Carlos Alberto Bavastri

On the passive control of vibrations with viscoelastic dynamic absorbers of ordinary and pendulum types

Abstract Dynamic vibration absorbers (DVA) provide a cheap and efficient means for vibration abatement in many complex systems, ranging from crankshafts of internal combustion engines, overhead transmission lines, machine casings, structural panels and large turbo machinery sets, to quote a few examples. One can provide a simple classification for them by considering the nature of the resilient material it contains as a form of “spring”: it may be viscous (CDVA), hysteretic (HDVA) or viscoelastic (VDVA). Viscous DVAs are the largely studied devices and one of their most remarkable applications is in mitigating crankshafts torsional vibrations and in very tall buildings. The most well known hysteretic DVA is the Stockbridge damper, largely applied in overhead electric power transmission lines. With modern use of fractional calculus, modelling viscoelastic materials became a routine work. The experimental identification of four fractional parameter models for viscoelastic material has become a standard technique amongst the authors of this work. Modelling viscoelastic materials by four fractional parameters has made advanced analysis of structures and systems where it is applied much more straightforward than it was before. This is true also for structures with VDVA and HDVA attached to it. In this paper it is shown that a hysteretic material model can be derived from a viscoelastic material model based on four fractional parameters. Generalized quantities of ordinary and pendulum type absorbers and for both viscoelastic and hysteretic materials are derived and their nature discussed. The performances of a system with absorbers of viscoelastic and hysteretic nature are compared. Input energy and dissipated energy by the absorbers of both natures and types are computed and compared, using the concept of generalized damping parameter of the absorbers. Conclusions are drawn from the comparisons. One of the ideas behind these computations is to check the validity of some international recommendations for the experimental assessment of Stockbridge dampers, which implicitly neglects the effect of the generalized mass parameter.

Modeling of dynamic rotors with flexible bearings due to the use of viscoelastic materials

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.

Optimal design of viscoelastic vibration absorbers for rotating systems

All rotating systems are subjected to residual unbalance forces that are proportional to speed squared. Systems that operate close to the critical speed and have low damping can generate destructive vibrations. Dynamic vibration absorbers are simple devices attached to a mechanical structure (the primary system) to reduce vibrations and noise levels and are extensively used in non-rotating systems. This study addresses the design of viscoelastic vibration absorbers for rotating systems. The primary system is modeled using modal parameters obtained in the frequency domain of the state-space representation. Using a methodology that has a more general application, the compound system (the primary system and absorbers) is represented in a modal subspace of the primary system state space. In this modal subspace, the optimal design of the dynamic viscoelastic absorbers is performed using an optimization algorithm. The objective function to be minimized is defined as the Euclidean norm of the vector composed of the maximal absolute values of the principal coordinates. The absorbers are attached to a floating bearing located away from a nodal point. Numerical and experimental results are presented and discussed.

Control of the long period grating spectrum through low frequency flexural acoustic waves

We have shown experimental results of the excitation of long period fiber gratings by means of flexural acoustic waves with a wavelength larger than the grating period, validated by numerical simulations. The effect of the acoustic wave on the grating is modeled with the method of assumed modes, which delivers the strain field inside the grating, then used as the input to the transfer matrix method, needed for calculating the grating spectrum. The experimental and numerical results are found to be in good agreement, even though only the strain-optic effects are taken into account.

Induction Motors Vibration Monitoring Using a Biaxial Optical Fiber Accelerometer

In this paper, the implementation, characterization, calibration, and testing of a biaxial optical fiber accelerometer for vibration monitoring in three-phase induction motors is presented. The optical sensor uses fiber Bragg gratings to measure the displacement of an inertial mass relatively to a support base. The sensor characterization was measured through the impact hammer, allowing the determination of the natural frequencies in both sensitive directions, the values of 747.5 Hz and 757.5 Hz were estimated for the x-axis and the y-axis, respectively. For calibration, an electromagnetic exciter was used to introduce a controlled harmonic excitation at different frequencies, with this analysis, a high SNR was observed, on average over 30 dB for both sensitive directions, and a sensitivity of 100 pm × g-1 was obtained, up to one third of the natural frequency, in each direction. The tests were developed with the main aim of the analysis in induction motors based in vibration monitoring, the analysis can help to prevent wear in motors, increasing its efficiency, and lowering maintenance costs. The optical accelerometer measurements were compared with the ones from a capacitive sensor, during regular operation and with a broken rotor bar operating with 75% and 100% load. The performed tests with the optical sensor allowed to successfully analyze the frequency components, and its changes, for the regular and damage operation.

