Predictions versus measurements of turbocharger nonlinear dynamic response
The present work advances progress on the validation against measurements of linear and nonlinear rotordynamic models for predicting the dynamic shaft response of automotive turbochargers (TCs) supported on floating ring bearings. Waterfall spectra of measured shaft motions at the compressor and turbine ends of a test TC rotor evidences a complex response, showing synchronous (1X) and multiple subsynchronous frequencies along the entire operating speed range (maximum shaft speed ~ 65 krpm). Postprocessing of the raw test data by mathematical software allows filtering the synchronous and subsynchronous vibration components for later comparisons to predicted shaft motions. The static performance of the floating ring bearings is analyzed with in-house software (XLSFRBThermal??), which considers thermal expansion of the shaft and bearing components as well as static loading on the bearing due to lubricant feed pressure. In addition, the program calculates rotordynamic force coefficients for the inner and outer films of the floating ring bearing. The turbocharger Finite Element (FE) structural model for the linear and nonlinear analyses includes lumped masses for the compressor and turbine wheels and the thrust collar. The mass imbalance distribution on the TC rotor is estimated from the test data using a procedure derived from the two-plane balancing method with influence coefficients. The linear model yields predictions of rotor synchronous (1X) response to imbalance and damped eigenvalues. The analysis evidences that the rotor cylindrical-bending mode is unstable at all shaft speeds while the rotor conical model becomes more unstable as lubricant feed pressure decreases. The predicted synchronous (1X) motions agree well with the test data, showing a critical speed at approximately 20 krpm. The linear stability results indicate the existence of three critical speeds occurring at 4, 20 and 50 krpm. The second critical speed corresponds to the rotor cylindrical-bending mode, showing larger amplitudes of motion at the compressor nose than at the turbine end. The third critical speed associated to the rotor first bending modes is well damped. In the nonlinear transient analysis, the nonlinear equations of motion of the system (rotor-FRB) are integrated, and the bearing reaction forces are calculated at each time step in a numerical integration procedure. The model then yields predictions of total motion which is decomposed into synchronous (1X) and subsynchronous motions, amplitudes and frequencies. The nonlinear analysis predicts synchronous (1X) amplitudes that correlate well with the test data at high shaft speeds (> 30 krpm) but underpredicts the imbalance response at low shaft speeds (<30 krpm). The time transient simulations predict multiple frequency subsynchronous motions for shaft speeds ranging from 10 krpm to 55 krpm, with amplitudes and frequencies that are in good agreement with the measurements. Finally, the shaft motion measurements and predictions demonstrate that the turbocharger dynamic response does not depend greatly on the lubricant feed pressure and inlet temperature for the conditions tested.