J. Cent. South Univ. (2012) 19: 1226-1233

DOI: 10.1007/s11771-012-1133-z

Roll shifting strategy with varying stroke and step in hot strip mill

LI Wei-gang(李维刚)^1,2, LIU Xiang-hua(刘相华)³, GUO Zhao-hui(郭朝晖)^1,2, HUANG Jian-ping(黄建平)⁴

1. College of Information Science and Engineering, Northeastern University, Shenyang 110819, China;

2. Automation Division, Baosteel Research Institute, Baoshan Iron & Steel Co., Ltd., Shanghai 201900, China;

3. Research Institute of Science and Technology, Northeastern University, Shenyang 110819, China;

4. Hot Strip Mill Plant, Baoshan Iron & Steel Co., Ltd., Shanghai 201900, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: A new roll shifting strategy with varying stroke and varying step was investigated. Two characteristic parameters including cat ear height and gap contour smoothness were introduced to assess the effect of shifting strategy on roll wear, and the relation between characteristic parameters and shifting strategy was established. Both varying stroke and varying step can reduce cat ear height and gap contour smoothness, so the shifting strategy with varying stroke and varying step is better than the one with either varying stroke or varying step. Based on the effect of shifting control parameters on characteristic parameters of roll wear, the selection principle of these shifting control parameters was gained. A case study was conducted to validate the proposed roll shifting strategy, reducing uncontrollable quartic loading gap contour, improving strip profile and extending rolling length of a rolling campaign.

Key words: hot rolling; work roll shifting; varying step; roll wear; roll contour; schedule free rolling

1 Introduction

Schedule free rolling (SFR) has broken restrictions on the rolling schedule in hot rolling and strengthened the connection between continuous casting and hot rolling [1-2]. So, it can save energy, increase productivity and reduce product costs. At the same time, SFR can meet flexible market demand, thus it has become a goal pursued by many manufacturers. Shape control, as one of the key technologies of SFR, is always the research focus and difficult point. However, it remains a major bottleneck in the implementation of SFR [3-4]. Limits of SFR in terms of rolls contour mainly come from roll wear [5]. Work roll wear imposes strong restrictions on rolling schedule. Especially, the effect of increased wear in the strip edge zones leads to anomalies in work roll contours and subsequently in strip contours [6]. SFR in a mill without specific tools to control the roll wear evolution will lead to a contour with pronounced high spots in the case of same-width rolling campaign or an irregular contour shape in the case of mix cross rolling campaign. The work roll shifting system is presently commonly used to avoid these contour problems [7-9].

To reduce undesired strip contours, much attention was paid to shape optimized shifting strategy for work roll shifting mills with conventional flat rolls. The shifting pattern was established to maintain the uniform roll wear [10]. The amount of rolling at the same width and the maximum amount of the narrow-to-wide transition in width according to the rolling history were calculated in the present work and an optimal shifting pattern was determined for the rolling campaign of stainless steel. A roll shift method was proposed by prediction of roll profile [11]. The most suitable roll shifting position, which provided the smoothest gap profile within the contact area, was determined. A cyclic fixed step method was adopted to determine the optimum shifting step [12]. Its limitation lays only in adjusting shifting step to optimize shifting strategy. In addition, a roll shifting strategy with varying stroke was presented [13]; also the roll shifting methods were studied [14-15]. However, these studies either are not for conventional flat work rolls, or rarely involve roll shifting strategy with varying stroke and varying step.

In this work, targeting at these existing problems, a new roll shifting strategy with varying stroke and varying step is proposed, which is helpful to schedule free rolling.

2 Relation between shifting strategy and roll wear

2.1 Work roll wear model

Roll wear calculation usually uses the slice method [16-17], which divides a work roll into many small slices. In a rolling process, roll wear w_ij generated by the i-th strip on the j-th slice of work roll can be expressed as

                (1)

where a_w, b_w, α and β are model parameters; D_WR is the working roll diameter; A_j is the impact factor of rolling force; B is the impacting factor of deformation geometry zone; C is the impacting factor of strip length.

Three impacting factors can be expressed as

                             (2)

                             (3)

                          (4)

where b_s is the strip width; l_d is the projected contact length; H_R is the strip hardness; h_in is the strip entry thickness; h_out is the strip exit thickness; L is the strip length; f_s is the forward slip; P_j is a function of uneven wear, which has different formulas in different roll regions (Fig. 1).

