CN115081144A - Thermoelectric device performance degradation prediction method and application - Google Patents
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Abstract
The invention 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; carrying out thermal cycle and/or power cycle on the thermoelectric device, and measuring the resistance value of each thermoelectric unit after regularly spacing a preset cycle number; obtaining the crack length of each thermoelectric unit after different cycle numbers, and fitting to obtain a linear function; acquiring a linear relation of the cycle number and a linear relation of the growth rate; inputting the average strain energy density of the bonding layer of the thermoelectric unit to be predicted into a linear relation of cycle numbers, obtaining the crack germination cycle number of the thermoelectric unit to be predicted, and if the cycle number is larger than the crack germination cycle number, degrading the performance of the thermoelectric unit to be predicted; otherwise, no degradation occurs; and adding the resistance of each thermoelectric unit and comparing the added resistance with the initial resistance superposition value to obtain the degradation condition of the whole thermoelectric device to be predicted. The method and the device can accurately predict the performance degradation condition of the thermoelectric device.
Description
Technical Field
The invention belongs to the related technical field of thermoelectric device performance prediction, and particularly relates to a thermoelectric device performance degradation prediction method and application.
Background
The thermoelectric device is a solid-state device manufactured based on five thermoelectric effects such as a Seebeck effect, a Peltier effect, a Thomson effect, a Fourier effect and a Joule effect, and can realize direct conversion of heat energy and electric energy. The thermoelectric device has the advantages of no moving part, 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 and high reliability requirements such as radioactive isotope power generation and the like, the prediction of the performance degradation condition of the thermoelectric device in the use process can optimize the system design and guarantee the system safety.
The existing research shows that the main mechanism of the performance degradation of the thermoelectric device is as follows: the thermoelectric unit bonding layer can become the weakest part in the device under the action of the cyclic thermal stress, cracks appear in the thermoelectric unit bonding layer, and further the electric connection is influenced, so that the performance degradation is caused.
However, there is no systematic and good-universality method for predicting the performance degradation of the thermoelectric device, and therefore, a scientific systematic 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 requirements 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 the thermoelectric device.
To achieve the above object, according to an aspect of the present invention, there is provided a thermoelectric device performance degradation prediction method, the method including: s1: respectively acquiring an initial resistance value of each thermoelectric unit in the thermoelectric device; s2: carrying out thermal cycle and/or power cycle on the thermoelectric device, and measuring the resistance value of each thermoelectric unit after regularly spacing preset cycle numbers; s3: obtaining a crack length within the bonding layer of each thermoelectric unit after different cycle numbers based on the cycle number of the thermoelectric unit, the resistance value, and the characteristic length of the thermoelectric unit; s4: obtaining a plurality of groups of results corresponding to the cycle number and the crack length, fitting to obtain a linear function of each thermoelectric unit with the crack length as a dependent variable and 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 linear function; s5: respectively constructing a linear relation between the cycle number of crack germination and the growth rate of the crack along with the cycle number and a linear relation between the cycle number of crack germination and the growth rate of the crack growth corresponding to the average strain energy density of the thermoelectric unit bonding layer; s6: inputting the average strain energy density of the thermoelectric unit bonding layer to be predicted into the cyclic number linear relation, obtaining the cyclic number of the thermoelectric unit to be predicted, if the cyclic number is larger than the cyclic number of crack germination, degrading the performance of the thermoelectric unit to be predicted, and obtaining the resistance of the corresponding thermoelectric unit to be predicted based on the relation in the steps S3-S5; otherwise, no degradation occurs; s7: and (4) obtaining the resistance of each thermoelectric unit by adopting the method in the step S6 for each thermoelectric unit in the thermoelectric device to be predicted, and comparing the added resistance with the initial resistance superposition value to obtain the degradation condition of the whole thermoelectric device to be predicted.
Preferably, the crack length a in step S3 i，Ncyc The expression of (a) is:
wherein l is the characteristic length of the thermoelectric unit, R 0i Is the initial resistance value of the ith thermoelectric unit, i is 1, 2, 3, …, n is the total number of thermoelectric units in the thermoelectric device, R ei，Ncyc The resistance value of the ith thermoelectric element measured after a predetermined number of cycles apart.
Preferably, the linear function expression in step S4 is:
wherein the content of the first and second substances,
the growth rate of the i-th thermoelectric unit crack with cycle number; n is a radical of 0，i The cycle number of crack initiation for the ith thermoelectric unit.
