The Engineering Design of Rolling Mill

The technological development of the cold rolling process and the new generation automatic control systems of the rolling mill

by Massimo Moschini, Ciro Sinagra (Laminazione Sottile Spa); Nicola Gioachin (Mino Spa)

The typical rolling mill can be defined by the number of rolls in the rolling stand: Two High Rolling Mill, IV-High Rolling Mill and VI-High Rolling Mill. Another way to classify the rolling mills is by the number of stands: Single Stand, Tandem Mill (II-Stand, III-Stand). A Cold Rolling Mill rolls, in subsequent short passes(due to the relative thick material), coiled strip from a thickness of up to 8 mm (coming from Hot Rolling Mill) down to 0.2 mm; the mill is designed with high rolling force and power capability and efficient and fast coil handling to minimize the waiting time. A Foil Rolling Mill rolls, in subsequent long passes(due to the relative thin material), coiled strip (coiled on steel spool) from a thickness of up to 0.6 mm (coming from Cold rolling Mill) down to 2 x 5 µm; the mill is designed in order to roll in closed gap.

The Mechanics of the Rolling Process
The target of Cold Rolling is to reduce the thickness of the strip, by applying a rolling force to the cold strip as it passes between two work rolls. In order to model the strip behavior, the Stress-Strain relationship of the material shall be considered. By applying the Three-axial stress and yield criteria to the plane strain condition (ε2 = 0) and (σ1>> σ2), it is possible to find the relationship between the stress in the thickness direction, the applied tension on the strip and the uniaxial Yield stress of the material:
(σ3 – σ2)2 + (σ2 – σ1)2 + (σ1 – σ3)2 = 2Y2
The rolling force can be determined by integrating the Rolling Pressure over the arc of contact:
Taking a 50% reduction in the material thickness as an example, it can be seen that in order to conserve the mass flow, the strip leaving the bite has twice the speed of the strip entering the bite. This means that the material is moving slower than the rolls at the entry side and faster on the exit side. The point at which the strip speed matches the roll speed is referred to as the Neutral Point. The difference in speed between the material and the rolls generates a friction that, upstream of neutral point, pushes the material into the bite and downstream of the neutral point pushes the material back to the neutral point. This friction produces a varying hydrostatic pressure on the strip. At the entry and exit of the roll bite the hydrostatic pressure is zero, increasing to a maximum at the neutral point where the friction is zero. By graphing the rolling pressure along the arc of contact (Figure 1) we obtain the area that is proportional to the total rolling force applied to the rolls (per meter of strip width).

Influence of main parameters
The area of the graphs (Rolling pressure vs. Arc of contact) is proportional to the rolling force. By adjusting the input parameters it is possible to evaluate their effect on the rolling force by observing the resulting effect on the area under the graph. Considering friction and reduction (Figure 2):
• an increase in the friction between the rolls and the strip (due to different roll roughness, coolant viscosity or speed for the hydrodynamic effect of the coolant) increases the rolling pressure area;
• an increase in the reduction, enlarges the arc of contact and therefore also increases the rolling pressure area.
Open Gap Rolling
For rolling of thinner gauges, work roll bending becomes an important actuator in order to maintain a gap between the top and bottom Work Roll faces outside of the strip width. This condition is referred to as Open Gap rolling. However, below a certain thickness (~0.080 mm), the Work Roll bending system is no longer able to compensate for the difference between D (nominal WR diameter) and D’ (diameter of the osculating circle approximating the WR diameter flattened under load). When this point is reached, the Work Roll faces touch each other. This condition is referred to as Closed Gap rolling. No further reduction in thickness is possible by increasing the rolling force, since in the closed gap condition the majority of the force is transmitted directly between the work rolls and not through the material (Figure 3).

