A novel equation and some surprising results in tuning fork mass sensors: Critique, validation, and comparison

IF 4.9 2区 工程技术 Q1 ACOUSTICS
Kadir Can Erbaş , Mebrure Erdoğan , Dilek Çökeliler Serdaroğlu , İsmail Cengiz Koçum
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Abstract

The use of Quartz Tuning Forks (QTF) as mass sensors in thin-film coating relies on a frequency shift formula derived from the Euler-Bernoulli equation, commonly cited in the literature. This study theoretically and experimentally evaluates the accuracy of this formula in film mass detection. Experiments were conducted using tuning forks (TF) larger than typical QTFs, and the calculated masses were compared to precision balance measurements. Results revealed that the conventional formula produced errors of up to 300%. Further investigation identified two primary error sources: the inability to account for the film's Young's modulus contribution and the assumption of longitudinally homogeneous coating. To address these issues, we developed a new mathematical model and validated it through extensive experiments. The proposed model predicts film mass and Young's modulus contributions with an error of approximately 1.5%. Conventional formulas predict a consistent frequency decrease with coating. However, our study demonstrates—both mathematically and experimentally—that frequency may increase or remain unchanged depending on the film’s Young’s modulus and coating uniformity. The proposed model effectively explains these unexpected results, and will very likely guide future studies involving QTF sensors by providing a more reliable framework for QTF-based mass sensing in thin-film applications.
音叉质量传感器中的一个新方程和一些令人惊讶的结果:批判、验证和比较
石英音叉(QTF)作为薄膜涂层质量传感器的使用依赖于从欧拉-伯努利方程推导出的频移公式,该公式在文献中经常被引用。本文从理论上和实验上对该公式在膜质量检测中的准确性进行了评价。利用比典型音叉更大的音叉进行了实验,并将计算质量与精确的平衡测量结果进行了比较。结果表明,常规公式的误差可达300%。进一步的调查确定了两个主要的误差来源:无法解释薄膜的杨氏模量贡献和纵向均匀涂层的假设。为了解决这些问题,我们开发了一个新的数学模型,并通过大量的实验对其进行了验证。该模型预测薄膜质量和杨氏模量贡献的误差约为1.5%。传统公式预测,随着涂层的增加,频率会逐渐降低。然而,我们的研究表明-数学和实验-频率可能会增加或保持不变,这取决于薄膜的杨氏模量和涂层均匀性。提出的模型有效地解释了这些意想不到的结果,并且很可能通过为薄膜应用中基于QTF的质量传感提供更可靠的框架来指导涉及QTF传感器的未来研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Sound and Vibration
Journal of Sound and Vibration 工程技术-工程:机械
CiteScore
9.10
自引率
10.60%
发文量
551
审稿时长
69 days
期刊介绍: The Journal of Sound and Vibration (JSV) is an independent journal devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. There is an emphasis on fundamental work that has potential for practical application. JSV was founded and operates on the premise that the subject of sound and vibration requires a journal that publishes papers of a high technical standard across the various subdisciplines, thus facilitating awareness of techniques and discoveries in one area that may be applicable in others.
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