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6. CONCLUSÕES E DESDOBRAMENTOS DO TRABALHO

6.1. Desdobramentos do Trabalho

A partir dos resultados encontrados nesse trabalho é possível dizer que foi desenvolvida uma simulação numérica capaz de representar, de forma satisfatória, o comportamento de máquinas rotativas no domínio do tempo com um custo computacional não proibitivo. Além disso, foi desenvolvido um método de identificação de desbalanceamento, sem necessidade de massa de triagem, baseado em técnicas de otimização determinísticas, que é promissor, porém em estado incipiente. Assim, são sugeridas possíveis desdobramentos da pesquisa, assim como novas etapas para aprimorar os métodos desenvolvidos:

 Investigação do efeito não linear para outras geometrias de mancais hidrodinâmicos, como por exemplo: mancais elípticos, trilobulares e segmentados, de modo a saber se apresentam comportamento com maior ou menor grau de não linearidade que o mancal cilíndrico;

 Utilização da técnica de ajuste das forças hidrodinâmicas para modelar as geometrias de mancais hidrodinâmicas apresentadas no item anterior, além da aplicação dessa técnica para rotores mais complexos;

 Investigação do uso de outros tipos de expansão para o ajuste das forças hidrodinâmicas, como por exemplo a expansão em série de Fourier;

 Nesse trabalho o método de identificação de desbalanceamento foi utilizado de forma a contemplar apenas uma massa desbalanceada. No entanto, aumentando o número de massas desbalanceadas contempladas é possível representar melhor o desbalanceamento ao longo do rotor. Assim, é interessante expandir o método para contemplar mais de uma massa de desbalanceamento por identificação, o que pode melhorar o posterior balanceamento do sistema;

 Também para o método de identificação, o vetor da DFT foi utilizado para determinar a função objetivo. Porém, nessa abordagem, pode-se estar ajustando valores residuais que atuam de forma negativa para a correta identificação do desbalanceamento. Assim, é sugerido um novo estudo utilizando somente as harmônicas mais importantes do espectro de frequências como 1x, 2x e 3x;

REFERÊNCIAS BIBLIOGRAFICAS

Adams Jr, M. L., “Rotating Machinery Vibration”, Taylor & Francis Group, 2ª Ed., Boca Raton, USA, 2010.

Alves, D. S., “Investigação do Efeito Térmico no Comportamento Dinâmico de Mancais Hidrodinâmicos” Campinas: Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, 144 p., 2011. Dissertação (Mestrado).

Archer, J., “Consistent Mass Matrix for Distributed Mass Systems”, Journal of Structural Division, Vol. 89, p. 161-178, 1963.

Asgharifard-Sharabiani, P., Ahmadian, H., “Nonlinear Model Identification of Oil- Lubricated Tilting Pad Bearings”, Tribology International, Vol. 92, p. 533–543, 2015.

Bachschmid, N.; Pennacchi, P.; Vania, A., “Identification of Multiple Faults in Rotor Systems”, Journal of Sound and Vibration, Vol. 254(2), p. 327-366, 2002.

Bachschmid, N.; Pennacchi, P.; Vania, A.; Zanetta, G. A.; Gregori, L., “Identification of Rub and Unbalance in 320 MW Turbogenerators”, International Journal of Rotating Machinery, Vol. 9(2), p. 91-112, 2003.

Balanço Energético Nacional 2017: Ano Base 2016 / Empresa de Pesquisa Energética – Rio de Janeiro: EP 2017, 292p, 2017.

Bathe, K., “Finite Element Procedures in Engineering Analysis”, Prentice-Hall, New Jersey, 1982.

Bazaraa, M. S., Sherali, H. D., Shetty, C. M., “”Nonlinear Programming – Theory and Algorithms”, Jhon Wiley and Sons, New Jersey, 2006.

Bishop, R. E. D., Gladwell, G. M. L., “The Vibration and Balancing of an Unbalanced Flexible Rotor”, Journal of Mechanical Engineering Science, Vol. 1(1), p. 66-77, 1959.