Closed Gap Rolling (Foil Rolling)
The graph in Figure 4 shows the effectiveness of the rolling force in the thickness control of the strip for a decreasing absolute exit thickness. For the thickness range below 50 µm, the rolling force becomes ineffective in controlling the thickness since the two work rolls are in contact. In Closed Gap Rolling, the strip tension and speed are used in order to control the thickness; by changing the speed (hydrodynamic effect of the coolant) and oil viscosity, the resulting rolling pressure can control the rolling force down to 10 µm.
Controls of Cold Rolling: measuring devices
Process parameters measured and controlled on a Cold Rolling Mill are:
• Strip Centerline Thickness (by X-Ray Thickness Gauge, Figure 5);
• Strip Speed (by Laser Speed Meter);
• Strip Flatness (by Shapemeter Roll, Figure 6);
• Strip Tension (by Load Cells and Motors Drives);
• Rolling Speed (by Motors Drives).

Typically, measuring devices are installed:
1 – Thickness gauge and Laser Speed Meter on entry and exit side;
2 – Shapemeter Roll on exit side;
3 – Load Cell under the deflector rolls (entry and exit) for tension measurement.

Control Actuators
By processing the online measurement, during rolling the following actuators are controlled (Figure 7):
• Work Roll Load and Gap (by AGC Cylinders);
• Work Roll bending to control the Work Roll profile of 2nd • and 4th order (by bending blocks);
• Work Roll Selective Cooling to control the Work Roll profile of higher order (by spray bars);
• Strip Tension and Rolling Speed (by main motors).

The two AGC cylinders act on the Back Up Roll and are controlled by servo valves. Position transducers are installed for position control of the Work Roll gap. The bending blocks are installed on the rolling stand and act on the Work Roll Chocks, controlled by servo valves. The spray bars, with nozzles typically arranged with a 52 mm pitch, are controlled in individual zones of 52 mm width with electrically actuated valves by a pulse width modulated (PWM) signal, in order to maintain an even temperature distribution over the roll length. The even temperature of the Work Rolls is essential for flatness quality of the strip.

Mill Automatic Controls
The TCS (Technological Control System) controls the Mill Actuators based on measured data. The system (HW and SW)is composed of:
• AGC (Automatic Gauge Control) System to control the strip thickness;
• AFC (Automatic Flatness Control) System to control the strip flatness.

AGC Feedback Control
The AGC Feedback Control (Figure 8) represents the traditional AGC controller. Controller gains are adapted based on the exit strip speed, to account for the changing transport time between the roll bite and the thickness gauge.
Weaknesses of this controller:
• The strip thickness is measured some time after it has passed through the roll bite: this inherent phase lag allows the achievement of only a moderate level of performance.
• Although open loop speed effect compensation is applied to adjust the actuators during speed changes in order to compensate for the change in bite lubrication effect, the compensation is imprecise; often the AGC performance during acceleration and deceleration is less than satisfactory because the open loop compensation is difficult to setup for all products and mill conditions.
• The sensitivity model, which includes consideration of the material hardness, is a simplistic approximation, which generalizes across the product range (widths and thicknesses); overall the gain of the AGC controller is often de-tuned to the lowest common denominator in order to ensure stability for all products that pass through the mill.

AGC Feedforward Control
The addition of an entry thickness gauge and an entry laser speed meter allows a feedforward control (Figure 9).
The feedforward controller aims to attack and compensate for any variations in the incoming strip thickness. Strip tracking is used to track the strip from the entry thickness gauge to the roll bite; a phase advance is applied in order to synchronize the action of the roll gap actuator with the variation in strip thickness.
Weaknesses of this controller:
• The use of a single actuator (roll gap) doesn’t consider the changing dynamics of the entry tension.
• The frequency response is limited by the time constant of the roll gap to entry tension interaction; although the FF controller may move the roll gap at a high rate, the entry coiler cannot keep up to maintain a constant entry tension: the correction of the feedforward controller on the incoming thickness variation is therefore reduced.
AGC Mass Flow Control
With the addition of an exit laser speed meter, a mass flow controller can be used (Figure 10).Using the measured entry thickness, entry strip speed and exit strip speed, the thickness of the strip leaving the roll bite can be calculated. This calculated thickness is used to adjust the roll gap. Since the mass flow controller calculates the strip thickness at the roll bite, there is a minimal delay (phase lag) in the exit thickness measurement. This provides a significant improvement over the traditional AGC feedback controller, allowing the controller gains to be much higher whilst maintaining stable control. The higher gains lead to a much higher performance for the thickness controller. The most obvious advantage observed with the mass flow controller is that it is able to react very fast during mill speed changes, making the exit thickness almost insensitive to speed changes.

