Abstract: Waviness in thick plate rolling is one of the common plate shape defects. During the thick plate rolling production process of Baosteel Co., Ltd., plate waviness often occurs. The most common varieties and specifications include low-temperature controlled rolling steel, B furnace steel, thin plates, etc. Based on its characteristics and combined with the actual production situation of the rolling line, it is known that the temperature difference between the upper and lower surfaces of the plate, uneven temperature distribution inside and outside, unreasonable setting of pass procedures, excessive setting of rolling speed, and inconsistent friction coefficients between the upper and lower surfaces during rolling are the main causes of plate waviness. By deeply analyzing these causes, finding relevant theoretical basis, and combining the characteristics of each process in the on-site production, a complete process system is formulated to effectively suppress the problem of plate waviness in rolling production and reduce the occurrence of abnormal rolling. 

Head warping in thick plate rolling process 

Plate shape refers to the straightness of the steel plate. Poor plate shape occurs when it is in the middle part of the steel plate and is called wavy shape, and when it is at the head or tail, it is called warping. Warping at the head is a common phenomenon during the rolling process of thick plates. The main reason for this is the uneven distribution of internal stress during the steel plate rolling process or the asymmetric deformation generated during the metal flow. Head warping of the steel plate can be divided into two situations: namely, warping head and folding head. Warping head refers to the upward bending of the steel plate head, and folding head refers to the downward bending. If the warping at the head is too large, it will affect the entry of the steel plate into the rolling mill in the next process, and in severe cases, it may even cause abnormal rolling and prevent the rolling process from continuing. Head folding of the steel plate will cause folding defects in the steel plate, reducing the yield rate; Head warping of the steel plate will cause the steel plate to jump during the transportation on the roller track, affecting the rolling rhythm; When the warping is severe, the steel plate head will penetrate the middle of the transportation roller track; Warping of the head of the steel plate increases the difficulty of the steel plate's entry into the rolling mill.

For the representation of the degree of plate shape warping (λ), there is currently no unified regulation. Generally, the curvature of the warping part is used, or the degree of warping can be expressed by the ratio of the bending height to the bending chord length. In the references, it is represented by the product of the height of the warping section and the curvature of the warping section, as shown in Figure 1. Picture

λ = ρH (1) 

In the formula, H represents the height of the warpage section relative to the straight section, and ρ represents the curvature of the arc of the warpage section.

In Equation (1), when the following situations occur, the degree of warpage of the steel plate can be clearly indicated:

① If the warpage height is the same but the curvature is different, then the greater the curvature, the greater the warpage degree;

② If the warpage height is different but the curvature is the same, then the greater the height, the greater the warpage degree;

③ If both the curvature and the warpage height are different, then the greater the product of the two, the greater the warpage degree.

In the 5m rolling mill production of the thick plate department of Baosteel, the steel plates prone to warping are mainly low-temperature controlled-rolled plates, thin plates, and B furnace heated plates (Table 1). Low-temperature controlled-rolled plates are those that require two or more stages of rolling and need to ensure the opening or final rolling temperature during the controlled-rolling stage. Controlled rolling is the main means to strengthen the steel plate, improve the steel plate performance, and refine the grain structure. The thin plates in the thick plate department refer to steel plates with a target thickness of less than 10mm, mainly including high-strength ship plates or high-strength engineering machinery structural steel. B furnace is a car bottom type furnace, mainly used for heating short-length billets. The common feature of B furnace heated billets is that the billet specifications are small and the length-to-width ratio of the billet is small. Picture

 

 

2. Analysis of the Causes of Steel Plate Buckling at the Rivet Head 

Any asymmetrical deformation conditions during the rolling process will cause changes in the internal stress state of the steel plate. When the uneven distribution of internal stress exceeds the limit that the steel plate can withstand, the steel plate will deform. The force distribution at the head of the steel plate during the rolling process is the most complex, mainly involving three-dimensional stress distribution. Therefore, it is most prone to cause stress imbalance and result in warping at the head of the steel plate. There are many asymmetrical factors that cause the warping of the steel plate, such as uneven heating temperatures on the upper and lower surfaces of the billet, uneven heating temperatures inside and outside the billet, temperature differences between the upper and lower surfaces of the steel plate due to different heat dissipation conditions during transportation, insufficient re-heating of the steel plate due to intermediate cooling before the second stage of rolling before waiting for temperature adjustment, unequal linear speeds of the upper and lower rolls, inconsistency in the height of the rolling line and the center height of the steel plate inlet, and different friction conditions on the surfaces of the upper and lower rolls, all of which will cause asymmetrical rolling conditions during the rolling process, resulting in warping at the head of the steel plate. In theory, the warping at the head of the steel plate will run through the entire length of the steel plate, but it is more obvious when the steel plate is shorter, and has a greater impact on the rolling process.

