An Investigation on Optimal Designing of Dynamic Vibration Absorbers Using Genetic Algorithm
Abstract. In this study reducing of the unwanted phenomenon in machine tools, Vibration, has been investigated. The machine tools has been simulated as a five-degree-of-freedom discrete system consisting of cutting tool, work piece, body, head and cantilever of the machine. In order to reduce the undesired vibrations, a dynamic vibration absorber (DVA) with three unknown parameters (mass absorber, damping coefficient , stiffness absorber has been added to the system in different positions. Utilizing Newton’s second law, the governing equations have been obtained and solved. A genetic algorithm is proposed to efficiently achieve the optimum value for each 3-fold parameters in each positions of the system. The effectiveness of the proposed algorithm and the designed DVA is evaluated through comparing the vibration amplitude of the machine tool in the presence and absence of the DVA, and the paper concludes the best place to situate the vibration absorber and its specifications.
Frederick W. Taylor. (1907), “On the art of cutting metals”, New York, American Society of mechanical engineers.
A.A. Tootoonchi, and M.S. Gholami. (2011), “Application of time delay resonator to machine tools,” Int J Adv Manuf Technol, pp. 56:879–891.
Frahm, H. (1909), ‘‘Device for damping vibrations of bodies,’’ U.S. Patent No. 989958.
J.P. Den Hartog. (1956), “Mechanical Vibrations,” 4'th Edition, McGraw Hill.
P. Watts. (1883), “On a method of reducing the rolling of ship at sea,” Transactions of the Institute of Naval Architects, Vol. 24, pp. 165–190.
Ormondroyd, J. and Den Hartog, J.P. (1928), ‘‘Theory of the dynamic vibration absorber,’’ Transactions of the American Society of Mechanical Engineers, Vol. 50, pp. 9–22.
J.E. Brock. (1946), ‘‘A note on the damped vibration absorber,’’ Journal of Applied Mechanics, Vol. 68, pp. A-284.
B.P. Wang, L. Kitis, D. Pilkey, and A. Palazzolo. (1985), “Synthesis of Dynamic Vibration Absorbers,” ASME J. of Vibration, Acoustics, Stress and Reliability in Design, V.107, pp. 161- 166.
YC. Shin, and KW. Wang. (1991), “Design of an optimal damper to minimize the vibration of machine tool structures subject to random excitation,” J Eng Computer, 9, pp. 199–208.
Y.M. Huang, and C.C. Chen. (2000), “Optimal design of dynamic absorbers on vibration and noise control of the fuselage,” Computers and Structures, 76, pp. 691-702.
P. Varpasuo. (2001), “optimization of designs one mass dynamic vibration absorber with stochastic system parameters,” Transactions, Paper 1862, SMIRT 16, Washington DC, August.  G.S. Duncan, M.F. Tummond, and T.L. Schmitz. (2005), “An investigation of the dynamic absorber effect in high-speed machining,” Int. J. Machine Tools & Manufacture, 45, pp. 497- 507.
Y.A. Amer. (2007), “Vibration control of ultrasonic cutting via dynamic absorber,” Chaos, Solutions and Fractals, 33, pp. 1703–1710.
M.M. Kamel, W.A.A. El-Ganaini, and Y.S. Hamed. (2013), “Vibration suppression in ultrasonic machining described by non-linear differential equations via passive controller,” Applied Mathematics and Computation, 219, pp. 4692–4701.
M.R. Elhami, and M. Heydari. (2009), “Vibration Analysis and Design of Dynamic Absorber in a Vertical Drilling Machine,” International journal advanced design and manufacturing technology, Vol 2, No 2.
Y.L. Cheung, and W.O. Wong. (2009), “Optimization of Dynamic Vibration Absorbers for Vibration Suppression in Plates,” Journal of Sound and Vibration, Volume 320, Issues 1–2, pp. 29-42.
B. Brown, and T. Singh. (2011), “Minimax design of vibration absorbers for linear damped systems,” Journal of Sound and Vibration, 330, pp. 2437–2448.
M. Zilletti, S.J. Elliott, and E. Rustighi. (2012), “Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation,” Journal of Sound and Vibration, 331, pp. 4093–4100.
O.F. Tigli. (2012), “Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads,” Journal of Sound and Vibration, 331, pp. 3035– 3049.
S.J. Jang, M.J. Brennan, E. Rustighi, and H.J. Jung. (2012), “A simple method for choosing the parameters of a two degree-of-freedom tuned vibration absorber,” Journal of Sound and Vibration, 331, pp. 4658–4667.
R.P. Eason, C. Sun, A.J. Dick, and S. Nagarajaiah. (2013), “Attenuation of a linear oscillator using a nonlinear and a semi-active tuned mass damper in series,” Journal of Sound and Vibration, 332, pp. 154–166.
D. Goldberg. (1989), “Genetic algorithms in search, optimization, and machine learning,” New York: Addison-Wesley.
Z. Michalewicz. (1992), “Genetic algorithms + data structures = evolution programs,” Berlin: Springer.
M. Solimanpur, and M.A. Kamran. (2010), “Solving facilities location problem in the presence of alternative processing routes using a genetic algorithm,” Computers & Industrial Engineering, 59, pp. 830–839.