Viscoelastic Relaxation Modulus Characterization Using Prony Series

The mechanical behavior of viscoelastic materials is influenced, among other factors, by parameters like time and temperature. The present paper proposes a methodology for a thermorheologically and piezorheologically simple characterization of viscoelastic materials in the time domain based on experimental data using Prony Series and a mixed optimization technique based on Genetic Algorithms and Nonlinear Programming. The text discusses the influence of pressure and temperature on the mechanical behavior of those materials. The results are compared to experimental data in order to validate the methodology. The final results are very promising and the methodology proves to be effective in the identification of viscoelastic materials.

Design of optimum system of viscoelastic vibration absorbers with a Frobenius norm objective function

Vibration absorbers, also called vibration neutralizers, are mechanical systems to be attached to another mechanical system, or structure, called the primary system, with the purpose of reducing vibration and sound radiation. The simplest form of a vibration absorber is that of a single degree of freedom system, where the “spring” is made of a viscoelastic material, perhaps with some metallic inserts. This paper sets out to describe how to design a best possible system of viscoelastic vibration absorbers for an available viscoelastic material, known by its four fractional parameter model, by using a novel objective function, defined through a Frobenius norm. A real example is presented and discussed. Keywords : vibration absorber, vibration neutralizer, viscoelastic material, vibration abatement, vibration control

Fiber Bragg grating tuning with notch-type spring device

This paper presents a notch-type spring mechanism based on the traction principle for tuning fiber Bragg gratings, which magnifies the displacement of piezoelectric actuators. Practical tuning ranges up to 8 nm and tuning times below 20 ms are demonstrated. Oscillations that affect the device due to the rapid voltage change applied to the actuator are mitigated using either an electronic filter or a viscoelastic neutralizer technique.

A methodology to mitigate chatter through optimal viscoelastic absorber

Chatter is an undesirable dynamic instability phenomenon, mainly due to the low dynamic stiffness, that, in turning processes, results in poor surface quality and in a reduction in the cutting tool life. To overcome this problem, viscoelastic dynamic absorbers can be employed. Those absorbers are able to introduce reaction forces and dissipate vibration energy. In previous works, the main difficulty in the use of viscoelastic dynamic absorbers was in tool modelling uncertainties and in inaccurate viscoelastic material models. To overcome those difficulties, this article presents a new methodology to identify the machine tool structure dynamic properties by using 1-degree-of-freedom equivalent model combined with a fractional derivative model to describe the behaviour of the viscoelastic material. As a result, it was possible to design an optimal viscoelastic dynamic absorber for chatter mitigation in internal turning using non-linear optimization techniques. The use of generalized equivalent parameters for the absorber allows obtaining a simple equation of motion for the compound system (primary system plus absorber). The numerical and experimental tests were performed, showing the efficacy of the proposed controlling method design.

Optimal design of a viscoelastic vibration neutralizer for rotating systems: Flexural control by slope degree of freedom

Rotating machines have become increasingly powerful and rapid over time, often working now close to, or even above, their critical speeds. When, as a result, resonance or dynamic instability occurs, it can cause high vibration levels in these machines, particularly when rolling bearings are used. Vibration control of rotating systems can be made by viscoelastic dynamic vibration neutralizers (VDVNs), which are relatively cheap passive devices with a wide range of applications. For the control of flexural vibration in dynamic rotors, a translational VDVN is usually employed. It should be attached to the rotor by means of a special support, commonly between bearings, where the amplitude of the vibration mode of concern is high. The particular point where this type of device is attached depends on the mode to be controlled and in machines with reduced internal space, it cannot be placed in a suitable position. Therefore, this paper introduces a new type of VDVN, the angular VDVN, and proposes a methodology for the optimal design of a set of these devices for shaft slope degree of freedom control. This control aims at indirectly reducing flexural vibration. According to this approach, the control device can be installed close to the bearing where the slope degree of freedom presents its highest value at any critical speed. The conceptual design of the angular VDVN is presented to illustrate the proposed methodology, and a numerical example is given to demonstrate the influence of the angular VDVN geometry on the response. The corresponding results are fully discussed.