Dynamic response characterization of complex systems through operational identification and dynamic substructuring- An application to gear noise propagation in the automotive industry

Abstract

This thesis deals with new methods, which can determine the dynamic response of a complex system identified in operation, based on the knowledge of its subsystem dynamics and excitation. In the first part of this thesis, the identification of component excitation and its transmission into the total system will be addressed. The identification of the internal component excitation is performed on a test bench, on which equivalent forces at the component interface to the test setup are measured. The total system’s response is calculated on the knowledge of its dynamic properties from the component interface onwards. It is shown that physically correct responses for the systems in front of the component’s interface can be calculated. A compensation technique is also outlined to eliminate possible test bench influences. In this thesis, this first approach is called the Gear Noise Propagation (GNP) method, which can be seen as a special class of the well known Transfer Path Analysis (TPA) method. The method could be partially validated on the vibration propagation of a Rear Axle Differential (RAD) in a vehicle, also showing that test bench influences can be minimized in real life applications. In the second part, a new experimental strategy is developed, which enables the identification of systems in operation. In this thesis the method is referred to as the Operational System Identification (OSI) method. It is shown that the signal processing involved yields better FRF estimates than the classical Cross Power Spectrum (CPS) and Auto Power Spectrum (APS) averaging technique. In addition the method has been successfully validated by comparison with the Principle Component Analysis (PCA) method on a test object. Application of the method to an operating vehicle reveals some interesting dependencies of its system dynamics on temperature and applied engine torque. The third part of this thesis deals with methods which improve coupling results in experimental Dynamic Substructuring (DS) applications. First a general framework is presented with which different kinds of substructuring methods developed in the past can be classified. Thereafter methods which improve subsystem connectivity and compensate for shaker’s side force excitation are presented. An error propagation method is also developed with which the uncertainty on the coupled system FRF can be determined, based on the uncertainties of its subsystems. Validation of the new methods on a vehicle’s Rear Axle system shows good improvements could be achieved. In addition it will be shown that random errors on the subsystem FRF only play a significant role for very lightly damped systems. Yet in general, bias errors in the subsystem measurement and in the subsystem coupling definition are found to yield most of the discrepancies in experimental DS. Combinations between the methods developed in the first three parts are made in the fourth part of this thesis. It is shown that experimental DS is an efficient tool to identify influences of component operational parameters on the total systems performance. Furthermore it is shown that DS is helpful in sensitivity analysis and simple component design.