臺灣博碩士論文加值系統

In the present machine tool industry, the calculation process of the bearing stiffness through a spindle''s dynamic state is still under development. Bearing stiffness is determined by the elastic deformation between bearing raceway surface and rolling element when bearing at force condition. The actual bearing stiffness can be known by inversing the natural frequency of the spindle through spindle dynamic experiment. Angular contact ball bearings are usually used in high-speed spindle. Bearing usually add preload to increase its stiffness. According the operation condition to select the preload force is important.

The study is given different preload levels and used three simulation methods to discuss the bearing properties. The spindle/shaft natural frequencies are predicted by the Rayleigh-Ritz method and the finite element method. The commercial software of BEARINX is used to predict the bearing life, bearing stiffness and spindle/shaft natural frequencies. The difference between the Rayleigh-Ritz method and the finite element method are assumptions. One is assumed as a rigid body and another is assumed as a beam. The experiment of spindle are the rotation experiment and modal testing. Find the actual spindle natural frequencies and compare the simulation results.

Acknowledgements..........i
摘要......................ii
Abstract..................iii
Table of Contents.........iv
List of Tables............vi
List of Figures...........vii
List of Symbols...........x
Chapter 1. Introduction............1
1.1 Background......................1
1.2 Literature Review...............2
1.2.1 Spindle analysis................2
1.2.2 Spindle bearing modeling........2
1.2.3 Spindle bearing analysis........3
1.3 Objectives......................4
1.4 Methodology.....................4
1.5 Structure of Thesis.............5
Chapter 2. Theoretical background..6
2.1 Spindle analysis................6
2.1.1 Spindle bearing..........6
2.1.2 Bearing preload..........6
2.1.3 Bearing life..........10
2.2 Rayleigh-Ritz method..........12
2.3 Operating deflection shape (ODS) analysis..........14
2.3.1 Cross spectrum analysis..........14
2.3.2 Transmissibility..........15
2.4 Waterfall diagram..........15
2.4.1 Translation among physical quantities..........17
2.5 Cutting force analysis..........20
Chapter 3. Simulation..........21
3.1 Shaft natural frequencies, bearing life and bearing stiffness using BEARINX..........22
3.2 Shaft natural frequency using the Rayleigh-Ritz method..........27
3.3 Shaft natural frequencies using the Finite element method..........29
Chapter 4. Experiment of the spindle..........33
4.1 Modal testing of spindle components..........33
4.1.1 Shaft of the spindle..........33
4.1.2 The front and rear spindle body..........36
4.2 Experiments on spindle..........37
4.2.1 Rotation Experiment..........37
4.2.2 Modal testing..........42
4.2.3 Operating deflection shape (ODS) analysis..........46
Chapter 5. Conclusions and Future work..........52
5.1 Conclusions..........52
5.2 Future work..........53
References..........54
Appendix A: Experimental instruments..........57
Appendix B: The front and rear of spindle body mode shapes..........57
Appendix C: The experiment of the front and rear of spindle body..........59