The formulas of P_j in different regions on operating side of a work roll are given as follows

1) Central region, 0≤ x_w≤ b_s/2–d_w0

2) Edge region 1, b_s/2-d_w0w≤b_s/2 –d_w1

3) Edge region 2, b_s/2–d_w1w≤b_s/2+d_w2

4) Edge region 3, b_s/2+d_w2w≤b_s/2+d_w3

5) Non-contact region, x_w>b_s/2+d_w3

where x_w is the coordinate of the j-th slice relative to strip center; f_r is the rolling force; d_w0, d_w1, d_w2 and d_w3 are region length; k_w1 and k_w2 are gain coefficients of roll edge wear distribution.

The coordinate x_w is given as

                     (5)

where d_x is the length of wear slices; l_wr is the work roll length; S_i is the shifting position of the i-th strip. Equation (5) indicates that the shifting position S_i affects the roll axial distribution of both A_j and w_ij.

Table 1 lists the units of physical and model parameters, and the remaining ones are dimensionless.

2.2 Characteristic parameters of roll wear

In a rolling campaign, the accumulative wear w_j^k of the j-th slice after rolling the k-th strip is

                         (6)

where p is the strip number of a rolling campaign.

A characteristic parameter, namely cat ear height (Fig. 2), is introduced to assess the effect of shifting strategy on wear contour, which is defined as

                (7)

where is the cat ear height after rolling the k-th strip; m is the number of wear slices in roll axial direction; is the wear in the center of rolled strip.

Fig. 1 Wear regions in roll axial direction

Table 1 Units of physical and model parameters

Fig. 2 Characteristic parameter of cat ear height of wear contour

Work roll shifting can smooth roll wear contour and reduce cat ear height, so the smaller the cat ear height, the better the roll shifting strategy.

The wear contour of top work roll and bottom work roll is gained by roll wear model. And then, the gap contour in the contact area between work roll and the rolled strip can be obtained. Another characteristic parameter is introduced to assess the effect of roll shifting strategy on gap contour in the contact area, namely gap contour smoothness.

Take all the points from gap contour in the contact area, and fit the curve with the piecewise polynomial:

        (8)

Define gap contour smoothness of the k-th strip as

                         (9)

where x is the coordinate relative to strip center; y_s and  are actual and fitting gap contour values, respectively; b_s is the strip width; ε is the proportional coefficient, usually 40%.

Work roll shifting can smooth gap wear contour and reduce gap contour smoothness, so the smaller the gap contour smoothness, the better the roll shifting strategy.

3 A new roll shifting strategy with varying stroke and varying step

3.1 Recursive algorithm of roll shifting strategy

A recursive algorithm is developed to gain roll shifting strategy with varying stroke and varying step. It can get shifting position of all strips in a roll campaign.

1) The first phase of a rolling campaign

Set the shifting position of the first strip:

S₁=t_s                                                           (10)

From the second strip, firstly update shifting step:

When S_i-1+t_s>M-dt or S_i-1+t_s

set t_s=-t_s;

When |S_i-1+t_s|≤M-dt and S_i-1>ρ,

set t_s=t_s+dt;

When |S_i-1+t_s|≤M-dt and S_i-1<-ρ,

set t_s=t_s–dt.

Secondly calculate shifting position:

                    (11)

where t_s is the basic shifting step; dt is the shifting step increment; S_i is the shifting position of the i-th strip; N is the stroke reduction starting point; M is the maximum of shifting stroke; ρ is a small positive number.

2) The second phase of a rolling campaign

Start from the (N+1)-th strip, firstly update shifting step:

When S_i-1+t_s>k_S(i)-dt or S_i-1+t_sS(i),

set t_s =-t_s;

When |S_i-1+t_s|≤k_S(i)-dt and S_i-1>ρ,

set t_s =t_s +dt;

When |S_i-1+t_s|≤k_S(i)-dt and S_i-1<-ρ,

set t_s =t_s–dt.

There is k_S(i)=M–M·A·(i-N).

Secondly, calculate the shifting position:

                     (12)

where A is the shifting stroke reduction rate; M and p are the known parameters for a specific rolling campaign; t_s, dt, N and A are shifting control parameters, which decide roll shifting strategy.

When dt>0, the algorithm gets shifting strategy with varying step; when N

0, the algorithm gets shifting strategy with varying stroke. Only when dt>0 and N

0, the algorithm gets shifting strategy with varying stroke and varying step.

3.2 Comparison of four types of shifting strategy

Four types of shifting strategy can be gained by limiting the range of shifting control parameters:

1) When dt=0 and A=0, shifting strategy with fixed stroke and fixed step is obtained.

2) When dt=0 and A>0, shifting strategy with varying stroke and fixed step is obtained.

3) When dt>0 and A=0, shifting strategy with fixed stroke and varying step is obtained.

