Modal Analysis of Machine Tool Column Using Finite Element Method

Authors: Migbar Assefa

Abstract:

The performance of a machine tool is eventually assessed by its ability to produce a component of the required geometry in minimum time and at small operating cost. It is customary to base the structural design of any machine tool primarily upon the requirements of static rigidity and minimum natural frequency of vibration. The operating properties of machines like cutting speed, feed and depth of cut as well as the size of the work piece also have to be kept in mind by a machine tool structural designer. This paper presents a novel approach to the design of machine tool column for static and dynamic rigidity requirement. Model evaluation is done effectively through use of General Finite Element Analysis software ANSYS. Studies on machine tool column are used to illustrate finite element based concept evaluation technique. This paper also presents results obtained from the computations of thin walled box type columns that are subjected to torsional and bending loads in case of static analysis and also results from modal analysis. The columns analyzed are square and rectangle based tapered open column, column with cover plate, horizontal partitions and with apertures. For the analysis purpose a total of 70 columns were analyzed for bending, torsional and modal analysis. In this study it is observed that the orientation and aspect ratio of apertures have no significant effect on the static and dynamic rigidity of the machine tool structure.

Keywords: Finite Element Modeling, Modal Analysis, Machine tool structure, Static Analysis.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1336334

References:

[1] A. Myers, D.G. Ford and Q. Xu; Finite Element Analysis of the structural dynamics of a vertical Milling Machine, International Conference on Laser Metrology, Machine Tool, CMM, and Robot Performance VI; 2003.
[2] Taylor S. and S.A. Tobias, ‘Lumped-constants method for the prediction of the vibration characteristics of machine tool structures’, Proc. 5th Int. M.T.D.R., Conf., pp.01-015, 1964.
[3] David Te-Yen Huang and Jyh-Jon Lee, "On obtaining machine tool stiffness by CAE techniques”, Int. J. of Machine Tools & Manufacture, Vol.41, pp.1149-1163, 2001.
[4] Martin, H., 1962. ‘The use of modals for analysis of machine tool structures’, Int. J. M.T.D.R.,Vol. 2, pp. 153-163.
[5] Maltbaek, J. C., 1964 September ‘Classical beam method for the prediction of vibration characteristics of machine tool structure’ Int.Machine Tool Design Research Conf. proceedings 5 pp 23-36.
[6] Taylor S. and S.A. Tobias, ‘Lumped-constants method for the prediction of the vibration characteristics of machine tool structures’, Proc. 5th Int. M.T.D.R., Conf., pp.01-015, 1964
[7] Badawi, M.W. & Thornley, R.H., 1965 ‘Comparison of static and dynamic characteristics of losed box section beams with and without core holes and for some other beam configurations’ Int. J. Mach.Tool Des. Res. Vol.6, pp. 199-206.
[8] Ganesan N. Ramamurti V. and Rao B.V.A., "Torsional behavior of machine tool columns”, Int. J. M.T.D.R., Vol.14, pp. 219- 231, 1974.
[9] Cowley, A. and Fawcett, M.A. "The analysis of a Machine Tool Structure by Computing Techniques” Proc.8th Int. M.T.D.R. Conf., pp. 119-138, 1967.
[10] Yoshimura Masataka "Analysis and optimization of structural dynamics of machine tools by a synthesis of dynamic rigidity program system”, Int. M.T.D.R. Conf. pp.209-215, 19 75.
[11] Reddy, C.P. and Rao, S.S "Dynamic Analysis of Machine Tool Structures, Journal of Engineering for Industry, Transaction of ASME, 1977, pp-882-888.
[12] Dube J.N., ‘computer aided design of machine tool structure with model technique’, Int. J.computers and structures Vol.28, No. 3, pp. 345-352, 1988.
[13] Yoshimura M. and T. Hoshi, ‘Computer Approach to Dynamically Optimum design of machine tool structures’, 12th Int. M.T.D.R.Conf. pp. 439-446, 1971.
[14] Ramana G.V. and Rao S.S., "Optimum design of plano- milling machine structure using finite element analysis”, Int. J. of computers and structures, Vol.18, No.2, pp. 247-253, 1984.
[15] K. Mao et al, Stiffness influential factors-based dynamic modeling and its parameter identification method of fixed joints in machine tools, International Journal of Machine Tools & Manufacture 50 (2010) 156–164
[16] Bath, K. J "Finite Element Procedures”, Prentice-Hall 1996
[17] ASYS Inc. (2005), ANSYS Advanced Analysis Techniques Guide.
[18] Koenigsberger, F. and Tlusty, "Machine Tool Structures” Vol. I, Pergamon, 1970.
[19] Mustafizur Rahhman etal, Non-Conventional Materials for Machine Tool Structures JSME international journal, Vol. 44 No. 1 2001
[20] Migbar Assefa "The Effect of Tapers, Apertures and Ribs on the Stiffness of Machine Tool Column Using Finite Element Method” Journal of 15th Annual Conference, Ethiopian Society of Mechanical Engineers Journal Vol. VIII No.I, October 2010.
[21] Migbar Assefa, "Finite Element Based Dynamic Analysis of Machine Tool Column”, International Journal of Engineering Science, Nigeria, Vol. 2, No. 4, 2010, pp 62-70
[22] Hinduja, S. and A. Cowley, ‘The finite element method applied to the deformation analysis of thin walled columns’. Proc. 12th Int. J. M.T.D.R., pp.455-477, 1971.
[23] Harris, C., 2002, "Shock and VibrationHandbook”, McGraw-Hill: New York, 5th Edn.ISBN 0-07-137081-1
[24] Cheng Zheng-ding and Xiong Huan-guo 1981 ‘finite element study of dynamic characteristics of main components of machine tools’ applied mathematics and mechanics English edition Vol.2.