Dynamic Instability Investigation of the Automotive Driveshaft’s Forced Torsional Vibration Using the Asymptotic Method

This paper aims to investigate using FOAM to analyze the dynamic instability in the APPR for ADFTV based on a dynamic model (DMADFTV). The DMADFTV considers the following aspects: AD kinematic nonuniformity (ADKN), AD geometric nonuniformity (ADGN) of inertial characteristics for the spinning movements (ICSM) of the AD elements (ADE), and the excitations induced by the gearbox–internal combustion engine modulations. The DMADFTV is considered the already-designed dynamic model developed by the first author of the ADFTV in a previous publication. This DMADFTV was used to compute the stationary frontiers of instability and the nonstationary spectral velocity amplitude (NSVA) versus nonstationary spectral amplitude (NSA) in the configuration space in transition through APPR, using the FOAM. The use of FOAM is much more versatile, from the analytical point of view, than the method of multiple scales and allows the computation of the NSA and the NSVA in the APPR. In contrast, these computations cannot be performed using the harmonic balance method. MATLAB Software R 2017 was developed based on DMADFTV and used the FOAM to compute the stationary frontiers of instability and the NSVA versus the NSA in transition through APPR for the ADFTV. The numerical results were compared with the experimental and numerical data published in the literature, finding agreements. The computation of the NSVA versus NSA in the configuration space using FOAM represents a method of detection of the chaotic manifestation of ADFTV.