2.1. The influence of uneven steel plate temperature 

2.1.1  The impact of inconsistent temperatures on the upper and lower surfaces 

The heat absorption and heat transfer conditions of the slab during its stay in the heating furnace are different. The differences in the heat dissipation conditions of the upper and lower surfaces of the slab during its transportation after leaving the furnace, as well as the uneven temperature drop during the holding stage before controlled rolling, all cause a temperature difference between the upper and lower layers of the slab during rolling. The deformation resistance of the upper layer with a higher temperature is less than that of the lower layer with a lower temperature. This results in inconsistent extension rates, pre-sliding, and outlet flow velocities of the metal particles on the upper and lower surfaces, ultimately causing the steel plate to warp. If the upper surface temperature is higher than the lower surface temperature, a "knobbed head" phenomenon occurs; if the lower surface temperature is higher than the upper surface temperature, a "waved head" phenomenon occurs, as shown in Figure 2. Picture

2.1.2  The Impact of Inconsistent Internal and External Temperatures 

The inconsistency of internal and external temperatures can be divided into two situations: the external temperature is higher than the internal temperature, and the internal temperature is lower than the external temperature. The former usually occurs when the rolled piece comes out of the heating furnace, due to insufficient heating; the latter usually occurs during the rolling process, due to the cooling effect of the descaling water on the rolled piece, heat transfer with the rolls and the conveyor belt, contact with the air, and the short time of intermediate cooling and rewarming, causing the surface temperature to be lower than the internal temperature. Figure 3 shows the influence of the inconsistency of internal and external temperatures on the warpage of the steel plate head (the shaded part represents high temperature, and the head is lifted when it is low temperature). When the external temperature of the rolled piece is high and the internal temperature is low, that is, the shaded part represents low temperature, the distance from the upper surface of the rolled piece to the low-temperature part is greater than the distance from the lower surface of the rolled piece to the low-temperature part, that is, h1 > h2. During the rolling process, the high-temperature part is more prone to deformation, and the proportion of the high-temperature part being pressed down is greater than that of the low-temperature part. Thus, the upper part of the rolled piece is pressed down more, according to the law of volume conservation, the extension of the upper part of the rolled piece is greater than that of the lower part, so the rolled piece bends downward, and vice versa. Picture

Picture

2.2  The impact of inconsistent heights between the rolling line and the center height of the steel plate inlet 

When the center height of the steel plate inlet (half of the steel plate reduction amount (Δh)) is consistent with the height of the rolling line (the height difference (δ) between the upper roller surface of the frame roller and the upper roller surface of the working roller), the steel plate can be ensured to be levelly entered and the steel plate outlet can be straight. If the height of the rolling line and the center height of the steel plate inlet are not consistent, it will cause the steel plate to tiltly enter, and it may cause the head of the steel plate to bend.

When δ < Δh/2, the steel plate enters with a downward inclination. During the entry process, the steel plate first contacts the upper roller surface, and the upper roller force causes the head of the steel plate to deviate downward, forming a forced inclined entry. At this time, the steel plate also receives an upward supporting force from the frame roller, and this force causes the pressure force in the contact area of the upper surface of the steel plate to move towards the inlet direction. These forces form an upward bending moment in the deformed area of the steel plate, causing the head of the steel plate to bend upward after exiting the die gap, as shown in Figure 4(a); at the same time, the movement of the force application point of the combined force of the upper and lower rollers will also cause the driving torque of the upper roller to increase relatively and the driving torque of the lower roller to decrease relatively.

