Feedforward active vibration control techniques aim at canceling vibrations occurring in a system by means of introducing intentional forces that generate destructively interfering vibrations. These forces are typically controlled using an adaptive filtering algorithm that tracks the system state in real time and seeks to minimize overall vibration. One important often-overlooked issue in such systems is related with the vibrations introduced by the adaptive control algorithm itself either during its transient learning phase or due to its nonideal characteristic. These vibrations may become very significant in several mechanical structures due to resonance phenomena. In this context, this work is dedicated to the development of an effective scheme for feedforward active vibration control that is capable of dealing with undesirable vibrations introduced by the adaptive controller. A particular version of the filtered-x normalized least-mean-squares algorithm tailored to the proposed scheme is also developed. Results obtained from numerical simulation as well as from an experimental device are presented, aiming to demonstrate the effectiveness of the proposed scheme.

Nowadays rotating machines produce or absorb large amounts of power in relatively small physical packages. The fact that those machines work with large density of energy and flows is associated to the high speeds of rotation of the axis, implying high inertia loads, shaft deformations, vibrations and dynamic instabilities. Viscoelastic materials are broadly employed in vibration and noise control of dynamic rotors to increase the area of stability, due to their high capacity of vibratory energy dissipation. A widespread model, used to describe the real dynamic behavior of this class of materials, is the fractional derivative model. Resorting to the finite element method it is possible to carry out the modeling of dynamic rotors with flexible bearings due to the use of viscoelastic materials. In general, the stiffness matrix is comprised of the stiffnesses of the shaft and bearings. As considered herein, this matrix is complex and frequency dependent because of the characteristics of the viscoelastic material contained in the bearings. Despite of that, a clear and simple numerical methodology is offered to calculate the modal parameters of a simple rotor mounted on viscoelastic bearings. A procedure for generating the Campbell diagram (natural frequency versus rotation frequency) is presented. It requires the embedded use of an auxiliary (internal) Campbell diagram (natural frequency versus variable frequency), in which the stiffness matrix as a frequency function is dealt with. A simplified version of that procedure, applicable to unbalance excitations, is also presented. A numerical example, for two different bearing models, is produced and discussed