CN111950187A - Method for optimizing bending vibration coupling stress of micro-scale CSP welding spot - Google Patents
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Abstract
The invention discloses a method for optimizing bending vibration coupling stress of a micro-scale CSP welding spot, which comprises the following steps: establishing a simulation model of a micro-scale CSP welding spot based on ANSYS software, obtaining a bending vibration coupling stress value of the welding spot and determining factors (the diameter of the welding spot, the diameter of a welding pad and the height of the welding spot) influencing the stress value, taking the bending vibration coupling stress of the welding spot as a target, designing 17 groups of welding spot models with different horizontal combinations according to the factors, carrying out simulation calculation, establishing a regression equation of the bending vibration coupling stress of the welding spot and the structural parameters of the welding spot by adopting a response surface method, optimizing the structural parameters of the welding spot by combining a particle swarm optimization algorithm, obtaining an optimal parameter combination of the bending vibration coupling stress of the welding spot, and further verifying the accuracy of an optimization result by ANSYS simulation software. The method is simple in calculation and excellent in performance, and has certain guiding significance for the optimization design of other welding spot interconnection structures.
Description
Technical Field
The invention relates to the technical field of electronic component packaging interconnection reliability, in particular to a method for optimizing bending vibration coupling stress of a welding spot of a micro-scale CSP (chip size package).
Background
With the increasing demands for miniaturization, multi-functionalization, high integration and low cost of consumer electronic products such as mobile phones, digital cameras, mobile storage devices, intelligent wearable devices and the like, various area array devices such as chip size packages and the like are widely applied to the electronic products, so that the assembly density of circuit modules in the products is improved on the premise of ensuring the product performance, and the volume and the weight of the products are reduced; however, the size of the interconnection welding spot playing an important role in signal transmission and mechanical support in the area array type device is very small, so that the connection rigidity is greatly reduced; the electronic product board-level assembly can be subjected to a certain impact load in an actual working environment to generate bending deformation, so that the welding spot can be damaged by cracks, deformation and the like, and the service life of the electronic product is further shortened; meanwhile, the electronic product is inevitably used in an onboard, vehicle-mounted, or ship-mounted environment, in which the area array type device pads in the electronic product thereby bear a random vibration load. Therefore, the actual complex usage environment of the electronic product determines that the solder joints of the area array device in the electronic product are inevitably under the combined action of bending load and vibration load, thereby bringing more serious reliability challenges.
The response surface method is an optimization method for building an empirical model by combining experimental design and mathematical statistics. The response surface equation is fitted by using experimental points in the experimental design space, and the optimal conditions can be intuitively reflected by the response surface image. It was proposed by Box et al in the 50's of the 20 th century by using a regression model as a tool for function estimation, and in a multifactorial test, the correlation between a factor and a test result (response value) was fitted with a polynomial, and the relationship between the factor and the test result was functionalized. Therefore, the method can study and optimize the correlation between the factors and the response values and the correlation between the factors by analyzing the surfaces of the functions, and is an effective method for optimizing the reaction conditions and the processing technological parameters.
The particle swarm algorithm is characterized in that a position of a particle in a solution space is searched in the optimization process, the position P with the optimal history of the particle is stored in each particle, and the positions of the particles are compared with one another by the algorithm to select the optimal position G in the whole space. And then changing the movement speed and direction of the particles, then learning from the historical optimal position and the global optimal position, and continuously updating the positions of the particles until the requirements are met. Therefore, a good result can be obtained by adopting the standard particle swarm optimization, and the optimization effect is easy to realize.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for optimizing the bending vibration coupling stress of a micro-scale CSP welding spot.
