Welding spot stress prediction method based on orthogonal design and regression analysis

Abstract

The invention discloses a welding spot stress prediction method based on orthogonal design and regression analysis, and the method comprises the steps: 1) building a welding spot finite element model, and applying any load to the model; 2) selecting structural parameters of the welding spots as influence factors, establishing an orthogonal test table considering interaction, and applying the same load to obtain the maximum stress of the welding spots; 3) performing variance analysis on the maximum stress to obtain the significance of the influence of each factor on the maximum stress of the welding spot; and 4) based on a variance analysis result, setting a multivariate nonlinear regression prediction model, and substituting data in the orthogonal test table into a prediction equation to obtain a stress prediction mathematical model with high fitting degree and high accuracy.

Description

Technical Field

[0001] This invention relates to a solder joint stress prediction method based on orthogonal design and regression analysis, belonging to the technical field of electronic packaging. Background Technology

[0002] Traditional methods for predicting weld stress have several limitations. On the one hand, experience-based methods rely on engineers' past experience and subjective judgment, lacking a systematic theoretical basis. This results in poor accuracy and stability of the predictions, making them ill-suited for complex and variable welding structures and process conditions. On the other hand, while some numerical simulation methods based on finite element analysis can provide relatively accurate stress distribution, they require precise geometric and material parameter models. The calculation process is complex and time-consuming, often proving impractical for large-scale welding production processes and complex structures, thus failing to meet the demand for rapid and efficient prediction.

[0003] With the continuous development of industrial production and the increasing demands for welding quality, there is an urgent need for a solder joint stress prediction method that can guarantee prediction accuracy while being efficient and convenient. Orthogonal design, as a scientific experimental design method, can rationally arrange experimental factors and levels within a limited number of experiments, comprehensively examining the influence of each factor on the experimental results, thus providing effective data support for establishing a solder joint stress prediction model. Regression analysis, on the other hand, is a powerful statistical analysis method that can establish mathematical models based on experimental data, reveal the intrinsic relationships between variables, and predict unknown situations. Combining orthogonal design and regression analysis for solder joint stress prediction is expected to overcome the shortcomings of traditional methods and provide a new and efficient solder joint stress prediction solution for the electronic packaging field.

[0004] Based on the above background, this invention proposes a method for predicting weld stress based on orthogonal design and regression analysis. It aims to fully utilize the experimental optimization capabilities of orthogonal design and the model building and prediction advantages of regression analysis to achieve rapid and accurate prediction of weld stress. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for predicting weld stress based on orthogonal design and regression analysis, which can achieve rapid and accurate prediction of weld stress.

[0006] To solve the above-mentioned technical problems, the present invention is implemented by the following technical solution:

[0007] A method for predicting weld stress based on orthogonal design and regression analysis includes the following steps:

[0008] Step 1: Establish a reasonable finite element model of the weld joint and apply arbitrary loads to the model to obtain the maximum stress result of the weld joint;

[0009] Step 2: Select the structural parameters of the weld joint as influencing factors, establish an orthogonal experimental table considering the interaction, and apply the same load to obtain the maximum stress of the weld joint;

[0010] Step 3: Perform variance analysis on the maximum stress in the orthogonal experimental table to obtain the significance of the influence of each factor and its interaction on the maximum stress of the weld joint.

[0011] Step 4: Based on the results of the analysis of variance, set up a multivariate nonlinear regression prediction model. Substitute the data from the orthogonal experimental table into the prediction model to obtain a stress prediction mathematical model with high fitting degree and high accuracy.

[0012] Step 1 includes the following specific methods:

[0013] Step 1-1: Use ANSYS software to establish a geometric model of the solder joint interconnection structure, which mainly includes the following parts: chip, solder joint and PCB board.

[0014] Steps 1-2: Apply arbitrary loads to the established finite element model to obtain the maximum stress at the weld joint.

[0015] Step 4 includes the following specific methods:

[0016] Step 4-1: If there are three factors, then set the basic form of the multivariate nonlinear regression prediction model as follows:

[0017] y = ax1 2 +bx2 2 +cx3 2 +dx1+ex2+fx3+g

[0018] Step 4-2: Based on the results of Step 3, if the interaction has a significant impact on stress, then add the interaction term to the prediction model. For example, if the interaction between x1 and x2 has a significant impact on stress, then the model is set as follows:

[0019] y = ax1 2 +bx2 2 +cx3 2 +dx1+ex2+fx3+gx1x2+h

[0020] The method of this invention can quickly and accurately predict the maximum stress of a weld joint under any load, effectively reducing the number of tests and obtaining more accurate stress prediction results. Attached Figure Description

[0021] Figure 1 This is a comparison chart of the prediction results and simulation results of this invention; Detailed Implementation

[0022] This invention relates to a method for predicting weld stress based on orthogonal design and regression analysis, used for rapid and accurate prediction of weld stress, comprising the following steps:

[0023] Step 1: This paper uses the MPC8245 chip manufactured by NXP Semiconductors (Netherlands) as the research object and establishes a finite element analysis model of the stacked solder joints. The dimensions of each part of the model are: chip 35mm×35mm×0.9mm, solder joint diameter 0.65mm, single-layer solder joint height 0.48mm, pad diameter 0.50mm, solder joint spacing 1.27mm, and PCB board 170mm×100mm×1.6mm. Bending-torsional coupled loads are applied to the model to obtain the maximum stress results of the solder joints.

