October 14, 2008

Equations help leveler operators significantly reduce the traditional trial and error during setup.

Today's leveler operator isn't given much to work with. He may have a sheet of paper that indicates the maximum penetration for a given gauge to avoid overloading the machine, but that's about it. To determine the right setting to attain the needed correction with appropriate penetration he goes through trial and error.

Once he finally finds the right settings, he records them for future use. The next time he runs similar material, he uses the recorded values as a starting point. But what if the material is of the same grade but slightly thicker? The operator would have to make a judgment to tweak the roll setting further, and he's offered little guidance as to what changes would produce optimal results.

This isn't the most efficient process.

Recent research may help matters. Newly developed calculations have been introduced that recommend roller penetration values for a given thickness and yield strength. In essence, it gives setup personnel a scientifically derived start point before they run material.

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In strip or coil processing, the flatter a strip is, the more accurate downstream blanking or stamping operations will be. To make sure strips are level, processors use roller leveling machines. These produce successive plastic penetration in strip through reverse bending, applying precise pressure to the strip to make it perfectly level. Parameters to achieve this relate to, among other things, the deflection of the strip during leveling.

The proper roll-gap setting produces the right amount of deflection so the strip exits the machine level and ready for downstream processes. Improper gap settings can produce either insufficient plastic penetration or overpenetration and poor-quality outgoing strip. Even worse, overpenetration may heavily overload the leveling machine and even damage the machine transmission, especially if leveling a wide strip. Starting at 85 percent plastic penetration in strip, torque on the work roll increases sharply; increase penetration by just 2 percentage points—to 87 percent—and torque on the roll shoots up 20 percent.

Challenges arise during machine setup. Technicians still set up levelers through trial and error, tweaking the roll-gap setting to achieve just the right amount of deflection. Recent developments, however, attempt to significantly reduce this trial and error.

The roll gap is defined as the vertical distance between the top of the bottom roll and the bottom of an adjacent top roll (see **Figure 1**). When the rolls penetrate the strip, the roll gap may be negative, with the top and bottom rolls descending into a mesh. For this reason, roll gap is sometimes called the roll penetration or roll intermeshing setting. The more a roll penetrates, the greater the negative gap will be.

Levelers come in many variations, but for this article, consider a conventional leveler with an upper and lower bank of rolls. In most setups the rolls exert the most deflection on the strip as it enters the machine and the least deflection as it exits. To create this gradual reduction of strip deformation, the roll gap starts at a small, sometimes negative value at the leveler entry point, then ends with the maximum positive value at the exit.

A strip's material properties complicate matters, however. Incoming strips aren't fully constrained, so in reality, plastic penetration isn't at its maximum when the strip first enters the machine. With this tilted setup of the rolls—from minimum to maximum roll gap—the greatest penetration in fact happens at the third roll set from entry. Meanwhile the last roll set must not exert any plastic deformation; if it did, it would leave coil-set effects on the material after it exits the leveler. For this reason, the second to last roll set exerts that least deformation. After this the strip springs back to straight, and the final roller set simply maintains the straightness.

The amount of plastic deformation at the third roll is especially critical, and so too is its roll-gap setting. So what, exactly, should this roll gap be? Most technicians determine this through trial and error. But what if you could calculate these roll-gap settings ahead of time and eliminate much of that trial and error?

To that end, a recent study has uncovered a calculation that helps determine the roll-gap setting based on the strip's physical properties and roll layout.

First, consider what actually happens inside a leveling machine. All levelers exert plastic-elastic bending. Plastic deformation permanently changes the shape, while elastic bending stretches the material temporarily but not enough to permanently deform it. Picture a cross section of a strip thickness. Plastic deformation happens on the top and bottom layers of this cross section, while elastic deformation occurs in the center.

The degree of deformation depends on the location of the strip within the leveler. The recent study reveals that roller leveling divides strip into three bending segments: an elastic bending segment spanned by two plastic-elastic bending segments that contact two adjacent rolls.

