In the present work a consideration is given to the speed effect on the mechanical performance of strip rolling process with time-dependent materials. The speed-governing dimensionless groups (Euler number and Bingham number) are identified. The suggested approach includes, in an upper bound sense (mixed with stress-equilibrium solutions), the dynamic stress distribution of a Bingham-like viscoplastic material, the speed-dependent energy dissipations, the self-heated surface temperature, and the associated material softening. All these effects are coupled and contributed for explaining the apparently puzzling empirical evidence showing reduction in the roll torque and separation force while increasing the rolling speed. For a relativelyl slow speed, the predicted roll separtion force matches very well an available experimental data as well as Kobayashi’s rigid-plastic finite element analysis. The predicted torque, however, is somewhat higher than the experiments, in particular when the roll-flatness correction is incorporated. The capability of forecasting the variation of roll force with various speeds (reaching high speeds), was checked versus Ford’s measurements and a satisfactory agreement is demonstrated.

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