CN115081144B - Thermoelectric device performance degradation prediction method and application - Google Patents
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Abstract
The application belongs to the technical field of thermoelectric devices, and discloses a thermoelectric device performance degradation prediction method and application, wherein the method comprises the following steps: acquiring an initial resistance value of each thermoelectric unit in the thermoelectric device; performing thermal cycle and/or power cycle on the thermoelectric device, and measuring the resistance value of each thermoelectric unit after periodically spacing a preset cycle number; obtaining crack lengths of each thermoelectric unit after different cycle numbers, and fitting to obtain a primary function; acquiring a cycle number linear relation and an increase rate linear relation; inputting the average strain energy density of the combined layer of the thermoelectric units to be predicted into a cycle number linear relation to obtain the crack germination cycle number of the thermoelectric units to be predicted, and if the cycle number is greater than the crack germination cycle number, degrading the performance of the thermoelectric units to be predicted; otherwise, no degradation occurs; and (3) adding the resistance of each thermoelectric unit and comparing the added resistance with the initial resistance added value to obtain the degradation condition of the whole thermoelectric device to be predicted. The application can accurately predict the performance degradation condition of the thermoelectric device.
Description
Technical Field
The invention belongs to the technical field related to performance prediction of thermoelectric devices, and particularly relates to a performance degradation prediction method and application of a thermoelectric device.
Background
The thermoelectric device is a solid-state device which is manufactured based on five thermoelectric effects such as Seebeck effect, peltier effect, thomson effect, fourier effect and Joule effect, and can realize direct conversion of heat energy and electric energy. The thermoelectric device has the advantages of no moving parts, no noise, quick response, easy control, easy integration and the like, and is widely applied to the fields of industrial waste heat and automobile exhaust waste heat recovery, radioisotope power generation, local power supply application, electronic device heat management, infrared detection, accurate temperature control, household refrigeration and the like.
The prediction of the performance degradation condition of the thermoelectric device in the use process has great significance for improving the reliability of the whole system, and particularly for the application fields with extreme working conditions, such as radioisotope power generation, and high reliability requirements, the prediction of the performance degradation condition of the thermoelectric device in the use process can optimize the system design and ensure the system safety.
The prior researches show that the main mechanism of the performance degradation of the thermoelectric device is as follows: the thermal cycle or power cycle conditions cause cyclic thermal stress in the thermoelectric device, and under the action of the cyclic thermal stress, the thermoelectric unit bonding layer becomes the weakest part in the device, cracks appear in the thermoelectric unit bonding layer, and further the electrical connection is affected, so that performance degradation occurs.
However, there is no systematic and universal method for predicting the performance degradation of the thermoelectric device, and therefore, a scientific method for predicting the performance degradation of the thermoelectric device is needed to improve the universality and accuracy of the performance prediction of the thermoelectric device.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides a thermoelectric device performance degradation prediction method and application, which can accurately predict the performance degradation condition of a thermoelectric device.
To achieve the above object, according to one aspect of the present invention, there is provided a thermoelectric device performance degradation prediction method, the method comprising: s1: respectively acquiring an initial resistance value of each thermoelectric unit in the thermoelectric device; s2: performing thermal cycle and/or power cycle on the thermoelectric device, and measuring the resistance value of each thermoelectric unit after periodically spacing a preset cycle number; s3: obtaining crack lengths in each thermoelectric unit bonding layer after different cycle numbers based on the cycle number, the resistance value and the characteristic length of the thermoelectric unit; s4: obtaining a plurality of groups of corresponding results of the cycle number and the crack length, fitting the results to obtain a primary function of each thermoelectric unit taking the crack length as a dependent variable and taking the cycle number as an independent variable, and further obtaining the growth rate of cracks along with the cycle number and the cycle number of crack germination according to the primary function; s5: respectively constructing a linear relation between the cycle number of crack germination and the linear relation between the growth rate of the crack along with the cycle number and the crack germination cycle number and the growth rate of the average strain energy density of the corresponding thermoelectric unit bonding layer; s6: inputting the average strain energy density of the combined layer of the thermoelectric units to be predicted into the cycle number linear relation, obtaining the cycle number of the thermoelectric units to be predicted, and obtaining the resistance of the corresponding thermoelectric units to be predicted based on the relation in the steps S3-S5 if the cycle number is greater than the cycle number of crack germination; otherwise, no degradation occurs; s7: and (3) obtaining the resistance of each thermoelectric unit by adopting the method in the step S6, adding the resistances of each thermoelectric unit, and comparing the added resistances with the initial resistance superposition value to obtain the degradation condition of the whole thermoelectric device to be predicted.
