臺灣博碩士論文加值系統

為了提升機器的精度，必須要預測其動態特性。近年來，電腦數值模型與實驗模型兩者之間的差異可透過模型更新法減少。本研究使用基於靈敏度的模型更新方法，辨識工具機機腳剛性，並透過將靈敏度矩陣作奇異值分解的探討，找出配重質量塊在實驗裝置中最佳的放置位置。本論文利用三種模型進行機腳剛性辨識：配有機腳的板模型、工具機模型以及配有彈簧的樑模型。配有機腳的板模型用於驗證機腳剛性鑑別技術之可行性；工具機模型視為有很大系統矩陣的複雜結構，並使用其降階模型減少鑑別機腳剛性所需的時間；配有彈簧的樑模型代表擁有眾多機腳的結構，並透過離散傅立葉級數減少設計參數的數目。最後，將前兩個模型透過實驗進行驗證。結果顯示，此方法可成功辨識機腳剛性，且使用完整模型的機腳剛性鑑別結果比降階模型準確，但是使用降階模型所需的鑑別時間遠少於完整模型。

In order to improve precision of machines, it is necessary to predict their dynamic characteristics. Model updating has been utilized to reduce the difference between the mathematical and experiment models in recent years.
Identified the footings stiffness of machine tool in this thesis using sensitivity-based model updating methodology. The positions of the perturbation mass are determined using the singular value decomposition (SVD) analysis of sensitivity matrix proposed by predecessors. Three models including plate-footings assembly, machine tool prototype, and beam-springs assembly are tested. Plate-footings assembly is utilized to demonstrate the feasibility of the model updating of footing stiffness. Machine tool prototype is regarded as a complex structure with large system matrices in the finite element method. The reduced order model is used to reduce the time of model updating process. Beam-springs assembly represents a multiple footings structure. The discrete Fourier series are utilized to reduce the number of design variables. Finally, the first two models are validated using experiment model analysis. The results show that this methodology successfully identifies the footings stiffness, and identification based on the full model is more accurate than that on the reduced order model, but the time of model updating of reduced order model is significantly less than the full model.

摘要 i
Abstract ii
Table of Contents iii
List of Tables v
List of Figures vii
List of Symbols ix
Chapter 1. Introduction 1
1.1 Background 1
1.2 Literature Review 2
1.3 Objectives 7
1.4 Methodology 7
1.5 Thesis Structure 8
Chapter 2. Theoretical Background 10
2.1 Sensitivity-based model updating 10
2.2 Singular value decomposition of the sensitivity matrix 11
2.3 Reissner-Mindlin plate element with three-dimensional degrees of freedom 12
2.4 Natural frequency sensitivity of multiple degree-of-freedom systems 19
2.5 Monte Carlo simulation 20
2.6 Reduced number of design variables by discrete Fourier series 21
Chapter 3. Simulation of footing stiffness model updating 23
3.1 Plate-footings assembly 24
3.2 Robustness of model updating 32
3.3 Identify the stiffness of machine tool prototype footings 36
3.4 Identify the stiffness of multiple footings model 42
Chapter 4. Experimental validation 46
4.1 Experimental validation of plate-footings assembly 46
4.2 Experimental validation of machine tool prototype 56
Chapter 5. Conclusions and future work 65
5.1 Conclusions 65
5.2 Future work 67
References 68

