CN109030548A - Based on the polymer material thermal lifetime appraisal procedure for becoming activation energy - Google Patents
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Abstract
The invention discloses a kind of based on the polymer material thermal lifetime appraisal procedure for becoming activation energy, the crucial performance indicator trend that changes with time is accelerated in Heat Ageing to carry out segment processing at equal intervals according to material, the ageing time at each interval is undergone to calculate corresponding average activation energy further according to material under different temperatures, and the average activation energy of different interval is introduced into thermal lifetime assessment models, life appraisal is finally carried out stage by stage.The method of applied regression analysis and correlation test analyzes gained regression equation in above-mentioned calculating process, the validity of confirmation gained regression equation；The not only perfect life appraisal model of this method, improves the accuracy of assessment, while from the angle of mathematical statistics method, it is ensured that the validity of test data and analysis method.
Description
Technical Field
The invention relates to an evaluation method of polymer material aging life, in particular to a polymer material thermal aging life evaluation method based on activation energy.
Background
Polymer materials generally exhibit a characteristic index during aging, which is a gradual change with aging of the polymer material, for example: at present, foreign researches show that the degree of polymerization is an important parameter for representing the mechanical strength of the insulating paper, and is the most direct and reliable index for determining the aging and residual life of the insulating paper. At present, most research results are that accelerated thermal aging tests are carried out on insulating paper in a laboratory environment, and service life prediction is carried out by combining an arrhenius service life evaluation model according to the change trend of obtained performance indexes along with aging time. The parametric activation energy in the arrhenius model is a characteristic parameter of the polymer material and is an internal factor for determining the chemical reaction rate of the polymer material, and the larger the activation energy of the material is, the smaller the reaction rate is.
However, the existing evaluation methods use average activation energy for life calculation, and do not consider the change of the activation energy in the process of accelerating aging of the material. Considering that molecular chains of partial polymer materials are broken after different aging times, the characteristic parameters of the partial polymer materials are irreversibly changed, so that the activation energy of the partial polymer materials is changed. It has been shown that the activation energy of the polymer material is not constant during aging. Therefore, when life evaluation is performed, the use of the average activation energy inevitably leads to inaccurate evaluation results.
On the other hand, the thermal aging test based on the arrhenius model does not have a step of evaluating the effectiveness of the tested structure, and the above problems are the problems to be solved in the art.
Disclosure of Invention
The invention aims to provide a polymer material thermal aging life evaluation method based on variable activation energy, which can evaluate the thermal aging life of a polymer material with variable activation energy more accurately.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: the method for evaluating the thermal aging life of the polymer material based on the activation energy is characterized by comprising the following steps of:
the method for evaluating the thermal aging life of the polymer material based on the activation energy comprises the following steps:
s1, carrying out an accelerated aging test on the polymer material, recording the performance index of the polymer material before aging as an initial performance index and the performance index of the polymer material at the end of life as an end performance index,
recording a plurality of intermediate performance indexes and aging time corresponding to the intermediate performance indexes between the initial performance index and the termination performance index, wherein the change process of two adjacent intermediate performance indexes is an aging interval, the performance indexes are parameters representing the aging degree of the polymer material,
s2, respectively calculating the average activation energy and the proportionality constant of the polymer material in the aging process for one aging interval at a time according to the temperature for carrying out the accelerated aging test and the time required for each aging interval at the temperature,
wherein y is lnt, x is 1/T, a is Ea/R, b is lnA, a represents a proportionality constant; eaR is the Boltzmann constant, which is the activation energy of the chemical reaction,
and S3, according to an Arrhenius model, obtaining the time required by each aging interval at the required evaluation temperature through the average activation energy and the proportionality constant of each aging interval in the aging process, and adding the time required by each aging interval at the required evaluation temperature to obtain the aging life at the required evaluation temperature.
According to the method, the aging process of the polymer is subjected to segmented treatment through the performance indexes of the polymer in the aging process, and the activation energy required by the aging interval of the material in the aging process is different, so that the time required by the aging interval of the material in the aging process at the required evaluation temperature is calculated in a segmented manner to evaluate the overall aging life of the polymer material at the required evaluation temperature, and the thermal aging life of the polymer material with the changeable activation energy can be evaluated more accurately.
Further, the method comprises the following steps: in step S1, the performance index is a degree of polymerization, and the polymer material is an insulating paper material.
