Novel design concept for shrink-fitted bimetallic sleeve roll in hot rolling mill

Abstract

The rolls are classified into two types; one is a single-solid type roll, and the other is a shrink-fitted assembled type sleeve roll consisting of a sleeve and a shaft. The sleeve roll is successfully used as a large back-up roll used in rolling. However, sometimes, the interfacial slip appears although the slippage resistance torque ${T}_{r}$ is designed to be larger than the motor torque. In this paper, the FEM simulation is performed to clarify the phenomena in real rolling. It is found that the interfacial slip is accelerated significantly with increasing the motor torque. The circumferential slippage under zero torque can be explained from the non-uniform deformation due to the rolling force $P$. This is because the displacement increase rate increases with increasing the force $P$. Finally, a novel design concept is proposed for sleeve rolls from the present discussion.

Appendix. Experimental confirmation for interfacial slip by using miniature roll under free rolling

In this paper, the effect of the motor torque on the interfacial slip is mainly investigated through numerical simulation. To verify the simulation experimentally, Fig. 10 illustrates the miniature roll specimen whose diameter is 60 mm used to confirm the interfacial slip [14]. Table 2 shows the experimental conditions with no motor torque because a similar phenomenon known as “interfacial creep” in ball bearing was under free rolling. The work roll consists of two sleeves and a shaft. To realize the slip between sleeve 1 and sleeve 2 in Fig. 10 sleeve 2 and the inserted shaft are fixed by the key. In the experiment, the work roll was cooled down by water at room temperature to prevent the change of the shrink-fitting ratio due to rising temperature. Under the steady rotation, the load of 1 ton was applied confirming the roll surface temperature change was within 5 °C or less during the experiment by a contact thermometer.

Table 2 Experimental conditions by using a miniature roll in Fig. 10

Fig. 10

FEM mesh for test specimen used in a miniature roll

The FEM simulation is also performed by using the mesh in Fig. 10. Four-node quadrilateral plane strain elements are used, and the total number of mesh elements is 7408. By assuming the loading P = 245 N/mm, the shrink-fitting ratio δ/d = 0.21 × 10⁻³ and the constant friction coefficient µ = 0.3 between sleeve 1 and sleeve 2, the numerical simulation is newly performed for the miniature roll. Similar to Fig. 3b, ${u}_{\theta }^{P\left(0\right)\sim P\left(\varphi \right)}\left(\theta \right)$ is defined as the relative displacement between sleeve 1 and sleeve 2. 

Table 3 Comparison of experimental data and simulation results for average displacement during one roll rotation

Table 3 summarizes the average values of the displacement obtained by the simulation in comparison with the slip distance in the experiment when δ/d = 0.21 × 10⁻³. The experimental value corresponds to ${u}_{\theta ,ave.}^{P\left(0\right)\sim P\left(2\pi \right)}$ during one roll rotation that can be calculated in the following way:

$$\begin{aligned}{u}_{\theta ,ave.}^{P\left(0\right)\sim P\left(2\pi \right)}&=\frac{{\theta }_{\mathrm{slip}}\times \pi d}{360^\circ \times n}\\&=\frac{77^\circ \times \pi \times 48 mm}{360^\circ \times 3\times {10}^{4}}\\&=\frac{32 mm}{3\times {10}^{4}}\\&=0.108\times {10}^{-2}mm\end{aligned}$$

(7)

In Eq. (7), ${\theta }_{slip}$ is the slip angle observed in the experiment, d is the inner diameter of sleeve 1 and n is the number of the roll rotation.

As shown in Table 3, although the numerical simulation result is 3.56 times larger than the experimental result, their orders are in agreement. The difference can be explained by the experimental observation. Due to the circumferential slip, slip defects start with thin and shallow scratches, then, it becomes thicker and deeper with erosive wear and cohesive wear, and eventually form large defects that completely stop the slip. In the simulation, a constant friction coefficient µ = 0.3 should be changed to $\mu =$ 0.3 $\sim \infty$, but actually the change reflecting the real defect evolution is almost impossible in practice. This is the reason why 3.56 times difference appears between the experiment and the simulation. Although the experimental and simulation results are not in good agreement, the model is useful for understanding the phenomenon especially when this is no slip defect, and the model can be used for comparative purposes or similar claims.