Case history: Computation of normalized dynamic mesh force and transmissibility spectra for vibro-acoustic control of roots-type supercharger systems

A linear dynamic finite element model of a geared supercharger is developed by following a systematic step-by-step modal based modeling and test-analysis correlation procedure. This entails analyzing and validating each major component individually, and combining them into a system representation. The assembled model is utilized to compute the normalized dynamic mesh force and vibration transmissibility response spectra assuming a uniform amplitude spectrum of gear transmission error excitation. It is shown in this paper how these response functions can be used to identify critical controlling parameters for the purpose of developing noise and vibration control strategies. An example case of a three-lobe rotor system is discussed to demonstrate the salient features and limitations of this proposed vibro-acoustic design methodology. Even though this study is aimed at analyzing the dynamics of superchargers with emphasis on gear whine, its proposed method is quite general and can be applied to other high-speed geared machinery.