A generalized eigenvalue method is used to determine the undamped and damped natural frequencies, coefficients of damping and mode shapes of a computer numerically controlled (CNC) machine tool drive. The calculated results compare well with the measured results obtained by using vibration analysis equipment. Then the sensitivity of the various modes to changes in the stiffness and damping characteristics of the machine drives is estimated. These values prove to be useful in adjusting the parameters of a hybrid model for a CNC machine tool axis drive in order to alter the simulated results in accordance with the measured results.
ErkorkmazK.AltintasY.High speed CNC system design. Part II: Modelling and identification of feed drives. Int. J. Mach. Tools Mf., August 2001, 41(10), 1487–1509.
2.
PislaruC.FordD. G.FreemanJ. M.A new approach to the modelling and simulation of a CNC machine tool axis drive. In Proceedings of the Fourth International Conference on Laser Metrology and Machine Performance (LAMDAMAP 1999), Longhirst Hall, North-umberland, July 1999, pp. 335–343.
3.
PislaruC.FordD. G.FreemanJ. M.Dynamic simulation of CNC machine tool axis drives. In International Conference PCIM 1999, Intelligent Motion Section, Nuremberg, Germany, 22–24 June 1999.
4.
PislaruC.FordD. G.FreemanJ. M.A new 3D model for evaluating the performance of CNC machine tool axis drives. In First International Conference of the European Society for Precision Engineering and Nano-technology (EUSPEN), Bremen, Germany, 31 May-4 June 1999, pp. 72–75.
5.
BlakeM. D.FordD. G.MortonD.Modelling and simulation of CNC machine tool axis drives. In Proceedings of the 10th International Conference on Systems Engineering, Coventry University, September 1994, Vol. 1, pp. 103–110.
6.
De SilvaC. W.Vibration—Fundamentals and Practice, 1999, pp. 349–398 (CRC Press, Boca Raton, Florida).
7.
PestelC. E.LeckieF. A.Matrix Methods in Elastomechanics, 1963 (McGraw-Hill, New York).
8.
HolroydG.PislaruC.FordD. G.Identification of damping elements in a CNC machine tool drive. In Proceedings of 5th International Conference on Laser Technology, Machine Tool, CMM and Robot Performance (LAMDAMAP 2001), Birmingham, July 2001, pp. 289–299 (WIT Press, Southampton).
9.
PislaruC.Parameter identification and hybrid mathematical modelling techniques applied to non-linear control systems. PhD thesis, The University of Huddersfield, 2001.
10.
AdhikariS.Calculation of derivative of complex modes using classical normal modes. Computers and Structs, 15 August 2000, 77(6), 625–630.
MurthyD. V.HaftkaR. T.Derivatives of eigenvalues and eigenvectors of a general complex matrix. Int. J. Numer. Meth. Engng, 1988, 26, 293–311.
14.
ZengQ. H.Highly accurate modal method for calculating eigenvector derivatives in viscous damping systems. Am. Inst. Aeronaut. Astronaut. J., 1995, 33(4), 746–751.
15.
CroninD. L.Eigenvalue and eigenvector determination for non-classically damped dynamic systems. Computers and Structs, 1990, 36(1), 133–138.
16.
WoodhouseJ.Linear damping models for structural vibration. J. Sound Vibr., 1998, 215(3), 547–569.
17.
HarrisC. M.Shock and Vibration Handbook, 3rd edition, 1985 (McGraw-Hill, New York).
18.
QuayleJ. P.Kempe's Engineers' Year Book, 89th edition, 1984, pp. A2/37–38 (Morgan Grampian, London).
19.
JamesM. L.SmithG. M.WolfordJ. C.WhaleyP. W.Vibration of Mechanical and Structural Systems: With Microcomputer Applications, 1989 (Harper and Row, New York).
20.
NewlandD. E.Mechanical Vibration Analysis and Computation, 1989 (Longman Scientific and Technical, Harlow).
21.
PressW. H.TeukolskyS. A.VetterlingW. T.FlanneryB. P.Numerical Recipes in C—The Art of Scientific Computing, 1992, (Cambridge University Press).