Further, the method comprises the following steps: the parameter a and the parameter b in the step S2 are obtained by the following steps:
according to the Arrhenius model, the following results are obtained:
K(t)＝Aaexp(-Ea/RT) (1)
wherein K (t) represents the reaction rate, AaRepresents a proportionality constant; eaR is the Boltzmann constant, which is the activation energy of the chemical reaction,
taking logarithm of two sides of the formula (1), and simply replacing the sign of the logarithm to obtain the logarithm,
lnτ＝lnA+Ea/(RT) (2)
wherein, tau represents the aging time,
order: lnt, x 1/T, Ea/R, b lnA, yielding: y is equal to ax + b and,
the least square method is utilized to obtain the result,
1. further, the method comprises the following steps: in step S3, the method specifically includes the steps of,
according to the Arrhenius model, it can be known that,
where Tu denotes the desired evaluation temperature, τ denotes the aging time,
the activation energy and the proportionality constant of each time of passing an aging interval in the aging process are taken into the formula (6) and summed to obtain a formula,
wherein n represents the number of aging intervals, τ, that the polymeric material needs to undergo in total when it ages to end-of-lifeUThe aging life is expressed, and the aging life at a desired evaluation temperature is evaluated according to equation (10).
Further, the method comprises the following steps: in the step S1, the polymer material is subjected to an accelerated aging test under at least two temperature conditions.
Further, the method comprises the following steps: in step S1, the difference between all adjacent intermediate performance indicators is the same.
Further, the method comprises the following steps: further comprising the steps of: the effectiveness of the aging life is evaluated,
the linear regression correlation coefficient r is calculated,
when r is less than 0.95, the significance of the obtained regression equation is low, the result is judged to be invalid,
when r is more than 0.95, the significance of the obtained regression equation is low, and the result is judged to be effective.
The invention has the beneficial effects that: according to the method, the aging degree of the material is represented by adopting the performance indexes, the average activation energy required by each performance index change in the aging process of the material is different, the time required by each performance index change in the aging process at the required evaluation temperature is calculated by segmentation, the total aging life of the material at the required evaluation temperature is evaluated, and the factors of the activation energy change of the polymer material in the aging process are fully considered, so that the thermal aging life of the polymer material with the changed activation energy can be evaluated more accurately, and further, the evaluation effectiveness is determined by calculating the linear regression correlation coefficient, and the effectiveness and the accuracy of an evaluation structure can be effectively improved.
Drawings
FIG. 1 shows the trend of activation energy with aging time in examples of the present application.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
The method for evaluating the thermal aging life of the polymer material based on the activation energy comprises the following steps:
s1, carrying out an accelerated aging test on the polymer material, recording the performance index of the polymer material before aging as an initial performance index and the performance index of the polymer material at the end of life as an end performance index,
recording a plurality of intermediate performance indexes and aging time corresponding to the intermediate performance indexes between the initial performance index and the termination performance index, wherein the change process of two adjacent intermediate performance indexes is an aging interval, the performance indexes are parameters representing the aging degree of the polymer material,
taking the insulating paper material as an example, in the aging process of the insulating paper material, the polymerization degree of the insulating paper material gradually decreases along with the aging of the insulating paper, and therefore, the polymerization degree is the performance index of the insulating paper material.
Taking a polymer material with polymerization degree as a performance index as an example, the method specifically comprises the steps of firstly, determining the polymerization degree P of the key performance index of the polymer material,
setting a periodic detection period according to actual conditions, periodically detecting and recording the numerical value of the polymerization degree of the tested polymer material and the corresponding aging time, thereby obtaining the linear relation between the aging time and the polymerization degree, and obtaining the initial value P of the polymerization degree of the polymer material before aging by carrying out an accelerated aging test or a known query0And an end-of-life value P at end-of-lifen，
At P0And PnIn which i represents in turn an integer from 1 to n, in particular P, an intermediate degree of polymerization Pi, in which P is a number of intermediate values1，P2…Pn-1While assuming P0>P1>P2>…>Pn-1>Pn. The performance index is from an initial value P0Initially, each time the next pre-specified intermediate degree of polymerization is reached, an aging interval is defined.
In order to ensure that the test result can effectively reflect the change rule of the material characteristics, the invention adopts the aging interval to set the intermediate value of the performance index, namely the adjacent two intermediate polymerization degrees Pi-1And PiThe difference values therebetween are the same value.
