Coupling nonlinear dynamics and multi-objective optimization for periodic response and reduced power loss in turbochargers with floating ring bearings.

The paper utilizes a novel approach for the dynamic design of automotive turbocharger rotors by employing nonlinear dynamics of time periodic systems, emphasizing the influence of bearing design variables to prevent sub-synchronous components in system's response. The investigation focuses on the response of an unbalanced turbocharger rotor on floating ring bearings using a collocation-type method which has been developed for the needs of the work, being then integrated with pseudo arc length continuation for the calculation of unstable solution branches of the system, in several design sets, and with poor initial values. The analytical model includes a rigid rotor model and short bearing approximations for the two floating ring bearings, which introduce strong nonlinear forces in series (inner film and outer film at each bearing). Floquet theory is employed to analyse the non-autonomous dynamic system, and stability characteristics of the response limit cycles are assessed through Floquet multipliers, whose magnitude serves as a stability index in the algorithm. A genetic algorithm based multi-objective optimization is combined to the robust collocation-type method to achieve reduced values for Floquet multipliers, ensuring that response limit cycles maintain stability and periodicity, thereby preventing the occurrence of bifurcations which normally lead to sub-synchronous response components. Twelve design variables are computed to satisfy low rotor eccentricity and power loss. Acceptable design sets are verified for efficacy by assessing system response through time integration, akin to a virtual experiment. This approach significantly reduces computational time and resource requirements compared to traditional Design of Experiment (DoE) procedures and is not constrained by complex models of the rotor, bearings, or other components. A feature of the method is that it offers an insight on the stability and its quality, rather than simply assessing a threshold speed of instability. [ABSTRACT FROM AUTHOR]