本研究量測滾珠螺桿系統不同位置振動和扭矩訊號，將振動訊號進行頻譜分析，找出各元件的特徵頻率、自然頻率與摩擦振動區間和發生原因，並比較兩組不同實驗條件下隨時間變化趨勢，發現有油冷情況下皆保持穩定；無油冷情況下振動會隨著時間而變大，尤其在前、後軸承的振動頻譜更為顯著且出現軸承元件的損傷頻率。從扭矩的頻譜分析發現，扭矩會隨軸承振動作調整。將不同位置振動與扭矩進行多重碎形分析，結果發現前軸承振動較其他位置趨勢明顯，比較扭矩與振動分析結果，發現扭矩變化趨勢較振動明顯。利用頻譜分析可以了解各元件振動情形，多重碎形分析提供無因次參數來解析這些徵兆。
將軸承各元件進行平面度與粗糙度分析，發現後軸承端平面度較前軸承端差，推測應該為無油冷時溫度上升，後軸承端施加的預拉力隨著時間消退，轉軸剛性下降使得轉軸產生撓曲現象，元件膨脹導致接觸應力分布不均勻，綜合這兩原因導致軸承磨損嚴重而使得振動隨時間變大。由此可知，預拉施加的大小與軸承端各元件接觸情況為影響軸承振動的關鍵。

In this research, we measure vibration signals of ball screw system and torque signal from different positions. We identify the characteristic frequency, the natural frequency and the friction vibration interval of the various components by using the spectral analysis of vibration signals. The trends under different experimental conditions in two long time experiments are compared. The vibration is stable with oil-cooling system but it became greater over time without oil cooling system. It is more obvious in the front and rear bearing vibration spectrum. And there are some damage frequencies of bearing element appearing in the vibration spectrum. From the torque spectrum analysis, we found out that the torque will feedback from the bearing vibration. The multifractal analysis results show that the trend of front bearing vibration is more obvious than other components. By comparing with the torque and the vibration multifractal analysis result, the trend of torque is more obvious than the vibration. The multifractal analysis provides dimensionless parameters to specify these signals.
By measuring and analyzing the bearing components flatness and roughness, we found that the flatness of rear bearing components are better than front bearing components. We speculate that the preload applied to the rear bearing will decline over time without oil cooling. The decline of spindle stiffness causes spindle to deflection. Elements expanding lead to uneven distribution of the contact stress. Those two reasons caused serious wear of bearings and vibration became larger with time passing. From the above, we know the force of pre-tension and the contact situation of each component are dominating the vibration behavior of bearings.

[1]H. Weule, H. U. Golz, “Preload-control in Ball Screw – A New Approach for Machine Tool Building” , Annals of the CIRP, vol. 40, pp. 383-386, 1991.
[2]Y. Tokunaga, T. Igarashi, T. Sugiura, “Studies on the Sound and Vibration of a Ball Screw”, Transactions of the Japan Society of Mechanical Engineers, Part C vol.31, No.4, pp.732-738, 1988.
[3]T. Igarashi, Y. Tokunaga, T. Sugiura, “Studies on the sound and vibration of a ball screw”, Transactions of the Japan Society of Mechanical Engineers, Part C, Vol.55, No.520, pp.2945-2950, 1989.
[4]H. Yamaguchi, “Development of NSK S1 Series Ball Screws and Linear Guides”, Motion & Control, NSK Ltd., No.11, pp.27-34, 1996.
[5]蘇栢賢，“滾珠導螺桿振動噪音之研究”，碩士論文，國立清華大學動力機械工程學系，2005。
[6]王建文，“滾珠導螺桿低頻噪音源之鑑別與改善研究”，碩士論文，國立清華大學動力機械工程學系，2006。
[7]魏進忠，“單螺帽雙圈滾珠螺桿在預負荷及潤滑作用條件下運動機制與機械性能的理論分析及實驗印證”，博士論文，國立成功大學機械工程學系，2003。
[8]J. P. Hung, S. S. Wu, and Y. Chiu, “Impact Failure Analysis of Re-circulating Mechanism in Ball Screw”, Engineering Failure Analysis, vol.11, pp.561-57, 2004.
[9]葉俊成，“直流馬達與齒輪箱之噪音分析與減量”，國立台灣科技大學機械工程研究所碩士論文，2005。
[10]R. C. Eisenmann, “Machinery Malfunction Diagnosis And Correction”, Prentice Hall, USA, 1998.
[11]R. S. Randy, G. H. Thomas, K. Farrukh, and R. G. Bartheld, “Motor Bearing Damage Detection Using Stator Current Monitoring” IEEE Transactions on Industry Applications, vol. 31, No. 6, November/December, 1995.
[12 ]劉家瑋， “馬達動態特性鑑別及故障診斷”，中原大學機械工程學系碩士學位論文，2002。
[13] TACB系列滾珠螺桿支撐軸承，興中軸承有限公司。
[14]B. B. Mandelbort, W. H. Freeman, “The Fractal Geometry of Nature” , New York, 1982.
