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Effect of rolling parameters on plate curvature during snake rolling

Effect of rolling parameters on plate curvature during snake

rolling

FU Yao, XIE Shuisheng, XIONG Baiqing, HUANG Guojie, CHENG Lei

State Key Laboratory of Non-ferrous Metals and Processes, General Research Institute for Non-ferrous Metals,

Beijing, 100088, China

Abstract: In order to predict the plate curvature during snake rolling, FE model was constructed based on plane strain assumption. The accuracy of the FE model was verified by the comparison between the plate curvature conducted by FE model and experiment respectively. By using FE model, the effect of offset distance, speed ratio, reduction, roll radius and initial plate thickness on the plate curvature during snake rolling was investigated. The results show that, a proper offsetting distance can efficiently decrease plate curvature, however a excessive offsetting distance will increase plate curvature. A larger speed ratio, reduction will cause a large plate curvature, however a larger roll radius has effect to reduce plate curvature. For plate which undergone a larger reduction and plate with a larger initial thickness always need a larger offset distance to keep the plate the minimum plate curvature, but for a larger roll radius a smaller offset distance is needed.

Keywords: Snake rolling; plate curvature; FE model; offset distance

1 Introduction

The ultra-thickness aluminum alloy plates with high strength and high toughness are very important structural materials which are widely used in industry of aerospace, aviation and vehicle. However, because they are difficult to have sufficient deformation in their core for such a large thickness by conventional rolling method, the ultra-thickness aluminum plates are always produced with poor texture homogeneity and high residual stress which may impair their performance and their service time. Asymmetrical rolling is a special rolling method characterized with different peripheral speed upon upper and lower work rolls[1-3]. Compared to symmetrical rolling (Fig.1(a)), asymmetrical rolling (Fig.1(b)) can produce extra shear strain in the rolled plate[4] which is helpful to strengthen overall deformation and reduce the unhomogeneity of the plate. However, due to mismatch of peripheral speed of work rolls, the plate will experience non-uniform deformation on its top and bottom, this may cause the plate bend toward one of the work rolls. Although, in symmetrical rolling, head up-bending of plate is needed, such as sledge rolling[5], which can prevent plate head down-bending and improve the rate of finished product. However, in asymmetrical rolling, the mismatch of peripheral speed of work rolls will make the plate bend seriously, the plate will be difficult to enter the roll gap of the next pass[6,7], even crack the rolling mills[8,9].

In order to deal with this problem, snake rolling was presented (Fig. 1(c)). Snake rolling was named after its characteristic which introduces an offset distance between upper and lower rolls along the rolling direction into asymmetrical rolling. Compared to asymmetrical rolling, this method has the advantage to control the plate bending to a low level, meanwhile increase the *Corresponding author: Fu Yao, PH.D candidate, Tel: +86135********, Email: fuyao634@https://www.doczj.com/doc/1f16929589.html,

Funded by Chinese 973 Project (No. 2010CB735811)

deformation in the central layer of plate. So, the ultra-thickness aluminum alloy plates produced by snake rolling may have a good texture homogeneity and straightness. However, the snake rolling is very different from asymmetrical rolling, the variation of the offset distance will have a considerable influence on the plate bending. To design the process of snake rolling, it is essential to investigate the influence of offset distance on the plate bending.

Fig.1 Diagram of different rolling methods

(a)Conventional rolling(

u l

ωω

=,

u l

d d

=); (b)Asymmetric rolling(

u l

ωω

<,

u l

d d

=); (c)Snake

rolling(

u l

ωω

<,

u l

d d

=,0

s>)

In the past, a lot of works were carried out to study plate bending in symmetrical and asymmetrical rolling by FEM and experiment.

In Philipp’s study, an implicit two-dimensional finite element model has been employed to simulate the front end bending based on fundamental geometric relations[10]. Knight and Hardy constructed a plane strain finite element model to investigate the influence of reduction on the magnitude of strip curvature during asymmetrical rolling[11]. By this model, Knight and Hardy also analyzed the effect of asymmetrical factors and rolling parameters on the direction and severity of strip curvature[12]. Nia predicted curvature development during asymmetric sheet rolling by using an elastic-plastic arbitrary Lagrangian-Eulerian(ALE) finite element method[13]. By using explicit analysis procedure, Mousavi and Ebrahimi found that increasing the length of the shear zone did not necessarily increase the sheet curvature [14]. Chen used a rigid-plastic model to examine the effect of rolling parameters on the curvature of the rolled beam during V-sectioned and T-sectioned porous beams rolling[15].

