Accelerated aging test method for small sample of rubber component

Abstract

The invention discloses an accelerated aging test method for a small sample of a rubber component. The method comprises the following steps: 1, collecting performance degradation data of the rubber component at an accelerated stress level; 2, based on the degradation track model, extrapolating the performance degradation index of the sample to obtain the pseudo failure life of the sample; 3, based on the pseudo failure life data, evaluating the reliable life single-side confidence limit with high confidence and high reliability of the rubber component under the accelerated stress level; and 4, based on the linear acceleration model and in combination with the confidence limit and difference product quotient theory, evaluating the high-confidence and high-reliability reliable life single-side lower confidence limit of the rubber component under the normal use stress level. According to the aging test data of the two accelerated stress levels, the evaluation of the single-side confidence lower limit of the reliable service life of the rubber component under the normal use stress level can be realized under the requirements of high confidence and high reliability without introducing the hypothesis of equal variance; and the method is of great significance to long-term safe and reliable use of the rubber component.

Description

[Technical field]

[0001] The invention belongs to the field of reliability engineering, and in particular relates to a small sample accelerated aging test method for a rubber component. [Background technology]

[0002] Rubber materials have been widely used in the industrial field due to their high elasticity, high damping, wear resistance and other characteristics, such as being used to make seals, vibration isolators and other components. During their long-term use or storage, rubber components will inevitably be corroded by environmental factors such as temperature, humidity, and oxygen, and their aging degree will continue to accumulate, their performance will gradually degrade, and they may even cause serious safety accidents. Therefore, in order to ensure the safe and reliable operation of rubber components during their service life, it is usually necessary to carry out aging tests on them to understand their aging laws and evaluate their reliability. In view of the relatively slow natural aging process of rubber components, accelerated aging test methods are often used in engineering practice to accelerate the aging process of rubber components by increasing temperature and humidity, so as to obtain their performance degradation information in a short time. However, traditional accelerated aging tests generally need to be carried out at about 5 accelerated stress levels, and there are still problems such as the number of specimens required, long test time and high cost. In addition, in engineering practice, the higher the stress level, the smaller the life dispersion is often, that is, the variance of the logarithmic life at each stress level is not equal, and the traditional accelerated aging test evaluation method can usually only consider the case of equal variance, which brings large errors to the evaluation results.

[0003] To this end, the present invention proposes a small sample accelerated aging test method for rubber components. Only two accelerated stress levels need to be selected to carry out accelerated aging tests on the rubber components, and there is no need to introduce the assumption of equal variances. The one-sided lower confidence limit of the reliable life of the rubber components under normal use stress levels can be evaluated with high confidence and high reliability. [Summary of the invention]

[0004] (1) The purpose of the present invention is to provide a small sample accelerated aging test method for rubber components. First, the performance degradation index of the rubber component sample is extrapolated through the degradation trajectory model to evaluate the pseudo failure life of each sample; then the one-sided confidence limit of the reliable life of the rubber component under the accelerated stress level is calculated; finally, combined with the acceleration model, a mathematical relationship between the one-sided confidence lower limit of the reliable life of the rubber component under the normal use stress level and the one-sided confidence limit of the reliable life under two accelerated stress levels is established, and a high confidence and high reliability one-sided confidence lower limit evaluation method for the reliable life of the rubber component under the normal use stress level is given.

[0005] (2) Technical solution:

[0006] The present invention is a small sample accelerated aging test method for rubber components, which comprises the following four steps:

[0007] Step 1: Collect performance degradation data of rubber components under accelerated stress levels;

[0008] Step 2: Based on the degradation trajectory model, the performance degradation index of the sample is extrapolated to obtain its pseudo failure life;

[0009] Step 3: Based on the pseudo-failure life data, evaluate the one-sided confidence limit of the reliable life of the rubber component with high confidence and high reliability under accelerated stress level;

[0010] Step 4: Based on the linear acceleration model and combined with the confidence limit and difference product quotient theory, the one-sided lower confidence limit of the reliable life of the rubber component with high confidence and high reliability under normal use stress level is evaluated.

[0011] Wherein, in step 1, "collecting performance degradation data of rubber components under accelerated stress levels" is performed as follows:

[0012] Under the premise of not changing the failure mode and failure mechanism of the rubber component, two accelerated stress levels S2 and S1 (S1<S2) are selected to conduct accelerated aging tests respectively, and the performance degradation data of each sample at different times are recorded. i (i=1,2) There are n i (n i ≥2) samples participated in the aging test, among which the jth (j=1,2,…,n i The performance degradation data of the kth test sample is y ijk , the corresponding time is t ijk .