More than predicting gap value, the study's equation also helps determine which materials can and can't be sent through the leveler. The equation incorporates some basic variables, including the roll pitch distance, defined as the center distance between two adjacent rolls in the same row. Other variables include the desired plastic penetration, a strip's yield strength, and its Young's modulus. Also incorporated is the strip plastic-elastic bending moment factor at the roll, which can be calculated using plastic penetration and is defined as the ratio of plastic-elastic bending moment divided by yield bending moment, or the maximum elastic bending moment. Finally, the calculations involve the strip yield bending diameter, or the bending diameter of the strip centerline at which the most outer fiber of strip starts yielding.

The roll gap equation is given as:

**(1)**

where:

t = strip thickness

L = roll pitch distance

k = strip plastic-elastic bending moment factor at the roll

D

_{y}= strip yield bending dia.

To obtain the strip plastic-elastic bending moment factor at roll contact point (k):

**(2)**

where:

p = plastic penetration desired

Strip yield bending diameter (D

_{y}) is:

**(3)**

where:

s

_{y}= strip yield strengthE = strip's Young's

modulus (stress/strain)

Most levelers require operators to set the gap settings between the first and second rolls, as well as between the second and last rolls. The calculations convert values to match the first rolls (roll gap at strip entry) as follows:

**(4)**

where:

n = number of total work rolls

While these calculations help produce guidelines for roll-gap settings, they do not eliminate trial and error completely. Coiled material may have various defects, such as center buckling and edge wave, so an operator still needs to fine-tune the rolls.

Still, using these calculations can create valuable guidelines and significantly reduce leveler setup time, something more valuable than ever as coil processors continue to squeeze inefficiencies out of their operations.

Consider a typical strip leveling application in which the steel strip thicknesses are between 0.02 inch and 0.09 in. and yield strengths are 50 KSI and 75 KSI, respectively. A 19-roll leveler has a work roll diameter of 1.5 in. and a roll pitch distance of 1.625 in. A plastic penetration of 85 percent is selected for the roll-gap calculation, which is performed using a spreadsheet.

Roll gap at the third roll is calculated first, showing the roll-gap setting increases with material thickness (see **Figure 2**). With strip yield strength of 50 KSI and a thickness less than 0.025 in., the roller requires a negative gap setting to achieve 85 percent plastic deformation. Strips thicker than 0.025 in., on the other hand, require a positive gap value.

After the third roll gap is calculated, the final equation**(4)**determines the gap at the entry rolls, assuming the roll gap at the exit roll equals the strip thickness. Figure 2 shows two curves for the entry gap when processing material with yield strengths of 50 KSI and 75 KSI. Note that the gap at the entry roll is actually smaller than the gap at the third roll.

In this example, strips thinner than 0.025 in. with 75-KSI yield strength have a bending diameter that is smaller than the work roll diameter of 1.5 in. (see**Figure 3**). Hence, the desired strip deformation cannot be achieved.

Using equation 3 and noticing the thickness of the strip's elastic core is reduced by plastic penetration, we can express the strip centerline bending diameter as:

where:

t = strip thickness

s

_{y}= strip yield strengthE = strip Young's modulus (stress/strain)

Centerline bending diameter is defined as the bending diameter of the line located at a half of strip thickness from strip surface. The centerline bending diameter of the strips on the third roll is calculated and plotted in Figure 3. The bending diameter of the strip surface that contacts the work roll should be less than its centerline diameter by a half of strip thickness. If the bending diameter is satisfied at the third roll, the bending diameter at other rolls will be automatically satisfied because plastic penetration at the other rolls is less than at the third roll with a tilted setting.

Linfa Yan, Ph.D., is senior engineering analyst and Brett Snider is managing director at SMS Demag Ltd., 2775 Coventry Road, Oakville, ON L6H 5V9, Canada, 905-829-2888, www.sms-demag.ca.

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