T. G. Ritto

Timoshenko beam with uncertainty on the boundary conditions

In mechanical system modeling, uncertainties are present and, to improve the predictability of the models, they should be taken into account. This work discusses uncertainties present in boundary conditions using the model of a vibrating Timoshenko beam, free in one end and pinned with rotation constrained by a linear elastic torsional spring in the other end. The Finite Element Method is used to discretize the system and two probabilistic approaches are considered to model the uncertainties: (1) the stiffness of the torsional spring is taken as uncertain and a random variable is associated to it (parametric probabilistic approach); (2) the whole stiffness matrix is considered as uncertain and a probabilistic model is constructed for the associated random matrix (nonparametric probabilistic approach). In both approaches, the probability density functions are deduced from the Maximum Entropy Principle. In the first approach only the uncertainty of a parameter is taken into account, and in the second approach, the uncertainties of the model are taken into account, globally. Both approaches are compared and their capability to improve the predictability of the system response is discussed.

A new algorithm for the robust optimization of rotor-bearing systems

This article presents a new algorithm for the robust optimization of rotor-bearing systems. The goal of the optimization problem is to find the values of a set of parameters for which the natural frequencies of the system are as far away as possible from the rotational speeds of the machine. To accomplish this, the penalization proposed by Ritto, Lopez, Sampaio, and Souza de Cursi in 2011 is employed. Since the rotor-bearing system is subject to uncertainties, such a penalization is modelled as a random variable. The robust optimization is performed by minimizing the expected value and variance of the penalization, resulting in a multi-objective optimization problem (MOP). The objective function of this MOP is known to be non-convex and it is shown that its resulting Pareto front (PF) is also non-convex. Thus, a new algorithm is proposed for solving the MOP: the normal boundary intersection (NBI) is employed to discretize the PF handling its non-convexity, and a global optimization algorithm based on a restart procedure and local searches are employed to minimize the NBI subproblems tackling the non-convexity of the objective function. A numerical analysis section shows the advantage of using the proposed algorithm over the weighted-sum (WS) and NSGA-II approaches. In comparison with the WS, the proposed approach obtains a much more even and useful set of Pareto points. Compared with the NSGA-II approach, the proposed algorithm provides a better approximation of the PF requiring much lower computational cost.

Proper orthogonal decomposition for model reduction of a vibroimpact system

The application that inspires this work is the percussion drilling. This problem has impacts and presents uncertainties. In this first analysis the focus is on the construction of an efficient reduced-order model to deal with the nonlinear dynamics due to the impacts. It is important to have an efficient reduced-order model to perform the stochastic analysis. The simplified full model is constructed using the finite element method, and three different bases are used to construct the reduced-order models: LIN-basis (composed by the normal modes of the associated linear problems), PODdir-basis (obtained through proper orthogonal decomposition -direct method) and PODsnap-basis (obtained through proper orthogonal decomposition -snapshot method). The shapes of the elements of LIN-basis, PODdir-basis, and PODsnap-basis are compared. One important conclusion is that the information necessary to represent the details of a vibroimpact dynamics, measured by the proper orthogonal values, is more than the usual 99% recommended.

Accuracy of maxillary positioning after standard and inverted orthognathic sequencing

OBJECTIVE This study aimed to compare the accuracy of maxillary positioning after bimaxillary orthognathic surgery, using 2 sequences. STUDY DESIGN A total of 80 cephalograms (40 preoperative and 40 postoperative) from 40 patients were analyzed. Group 1 included radiographs of patients submitted to conventional sequence, whereas group 2 patients were submitted to inverted sequence. The final position of the maxillary central incisor was obtained after vertical and horizontal measurements of the tracings, and it was compared with what had been planned. The null hypothesis, which stated that there would be no difference between the groups, was tested. RESULTS After applying the Welch t test for comparison of mean differences between maxillary desired and achieved position, considering a statistical significance of 5% and a 2-tailed test, the null hypothesis was not rejected (P > .05). Thus, there was no difference in the accuracy of maxillary positioning between groups. CONCLUSIONS Conventional and inverted sequencing proved to be reliable in positioning the maxilla after LeFort I osteotomy in bimaxillary orthognathic surgeries.