Preferably, the linear relationship between the crack initiation cycle numbers in step S5 is:
lg N 0，i ＝K 1 +K 2 *lg(ΔW ave，i )
the linear relationship of the growth rate is as follows:
wherein the content of the first and second substances,
the growth rate of the i-th thermoelectric unit crack with cycle number; n is a radical of hydrogen 0，i Number of cycles of crack initiation for the ith thermoelectric cell, K 1 ，K 2 ，K 3 ，K 4 Is a coefficient, Δ W ave，i The average strain energy density of the bonding layer for the ith thermoelectric cell.
Preferably, the resistance of the corresponding thermoelectric unit to be predicted is obtained in step S6 based on the relationship in steps S3-S5The resistance R of the thermoelectric unit to be predicted is obtained based on the linear relationship of the growth rate, the linear function and the crack length formula e，j ：
Wherein R is 0，j For the initial resistance value of the jth thermoelectric cell to be predicted, N 0，j For the jth cycle number of crack initiation, Δ W, of the thermoelectric cell to be predicted ave，j And bonding the layer average strain energy density for the jth thermoelectric unit to be predicted.
Preferably, the average strain energy density of the bonding layer of the thermoelectric unit is obtained by finite element simulation calculation according to working conditions.
Preferably, the characteristic length of the thermoelectric unit is the thermoelectric arm cross section side length for a square thermoelectric arm and the thermoelectric arm cross section diameter for a round thermoelectric arm.
According to another aspect of the present invention, there is provided an application of the thermoelectric device performance degradation prediction method described above, which is applied to a thermoelectric device in which thermoelectric cells are arranged in an array.
Preferably, the thermoelectric unit is composed of a pair of PN thermoelectric legs, the thermoelectric units 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.
Generally, 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 method, the thermoelectric performance degradation is predicted based on a crack growth mechanism and is completely consistent with the thermoelectric device performance degradation mechanism, then the relation between cracks and the cycle number is obtained, the crack growth rate and the cycle number of crack germination can be further obtained, the performance degradation prediction of the thermoelectric device is further performed by combining the average strain energy density of the bonding layer, and compared with the prediction based on stress, strain or temperature difference, the method can cover wider cycle characteristics including a generalized stress peak value, a generalized stress growth slope, generalized stress duration and the like, so that the prediction method has higher universality.
2. A linear function of the cycle number and the crack length is established, and then the growth 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 a basis is provided for the preliminary evaluation of the thermoelectric unit at the later stage.
3. The scheme in the application is particularly suitable for thermoelectric devices arranged in the thermoelectric unit array, the structure can obtain model parameters only under the experimental conditions of a single working condition and a single device, the method is convenient and fast, the method has universality, and the method is particularly suitable for a series of predicted samples with the same geometric dimension of the substrate and the thermoelectric arms and different thermoelectric arm arrays.
Drawings
FIG. 1 is a diagram of steps of a method for predicting degradation in thermoelectric device performance according to the present application;
FIG. 2 is a flow chart of a method for predicting degradation in performance of a thermoelectric device according to the present application;
fig. 3 is a schematic structural view of the thermoelectric device in the embodiment of the present application, in which (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
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Referring to fig. 1 and 2, the present invention provides a method for predicting the performance degradation of a thermoelectric device, which includes the following steps S1-S7.
S1: the initial resistance value of each thermoelectric unit in the thermoelectric device is acquired respectively.
As shown in fig. 3, a block diagram of a thermoelectric device for conducting experiments and obtaining model data, the experimental device has an array of thermoelectric units radiating from the center to the top corners, each thermoelectric unit is formed by connecting a pair of PN thermoelectric arms in series, and the thermoelectric units are electrically insulated from each other by being connected in parallel.
Assuming n thermoelectric units in the thermoelectric device, the initial resistance value R of each thermoelectric unit in the thermoelectric device is measured separately 0i ，i＝1，2，3，…，n。
S2: and carrying out thermal cycle and/or power cycle on the thermoelectric device, and measuring the resistance value of each thermoelectric unit after regularly spacing preset cycle numbers.
