Roll Levelling

Synonyms

Roll levelling; Straightening (for reduced number of rolls having bigger diameter)

Definition

In accordance to DIN 8586 (2003) “Manufacturing processes forming by bending – classification, subdivision, terms and definitions,” roll levelling is classified as a bending process using rotating tool motion.

In more technological and industrial terms, roll levelling is the process where a sheet having flatness defects is straightened by imparting alternating bending operations using a set of bending rolls. The objective of the process is to minimize flatness imperfections and to level internal residual stresses of the material (Schuler 1998).

Theory and Application

Flatness Defects

During the hot and cold rolling of coils, work rolls are subjected to bending moments that produce heterogeneous plastic strains and thicknesses along the width of the sheet. As a consequence, different fiber lengths are generated, and diverse shape defects appear in the resulting coils. Furthermore, besides the bending deformation of the work rolls, other process variables, such as nonhomogeneous cooling, coil up, and impurities in the lattice of the material, play an important role during the generation of coil defects.

Most of the authors have classified those defects depending on whether they are caused by a heterogeneous stress distribution through the thickness or through the width (Bräutigam and Becker 2009; Mathieu 2011). In Fig. 1 the most typical coil defects are presented.

Fig. 1

Typical coil shape defects

The metal industry has developed several methods and standards to measure the flatness of the coils (Müller et al. 2013). The DIN EN 10131 (2006) and DIN EN 10051 (2010) standards define the tolerances on dimensions and shape of cold-rolled flat products and hot-rolled strip and plate/sheet, respectively.

In industrial environments, the flatness measurement is traditionally also expressed in international units (Mathieu 2011). This unit relates the height and the length of a wave in a sheet (see Fig. 2) by the following formula:

$$ \mathrm{IU}={\left(\frac{\pi }{2}\cdotp \frac{A}{L}\right)}^2\cdotp 100,000 $$

(1)

where A is the amplitude and L is the length of the measured wave.

Fig. 2

Flatness measurement

Levelling Methods

Levelling is not a new process and exists since several dozens of years. Before the advent of modern levelling technologies for coil processing lines, bending presses using shims to support the sheet and to concentrate the applied load were used to level individual sheets (Fig. 3a). However, such a process was slow and inefficient, requiring a different bending strategy and sequence for each flatness defect, and residual stresses were present after the flattening operations.

Fig. 3

Levelling technologies. (a) press levelling, (b) roll levelling, (c) stretch levelling, and (d) tension levelling

Currently, three different industrial technologies are used to level metal strips and coils. The roll levelling (Fig. 3b), described in this essay, is the most widely used method due to the low cost of the industrial facilities and the high processing speeds. The stretch levelling is used to noncontinuously level high-thickness hot-rolled coils and strips (Fig. 3c). During the process, the metal strip is fully stretched by the use of two clamps so that, theoretically, no through-thickness residual stress is present after the process. The tension levelling is commonly used for levelling thin cold-rolled materials (Fig. 3d). During the process, S-type tension rolls are used to stretch the material, while a reduced amount of bending rolls create an extra plastification of the coil. As in the stretch levelling technology, 100% of the thickness is plastified using this technology.

Roll Levelling Machines

A roll leveller consists of four main parts (Fig. 4). The active part of a roll leveller is known as the cassette. Generally speaking, it comprises an upper and a lower row of straightening rolls with the same diameter. The rollers in the upper row are generally arranged precisely above the gaps between the rollers of the bottom row. The distance between roll centers is known as the roller pitch (p) and varies in different machines, as does the roller radius (R) and the number of straightening rolls (Silvestre 2015). Different cassettes are commonly used in the same leveller to process different thickness materials. A cassette for precision levelling of thin coils with intermediate rolls is shown in Fig. 5.

Fig. 4

Roll levelling machine. (Courtesy of FAGOR ARRASATE)

Fig. 5

Layout of a precision leveller with intermediate rolls. (a) Front view. (b) Detail showing arrangement of backup rolls. (Courtesy of FAGOR ARRASATE)

The drive unit, typically placed in the back of the machine, includes the motor and reducer and the gearbox, where the motor motion is derived to the different working axis and the shafts connecting the gearbox with the levelling rolls.

The leveller frame absorbs the vertical forces and is normally constructed in a gantry-type design. The lower bed, the two uprights, and the crown form the frame of the machine. In conventional machines, the cylinders to vertically move the backup rolls are introduced in the bed of the machine and are used for the selective deflection of the levelling rolls.

The lifting or elevation mechanism is integrated in the crown to allow modification of the rolling gap. Although individual adjustment of the rolls is possible using hydraulic actuators, typically the whole row of upper rolls is vertically moved and rotated using spindles to obtain a progressively increasing rolling gap configuration.

Roll Levelling Principle

As mentioned before, in roll levellers the metal strip is subjected to alternating bends. As it can be observed in Fig. 5a, the depth of the bends continually decreases in size as the sheets run through the machine from the inlet to the outlet. For that, the roll penetration or adjustment at the entry of the leveller (z) is higher than the exit.