Bonami, P., Kilinc, M., Linderoth, J. T. "Algorithms and Software for Convex Mixed Integer Nonlinear Programs." in Mixed Integer Nonlinear Programming, The IMA Volumes in Mathematics and its Applications, Vol. 154, Springer, New York, p. 1-39, 2012.

Braun, M. J., Choy, F. K., Hu, Y., “Nonlinear Effects in a Plain Journal Bearing: Part 2 – Results”, Journal of Tribology, Vol. 113, p. 563-570, 1991.

Camargo, L. W. F.; Castro, H. F.; Cavalca, K. L.; “Identification of Misalignment and Unbalance in Rotating Machinery Using Multi-Objective Genetic Algorithms”, Proceedings of IFToMM 2010 – 8th International Conference on Rotor Dynamics, Seoul, Korea, pp. 571- 578, 2010.

Capone, G., “Orbital Motions of Rigid Symmetric Rotor Supported on Journal Bearings”, La Meccanica Italiana, Vol. 199, p. 37–46, 1986.

Capone, G., “Analytical Description of Fluid –Dynamic Force Field in Cylindrical Journal Bearing”, L’ Energia Elettrica, Vol. 3, p. 105–110, 1991.

Castro, H. F.; Cavalca, K. L.; Pennacchi, P., “Parameter Estimation of Rotor-Bearing System using Genetic Algorithm and Simulated Annealing”, Proceedings of the XII International Symposium on Dynamic Problems of Mechanics (DINAME 2007), Ilhabela, SP, Brazil, 2007.

Castro, H. F., Cavalca, K. L., Nordmann, R., “Whirl and Whip Instabilities in Rotor- Bearing System Considering a Nonlinear Force Model”, Journal of Sound and Vibration, Vol. 317, p. 273–293, 2008.

Chatzisavvas, I.; Dohnal, F., “Unbalance Identification using Least Angle Regression Technique”, Mechanical Systems and Signal Processing, In Press, Available on line 2014.

Chen, J.; Patton, R. J., “Robost Model-Based Fault Diagnosis for Dynamic Systems”, Kluwer Academic Publishers, Massachusetts, USA, 1999.

John Wiley & Sons, 1 ed., 1993.

Childs, D. W., “Rotordynamics of Turbomachinery… Looking Back... Looking Forward”, Proc. of the International Conference in Rotor Dynamics IFToMM, Vol. 2, p. 759- 766, Sidney, Australia, 2002.

Choy, F. K., Braun, M. J., Hu, Y., “Nonlinear Effects in a Plain Jounral Bearing: Part 1 – Analytical Study”, Journal of Tribology, Vol. 113, p. 555-561, 1991.

Chu, C. S., Wood, K. L., Busch-Vishniac, I. J., “A Nonlinear Dynamic Model With Confidence Bounds for Hydrodynamic Bearings”, Journal of Tribology, Vol. 120, p. 595-604, 1998.

Chu, F., Lu, W., “Determination of the Rubbing Location in a Multi-Disk Rotor System by Means of Dynamic Stiffness Identification”, Journal of Sound and Vibration, Vol. 248(2), p. 235-246, 2001.

Cowper, G., “The Shear Coefficient in Timoshenko’s Beam Theory”, Journal of Applied Mechanics, Vol. 33, p. 335–340, 1966.

Daniel, G. B., “Desenvolvimento de um Modelo Termohidrodinâmico para Análise em Mancais Segmentados”, Campinas: Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, 218 p., 2012, Tese (Doutorado).

Dakel, M., Baguet, S., Dufour, R., “Nonlinear Dynamics of a Support-Excited Flexible Rotor With Hydrodynamic Journal Bearings”, Journal of Sound and Vibration, Vol. 333, p. 2774–2799, 2014.

Darlow, M. S., “The Identification and Elimination of Non-Independent Balance Planes in Influence Coefficient Balancing”, ASME 1982 International Gas Turbine Conference and Exhibit, Paper No. 82-Gt-269, doi:10.1115/82-GT-269, 1982.

