Conformal antenna welding spot thermal vibration coupling fatigue life prediction method based on damage superposition

Abstract

The invention relates to the technical field of structural reliability, in particular to a conformal antenna welding spot thermal vibration coupling fatigue life prediction method based on damage superposition, and the method comprises the steps: constructing a finite element model of a conformal antenna; obtaining a thermal damage value of a conformal antenna structure welding spot under a single temperature cycle; obtaining a vibration damage value of a conformal antenna structure welding spot under a single temperature cycle; obtaining a thermal vibration coupling damage value in a single cycle period; and obtaining the fatigue life of the conformal antenna welding spot under thermal vibration coupling. According to the method, the purpose of evaluating the fatigue life through thermal vibration damage time domain superposition is achieved, and meanwhile the fluctuation influence of vibration load randomness on the fatigue life evaluation result is fully considered.

Description

Technical Field

[0001] The present invention relates to the technical field of structural reliability, and in particular to a method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition. Background Art

[0002] With the development of modern aerospace, more and more equipment is being installed on aircraft. To meet the needs of electronic systems such as communications, radar, and satellite navigation, a variety of antennas are deployed throughout aircraft. According to statistics, over 70 different types of antennas are installed on modern high-performance aircraft. With the increasing reliance on data transmission reliability, the increasing volume of data, and the increasing transmission distances, the need to improve the performance of these devices inevitably increases their size and weight. These changes have led to significant conflicts: a reduction in aircraft payload and available internal space, as well as numerous undesirable factors. 1) Surface-mounted receiving and transmitting antennas alter the aircraft's aerodynamic shape to varying degrees, increasing flight drag, leading to increased fuel consumption or a reduction in the maximum range per refueling; 2) some large reflector antennas require protective shielding, which not only complicates aircraft design but also negatively impacts aerodynamic stability; 3) increasing the number of antennas also creates issues such as antenna shielding and electromagnetic compatibility. These issues can be addressed in two ways: 1) expanding antenna bandwidth and consolidating some antenna functions, but unlimited expansion and consolidation are clearly unrealistic; and 2) achieving conformal alignment between the antenna and the fuselage. Therefore, with the research on antenna miniaturization, the development of material processing technology and the progress of theoretical research, the development of conformal antenna structure has become a feasible approach.

[0003] The conformal antenna structure for aviation is an antenna array that is consistent with the aircraft's shape and does not impose additional burdens on it. It can achieve the electromagnetic performance requirements of traditional antennas for communication and navigation without affecting the structural shape and aerodynamic characteristics of the aircraft carrier. The conformal antenna structure is usually located in the key position of the aircraft's wing structure. In order to fit the wing structure, such as Figure 2 The conformal antenna shown here is a U-shaped sandwich structure consisting of a skin, foam core, mounting plate, and PCB. Conformal antennas are mechatronic products that experience harsh operating conditions, including temperature fluctuations and vibration shock, which can lead to electrical failures. Solder joints are often a key area of ​​failure, causing the antenna to disconnect and disrupt normal communication and navigation functions.

[0004] At present, the research work on solder joint degradation failure test mainly tends to study the influence of single environmental factors on solder joint degradation, such as the relationship between solder joint life and heating and cooling rates, high and low temperature residence time under temperature test; the relationship between solder joint life and vibration frequency and vibration amplitude under vibration test, guiding the formulation of stress screening test and strengthening test profile, while the research on further quantitative evaluation of fatigue life is relatively weak.

[0005] Therefore, it is necessary to provide a thermal-vibration coupled fatigue life prediction method for conformal antenna solder joints based on damage superposition to solve the above problems. Summary of the Invention

[0006] In order to solve the problem that the current research work on solder joint degradation failure test mainly tends to study the impact of single environmental factors on solder joint degradation, such as the relationship between solder joint life and heating and cooling rates, and high and low temperature residence time under temperature test; the relationship between solder joint life and vibration frequency and vibration amplitude under vibration test, guiding the formulation of stress screening test and strengthening test profile, while the quantitative evaluation research on further fatigue life is relatively weak, the present invention provides a conformal antenna solder joint thermal vibration coupling fatigue life prediction method based on damage superposition to solve the existing problem.

[0007] The present invention provides a method for predicting the thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition, which adopts the following technical solutions, including: Construct a finite element model of a conformal antenna; Input the industry standard temperature acceleration test spectrum into the transient thermal-structural coupling module of the finite element analysis software to obtain the thermoplastic strain data of the critical parts of the conformal antenna structure solder joint under thermal cycling conditions; Based on the thermoplastic strain data and the Engelmaier failure physics model, the thermal fatigue life under a single thermal cycle is obtained. Based on the thermal fatigue life, the thermal damage value of the solder joint of the conformal antenna structure under a single temperature cycle is obtained. Input the industry standard vibration acceleration test spectrum into the modal analysis-random vibration module in the finite element analysis software to obtain the strain frequency response data of the dangerous parts of the conformal antenna structure weld point; Based on the strain frequency response data and the vibration fatigue failure physical model, the vibration fatigue life under a single vibration cycle is obtained. Based on the vibration fatigue life and strain frequency response data, and using the inverse Fourier transform-rainflow counting statistics-random law test method, the vibration damage value of the conformal antenna structure solder joint under a single temperature cycle is obtained; Based on the vibration damage value and thermal damage value, the thermal-vibration coupling damage value under a single cycle is obtained using Miner's linear superposition theory of damage; According to the thermal-vibration coupling damage value and based on the Monte-Carlo random assignment algorithm, the process growth curve of the thermal-vibration coupling damage value of the dangerous parts of the conformal antenna structure solder joint as a function of the number of cycles is obtained; based on each thermal-vibration coupling damage value in the process growth curve and the preset coupling damage threshold, the fatigue life of the conformal antenna solder joint under thermal-vibration coupling is obtained.

