由球與牆面濕碰撞之聲壓訊號量測水平液膜厚度及黏滯係數之新方法

Novel measurement of horizontal liquid film thickness and viscosity from acoustic signal of a sphere – wall wet impact

盧勁宏(Jing-Hung Lu)

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(2016年)

https://doi.org/10.6342/NTU201603239

摘要

本論文以系統性精密實驗搭配理論分析探討一固體球撞擊水平面上之牛頓流體液膜時，所發出之聲壓訊號和液膜黏度與厚度間之關係。其理論基礎由乾球體碰撞聲壓之既有理論模型出發，整合潤滑理論作推廣，憑藉理論提出如何由聲壓訊號反向計算球體在濕碰撞不同過程中穿透液膜、以及近似乾碰撞的加速度過程，並進一步搭配系統性的乾、濕碰撞實驗數據濾定理論參數。研究發現所探討之球體加速度時間歷史在乾碰撞中可由既存觸力學中的赫茲碰撞理論有效估計，但濕碰撞中僅有後期加速度歷史符合該理論預測。因此確認濕碰撞的前期加速度來自球體穿越液膜時之潤滑阻力，我們進而發展一套方法在球體於濕碰撞的加速度歷史中界定此由液體潤滑力統御的前期訊號，由該部分訊號搭配潤滑理論模型反向計算液膜黏度及厚度，並透過實驗評估此間接量測方法的準確性，以及該準確性和黏度及厚度本身的相關性。

關鍵字

聲壓 ； 接觸力學 ； 赫茲碰撞 ； 潤滑理論 ； 黏度量測 ； 液膜厚度量測 ； 固體碰撞加速度量測

並列摘要

This thesis studies how the acoustic pressure from an impact between a solid sphere and a horizontal wall is modified by the presence of a thin film of Newtonian liquid via systematic precise measurements and integrated theoretical analysis. We first extend an existing acoustic theory describing the pressure radiated from dry impacts between two solid objects according to their acceleration history to incorporate hydrodynamic deceleration via partially – immersed lubrication theory developed herein. We then propose a method to extract acceleration history based on the acoustic signals and determine the model coefficients via systematic experiments. Acceleration predicted by Hertz contact theory fairly matches to the dry impact data but only agrees to the later – time acceleration signal from a wet impact. The early-time acceleration signal from a wet impact, on the other hand, matches to the partially – immersed lubrication theory. Hence, we propose a method to extract film thickness and viscosity from the acoustic signal and evaluate its effectiveness and accuracy via complementary experiment. We also comment on how the accuracy varies with film thickness and viscosity.

並列關鍵字

Acoustic model ； Hertz contact theory ； lubrication theory ； viscosity measurement ； film thickness measurement ； impact acceleration measurement

參考文獻

[1] Adnan Akay, “A review of impact noise,” J. Acoust. Soc. Am. 64(4), pp. 977-987, 1978.

[2] L. L. Koss & R. J. Alfredson, “Transient sound radiated by spheres undergoing an elastic collision,” J. Sound Vib. 27(1), pp. 59-75, 1973.

[3] Adnan Akay & Thomas H. Hodgson, “Acoustic radiation from the elastic impact of a sphere and a slab,” Appl. Acoust. (11), pp. 285-304, 1978.

[5] W. Goldsmith, “Impact: The theory and physical behavior of colliding solids,” Dover, New York, 2001.

[7] D. Gugan, “Inelastic collision and the Hertz theory of impact,” Am. J. Phys. 68(10), pp. 920-924, 2000.