However, until now there were few investigations focus on plate bending in snake rolling. In present work, both experiment and FEM were carried out to investigate the effect of rolling parameters on the plate curvature.

Fig.2 Geometrical relations during snake rolling Fig.3 Flow stress of 7150 aluminum alloy against

strain and strain rate at 410℃

2 FE model of snake rolling

In this work, the rolling model has been constructed by using MSC.MARC procedure. The workpiece was modeled using 4-node plane strain full integration elements. The work rolls and roll table were assumed rigid and modeled with rigid circles. Upper and lower work roll diameters were equal. Rolling temperature is assumed to remain constant. In these investigations the boundary conditions and rolling parameters are given in Table 1.

Table 1 Boundary conditions and rolling parameters

Symbol Value Rolling temperature(℃)

T 410 Friction coefficient

μ 0.4 Upper work rolls diameter (mm)

u d 525, 625, 725, 825 Lower work rolls diameter (mm)

l d 525, 625, 725, 825 Angular velocity of upper work roll (rad/s)

u ω 3.05 (fixed) Angular velocity of lower work roll (rad/s)

l ω 3.2, 3.4, 3.6, 3.8 Offset displacement (mm)

s 0, 10, 20, 30, 40, 50, 60 Initial plate thickness (mm)

1h 300, 200 Reduction (mm)

h ? 50, 40, 30, 20 Workpiece length (mm)

L 3000 Roll table diameter (mm)

0d 120 0ω2.1 Friction model

A Coulomb friction model is used which assumes that no relative motion occurs, if the equivalent frictional stress is less than the critical stress, where the critical stress is proportional to the contact pressure. If the equivalent stress is at the critical stress then slip can occur.[13] The shear friction model can be characterized by:

t n σμσ< (stick) and t n t σμσ=-? (slip)

t σ is the tangential (friction) stress, n σ is the normal stress, μ is the friction coefficient, t is

the tangential vector in the direction of the relative velocity: /r r t v v = , in which r v is the relative sliding velocity.

2.2 Material model

During hot rolling the rolled workpiece experiences a series of inhomogenous deformation, so the property of workpiece metal is strain rate, strain and temperature dependant. The effect of temperature on yield stress can be ignored since the plate temperature is assumed to remain constant. Flow stress of 7150 aluminum alloy was acquired by compression deformation on Gleeble-1500D thermal-mechanical simulator with various strain and strain rate. Fig.3 shows the flow stress of 7150 aluminum alloy against plastic strain and strain rate at the temperature of 410℃. Meanwhile, in the elastic region we assume that Young ’s modulus is 31.5GPa and Poisson ’s ratio is 0.33 when temperature is 410℃. The material behavior is assumed isotropic and the density of 7150 aluminum alloy remains constant at 2830kg/m 3.

3 Experiment

A serial of experiments were carried out to verify the constructed FE model. As shown in Fig.4(a), a metal board was fixed on an asymmetrical roll mill, which enable the workpiece enter into the rolls gap with an angle θ. Rotating the Fig.4(a) clockwise with an angle θ then Fig.4(b) is acquired, we find that rolling method shown in Fig4.(b) has the same effect of snake rolling. So, by using the rolling method shown in Fig.4(a) we can realize snake rolling on an asymmetrical rolling mill. During the experiment, we controlled the offset distance by adapting the entering angle of the workpieces.

Fig.4 Rolling experiment configuration

(a)before rotation; (b)after rotation

Fig.5 shows the plate bending under different rolling parameters. Fig.5(a-c) show the shape of the plates undergone symmetrical rolling process with different offset distances. It is very clear that the offset distance has an effect of down-bending on the plate, with the increasing of offset distance the plate bends more seriously. Fig.5(d-f) show the shape of the plates undergone snake rolling with different offset distances. It can be seen that, the offset distance has a positive effect to depress the plate bending.