[0008] A further technical solution of the present invention is: the steps of constructing a finite element model of a conformal antenna are: Construct a finite element model of the conformal antenna based on its geometric dimensions. The components of the conformal antenna include the skin, foam core, antenna substrate, antenna, and solder joints. Import the finite element model into ANSYS Workbench and set the material properties of each component in Engineering Data.

[0009] A further technical solution of the present invention is: the steps of constructing a transient thermal-structural coupling module are: Establish a transient thermal module in the finite element analysis software; Insert the transient structural module after the transient thermal module to obtain the transient thermal-structural coupling module.

[0010] A further technical solution of the present invention is: the steps of obtaining thermoplastic strain data of dangerous parts of the solder joints of the conformal antenna structure under thermal cycling conditions are: Insert the "convection" environmental condition into the transient thermal module, input the industry standard temperature acceleration test spectrum into the transient thermal module, and output the transient temperature data of the dangerous parts of the solder joints of the conformal antenna structure under thermal cycling conditions; The transient structural module of the transient thermal-structural coupling module shares transient temperature data, selects fixed support surfaces of the finite element model, and outputs thermoplastic strain data of critical areas of the solder joints of the conformal antenna structure under thermal cycling conditions.

[0011] A further technical solution of the present invention is: the expression of the failure physics Engelmaier model is:

[0012]

[0013] Where, It represents the thermal fatigue life of the solder joints of the conformal antenna structure under a single thermal cycle; It represents the difference between the maximum thermoplastic strain and the minimum thermoplastic strain in the thermoplastic strain data of the dangerous part of the solder joint of the conformal antenna structure under thermal cycling conditions; Indicates the change in shear plastic strain within a single cycle; Indicates the solder thermal cycle fatigue toughness index; Indicates the solder thermal cycle fatigue toughness coefficient.

[0014] A further technical solution of the present invention is: the steps of obtaining the thermal damage value of the solder joint of the conformal antenna structure under a single temperature cycle are:

[0015] Where, Indicates the thermal damage value of the solder joint of the conformal antenna structure under a single temperature cycle; Represents the thermal fatigue life of the solder joints of the conformal antenna structure under a single thermal cycle.

[0016] A further technical solution of the present invention is: the steps of obtaining the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle are: The strain frequency response data is transformed from the frequency domain to the time domain based on the inverse Fourier transform to obtain the transformed strain time domain data; Based on the strain time domain data, the rain flow counting method is used to count the frequencies of each strain range in the 1s time domain. According to the vibration fatigue life and the frequencies of each strain range in the 1s time domain, a random distribution law statistical test is performed to obtain the vibration damage value within 1s. Based on the vibration damage value within 1s and the time at different temperature stages, the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle is obtained.

[0017] A further technical solution of the present invention is: based on the vibration damage value within 1s and the time at different temperature stages, the steps of obtaining the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle are as follows:

[0018] Where, Represents the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle; Indicates the vibration damage value within 1s at normal temperature; Indicates the vibration damage value within 1s during the high temperature insulation stage; Indicates the vibration damage value within 1s during the low temperature insulation stage; Indicates the time in the high temperature insulation stage during the temperature cycle; Indicates the time in the low temperature insulation stage during the temperature cycle; Indicates the time at normal temperature during the temperature cycle.

[0019] A further technical solution of the present invention is to obtain a curve showing the growth of thermal-vibration coupling damage values ​​at dangerous locations of solder joints in conformal antenna structures as a function of the number of cycles based on a Monte-Carlo random assignment algorithm.

[0020] A further technical solution of the present invention is: taking the sum of the vibration damage value and the thermal damage value as the thermal-vibration coupling damage value.