[1]J.S. Chen , Y.W. Hwang, "Centrifugal force induced dynamics of a motorized high-speed spindle," Int J Adv Manuf Technol, vol. 30, pp. 10-19, 2006.
[2]M. Rantatalo, "Non-contact measurements and modelling of milling machine tool vibrations," Luleå University of Technology Department of Human Work Sciences Division of Sound & Vibration, 2006.
[3]E. Abele , Y. Altintas , C. Brecher, "Machine tool spindle units," CIRP Annals - Manufacturing Technology, vol. 59, pp. 781-802, 2010.
[4]A.W. Lee, "Misalignment in rigidly coupled rotors," Journal of Sound and Vibration, vol. 305, pp. 261-271, 2007.
[5]V. Gagnol, T.P. Le , P. Ray, "Modal identification of spindle-tool unit in high-speed machining," Mechanical Systems and Signal Processing, vol. 25, pp. 2388-2398, 2011.
[6]Z.Y. Rui , T. Li , C.L. Lei , C.B. Hu, "Centrifugal phenomenon and its influence on high speed spindle," Chinese Society of Mechanical Engineers, vol. 26, pp. 2853-2861, 2015.
[7]A.K. Telang, "Static stiffness analysis of high frequency milling spindle," International Journal of Research in Engineering and Technology, vol. 03, pp. 577-585, 2014.
[8]Central machine Tool institute, "Machine tool design handbook", McGraw-Hill, 1982.
[9]E.I. Rivin, "Stiffness and damping in mechanical design", CRC Press, 1999.
[10]Y. Cao , Y. Altintas, "A general method for the modeling of spindle-bearing systems," Journal of Mechanical Design, vol. 126, pp. 1089-1104, 2004.
[11]Y. Cao , Y. Altintas, "Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations," International Journal of Machine Tools & Manufacture, vol. 47, pp. 1342-1350, 2007.
[12]R. Aini, H. Rahnejat, R. Gohar, "An experimental investigation into bearing-induced spindle vibration," Proceedings of the Institution of Mechanical Engineers, vol. 209, pp. 107-114, 1995.
[13]Y.S. Lee, C.W. Lee, "Modelling and vibration analysis of misaligned rotor-ball bearing systems," Journal of Sound and Vibration, vol. 224, pp. 17-32, 1999.
[14]D. Mourad , N.E. Titouche , M. Djaoui , O. Mohammed, "The calculation of ball bearing nonlinear stiffness theoretical and experimental study with comparisons," Journal of Engineering and Applied Sciences, vol. 03, pp. 872-883, 2008.
[15]Y.K. Hwang , C.M. Lee, "A review on the preload technology of the rolling bearing for the spindle of machine tools," International Journal of Precision Engineering and Manufacturing, vol. 11, pp. 491-498, 2010.
[16]A. Gunduz , J.T. Dreyer , R. Singh, "Effect of bearing preloads on the modal characteristics of a shaft-bearing assembly : Experiments on double row angular contact ball bearings," Mechanical Systems and Signal Processing, vol. 31, pp. 176-195, 2012.
[17]DYNOMAX "Spindle facts," DYNOMAX, [Online].
Available: http://dynospindles.com/vault/technical/Book-of-Spindles-Part-1.pdf.
[18]T.A. Harris, M.N. Kotzalas, "Essential concepts of bearing technology", Taylor & Francis Group, 2006.
[19]S. Ilanko , L.E. Monterrubio , Y. Mochida, "The Rayleigh-Ritz method for structural analysis", John Wiley & Sons, Inc., 2014.
[20]D.L. Hartmann, "Cross spectrum analysis," [Online].
Available: http://www.atmos.washington.edu/~dennis/552_Notes_6c.pdf.
[21]J. He, Z.F. Fu, "Modal analysis", Butterworth-Heinemann, 2001.
[22]D. J. Ewins, "Modal Testing:Theory, Practice and Application", Research Studies Press, 2000.
[23]M.I Friswell, "Dynamics of rotating machines", Cambridge university press, 2010.
[24]Y.K. Liu, “An investigation on cutting force of high-speed milling,” National Chung Hsing University, 2001.
[25]C.Y. Tai, "High-order Finite Element Model for Rotating Shafts with Uncertain Parameters," National Chung Hsing University, 2015.
[26]F. Forestier, V. Gagnol , P. Ray , H. Paris, "Modeling of Self-Vibratory Drilling Head-Spindle System for Predictions of Bearings Lifespan," Advances in Acoustics and Vibration, vol. 2011, pp. 1-10, 2011.
[27]E. Barkanov, "Introduction to the Element Method," Institute of Materials and Structures Faculty of Civil Engineering Riga Technical University, 2001.
[Online]. Available: http://icas.bf.rtu.lv/doc/Book.pdf.