Methematical models for estimating rolling force
P, rolling torque
G and forward slip
f were developed. These models consist of equations for calculating rolling force function
QP, rolling torque function
QG, forward slip
f, mean flow stress
Kfm, temperature of rolled material
T and friction coefficient, μ.
QP,
QG and
f equations are derived by the multiple regression analysis of calculated values of Orowan's exact theory,
Kfm equation is based on the empirical expression of the experimental data of cam plastometer and besides corrected by the correction parameter.
T equation is derived theoretically considering temperature change during air cooling, spray cooling and roll gap. Heat transfer coefficients decided in the former study are used. The values of μ and correction parameter of
Kfm are decided simultaneously by substituting measured values of
f and
P into the
f and
P models and solving them. Almost satisfactory accuracy is achieved in estimating
P,
G and
f. Improving the accuracy is expected by the use of (coil to coil) plus (lot to lot) adaptive control method.
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