[0021] The beneficial effects of the present invention are: This paper addresses the degradation and failure of solder joints in aviation mechatronic structures, which are subject to harsh environments of temperature fluctuations and vibration shock during service. Taking aviation conformal antenna structures as the research object, this paper studies the fatigue life of solder joints under thermal-vibration coupling loading, thereby providing design guidance for maintenance interval planning and structural material selection. This paper addresses the current lack of research on solder joint life tests under coupled stress. This paper uses finite element technology to establish a research model for fatigue life assessment under thermal-vibration coupling based on damage superposition. The material parameters of the conformal antenna structure (elastic modulus, thermal conductivity, and thermal expansion coefficient) are used as finite element calculation inputs. The output strain results are substituted into the failure physics Engelmaier model and the vibration fatigue failure physics model to solve for thermal damage and vibration damage. The thermal-vibration coupling damage value of the solder joint is also solved, thereby achieving fatigue life under thermal-vibration coupling. The method of this invention covers the implicit relationship between fatigue life results and material parameters and demonstrates this process through case applications. Based on this, material parameter sensitivity analysis can provide design guidance for structural material selection. The output service life of the aviation conformal antenna structure under solder joint failure can guide the establishment of maintenance intervals. To address the problem that the strain frequency response data output by the random vibration finite element is in the frequency domain and cannot be used for life assessment through thermal-vibration damage superposition during theoretical model construction, a data processing process based on inverse Fourier transform, rain flow counting statistics, and random law verification is developed. On the one hand, the inverse Fourier transform method is used to output the strain time domain history curve; on the other hand, considering the problem that the strain history is fluctuating under the influence of random vibration, the rain flow counting method is combined with random law test to obtain the frequency of each discrete strain range. The continuous probability distribution of is substituted into the Manson empirical formula based on the strain concentration failure mechanism to calculate the vibration damage value of the solder joint. In summary, this method satisfies the goal of evaluating fatigue life by superimposing thermal vibration damage in the time domain, while also fully considering the impact of the randomness of vibration loads on the volatility of fatigue life assessment results. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0023] Figure 1This is a flow chart of a method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition according to the present invention; Figure 2 Schematic diagram of a conformal antenna structure model in an embodiment of the present invention; Figure 3 Schematic diagram of industry standard temperature load spectrum in an embodiment of the present invention; Figure 4 Schematic diagram of industry standard vibration load spectrum in an embodiment of the present invention; Figure 5 1. Plastic strain distribution cloud diagram of solder joints of conformal antenna structure under thermal cycling in an embodiment of the present invention; Figure 6 1. is a graph showing the time history of plastic strain at a dangerous location of a solder joint of a conformal antenna structure under thermal cycling in an embodiment of the present invention; Figure 7 : This is a strain distribution diagram of dangerous parts of the welding point of the conformal antenna structure under random load in an embodiment of the present invention; Figure 8 : is a PSD curve diagram of strain frequency response of dangerous parts of solder joints of conformal antenna structure under random vibration load in an embodiment of the present invention; Figure 9 A time-domain curve diagram of strain at a dangerous location of a weld point of a conformal antenna structure under random vibration load in an embodiment of the present invention; Figure 10 A statistical diagram of the vibration strain range distribution of dangerous parts of the weld points of the conformal antenna structure under random vibration loads in an embodiment of the present invention; Figure 11 This is a Gamma distribution fitting diagram of the vibration strain range of the dangerous parts of the weld point of the conformal antenna structure under random vibration load in an embodiment of the present invention; Figure 12 This is a curve diagram of the cumulative damage history of a critical part of a solder joint under a single cycle of thermal vibration coupling in an embodiment of the present invention; Figure 13 This is a statistical distribution diagram of cumulative damage to a dangerous part of a solder joint under a single cycle of thermal-vibration coupling in an embodiment of the present invention; Figure 14 The curve of thermal vibration coupling cumulative damage versus cycle number of the dangerous parts of the solder joint in the embodiment of the present invention; Figure 15 Statistical distribution diagram of thermal vibration coupling life of dangerous parts of solder joints in an embodiment of the present invention. DETAILED DESCRIPTION

[0024] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0025] An embodiment of the present invention is a method for predicting the thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition. In this embodiment, a certain type of aviation conformal antenna structure model is selected to carry out fatigue life research, such as Figure 1 Shown, including: S1. Construct a finite element model of the conformal antenna; Exemplarily, in a specific embodiment, the steps of constructing a finite element model of a conformal antenna are as follows: constructing a finite element model of the conformal antenna according to the geometric dimensions of the conformal antenna, wherein the components of the conformal antenna include a skin, a foam core, an antenna substrate, an antenna, and solder joints; importing the finite element model into ANSYS Workbench, and setting the material properties of each component in Engineering Data.

[0026] S2. Obtaining thermal damage values ​​of solder joints of the conformal antenna structure under a single temperature cycle; Specifically, the industry standard temperature acceleration test spectrum is input into the transient thermal-structural coupling module in the finite element analysis software to obtain the thermoplastic strain data of dangerous parts of the conformal antenna structure solder joints under thermal cycling conditions; the thermoplastic strain data and the failure physics Engelmaier model are combined to obtain the thermal fatigue life under a single thermal cycle, and the thermal damage value of the conformal antenna structure solder joints under a single temperature cycle is obtained based on the thermal fatigue life.

[0027] For example, in a specific embodiment, the steps of constructing a transient thermal-structural coupling module are: establishing a transient thermal module in finite element analysis software (ANSYS Workbench), and inserting a transient structural module after the transient thermal module to obtain a transient thermal-structural coupling module.

