set up the degradation model of sealing member material:

Y(x)＝Ax+B (3)

A, B are undetermined parameter, wherein, and the performance degradation curve journey monotone increasing of product in the time of A>0; In the time of A<0, the performance degradation curve journey monotone decreasing of product, A represents the performance degradation speed of product, i.e. d (s)=A;

Degraded data under each stress is carried out to matching, obtain degradation ratio d (s under each stress _l)=A _l, according to Arrhenius modular form (1),,

d(S _l)＝exp[a+b/S _l] (1)

In formula, S _lfor absolute temperature; A, b are model parameter, and a is constant, a>0, b=-E _a/ (kS ₀); E _afor material activation energy, unit: electron-volt, ev; K is Boltzmann constant, k=8.617 × 10 ^-5ev/ DEG C; D (S _l) expression temperature stress S _lthe performance degradation rate of lower product;

Obtain a+b/S _l=lnA _l

Adopt least square fitting, try to achieve parameter a and b, and then try to achieve the activation energy E of normal stress lower seal material _a=-bk;

Second step calculates the performance detection data of product under each stress level, by estimation of test data model parameter θ={ a, E _a, σ }, parameter a and E that the first step is obtained _aand the initial value of σ revises adjustment, by model parameter estimation value substitution Reliability Function formula (6):

$R\left(t\right)=\mathrm{\&Phi;}\left[\frac{c-y_0-d\left(S\right)\&CenterDot;t}{\mathrm{\&sigma;}\sqrt{t}}\right]-\exp \left(\frac{2d\left(S\right)\&CenterDot;(c-y_0)}{{\mathrm{\&sigma;}}^2}\right)\mathrm{\&Phi;}[-\frac{c-y_0+d\left(S\right)\&CenterDot;t}{\mathrm{\&sigma;}\sqrt{t}}]---\left(6\right)$

In formula, c is properties of product degradation failure threshold value;

The storage Q-percentile life that obtains normal stress lower seal product, method for parameter estimation is as follows:

A and E _aestimate according to second step method,

σ adopts maximum likelihood to estimate to solve, as follows:

${\widehat{\mathrm{\&sigma;}}}^2=\frac{1}{n\&CenterDot;(m-L)}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n_l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m_l-1}{\mathrm{\&Sigma;}}}\frac{{[x_{\mathrm{lij}}-\exp (\hat{a}-{\hat{E}}_a/\left({\mathrm{kS}}_l\right))\&CenterDot;\mathrm{\&Delta;}{t}_{\mathrm{lij}}]}^2}{\mathrm{\&Delta;}{t}_{\mathrm{lij}}}\left(15\right)$

Will with substitution formula (6) can obtain storage life and the reliability of seal product under normal stress level.

2. the accelerated storage test method of seal on bullet according to claim 1, is characterized in that: described in the first step, accelerated storage test scheme comprises following key element: assay intervals and detect number of times, experimental test project under sample size, each stress under proof stress, acceleration model, acceleration stress level number, stress intensity, each stress;

Described proof stress is temperature,

Described acceleration model is Arrhenius model

Described acceleration stress level is counted L and is got 3～5, l=1 ..., L;

Described stress intensity comprises high stress level S _l, minimum acceleration stress level S ₁with intermediate stress level; Described high stress level S _lfor there is the temperature before obvious downtrending in quality of materials; Described minimum acceleration stress level S ₁determined by extrapolation accuracy and acceleration effect; Described intermediate stress level is according to value uniformly-spaced;

Assay intervals Δ t under described each stress _lwith detection number of times m _lbe less than assay intervals under low stress according to heavily stressed lower assay intervals, under each stress, detect number of times m _lall be not less than 10;

Sample size n under described each stress _l: heavily stressed lower sample size is generally less than sample size under low stress, and under each stress, sample size is all no less than 5;

Described experimental test project is that compression set rate is the performance degradation parameter y (t) of sealing member material test.

3. the accelerated storage test method of seal on bullet according to claim 1, it is characterized in that: the accelerated storage test of implementing sealing member material described in the first step is to adopt constant stress to apply mode, record each test data y (t), carry out Fitting Analysis by multiple mathematical model, set up y (t) the degenerative process model of t in time.