[0013] Among them, in step 2, "based on the degradation trajectory model, the performance degradation index of the sample is extrapolated to obtain its pseudo failure life", the method is as follows:

[0014] Assume that the performance degradation trajectory model of the rubber component is y=f(t; y0, α, β), and its common form is as follows:

[0015] y=y0exp(αt β ) (1)

[0016] y=y0+αt β (2)

[0017] Where y is the performance degradation at time t, y0 is an undetermined parameter characterizing the initial value of performance degradation, and α and β are both undetermined parameters characterizing the performance degradation rate.

[0018] Using accelerated stress level S i The performance degradation data of the jth sample (t ijk ,yijk ) is used to fit the parameters y0, α, and β, and their estimated values ​​are According to the performance degradation index threshold y th , we can get S i The pseudo failure life of the next j-th specimen is t ij for:

[0019]

[0020] In the formula, f -1 (·) is the inverse function of f(·).

[0021] Among them, in step 3, "based on the pseudo-failure life data, the high confidence and high reliability one-sided confidence limit of the reliable life of the rubber component under the accelerated stress level is evaluated", and the method is as follows:

[0022] Assume that the rubber component is at stress level S i The logarithmic life under (covering accelerated stress levels S2, S1 and normal use stress level S0) follows a normal distribution, and its reliability function is:

[0023]

[0024] In the formula, x = lnt is the logarithmic life span, μ i is the stress level S i The mean logarithmic lifespan under i is the stress level S i The standard deviation of the logarithmic lifespan under , Φ(·) is the standard normal distribution function.

[0025] According to the pseudo failure life data t under accelerated stress level ij , the one-sided confidence upper limit x of the logarithmic reliable life of the rubber component with confidence level γ and reliability R under accelerated stress levels S2 and S1 can be obtained respectively RU2,γ and the lower limit x RL1,γ for:

[0026]

[0027] In the formula, is the log-life sample mean, is the logarithmic life sample standard deviation, u R =Φ -1 (R) is the standard normal deviation with reliability R, and The degrees of freedom are n i -1, non-central parameter is The lower γ quantile and the 1-γ lower quantile of the noncentral t distribution of .

[0028] Among them, in step 4, "based on the linear acceleration model, combined with the confidence limit and difference product quotient theory, the one-sided confidence lower limit of the reliable life of the rubber component with high confidence and high reliability under the normal use stress level is evaluated", the method is as follows:

[0029] Assume the acceleration model of the rubber component is:

[0030]

[0031] In the formula, x Ri =μ i -u R σ i is the stress level S i The logarithmic reliable life with the reliability R, a and b are unknown parameters, YesS i is a known function of . At this time, μ i and σ i Respectively It is a linear relationship, and does not require the logarithmic life variance at each stress level to be equal. According to the logarithmic reliable life x under accelerated stress levels S2 and S1 R2 、x R1 , formula (7) can be further transformed into:

[0032] x Ri =ω(S i )x R1 +[1-ω(S i )]x R2 (8)

[0033]

[0034] In the formula, ω(S i ) is the stress difference coefficient.

[0035] Therefore, the logarithmic reliable life x of the rubber component under the normal use stress level S0 (S0<S1<S2) R0 It can be expressed as:

[0036] x R0 =ω(S0)x R1 +[1-ω(S0)]x R2 (10)

[0037] Then, using the one-sided confidence limits of the logarithmic reliable life under the two accelerated stress levels given by equations (5) and (6), the logarithmic reliable life x of the rubber component with a confidence level of γ and a reliability of R under the normal use stress level S0 can be obtained: R0 One-sided lower confidence limit for:

[0038]

[0039] Furthermore, according to the confidence limit and product-difference quotient theory, we can The confidence level γ * For precise calculation, the numerical calculation formula is:

[0040]

[0041] γ k =1-(k-0.5) / M,k=1,2,…,M (15)

[0042] In the formula, M is set according to the numerical calculation accuracy requirements (such as 10 3 , 10 4 wait), The degrees of freedom are n1-1 and the noncentrality parameter is The cumulative distribution function of the noncentral t distribution.

[0043] Finally, adjust γ in equation (13) to γ ** , so that the γ obtained by formula (12) * = equal to the preset confidence level γ, the reliable life t of the rubber component with confidence level γ and reliability level R under normal use stress level S0 can be obtained. R0 One-sided confidence lower limit t RL0,γ for:

[0044]

[0045] t RL0,γ =exp(x RL0,γ ) (17)

[0046] Through the above four steps, the accelerated aging test information of small samples of rubber components can be fully utilized to achieve a high-confidence and high-reliability assessment of the one-sided confidence lower limit of the reliable life of rubber components under normal use stress levels.

[0047] The beneficial effects of the present invention are as follows: the present invention can design and carry out accelerated aging tests for rubber components under small sample conditions, and evaluate the one-sided lower confidence limit of the reliable life of the rubber components under normal use stress levels under high confidence and high reliability requirements, which can greatly shorten the test cycle and save a large number of samples, and is of great significance for ensuring the long-term safe and reliable use of rubber components.