Darlow, M. S., “Balancing of High-Speed Machinery: Theory, Methods and Experimental Results”, Mechanical Systems and Signal Processing, Vol. 1(1), p. 105-134,

1987.

Darlow, M. S., “Balancing of High Speed Machinery”, Springer-Verlag New York Inc., New York, USA, 1989.

Deepthikumar, M. B., Sekhar, A. S., Srikanthan, M. R., “Modal Balancing of Flexible Rotors with Bow and Distributed Unbalance”, Journal of Sound and Vibration, vol. 332, p. 6216-6233, 2013.

Dedini, F. G., “Identificazione dei Cuscinetti e della Fondazione di Rotori: Metodologie e Risultati Sperimentali”. Itália, Milão: Departamento de Mecânica, Politécnico de Milão, 1993. 120 p., Tese (Doutorado).

Dennis, J. E., Jr., Gay, D. M., Welsch, R. E., “An Adaptative Nonlinear Least-Squares Algorithm”, TOMS 7, p. 348-368, 1981.

Dennis, J. E., Schnabel, R. B., “Numerical Methods for Unconstrained Optimization and Nonlinear Equations”, Prentice-Hall, Philadelphia, 1996.

Dimarogonas, A. D., “A Brief History of Rotor Dynamics”, Proc. of the International Conference on Rotating Machine Dynamics, Hotel des Bains, Venice, p. 1-10, 1992.

Dowson, D., “A Generalized Reynolds Equation for Fluid-film Lubrication”, Int. Journal of Mechanical Science, Vol. 4, p.159-170, 1962.

Dunkerley, S., “On the whirling and vibration of shafts”, Philosophical Transactions A, Vol. 185, 1894.

Edney, S. L., Fox, C. H. J., and Williams, E. J., "Tapered Timoshenko Finite Elements for Rotor Dynamics Analysis,'' Journal of Sound and Vibration, Vol. 137, n. 3, p. 463-481, 1990.

Edwards, S., Lees, A. W., Friswell, M. I., “Fault Diagnosis of Rotating Machinery”, The Shock and Vibration Digest, Vol. 30(1), p. 4-13, 1998.

Edwards, S., Lees, A. W., Friswell, M. I., “Estimating Rotor Unbalance from a Single Run-Down”, IMechE Conference Transactions 2000-6, p. 323-333, 2000.

Floudas, C. A., “Nonlinear and Mixed-Integer Optimization – Fundamentals and Applications”, Oxford: OXFORD UNIVERSITY PRESS, New York, 1995.

Foiles, W. C., Allaire, P. E., Gunter, E. J., “Review: Rotor Balancing”, Shock and Vibrations, Vol. 5, p. 325-336, 1998.

Föppl, A., “Das Problem der Lavalschen Turbinewelle”, Civilingieur, 41, p. 332-342, 1895.

Furtado, R. M.; Cavalca, K. L.; Pennacchi, P.; Lopes Jr, V., “Fault Identification in Rotor System Using Model Based Methods, Experimental Data and Artificial Neural Network”, Proccedings of COBEM 2005, 2005, Available on line COBEM2005-2596.

Gasch, R., Drechsler, J., “Modales Auswuchten Elastischer Läufer ohne Testgewichts- setzungen”, VDI-Berichte, Vol. 320, p. 45-54, 1978.

Genta, G., “Dynamics of Rotating Systems”, Springer Science+Business Media Inc., New York, USA, 2005.

Gnielka, P., “Modal Balancing of Flexible Rotors Without Test Runs: An Experimental Investigation”, Journal of Sound and Vibration, Vol. 90(2), p. 157-172, 1983.

Golub, G., “Tikhonov Regularization and Total Least-Square”, SIAM Journal on Matrix Analysis and Applications, Vol. 21(1), p. 185-1974, 1999.

Goodman, T. P., “A Least-Squares Method for Computing Balance Corrections”, Journal of Engineering for Industry, Vol. 86(3), p. 273-277, 1964.

Hastie, T., Tibshirani, R., Friedman, J. H., “The Elements of Statistical Learning : Data Mining, Inference, and Prediction”, 2nd ed., Spring-Verlag, 2008.