After the test is finished, finding out the time points corresponding to the intermediate polymerization degrees and the final polymerization degree at each temperature point, and considering that the performance index acquisition in the accelerated aging test process adopts a periodic detection mode, the numerical value is difficult to correspond to the pre-specified intermediate polymerization degree. Therefore, according to the linear relationship between the aging time and the polymerization, the invention finds out the pre-specified performance index and the aging time at different corresponding temperature points on the basis of the initial data by adopting the interpolation principle, as shown in table 1.
TABLE 1 aging time (h) for each performance index value at different temperature points
And S2, respectively calculating the average activation energy and the proportionality constant of the polymer material subjected to one aging interval each time in the aging process at the temperature through an Arrhenius model according to the temperature for carrying out the accelerated aging test and the time required for the polymer material subjected to the aging interval each time at the temperature.
Taking the polymer material with the polymerization degree as the performance index as an example, the method specifically comprises the step of respectively calculating the test time required by the performance index of a test sample at a plurality of temperatures for each aging interval, namely from Pi-1Change to PiTime when i is 1, 2, …, n, i.e. t1i-t1(i-1),…,tji-tj(i-1),…,tmi-tm(i-1)。
According to the Arrhenius model, the following results are obtained:
K(t)＝Aaexp(-Ea/RT) (1)
wherein K (T) represents the reaction rate, which is inversely related to the operating time τ at the operating temperature T; a. theaRepresents a proportionality constant; eaActivation energy for chemical reaction, which indicates the aging sensitivity of the material; r is the Boltzmann constant, whose values are: 0.816X 10-4eV/K。
Taking logarithm of two sides of the formula (1) and simply processing to obtain:
lnτ＝lnA+Ea/(RT) (2)
the formula (2) is a traditional model for predicting the thermal aging life of the insulating paper material, wherein tau represents aging time, and A represents a proportionality constant.
Finishing the formula (2) to ensure that: y — ln τ, x — 1/T, a — Ea/R, and b — lnA, we can obtain: and y is ax + b. Parameters a and b can be directly calculated by combining accelerated aging test data at multiple temperature points by using a least square method, wherein the calculation method is as shown in formula (3) and formula (4).
On the basis of the above, the significance of the regression equation can be confirmed by the linear regression correlation coefficient r, which can be calculated by the following formula (5).
When r is less than 0.95, the obtained regression equation is considered to have low significance and no practical value, and the validity of the evaluation result is also reduced.
Will be T in Table 1jThe data of (a) is substituted into the expressions (3), (4) and (5), thereby obtaining the expressions (7), (8) and (9).
P can be calculated from the following equations (7), (8) and (9)i-1To reach PiCorresponding parameter aj、bjAnd the correlation coefficient rjAnd further obtained from Pi-1To reach PiCorresponding average activation energy EaiAnd Ai。
Wherein x isj＝1/Tj,yji＝ln(tji-tj(i-1))。
Since there are two parameters in the arrhenius model: activation energy EaAnd the proportional constant A, so that the experimental formula at least under two temperature conditions can be calculated, the accelerated aging test is started under at least two temperature conditions, the test error and other factors are considered, the adopted accelerated aging test has the temperature as much as possible, and the linear regression correlation coefficient r is calculated through regression analysis, so that the activation energy E can be more accurately calculatedaAnd the proportionality constant a.
And S3, according to an Arrhenius model, obtaining the time required by each aging interval at the required evaluation temperature through the average activation energy and the proportionality constant of each aging interval in the aging process, and adding the time required by each aging interval at the required evaluation temperature to obtain the aging life at the required evaluation temperature.
In particular, the formula (2) is modified in accordance with the activation energy E obtainedaWith the proportionality constant A, the desired estimated temperature T can be calculatedUAging time τ of the following materials:
average activation energy E according to aging intervala1、Ea2……EanWith proportionality constants Ai, A2……AnBringing in formula (6) and summing to obtain:
wherein tau isUIndicating the aging life.
By means of the formula (10), the different required evaluation temperatures T can be calculatedUThe service life of the material was evaluated, and thus the heat aging life of the polymer material was evaluated.
To facilitate an understanding of the present application, the present application also provides the following specific examples:
the transformer insulating paper is a polymer material, and the aging sensitive state index of the transformer insulating paper is the polymerization degree. The polymerization degree of the new insulating paper is between 1000 and 1200, and when the polymerization degree of the new insulating paper is reduced to about 250, the mechanical property of the insulating paper does not meet the requirement any more, namely the service life is considered to be terminated.