[0028] Exemplarily, in a specific embodiment, the steps for obtaining thermoplastic strain data of dangerous parts of the solder joints of the conformal antenna structure under thermal cycling conditions are as follows: inserting the "convection" environmental condition into the transient thermal module, inputting the industry standard temperature acceleration test spectrum into the transient thermal module, and outputting the transient temperature data of the dangerous parts of the solder joints of the conformal antenna structure under thermal cycling conditions; the transient structure module of the transient thermal-structural coupling module shares the transient temperature data, selects the fixed support surface of the finite element model, and outputs the thermoplastic strain data of the dangerous parts of the solder joints of the conformal antenna structure under thermal cycling conditions.

[0029] For example, in a specific embodiment, the steps of obtaining the thermal fatigue life under a single thermal cycle based on the thermoplastic strain data and the failure physics Engelmaier model are as follows: In this embodiment, the failure physics Engelmaier model is first selected: that is, the failure physics Engelmaier model is selected to study the life of the solder joint under thermal cycle loading, taking into account the influence of thermal cycle and temperature value on fatigue life. The failure physics Engelmaier model fully covers two types of thermal failure mechanisms: temperature alternating fatigue and high temperature creep. The failure physics Engelmaier model is in the form of:

[0030]

[0031] Where, It represents the thermal fatigue life of the solder joints of the conformal antenna structure under a single thermal cycle; It represents the difference between the maximum thermoplastic strain and the minimum thermoplastic strain in the thermoplastic strain data of the dangerous part of the solder joint of the conformal antenna structure under thermal cycling conditions; Indicates the change in shear plastic strain within a single cycle; Indicates the solder thermal cycle fatigue toughness index; Indicates the solder thermal cycle fatigue toughness coefficient; is the solder thermal cycle fatigue toughness index, and the expression of the solder thermal cycle fatigue toughness index is:

[0032] Where: is the average temperature of the temperature cycle load spectrum; is the number of cycles of thermal cycling that occurs in one day. The expression for the number of cycles of thermal cycling that occurs in one day is:

[0033] Where: is the single-cycle thermal cycle time, in seconds.

[0034] That is, at this time, the difference between the maximum thermoplastic strain and the minimum thermoplastic strain in the thermoplastic strain data of the dangerous parts of the conformal antenna structure solder joint under thermal cycling conditions is input into the failure physics Engelmaier model to obtain the thermal fatigue life under a single thermal cycle. .

[0035] For example, in a specific embodiment, the steps of obtaining the thermal damage value of the solder joint of the conformal antenna structure under a single temperature cycle according to the thermal fatigue life are as follows:

[0036] Where, Indicates the thermal damage value of the solder joint of the conformal antenna structure under a single temperature cycle; Represents the thermal fatigue life of the solder joints of the conformal antenna structure under a single thermal cycle.

[0037] S3, obtaining the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle; Specifically, the industry standard vibration acceleration test spectrum is input into the modal analysis-random vibration module in the finite element analysis software to obtain the strain frequency response data of the dangerous parts of the conformal antenna structure solder joints; based on the strain frequency response data and the vibration fatigue failure physical model, the vibration fatigue life under a single vibration cycle is obtained; based on the vibration fatigue life and strain frequency response data, and using the Fourier inverse transform-rain flow counting statistics-random law test method, the vibration damage value of the conformal antenna structure solder joints under a single temperature cycle is obtained.

[0038] Exemplarily, in a specific embodiment, the steps of constructing a modal analysis-random vibration module are as follows: considering the fact that the temperature field affects the vibration frequency response, a modal analysis study under temperature prestress is performed, a steady-state thermal module is established in the finite element analysis software (ANSYS Workbench), the conformal antenna model is imported and the material properties of each component are set, the temperature field temperature is set, and the steady-state temperature field distribution and heat flux distribution are output; a static structure module is inserted after the steady-state thermal module, the temperature field temperature setting is shared and the fixed support surface of the finite element model is selected as input, and the prestress distribution is output; the modal module is inserted to share the pre-settings as input, a vibration modal analysis is performed, and the natural frequency and mode shape are output; a random vibration module is inserted after the modal module, the settings and solution results of the previous steps are transferred, the vibration acceleration test spectrum is written in the "PSD G acceleration" as input, and the strain frequency response PSD curve (i.e., strain frequency response data) of the dangerous parts of the conformal antenna structure weld is output.

[0039] For example, in a specific embodiment, the steps of obtaining the vibration fatigue life under a single vibration cycle based on the strain frequency response data and the vibration fatigue failure physical model are as follows: The vibration fatigue failure physical model of the weld under random vibration loading uses the strain-based Manson high-cycle fatigue empirical formula to calculate the vibration fatigue life. The Manson high-cycle fatigue empirical formula is:

[0040] Where: is the vibration fatigue life of the solder joint under a single vibration cycle, the unit is the number of cycles; is the strain range within a single vibration cycle, obtained through finite element calculation; is the elastic modulus; is the fatigue strength index, is a constant value of -0.12; represents the fatigue strength coefficient; The initial stress, i.e. the temperature field prestress of random vibration, can be obtained by finite element calculation of thermal cycle.