The technical scheme for realizing the purpose of the invention is as follows:
a method for optimizing flexural vibration coupling stress of micro-scale CSP welding spots specifically comprises the following steps:
1) establishing a micro-scale CSP welding spot simulation analysis model by using ANSYS software;
2) acquiring a maximum bending vibration coupling stress value under the condition of bending vibration coupling loading of the micro-scale CSP welding spot;
3) determining influence factors influencing the bending vibration coupling stress of the welding spot;
4) determining parameter level values of the influence factors;
5) obtaining 17 groups of welding point influence factor horizontal combinations by adopting a Box-Behnken test design method for experimental error estimation;
6) acquiring a functional relation between the influence factors and the bending vibration coupling stress of the welding spots;
7) carrying out variance analysis and significance verification on the functional relation;
8) establishing the number of particles and the maximum iteration number;
9) setting learning parameters and inertia weight;
10) randomly initializing the position and the speed of the particles;
11) setting the maximum velocity V of each dimension of the particlemaxAnd minimum velocity V in each dimensionmin;
12) Calculating a fitness function value of each particle, comparing the calculation result with the historical optimal value of the particle, and updating the historical optimal fitness function value if the fitness function value calculated at this time is superior to the historical optimal value of the particle;
13) for each particle, comparing the historical optimal fitness function value of the particle with the global optimal fitness function value of the particle swarm, and if the historical optimal fitness function value of the particle is superior to the global optimal fitness function value of the particle swarm, updating the global optimal fitness function value of the particle swarm;
14) and judging whether the termination condition is reached, if so, stopping searching, and otherwise, continuing to calculate until the termination condition is reached.
In the step 1), the micro-scale CSP welding spot simulation analysis model comprises a chip, a welding spot and a PCB which are sequentially arranged from top to bottom, wherein the size of the PCB is 132mm multiplied by 77mm multiplied by 1mm, the size of the chip is 1.63mm multiplied by 0.4mm, the height of the welding spot is 0.18mm, the diameter of the welding spot is 0.23mm, the diameter of the welding spot is 0.18mm, the distance between the welding spots is 0.4mm, the distance between the chips is 5mm, and the CSP welding spot material is lead-free solder SAC 305.
In the step 3), the influencing factors are the radial size of the welding spot of the micro-scale CSP, the height of the welding spot and the diameter of the welding spot.
In step 4), the parameter level number of each influence factor is 3.
And in the step 5), the 17 groups of welding point factors are combined horizontally, wherein 12 groups are analysis factors, and 5 groups are zero point factors.
In step 8), the number of particles is 1000, and the maximum number of iterations is 1500.
In step 9), the learning parameter is 1.4962, and the inertial weight is 0.6.
In step 11), the maximum velocity V of the particles in each dimensionmaxThe limit is 0.1 times the upper limit of the independent variable of the dimension, the minimum speed V of each dimensionminLimited to the computational accuracy of the software.
The invention provides a method for optimizing bending vibration coupling stress of a micro-scale CSP welding spot, which combines response surface regression analysis and particle swarm optimization to reduce the maximum bending vibration coupling stress in the CSP welding spot under the bending vibration coupling loading condition, obtains a regression equation through fitting data of the regression analysis, performs random search based on the particle swarm optimization and on the basis of a group, finds out the optimal position in the space by the group according to a smart search method, and searches for a global optimal solution in a larger range so as to achieve the purpose of optimizing structural parameters of the welding spot. The algorithm has obvious advantages in the aspects of keeping population diversity and searching for a global optimal solution, and the maximum bending vibration coupling stress value of the welding spot is greatly reduced. The method achieves the aim of reducing the internal stress of the micro-scale CSP welding spot under the condition of power bending vibration coupling loading, and provides certain theoretical guidance for improving the interconnection reliability of the micro-scale CSP welding spot.
Drawings
FIG. 1 is a simulation analysis model diagram of a micro-scale CSP solder joint under a bending vibration coupling loading condition;
FIG. 2 is a cloud diagram of stress distribution of a micro-scale CSP solder joint array;
FIG. 3 is a graph of the mean change and the optimal solution change of a population objective function in an iterative process;
FIG. 4 is a simulation diagram of the optimum horizontal combined bending-vibration coupling stress of the micro-scale CSP solder joint.
