Abstract
Near-field acoustic levitation is a physical phenomenon that occurs when a planar object is placed in the proximity of a vibrating surface. Consequently, a thin layer of ambient gas, commonly referred to as squeeze film, is trapped in the clearance between a vibrating surface and an adjacent planar object performing its levitation. Mathematically, this phenomenon is described by using the Reynolds equation, which is derived from the Navier–Stokes momentum and continuity equations. The equation of motion that represents the dynamic behavior of the levitated object is also considered. However, the performance of the near-field acoustic levitation can be significantly affected by uncertainties on its geometrical parameters and operating conditions. Thus, the present contribution aims to evaluate the influence of uncertain parameters on the resulting levitation force. For this purpose, the differential evolution algorithm is associated with two strategies (inverse reliability analysis and effective mean concept). This multi-objective optimization problem considers the maximization of the levitation force associated with the maximization of both the reliability and robustness coefficients. Numerical simulations demonstrated the sensitivity of each uncertain parameter associated to the obtained levitation forces. As expected, it was verified that the levitation force decreases as the considered reliability and robustness coefficients increases.
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References
Choi, S.K., Grandhi, R., Canfield, R.A.: Reliability-Based Structural Design. Springer, London (2006)
Carter, D.S.: Mechanical Reliability and Design. Wiley, New York (1997)
Melchers, R.E.: Structural Reliability Analysis and Prediction. Wiley, Chichester (1999)
Deb, K., Gupta, H.: Introducing robustness in multi-objective optimization. Evol. Comput. 14(4), 463–494 (2006)
Deb, K., Padmanabhan, D., Gupta, S., Mall, A.K.: Handling uncertainties through reliability-based optimization using evolutionary algorithms. IEEE Trans. Evol. Comput. 13(5), 1054–1074 (2009)
Wang, P., Wang, Z., Almaktoom, A.T.: Dynamic reliability-based robust design optimization with time-variant probabilistic constraints. Eng. Optim. 246(6), 784–809 (2013)
Gu, X., Sun, G., Li, G., Mao, L., Li, Q.: A comparative study on multi-objective reliable and robust optimization for crashworthiness design of vehicle structure. Struct. Multidiscip. Optim. 48(3), 669–684 (2013)
Prigent, S., Maréchal, P., Rondepierre, A., Druot. T., Belleville, B.: A robust optimization methodology for preliminary aircraft design. Eng. Optim. 48(5), 883–899 (2015)
Doh, J., Kim, Y., Lee, J.: Reliability-based robust design optimization of gap size of annular nuclear fuels using kriging and inverse distance weighting methods. Eng. Optim. 1(1), 1–16 (2018)
Du, X., Chen. W. Sequential optimization and reliability assessment method for efficient probabilistic design. J. Mech. Des. 126(2), 225–233 (2004)
Poles, S., Lovison, A.: A polynomial chaos approach to robust multiobjective optimization, hybrid and robust Approaches to multiobjective optimization. In: Deb, K., Greco, S., Miettinen, K., Zitzler, E. (eds.) Proceedings of Dagstuhl Seminar, pp. 1–15. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl. (2009)
Du, X., Sudjianto, A., Chen, W.: An integrated framework for optimization under uncertainty using inverse reliability strategy. J. Mech. Des. 126(4), 562–570 (2004)
Vandaele, V., Lambert, P., Delchambre, A.: Non-contact handling in microassembly: acoustical levitation. Precis. Eng. 29(4), 491–505 (2005)
Yamazaki, T., Hu, J., Nakamura, K., Ueha, S.: Trial construction of a noncontact ultrasonic motor with an ultrasonically levitated rotor. Jpn. J. Appl. Phys. 35(5S), 3286 (1996)
Peng, T., Yang, Z., Kan, J., Tian, F., Che, X.: Performance investigation on ultrasonic levitation axial bearing for flywheel storage system. Front. Mech. Eng. China 4(4), 415 (2009)
Stolarski, T.A., Xue, Y., Yoshimoto, S.: Air journal bearing utilizing near-field acoustic levitation stationary shaft case. Proc. Inst. Mech. Eng. J J. Eng. Tribol. 225(3), 120–127 (2011)
Thomas, G.P., Andrade, M.A., Adamowski, J.C., Silva, E.C.N.: Development of an acoustic levitation linear transportation system based on a ring-type structure. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 64(5), 839–846 (2017)
Ilssar, D., Bucher, I.: On the slow dynamics of near-field acoustically levitated objects under High excitation frequencies. J. Sound Vib. 354, 154–166 (2015)
Hrka, S.: Acoustic Levitation. University of Ljubljana, Faculty of Mathematics and Physics, Ljubljana (2015)
Ilssar, D., Bucher, I.: The effect of acoustically levitated objects on the dynamics of ultrasonic actuators. J. Appl. Phys. 121(11), 114504 (2017)
Lobato, F.S., Steffen Jr., V.: A new multi-objective optimization algorithm based on differential evolution and neighborhood exploring evolution strategy. J. Artif. Intell. Soft Comput. Res. 1, 1–12 (2011)
Zhao, S.: Investigation of Non-contact Bearing Systems Based on Ultrasonic Levitation. PZH, Produktionstechn (2010)
Rosenblatt, M.: Remarks on a multivariate transformation. Ann. Math. Stat. 23, 470–472 (1952)
Zhao, Y.G., Ono, T.: A general procedure for first/second-order reliability method (FORM/SORM). Struct. Saf. 21(1), 95–112 (1999)
Storn, R., Price, K.V.: Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces. Int. Comput. Sci. Inst. 12, 1–16 (1995)
Deb. K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Chichester (2001)
Hu, X., Coello, C.A.C., Huang, Z.: A new multi-objective evolutionary algorithm: neighborhood exploring evolution strategy. Eng. Optim. 37(4), 351–379 (2005)
Villadsen, J.V., Michelsen, M.L.: Solution of differential equation models by polynomial approximation. Prentice-Hall, New Jersey (1978)
Acknowledgements
The authors are thankful for the financial support provided to the present research effort by CNPq (574001/2008-5, 304546/2018-8, and 431337/2018-7), FAPEMIG (TEC-APQ-3076-09, TEC-APQ-02284-15, TEC-APQ-00464-16, and PPM-00187-18), and CAPES through the INCT-EIE.
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Lobato, F.S., Zuffi, G.A., Cavalini, A.A., Steffen, V. (2020). Uncertainty Analysis of a Near-Field Acoustic Levitation System. In: Llanes Santiago, O., Cruz Corona, C., Silva Neto, A., Verdegay, J. (eds) Computational Intelligence in Emerging Technologies for Engineering Applications. Studies in Computational Intelligence, vol 872. Springer, Cham. https://doi.org/10.1007/978-3-030-34409-2_1
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