Method for preheating a working roll for rolling

A process for preheating at least one work roll of a rolling mill intended to roll a metallic strip so that the work roll has a target thermal expansion profile (Δd(i)c)1≤i≤Ns determined along Ns longitudinal segments of the work roll, the rolling mill including a thermal control device including Ni induction coils distributed along the longitudinal axis of the work roll facing the Ns longitudinal segments, the process comprising the following phases:

• a. determining the target thermal expansion profile (Δd(i)c)1≤i≤Ns, at a calculation time tk,
• based on predefined values of input parameters Pe representative of the dimensions and mechanical and thermal properties of the metallic strip to be rolled,
• and a first predefined physical model M1 expressing a relationship between the input parameters Pe and the target thermal expansion profile (Δd(i)c)1≤i≤Ns;
• b. determining an effective mean temperature profile (T(i)eff(tk))1≤i≤Ns along Ns longitudinal segments of the work roll,
• based on an effective thermal power profile (PQ(i)eff(tk+1))1≤i≤Ni generated by the Ni induction coils and measured beforehand,
• and a second predefined physical model M2 expressing a relationship between the effective thermal power profile (PQ(i)eff(tk))1≤i≤Ni and the effective mean temperature profile (T(i)eff(tk))1≤i≤Ns;
• c. determining (30) a target mean temperature profile (T(i)c(tk))1≤i≤Ns along the Ns longitudinal segments of the work roll, based on the target thermal expansion profile (Δd(i)c (tk))1≤i≤Ns determined and the effective mean temperature profile (T(i)eff(tk))1≤i≤Ns determined;
• d. determining a deviation ΔT(tk) between the target mean temperature profile (T(i)c(tk))1≤i≤Ns and the effective mean temperature profile (T(i)eff(tk))1≤i≤Ns;
• e. determining a convergence criterion based on the deviation ΔT(tk) determined, and stopping the preheating when the convergence criterion is satisfied, and continuing the phases of the preheating process when the convergence criterion is not satisfied;
• f. activating of the induction coils including the following:
• determining a target thermal power profile (PQ(i)c (tk))1≤i≤Ni to be supplied by the Ni induction coils based on the deviation ΔT(tk) determined;
• activating the induction coils such that they supply the target thermal power profile (PQ(i)c (tk))1≤i≤Ni determined;
• measuring an effective thermal power profile (PQ(i)eff(tk))1≤i≤Ni actually supplied by the induction coils;
• g. repeating b/ to f/ until the convergence criterion is satisfied, by incrementing the calculation time tk.