Preferably, the crack length a i,Ncyc in step S3 has the expression:
Where l is the characteristic length of the thermoelectric unit, R 0i is the initial resistance value of the i-th thermoelectric unit, i=1, 2,3, …, n, n is the total number of thermoelectric units in the thermoelectric device, and R ei,Ncyc is the resistance value of the i-th thermoelectric unit measured after a preset number of cycles.
Preferably, the first order function expression in step S4 is:
Wherein, Is the growth rate of the ith thermoelectric unit crack with the number of cycles; n 0,i is the number of cycles of crack initiation for the ith thermoelectric unit.
Preferably, the linear relationship of the crack initiation cycle number in step S5 is:
lg N0,i＝K1+K2*lg(ΔWave,i)
the linear relation of the growth rate is as follows:
Wherein, Is the growth rate of the ith thermoelectric unit crack with the number of cycles; n 0,i is the number of cycles of crack initiation for the ith thermoelectric unit, K 1,K2,K3,K4 is the coefficient, and aw ave,i is the average strain energy density of the ith thermoelectric unit bond line.
Preferably, the obtaining the resistance of the corresponding thermoelectric unit to be predicted based on the relation in steps S3 to S5 in step S6 is specifically obtaining the resistance R e,j of the thermoelectric unit to be predicted based on the growth rate linear relation, the linear function and the crack length formula:
Wherein R 0,j is the initial resistance value of the j-th thermoelectric unit to be predicted, N 0,j is the cycle number of crack germination of the j-th thermoelectric unit to be predicted, and DeltaW ave,j is the average strain energy density of the j-th thermoelectric unit bonding layer to be predicted.
Preferably, the average strain energy density of the bonding layer of the thermoelectric unit is obtained by adopting a finite element simulation calculation mode according to working conditions.
Preferably, the characteristic length of the thermoelectric unit is the thermoelectric leg cross-sectional side length for a square thermoelectric leg and the thermoelectric leg cross-sectional diameter for a circular thermoelectric leg.
According to another aspect of the present invention, there is provided the use of the above-described thermoelectric device performance degradation prediction method, which is applicable to a thermoelectric device of a thermoelectric cell array arrangement.
Preferably, the thermoelectric unit is comprised of a pair of PN thermoelectric legs, the thermoelectric units being thermally connected in parallel with each other and electrically connected in series or electrically isolated, the resistance of each pair of thermoelectric units being measured separately.
In general, compared with the prior art, the thermoelectric device performance degradation prediction method and application provided by the invention have the following beneficial effects:
1. According to the application, the thermoelectric performance degradation is predicted based on a crack growth mechanism, the predicted thermoelectric performance degradation is completely consistent with the thermoelectric device performance degradation mechanism, then the relation between the crack and the cycle number is obtained, and further the crack growth rate and the cycle number of crack germination can be obtained, and the thermoelectric device performance degradation is further predicted by combining the average strain energy density of the bonding layer.
2. The linear function of the cycle number and the crack length is established, and then the increase rate of the crack along with the cycle number and the cycle number of crack germination can be directly seen from the slope and the intercept of the linear function, so that the basis is provided for the preliminary evaluation of the thermoelectric unit in the later stage.
3. The scheme of the application is particularly suitable for thermoelectric devices arranged in the thermoelectric unit array, the model parameters can be obtained by the structure only under single working condition and experimental condition of a single device, the method is convenient and quick, and the method has universality and is particularly suitable for a series of predicted samples with the same geometric dimensions of a substrate and thermoelectric arms and different thermoelectric arm arrays.
Drawings
FIG. 1 is a step diagram of a method of predicting performance degradation of a thermoelectric device according to the present application;
FIG. 2 is a flow chart of a method of predicting performance degradation of a thermoelectric device according to the present application;
Fig. 3 is a schematic structural view of the thermoelectric device according to an embodiment of the present application, wherein (a) is a schematic view of the thermoelectric unit, (b) is an external front view of the thermoelectric device, (c) is a bottom view of an internal structure of the thermoelectric device, and (d) is a top view of the internal structure of the thermoelectric device.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
Referring to fig. 1 and 2, the present invention provides a method for predicting performance degradation of a thermoelectric device, which includes the following steps S1 to S7, specifically the following steps.
S1: the initial resistance value of each thermoelectric unit in the thermoelectric device is obtained separately.
As shown in fig. 3, which shows a structure diagram of a thermoelectric device for performing experiments and obtaining model data, the experimental device has an array of thermoelectric units radiating from the center to the top angle, each thermoelectric unit is composed of a pair of PN thermoelectric arms connected in series, and the thermoelectric units are electrically insulated from each other by being connected in thermal parallel.