[0041] For example, in a specific embodiment, based on the vibration fatigue life and strain frequency response data, and using the inverse Fourier transform-rain flow counting statistics-random law test method, the steps for obtaining the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle are as follows: The direct calculation result of random vibration finite element is the strain frequency response PSD curve (strain frequency response data), that is, the strain response With frequency The change curve belongs to the frequency domain. In order to meet the subsequent time domain superposition of fatigue damage under random vibration and thermal cycle loading to achieve the purpose of evaluating thermal vibration coupled fatigue life, it is necessary to transform the strain results from the frequency domain to the time domain. Therefore, this embodiment transforms the strain frequency response data from the frequency domain to the time domain based on the inverse Fourier transform to obtain the transformed strain time domain data, namely:

[0042] Where: For time; is the frequency, where is Euler's formula; Based on the strain time domain data, the rain flow counting method is used to count the frequencies of each strain range in the 1s time domain. According to the vibration fatigue life and the frequencies of each strain range in the 1s time domain, the random distribution law statistical test is performed to obtain the vibration damage value within 1s, that is: in the strain time domain data distribution Based on the known basis, the rain flow counting method can count the strain ranges in the 1s time domain. Down frequency , and corresponding to the strain range The probability density function of A statistical test of random distribution law is performed, so the vibration damage value within 1s can be expressed as:

[0043] Where: is the total frequency of strain range within 1s counted by the rain flow counting method; for Randomly assign values ​​under known distribution rules and randomly select values ​​within 1s Second-rate; for The vibration fatigue life is obtained based on the Manson high cycle fatigue empirical formula under the given value; Considering the fact that the temperature field affects the vibration frequency response, the temperature prestressing is a variable value, and the material parameter 、 As it changes, The spectrum is not unique, which leads to The random distribution parameters vary with the temperature stage. In view of this, the present embodiment divides the thermal cycle load spectrum into the high temperature insulation stage , low temperature insulation stage , the heating stage is regarded as the normal temperature stage Three temperature environment stages. Then, based on the vibration damage value within 1s and the time under different temperature stages, the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle is obtained. That is, the expression of the vibration damage value is:

[0044] Where, Represents the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle; Indicates the vibration damage value within 1s at normal temperature; Indicates the vibration damage value within 1s during the high temperature insulation stage; Indicates the vibration damage value within 1s during the low temperature insulation stage; Indicates the time in the high temperature insulation stage during the temperature cycle; Indicates the time in the low temperature insulation stage during the temperature cycle; Indicates the time at normal temperature during the temperature cycle. value, There are still differences between the forms, which need to be solved and substituted into the calculation. On this basis, the Monte-Carlo method is used to extract the vibration damage frequency statistics and Statistical test of random distribution patterns.

[0045] S4, obtaining the thermal-vibration coupling damage value under a single cycle; Specifically, the thermal-vibration coupling damage value is obtained based on the vibration damage value and the thermal damage value and using Miner's damage linear superposition theory.

[0046] For example, in a specific embodiment, according to Miner's linear superposition theory of damage, the thermal-vibration coupling damage value under a single cycle can be obtained: The expression is:

[0047] The thermal damage value of step S2 and vibration damage value of S3 The thermal-vibration coupling damage value can be obtained by summing .

[0048] S5. Obtain fatigue life of conformal antenna solder joints under thermal-vibration coupling; For example, in a specific embodiment, the uncertainty characteristics of the vibration load are analyzed to obtain Randomly distributed data processing flow, and realize the calculation of solder joint thermal vibration coupling damage evolution trajectory, Gamma distribution characteristic parameters, life distribution, according to the thermal vibration coupling damage value under a single cycle Based on the Monte-Carlo random assignment algorithm, the process growth curve of the thermal-vibration coupling damage value of the dangerous parts of the conformal antenna structure solder joints as the number of cycles is obtained; according to the thermal-vibration coupling damage value in the process growth curve and the preset coupling damage threshold, the fatigue life of the conformal antenna solder joints under thermal-vibration coupling is extracted.

[0049] That is, Thermal-vibration coupling damage value within the sub-cycle period For example, Thermal-vibration coupling damage value within the sub-cycle period As failure judgment indicators:

[0050] Where, Indicates the Vibration damage value within the sub-cycle period; Indicates the Thermal damage value within the sub-cycle period.