Detailed Description
The invention is further illustrated but not limited by the following figures and examples.
A method for optimizing flexural vibration coupling stress of micro-scale CSP welding spots specifically comprises the following steps:
1) establishing a micro-scale CSP welding spot simulation analysis model by using ANSYS software;
2) acquiring a maximum bending vibration coupling stress value under the condition of bending vibration coupling loading of the micro-scale CSP welding spot;
3) determining influence factors influencing the bending vibration coupling stress of the welding spot;
4) determining parameter level values of the influence factors;
5) obtaining 17 groups of welding point influence factor horizontal combinations by adopting a Box-Behnken test design method for experimental error estimation;
6) obtaining a functional relation between the influence factors and the bending vibration coupling stress of the welding spots;
7) carrying out variance analysis and significance verification on the functional relation;
8) establishing the number of particles and the maximum iteration number;
9) setting learning parameters and inertia weight;
10) randomly initializing the position and the speed of the particles;
11) setting the maximum velocity V of each dimension of the particlemaxAnd minimum velocity V in each dimensionmin;
12) Calculating a fitness function value of each particle, comparing the calculation result with the historical optimal value of the particle, and updating the historical optimal fitness function value if the fitness function value calculated at this time is superior to the historical optimal value of the particle;
13) for each particle, comparing the historical optimal fitness function value of the particle with the global optimal fitness function value of the particle swarm, and if the historical optimal fitness function value of the particle is superior to the global optimal fitness function value of the particle swarm, updating the global optimal fitness function value of the particle swarm;
14) and judging whether the termination condition is reached, if so, stopping searching, and otherwise, continuing to calculate until the termination condition is reached.
In the step 1), the micro-scale CSP welding spot simulation analysis model comprises a chip, a welding spot and a PCB which are sequentially arranged from top to bottom, wherein the size of the PCB is 132mm multiplied by 77mm multiplied by 1mm, the size of the chip is 1.63mm multiplied by 0.4mm, the height of the welding spot is 0.18mm, the diameter of the welding spot is 0.23mm, the diameter of the welding spot is 0.18mm, the distance between the welding spots is 0.4mm, the distance between the chips is 5mm, and the CSP welding spot material is lead-free solder SAC 305.
In the step 3), the influencing factors are the radial size of the welding spot of the micro-scale CSP, the height of the welding spot and the diameter of the welding spot.
In step 4), the parameter level number of each influence factor is 3.
And 5), adopting 17 groups of horizontal combinations of the welding point influence factors obtained by a Box-Behnken test design method, wherein 12 groups are analysis factors, and 5 groups are zero factors.
In step 8), the number of particles is 1000, and the maximum number of iterations is 1500.
In step 9), the learning parameter is 1.4962, and the inertial weight is 0.6.
In step 11), the maximum velocity V of the particles in each dimensionmaxThe limit is 0.1 times the upper limit of the independent variable of the dimension, the minimum speed V of each dimensionminLimited to the computational accuracy of the software.
Example (b):
a method for optimizing flexural vibration coupling stress of micro-scale CSP welding spots specifically comprises the following steps:
(1) establishing a micro-scale CSP welding spot simulation analysis model, as shown in figure 1, wherein the material parameters are shown in the following table 1;
(2) obtaining the maximum bending vibration coupling stress value of the micro-scale CSP, wherein a stress cloud chart is shown in figure 2;
(3) determining the influence factors influencing the bending vibration coupling stress of the welding spot as the diameter of the welding spot, the height of the welding spot and the diameter of the welding pad; selecting 3 level values for each influence factor, wherein the factor level table is shown in table 2;
(4) 17 groups of welding point factor horizontal combinations are obtained by adopting a Box-Behnken test design method and are used for experimental error estimation, wherein 12 groups are analysis factors, 5 groups are zero factors, and simulation result values are shown in a table 3.
