球柵陣列構裝元件於振動環境下之壽命計算及錫球尺寸最佳化設計

The Fatigue Life Estimation and Solder Balls Optimum Design for the PBGA Components under Vibration Loading

王慶順(Ching-Shun Wang)

指導教授 ： 陳永樹

元智大學/工程學院/機械工程學系/博士(2007年)

摘要

本研究主要針對PBGA元件，以實驗、有限元素分析與理論的相互配合，探討PBGA元件於共振環境下之振動壽命。實驗部分，以正弦波用待測電路板之第一自然振動頻率進行振動測試直到元件失效，取得PBGA元件之振動壽命實驗數據。同時，本研究亦透過理論計算方式，對PBGA元件之振動壽命進行估算。然而進行壽命估算，必先掌握PBGA元件內錫球之振動應力及應變。因此採用有限元素分析，對PBGA元件在實際振動測試條件下同步進行振動模擬分析，計算其內部錫球之應力、應變值。在進行振動分析時，電路板之楊氏係數及阻尼係數，影響分析結果至鉅。有鑑於此，針對這些關鍵性係數，利用板及薄膜理論以有限元素法寫成質量、剛性及阻尼矩陣，建構成平板之數學系統方程式，進而求得數值上之頻率響函數，然後與模態實驗取得電路板之頻率響函數作比對，並運用基因演算法鑑別出電路板之楊氏係數與阻尼值(?悀????nDamping)做為振動分析之用。

經由振動分析所得振動負載下之錫球應變，為彈性應變及塑性應變之總合。而當外加負載增加時，錫球所承受之塑性效應亦提高，而其塑性效應影會響壽命預估之準確性。因此，利用總應變壽命理論將塑性應變值納入疲勞壽命計算內，用以修正塑性應變造成之效應，並得到較佳之壽命預估值。此外，研究亦以應變能理論計算電子元件之振動壽命值，並與實驗比對。然而其結果顯示，配合文獻中之材料疲勞常數，應用上述總應變壽命理論及應變能理論，計算所得之壽命值與實驗值略有差異。因此，本研究更進一步，以實驗壽命值及分析所得之應力、應變、應變能數據進行曲線嵌合，找出更符合實驗壽命值之材料疲勞常數。最後更以基因演算法，配合ANSYS對錫球尺寸做最佳化設計，提供一個在設計階段即可預先掌握元件可靠度之有效方法。

關鍵字

壽命 ； 球柵陣列構裝 ； 有限元素分析 ； 振動 ； 基因演算法

並列摘要

In this study, the reliability of the PBGA components under vibration loading when at resonance is investigated by integrating practices of vibration fatigue life test, finite element analysis and theoretical estimation. In the fatigue life test, the printed circuit board(PCB) is excited at its first natural frequency with a series of sinusoidal vibrations of various displacement amplitudes until component failure is observed. Meanwhile, the theoretical calculations for the fatigue life are also conducted. However, the prerequisites such as the strain and stress data for the calculation are obtained firstly with the finite element analysis(FEA). But the material properties, especially the damping and the Young’s modulus of the printed circuit board, dominate the simulated results. Therefore, these mass, damping and stiffness matrices are deduced with the plate and membrane theories are determined with a self written FEA program. And the resulting theoretical frequency response function can thus be calculated. Besides, the results are compared with the real frequency response function from the modal test of the printed circuit board. Further, the Yong’s modulus and damping of the PCB are obtained by coping with the genetic algorithm in the comparison process. These material properties are then finally used in the further analysis.

The stress and strain data as obtained with the FEA are typically resulted from both the elastic and plastic deformation of the PCB. With the increase of excitation, the plastic effect will be enhanced and then causes the inaccuracy of the estimated life which is based on the life theory. Therefore, the life theory of total strain which includes the plastic strain effects is utilized to evaluate the fatigue life of the PBGA components. It is found that the fatigue life as calculated with the total strain life theory has better consistency with that from the experimental life data. In addition, the life estimation with stain energy density method is also conducted for the study. However, the estimated life from both methods has some extent of inconsistency with the experimental life. It is suspected that the material fatigue constants as referred from the literatures might be the reason. For better improve the accuracy, both the life tested and the stress and strain calculated are processed with the curve fitting method to find out a set of material fatigue constants for the current case. The life calculated by this way turns out to have better match with the experimental data. Finally, the optimum design of the solder balls is undertaken with the genetic algorithm and ANSYS analysis. It is believed that method developed can offer a systematic approach to predict and manipulate the life of PBGA components at the design stage.

並列關鍵字

Finite Element Analysis, Genetic Algorithm, Life, PBGA, Vibration

參考文獻

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