[0051] When the thermal vibration coupling damage value Exceeding the damage threshold When the failure is determined, the fatigue life of the conformal antenna solder joint under thermal vibration coupling is The expression is:

[0052] If the randomness is not considered, the thermal vibration coupling damage value The expression should be:

[0053] This embodiment focuses on the reliability calculation problem of the solder joint fracture failure mode and considers the randomness of the vibration load. The randomness of the vibration load will directly lead to the strain range. The randomness of the value makes The value fluctuates. It is clear that the thermal-vibration coupling damage evolution trajectory of the integrated antenna functional structure solder joint has the properties of non-negative increment and independent increment, and obeys the characteristics of the Gamma random process. The thermal-vibration coupling damage value under a single cycle is Will obey the following Gamma distribution:

[0054] in, represents the shape parameter, which is related to the single cycle time Related functions; represents the scale parameter. Then it corresponds to The probability density function of is:

[0055] but Thermal-vibration coupling damage value within the sub-cycle period The expression can be expressed as follows after considering randomness:

[0056] clear After the Gamma distribution form is obtained, the Monte Carlo method can be used to randomly assign values ​​and substitute In the expression, the fatigue life of the conformal antenna solder joint under thermal vibration coupling is The fatigue life solved by the expression is still in a random distribution form.

[0057] The present invention is described below with reference to specific data and accompanying drawings: Step 1: Establish a finite element model: like Figure 2 As shown, in this embodiment, a certain type of aviation conformal antenna structure model is selected to carry out fatigue life research. The composition and material properties of each component are shown in Table 1, and the material parameters are shown in Table 2.

[0058] Table 1

[0059] Table 2

[0060] Among them, the material parameters of the Anand viscoplastic model corresponding to the solder Pb37Sn63 are shown in Table 3.

[0061] Table 3

[0062] The finite element model of the conformal antenna structure is constructed according to the parameters in Tables 1 to 3.

[0063] Step 2: Calculate the thermal damage value of the solder joints of the conformal antenna structure; In thermal-vibration coupling analysis, the temperature cycle load comes from Figure 3 The industry standard temperature acceleration test spectrum shown is Figure 3It can be seen that the highest temperature is 125℃ and the lowest temperature is -55℃, the temperature rise and fall rate is 36℃ / min, and the high and low temperature holding time is 10min. The plastic strain distribution cloud diagram of the conformal antenna structure solder joint under the thermal cycle loading condition is obtained after calculation in this embodiment. Figure 5 As shown, from Figure 5 It can be seen that the dangerous part is located in the solder joint-antenna substrate interface area, which is caused by the strain concentration due to the mismatch of the thermal expansion coefficient of the interface material. The time history curve of the dangerous part is extracted as follows Figure 6 As shown in the figure, the maximum thermoplastic strain in this time period is 6.7e-3 and the minimum thermoplastic strain is 5.9e-3, and the difference in plastic strain is 8e-4. The thermal fatigue life of the solder joint of the conformal antenna structure under a single thermal cycle can be obtained. Change of shear plastic strain is 1.4e-3. Secondly, the formula Pb37Sn63 solder is equal to 0.325, middle Equal to (125℃+(-55℃)) / 2=90℃, is equal to 48, so we get Equal to -0.428, the final thermal fatigue life =850700 times, so the thermal damage value in a single temperature cycle is 1.176×10 -6 .

[0064] Step 3, calculating the vibration damage value of the solder joint of the conformal antenna structure; In thermal-vibration coupling analysis, the PSD acceleration power spectrum condition of random vibration load is derived from Figure 4 The industry standard vibration acceleration test spectrum shown is from Figure 4 It can be seen that the 20Hz power spectrum density amplitude is 0.01g 2 / Hz, 80~350Hz power spectrum density amplitude 0.04g 2 / Hz, 2000Hz power spectrum density amplitude 0.01g 2 / Hz. After the finite element calculation of modal analysis and vibration response, the strain distribution cloud diagram of the conformal antenna structure solder joint after random vibration loading at different temperature stages (normal temperature 25℃, high temperature insulation 125℃, low temperature insulation -55℃) is obtained. Figure 7 As shown, Figure 7 It can be seen that the dangerous part is located in the solder joint-antenna substrate interface area. This is due to the strain concentration phenomenon caused by geometric discontinuity and mismatch of material properties. The strain frequency response PSD curve of the dangerous part is extracted as shown in Figure 8 As shown in the figure, the result of converting the spectrum into strain time domain data by inverse Fourier transform is as follows: Figure 9 As shown, Figure 9 (a) Time domain spectrum of strain response of the dangerous part of the solder joint under 25℃ temperature field; Figure 9 (b) Time domain spectrum of strain response of the dangerous part of the solder joint under 125℃ temperature field; Figure 9 (c) is the strain response time domain spectrum of the dangerous part of the solder joint under the temperature field of -55℃; based on the strain time domain data of the dangerous part of the solder joint, the statistical results of the vibration strain range distribution of the dangerous part of the solder joint under different temperature fields are statistically analyzed by the rain flow counting method. Figure 10 As shown, Figure 10 (a) Time domain spectrum of strain response of dangerous parts of solder joint under 25℃ temperature field; Figure 10 (b) Time domain spectrum of strain response of dangerous parts of solder joint under 125℃ temperature field; Figure 10 (c) is the time domain spectrum of strain response of dangerous parts of solder joints under -55℃ temperature field; Gamma KS goodness of fit test is performed, and all of them obey Gamma distribution at 5% significance level, such as Figure 11 As shown, Figure 11 (a) is the temperature field at 25°C (normal temperature stage); Figure 11 (b) is the temperature field at 125℃ (high temperature holding stage); Figure 11 (c) is the -55℃ temperature field (low temperature insulation stage), where the strain range Gamma distribution The fitting parameters are shown in Table 4.