Assuming a total of n thermoelectric units in the thermoelectric device, the initial resistance value R 0i, i=1, 2,3, …, n of each thermoelectric unit in the thermoelectric device is measured separately.
S2: and performing thermal cycle and/or power cycle on the thermoelectric device, and measuring the resistance value of each thermoelectric unit after periodically spacing a preset cycle number.
For example, the resistance value R ei,Ncyc, i=1, 2,3, …, n of each thermoelectric unit is obtained by performing a measurement after 10 intervals of each cycle.
S3: the crack length a i,Ncyc in each thermoelectric unit bonding layer after different cycle numbers is obtained based on the cycle number N of the thermoelectric unit, the resistance value R ei,Ncyc, and the characteristic length l of the thermoelectric unit.
Specifically, the crack length a i,Ncyc has the expression:
Where l is the characteristic length of the thermoelectric unit, R 0i is the initial resistance value of the i-th thermoelectric unit, i=1, 2,3, …, n, n is the total number of thermoelectric units in the thermoelectric device, and R ei,Ncyc is the resistance value of the i-th thermoelectric unit measured after a preset number of cycles.
The characteristic length l of the thermoelectric unit is the thermoelectric leg cross-sectional side length for square thermoelectric legs and the thermoelectric leg cross-sectional diameter for circular thermoelectric legs.
S4: and obtaining a plurality of groups of corresponding results of the cycle number and the crack length, fitting the results to obtain a primary function of each thermoelectric unit taking the crack length as a dependent variable and taking the cycle number as an independent variable, and further obtaining the growth rate of the crack along with the cycle number and the cycle number of crack germination according to the primary function.
Obtaining a plurality of groups of corresponding results of the cycle number and the crack length, and further performing linear fitting according to the plurality of groups of data to obtain a linear function of each thermoelectric unit taking the crack length as a dependent variable and the cycle number as the independent variable:
Wherein, Is the growth rate of the ith thermoelectric unit crack with the number of cycles; n 0,i is the number of cycles of crack initiation for the ith thermoelectric unit.
Further, the slope in the linear function may be the growth rate of the crack with the number of cycles, and the intercept may be the number of cycles of crack initiation.
S5: and respectively constructing a cycle number linear relation and a cycle rate linear relation of crack germination and the cycle rate of crack growth along with the cycle number and the average strain energy density of the corresponding thermoelectric unit bonding layer.
Using the crack initiation cycle number N 0,i, the crack growth rate with cycleLinear fitting is performed on the average strain energy density Δw ave,i of the thermoelectric unit bonding layer to obtain a coefficient K 1,K2,K3,K4.
The linear relation of the crack germination cycle numbers is as follows:
lg N0,i＝K1+K2*lg(ΔWave,i)
the linear relation of the growth rate is as follows:
Wherein, Is the growth rate of the ith thermoelectric unit crack with the number of cycles; n 0,i is the number of cycles of crack initiation for the ith thermoelectric unit, K 1,K2,K3,K4 is the coefficient, and aw ave,i is the average strain energy density of the ith thermoelectric unit bond line.
S6: inputting the average strain energy density of the combined layer of the thermoelectric units to be predicted into the cycle number linear relation, obtaining the cycle number of crack germination of the thermoelectric units to be predicted, and obtaining the resistance of the corresponding thermoelectric units to be predicted based on the relation in the steps S3-S5 if the cycle number is larger than the cycle number of crack germination; otherwise no degradation occurs.
If the thermoelectric device to be predicted includes m thermoelectric units, predicting performance degradation of each thermoelectric unit of the thermoelectric device to be predicted according to the coefficient obtained in the step S5, K 1,K2,K3,K4, and the average strain energy density Δw ave of the thermoelectric unit bonding layer.
If the cycle number N is less than N 0,j, the performance of the j-th thermoelectric unit is considered not to be degraded;
If the number of cycles N is greater than N 0,j, then the jth thermoelectric unit resistance should be:
Wherein R 0,j is the initial resistance value of the j-th thermoelectric unit to be predicted, N 0,j is the cycle number of crack germination of the j-th thermoelectric unit to be predicted, and DeltaW ave,j is the average strain energy density of the j-th thermoelectric unit bonding layer to be predicted.
The average strain energy density of the bonding layer of the thermoelectric unit is obtained by adopting a finite element simulation calculation mode according to working conditions.
S7: and (3) obtaining the resistance of each thermoelectric unit by adopting the method in the step S6, adding the resistances of each thermoelectric unit, and comparing the added resistances with the initial resistance superposition value to obtain the degradation condition of the whole thermoelectric device to be predicted.
