Minimizing noise and vibration by using machine motion profile that is represented by a truncated Fourier series

An engineer must often design a motion profile (e.g., a plot of position versus time) for a machine that performs repetitive motions. Such a machine, when operated at high speed, can produce objectionable noise and/or vibration. This paper proposes an algorithm by means of which an engineer may design a machine’s motion-versus-time profile that consists of a minimum number of harmonics of the machine’s repetition rate, consistent with the position and timing accuracies required of that machine’s operation. This algorithm is intended to enable the designer to minimize the noise and/or vibration caused by the motion of such a machine.