本論文主要利用有限元素法配合赫茲3D接觸理論，探討線性滑軌設計中，採用鋼珠陶瓷鍍膜滾珠式全陶瓷滾珠時，其負載導致之3D接觸應力變化。文中對滾珠與滑軌參數之影響，亦進行分析探討。因陶瓷鍍膜後的滾珠，鍍膜與核心材料性質的差異，使得接觸點赫茲接觸應力分佈極為複雜，膜厚及介面應力變化為本論文探討分析重點。
文中使用ANSYS 14.0 有限元素套裝分析軟體。配合彈-塑有限元素模式對具有陶瓷鍍膜的鋼珠與滑槽進行模擬。探討接觸曲率、摩擦係數、鍍膜厚度、陶瓷材料、溫度及負載等參數，對於其三維接觸應力分佈、及變化的影響。最後分別依照最大畸變能及最大主應力理論，對鋼材質滑槽及陶瓷膜層得到的應力數據進行強度分析，分析不同陶瓷鍍膜材料在不同負載下的理想鍍膜厚度。

The 3D Hertz stress distributions of steal, ceramic film coated and ceramic rollers in linear guide design are simulated and investigated. The ANSYS 140 Finite Element software package with elastic-plastic element model is employed in the stress and deformation simulation. The difference of material properties of coating film make the 3D contact stress distribution so very complicate. The effect of film thickness on the contact stress and deformation are the spot points be evaluated in this study.
The geometry parameters ; i.e. the radii of curvature of roller and rail, coated film thickness, film material, friction coefficient, and temperature, on the effect of contact stress and deformation are investigated. The maximum principle stress and distribution energy failure theories have been employed to illustrate the brittle and elastic features of coated ceramic film and steel rail in the linear guide design. The best film thickness of coated ceramic film for different loading cases have also been proposed.

論文審定書 i
謝誌 ii
摘要 iii
Abstract iv
目錄 v
圖目錄 vii
表目錄 x
符號說明 xi
第一章 緒論 1
1.1 前言 1
1.2 研究動機 2
1.3 文獻回顧 2
1.4 組織章節 4
第二章 研究理論與方法 5
2.1 有限元素法理論介紹 5
2.2赫茲接觸應力介紹 10
2.3應力分析理論介紹 15
第三章 有限元素模型建立 18
3.1 幾何外觀與網格切割 18
3.2 邊界條件與接觸設定 26
3.3 收斂性分析 32
第四章 結果討論 34
4.1 參數規劃 34
4.2軌道曲率半徑 37
4.3 滾動摩擦接觸 48
4.4 球陶瓷鍍膜 57
4.4.1氧化鋁陶瓷鍍膜 57
4.4.2氮化矽陶瓷鍍膜 83
4.4.3碳化矽陶瓷鍍膜 89
4.4.4不同陶瓷材料鍍膜的比較 95
4.5陶瓷鍍膜受環境溫度的影響 97
第五章 結論與未來工作 104
5.1 結論 104
5.2 未來工作 104
參考文獻 105