In another aspect, the present application provides an application of the above thermoelectric device performance degradation prediction method, where the method is applicable to thermoelectric devices arranged in a thermoelectric cell array.
Further preferably, the thermoelectric unit is composed of a pair of PN thermoelectric legs, and the thermoelectric unit arrays are thermally connected in parallel with each other and electrically connected in series or electrically insulated, and the resistance of each pair of thermoelectric units can be measured separately.
Examples
The array of thermoelectric units provided with the predicted thermoelectric device consisted of 6*6 total 36 thermoelectric units, each consisting of a pair of PN thermoelectric legs with a cross-sectional dimension of 2x 2mm. The thermoelectric element array of the thermoelectric device for experiments comprises 12 thermoelectric elements which are divided into 4 groups and radiate from the center to the apex angle.
The set circulation working condition is as follows: one end maintains 25 ℃, and the other end is subjected to a 450s heating stage (-40 ℃ to 125 ℃), a 900s constant temperature stage (125 ℃) and a 450s cooling stage (125 ℃ to-40 ℃). The average strain energy density of the thermoelectric unit bonding layer is related to the azimuth and working condition of the thermoelectric device, and because the experimental thermoelectric device is highly symmetrical with the structure of the predicted sample, the single cycle average strain energy density of the thermoelectric unit in the experimental device has only 3 groups of different values, the values are 206850Pa, 137900Pa and 68950Pa from the edge of the array to the center, and the thermoelectric unit is numbered 1, 2 and 3 from the top angle to the center; the single cycle average strain energy density of the thermoelectric units in the predicted sample is only 6 groups of different values, the values are 206850Pa, 172375Pa, 151690Pa, 137900Pa, 103125 Pa and 68950Pa from the edge of the array to the center, and the corresponding thermoelectric units are numbered as 1, 2,3, 4, 5 and 6.
S1: measuring an initial resistance value R 0,i of each thermoelectric unit in the experimental device, wherein no performance degradation condition of the device is used, so that the initial resistance values of all thermoelectric units are the same, and R 0 =0.015 omega;
S2: measuring the resistance value R e,i of each thermoelectric unit in the experimental device after 1000 times, 2000 times and 4000 times of thermal cycles respectively, wherein the measurement results are shown in table 1;
TABLE 1
S3: calculating the crack length a in each thermoelectric unit bonding layer after different cycle numbers according to the cycle number N and the characteristic length l of the thermoelectric unit with the resistance value R ei,Ncyc, wherein the calculation result is shown in table 2;
TABLE 2
S4: and obtaining a plurality of groups of corresponding results of the cycle number and the crack length, and obtaining a linear fitting mode to obtain a linear function expression taking the crack length a i,Ncyc as a dependent variable and the cycle number N as an independent variable. The corresponding slope of the function is the crack growth rate along with the cycleThe crack initiation cycle number N 0,i was obtained from the intercept.
For each pair of thermoelectric pairs of the experimental device, a crack initiation cycle number N 0,i and a crack growth rate with cycle were obtainedThus, a set of crack initiation cycle numbers and crack growth rates with cycle are obtained, and the results are shown in table 3;
TABLE 3 Table 3
S5: the number of crack initiation cycles, crack growth rate with cycle, and thermoelectric unit bond line strain energy density Δw ave,i were linearly fitted to yield coefficient K 1,K2,K3,K4.
lg N0,i＝K1+K2*lg(ΔWave,i)
K 1＝11.263,K2＝-1.65,K3＝-13.383,K4 =1.25 was calculated.
S6: and according to the coefficient K 1,K2,K3,K4 obtained in the step S5, calculating delta W ave by combining the strain energy density of the thermoelectric unit bonding layer, and predicting the performance degradation condition of each thermoelectric unit of the predicted sample.
The results of calculation of the number of crack initiation by thermoelectric units of samples 1 to 6 are shown in Table 4.
| Thermoelectric cell numbering | No. 1 | No. 2 | No. 3 |
| N0 | 310.5763512 | 419.5826 | 518.1089 |
| Thermoelectric cell numbering | No. 4 | No. 5 | No. 6 |
| N0 | 606.3438 | 974.6931 | 1902.911 |
TABLE 4 Table 4
If the cycle number N is less than N 0,j, the performance of the j thermoelectric unit is not degraded, and R e,j＝R0.