Hattori, H., “Dynamic Analysis of a Rotor-Journal Bearing System with Large Dynamic Loads (Stiffness and Damping Coefficients Variation in Bearing Oil Films)”, JSME International Journal, Series C, Vol. 36(2), p. 251-257, 1993.

Hu, A., Hou, L., Xiang, L., “Dynamic Simulation and Experimental Study of an Asymmetric Double-Disk Rotor-Bearing System with Rub-Impact and Oil-Film Instability”, Nonlinear Dynamics, Vol. 84, p. 641-659, 2016.

Hummel, C., “Kristische Drehzahlen als Folge der Nachgiebigkeit des Schmiermittels im Lager”, VDI-Forschungsheft 287, 1926.

Jeffcott, N., “Lateral Vibration of Laded Shafts in the Neighborhood of a Whirling Speed: Effect of Want of Balance”, Philosophical Magazine, Vol. 37, p. 304-314, 1919.

Kellenberger, W., “Should a Flexible Rotor Be Balanced in N or (N + 2) Planes?”, Journal of Engineering for Industry, Vol. 94, p.548-560, 1972.

Khonsari, M., M., Chang, Y., J., “Stability Boundary of Non-Linear orbits Within Clearance Circle of Journal Bearings”, Journal of Vibrations and Acoustics, Vol. 115, p. 303- 307, 1993.

Kramer, E., “Dynamics of rotors and foundations”, Springer-Verlag, New York, 381p., 1993.

Ku, D. M., “Finite Element Analysis of Whirl Speeds for Rotor-Bearing Systems With Internal Damping”, Mechanical Systems and Signal Processing, Vol. 12(5), p. 599–610, 1998.

Lalanne, M., Ferraris, G., “Rotordynamics Prediction in Engineering”, John Wiley & Sons, England, 266 p., 1998.

Lang, G., Liao, Y., Liu, Q., Lin, J., “Study on the Precession Orbit Shape Analysis- Based Linear Fault Qualitative Identification Method for Rotating Machinery”, Journal of Sound and Vibration, Vol. 335, p. 321-337, 2015.

Lee, J., Leyffer, S., “Mixed Integer Nonlinear Programming”, in The IMA Volumes in Mathematics and its Applications”, Vol. 154, Springer, New York, 2012.

Lees, A. W.; Friswell, M. I., “The Evaluation of Rotor Imbalance in Flexibly Mounted Machines”, Journal of Sound and Vibration, Vol. 208(5), p. 671-683, 1997.

Li, C., She, H., Tang, Q., “The Effect of Blade Vibration on the Nonlinear Characteristics of Rotor-Bearing System Supported by Nonlinear Suspension”, Nonlinear Dynamics, Vol. 89, p. 987-1010, 2017.

Luenberger, D. G.; Ye, Y., “Linear and Nonlinear Programing”, Springer Science+Business Media LLC, New York, 2008.

Lund, J., “Spring and Damping Coefficients for the Tilting Pad Journal Bearing”, ASLE Transactions, Vol. 7, p. 342–352, 1964.

Lund, J. W., Tonnesen, J., “Analysis and Experiment on Multi-Plane Balancing of a Flexible Rotor”, Journal of Engineering for Industry, Vol. 94, p. 233-242, 1972.

Lund, J. W., Thomsen, K. K., “A Calculation Method and Data for the Dynamic Coefficients of Oil-Lubricated Journal Bearings”, Topics in Fluid Bearing and Rotor Bearing System Design and Optimization, ASME, p. 11-28, 1978.

Lund, J. W., “Review of the Concept of Dynamic Coefficients for Fluid Film Journal Bearings”, ASME Journal of Tribology, Vol. 109, pp. 37- 41, 1987.

Machado, T. H., “Avaliação de Mancais Hidrodinâmicos com Descontinuidades Geométricas”, Campinas: Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, 122 p., 2011 Dissertação (Mestrado).

