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    Numerical Investigation of a Nonsmooth Rotor-stator System Considering a Shape Memory Alloy Coated Stator
    Alberto Paiva1; Rodrigo Veronese Moreira1; Alex Brandão1;
    1FEDERAL FLUMINENSE UNIVERSITY (UFF), Volta Redonda, Brazil;
    PAPER: 356/Manufacturing/Regular (Oral)
    SCHEDULED: 14:25/Wed./Mar Azul (50/1st)



    ABSTRACT:
    Rotating systems have been a subject of great relevance since the first industrial revolution, when the first rotating machines started to appear. Since then, several dynamical models have been proposed to describe the behavior of such systems. In the early 19th century, the first rotor models did not consider any interaction with adjacent parts [1] but, as more complete models were developed and solved by numerical methods, nonlinear behavior and chaotic responses were observed as a result from contact and friction between the rotating and stationary parts of the system [2]. The contact phenomenon is still a challenging topic; therefore, recent authors are still interested in its effects considering different approaches [3-5]. Recently, with the increasing Shape Memory Alloy (SMA) exploration [6], a new branch of nonlinear dynamic systems have arisen [7], including nonsmooth systems [8] and rotordynamics applications [9].<br /> This work deals with the numerical simulation of a planar rotor-stator model based on the Jeffcott rotor with four degrees of freedom, namely: two of them related to the rotor, while the other two refer to the surrounding bearing (or stator). The bearing inner surface is subjected to contact and friction and is coated with an SMA layer, whose behavior is described by a first-order phase transition polynomial constitutive model [10].<br /> The SMA layer thermomechanical behavior influences the contact forces between rotor and stator, as its temperature is subjected to two competing phenomena: heating from friction during impact and cooling from convection caused by the interaction with the nearby environment.<br /> The nonlinear system characteristics result from both the intermittent contact possibility and the nonlinear temperature-dependent SMA layer behavior. Such features lead to a vast richness of dynamical behavior, including chaotic responses. The numerical results analyze the dynamical response of the SMA rotor-stator system and investigate the influence of the convective coefficient over the system dynamics.

    References:
    [1] Jeffcott, H.H. (1919) The Lateral Vibration of Loaded Shafts in the Neighbourhood of a Whirling Speed: The Effect of Want of Balance. Philosophical Magazine 37, p. 304-315.<br />[2] Muszynska, A., Goldman, P. (1995) Chaotic Responses of Unbalanced Rotor/Bearing/Stator Systems with Looseness or Rubs. Chaos, Solitons and Fractals 5 (9), p. 1683-1704.<br />[3] Edwards, S., Lees, A.W., Friswell, M.I. (1999) The influence of Torsion on Rotor/Stator Contact in Rotating Machinery. Journal of Sound and Vibration 225(4), p. 767-778.<br />[4] Popprath, S., Ecker, H. (2007) Nonlinear Dynamics of a Rotor Contacting an Elastically Suspended Stator. Journal of Sound and Vibration 308, p. 767-784.<br />[5] Fonseca, C.A.L.L., Aguiar, R.R., Weber, H.I. (2016) On the Non-Linear Behaviour and Orbit Patterns of Rotor/Stator Contact with a Non-Conventional Containment Bearing. International Journal of Mechanical Sciences 105, p. 117-125.<br />[6] Cisse, C., Zaki, W., Zineb, T.B. (2016). A Review of Constitutive Models and Modeling Techniques for Shape Memory Alloys. International Journal of Plasticity 76; p. 244-284.<br />[7] Savi, M.A. (2015) Nonlinear Dynamics and Chaos in Shape Memory Alloy Systems. International Journal of Non-Linear Mechanics 70, p. 2-19.<br />[8] Sitnikova, E., Pavlovskaia, E., Wiercigroch, M., Savi, M.A. (2010) Vibration Reduction of the Impact System by an SMA Restraint: Numerical Analysis. International Journal of Nonlinear Mechanics 45(9), p. 837-849.<br />[9] Silva, L.C., Savi, M.A., Paiva, A. (2013) Nonlinear Dynamics of a Rotordynamic Nonsmooth Shape Memory Allow System. Journal of Sound and Vibration 332, p. 608-621.<br />[10] Falk, F. (1983) One-Dimensional Model of Shape Memory Alloys. Archives of Mechanics 35, p. 63-84.