When δ > Δh/2, the situation is opposite. The center of the steel plate is lower than the center of the die gap, which is equivalent to the steel plate climbing-in entry. After exiting the die gap, the head of the steel plate bends downward, as shown in Figure 4(b). When climbing-in entry occurs, the reduction amount of the upper working roller is greater than that of the lower working roller, causing the elongation of the upper surface of the slab to be greater than that of the lower surface of the slab, resulting in the upper surface speed of the slab at the die outlet being greater than the lower surface speed, thereby forming the slab to bend downward after leaving the die, that is, the head-down phenomenon.

2.3, The influence of asymmetric friction conditions 

The oxide scale on the surface of the slab will affect the friction coefficient. If the oxide scale on the upper and lower surfaces cannot be completely removed, it will affect the steel bite and cause phenomena such as front sliding and back sliding during stable rolling. Warping of the steel plate occurs on the side where the contact friction between the roller and the steel plate is small. This is because there will be a phenomenon of back sliding. The torque on this side of the steel plate is small, and the plastic deformation and the flow of metal particles are significantly inhibited, thus causing the head of the steel plate to翘 up or bend downward. This is particularly obvious when rolling the steel slab of furnace B. If the slab is heated in the heating furnace for too long for some reason， the secondary oxide scale produced is not easily removed during descaling， and the friction coefficient during steel rolling between the steel plate and the roller will decrease， resulting in warping.

2. 4. The influence of rolling speed on head warping 

The deformation resistance increases with the increase of the deformation rate, mainly because as the deformation rate increases, the movement speed of dislocations accelerates, and a greater shear stress is required, which leads to an increase in the deformation resistance. Additionally, from the perspective of the contradiction between hardening and softening during plastic deformation, when the deformation rate increases, there is not enough time to complete the plastic deformation, shortening the time for the metal to recover and undergo recrystallization softening, making it insufficient and thus exacerbating the processing hardening and increasing the metal's deformation resistance. Besides considering the influence of the deformation rate on the deformation resistance, thermal effects must also be taken into account. During plastic deformation, the energy absorbed by the object will be converted into elastic deformation potential energy and plastic deformation heat energy. This phenomenon where the deformation energy in the plastic deformation process is converted into heat energy is known as the thermal effect. When the deformation rate is high, sometimes due to the significant thermal effect, the metal temperature rises, which also has an impact on the deformation resistance. Moreover, the deformation rate may also change the friction coefficient, affecting the metal's deformation resistance. The combined effect of these factors causes the deformation resistance to increase with the increase of the deformation rate. However, the degree of increase in deformation resistance will vary significantly in different temperature ranges. 

The rolling speed model is set as the process of biting the steel, applying load for acceleration, decelerating to a low speed and then throwing the steel. The steel plates in the first few rolling passes are shorter, and the rolling speed does not reach the maximum speed before throwing the steel. Therefore, during deceleration, the deformation rate will change, causing uneven longitudinal stress distribution in the steel plate, resulting in warping of the steel plate, as shown in Figure 5. Picture

 

 

3. Solution for the problem of steel plates warping 

3.1. Ensure uniform temperature 

3.1.1. Reasonable planning and arrangement 

The billets of Baosteel thick plates mainly include continuous casting billets and purchased billets. The commonly used plate thickness is usually between 120 and 400 mm. During the planning arrangement, it is necessary to place billets of the same thickness as much as possible within each plan to facilitate the heating control of the furnace and avoid excessive temperature fluctuations in the furnace chamber of the transition section of the plan. During loading, when changing the thickness of the plates, an empty furnace should be placed. The length of the empty furnace should be appropriate to ensure a smooth transition of the target heating temperature for plates of different thicknesses, thus ensuring the uniformity of the heating temperature.

3.1.2 Improvement of Plate Heating Temperature Control Strategy 

To compensate for the temperature gradient formed during the transportation and rolling of the slab, where the surface temperature of the slab is lower than the central temperature due to rapid heat dissipation on the surface, it is necessary to increase the temperature difference between the upper surface and the center temperature during the slab heating process. During the heating process, the heating temperature of the second heating section in the continuous heating furnace should be reduced to reserve the temperature rise space for the subsequent equalizing stage. In the equalizing stage, the furnace temperature should be increased, so that the temperature on the upper surface of the slab can be rapidly raised, while the central temperature increases little, thereby creating a certain temperature difference between the surface and the center, and forming a certain temperature gradient.

