Vibration analysis of thin plate under time varying tension and external excitation in sheet metal coating process

Abstract

In the sheet metal coating process, a plate is transported by rollers. In this process, the transport speed, motion of the rollers and tension can cause a vibration of the plate. The vibration of the plate during the process can adversely affect the quality of the finished product. The non-uniform edge tension in width direction due to the crowned shape of the roller affects linear vibration characteristics and the transport speed and time-varying tension affect the stability and the response of the plate. Thus, the study about the vibration of the plate, including modal analysis and forced vibration analysis that gives an insight of the vibration mechanism, is very important work to improve the quality of the products. The vibration response shows mainly two components: natural frequency and roller rotating frequency. The plate vibration derives from two principal mechanisms. The first mechanism is an external excitation that results from the eccentric rotation of the roller(s) and/or supporting bearings. Eccentric roller/bearing rotation produces motion normal to the sheet at the boundary formed by the roller. The second mechanism is a parametric excitation that develops from the time varying tension experienced by the sheet metal plate. The magnitude of the time varying tension is on the order of 10% of the mean tension, and it is a likely source of parametric resonance. In this study, there are mainly two parts of researches. One is the modal analysis of the plate based on the linear model, and the other is the forced vibration analysis based on the linear/nonlinear model. In the modal analysis, first, the natural frequencies and the mode shapes are examined under the effect of the non-uniform tension in width direction. In this analysis, to find the internal stress distributions under the non-uniform edge tension, modified Fourier series method is proposed and the changes of the linear vibration characteristics (natural frequencies and mode shapes) are fou...