If the cycle number N is larger than N 0, the resistances of the thermoelectric units 1 to 6 are respectively
S7: the predicted sample thermoelectric unit array should include 4 number 1 thermoelectric units, 8 number 2 thermoelectric units, 8 number 3 thermoelectric units, 4 number 4 thermoelectric units, 8 number 5 thermoelectric units, 4 number 6 thermoelectric units, so the total resistance of the thermoelectric units should be R e:
Re＝4Re,1+8Re,2+8Re,3+4Re,4+8Re,5+4Re,6
thus, the performance degradation condition of the thermoelectric device along with the cycle degradation condition can be obtained, and the performance degradation prediction of the thermoelectric device is realized.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (9)
1. A method for predicting performance degradation of a thermoelectric device, the method comprising:
s1: respectively acquiring an initial resistance value of each thermoelectric unit in the thermoelectric device;
s2: performing thermal cycle and/or power cycle on the thermoelectric device, and measuring the resistance value of each thermoelectric unit after periodically spacing a preset cycle number;
S3: obtaining crack lengths in each thermoelectric unit bonding layer after different cycle numbers based on the cycle number, the resistance value and the characteristic length of the thermoelectric unit;
S4: obtaining a plurality of groups of corresponding results of the cycle number and the crack length, fitting the results to obtain a primary function of each thermoelectric unit taking the crack length as a dependent variable and taking the cycle number as an independent variable, and further obtaining the growth rate of cracks along with the cycle number and the cycle number of crack germination according to the primary function;
S5: respectively constructing a linear relation between the cycle number of crack germination and the linear relation between the growth rate of the crack along with the cycle number and the crack germination cycle number and the growth rate of the average strain energy density of the corresponding thermoelectric unit bonding layer;
S6: inputting the average strain energy density of the combined layer of the thermoelectric units to be predicted into the cycle number linear relation, obtaining the cycle number of crack germination of the thermoelectric units to be predicted, and obtaining the resistance of the corresponding thermoelectric units to be predicted based on the relation in the steps S3-S5 if the cycle number is larger than the cycle number of crack germination; otherwise, no degradation occurs;
s7: and (3) obtaining the resistance of each thermoelectric unit by adopting the method in the step S6, adding the resistances of each thermoelectric unit, and comparing the added resistances with the initial resistance superposition value to obtain the degradation condition of the whole thermoelectric device to be predicted.
2. The method according to claim 1, wherein the crack length a i,Ncyc in step S3 is expressed as:
Where l is the characteristic length of the thermoelectric unit, R 0i is the initial resistance value of the i-th thermoelectric unit, i=1, 2,3, …, n, n is the total number of thermoelectric units in the thermoelectric device, and R ei,Ncyc is the resistance value of the i-th thermoelectric unit measured after a preset number of cycles.
3. The method according to claim 1, wherein the linear function expression in step S4 is:
Wherein, Is the growth rate of the ith thermoelectric unit crack with the number of cycles; n 0,i is the number of cycles of crack initiation for the ith thermoelectric unit.
4. A method according to claim 1 or 3, wherein the number of crack initiation cycles in step S5 is linearly related to:
lgN0,i＝K1+K2*lg(ΔWave,i)
the linear relation of the growth rate is as follows:
Wherein, Is the growth rate of the ith thermoelectric unit crack with the number of cycles; n 0,i is the number of cycles of crack initiation for the ith thermoelectric unit, K 1,K2,K3,K4 is the coefficient, and aw ave,i is the average strain energy density of the ith thermoelectric unit bond line.
5. The method according to claim 1 or 4, wherein the obtaining of the resistance of the corresponding thermoelectric unit to be predicted based on the relation in steps S3-S5 in step S6 is specifically obtaining the resistance R e,j of the thermoelectric unit to be predicted based on the growth rate linear relation, the linear function and the crack length formula:
Wherein R 0,j is the initial resistance value of the j-th thermoelectric unit to be predicted, N 0,j is the cycle number of crack germination of the j-th thermoelectric unit to be predicted, and DeltaW ave,j is the average strain energy density of the j-th thermoelectric unit bonding layer to be predicted.
6. The method of claim 4 or 5, wherein the average strain energy density of the bonding layer of the thermoelectric unit is obtained by finite element simulation calculation according to working conditions.
7. The method of claim 1, wherein the characteristic length of the thermoelectric unit is a thermoelectric leg cross-sectional side length for a square thermoelectric leg and a thermoelectric leg cross-sectional diameter for a circular thermoelectric leg.
8. Use of a method for predicting the performance degradation of a thermoelectric device according to any one of claims 1 to 7, wherein the method is applicable to a thermoelectric device arranged in an array of thermoelectric cells.
9. The use of claim 8, wherein the thermoelectric unit is comprised of a pair of PN thermoelectric legs, the array of thermoelectric units being thermally parallel to each other and electrically series or electrically insulated, the resistance of each pair of thermoelectric units being measured separately.
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