4) When dt>0 and A>0, shifting strategy with varying stroke and varying step is obtained.

Two characteristic parameters are compared in rolling process for four types of shifting strategy by numerical simulation. Take a typical same width rolling campaign as example. There are 102 strips in the rolling campaign, p=102. The maximum of shifting stroke is 200 mm, M=200 mm.

Four sets of shifting control parameters are listed in Table 2, and the corresponding shifting strategy is shown in Fig. 3. Four shifting strategies need six steps up to the maximum of shifting stroke. For the shifting strategy with varying stroke, shifting stroke in the end of a rolling campaign is set to be a half of the maximum stroke:

 M-M·A·(p-N)=M/2

that is

A=0.5/(p-N)

Table 2 Control parameters of four types of shifting strategy

The corresponding characteristic parameters are shown in Figs. 4 and 5, including cat ear height and gap contour smoothness of all strips.

Figure 4 indicates that the shifting strategy with varying stroke can gain smaller cat ear height than the one with fixed stroke, and the shifting strategy with varying step can gain smaller cat ear height than the one with fixed step. Varying step is more effective than varying stroke in reducing cat ear height.

Figure 5 indicates that the shifting strategy with varying stroke can gain smaller gap contour smoothness than the one with fixed stroke, and the shifting strategy with varying step can gain smaller gap contour smoothness than the one with fixed step. Varying stroke is more effective than varying step in reducing gap contour smoothness.

Fig. 3 Comparison of four types of roll shifting strategy: (a) Shifting strategy with fixed stroke and fixed step; (b) Shifting strategy with varying stroke and fixed step; (c) Shifting strategy with fixed stroke and varying step; (d) Shifting strategy with varying stroke and varying step

Fig. 4 Cat ear height of four types of shifting strategy

Fig. 5 Gap contour smoothness of four types of shifting strategy

Based on the above analyses, it is concluded that both varying stroke and varying step can reduce cat ear height and gap contour smoothness, so the shifting strategy with varying stroke and varying step is better than the one with either varying stroke or varying step.

4 Effect of shifting control parameters on characteristic parameters of roll wear

The cat ear height in the end of a rolling campaign and the average gap contour smoothness of all strips in a rolling campaign can be taken as two evaluation factors to assess the integrated effect of roll shifting strategy on the roll wear. Two evaluation factors are as follows:

                                   (13)

                          (14)

The effect of shifting control parameters on two evaluation factors is analyzed to provide the optimal selection of shifting control parameters.

To make good use of shifting stroke, suppose n steps up to the maximum of shifting stroke, where n is the quarter cyclic shifting number. The various shifting steps are gained by the recursive algorithm of shifting strategy, and they are t_s, t_s+dt, t_s+2dt, …, t_s+(n-1)dt. Then there is

t_s+(t_s+dt)+(t_s+2dt)+…+ [t_s+(n-1)dt]=M

That is

                            (15)

Equation (15) indicates that shifting step increment dt can be converted to quarter cyclic shifting number n.

4.1 Effect of basic shifting step

Set quarter cyclic shifting number to be 6, stroke reduction starting point 30, stroke reduction rate 0.006 9, basic shifting step from 5 mm to 50 mm, and then the effect of basic shifting step on two evaluation factors is gained in Fig. 6. Basic shifting step significantly affects two evaluation factors. With the increase of basic shifting step, cat ear height decreases from 3.3 μm to 2.7 μm, and then increases from 2.7 μm to 4.5 μm. Gap contour smoothness increases linearly from 10.6 μm to 25.4 μm. Figure 6 indicates that two good evaluation factors are gained when basic shifting step is equal to 10 mm.

Fig. 6 Effect of basic shifting step on characteristic parameters

4.2 Effect of quarter cyclic shifting number

Set basic shifting step to be 10 mm, stroke reduction starting point 24, stroke reduction rate 0.006 4, quarter cyclic shifting number from 4 to 8, and then the effect of quarter cyclic shifting number on two evaluation factors is gained in Fig. 7. With the increase of quarter cyclic shifting number, cat ear height sharply decreases from 4.9 μm to 2.7 μm, and then increases from 2.7 μm to   3.8 μm. Gap contour smoothness increases slowly from 9.1 μm to 15.4 μm. Figure 7 indicates that two good evaluation factors are gained when quarter cyclic shifting number is equal to 6.