Brief Description of the Drawings

[0048] Figure 1 It is a schematic diagram of the process of the present invention.

[0049] Figure 2This is a line graph of the compression permanent deformation rate of a certain type of O-ring rubber seal at a temperature of 413K.

[0050] Figure 3 This is a line graph of the compression permanent deformation rate of a certain type of O-ring rubber seal at a temperature of 373K. [Specific implementation method]

[0051] The present invention is described in detail below with reference to the accompanying drawings.

[0052] The present invention proposes a small sample accelerated aging test method for rubber components, the flow chart of which is as follows: Figure 1 shown.

[0053] In the present invention, an example of a high temperature accelerated aging test of a certain type of O-shaped rubber sealing ring is used to illustrate the implementation mode of the present invention, and the specific steps are as follows:

[0054] Wherein, in step 1, "collecting performance degradation data of rubber components under accelerated stress levels" is performed as follows:

[0055] Under the premise of not changing the failure mode and failure mechanism of the O-ring rubber seal, two accelerated temperature levels S2 = 413K and S1 = 373K were selected to conduct high temperature aging tests respectively, and the compression permanent deformation rate ε of each sample at different times was recorded. There are 4 samples at each accelerated temperature level, and the test results at the accelerated temperature levels S2 and S1 are as follows: Figure 2 , Figure 3 shown.

[0056] Among them, in step 2, "based on the degradation trajectory model, the performance degradation index of the sample is extrapolated to obtain its pseudo failure life", the method is as follows:

[0057] The following formula is used to describe the performance degradation law of this type of O-ring rubber seal:

[0058] y=1-ε=y0exp(αt β ) (18)

[0059] The aging test data of a single sample is used to fit and estimate the parameters y0, α, and β, and then the degradation performance threshold y th =0.25 Substituting into formula (18), we can obtain the acceleration temperature level S i The pseudo failure life of the next j-th specimen is:

[0060]

[0061] The calculated results of pseudo failure life of each sample are summarized in Table 1.

[0062] Table 1 Calculation results of pseudo failure life of O-ring rubber seal

[0063]

[0064]

[0065] Among them, in step 3, "based on the pseudo-failure life data, the high confidence and high reliability one-sided confidence limit of the reliable life of the rubber component under the accelerated stress level is evaluated", and the method is as follows:

[0066] It is known that the logarithmic life x = lnt of this type of O-shaped rubber sealing ring follows a normal distribution. According to the pseudo-failure life data in Table 1, the one-sided confidence upper limit x of the logarithmic reliable life of this type of O-shaped rubber sealing ring with a confidence level of γ = 0.90 and a reliability of R = 0.95 at the accelerated temperature level S2 = 413K and S1 = 373K can be obtained respectively. RU2,γ and the lower limit x RL1,γ for:

[0067] x RU2,γ =3.781-1.845×0.096 / 2=3.692 (20)

[0068] x RL1,γ =5.599-7.913×0.132 / 2=5.075 (21)

[0069] Among them, in step 4, "based on the linear acceleration model, combined with the confidence limit and difference product quotient theory, the one-sided confidence lower limit of the reliable life of the rubber component with high confidence and high reliability under the normal use stress level is evaluated", the method is as follows:

[0070] Using the Arrhenius model as the acceleration model, the logarithmic reliable life x of this type of O-ring rubber seal at the normal operating temperature level S0 = 313K with a confidence level of γ = 0.90 and a reliability of R = 0.95 is R0 One-sided lower confidence limit for:

[0071]

[0072] Furthermore, the confidence γ can be obtained * for:

[0073] γ * =0.9484>γ (23)

[0074] Finally, adjust γ in equation (22) to γ ** =0.8076, so that the obtained γ *= 0.90, we can obtain the reliable life t of this type of O-shaped rubber sealing ring at the normal operating temperature level S0 = 313K with a confidence level of γ = 0.90 and a reliability of R = 0.95 R0 One-sided confidence lower limit t RL0,γ for:

[0075] x RL0,γ =2.979×5.199-1.979×3.670=8.226 (24)

[0076] t RL0,γ =exp(8.226)=3735 days=10.2 years(25).

Claims

1. A small sample accelerated aging test method for rubber components, characterized in that: The steps include: Step 1: Collect performance degradation data of rubber components under accelerated stress levels; Step 2: Based on the degradation trajectory model, the performance degradation index of the sample is extrapolated to obtain its pseudo failure life; Step 3: Based on the pseudo-failure life data, evaluate the one-sided confidence limit of the reliable life of the rubber component with high confidence and high reliability under accelerated stress level; Step 4: Based on the linear acceleration model and combined with the confidence limit and difference product quotient theory, the one-sided lower confidence limit of the reliable life of the rubber component with high confidence and high reliability under normal use stress level is evaluated.