4. the accelerated storage test method of seal on bullet according to claim 1, is characterized in that: described in second step, testing program optimization method process is as follows:

Seal properties of product degenerative process adopts Brownian Motion with Drift model modeling, and model is as follows:

Y _l(t)＝σB(t)+d(S _l)·t+y ₀ (4)

In formula, Y _l(t) be S _lthe performance degradation curve of lower product, σ is coefficient of diffusion, does not change with stress level, and B (t) is standard Brownian movement, and t is the time, y ₀for performance initial value;

Obtained by formula (1) and formula (4):

Y _l(t)＝σB(t)+exp[a-E _a/(k·S _l)]·t+y ₀ (5)

Model parameter is θ={ a, E _a, σ }, wherein parameter a and E _adetermine initial value by second step, σ is the impact of enchancement factor on properties of product such as measurement capability and measuring error and process of the test peripheral noise of inconsistency and instability in process of producing product, measuring equipment, and the initial value that makes σ is 0.01,

Reliability Function is:

$R\left(t\right)=\mathrm{\&Phi;}\left[\frac{c-y_0-d\left(S\right)\&CenterDot;t}{\mathrm{\&sigma;}\sqrt{t}}\right]-\exp \left(\frac{2d\left(S\right)\&CenterDot;(c-y_0)}{{\mathrm{\&sigma;}}^2}\right)\mathrm{\&Phi;}[-\frac{c-y_0+d\left(S\right)\&CenterDot;t}{\mathrm{\&sigma;}\sqrt{t}}]---\left(6\right)$

In formula, c is properties of product degradation failure threshold value;

Log-likelihood function is:

$\ln L\&Proportional;-\frac{1}{2}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n_L}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m_L}{\mathrm{\&Sigma;}}}\left\{\right[\ln \left(2\mathrm{\&pi;\&Delta;t}\right)+\ln \left({\mathrm{\&sigma;}}^2\right)]+\frac{{[x_{\mathrm{lij}}-d\left(S\right)\&CenterDot;\mathrm{\&Delta;}t]}^2}{{\mathrm{\&sigma;}}^2\mathrm{\&Delta;}t}\}\left(7\right)$

In formula, x _lij=y _{li (j+1)}-y _lij, represent interval of delta t detection time _lon performance increment;

Divide the fiduciary level R (t of a life estimation value with p _p) asymptotic variance minimum as objective function,

min AsVar(R(t _p)) (8)

In formula, tp is the estimated value that product p under normal operation divides a life-span;

Congruence and the asymptotic normality estimated according to maximum likelihood, in the time of n → ∞, R (t _p) obey average be variance is h ^tf ^-1(θ) asymptotic normality of h distributes, asymptotic variance AsVar (R (t _p)) be

AsVar(R(t _p))＝h ^TF ^-1(θ)h (9)

In formula,

θ＝(a,E _a,σ ²) (10)

$h^T=(\frac{\&PartialD;R\left(t_p\right)}{\&PartialD;a},\frac{\&PartialD;R\left(t_p\right)}{\&PartialD;E_a},\frac{\&PartialD;R\left(t_p\right)}{\&PartialD;{\mathrm{\&sigma;}}^2})---\left(11\right)$

$F\left(\mathrm{\&theta;}\right)=\left[\begin{array}{ccc}E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;a^2})& E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;a\&PartialD;E_a})& E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;a\&PartialD;{\mathrm{\&sigma;}}^2})\\ & E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;{E_a}^2})& E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;E_a\&PartialD;{\mathrm{\&alpha;}}^2})\\ \mathrm{symmetrical}& & E(-\frac{{\&PartialD;}^2\ln L}{\&PartialD;{\left({\mathrm{\&sigma;}}^2\right)}^2})\end{array}\right]---\left(12\right)$

The Fisher information matrix that F (θ) is θ is three rank Positive Definite Square Matrices;

Under each stress level and each stress, the constraint condition of assay intervals, detection number of times is:

S ₀<S ₁<S ₂<…<S _L≤S _max

Δt ₁>Δt ₂>…>Δt _L

m _l≥10(l＝1,2,…,L) (13)

Optimization aim and constraint condition form Optimized model:

min AsVar(R(t _p))

s.t.S ₀<S ₁<S ₂<…<S _L≤S _max

Δt ₁>Δt ₂>…>Δt _L

m _l≥10(l＝1,2,…,L) (14)

Solve formula (14) and obtain each test variable, thereby obtain the accelerated storage test scheme of seal product;

Implement the accelerated storage test of seal product, obtain the performance detection data of product under each stress level, by estimation of test data model parameter θ={ a, E _a, σ }, parameter a and E that the first step is obtained _aand the initial value of σ revises adjustment, model parameter estimation value substitution formula (6) is obtained to the storage Q-percentile life of normal stress lower seal product, method for parameter estimation is as follows:

A and E _aestimate according to second step method,

σ adopts maximum likelihood to estimate to solve, as follows:

${\widehat{\mathrm{\&sigma;}}}^2=\frac{1}{n\&CenterDot;(m-L)}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n_l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m_l-1}{\mathrm{\&Sigma;}}}\frac{{[x_{\mathrm{lij}}-\exp (\hat{a}-{\hat{E}}_a/\left({\mathrm{kS}}_l\right))\&CenterDot;\mathrm{\&Delta;}{t}_{\mathrm{lij}}]}^2}{\mathrm{\&Delta;}{t}_{\mathrm{lij}}}---\left(15\right)$

Will with substitution formula (6) can obtain storage life and the reliability of seal product under normal stress level.