For example, a measurement is made after 10 cycles per cycle interval to obtain the resistance value R of each thermoelectric unit ei，Ncyc ，i＝1，2，3，…，n。
S3: based on the cycle number N and the resistance value R of the thermoelectric unit ei，Ncyc And the characteristic length l of the thermoelectric unit, the crack length a in the bonding layer of each thermoelectric unit after obtaining different numbers of cycles i，Ncyc 。
In particular, the crack length a i，Ncyc The expression of (a) is:
wherein l is the characteristic length of the thermoelectric unit, R 0i Is the initial resistance value of the ith thermoelectric unit, i is 1, 2, 3, …, n is the total number of thermoelectric units in the thermoelectric device, R ei，Ncyc The resistance value of the ith thermoelectric element measured after a predetermined number of cycles apart.
The characteristic length l of the thermoelectric unit is the side length of the cross section of the thermoelectric arm for the square thermoelectric arm, and the diameter of the cross section of the thermoelectric arm for the round thermoelectric arm.
S4: and obtaining a plurality of groups of corresponding results of the cycle number and the crack length, fitting to obtain a linear function of each thermoelectric unit with the crack length as a dependent variable and 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 linear function.
Obtaining a plurality of groups of corresponding results of the cycle number and the crack length, further performing linear fitting according to the plurality of groups of data, and obtaining a linear function of each thermoelectric unit by taking the crack length as a dependent variable and the cycle number as an independent variable:
wherein the content of the first and second substances,
the growth rate of the i-th thermoelectric unit crack with cycle number; n is a radical of 0，i The number of cycles of crack initiation for the ith thermoelectric unit.
The slope from this linear function can then be the rate of crack growth with cycle number, and the intercept is the number of cycles at which the crack is initiated.
S5: and respectively constructing a cycle number of crack germination and a linear relation of the growth rate of the crack along with the cycle number and a growth rate of the bonding layer average strain energy density of the corresponding thermoelectric unit.
Using number of crack initiation cycles N 0，i Rate of crack growth with cycle
And thermoelectric cell bonding layer average strain energy density Δ W ave，i Linear fitting is carried out to obtain a coefficient K 1 ，K 2 ，K 3 ，K 4 。
The linear relation of the crack initiation cycle number is as follows:
lg N 0，i ＝K 1 +K 2 *lg(ΔW ave，i )
the linear relationship of the growth rate is as follows:
wherein the content of the first and second substances,
the growth rate of the i-th thermoelectric unit crack with cycle number; n is a radical of hydrogen 0，i Number of cycles of crack initiation for the ith thermoelectric cell, K 1 ，K 2 ，K 3 ，K 4 Is a coefficient, Δ W ave，i The average strain energy density of the bonding layer for the ith thermoelectric cell.
S6: inputting the average strain energy density of the thermoelectric unit bonding layer to be predicted into the cyclic number linear relation, obtaining the cyclic number of crack initiation of the thermoelectric unit to be predicted, if the cyclic number is larger than the cyclic number of crack initiation, degrading the performance of the thermoelectric unit to be predicted, and obtaining the resistance of the corresponding thermoelectric unit to be predicted based on the relation in the steps S3-S5; otherwise no degradation occurs.
If the thermoelectric device to be predicted includes m thermoelectric cells, K is the coefficient obtained in step S5 1 ，K 2 ，K 3 ，K 4 And thermoelectric cell bonding layer average strain energy density Δ W ave And predicting the performance degradation condition of each thermoelectric unit of the predicted thermoelectric device.
If the number of cycles N is less than N 0，j If so, the performance of the jth thermoelectric unit is not degraded;
if the number of cycles N is greater than N 0，j Then the jth te cell resistance should be:
wherein R is 0，j For the initial resistance value of the jth thermoelectric cell to be predicted, N 0，j For the jth cycle number of crack initiation, Δ W, of the thermoelectric cell to be predicted ave，j For the j-th thermoelectric cell junction to be predictedThe laminate layer has an average strain energy density.
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 (4) obtaining the resistance of each thermoelectric unit by adopting the method in the step S6 for each thermoelectric unit in the thermoelectric device to be predicted, and comparing the added resistance of each thermoelectric unit with the initial resistance superposition value to obtain the degradation condition of the whole thermoelectric device to be predicted.
The application provides an application of the thermoelectric device performance degradation prediction method, and the method is suitable for thermoelectric devices with thermoelectric unit arrays.
Further preferably, the thermoelectric unit is composed of a pair of PN thermoelectric arms, 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
Let the thermoelectric unit array of the predicted thermoelectric device consist of 36 thermoelectric units of 6 x 6, each thermoelectric unit consists of a pair of PN thermoelectric legs, the thermoelectric legs have a cross-sectional dimension of 2 x 2 mm. The thermoelectric unit array of the experimental thermoelectric device comprises 12 thermoelectric units which are divided into 4 groups and radiate from the center to the top corner.
