Nobel approach in signifying damage for a bellows type flexible joint

•The exhaust system is in fact a hanging system.•Movement of exhaust system deviates from that of the vehicle body due to the changes of inertia force.•The objective is to signify uncertainties associated with aging those which are hardly noticed with RFCC•PSD has been displayed to quantify change of the given system under aging.•Both RFCC and PSD methods give signs for abnormal consequences of aging, shock and impact.

The durability of an exhaust system, particularly for a flexible joint, has been addressed in terms of damage augmented by energy spectral densities. Movement of a flexible joint in motion is calculated by solving forward kinematics of the Stewart platform, converting displacement signals obtained by a set of potentiometers into a Cartesian pose. Those time series are then projected onto the uni-directional field thus defined separately, i.e., damage for the application of the Minor rule and energy for power spectrum densities. Parseval's theorem allows us to bridge two fields so that one can access not only information on fatigue properties, but also on effect of aging in the presence of shock and impact.