[1]Z. Su and L. Wang, “Effect of the dynamic characteristics of a five-axis machine tool on the surface quality of complex surface,” Procedia CIRP, vol. 72, pp. 1505–1511, 2018.
[2]J. E. Mottershead, M. Link, and M. I. Friswell, “The sensitivity method in finite element model updating: A tutorial,” Mechanical System and Signal Processing, vol. 25, no. 7, pp. 2275–2296, 2011.
[3]Y. C. Hong, “Model updating of machine tool feet and sliders,” Master thesis, National Chung Hsing University, 2018.
[4]Y. K. Lin, “Application of superelement-based analysis and Guyan reduction in machine tool analysis,” Master thesis, National Chung Hsing University, 2019.
[5]M. Zaeh and D. Siedl, “A new method for simulation of machining performance by integrating finite element and multi-body simulation for machine tools,” CIRP Annals - Manufacturing Technology, vol. 56, no. 1, pp. 383–386, 2007.
[6]W. R. Wang, “Dynamic analysis and design of a machine tool spindle-bearing system,” Journal of Vibration and Acoustics, vol. 116, pp. 280–285, 1994.
[7]H. Ahmadian, J. E. Mottershead, S. James, M. I. Friswell, and C. A. Reece, “Modelling and updating of large surface-to-surface joints in the AWE-MACE structure,” Mechanical System and Signal Processing, vol. 20, no. 4, pp. 868–880, 2006.
[8]C. Farhat and F. M. Hemez, “Updating finite element dynamic models using an element-by-element sensitivity methodology,” AIAA Journal, vol. 31, no. 9, pp. 1702–1711, 2008.
[9]P. G. Bakir, E. Reynders, and G. DeRoeck, “Sensitivity-based finite element model updating using constrained optimization with a trust region algorithm,” Journal of Sound and Vibration, vol. 305, no. 1–2, pp. 211–225, 2007.
[10]M. Imregun, W. J. Visser, and D. J. Ewins, “Finite element model updating using frequency response function data—I. theory and initial investigation,” Mechanical System and Signal Processing, vol. 9, no. 2, pp. 187–202, 1995.
[11]M. Imregun, K. Y. Sanliturk, and D. J. Ewins, “Finite element model updating using frequency response function data—II. case study on a medium-size finite element model,” Mechanical System and Signal Processing, vol. 9, no. 2, pp. 203–213, 1995.
[12]T. Yang, S. H. Fan, and C. S. Lin, “Joint stiffness identification using FRF measurements,” Computer and Structures, vol. 81, no. 28–29, pp. 2549–2556, 2003.
[13]S. Pradhan and S. V. Modak, “Normal response function method for mass and stiffness matrix updating using complex FRFs,” Mechanical System and Signal Processing, vol. 32, pp. 232–250, 2012.
[14]S. Adhikari and M. I. Friswell, “Distributed parameter model updating using the Karhunen – Loe ̀ve expansion,” Mechanical System and Signal Processing, vol. 24, no. 2, pp. 326–339, 2010.
[15]H. P. Chen, “Efficient methods for determining modal parameters of dynamic structures with large modifications,” Journal of Sound and Vibration, vol. 298, no. 1–2, pp. 462–470, 2006.
[16]S. V. Modak, “Model updating using uncorrelated modes,” Journal of Sound and Vibration, vol. 333, no. 11, pp. 2297–2322, 2014.
[17]H. Ahmadian, J. E. Mottershead, M. I. Friswell, “Regularisation methods for finite element model updating,” Mechanical System and Signal Processing, vol. 12, pp. 47–64, 1998.
[18]R. S. Bais, A. K. Gupta, B. C. Nakra, and T. K. Kundra, “Studies in dynamic design of drilling machine using updated finite element models,” Mechanism and Machine Theory, vol. 39, no. 12, pp. 1307–1320, 2004.
[19]D. Kono, T. Inagaki, A. Matsubara, and I. Yamaji, “Stiffness model of machine tool supports using contact stiffness,” Precision Engineering, vol. 37, no. 3, pp. 650–657, 2013.
[20]D. Kono, S. Nishio, I. Yamaji, and A. Matsubara, “A method for stiffness tuning of machine tool supports considering contact stiffness,” International Journal of Machine Tools and Manufacture, vol. 90, pp. 50–59, 2015.
[21]P. Koutsovasilis and M. Beitelschmidt, “Model reduction of large elastic systems,” in IFToMM World Congresses, France, 2007.
[22]P. Maglie, R. Carbini, S. Weikert, and K. Wegener, “Efficient mechatronic evaluation of machine tool designs using model reduction,” in 12th Mechatronic Forum Biennial International Conference, Zurich Switzerland, 2010.
[23]I. Garitaonandia, M. H. Fernandes, and J. Albizuri, “Dynamic model of a centerless grinding machine based on an updated FE model,” International Journal of Machine Tools and Manufacture, vol. 48, no. 7–8, pp. 832–840, 2008.
[24]A. J. M. Ferreira, “MATLAB codes for finite element analysis: solids and structures,” Springer Publishing Company, Incorporated, 2009.
[25]C. Y. Tai and Y. J. Chan, “A hierarchic high-order Timoshenko beam finite element,” Computer and Structures, vol. 165, pp. 48–58, 2016.
[26]M. S. Choi, “Free vibration analysis of plate structures using finite element-transfer stiffness coefficient method,” KSME International Journal, vol. 17, no. 6, pp. 805–815, 2003.
[27]K. -J. Bathe, “Finite Elment Procedures,” Prentice Hall, 2nd edition, 2014.
[28]D. V. Griffiths, “Stiffness matrix of the four-node quadrilateral element in closed form,” International Journal for Numerical Methods Engineering, vol. 37, pp. 1027–1038, 1994.
[29]Y. J. Chan, “Variability of blade vibration in mistuned bladed discs,” PhD thesis, Imperial College London, 2009.
[30]D. J. Ewins, “Modal testing theory, practice and application,” Research Studies Press, 2000.