Stochastic Method to Predict Effects of Roll Grinding Deviations on Sheet Flatness in Cold Rolling

Industrial measurements of the diameter profiles of work-rolls used in cold sheet rolling are applied with a stochastic roll-stack model to better understand how residual error from the roll grinding process affects the rolled sheet flatness quality. Roll diameter measurements taken via a noncontact, optical device on new, warm, and worn work-rolls show that the diameter deviations vary along the roll lengths, across roll samples, and at different operational states, suggesting a multidimensional random field problem. Studies are conducted for a 4-high rolling mill with 301 stainless steel sheet to investigate the reliability in achieving target flatness considering the work-roll diameter random field. Also investigated is the sensitivity of the flatness reliability to roll diameter deviations at different locations along the roll lengths and for the three operational states (newly machined, warm, and worn following several passes). The results lead to several key findings. Foremost, it is shown that an assumption of statistical independence among the residual grinding errors at different roll axis locations is improper. Furthermore, it is demonstrated that, for the measured grinding error correlation patterns, the roll diameter deviations external to the roll/sheet contact region play an important role in contributing to flatness defects within the sheet and that these influences vary according to the roll operational state (new, warm, worn). The presented stochastic model and applied measurement data thus provide for a new understanding into how roll grinding performance influences dimensional quality in the sheet rolling process.