(5) According to the calculus knowledge, any function can be approximately represented by a plurality of polynomials in a segmented mode, so that in the practical problem, no matter how complex the relation between variables and results is, the polynomial regression can be used for analyzing and calculating, as the number of the designed variables is 3 and the function relation between the variables and the target is nonlinear, the second-order polynomial model based on the Taylor expansion is selected by combining the test sample number of the table 3:
in the above formula (A), α0Is a constant term,Is a linear term,Is a linear cross term,Is a quadratic term, αiIs a linear term coefficient; alpha is alphaijIs a linear cross term coefficient; alpha is alphaiiIs a quadratic coefficient; is a random error; x is a design variable; y is a target value; n is the number of variables.
(6) Performing quadratic multiple regression fitting on the experimental factor combination and the result in the table 3 to obtain the diameter (X) of the welding point of the stress value (Y)1) Pad diameter (X)2) And height of solder joint (X)3) The second order polynomial regression equation is:
(7) in order to ensure credibility of the regression equation, variance analysis and model significance verification are carried out on the data in the table 3 to obtain a regression equation related evaluation index, and the result is shown in the table 4;
(8) p value inspection is carried out on the model obtained by analyzing the response surface, namely Prob > F is less than 0.0001, which shows that the regression effect of the response surface model is particularly obvious; the regression equation coefficient R-Squared is 0.9872, the regression equation adjustment coefficient Adj R-Squared is 0.9708, the regression equation prediction coefficient PredR-Squared is 0.7957, and the result coefficients all show that the equation (B) can be highly fitted with the test result in the table 3, so that the equation prediction accuracy is good, and the regression equation is accurate and reliable;
(9) the regression equation is optimized by utilizing a particle swarm algorithm, the algorithm is a random search algorithm based on a group, a position of a particle in a solution space is searched in the optimization process, a historical optimal position P of the particle is stored in each particle, the positions of the particles are compared with one another by the algorithm, an optimal position G in the whole space is selected, the moving speed and direction of the particle are changed, the historical optimal position and the global optimal position are learned, and the positions of the particles are continuously updated until the requirements are met. The global optimal solution can be searched in a larger range;
the optimization process of the particle swarm algorithm specifically comprises the following steps:
step a: determining the number of particles to be 1000 and the maximum iteration number to be 1500;
step b: setting 1.4962 learning parameters, inertial weight 0.6;
step c: randomly initializing the position and the speed of the particles;
step d: maximum velocity V of each dimensionmaxThe limit is 0.1 times the upper limit of the independent variable of the dimension, the minimum speed V of each dimensionminLimited to the computational accuracy of the software;
step e: calculating the fitness function value of each particle, comparing the calculation result with the historical optimal value of the particle, and if the calculation result is better, updating the historical optimal fitness function value of the particle;
step f: for each particle, comparing the historical optimal fitness function value of the particle with the global optimal fitness function of the particle swarm, and if the historical optimal fitness function value of the particle is better than the global optimal fitness function value of the particle swarm, updating the global optimal fitness function value of the particle swarm;
step g: and judging again after the population is updated, judging whether a termination condition is reached, stopping searching if the termination condition is reached, and otherwise, continuing to calculate.
(10) Performing parameter optimization by using a MATLAB genetic algorithm toolbox to aim at the lowest bending vibration coupling stress value of the micro-scale CSP welding spot; the problem mean and optimal solution variation are shown in fig. 4.
(11) According to the value range of the horizontal values of the various influence factors, the optimal welding spot horizontal combination is obtained as follows: the diameter of the welding spot is 0.18mm, the diameter of the welding pad is 0.15mm, and the height of the welding spot is 0.16 mm.
(12) And establishing a corresponding welding spot simulation model according to the optimal parameter combination, wherein the simulation result is shown in figure 4, the maximum bending vibration coupling stress value of the micro-scale CSP welding spot is 24.8MPa and is very close to the predicted value of the particle swarm algorithm, and the effectiveness of the regression analysis and the particle swarm algorithm in optimizing the structural parameters of the welding spot is proved.