Fig. 7 Effect of quarter cyclic shifting number on characteristic parameters

4.3 Effect of stroke reduction starting point

Set basic shifting step to be 10 mm, quarter cyclic shifting number 6, stroke reduction rate 0.006 8, stroke reduction starting point from 12 to 52, and then the effect of stroke reduction starting point on two evaluation factors is gained in Fig. 8. With the increase of stroke reduction starting point, cat ear height sharply decreases from 3.7 μm to 2.73 μm, and then slowly increases from

Fig. 8 Effect of stroke reduction starting point on characteristic parameters

2.73 μm to 2.81 μm. Gap contour smoothness increases from 9.8 μm to 13.4 μm. Therefore, two good evaluation factors can be gained when stroke reduction starting point is equal to 24.

4.4 Effect of shifting stroke reduction rate

Set basic shifting step to be 10 mm, quarter cyclic shifting number 6, stroke reduction starting point 24, shifting stroke reduction rate from 0 to 0.007 7, and then the effect of shifting stroke reduction rate on two evaluation factors is gained in Fig. 9. With the increase of stroke reduction rate, cat ear height slowly changes from 2.5 μm to 2.7 μm, and sharply increases from 2.7 μm to 3.9 μm. Gap contour smoothness sharply decreases from 19.8 μm to 12.3 μm, and then slowly decreases from 12.3 μm to 9.7 μm. Therefore, two good evaluation factors can be gained when stroke reduction starting point varies from 0.005 5 to 0.006 3.

Fig. 9 Effect of stroke reduction rate on characteristic parameters

4.5 Optimal selection of shifting control parameters

Combined with simulation analysis of a large number of rolling campaigns, the selection ranges of optimal shifting control parameters are listed in Table 3.

Table 3 Selection range of optimal shifting control parameters

5 Application example and discussion

5.1 Practical example

Take the above rolling campaign as an application case (p=102, M=200 mm). According to the simulation analysis, a set of optimal shifting control parameters are listed as follows: n=6, N=24, t_s=10 mm, and A=0.006 4. The corresponding shifting strategy is given in Fig. 10.

Fig. 10 Roll shifting position and quartic loading gap profile

5.2 Application effect

The optimal roll shifting strategy was applied to practical production in a hot strip mill. Strip flatness value stays in the range of (0±35) IU (1 IU=1 mm/    100 m=10^-5), and does not deteriorate in the later rolling stage. Strip edge drop value is less than 30 μm, and the trend keeps steady with the advance of a rolling campaign. Compared with traditional shifting strategy, the optimal shifting strategy with varying stroke and varying step can gain better strip profile and extend rolling length of a rolling campaign.

5.3 Discussion

The relation between quartic loading gap profiles and shifting positions of all strips is analyzed. Gap contour in the contact area is obtained from wear contour of the upper and lower work roll, and the gap contour curve is fitted with the polynomial equation [18]:

,           (16)

Get the coefficients a₂, a₄, and then calculate quartic loading gap profile:

                           (17)

Figure 10 gives the gained quartic loading gap profile, which is related to strip edge wave or composite wave [13]. Figure 10 indicates that quartic loading gap profile significantly increases with the increase of roll shifting positions. Varying stroke makes the maximum of shifting positions in the following phase of a rolling campaign smaller than the one in the initial phase, and varying step makes the most of roll shifting positions distributed around zero. Both of them can reduce the effect of shifting positions on loading gap after roll wear accumulating to a certain extent, and reduce uncontrollable quartic loading gap profiles. Therefore, the shifting strategy with varying stroke and varying step is effective in reducing quartic loading gap profile.

In the on-line control of work roll contour, roll thermal contour can be somehow controlled by conventional means like work roll bending, as thermal contour is smooth enough due to heat exchange between roll body centre and edges. But roll wear is not. To some extent, this work provides some control means for roll wear and reduces some restrictions on rolling schedule.

6 Conclusions

1) A new roll shifting strategy with varying stroke and varying step is presented, and a recursive algorithm of establishing the new shifting strategy is proposed.

2) Characteristic parameters of cat ear height and gap contour smoothness are introduced to assess the effect of shifting strategy on roll wear. Both varying stroke and varying step can reduce cat ear height and gap contour smoothness, so the shifting strategy with varying stroke and varying step is better than the one with either varying stroke or varying step.

3) A case study is conducted to validate the proposed shifting strategy, which can improve strip profile and extend rolling length of a rolling campaign. Analysis indicates that both varying stroke and varying step can reduce uncontrollable quartic loading gap profile.

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(Edited by YANG Bing)

Foundation item: Project(50974039) supported by the National Natural Science Foundation of China

Received date: 2011-05-24; Accepted date: 2011-09-23

Corresponding author: LI Wei-gang, PhD Candidate; Tel: +86-21-26641062; E-mail: liweigang@baosteel.com