[0065] Table 4

[0066] Young's modulus of lead-tin solder joints in a 25°C temperature field environment , fatigue strength coefficient , mean stress Therefore, based on the vibration fatigue life Manson formula It can be obtained that the relationship between vibration fatigue life and strain range under a temperature field environment of 25°C is: ; Under the temperature field environment of 25℃, the total frequency of strain range in 1s time domain is 424, so according to the formula It can be obtained that the vibration damage relationship in the 1s time domain is:

[0067] Young's modulus of lead-tin solder joints in a 125°C temperature field environment , fatigue strength coefficient , mean stress ; Under the temperature field environment of 125℃, the total frequency of strain range in 1s time domain is 432, so according to the formula It can be obtained that the vibration damage relationship in the 1s time domain is:

[0068] Young's modulus of lead-tin solder joints in a -55°C temperature field environment , fatigue strength coefficient , mean stress The total frequency of strain range in the 1s time domain under the temperature field environment of -55℃ is 430, so according to the formula It can be obtained that the vibration damage relationship in the 1s time domain is:

[0069] The vibration damage relationship within a single temperature cycle of 1800s is:

[0070] At this point, the vibration damage value of the solder joint of the conformal antenna structure can be obtained.

[0071] Step 4: Obtain the thermal-vibration coupling damage value and obtain the fatigue life of the conformal antenna solder joint under thermal-vibration coupling; The Monte-Carlo algorithm is used to obtain the thermal-vibration coupling damage value growth curve of the dangerous parts of the solder joint under a single cycle of thermal-vibration coupling. Figure 12 As shown in the figure, the vibration damage statistical graph was extracted and the Gamma KS goodness of fit test was performed. It was found that the Gamma distribution was followed at the 5% significance level. Figure 13 As shown, the shape parameter is 113.77 and the size parameter is 3.857e-5. Based on the clear thermal damage value and vibration damage value, the Miner superposition method is combined with the Monte-Carlo random assignment algorithm to output the thermal-vibration coupling damage value of the dangerous part of the solder joint with the number of cycles. N Process Figure 14 The growth curve shown.

[0072] This embodiment sets the damage value threshold =1, according to N Thermal vibration coupling damage value and damage value threshold corresponding to each cycle in the sub-cycle The thermal-vibration coupling life corresponding to each cycle is obtained, and the coupling life of all cycles is counted to obtain the coupling life statistical graph, and the log-normal KS goodness of fit test is performed. It is believed that the following is obeyed at the 5% significance level: Figure 15 The lognormal distribution is shown in Figure 2. The lognormal mean of the thermal-vibration coupling lifetime is 5.429, and the lognormal standard deviation is 0.015.

[0073] Taking a certain type of conformal antenna structure as an example, the invention selects the industry standard thermal vibration acceleration test spectrum to carry out the theoretical model research of solder joint fatigue life, and obtains a log-normal distribution. Fatigue life results. Since conformal antennas are composite materials, the B reference value, which is the lower limit of fatigue life with 95% confidence and 90% reliability, is often selected as the allowable value. If the service life is lower than this value, it is considered that no fault will occur. Therefore, from a conservative point of view, the B reference value can be selected as the maintenance interval of the antenna structure. Figure 15 The statistical sample of the medium life distribution is n =80, then the single-side tolerance coefficient under B reference can be obtained by looking up the table k =2.347, so the fatigue life B reference value under the accelerated spectrum is exp(5.429-0.015×2.347)≈220 cycles. Assuming that the acceleration factor between the cycle accelerated spectrum and the service flight cycle spectrum is , the service life B benchmark value of the aviation conformal antenna structure under weld failure is calculated to be 11,000 flight cycles, which can guide the formulation of maintenance intervals.

[0074] In summary, this paper provides a method for predicting the thermal-vibration-coupled fatigue life of conformal antenna solder joints based on damage superposition. Parameters of the conformal antenna's structural materials, such as elastic modulus, thermal conductivity, and thermal expansion coefficient, are used as inputs in a finite element method. The resulting strain output is processed using methods such as an inverse Fourier transform and then applied to the Engelmaier and Manson models to determine the damage value, ultimately solving for the thermal-vibration-coupled fatigue life of the solder joints. This theoretical model explores the implicit relationship between fatigue life results and material parameters, demonstrating this process through case studies. Furthermore, sensitivity analysis of these material parameters can provide design guidance for structural material selection.