Machado, T. H., Cavalca, K. L., “Investigation on an experimental approach to evaluate a wear model for hydrodynamic cylindrical bearings systems”, Applied Mathematical Modelling, Vol. 40, p. 9546–9564 69, 2016.

Machado, T. H., Alves, D. S., Cavalca, K. L., “Discussion about Nonlinear Boundaries for Hydrodynamic Forces in Journal Bearings”, Nonlinear Dynamics, available on line https://doi.org/10.1007/s11071-018-4177-2, p. 1-18, 2018.

Maliska, C. R., “Transferência de Calor e Mecânica dos Fluidos Computacional”, LTC, 2ª Edição, Rio de Janeiro, Brasil, 2004.

Markert, R.; Platz, R.; Seidler, M., “Model Based Fault Identification in Rotor Systems by Least Squares Fitting”, International Journal of Rotating Machinery, Vol. 7(5), p. 311-321, 2001.

Mendes, R. U., “Desenvolvimento de um Sistema de Atuação Magnética para Excitação de Sistemas Rotativos”, Campinas: Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, 119 p., 2011 Dissertação (Mestrado).

Mendes, R. U., Machado, T. H., Cavalca, K. L., “Experimental Wear Parameters Identification in Hydrodynamic Bearings Via Model Based Methodology”, Wear, Vol. 272- 273, p. 116-129, 2017.

Meruane, V., Pascual, R., “Identification of Nonlinear Dynamic Coefficients in Plain Journal Bearings”, Tribology International, Vol. 41, p. 743–754, 2008.

Morais, T. S., Der Hagopian, J., Steffen Jr. V., Mahfoud, J., “Optimization of Unbalance Distribution in Rotating Machinery with Localized Non Linearity”, Mechanism and Machine Theory, Vol. 72, p. 60-70, 2014.

Morrison, D. R., Jacobson, S. H., Sauppe, J. J., Sewell, E. C., “Branch-and-Bound Algorithms: A Survey of Recent Advances in Searching, Branching, and Pruning”, Discrete Optimization, Vol. 19, p. 79-102, 2016.

Müller-Karger, C. M., Granados, A. L., “Derivation of Hydrodynamic Bearing Coefficients Using the Minimum Square Method”, Transactions of the ASME, Vol. 119, p. 802-807, 1997.

Muszynska, A., “Rotordynamics”, Taylor & Francis Group, Boca Raton, USA, 2005.

Myklestad, N., “A New Method for Calculating Natural Modes of Uncoupled Bending Vibrations of Airplanes Wings and Other Types of Beams”, Journal of Aeronautical Science, Vol. 11, p. 153-162, 1944.

Nelson, H. D., McVAUGH, J. M., “The dynamics of rotor-bearing systems using finite elements”, ASME Journal of Engineering for Industry, Vol. 98, n. 2, p. 593-600, 1976.

Nelson, H. D., “A finite rotating shaft element using timoshenko beam theory”, ASME Journal of Mechanical Design, Vol. 102, n. 4, p. 793-803, 1980.

Newkirk, D. L., “Shaft Whipping”, General Electric Review, Vol. 25, p. 169-178, 1924.

Newkirk, D. L., Taylor, H. D., “Shaft Whipping due to Oil Action in Journal Bearings”, General Electric Review, Vol. 25(8), p. 559-568, 1925.

Nocedal, J., Wright, S. J., “Numerical Optimization”, Springer-Verlag, New York, 1999.

Ocvirk, E., “Short Bearing Approximation for Full Journal Bearings”, National Advisory Committee for Aeronautics TN2808, 1952.

Özgüven, H. N., Özkan, Z. L., ‘‘Whirl Speeds and Unbalance Response of Multibearing Rotors Using Finite Elements,’’ ASME Journal of Vibration Acoustics Stress and Reliability in Design, Vol. 106, p. 72–79, 1984.

Pennacchi, P.; Bachschmid, N.; Vania, A., “Use of Modal Representation for the Supporting Structure in Model-Based Fault Identification of Large Rotating Machinery: Part 1 – Theoretical Remarks”, Mechanical System and Signal Processing, Vol. 20, p. 662-681, 2006.

