球與薄板上液膜碰撞之動態過程及其應用於黏滯係數量測之研究

Investigation on the dynamic process between a sphere and a liquid film on a thin plate and its application in viscosity measurement

呂孟僑(Meng-Ciao Lyu)

指導教授 ： 楊馥菱

國立臺灣大學/工學院/機械工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201801879

摘要

本論文探討一球體與添加液膜之薄板之聲壓訊號與動態過程，並由此發想，發展了三種方法試圖以此估計出液膜黏滯係數以發展一個不需使用太多待測液體即能估計出黏滯係數的量測方法。方法一利用球體以及板子的聲壓模型，並以潤滑理論做為固體 – 液體碰撞的作用力模型，藉此預測出聲壓訊號，其中黏滯係數為唯一未知數，藉由與實驗量測到的聲壓訊號比較、反求，並能以此決定出液膜黏滯係數。而方法二則針對聲壓訊號峰值使用無因次分析，找出影響濕碰撞聲壓訊號峰值的相關物理參數，並透過無因次參數間的擬合關係式能得到聲壓訊號峰值與黏滯係數的一對一隱式關係。方法三則是藉著球體以及板子的聲壓模型，可以直接由實驗訊號之中得到實際的作用力歷史，再藉著調整黏滯係數，使潤滑理論所預測的曲線能貼近實際求出之作用力曲線，並以此估計出黏滯係數。我們同時展示了部分現存理論的使用限制，同時討論未來可行的改善方法。

關鍵字

聲壓模型 ； 固體碰撞 ； 潤滑理論 ； 黏度量測 ； 頻譜分析

並列摘要

The thesis studies how the impact sound and the dynamic process when a solid sphere impacts a liquid film on a thin plate. Three methods were attempted to estimate the liquid viscosity with a given film thickness. The first uses the lubrication theory as the solid – liquid contact model and integrates it with the acoustic model of the sphere – plate collision to predict a wet impact signals. By fitting the predicted signal to the measured data, we can estimate the liquid viscosity. The second one uses dimensional analysis to find how the wet impact pressure peak changes with the liquid film physical properties. Hence, we can predict the viscosity by plugging in a measure pressure peak into the empirical relations. Experimental data were used to extract the pertinent parameters and their correlations were fitted. The last one extracts the impact force directly from the impact signal spectrum. By adjusting the viscosity in the lubrication theory to fit the extracted force, we can determine the viscosity. We demonstrate the limits of a few existing theories and discuss future improvements.

並列關鍵字

Acoustic model ； solid contact ； lubrication theory ； viscosity measurement ； frequency spectrum analysis

參考文獻

References

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[2] Toshio Takahagi, Masayuki Yokoi & Mikio Nakai, “The sound generated by a transverse impact of a ball on a circular plate,” J. Acoustic. Soc. Jpn. (E) 1, 2 (1980).

[3] Toshio Takahagi & Mikio Nakai, “The approximation of pressure waveforms of impact sound radiation from clamped circular plates of various thicknesses,” J. Acoust. Soc. Am. 78, 2049 (1985).

[4] Arthur W. Leissa, “Vibration of Plates,” Superintendent of Documents, 1969.