Fig.5 Plate bending under different rolling parameters

(a)v2/v1=1.0,s=0mm; (b)v2/v1=1.0,s=9.79mm; (c)v2/v1=1.0,s=25mm;

(d)v2/v1=1.3,s=0mm; (e)v2/v1=1.3,s=9.79mm; (f)v2/v1=1.3,s=25mm

The comparison between the plate curvature conducted by FEM and experiment is shown in Fig.6, (a) and (b) represents reduction is 0.8mm and 1.0mm respectively. It is found that, the FEM results can mainly reflect the variation of the experimental results, they all decrease at first and they increase with the increasing of offset distance. The largest difference between FEM results and experimental results appears at 10mm offset distance when reduction is 0.8mm, which is no more than 26% of the experimental result. The main reason cause that difference is the assumption of constant temperature in the FE model. Because the FE model was constructed to predict ultra-thickness plate curvature during snake rolling, in which the temperature has little influence on the ultimate plate curvature but it is not the case for the small thickness plate. So, the FE model has a better accuracy to predict large thickness plate curvature than small thickness one.

Fig.6 Comparison between the FEM results and experimental results

(a)Δh=0.8mm; (b)Δh=1.0mm 4 Results and discussion

A series of FE models have been computed and corresponding results are shown in graphical form in Figs.5-20. A total 144 models have been run, considering the influence of offsetting distance on plate curvature with different speed ratios, reduction and radius of rolls. Two typical workpiece thicknesses were selected to investigate their effect on curvature. All the rolling parameters involved are given in Table 1.

Fig.7 Variation of plate curvature with offset distance for different speed ratio

(a) 1200h =mm; (b) 1300h =mm

Fig.7 shows the effect of offset distance on the plate curvature for different speed ratio, for (a) and (b) the initial plate thickness is 200mm and 300mm respectively. It is observed that, for both two thicknesses, with increasing of offset distance the plate curvature decrease at first and then increase. This means a suitable offset distance can effectively depress the plate bending, but if the offset distance exceed a certain value it will cause a negative effect. The “right ” offset distance is different for different speed ratio, initial plate thickness, reduction and roll radius. A larger speed ratio always needs a larger offset distance to ensure the plate at the least curvature. Also, compared to the smaller initial plate thickness, the larger initial plate thickness needs a larger offset distance to enable the plate at the least bending. A higher speed ratio always produces a larger plate curvature. Comparing (a) and (b), for a same speed ratio and offset distance, a smaller initial plate thickness always produces a larger plate curvature.

Fig.8 Variation of plate curvature with offset distance for different reduction

(a) 1200h =mm; (b) 1300h =mm Fig.8 illustrates the variation of plate curvature with offset distance for different reduction. A bigger reduction always produces a higher plate curvature. Also with the increasing of reduction, the “right ” offset distance decreases, meanwhile the least plate curvature increases. Comparing (a) and (b), it is found that plate with a larger initial thickness will produce lower curvature than the plate with a smaller initial thickness.

Fig.9 Variation of plate curvature with offset distance for different roll radius

(a) 1200h =mm; (b) 1300h =mm Fig.9 shows the variation of plate curvature with offset distance for different roll radius, for (a) and (b), the initial plate thickness is 200mm and 300mm respectively. A larger roll radius

results in lower degree of plate curvature, also a larger roll radius needs a smaller offset distance to keep the minimum plate curvature.

5 Conclusion

The plate curvature conducted by FE model is agree with that conducted by experiment well, the largest difference between them is no more than 26% of the experimental results. A proper offsetting distance can efficiently decrease plate curvature, however a excessive offsetting distance will increase curvature. A larger speed ratio, reduction will cause a large plate curvature, however a larger roll radius has effect to reduce plate curvature. For plate which undergone a larger reduction and plate with a larger initial thickness always need a larger offset distance to keep the plate the minimum plate curvature, but for a larger roll radius a smaller offset distance is needed.

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修改说明:

1)在结论中指出了模型的具体精度;

2)在文章的第三部分添加了内容,说明了误差产生的原因,指出了模型的局限性及使用范围;

3)对图4进行了修改,使实验方法的表现更为直观。

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