Pennacchi, P.; Bachschmid, N.; Vania, A., “Use of Modal Representation for the Supporting Structure in Model-Based Fault Identification of Large Rotating Machinery: Part

2 – Application to a Real Machine”, Mechanical System and Signal Processing, Vol. 20, p. 682-701, 2006.

Petrov, N., “Friction in Machines and the Effect of Lubricant”, Inzhenernyj Zhurnal, Vol. 1, p. 71–140, 1883a.

Petrov, N., “Friction in Machines and the Effect of Lubricant”, Inzhenernyj Zhurnal, Vol. 2, p. 228–279, 1883b.

Petrov, N., “Friction in Machines and the Effect of Lubricant”, Inzhenernyj Zhurnal, Vol. 3, p. 377–436, 1883c.

Petrov, N., “Friction in Machines and the Effect of Lubricant”, Inzhenernyj Zhurnal, Vol. 4, p. 535–564, 1883d.

Pinkus, O., “Analysis of Eliptical Bearings”, Transactions of ASME, Vol. 78, p.965- 973, 1956.

Pinkus, O. “Solution of Reynolds Equation for Finite Journal Bearings”, Transactions of ASME, Vol. 80, p.858-864, 1958.

Pinkus., O. “The Reynolds Centennial: A Brief History of the Theory of Hydrodynamic Lubrication”, Transactions of the ASME, Vol. 109, p. 2-20, 1987.

Prohl, M., “A General Method for Calculating Critical Speeds of Flexible Rotors”, Transactions of the ASME 67; Journal of Applied Mechanics 12, p. A142-A148, 1945.

Qiu, Z. L., Tieu, A. K., “The Effect of Perturbation Amplitudes on Eight Force Coefficients of Journal Bearing”, Tribology Transactions, Vol. 39(2), p. 469-475, 1996.

Qin, Q. H., Mao, C. X., “Coupled Torsional-Flexural Vibration of Shaft Systems in Mechanical Engineering – I: Finite Element Model”, Computers and Structures, Vol. 58(4), p. 835–843, 1996.

Racid, Z., Hidalgo, J., “Practical Balancing of Flexible Rotors for Power Generation”, Proc. ASME 2007 Int. Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDECT/CIE 2007, p. 1-10, 2007.

Rao, J. S., “History of Rotating Machinery Dynamics”, Springer Science+Business Media B.V., Chennai, India, 2011.

Rankine, W. A. “On the centrifugal force of rotating shafts”, Engineer (London), Vol. 27, 1869.

Rathbone, T. C., “Turbine Vibration and Balancing”, Trans. of American Society of Mechanical Engineers, Vol. 51, Part I, p. 267-284, 1929.

Reynolds, O., “On the Theory of Lubrication and its Application to Mr. Beauchamp Tower's Experiments, including an Experimental Determination of the Viscosity of Olive Oil”, Philosophical Transactions of Royal Society of London, Series A, Vol. 177, Part 1, p. 157-234, 1886.

Ruhl, R., Booker, J., “A Finite Element Model for Distributed Parameter Turborotor Systems”, Journal of Engineering for Industry, Vol. 94, p. 128-132, 1972.

Sawicki, J. T., Rao, T. V. V. L. N., “A Nonlinear Model for Prediction of Dynamic Coefficients in a Hydrodynamic Journal Bearing”, International Journal of Rotating Machinery, Vol. 10(6), p. 507-513, 2004.

Shen, G., Xiao, Z., Zhang, W., Zheng, T., “Nonlinear Behavior Analysis of a Rotor Supported on Fluid-Film Bearings”, Journal of Vibration and Acoustics, Vol. 128, p. 35-40, 2006.

Sinha, J. K., Lees, A. W., Friswell, M. I., “Estimating the Unbalance of Rotating Machine From a Single Run-Down”, Proc. Of 19th IMAC, Vol. 1, p. 109-115, 2001.

Smith, D. M., “The Motion of a Rotor Carried by a Flexible Shaft in Flexible Bearings”, Proc. Of the Royal Society of London Series A, Vol. 142, p. 92-119, 1933.