TABLE 1 Material parameters
TABLE 2 factor level table
TABLE 3 response surface combinations and stress analysis results
TABLE 4 results of response surface analysis
Claims (8)
1. A method for optimizing flexural vibration coupling stress of a micro-scale CSP welding spot is characterized by comprising the following steps:
1) establishing a micro-scale CSP welding spot simulation analysis model by using ANSYS software;
2) acquiring a maximum bending vibration coupling stress value under the condition of bending vibration coupling loading of the micro-scale CSP welding spot;
3) determining influence factors influencing the bending vibration coupling stress of the welding spot;
4) determining parameter level values of the influence factors;
5) obtaining 17 groups of welding point influence factor horizontal combinations by adopting a Box-Behnken test design method for experimental error estimation;
6) acquiring a functional relation between the influence factors and the bending vibration coupling stress of the welding spots;
7) carrying out variance analysis and significance verification on the functional relation;
8) establishing the number of particles and the maximum iteration number;
9) setting learning parameters and inertia weight;
10) randomly initializing the position and the speed of the particles;
11) setting the maximum velocity V of each dimension of the particlemaxAnd minimum velocity V in each dimensionmin;
12) Calculating a fitness function value of each particle, comparing the calculation result with the historical optimal value of the particle, and updating the historical optimal fitness function value if the fitness function value calculated at this time is superior to the historical optimal value of the particle;
13) for each particle, comparing the historical optimal fitness function value of the particle with the global optimal fitness function value of the particle swarm, and if the historical optimal fitness function value of the particle is superior to the global optimal fitness function value of the particle swarm, updating the global optimal fitness function value of the particle swarm;
14) and judging whether the termination condition is reached, if so, stopping searching, and otherwise, continuing to calculate until the termination condition is reached.
2. The method for optimizing the flexural vibration coupling stress of the solder joint of the micro-scale CSP according to claim 1, wherein in the step 1), the simulation analysis model of the solder joint of the micro-scale CSP comprises a chip, a solder joint and a PCB board which are sequentially arranged from top to bottom, wherein the size of the PCB board is 132mm x 77mm x 1mm, the size of the chip is 1.63mm x 0.4mm, the height of the solder joint is 0.18mm, the diameter of the solder joint is 0.23mm, the diameter of the solder joint is 0.18mm, the space between the solder joints is 0.4mm, the space between the chips is 5mm, and the solder joint material of the CSP is lead-free solder SAC 305.
3. The method for optimizing the flexural vibration coupling stress of the micro-scale CSP solder joint according to claim 1, wherein the influencing factors in step 3) are the radial dimension of the solder joint, the height of the solder joint and the diameter of the pad of the micro-scale CSP.
4. The method for optimizing flexural vibration coupling stress of solder joints of micro-scale CSP according to claim 1, wherein in step 4), the number of parameter levels of each influence factor is 3.
5. The method according to claim 1, wherein in step 5), the 17 sets of pad factor levels are combined, wherein 12 sets are analytical factors and 5 sets are zero factors.
6. The method for optimizing flexural coupling stress of solder joints of micro-scale CSP according to claim 1, wherein in step 8), the number of particles is 1000, and the maximum number of iterations is 1500.
7. The method for optimizing the flexural coupling stress of the solder joint of the micro-scale CSP according to claim 1, wherein in the step 9), the learning parameter is 1.4962, and the inertia weight is 0.6.
8. The method for optimizing flexural vibration coupling stress of solder joint of micro-scale CSP according to claim 1, wherein in step 11), the maximum velocity V of each dimension of the particles ismaxThe limit is 0.1 times the upper limit of the independent variable of the dimension, the minimum speed V of each dimensionminLimited to the computational accuracy of the software.
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CN113076595B (en) * | 2021-03-15 | 2022-05-31 | 东风商用车有限公司 | Method for analyzing durability of welding spot of commercial vehicle cab |
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