Model uncertainties of flexible structures vibrations induced by internal flows

In many situations analysts use incomplete models to design a system, or to make decisions. These models are incomplete due to unmodeled phenomena, which means that some features are not included in the model (either because it was not previously thought about or because it would be too expensive to include). These uncertainties related to the model are difficult to take into account. In this paper, the nonparametric probabilistic approach is used to investigate model uncertainties in the problem of structures excited by internal flow. A reference model is constructed, where an Euler-Bernoulli beam is used to model the structure, and the fluid is added to the model by means of a constant mass, damping and stiffness. Then, an incomplete model of the reference model is considered. In it the influence of the fluid stiffness is not taken into account, hence, the uncertainty is related to this unmodeled feature (fluid stiffness). The incomplete model is then used together with the nonparametric probabilistic approach to infer the behavior of the reference model. Besides, a procedure is proposed to calibrate the dispersion parameter of the probabilistic model.

Reliability Analysis of the Dynamics of a Horizontal Drill-String

Nowadays directional drilling, such as horizontal drilling, is very common. This chapter deals with the reliability analysis of a horizontal drill-string dynamics. A stochastic probabilistic computational model is considered, where a bar model (tension/compression) is used for the drill-string, and the system is discretized by means of the finite element method. The frictional forces between the column and the borehole are uncertain and relevant to the dynamic behavior of the structure. Therefore, a stochastic model is used for the frictional coefficient: a random field with exponential autocorrelation function. Because a probabilistic approach is employed, the reliability is measured in terms of the probability of the system not perform as it should, i.e., exceed stress limit, start a crack, or do not achieve a target efficiency. For the computation of the failure probability, importance sampling is applied to avoid too many stochastic simulations, and the stochastic system is analyzed for different scenarios.

Active control of stick-slip torsional vibrations in drill-strings

This paper presents active vibration control to reduce the stick-slip oscillations in drill-strings. A simplified two degrees-of-freedom drill-string torsional model is considered. The nonlinear interaction between the rock and the bit is included in the model, where its parameters are fitted with field data from a 5 km drill-string system. Different proportional-derivative (PD)-control strategies are employed and compared, including the one that takes into account the weight-on-bit (axial force) and the bit speed. Optimization problems are proposed to obtain the values of the gain coefficients, and a torsional stability map is constructed for different weight-on-bit values and top-drive speeds. It is noted that the information of the dynamics at the bottom increases the performance of the PD-controller significantly in terms of the torsional vibration suppression, for the system analyzed.

Simulation of a Test Rig and Identification of Annular Gas Seals Coefficients

This paper shows some preliminary results of an ongoing test rig for coefficients identification of annular gas seals. The test rig is being built in the Laboratory of Vibrations and Acoustics (LAVI) at the Federal University of Rio de Janeiro. The main objective of the rig is to determine both the damping and stifness created by annular gas seals (honeycomb, labyrinth, hole-pattern, etc.) to a flexible rotor. The paper is divided in three parts. First, the characteristics and components of the rig are shown. Then, a rotordynamic model is proposed based on the finite elementh method, in which the rotor is divided into smaller elements and the seals are represented as punctual stiffness and damping. Some simulated results of this model is shown and analyzed. Finally, preliminary experimental results are shown and discussed.

Hysteretic (Non-reversible) Bit-Rock Interaction Model for Torsional Vibration Analysis of a Drillstring

This paper aims at constructing a novel hysteretic (non-reversible) bit-rock interaction model for the torsional dynamics of a drillstring. Non-reversible means that the torque on bit is not represented only in terms of the bit speed, but also of the bit acceleration, producing a hysteretic behavior. Here, the drillstring is considered as a continuous system which is discretized by means of the finite element method, where a reduced-order model is applied using the normal modes of the associated conservative system. The nonlinear torsional vibrations of the drillstring system are analyzed comparing the proposed bit-rock interaction model to a commonly used reversible model (without hysteresis). The parameters of the proposed hysteretic bit-rock interaction and of the commonly used reversible model are fitted to field data. Results show the system including a bit-rock interaction model with hysteresis effects reproduces a good approach of stick-slip cycle, and the simulated drillstring dynamics using the bit-rock interaction presents a similar behavior comparing to the field data.

Bred Vector for Analysis of Helicopter Main Rotor Dynamics

The dynamics of helicopter main rotor is described by a highly nonlinear equations, and it is responsible to provide the sustentation of the rotorcraft. The representative frequency to this dynamics are associated to different regimes: unstable, periodic, and even chaotic behavior. The system responses are investigate performing several simulations under a set of numerical values of frequency. One important subject is to evaluate the goodness of the prediction of the simulated dynamics. The dynamical analysis is performed by bred vector approach. The breeding technique executes the model with a perturbed initial condition. The difference between the reference and the perturbed dynamics is called bred vector. The procedure can be employed systematically, producing a time series of bred vector. The bred vector magnitude is applied for addressing the predictability of the model, i.e., the degree of confidence from the simulation.