The set cycle conditions are: one end is maintained at 25 ℃, and the other end is subjected to a heating stage of 450s (-40 ℃ to 125 ℃), a constant temperature stage of 900s (125 ℃), and a cooling stage of 450s (125 ℃ to-40 ℃). The average strain energy density of the thermoelectric unit bonding layer is related to the orientation and the working condition of the thermoelectric device, and the experimental thermoelectric device is highly symmetrical to the structure of a sample to be predicted, so that the average strain energy density of the thermoelectric unit in a single cycle in the experimental device is only 3 groups of different values, the average strain energy density is 206850Pa, 137900Pa and 68950Pa from the edge of the array to the center in sequence, and the thermoelectric units are numbered from the top angle to the center as 1, 2 and 3 respectively; the thermoelectric unit single-cycle average strain energy density in the sample to be predicted is only 6 groups of different values, 206850Pa, 172375Pa, 151690Pa, 137900Pa, 103425Pa and 68950Pa are sequentially arranged from the edge of the array to the center, and the corresponding thermoelectric units are numbered as No. 1, 2, 3, 4, 5 and 6.
S1: measuring an initial resistance value R of each thermoelectric unit in the experimental device 0，i No performance degradation of the device is observed, so that the initial resistance values of all the thermoelectric units are the same, R 0 ＝0.015Ω；
S2: the resistance value R of each thermoelectric unit in the experimental device is measured after 1000 times, 2000 times and 4000 times of thermal cycles respectively e，i The measurement results are shown in table 1;
TABLE 1
S3: resistance value R according to cycle number N ei，Ncyc Calculating the length a of the crack in each thermoelectric unit bonding layer after different cycle numbers are obtained by calculating the characteristic length l of the thermoelectric unit, wherein the calculation result is shown in table 2;
TABLE 2
S4: obtaining a plurality of groups of corresponding results of the cycle number and the crack length, and obtaining the crack length a by adopting a linear fitting mode i，Ncyc Is a linear function expression with a dependent variable and a cycle number N as an independent variable. The function corresponds to a slope of the crack growth rate with cycle
Number of crack initiation cycles N from intercept 0，i 。
For each thermoelectric pair of the experimental device, a crack germination cycle number N was obtained 0，i And rate of crack growth with cycle
A set of crack germination cycles and crack growth rates with cycle were thus obtained, with the results shown in table 3;
TABLE 3
S5: crack initiation cycle number, crack growth rate with cycle, and thermoelectric cell bond line strain energy density Δ W ave，i Linear fitting is carried out to obtain a coefficient K 1 ，K 2 ，K 3 ，K 4 。
lg N 0，i ＝K 1 +K 2 *lg(ΔW ave，i )
Calculating to obtain K 1 ＝11.263，K 2 ＝-1.65，K 3 ＝-13.383，K 4 ＝1.25。
S6: coefficient K obtained from S5 1 ，K 2 ，K 3 ，K 4 Calculating Δ W in conjunction with the strain energy density of the layer of thermoelectric elements ave And predicting the performance degradation condition of each thermoelectric unit of the sample to be predicted.
The results of calculating the number of cracks that occurred in thermoelectric units No. 1 to No. 6 of the sample to be predicted are shown in Table 4.
| Thermoelectric Unit numbering | Number 1 | Number 2 | No. 3 |
| N 0 | 310.5763512 | 419.5826 | 518.1089 |
| Thermoelectric Unit numbering | Number 4 | Number 5 | Number 6 |
| N 0 | 606.3438 | 974.6931 | 1902.911 |
TABLE 4
If the number of cycles N is less than N 0，j Then, the performance of the No. j thermoelectric unit is not degraded, and R e，j ＝R 0 。
If the number of cycles N > N 0 The resistances of No. 1-6 thermoelectric units should be
S7: the thermoelectric unit array of the sample to be predicted comprises 4 thermoelectric units No. 1, 8 thermoelectric units No. 2, 8 thermoelectric units No. 3, 4 thermoelectric units No. 4, 8 thermoelectric units No. 5 and 4 thermoelectric units No. 6, so the total resistance of the thermoelectric units is R e ：
R e＝4R e，1 +8R e，2 +8R e，3 +4R e，4 +8R e，5 +4R e，6
Therefore, the situation that the performance of the thermoelectric device degrades along with circulation can be obtained, and the performance degradation prediction of the thermoelectric device is realized.
