A Design Method to Eliminate Sub Synchronous Response in Automotive Turbochargers utilizing Nonlinear Dynamics of Time Periodic Systems

The present work introduces a methodology for the dynamic design evaluation of high-speed rotors, applying nonlinear dynamics of time periodic systems. The paper focuses on the definition of design variables so as the system to avoid sub synchronous components in the response. The response of an unbalanced turbocharger rotor mounted on oil bearings with wire mesh dampers (WMDs) is evaluated with an efficient collocation method coupled to the pseudo arc length continuation to evaluate response limit cycles in the entire range of the rotating speed, which acts as bifurcation parameter. The specific system is used to demonstrate the method without loss of generality. The analytical model of the WMD component is implemented directly from the literature, while rigid rotor model and short bearing approximations are used for the rest components. Floquet theory is applied in the non-autonomous dynamic system and the stability characteristics of the response limit cycles are evaluated through Floquet multipliers, the magnitude of which act in the algorithm as stability index. A sensitivity analysis is performed at first to evaluate the correlation between WMD key design parameters and the time response of the system. A multi objective optimization method is embedded to set Floquet multipliers at specific values; in this way the response limit cycles retain stability and periodicity, avoiding any type of bifurcation which would render sub-synchronous component. Acceptable sets for design variables of journal bearings and WMDs are defined by multi-objective optimization and these are verified in efficiency by evaluating the response of the system by time integration, as a virtual experiment, for several operating conditions. The method requires severely lower computational time and capacity to render an acceptable design compared to the conventional design of experiment DoE procedure, and it is not limited on the analytical models of rotor, bearing, or other component.