[15]葛世榮，朱華，“摩擦學的分形”，機械工業出版社，中國，2005。
[16]G. Zhou, M. Leu and D. Blackmore, “Fractal Geometry Modeling with Applications in Surface Characterisation and Wear Prediction”, International Journal of Machine Tools and Manufacture, vol.35, No.2, pp.203-209, 1995.
[17]H. Zhou, S. Ge, X. Cao and W. Tang, “The Changes of Fractal Dimensions of Frictional Signals in the Running-In Wear Process”, Wear, vol.263, pp.1502–1507, 2007.
[18]孫毅興，“利用碎形理論建立量測訊號即時監測技術與磨潤行為關聯性之研究”，國立成功大學碩士論文，2010。
[19]U. Frisch, and G. Parisi, “On the Singularity Structure of Fully Developed Turbulence”, Turbulence and Predictability in Geophysical Fluid Dynamics, Amsterdam, North-Holland, 1985.
[20]A. R. Rojas, A. M. Diosdado, C. G. P. Miller, and F. A. Brown, “Spectral and Multifractal Study of Electroseismic Time Series Associated to the Mw=6.5 Earthquake of 24 October 1993 in Mexico” Natural Hazards and Earth System Sciences, vol.4, pp. 703–709, 2004.
[21]C. Godano and V. Caruso, “Multifractal Analysis of Earthquake Catalogues”, Geophysical Journal International , vol.121, pp.385-392, 1995.
[22]S. J. Loutridis, “Self-Similarity in Vibration Time Series: Application to Gear Fault Diagnostics”, Journal of Vibration and Acoustics, vol. 130, pp.0310041-0310049, 2008.
[23]張閔期，“運用多重碎形理論於滾珠螺桿系統之訊號分析”，國立成功大學碩士論文，2011。
[24]C. E. Shannon, “Communication in the Presence of Noise”, Proc. Institute of Radio Engineers, vol.37, no.1, pp.10-21 , 1949.
[25] H. Nyquist, “Certain Topics in Telegraph Transmission Theory”, Trans. AIEE, vol.47, pp.617-644 , 1928.
[26]E. T. Whittaker, “On the Functions Which Are Represented by the Expansions of the Interpolation Theory”, Proc. Royal Soc. Edinburgh, Sec. A, vol.35, pp.181-194, 1915.
[27] P. Malliavin, G. Letac, “傅立葉分析及譜分析” ，武漢大學出版社， 1993。
[28]T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, “Fractal measure and their singularities: The characterization of strange sets”, Physical Review A, vol.33, pp.1141–1151, 1986.
[29]S. Laurent, “Fractals and Multifractals in Ecology And Aquatic Science”, CRC Press/Taylor & Francis, U. S. A. , 2010.
[30]A. Rneyi, “Probability Theory”, North-Holland, Amsterdam, 1970.
[31]P. Grassberger, “Generalized Dimensions of Strange Attractors”, Physica Letters A, vol.97, pp.227-230, 1983.
[32]H. Hentschel and I. Procaccia,” The Infinite Number of Generalized Dimensions of Fractals and Strange Attractors”, Physica D: Nonlinear Phenomena, vol.8, pp. 435-444, 1983.
[33]T. Vicsek, “Fractal Growth Phenomena”, Word Scientific, Singapore, 1993.
[34]H. Takayasu, “Fractals in the Physical Sciences”, Manchester University Press, Manchester, 1997.
[35]蘇致遠，“音樂及DNA序列之多重碎形分析”，國立台灣大學博士論文，2004。
[36]C. J. G. Evertsz and B. B. Mandelbrot, “Multifractal Measures, Chaos and Fractals: New Frontier of Science”, Springer, USA, 1992.
[37] 滾珠螺桿技術手冊，上銀科技股份有限公司，2012。
[38]YSPL series 精密鎖定螺帽產品型錄，盈錫精密工業股份有限公司。
[39] 國光牌潤滑油脂產品說明書，台灣中油股份有限公司。
[40]黃運琳，“機械振動概論與實務”，五南圖書出版公司，2009。
[41]F. P. Bowdon, D. Tabor, 1964, "The Friction and Lubrication of Solids
Part II," Oxford University Press.
[42]J. K. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H. E. Stanley, “Multifractal detrended fluctuation analysis of nonstationary time series”, Physica A, vol.316, pp.87-114, 2002.
[43]R. S. Randy, G. H. Thomas, K. Farrukh, G. B. Robert “Motor Bearing Damage Detection Using Stator Current Monitoring”, IEEE Transactions on Industry applications, vol. 31, NO. 6, November, 1995.
[44]S. Izumi, T. Yokoyama, A. Iwasaki, S. Sakai, “Three-dimensional finite element analysis of tightening and loosening mechanism of threaded fastener”, Department of Mechanical Engineering, The University of Tokyo, 7-3-1, Bunkyo-ku, Hongo, Tokyo 113-8656, September, 2004.
[45]C. Jin, B. Wu, Y. Hu, “Heat generation modeling of ball bearing based on internal load distribution”, Tribology International 45 8–15, 2012.
[46]T. Holkup, H. Cao, P. , Y. Altintas, J. , “CIRP Annals - Manufacturing Technology”, CIRP Annals - Manufacturing Technology 59 365–368, 2010.