Residual vibrations affect machines at the end of commanded motion and represent an amplification factor for the work cycle. Furthermore, in repetitive cyclic movements, residual vibrations can lead to an important degeneration of the executed motion, due to a summation effect of undesired dynamic phenomena. For these reasons, the problem of residual vibrations is widely studied in literature and it is faced with different techniques. A first type of approach consists in the production of a structural device realized with proper mechanical solutions devoted to avoid the sources of vibrations. The second approach consists in introducing passive/active physical elements able to attenuate vibrations, by passively consuming their mechanical power or by actively counteracting them with external mechanical power. A third approach is the smart definition of the motion profile of each machine movable part to minimize the vibrational effects. The proposed work is addressed in this direction, with an optimization approach based on the Fourier transformation of the motion profile. More precisely, the natural frequencies of the system are evaluated through experimental tests, the designed motion profile is transformed with a Fourier analysis, a band around the natural frequencies of the system is suppressed from the motion profile spectrum, an antitransformation is implemented to obtain a temporal function, and, finally, a proper optimization is implemented to respect desired kinematical constraints. Experimental results confirmed a significant improvement, in terms of residual vibrations, with respect to the state of the art of motion profiles specifically designed for residual vibrations reduction.

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