It will be understood by those skilled in the art that the foregoing is only an exemplary embodiment of the present invention, and is not intended to limit the invention to the particular forms disclosed, since various modifications, substitutions and improvements within the spirit and scope of the invention are possible and within the scope of the appended claims.
Claims (9)
1. 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: carrying out thermal cycle and/or power cycle on the thermoelectric device, and measuring the resistance value of each thermoelectric unit after regularly spacing preset cycle numbers;
s3: obtaining a crack length within the bonding layer of each thermoelectric unit after different cycle numbers based on the cycle number of the thermoelectric unit, the resistance value, and the characteristic length of the thermoelectric unit;
s4: obtaining a plurality of groups of results corresponding to the cycle number and the crack length, fitting to obtain a linear function of each thermoelectric unit with the crack length as a dependent variable and 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 linear function;
s5: respectively constructing a linear relation between the cycle number of crack germination and the growth rate of the crack along with the cycle number and a linear relation between the cycle number of crack germination and the growth rate of the average strain energy density of the bonding layer corresponding to the thermoelectric unit;
s6: inputting the average strain energy density of the bonding layer of the thermoelectric unit to be predicted into the cyclic number linear relation, obtaining the cyclic number of crack germination of the thermoelectric unit to be predicted, if the cyclic number is larger than the cyclic number of crack germination, degrading the performance of the thermoelectric unit to be predicted, and obtaining the resistance of the corresponding thermoelectric unit to be predicted based on the relation in the steps S3-S5; otherwise, no degradation occurs;
s7: and (4) obtaining the resistance of each thermoelectric unit by adopting the method in the step S6 for each thermoelectric unit in the thermoelectric device to be predicted, and comparing the added resistance of each thermoelectric unit with the initial resistance superposition value to obtain the degradation condition of the whole thermoelectric device to be predicted.
2. The method of claim 1, wherein the crack length a in step S3 i，Ncyc The expression of (a) is:
wherein l is the characteristic length of the thermoelectric unit, R 0i Is the initial resistance value of the ith thermoelectric unit, i is 1, 2, 3, …, n is the total number of thermoelectric units in the thermoelectric device, R ei，Ncyc For preset cycles of intervalsThe resistance value of the ith thermoelectric cell measured several times later.
3. The method according to claim 1, wherein the linear function expression in step S4 is:
wherein the content of the first and second substances,
the growth rate of the i-th thermoelectric unit crack with cycle number; n is a radical of 0，i The cycle number of crack initiation for the ith thermoelectric unit.
4. The method according to claim 1 or 3, wherein the linear relationship between the crack initiation cycle numbers in step S5 is:
lgN 0，i ＝K 1 +K 2 *lg(ΔW ave，i )
the linear relationship of the growth rate is as follows:
wherein the content of the first and second substances,
the growth rate of the i-th thermoelectric unit crack with cycle number; n is a radical of hydrogen 0，i Number of cycles of crack initiation for the ith thermoelectric cell, K 1 ，K 2 ，K 3 ，K 4 Is a coefficient, Δ W ave，i The average strain energy density of the bonding layer for the ith thermoelectric cell.
5. The method according to claim 1 or 4, wherein the resistance of the corresponding thermoelectric cell to be predicted is obtained in step S6 based on the relationship in steps S3-S5The resistance R of the thermoelectric unit to be predicted is obtained based on the linear relationship of the growth rate, the linear function and the crack length formula e，j ：
Wherein R is 0，j For the initial resistance value of the jth thermoelectric cell to be predicted, N 0，j For the jth cycle number of crack initiation, Δ W, of the thermoelectric cell to be predicted ave，j And bonding the layer average strain energy density for the jth thermoelectric unit to be predicted.
6. The method of claim 4 or 5, wherein the average strain energy density of the bonding layer of the thermoelectric element is calculated by finite element simulation according to the operating conditions.
7. The method of claim 1, wherein the characteristic length of the thermoelectric element 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 the method for predicting the performance degradation of the thermoelectric device according to any one of claims 1 to 7, wherein the method is suitable for thermoelectric devices with thermoelectric cells arranged in an array.
9. The use according to claim 8, wherein said thermoelectric elements are comprised of a pair of PN thermoelectric legs, and wherein said array of thermoelectric elements are thermally parallel to each other and electrically connected in series or electrically isolated, and wherein the resistance of each pair of thermoelectric elements can be measured separately.
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