A study on vibration of Stewart platform-based machine tool table

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 effective on the mass and stiffness matrices of the platform, natural frequencies for different configurations are investigated. The results obtained by analytical approach are further 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 configurations 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.