1. Introduction
Hot strip mills work under conditions of high temperature and heavy load. Due to the long service time, the back-up rolls of the mill will wear seriously, which will affect the service period of the rolls and the stability of the strip profile control. In particular, the axial uneven wear of the back-up roll in CVC mills is serious; therefore, self-sustaining of the roll contour is poor, due to the coupling relationship between the roll deflection and the roll contour, which will adversely affect the strip profile control. In addition, long-term excessive contact pressure between the rolls somewhere in the roll makes spalling easy to occur [
1,
2,
3,
4,
5].
A reasonable back-up roll contour design can improve the contact pressure distribution between the back-up roll and the work roll, and effectively improve the uneven wear of the back-up roll [
6,
7]. In addition, this area, called the ‘harmful contact area’, where the length of the contact line between the work roll and the back-up roll exceeds the width of the strip, is one of the main factors affecting the deflection of the roll system. The variable contact back-up roll, the VCR (varying contact roll), a specially designed roll contour, can effectively reduce ‘the harmful contact zone’ and improve the strip profile control ability [
8,
9]. The VCR technology is introduced into the design of the back-up roll contour of the CVC mill, and the contact pressure distribution between the back-up roll and work roll is considered comprehensively, which can improve the initial strip profile control ability of the mill and the stability of the strip profile control during the service period of the back-up rolls [
10,
11,
12].
Li et al. [
13] proposed a novel back-up roll contour for CVC mills in the form of a central CVC for the wear characteristics of the back-up rolls in CSP production lines, and proved that the new roll contour has good strip profile control ability and is self-sustaining through theoretical analysis and field test. Hao et al. [
14] analyzed the problem of uneven wear when the VCR back-up roll contour was matched with the CVC work roll contour, and improved the VCR roll contour. Shao et al. [
15] optimized the back-up roll contour of CVC mills in the CSP production line of Maanshan Iron and Steel Co., Ltd., Maanshan, China. And designed a VCRplus back-up roll contour using the conventional VCR roll contour method, superposing the CVC roll contour. They also compared it with the original roll contour, the contact pressure between the rolls, crown adjustment domain, roll gap transverse stiffness, roll bending force control efficiency, and other indicators. Liu et al. [
16] further studied the influence of chamfering at both ends of the VCRplus roll on the contact pressure distribution between the rolls, and optimized the chamfering of VCRplus roll. In order to solve the problem of the insufficient utilization of the back-up roll surface in a Hansteel 2250 mm production line, Li et al. [
17] flattened the roll contour of the CVC work roll and superimposed chamfering as a new back-up roll contour, which extended the service period of the back-up roll. It can be seen that the back-up roll contour design is of great significance to its working characteristics.
In a 1500 mm continuous hot rolling production line, the finishing mill is a seven-stand four-high mill. The upstream stand is a CVC mill. The contour of the back-up roll is flat with a chamfer at the edge. Additionally, the service period of the back-up roll is short. The rolling capacity during the service period is approximately 150,000,000 kg, which will yield cross-use of the back-up rolls of different service periods, exerting a certain pressure on the stability of production, as well as occasional spalling problems. In this study, based on finite element simulation, the contact pressure distribution between the rolls at the existing roll contour configuration was analyzed, and the improvements of the back-up roll contours were applied to improve the service life of the rolls.
5. VCRplus Back-Up Roll Contour Design
Through the analysis in
Section 4, although the contact pressure between the rolls is different under different working conditions, its main form is still determined. Equation (3) is the geometric coordination equation for solving the deflection deformation of four-high mills [
21], which can be used to further analyze the uneven contact pressure between the rolls and provide direction for the optimization of back-up roll contour.
In Equation (3), x is the coordinate of the roll body, and its origin is at the midpoint of the roll body (mm); ∆Y(x) is the deflection difference between the work roll and the back-up roll (mm); F(x) is the force between the rolls (kN), which is positively correlated with the contact pressure between the rolls; αF(x) is the absolute value of the variation in the axial distance between the work roll and the back-up roll in the reduction direction caused by the roll flattening (mm), and it is assumed that the force between the rolls is linear with the flattening amount, and the linear coefficient is α (mm/kN); δ(x) is the gap between the rolls, which is determined by the initial roll contour of the back-up roll and the work roll (mm).
The deflection deformation theory of the four-high mill has proven that ∆
Y(
x) is closer to the edge of the roll body, the larger it is. In the area beyond the strip, the rolling force of the roll system is instantly from there to nothing, which will form an effect similar to the cantilever beam, ‘the harmful contact zone’, which will further cause excessive ∆
Y(
x). If the larger ∆
Y(
x) is not adapted and compensated by
δ(
x), it will lead to a sharp increase in the contact pressure between the rolls, forming a pressure peak, until the edge chamfering of the back-up roll makes
δ(
x) larger, so that the contact pressure between the rolls can be reduced. This is the reason why the contact pressure between the rolls exhibits a peak and the peak decreases rapidly to 0 MPa in
Figure 5,
Figure 6,
Figure 7 in
Section 4. In the case of a certain ∆
Y(
x), the smaller the
δ(
x) and the greater the contact pressure between the rolls, which is the reason why the contact pressure between the rolls is distributed in an ‘anti-CVC shape’.
If the back-up roll contour can be designed to enlarge the δ(x) in the ‘harmful contact zone’ and adapt to the change in ∆Y(x), it will weaken the adverse effect of ‘the harmful contact zone’, weaken the contact pressure peak between the rolls, and improve the strip profile control ability. This is the basic concept of the variable contact roller (VCR). At the same time, if δ(x) can offset the influence of roll contour difference, it will weaken the distribution form of the contact pressure between the rolls of ‘anti-CVC shape’, so that the contact pressure between the rolls is uniform.
It is necessary to optimize the back-up roll contour for improving the uneven distribution of the contact pressure between the rolls and further improving the strip profile control ability. A certain proportion of the CVC roll contour is superimposed on the basic VCR roll contour to form the VCRplus roll contour for the 1500 mm CVC roll mill based on the technology of the VCR variable contact backup roll contour (
Figure 9). The roll contour can be realized by arc, trigonometric function, polynomial, etc. According to the characteristics of field grinder, the roll contour design is completed in the form of six polynomials.
Taking the upper back-up roll as an example, the VCRplus roll contour function is shown in Equation (4):
In Equation (4), x is the coordinate of the roll body, and its origin is at the midpoint of the roll body; h(x) is VCRplus roll contour; w’(x) is the anti-symmetric roll contour of the middle part of the upper work roll with a length of 1500 mm; g(x) is the VCR roll contour (Equation (5)); λ is the coefficient. In order to achieve the effect of uniformize the contact pressure between the rolls and avoid affecting the work roll shifting, λ should satisfy 0 < λ < 1, and the specific value of λ is optimized by finite element simulation, is 0.8.
In Equation (5), b1~b5 is the coefficient.
According to the actual situation of the field and the finite element simulation results, the back-up roll contour is optimized. The final VCRplus roll contour design is shown in
Figure 10. The coefficients of VCRplus roll contour in the field grinder are shown in
Table 5.