Sommerfeld, A., “Zur Hydrodynamischen Theorie der Schmiermittelreibung”, Zs. Math. And Phys, Vol. 50, p. 97–155, 1904.

Stodola, A., “Steam and Gas Turbines”, McGraw-Hill Book Company, New York and London, traduzido da sexta edição alemã, primeiramente publicado em alemão em 1924 como Dampf und Gas Turbinen, Springer, Berlin, 1927.

Stodola, A., “Kristische Wellenstörung infloge der Nachgiebigkeit des Oelpolsters im Lager”, Schweizerische Bauzeiting, Vol. 85, p. 265-266, 1925.

Sudhakar, G. N. D. S., Sekhar, A. S., “Identification of Unbalance in a Rotor Bearing System”, Journal of Sound and Vibration, Vol. 330, p. 2299-2313, 2011.

Tieu, A. K., Qiu, Z. L., “Identification of Sixteen Dynamic Coefficients of two Journal Bearings from Experimental Unbalance Response”, Wear, Vol. 177, p. 63-69, 1994.

Tiwari, R., Chakravarthy, V., “Simultaneous Estimation of the Residual Unbalance and Bearing Dynamic Parameters from the Experimental Data in a Rotor-Bearing System”, Mechanism and Machine Theory, Vol. 44, p. 792-812, 2009.

Thearle, E. L., “Dynamic Balancing of Rotating Machinery in the Field”, Trans. of American Society of Mechanical Engineers, Journal of Applied Mechanics, Vol. 56, p. 745- 753, 1934.

Thomas, J.W., “Numerical Partial Differential Equations – Finite Difference Methods”, Springer Science+Business Media Inc., New York, 1995.

Thorkildsen, T., “Solution of a Distributed Mass and Unbalanced Rotor System Using a Consistent Mass Matrix Approach”, MSE Engineering Report, 1972.

Tower, B., “First Report on Friction Experiments (Friction of Lubricated Bearings)”, In Proceedings of the Institution of Mechanical Engineers (IMechE), p. 632–659, 1883.

Tower, B., “Second Report on Friction Experiments (Friction of Lubricated Bearings)”, In Proceedings of the Institution of Mechanical Engineers (IMechE), p. 58-70, 1885.

Tuckmantel, F. W. S., “Integração de Sistemas Rotor-Mancais Hidrodinâmicos- Estruturas de Suporte para Resolução Numérica”, Campinas: Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, 159 p., 2010., Dissertação (Mestrado).

Untaroiu, C. D., Allaire, P. E., Foiles, W. C., “Balancing of Flexible Rotors Using Convex Optimization Techniques: Optimum Min-Max LMI Influence Coefficient Balancing”, Journal of Vibration and Acoustics, Vol. 130, p. 021006-1 – 021006-5, 2008.

Vance, J.; Zeidan, F.; Murphy, B., “Machinery Vibration and Rotordynamics”, Jhon Wiley & Sons New Jersey, USA, 2010.

Xiang, L., Gao, X., Aijun, H., “Nonlinear Dynamics of an Asymmetric Rotor-Bearing System with Coupling Faults of Crack and Rub-Impact under Oil-Film Forces”, Nonlinear Dynamics, Vol. 86, p. 1057-1067, 2016.

Wale, G. D., Mba, D., “Non-linearity in Experimental Journal Bearing Dynamics – A new Approach”, Proc. IMechE, Vol. 223, Part J: Journal of Engineering Tribology, p. 125- 135, 2008.

Wang, Y. L., Liu, Z. S., Kang, W. J., Yan, J. J., “Approximate Analytical Model for Fluid Film Force of Finite Length Plain Journal Bearing”, Proc. of IMechE, Vol. 226, Part C: Journal of Mechanical Engineering Science, p. 1345-1355, 2011.

Yu, X., “General Influence Coefficient Algorithm in Balancing of Rotating Machinery”, International Journal of Rotating Machinery, Vol. 10, p. 85-90, 2004.