2. A small sample accelerated aging test method for rubber components according to claim 1, characterized in that: In step 1, specifically: without changing the failure mode and failure mechanism of the rubber component, select two accelerated stress levels S2 and S1, S1 < S2; conduct accelerated aging tests respectively, and record the performance degradation data of each sample at different times; set the accelerated stress level S i There are n i The samples participate in the aging test, and the performance degradation data of the jth sample detected for the kth time is y ijk , the corresponding time is t ijk ; where i = 1, 2; n i ≥2; j=1,2,…,n i .

3. The method for accelerated aging test of a small sample of a rubber component according to claim 1, characterized in that: In step 2, specifically: assume that the performance degradation trajectory model of the rubber component is y=f(t; y0, α, β), which is in the following form: y=y0exp(αt β ) (1) y=y0+αt β (2) Where y is the performance degradation at time t, y0 is an undetermined parameter characterizing the initial value of performance degradation, and α and β are both undetermined parameters characterizing the performance degradation rate.

4. A small sample accelerated aging test method for rubber components according to claim 3, characterized in that: Using accelerated stress level S i The performance degradation data of the jth sample (t ijk ,y ijk ) is used to fit the parameters y0, α, and β, and their estimated values ​​are According to the performance degradation index threshold y th , get S i The pseudo failure life of the next j-th specimen is t ij for: In the formula, f -1 (·) is the inverse function of f(·).

5. The method for accelerated aging test of a small sample of a rubber component according to claim 1, characterized in that: In step 3, specifically: assume that the rubber component is at a stress level S i The logarithmic life under follows a normal distribution, and the reliability function is: In the formula, x = lnt is the logarithmic life span, μ i is the stress level S i The mean logarithmic lifespan under i is the stress level S i The standard deviation of the logarithmic lifespan under , Φ(·) is the standard normal distribution function.

6. A small sample accelerated aging test method for rubber components according to claim 5, characterized in that: According to the pseudo failure life data t under accelerated stress level ij , respectively obtain the upper confidence limit x of the logarithmic reliable life of the rubber component with confidence level γ and reliability R under accelerated stress levels S2 and S1 RU2,γ and the lower limit x RL1,γ for: In the formula, is the log-life sample mean, is the logarithmic life sample standard deviation, u R =Φ -1 (R) is the standard normal deviation with reliability R, and The degrees of freedom are n i -1, non-central parameter is The lower γ quantile and the 1-γ lower quantile of the noncentral t distribution of .

7. The method for accelerating aging of a small sample of a rubber component according to claim 1, characterized in that: In step 4, specifically: assume that the acceleration model of the rubber component is: In the formula, x Ri =μ i -u R σ i is the stress level S i The logarithmic reliable life with the reliability R, a and b are unknown parameters, YesS i A known function of i and σ i Respectively It is a linear relationship, and does not require the variance of the logarithmic life at each stress level to be equal; according to the logarithmic reliable life x under the accelerated stress levels S2 and S1 R2 、x R1 , and further transform formula (7) into: x Ri =ω(S i )x R1 +[1-ω(S i )]x R2 (8) In the formula, ω(S i ) is the stress difference coefficient.

8. A small sample accelerated aging test method for rubber components according to claim 7, characterized in that: Logarithmic reliable life x of rubber components under normal use stress level S0 R0 It is expressed as: x R0 =ω(S0)x R1 +[1-ω(S0)]x R2 (10) Where S0<S1<S2; Using the one-sided confidence limits of the logarithmic reliable life under the two accelerated stress levels given by equations (5) and (6), the logarithmic reliable life x of the rubber component with a confidence level of γ and a reliability of R under the normal use stress level S0 is obtained. R0 One-sided lower confidence limit for:

9. A small sample accelerated aging test method for rubber components according to claim 8, characterized in that: According to the confidence limit and product-difference quotient theory, The confidence level γ * For precise calculation, the numerical calculation formula is: γ k =1-(k-0.5) / M,k=1,2,…,M (15) In the formula, M is determined according to the numerical calculation accuracy requirements. The degrees of freedom are n1-1 and the noncentrality parameter is The cumulative distribution function of the noncentral t distribution.

10. A small sample accelerated aging test method for rubber components according to claim 9, characterized in that: Adjust the value of γ in equation (13) to γ ** , so that the γ obtained by formula (12) * = equal to the preset confidence level γ, and the reliable life t of the rubber component with confidence level γ and reliability R under normal use stress level S0 is obtained. R0 One-sided confidence lower limit t RL0,γ for: t RL0,γ =exp(x RL0,γ ) (17)。

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