In the first working rolls, approximately corresponding to the first five rolls, in-width stress profile is homogenized. Plastic straining of the longitudinal fibers along the coil width removes typical defects such as coil set and crossbow. To effectively remove local defects such as central buckles or edge waves, a selective deflection of the levelling rolls is performed vertically moving the backup rolls so that the flat areas of the coil suffer more stretching and end with the same length of the wavy fibers (Semiatin et al. 2006). Typical backup rolls arrangements to remove central buckles and edge waves are shown in Fig. 6.

Fig. 6

Backup rolls arrangement to remove central buckles (a) and edge waves (b)

However, due to the strong bends in the first rolls, a pronounced through-thickness stress profile is generated. The aim of the subsequent rolls is to gradually reduce this stress profile so that a homogeneous narrow stress profile is obtained at the end of the leveller. Five straightening rollers are sufficient to level thick plates or coils or where no special demands are made on straightening accuracy. Where thinner materials or more stringent levelling requirements are involved, for example, for fine blanking or laser cutting, machines with up to 21 rollers are used. Commonly the exit penetration value corresponds to the sheet metal thickness and is adjusted to obtain a completely flat coil at machine exit.

It is industrially demonstrated that for a good levelling quality, a minimum of 70–80% of the thickness must be plastified in the first rolls. This maximum straining of the material is obtained by the first three fully effective levelling rolls, and normally peak strain along the machine corresponds to the third roll in the machine. Thus, the penetration or roll gap at the third roll is first calculated to then obtain the second roll gap, also called as entry value, which is of a relevant importance for a proper levelling of the material.

Considering plane strain conditions and the bending theory for high bending radius to thickness ratios (see “Bending (Sheets)” entry), it is easily obtained that the bending strain at a certain fiber of the bend is

$$ {\varepsilon}_{\mathrm{b}}=\frac{y}{\rho } $$

(2)

where y is the distance from the neutral fiber to the analyzed fiber and ρ is the current bending radius of the neutral fiber (see Fig. 7).

Fig. 7

(a) Schematic view of first three fully effective levelling rolls (a) and (b) stress and strain components in bending

Assuming a lineal through-thickness strain profile and using Hooke’s law, the bending radius causing the yielding (ρ _y) of a given thickness percentage (e.g., pr, 80%) can be calculated by the following equation:

$$ {\rho}_{\mathrm{y}}=\frac{E^{\prime}\bullet t\bullet \left(100-\mathrm{pr}\right)}{2\bullet {\sigma}_1\bullet 100} $$

(3)

where E′ is the modulus of elasticity in plane strain given by Eq. 4 and σ ₁ is the plane strain yield stress given by Eq. 5 if von Mises yield criteria are assumed (Hu et al. 2002).

$$ {E}^{\prime }=\frac{E}{1-{\vartheta}^2} $$

(4)

$$ {\sigma}_1=\frac{2}{\sqrt{3}}\bullet YS $$

(5)

where E is the uniaxial modulus of elasticity, ϑ is the Poisson’s ratio, and YS is the uniaxial yield stress of the material.

From geometrical calculations, the equivalent roll penetration or adjustment causing this bending radius can be calculated as follows:

$$ {z}_3=2\bullet {\rho}_{\mathrm{y}}-\sqrt{4\bullet {\rho}_{\mathrm{y}}^2-{\left(\frac{t}{2}\right)}^2} $$

(6)

The maximum roll penetration (z _max) is however defined by the upper and bottom rolls geometrical collision and can be calculated for a given material thickness using Eq. 7.

$$ {z}_{\mathrm{max}}=2R+t-\sqrt{{\left(2R+t\right)}^2-{\left(\frac{p}{2}\right)}^2} $$

(7)

where R is the roll radius, t is the material thickness, and p is the roll pitch.

Process Limitations and Levelling Window

The proper working of a roll leveller highly depends on the correct selection of the roll diameter, the roll pitch, the number of rolls, and the entry and exit penetration or adjustment values. These design parameters: the maximum available drive power and the maximum vertical levelling force, going to the machine frame, define the limits of a specific roll leveller to process a coil.

A typical limit processing window, called as levelling window, is shown in Fig. 8. This diagram represents a levelling process window which is the result of the intersection of three different limiting curves. Levelling operations below the limit curve are possible with the studied machine design.

Fig. 8

Example of levelling window

The left side of the window is limited by the maximum tilting or rotation capability of the leveller (the maximum allowed difference between the entry and exit penetration) and the maximum penetration of the rolls before physical collision obtained by Eq. 7.

The second part of the levelling window is limited by the maximum power/torque of the driving motor. The coil width and the yield stress of the material are the most affecting parameters, together with the thickness of the processed material.

The maximum vertical force the machine frame can support limits last part of the window, the right side. The thickness of the material together with the coil width and yield stress are the most affecting parameters for this limit.

The levelling forces and torques can be calculated using simple pure analytical or advanced semi-analytical models (Tselikov and Smirnov 1965; Doege et al. 2002). However, taking into account complex material behaviors, such as mixed kinematic hardening models, tribological behavior under different contact conditions, working speed influence, etc., is difficult when using these types of torque and force prediction methods. For that reason, different scientific papers have been recently published where finite element modeling (FEM) has been used to model and understand the levelling mechanism (e.g., Madej et al. 2011). Taking into account the mixed kinematic hardening models and considering a nonconstant friction coefficient have been recently demonstrated to be critical for roll levelling FEM optimization (Silvestre 2015).

Cross-References

• Bending (Sheets)