ORIGINAL ARTICLE A study on vibration of Stewart platform-based machine tool table Siamak Pedrammehr & Mehran Mahboubkhah & Navid Khani Received: 27 May 2011 / Accepted: 8 May 2012 / Published online: 31 May 2012 # Springer-Verlag London Limited 2012 Abstract In this paper, an analytical study on the vibrations of a parallel manipulator is addressed. In the vibration equation of the moving platform, the damping and stiffness of the pods are taken into account. The eigenvalue problem of the moving platform is solved to obtain the natural frequencies. Considering the role of different factors effec- tive on the mass and stiffness matrices of the platform, natural frequencies for different configurations are investi- gated. The results obtained by analytical approach are fur- ther verified through FEM simulation. The effect of variation in position and orientation of the moving platform on the change in stiffness of its supporting chain, inertia tensor and natural frequencies and mode shapes of the platform as well as the effects of different payloads are studied. The vibration of the platform in different configu- rations is studied in different cutting conditions. The ranges of resonance frequencies and vibration amplitudes are then investigated. Finally, proper configurations of the moving platform are determined to avoid dynamic instability in different machining conditions. It also will be illustrated in this paper that some specific features embodied in the mechanism are appropriate for high-speed milling. Keywords Stewart platform . Vibration . Modal analysis . Machine tool . FEM . MAC 1 Introduction In recent years, parallel mechanisms have gained significant attention for applications as the table or spindle of machine tools which, for a precise machining of the workpiece, require precise, stiff and easily controllable elements. The stiffness and vibration behaviour are among the require- ments for precision machining. This requires a thorough understanding of the dynamics behaviour of the mechanism. The examination of the methods conducive to achieve this understanding is one of the vital research issues which fill the gap existing in the literature in this respect. The control of vibration in the machine tools with the aim of improving their performance has been the focus of much research in the literature. Dohner et al. [1] have proposed an FEM model to analyse chatter in the spindle of a milling machine set on a hexapod platform. In their model, in order to effectively control the chatter, flexible parts have been added to the borders of the spindle. However, the relations of the vibration behaviour of the hexapod have not been given. Their results could not be generalized to hexapods used as a table of the machine. Studies to examine vibrations of hexapods with applications in vibration isolation have been carried out. Hardage and Wiens [2] have presented the results of a review of a mini modal in Hexel Tornado2000, where they have discussed flexibility modelling through using finite elements. Their investigation suggested that characteristics of resonant frequency and stiffness are de- pendent on the configuration of the machine. Hardage [3] has studied the structural dynamics of parallel kinematic machine tools (PKMs) and some introductory has been S. Pedrammehr (*) : M. Mahboubkhah Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran e-mail: s.pedrammehr87@ms.tabrizu.ac.ir e-mail: s.pedrammehr@gmail.com N. Khani School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Int J Adv Manuf Technol (2013) 65:991–1007 DOI 10.1007/s00170-012-4234-9