Zhang, Y., “Efficient Procedures for Structural Optimization with Integer and Mixed- Integer Design Variables”, München: Fakultät für Maschinenwesen, Technische Universität München, 127 p., 2015, Tese (Doutorado).

Film Forces of a Journal Bearing”, Journal of Sound and Vibration, Vol. 287, Issue 4-5, p. 827-843, 2005.

Zhao, S. X., Zhou, H., Meng, G., Zhu, J., “Experimental Identification of Linear Oil- Film Coefficients using Least-Mean-Square Method in Time Domain”, Journal of Sound and Vibration, Vol. 287, p. 809-825, 2005b.

Zhao, S. X., Xu, H., Meng, G., Zhu, J., “Stability and Response Analysis of Symmetrical Single-Disk Flexible Rotor-Bearing System”, Tribology International, Vol. 38, p. 749-756, 2005c.

Zheng, T., Hasebe, N., “Nonlinear Dynamic Behaviors of a Complex Rotor-Bearing System”, Journal of Applied Mechanics, Vol. 67, p. 485-495, 2000.

Zheng, T., Yang, S., Xiao, Z., Zhang, W., “A Ritz Model of Unsteady Oil-Film Forces for Nonlinear Dynamic Rotor-Bearing System”, Journal of Applied Mechanics, Vol. 71, p. 219-224, 2004.

Zorzi, E., Nelson, H., “Finite Element Simulation of Rotor-Bearing System With Internal Damping”, Journal of Engineering for Power, Vol. 99, n. 1, p. 71-76, 1977.

Zorzi, E., Nelson, H., “The Dynamics of Rotor-Bearing Systems With Axial Torque - A Finite Element Approach”, Journal of Mechanical Design, Vol. 102(1), p. 158-161, 1980.

BIBLIOGRAFIA COMPLEMENTAR

Baumann, K.; Felscher, P.; Markert, R.; Cavalca, K.L.; “Experimental Identification of Journal Bearing Stiffness and Damping Coefficients in Non-stationary Run-up and Run-down Processes”, Proceedings of 14th International Symposium on Dynamic Problems of Mechanics (DINAME 2011), São Sebastião, SP, Brazil, Vol. 1, pp. 1-10, 2011.

Castro, H. F.; Cavalca, K. L.; Camargo, L. W. F.; Bachschmid, N., “Identification of unbalance forces by metaheuristic search algorithms”, Mechanical Systems and Signal Processing, Vol. 24, p. 1785-1798, 2010.

Cavalca, K. L, “L'Interazione tra rotori e struttura portante: metodologie per la sua modellazione”, Milano: Dipartimento di Meccanica, Politecnico di Milano, 143 p., 1993. Tese (Doutorado).

Cavalca K. L., Okabe E. P., “On the analysis of rotor-bearing-foundation systems”, In: Palestra convidada (lecture ou keynote), IUTAM Symposium on Emerging Trends in Rotor Dynamics, New Delhi, India, March 23-27, 2009.

Cloud, C. H.; Maslen, E. H.; Barret, L. E., “Damping Ratio Estimation Techniques for Rotordynamic Stability Measurements”, ASME Journal of Engineering for Gas Turbines and Power, Vol. 131, p. 012504-1-11, 2009.

Gasch, R.; Nordmann R.; Pfützner, H., “Rotordynamik”, Springer, Berlin, Germany, 2002.

Isermann, R., “Fault-Diagnosis Systems”, Springer-Verlag, Berlin, Germany, 2006.

Machado, T. H., “Identificação do Desgaste em Mancais Hidrodinâmicos Através do Efeito de Anisotropia”, Campinas: Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, 136 p. 2014. Tese (Doutorado).

Actuator Modelling for Rotating Machinery Analysis”, In: International Conference on Vibration Problems, 2011, Praga. Proceedings of International Conference on Vibration Problems, 2011.

Pettinato, B. C.; Cloud, C. H.; Campos, R. S., “Shop Acceptance Testing of Compressor Rotordynamic Stability and Theoretical Correlation”, Proceedings of the Thirty-ninth Turbomachinery Symposium, p. 31-42, 2010.