Weaknesses of this controller:
• Since mass flow is a highly reactive controller, it will react to any variation in either the measured entry thickness, entry strip speed, exit strip speed. A filter could be applied to these measurements, but thiswould introduce phase delays in the signals, not desirable for the impact on the controller performance. Validation techniques are required in order to try and ‘catch’ any erroneous measurements and to prevent mass flow from reacting to them.
• No consideration is given to the dynamics of the entry tension.
• No adaptation is made for the frequency response characteristic of the mill.

AGC Roll Eccentricity Compensation
The REC controller (Figure 11) compensates for any eccentricity in the back rolls, so that the eccentric effect is not rolled into the strip thickness. The system is able to analyze the rolling force, the exit thickness and the entry tension measurements to identify any eccentricity. By using encoders or proximity switches, mounted in the end caps of the backup rolls, the system is able to accurately synchronize to the precise back roll frequency, instantaneously compensating for the thermal expansion/contraction of the rolls. The REC gains are adapted on the backup roll rotational frequencies, allowing some modulation of the controller with respect to frequency.
Weaknesses of this controller:
• No compensation is provided for work rolls eccentricity or ovality.
• Gains adaptation doesn’t consider the mill transfer functions.

AGC controls and parameters influence
Each of the actuators has a different frequency response:
• High frequency response for AGC Cylinders(up to 20 Hz);
• Low frequency response for Strip Tension Control;
• Very low frequency response for Strip selective cooling(up to 2 Hz).

The effect of Entry and Exit tensions applied on the strip by the reels can be seen on the Rolling Load (Figure 12). Due to different frequency response in the actuators (AGC Cylinder vs Entry Tension control by Main Motors Drive) any fluctuation in the strip entry tension will deteriorate the performance of the AGC controllers. If the entry tension is increased, the rolling pressure at entry will also decrease as for Tresca yield criteria. This reduces the area under the friction hill and thus the load, the magnitude of the reduction in the pressure is equal to the increase in applied tension stress in the metal. Another important effect of increasing entry tension is that the neutral point moves further towards the exit. If the exit tension is increased, the rolling pressure at exit will also decrease as seen by applying the Tresca yield criteria. This reduces the area under the friction hill and thus the load, the magnitude of the reduction in the pressure is equal to the increase in applied tension stress in the metal. Another important effect of increasing exit tension is that the neutral point moves further towards the entry. The result of the state of the art in traditional AGC controllers is shown in Figure 13: the blue trace shows the entry gauge deviation, while the superimposed yellow trace shows the exit gauge deviation. Using new control techniques, the issues with the frequency response and phase can be addressed in order to further improve the performance of the AGC controllers. The current AGC performance for 0.2 mm products is 2 sigma ±1.0%, while the enhanced AGC performance reaches 3 sigma ±0.75%.

