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壓染機輥輪系統之動態建模與分析

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,It Wd~fl~ ~Ntzi/] ~ ~;f~~>t;flT Dynamic modeling and analysis of a

padder roller system

$~ '" ~* Ft. ~#

Abstract

This paper is intended to deal with the dynamic modeling and analysis of a padder roller system. First, the method of dynamics is utilized for the development of the kinetic and potential energy ofthe system and the governing equations of motion are derived from Hamilton's principle. Afterwards, the open loop transfer function is obtained from the actuator and sensor's locations, and the IMSL . subroutine is used to find all the poles and zeros of the corresponding open loop system. The dynamic characteristics such as natural frequencies and mode shapes are analyzed by the frequency equation acquired by assume-mode method. Through the transfer function and dynamic characteristics developed by this research, it is expected to be used as the key for the design of controllers.

Keywords: Dynamic modeling, Padder roller, Assume-made-method, Natural frequencies, critical speeds

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~~~

1. Chives, D. R. and Nelson, H. D., "The Natural Frequencies and Critical Speed of a Rotating, Flexible Shaft-Disk System" , ASME Journal of Engineering for Industry, pp. 881-886,(1975).

2. Ozguven, H Nevzat, "On the Critical Speed of Continuous Shaft-Disk System" , ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design, 106, pp. 59-61(1984).

3. Nelson, N. D. and McVaugh, J. M., "The Dynamics of Rotor-Bearing System Using Finite Element" , ASME Journal of Engineering for Industry, pp. 593-600,(1976).

4, Child, D. Wand Graviss, K" "A Note on Critical Speed Solutions for Finite-Element-Based Rotor models" , ASME Journal of Mechanical Design, 104, ppA12-416(1982).

5. Lund, J. W, "Stability and Damped Critcal Speeds of a Flexible Rotor in Fluid-Film Bearings" , ASME Journal of Engineering for Industry, 96, pp. 593-600,(1976).

6. Chiau, S. Wand Huang, S, c., "On the Flexural Vibrations of Rotor System Using a Modified Transfer Matrix Method" , Proceedings of the 6th Chinese Society of Mechanical Engineering, pp.

1607-1618(1989),

7, Meriam, J. L. and Kraige, L. G., "Engineering Mechanics Dynamics" , Fourth Edition ,1998, pp.90-91.

8. L. Meirovitch, "Dynamics and Conyrol of structures",John Wiley and Sons,NY, 1992.

9. E. Kreyszig, "Advanced Engineering Mathematics", Seven Edition ,1993,pp.141-146.

10. IMSL Fortran Library Version 5,0," IMSL Fortran Library User's Guide Stat/Library Volume 2 of2", http://www.vni.com.tw/tw Ibooks! docs!

11. L. Meirovitch, "Elements of Vibration Analysis", Fourth Edition ,McGraw-Hill, 1 986,pp.282-285 , 12. M, Lalanne and G.. Ferraris, "Rotordynamics

Prediction in Engineering", John Wiley and Sons,NY, 1990

13. Andrew D. D. and Stephen A. P., "Analytical Methods in Rotor Dynamics" ,Applied Science Publishers ,1983

14, Fredric F. E., "Handbook of rotordynamics" , McGraw-HiIl,l992

158

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