3.1.3 Ensure the uniformity of the slab heating temperature in furnace B 

During the steel heating process in Furnace B, due to poor sealing at the furnace tail and the furnace door, uneven lateral temperatures will occur when the steel plate near the furnace door is heated. The temperature on one side near the furnace door or the furnace tail is lower, while the temperature on the other side is higher. This will result in warping during the rolling process due to the uneven temperature. Therefore, during the heating process of Furnace B, the heating time should be appropriately extended to ensure uniform heating, and the temperature should be appropriately increased just before unloading to make up for the slow steel extraction in Furnace B.

3.1.4 Ensure temperature uniformity during the holding process 

The intermediate billets in the warm-temperature process do not allow for intermediate cooling for steel plates with a small target thickness; instead, they should be cooled by air cooling. For steel plates with a target thickness greater than a certain value, it is recommended to adopt a batch rolling method, so that the steel plates have sufficient re-warming time, ensuring a relatively uniform temperature and avoiding the occurrence of uneven extension of the upper and lower layers during rolling due to temperature differences.

3.2 Reasonably set the rolling speed 

The setting of the rolling speed in the rolling model includes the biting steel speed, biting steel acceleration, and the maximum rolling speed. For steel types and specifications prone to head-up, the biting steel speed, acceleration, and maximum rolling speed should be appropriately reduced. However, the reduction of the rolling speed should be based on setting a minimum speed limit without damaging the oil film bearings.

3. 3 Control of Head-Up by Using SKI Coefficient 

The adjustment of the SKI coefficient can be used to control the plate shape at the head of the billet. When the speed of the upper roller is greater than that of the lower roller, the plate head sinks; when the speed of the upper roller is less than that of the lower roller, the plate head rises. The movement of the steel plate driven by the rollers is mainly accomplished through friction. The magnitude of the friction force is proportional to the normal pressure between the roller and the steel plate. During the first few rolling passes, due to the large rolling force and absolute reduction amount, the friction force between the steel plate and the roller is relatively large. A large difference in roller speeds can be used to control the warping of the steel plate. As the rolling progresses, the absolute reduction amount and rolling force of the steel plate gradually decrease. A large SKI value will cause an excessive difference in roller speeds between the upper and lower rollers, resulting in a sliding phenomenon on the surface of the steel plate in contact with the upper roller, and the upper part of the steel plate extends less than the lower part. This will not achieve the purpose of controlling the head-up phenomenon.

3.4 Appropriately reduce the rolling load 

On the premise of meeting the process requirements, reasonably determine the absolute reduction amount and reduction rate for each pass. Different reduction amounts will cause the steel plate to bend in different directions. Controlling the reduction amount within a certain range is beneficial to reducing the warpage degree. However, a too small reduction range is not conducive to exerting the potential of the equipment and fully utilizing the ability of metal deformation, prolonging the rolling time of a single steel plate, and reducing the rolling speed. This method is only suitable for small-batch steel plates that are prone to warping.

3.5 Increase the elevation of the rolling line 

According to the theory of rolling process, under the condition of uniform and symmetrical other factors, the most ideal height of the rolling line is half of the reduction amount of each pass. At this time, the rolled piece can be ensured to be levelly engaged and straight after rolling. During the rolling process, if the head of the steel plate becomes warped, the height of the rolling line can be raised to suppress it. Especially when rolling three types of steel plates that are prone to warping, the height of the rolling line should be preset in advance, and different specifications should have different parameters. 

4. Conclusion 

The steel plate rolling process is a complex thermomechanical coupling process. Therefore, the initial stress state of the steel plate, temperature distribution, rolling speed setting, pass sequence allocation, reduction system setup, etc. are all factors that cause the head to warp. Moreover, these factors interact and influence each other. Controlling and adjusting any single factor alone cannot completely ensure a straight head. Therefore, it is necessary to conduct a comprehensive analysis and coordinate the planning of the billet, heating, transportation, and rolling processes to ensure that the steel plate is in the optimal state during rolling and to reduce the occurrence of warping. Through the implementation of various measures together, the incidence of rolling abnormalities caused by warping has been significantly reduced. In 2011, the incidence of rolling abnormalities caused by warping was only 0.15%, a 60% decrease compared to 2010, and the improvement effect was obvious.