AGC Model Based Predictive Control
The introduction of an accurate model provides improvement to the feedback controllers (including mass flow) allowing the possibility to predict the results of the AGC correction. When this prediction is tuned accurately, the controller can have higher gains and therefore a better performance compared to the conventional controllers previously described. The model is also helpful for feedforward control, allowing a second actuator (Entry Tension) to be adjusted in order to tighten up the dynamics of the entry tension control. This gives to the feed forward controller a higher bandwidth capable of removing higher frequency disturbances. The improvement to the entry tension dynamics allows the eccentricity controller to work at higher frequencies, so work rolls eccentricity compensation is feasible. Thanks to identification of the mill transfer characteristics, such as roll gap to exit thickness and entry tension to exit thickness, the eccentricity controller can be better mapped for the full range of frequencies. Chatter compensation is similar to the eccentricity controller, but rather than locking on to periodic disturbances due to the rolls, it locks on to periodic disturbances in the entry thickness caused by an upstream process. The advantage of this controller over the standard feedforward controller is that the compensation is integrated to a point such that all the disturbance is eliminated in the outgoing strip. The model uses the transfer function characteristic between roll gap and exit thickness to adjust the controller gains.
The graph in Figure 14 (amplitude of the HGC position measurement vs. frequency) shows how the roll gap actuator degrades as the frequency increases. The graph in Figure 15 (amplitude of the signal present in the exit strip thickness vs. frequency) shows the characteristic ‘notch’ in the transfer function from roll gap to exit thickness. The notch is caused by the dynamic response of the entry coiler: when the roll gap is moved at around 3.7 Hz, very little of that movement will be seen reflected in the exit thickness. This phenomenon, common to all rolling mills at 3÷5 Hz, is mostly caused by the inability of the entry tension controller to maintain a constant tension as the roll gap is opened and closed at these frequencies. So the AGC controller will not be so effective at correcting for errors in the strip thickness at around 4 Hz: in order to maintain stability, the AGC controller has not to be excited at these frequencies. This effect needs to be characterized to prevent any of the AGC controllers from going into oscillation at the notch frequency. When the effect is considered properly, it means that the AGC controller gains can be optimized and adapted according to the frequency of the disturbance.

AFC System
The AFC System (Figure 16) includes a series of functions to control the flatness of the strip using:
• Roll tilting, 1st and 3rd order correction by differential position of the AGC cylinders;
• Work Roll Bending, 2nd and 4th order correction by bending blocks;
• Work Roll Cooling, higher order non symmetrical correction by spray bars.

Hot Edge System
During rolling, the heat transfer due to the deformation from the strip to the Work Roll produces a thermal camber on the Work Rolls. The thermal camber gradient at the edge of the strip creates an inconsistent profile in the roll gap which causes the edge of the strip to be tight during Cold Rolling. In order to reduce the tight edge problem, a Hot Edge system is used; heating up the portion of the Work Rolls near the edge of the strip moves the thermal camber gradient away from the edge of the strip.

Industry 4.0
Industry 4.0 is the current trend of automation and data exchange in manufacturing technologies and it is seen as the 4th Industrial Revolution, based on the use of smart machines connected to each other and to the internet. Industry 4.0 achieves connections between physical and digital systems, complex analysis through Big Data and real-time adjustments.

Big Data (Predictive Maintenance)
Real-time condition monitoring of bearings and gearboxes is provided using accelerometers to measure and record vibration effects.
By analyzing the stored data, predictive faults of bearings and gears can be spotted in advance, avoiding costly stop times.

Vertical integration
By vertically correlating the Strip Flatness defect on a coil coming from the Cold Rolling Mill with the Strip Profile measured (crown) on the same coil in the Hot Rolling Mill, it is possible to identify specific crown-related defects and to try to minimize it in order to increase the quality. By vertically correlating a Strip Surface defect on a coil coming from the Cold Rolling Mill with a Strip Surface defect on the same coil in the Hot Rolling Mill, it is possible to identify where the defect originated looking for specific solutions.

Simulation and Augmented Reality
By simulating the heat transfer in the Rolling Process, it is possible to optimize the cooling and the process scheduling decreasing the amount of waste and the power consumption from the cooling system and increasing the strip quality.
With advanced 3D Human Machine Interface, it is possible to remotely control the position and the status of each coil and of each equipment with an easy to use iPad or PC from internet (Figure 17).