Polynomial path profiles for Machine Tools with low frequency excitation

The aim of this job is to study the polynomial path profiles with low frequency excitation. In one dimension, time dependent, kinematical path profiles frequency spectrums are studied. We show that any discontinuity on the k-th order position derivative of the path profile lead to the excitations on the whole frequency spectrum. The decay on frequency is faster as the order of the discontinuity raises. Therefore, Machine Tools will have less frequency excitation if higher order path profiles are used. Fourth order path profiles are generated combined with low pass filters. The path profile design procedure is the following: to find an optimal function effected by the jerk derivative, with the cost functional of frequency weighted energy. The profile optimization is more effective if a Particle Swarm optimization is used. For simulation, frequency spectrums of both path profiles are represented.