The finite element analysis of thickness-shear vibrations of quartz crystal plates with ANSYS

Abstract

With the fast growth of electronic products such as wireless telecommunication devices and personal computers, quartz crystal resonators are widely used as stable and precise frequency control components. Due to miniaturization of practical product and higher frequency requirements, how to avoid mode coupling which will severely affect product's quality becomes a key problem to be solved during the design stage. However, designers can only adjust the size and shape of quartz plate based on experiences. The Mindlin plate theory can be used to obtain analytical solutions of the straight-crested wave displacements and vibration frequency, but the effects of complex structure such as change of the three-dimensional sizes of the chip, electrodes, packaging and mounting on the quality factor cannot be accurately analyzed by this theory. Therefore, the sophisticated FEM becomes important for this problem. In this study, we employed the general purpose finite element method software ANSYS to analyze the fundamental thickness-shear vibrations of typical rectangular AT-cut quartz crystal plates, and obtained its free vibration frequencies and spatial distributions of displacements which verify known results. Based on these results, we further extended our research to investigate the effect of length of the rectangular plate on the vibration mode, establishing a plate model with conductive adhesive and analyze the impact of the position and the size of adhesive. These studies showed we can adjust these small sizes to enable quartz crystal resonator work in a stable thickness-shear vibration state. Our work is to establish a complete procedure of quartz crystal resonators with ANSYS and form the base of FEM analysis for product design. 随着无线通信设备、个人电脑等电子产品的普及，石英晶体谐振器这种稳定、精确的频率控制元件的需求也不断增加。由于实际产品越来越小的尺寸和更高的频率要求，使得怎样避免模态耦合带来的产品性能降低成为了需要 在设计阶段克服的技术难点之一， 而设计人员通常只能根据经验对石英晶片的尺寸和外形进行调整。 使用 Mindlin 板理论分析虽然可以得到直行波位移和振动频率的解析解，但是对晶片的三维尺寸变化、附加电极和封装固定等 复杂结构对产品品质因数的影响难以做出全面的精确分析。采用成熟的有限元方法可以较好地解决这一问题。本 文使用了通用有限元软件 ANSYS，对典型的矩形 AT 切石英晶体板的厚度剪切基频模态进行了分析，得到了自由 振动条件下该模态的频率和位移的空间分布，验证了已知的振动分析结果。在此基础上，我们进一步讨论了矩形 板的长度变化对这一模态的影响；建立了附加导电胶的板模型，分析了点胶的位置和大小变化带来的影响，说明 了如何对这些微小的尺寸进行调整，使石英晶体谐振器在较好的剪切振动状态工作。我们的工作建立了完整的石 英晶体谐振器 ANSYS 模型，为基于有限元分析的产品设计打下了基础，也为设计人员提供了建模的基本信息。 关键词：石英晶体谐振器，厚度剪切振动，有限元，ANSYS，尺寸 1. 引言 对石英晶体板厚度剪切 (thickness-shear, TSh) 振动 进行分析的经典方法是使用 Mindlin 板理论，在给定 结构参数，诸如长厚比和宽厚比的情况下，对简化后 模型的振动特性进行预测 [1]。但是这样的方法在结 构和边界复杂时显得无能为力， 位移的空间位移分布 也很难获得， 因为采用板振动近似方程得到的解析解 只能是直行波或者一维解。 解决这个问题的有效途径 是使用有限元方法。 而有限元方法的实现可以通过三 维压电理论或者 Mindlin 板理论 [2-5]。由于用于求 解特征值的线性体系的规模的不同， 两者消耗的计算 978-1-4244-9821-5/10/$26.00 ©2010 IEEE

The analysis of harmonic frequency of AT-cut disc-typed quartz crystals resonator

“…The parameters of this model are as follows: R (radius of disc-type quartz crystal) is 7 mm, t (thickness of disc-typed quartz crystal) is 0.27 mm, and r (radius of electrodes) is 3 mm. As well known, the number of modal is very large and the coupling of different vibrations mode is very frequent and complicated at the high-frequency vibration [5]. When the crystal resonator doing the thickness-shear mode vibration, the top and bottom surfaces are doing plane-movement along the opposite direction.…”