[1] 王正青，2013年中國北京機床展概況，台灣機械工業同業公會，台灣機械工業同會機械資訊 676 期。
[2] 盧素涵，我國線性滑軌市場現況，經濟部技術處金屬中心，2006。
[3] 張永乾，陶瓷軸承技術發展與應用，洛陽軸研科技股份有限公司，2010。
[4] Turnes, M. J., Clough, R. W., Martin, H. C., and Topp, J. L., “Stiffness and Deflection Analysis of Complex Structures,” Journal of Aeronautical Science, 23(9), pp. 805-824, 1956.
[5] Shaw, D., and Su, W. L., “Study of Stiffness of a Linear Guideway by FEA and Experiment,” Journal of Tech Science Press, 5(3), pp. 129-138, 2011.
[6] 賴正平，虛擬精密線性滑動平台剛性分析及動態模擬之研究，碩士論文，國立雲林科技大學機械工程系，雲林，2000。
[7] Young, W. C., Roark’s Formulas for Stress and Strain, 6th. ed., McGraw-Hill, New York, 1989.
[8] Bhushan, B., “Contact Mechanics of Rough Surfaces in Tribology: Multiple Asperity Contact,” Tribology Letters, 4(1), pp. 1-35, 1998.
[9] Komvopoulos, K., and Gong, Z. Q., “Stress Analysis of Layered Elastic Solid in Contact with a Rough Surface Exhibiting Fractal Behavior,” International Journal of Solids and Structures, 44, pp. 2109-2129, 2007.
[10] Park, J., Chung, W. K., and Youm, Y., “Second-Order Contact Kinematics for Regular Contacts,” IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1723-1729, 2005.
[11] Robert, L. J., Ravi, D. D., Hasnain, M., and Manoj, M., “An Analysis of Elasto-Plastic Sliding Spherical Asperity Interaction,” Wear, 262(1-2), pp. 210-219, 2007..
[12] Ohta, H., “Sound of Guideway Type Recirculating Linear Ball Bearings,” Journal of Tribology, Transactions of the ASME, 121, pp. 678~685, 1999.
[13] Ohta, H., and Hayashi, E., “Vibration of Linear Guideway Type Recirculating Linear Ball Bearings,” Journal of Sound and Vibration, 235(5), pp. 847~861, 2000.
[14] Chang, J. C., Wu, J. S. S., Hung, J. P., “The Effect of Contact Characteristic on Dynamic Behaviors of Rolling Contact Elements,” Mathematics and Computers in Simulation, 74(6), pp. 454~467, 2007.
[15] 孫健利，精密直線滾動導軌的預加載荷及剛度計算，華中理工大學學報，第16卷第6期，1988。
[16] Ninomiya, M. and Kato, S., “Analysis of Linear Guide and Ball Screw Stiffness,” International Journal of the Japan Society for Precision Engineering, 33, pp. 173-177, 1999.
[17] 蕭德瑛、徐耿豪，線性滑軌剛性分析與實驗，中華民國力學學會第三十屆全國力學會議論文集，台灣彰化，2006。
[18] Shkapenyuk, M. B., “Ways of Improving the Performance of Ball-Screw Drives,” Stanki Instrument, 61(4), pp. 9-11, 1990.
[19] 金洙吉、張錫水、齊毓霖、李新元，陶瓷軸承的研製及其台架試驗研究，哈爾濱工業大學學報，第15卷第2期，1995。
[20] Wang, L. Q., Jia, H. X., Zheng, D. Z., and Ye, Z. H., “Advances in High-reliability Ceramic Rolling Element Bearing Technology,” Aeroengine, 39(2), pp. 6~13, 2013.
[21] Turnes, M. J., Clough, R. W., Martin, H. C., and Topp, J. L., “Stiffness and Deflection Analysis of Complex Structures,” Journal of Aeronautical Science, 23(9), pp. 805-824, 1956.
[22] Chandrupatla, T. R. and Belegundu, A. D., Introduction to Finite Elements in Engineering, 3rd ed., Prentice Hall, New Jersey, 2002.
[23] 陸明萬、羅學富，彈性理論基礎，第二版，清華大學出版社，2001。
[24] 陳恩傑、王靖霈，如何正確選用線性滑軌，上銀科技股份有限公司，台灣機械工業同業公會機械資訊568期。
[25] Guo, Y. B., and Liu, C. R., “Mechanical Properties of Hardened AISI 52100 Steel in Hard Machining Processes,” Journal of Manufacturing Science and Engineering, Transactions of the ASME, 124, pp. 1~9, 2002.
[26] Parker, R. J., Grisaffe, S. J., and Zaretsky, E. V., “Surface Failure of Alumina Balls Due to Repeated Stresses Applied in Rolling Contact at Temperatures to 2000 ̊F,” National Aeronautics and Space Administration, 1964.
[27] Nishihara, Y., Nakashima, H., Tsushima, N., and Ito, S., “Factors that affect rolling contact fatigue life of ceramics and rolling contact fatigue life of ceramic balls and rollers,” ASME International Gas Turbine and Aeroengine Congress and Exposition, Brussels, 1990.
[28] Parker, R. J., Grisaffe, S. J., and Zaretsky, E. V., “Surface Failure of Titanium Carbide Cermet and Silicon Carbide Balls in Rolling Contact at Temperatures to 2000 ̊F,” National Aeronautics and Space Administration, 1964.
[29] ISO.14728-2, “Rolling bearings-Linear motion rolling bearings-Part 2：Static load ratings,” 2004.
[30] Budynas, R. G., Nisbett, J. K., Shigley’s Mechanical Engineering Design, 9th. ed., McGraw-Hill, Singapore, 2011.
[31] NSK Corp., “Technical Report,” Cat. No. E728g, 2009.
[32] Zaretsky, E. V., and Poplawski, J. V., “Comparison of Life Theories for Rolling-Element Bearings,” Society of Tribologists and Lubrication Engineers, Chicago, 1995.
[33] 李岡晏，蝸桿蝸輪囓合齒對間之負載與應力分佈及強度設計，碩士論文，國立中山大學機械與機電工程學系，高雄，2013。