Modeling and control methods for thermal regimes in the bending of automotive glass

Abstract

This paper reviews the scientific literature on modeling and control of thermal regimes in the gravity bending (sagging) of automotive windshields. Existing approaches are classified into three groups: physics-based (numerical) models, simplified and data-driven models, and furnace temperature control methods. The groups are compared in terms of accuracy, computational speed, data requirements and the feasibility of implementation on industrial programmable logic controllers (PLCs). In addition, a lumped thermal model and a simplified viscous-flow estimate are used to show that, during an unplanned stoppage, glass in the bending zone reaches the zone temperature within 1-2 minutes, and that the permissible stoppage time depends quadratically on glass thickness and inversely on the fourth power of the windshield length. The analysis shows that most studies address the normal operating mode, whereas control of the bending process under abnormal conditions, such as unplanned stoppages, remains insufficiently studied. Directions for future research are proposed.