Parametric resonance of plates in a sheet metal coating process

The vibration of sheet metal during zinc coating processes can lead to non-uniform coating thickness and overall poor product quality. This vibration develops from two principal mechanisms, namely, the run-out associated with the supporting rollers and/or bearings, and the time-varying tension associated with the manufacturing process. This study focuses on the second of these mechanisms (time-varying tension) that becomes significant under conditions leading to parametric resonance. The parametric resonance of the sheet metal is captured in a proposed model of a plate subject to time-varying and non-uniform edge tension. The model accounts for these effects as well as the non-linear stretching of the plate mid-plane as a result of transverse plate vibration. The linear vibration characteristics of the plate are studied first and are then used in deriving a single mode approximation of the non-linear, parametrically excited plate model. A perturbation solution of this model reveals the major parameters that influence parametric resonance in this application. Theoretical results for plate vibration are compared to experimental measurements of sheet metal vibration in a production facility. This comparison demonstrates that the model accurately captures the physical mechanisms responsible for sheet metal vibration and therefore, the physical parameters (such as damping) have the greatest impact on this vibration.