[0024] Step 2: Select the solder ball diameter, solder pad diameter, and solder joint height as three influencing factors. Each factor has three levels, resulting in the factor level table shown in Table 1. An orthogonal experimental design table L considering interactions was established. 18 (3 6 The table contains 18 different horizontal combinations. AB represents the interaction between the solder joint diameter and the pad diameter, AC represents the interaction between the solder joint diameter and the solder joint height, and BC represents the interaction between the pad diameter and the solder joint height. Based on the orthogonal experimental table, finite element models of the corresponding 18 laminated solder joints were established, and bending-torsional coupling loading was applied to obtain the maximum bending-torsional coupling stresses of the 18 laminated solder joints, as shown in the last column of Table 2.

[0025] Table 1 Factor Level Table

[0026]

[0027] Table 2L 18 (3 6 Orthogonal design of horizontal combinations and bending-torsional coupled stress

[0028]

[0029]

[0030] Step 3: Based on the data in Table 2, perform an analysis of variance on the stress, and the results are shown in Table 3.

[0031] Table 3 Results of stress variance analysis

[0032]

[0033] If the F-value of a certain factor is greater than F 0.01This indicates that, at a confidence level of 99%, this factor has a significant impact on the target. Table 3 shows that solder joint diameter, pad diameter, and solder joint height have a significant impact on the layered bending-torsional coupling stress, while the interaction between these three structural parameters has no significant effect on the bending-torsional coupling stress.

[0034] Step 4: The analysis of variance results show that the interaction between structural parameters has no significant impact on the bending-torsional coupling stress of the laminated weld joints. Therefore, the interaction between factors is not considered, and the multivariate nonlinear regression prediction model is set as follows:

[0035] y = ax1 2 +bx2 2 +cx3 2 +dx1+ex2+fx3+g

[0036] In the formula, the solder joint diameter, solder pad diameter, and solder joint height are the independent variables, named x1, x2, and x3, respectively, and the maximum stress is the dependent variable, named y. a to g are seven undetermined coefficients, where g is the undetermined error term, and the initial value of all undetermined coefficients is set to 1.

[0037] Using the data in Table 2 as a sample, regression analysis was performed, and the estimated values ​​of the parameters are shown in Table 4, where the upper and lower confidence intervals are 95%.

[0038] Table 4 Estimated Parameter Values

[0039]

[0040] Substituting the estimated parameters into the multivariate nonlinear regression prediction model, we can obtain the prediction model for the maximum stress of the bending-torsional coupling at the laminated weld joint as follows:

[0041] y = 40.739x1 2 +361.668x2 2 +56.237x3 2 -39.290x1-394.685x2-94.029x3+180.692

[0042] To evaluate the performance of the multivariate nonlinear regression model and its good fit to the data, an analysis of variance was performed, and the results are shown in Table 5.

[0043] Table 5. Results of Model Variance Analysis

[0044]

[0045] As shown in Table 5, the sum of squared residuals is 0.381, and the coefficient of determination R0 is... 2 =1 - (0.381 / 49.661) = 0.992. The smaller the sum of squared residuals and R... 2The closer the value is to 1, the higher the model fit. As you can see, the model fits very well.

[0046] To verify the accuracy of the prediction model, six sets of stacked weld joints with different horizontal combinations of structural parameters than those in Table 2 were randomly selected, and a finite element model was established. The same bending-torsional coupled load was applied, the maximum stress was obtained, and compared with the predicted value. The results are shown in Table 6. Figure 1 This is a comparison chart of the predicted results and the simulation results.

[0047] Table 6. Prediction and Simulation Results of Bending-Torsion Coupling Stress

[0048]

[0049]

[0050] As shown in Table 6, the maximum prediction error is 3.35%, and the average error is 1.31%. Therefore, the accuracy of the multivariate nonlinear regression prediction model is verified. This mathematical model can predict the bending-torsional coupling stress of the laminated weld joints relatively accurately.

[0051] The method of this invention can predict the maximum stress of a solder joint under arbitrary loads. It requires fewer tests and achieves high prediction accuracy. The loads used in this method are not limited to bending-torsional coupling loads, but also include thermal, electrical, vibrational, and multi-physics coupling loads. The solder joint types covered by this method include BGA, QFP, QFN, and DIP, and are not limited to BGA solder joints.

Claims

1. A method for predicting weld stress based on orthogonal design and regression analysis, characterized in that, Includes the following steps: Step 1: Establish a reasonable finite element model of the weld joint and apply arbitrary loads to the model to obtain the maximum stress result of the weld joint; Step 2: Select the structural parameters of the weld joint as influencing factors, establish an orthogonal experimental table considering the interaction, and apply the same load to obtain the maximum stress of the weld joint; Step 3: Perform variance analysis on the maximum stress to obtain the significance of the influence of each factor on the maximum stress of the weld joint. Step 4: Based on the results of the analysis of variance, set up a multivariate nonlinear regression prediction model. Substitute the data from the orthogonal experimental table into the prediction model to obtain a stress prediction mathematical model with high fitting degree and high accuracy.

2. The method for predicting weld stress based on orthogonal design and regression analysis according to claim 1, characterized in that: The arbitrary loads in step 1 include thermal, electrical, vibrational, bending, and torsional loads, as well as multi-physics coupling.

3. The method for predicting weld stress based on orthogonal design and regression analysis according to claim 1, characterized in that: The solder joint structural parameters in step 2 include solder joint diameter, solder pad diameter, and solder joint height.

4. The method for predicting weld stress based on orthogonal design and regression analysis according to claim 1, characterized in that: If there are three factors in step 4, then the basic form of the multivariate nonlinear regression prediction model is set to [the specified form].

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