Under the condition of full-load operation of the transformer, the top oil temperature is about 90 ℃, but the oil temperature is influenced by load change and seasonal change, so that the oil temperature of the transformer is assumed to be 80 ℃, namely the service life of the insulating paper under the condition of 80 ℃ is evaluated.
The accelerated aging test is carried out on the insulating paper at three temperatures of 110 ℃, 120 ℃ and 130 ℃, the polymerization degree of the insulating paper is periodically detected, and the test results are shown in table 2.
TABLE 2 polymerization degree as a function of aging time at different temperatures
Assuming that the activation energy of the insulating paper does not change, the heat aging life was evaluated in the prior art:
the test cut-off times for the reduction of the degree of polymerization from 1150 to 250 at the different test temperatures are shown in Table 3,
TABLE 3 conventional activation energy calculation
Calculated according to the formulas (3) and (4):
a＝9776.425
b＝-15.926
thereby, it is possible to obtain:
Ea＝0.8427
A＝1.2115×10-7
the correlation coefficient of the regression equation can be calculated according to equation (5):
r＝0.9926
i.e., the linear relationship between x and y is significant, the resulting linear regression equation is valid.
The service life of the insulating paper at 80 ℃ can be calculated according to the formula (6): 127676.1 hours, about 14.57 years.
In fact, the activation energy of the above insulating paper is changed during aging, so the heat aging life is evaluated by the method of the present application, and the results are as follows:
with each 100-degree-of-polymerization decrease as an aging interval, a set of intermediate degrees of polymerization with equal intervals of decreasing degree of polymerization with aging is preset, as shown in table 4, and time points corresponding to the preset intermediate degrees of polymerization at different temperatures are obtained by interpolation calculation based on the above test data, as shown in table 4.
TABLE 4 aging time (h) corresponding to the preset polymerization degree at different temperatures
The test time for the decrease in polymerization from 1150 to 1050 was calculated as shown in table 5:
TABLE 5 calculation of activation energy at polymerization degree drop from 1150 to 1050
Calculated by using equations (7) and (8):
a1＝6166.856
b1＝-12.325，
thereby, it is possible to obtain:
Ea1＝0.5316
A1＝1.206×10-5
the correlation coefficient of the regression equation can be calculated according to equation (9):
r＝0.9887
i.e., the aging interval during which the degree of polymerization decreases from 1150 to 1050, the linear relationship between x and y is significant and the resulting linear regression equation is valid.
The aging time corresponding to the aging interval at 80 ℃ can be calculated according to the formula (10) to be 462.7 hours, which is about 0.053 years.
Similarly, the test time for each aging interval for which the polymerization degree was subjected to different temperatures was calculated, and the average activation energy for the aging interval and the aging time for each aging interval were calculated, wherein the results of the aging time calculation for each aging interval at 80 ℃ are shown in table 6.
TABLE 6 results of activation energy calculation for different test intervals
Finally, the life evaluation result considering the change of the activation energy is calculated according to the formula (10).
I.e., a service life of 133478 hours under actual use conditions, which is about 15.24 years.
It can be seen that the method has a larger result than that of the conventional heat aging evaluation method, and the method is more suitable for the actual aging process of the insulating paper than the conventional heat aging life evaluation method in consideration of the fact that the activation energy of the polymer material is continuously changed in the actual aging process, so that the evaluation result has more reference value.
As shown in table 6 and fig. 1, it can be seen that the activation energy showed an upward trend as a whole, conforming to the characteristics of the insulating paper material. This is because the degree of polymerization of the insulating paper is 1000 to 1300, and the molecular chain thereof contains the number of glucose monomers, but is cracked by heat, i.e., the molecular chain is broken, resulting in a decrease in the degree of polymerization. With the progress of thermal cracking, molecular chains are continuously reduced, the difficulty of thermal cracking is gradually increased, and macroscopically, the aging speed is reduced.
According to the method, the ageing degree of the material is represented by adopting the degree of polymerization, the average activation energy required by every reduction of the degree of polymerization in the ageing process is different according to the material, the time required by every reduction of the degree of polymerization in the ageing process at the required evaluation temperature is calculated by segmentation, the total ageing life of the material at the required evaluation temperature is evaluated, the thermal ageing life of the polymer material with the changed activation energy can be more accurately evaluated, further, the linear regression correlation coefficient is calculated, the evaluation effectiveness is determined, and the evaluation structure effectiveness and accuracy can be effectively improved.