[0075] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition, characterized in that: include: Construct a finite element model of a conformal antenna; Input the industry standard temperature acceleration test spectrum into the transient thermal-structural coupling module of the finite element analysis software to obtain the thermoplastic strain data of the critical parts of the conformal antenna structure solder joint under thermal cycling conditions; Based on the thermoplastic strain data and the Engelmaier failure physics model, the thermal fatigue life under a single thermal cycle is obtained. Based on the thermal fatigue life, the thermal damage value of the solder joint of the conformal antenna structure under a single temperature cycle is obtained. Input the industry standard vibration acceleration test spectrum into the modal analysis-random vibration module in the finite element analysis software to obtain the strain frequency response data of the dangerous parts of the conformal antenna structure weld point; Based on the strain frequency response data and the vibration fatigue failure physical model, the vibration fatigue life under a single vibration cycle is obtained. Based on the vibration fatigue life and strain frequency response data, and using the inverse Fourier transform-rainflow counting statistics-random law test method, the vibration damage value of the conformal antenna structure solder joint under a single temperature cycle is obtained; Based on the vibration damage value and thermal damage value, the thermal-vibration coupling damage value under a single cycle is obtained using Miner's linear superposition theory of damage; According to the thermal-vibration coupling damage value and based on the Monte-Carlo random assignment algorithm, the process growth curve of the thermal-vibration coupling damage value of the dangerous parts of the conformal antenna structure solder joint as a function of the number of cycles is obtained; based on each thermal-vibration coupling damage value in the process growth curve and the preset coupling damage threshold, the fatigue life of the conformal antenna solder joint under thermal-vibration coupling is obtained.

2. The method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition according to claim 1, characterized in that: The steps to construct the finite element model of the conformal antenna are: Construct a finite element model of the conformal antenna based on its geometric dimensions. The components of the conformal antenna include the skin, foam core, antenna substrate, antenna, and solder joints. Import the finite element model into ANSYS Workbench and set the material properties of each component in Engineering Data.

3. The method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition according to claim 1, characterized in that: The steps to build the transient thermal-structural coupling module are: Establish a transient thermal module in the finite element analysis software; Insert the transient structural module after the transient thermal module to obtain the transient thermal-structural coupling module.

4. The method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition according to claim 1, characterized in that: The steps to obtain the thermoplastic strain data of the critical parts of the solder joints of the conformal antenna structure under thermal cycling conditions are as follows: Insert the "convection" environmental condition into the transient thermal module, input the industry standard temperature acceleration test spectrum into the transient thermal module, and output the transient temperature data of the dangerous parts of the solder joints of the conformal antenna structure under thermal cycling conditions; The transient structural module of the transient thermal-structural coupling module shares transient temperature data, selects fixed support surfaces of the finite element model, and outputs thermoplastic strain data of critical areas of the solder joints of the conformal antenna structure under thermal cycling conditions.

5. The method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition according to claim 1, characterized in that: The expression of the failure physics Engelmaier model is: Where, It represents the thermal fatigue life of the solder joints of the conformal antenna structure under a single thermal cycle; It represents the difference between the maximum thermoplastic strain and the minimum thermoplastic strain in the thermoplastic strain data of the dangerous part of the solder joint of the conformal antenna structure under thermal cycling conditions; Indicates the change in shear plastic strain within a single cycle; Indicates the solder thermal cycle fatigue toughness index; Indicates the solder thermal cycle fatigue toughness coefficient.

6. The method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition according to claim 1, characterized in that: The steps to obtain the thermal damage value of the solder joint of the conformal antenna structure under a single temperature cycle are: Where, Indicates the thermal damage value of the solder joint of the conformal antenna structure under a single temperature cycle; Represents the thermal fatigue life of the solder joints of the conformal antenna structure under a single thermal cycle.

7. The method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition according to claim 1, characterized in that: The steps to obtain the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle are as follows: The strain frequency response data is transformed from the frequency domain to the time domain based on the inverse Fourier transform to obtain the transformed strain time domain data; Based on the strain time domain data, the rain flow counting method is used to count the frequencies of each strain range in the 1s time domain. According to the vibration fatigue life and the frequencies of each strain range in the 1s time domain, a random distribution law statistical test is performed to obtain the vibration damage value within 1s. Based on the vibration damage value within 1s and the time at different temperature stages, the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle is obtained.

8. The method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition according to claim 1, characterized in that: Based on the vibration damage value within 1s and the time at different temperature stages, the steps for obtaining the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle are as follows: Where, Represents the vibration damage value of the solder joint of the conformal antenna structure under a single temperature cycle; Indicates the vibration damage value within 1s at normal temperature; Indicates the vibration damage value within 1s during the high temperature insulation stage; Indicates the vibration damage value within 1s during the low temperature insulation stage; Indicates the time in the high temperature insulation stage during the temperature cycle; Indicates the time in the low temperature insulation stage during the temperature cycle; Indicates the time at normal temperature during the temperature cycle.

9. The method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition according to claim 1, characterized in that: Based on the Monte-Carlo random assignment algorithm, the growth curve of the thermal-vibration coupling damage value of the dangerous parts of the solder joint of the conformal antenna structure with the number of cycles is obtained.

10. The method for predicting thermal-vibration coupled fatigue life of conformal antenna solder joints based on damage superposition according to claim 1, characterized in that: The sum of the vibration damage value and the thermal damage value is taken as the thermal-vibration coupling damage value.

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