A Damage Estimation Method for Packaging Systems Based on Power Spectrum Densities Using Spectral Moments

Abstract

Packaging systems always endure some type of damage during transportation, and Wöhler curves are typically used to determine the mechanical wear evolution of a packaging system. Damage estimations can be performed using a Rainflow method, but continuous stress recording is required. However, this recording is not always possible, so global transportation vibrations are represented by the power spectral density (PSD). In this paper, the damage of a system according to the Wöhler curve was studied. The Basquin model was used to determine the mechanical wear evolution of the system, and the mechanical behaviour was established by extracting the Basquin coefficient b and the constant system C from the Wöhler curves. A Wöhler curve was further realized for a packaging system, and its Basquin coefficient b and system constant C were also extracted. Damage is estimated by the accumulation of the stress cycles using the PalmgrenMiner rules. In this paper, the maximum peaks of the cycle were detected in a signal. The density probability of the maximum stress apparition was also constructed from a multivariate Gaussian model. PSDs have the same statistical properties as the corresponding temporal events, so these statistical properties were extracted by the spectral moment method. Furthermore, a damage equation was proposed using the PSD, and the damage induced by different PSDs was determined from the damage equation and compared with the actual duration on a vibration table. INTRODUCTIONThe global road network is growing each year, and it is composed of millions of kilometres. Various types of roads or road conditions are often encountered with longer travel distances with countless stress possibilities. The study of these stresses is a crucial point for determining the viability of products. It is also important to design product packaging with transportation in mind.Many packaging solutions exist to protect goods against transportation hazards, but these stresses induce some modifications to the mechanical properties of these systems by damage accumulation. If the damage accumulation is too important, then the packaging system cannot properly protect the packaged goods.Some damage measurement approaches were proposed in the literature, but they are mainly based on continuous acceleration recording 1 or on the consideration of a particular parameter or phenomenon of a packaging system. 2,3 This method uses continuous signal recording. The most widely used method to estimate damage from a continuous recording is based on the study of the evolution of the mechanical properties by accumulating the cycle stress. This method uses the Wöhler curves.These curves describe the damage wear evolution of a system by counting the number of stress cycles for a particular magnitude until the cycle breaks. The system mechanical wear evolution knowledge is based on a temporal cycle extraction method, such as Rainflow, for determining the global damage.In transportation studies, power spectrum densities (PSDs) are traditionally used to ...

Decomposition of the acceleration levels distribution of a road transport into a sum of weighted Gaussians: Application to vibration tests

“…In a future work, it would be interesting to develop this method to a damage estimation based on the PSD defined by the decomposition. Indeed, the decomposition of a modified Gaussian into a sum of weighted Gaussians would be all the more relevant as it induces the same damage on a packaging system as the actual transport.…”

Experimental investigation on bending fatigue failure of corrugated paperboard

“…The S‐N equations and curves of corrugated paperboards are obtained in this article, and the exponent b in Equation is available, which can be applied to the accelerated random vibration test of stacked corrugated boxes. Huart et al obtained the Basquin ‐type constants of loaded corrugated box and estimated the life duration of box . The present paper may use the material fatigue constants of corrugated paperboard to estimate the time scale or vibration power spectrum density (PSD) scale of corrugated box in the accelerated random vibration test.…”

“…On the other hand, to evaluate the packaging performance effectively and suitably under the action of random vibration in logistics, the accelerated random vibration testing becomes one of important tools in laboratory. 31,32,[37][38][39] The tested duration T s of packaging in laboratory simulated vibration may be estimated, according to the damage equivalent principle, by using the transport duration T r in real The bending fatigue behaviour is discussed according to the S-N curves, hysteresis loops, bending stiffness-cycles curves, and failure modes. Following conclusions can be reached.…”

Accelerated Random Vibration Testing of Transport Packaging System Based on Acceleration PSD

“…Griffiths and Shires carried out a correlation study simulating the scuffing by using a specially designed and proven test rig, to understand how various test approaches correlate with each other and with a benchmark time replicated journey . Huart estimated the damage by using a PSD rather than the cycle extraction method based on continuous temporal recording . Kipp discussed the accelerated random vibration testing for transport packaging and pointed out the complexity…”