The above-described embodiments are merely preferred embodiments for fully illustrating the invention, and the scope of the invention is not limited thereto. The equivalent substitution or change made by the person skilled in the art on the basis of the invention is within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (7)
1. The method for evaluating the thermal aging life of the polymer material based on the activation energy is characterized by comprising the following steps of:
s1, carrying out an accelerated aging test on the polymer material, recording the performance index of the polymer material before aging as an initial performance index and the performance index of the polymer material at the end of life as an end performance index,
recording a plurality of intermediate performance indexes and aging time corresponding to the intermediate performance indexes between the initial performance index and the termination performance index, wherein the change process of two adjacent intermediate performance indexes is an aging interval, the performance indexes are parameters representing the aging degree of the polymer material,
s2, respectively calculating the average activation energy and the proportionality constant of the polymer material in the aging process for one aging interval at a time according to the temperature for carrying out the accelerated aging test and the time required for each aging interval at the temperature,
wherein, y is ln T, x is 1/T, a is Ea/R, b is ln a, a represents a proportionality constant; eaR is the Boltzmann constant, which is the activation energy of the chemical reaction,
and S3, according to an Arrhenius model, obtaining the time required by each aging interval at the required evaluation temperature through the average activation energy and the proportionality constant of each aging interval in the aging process, and adding the time required by each aging interval at the required evaluation temperature to obtain the aging life at the required evaluation temperature.
2. The method for evaluating the thermal aging life of a polymer material based on activation energy according to claim 1, wherein the performance index in step S1 is the degree of polymerization, and the polymer material is an insulating paper material.
3. The method for evaluating the thermal aging life of a polymer material based on activation energy according to claim 1, wherein the parameter a and the parameter b in the step S2 are obtained by the following steps:
according to the Arrhenius model, the following results are obtained:
K(t)＝Aaexp(-Ea/RT) (1)
wherein,k (t) represents the reaction rate, AaRepresents a proportionality constant; eaR is the Boltzmann constant, which is the activation energy of the chemical reaction,
logarithm is taken from two sides of the formula (1) and the logarithm is simply processed to obtain the product,
lnτ＝ln A+Ea/(RT) (2)
wherein τ represents aging time, and A represents proportionality constant
Order: y ═ ln T, x ═ 1/T, a ═ Ea/R, b ═ ln a, we can derive: y is equal to ax + b and,
the parameters can be derived using a least squares method,
4. the method for evaluating the thermal aging life of a polymer material based on activation energy as claimed in claim 2, wherein the step S3 specifically comprises the steps of,
according to the Arrhenius model, it can be known that,
where Tu denotes the desired evaluation temperature, τ denotes the aging time,
the activation energy and the proportionality constant of each time of passing an aging interval in the aging process are taken into the formula (6) and summed to obtain a formula,
wherein n represents the number of aging intervals, τ, that the polymeric material needs to undergo in total when it ages to end-of-lifeUExpressing the aging life, the aging life at the desired evaluation temperature is determined according to the formula (10)And (6) evaluating.
5. The method for evaluating the thermal aging life of a polymer material based on activation energy according to claim 1, wherein the polymer material is subjected to an accelerated aging test under at least two temperature conditions in step S1.
6. The method for evaluating the thermal aging life of a polymer material based on activation energy of claim 1, wherein in step S1, the difference between all adjacent intermediate performance indicators is the same.
7. The method for assessing the thermal aging life of a polymer material based on activation energy as claimed in claim 2, further comprising the steps of: the effectiveness of the aging life is evaluated,
the linear regression correlation coefficient r is calculated,
when r is less than 0.95, the significance of the obtained regression equation is low, the result is judged to be invalid,
when r is more than 0.95, the significance of the obtained regression equation is low, and the result is judged to be effective.
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| CN111859727A (en) * | 2020-06-02 | 2020-10-30 | 南方电网科学研究院有限责任公司 | Method for establishing relation between basin-type insulator activation energy and insulation margin |
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| CN114062232A (en) * | 2021-09-30 | 2022-02-18 | 国高材高分子材料产业创新中心有限公司 | Oven, and automatic measuring system and method for thermal-oxidative aging life of polymer material |
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