A tandem rolling mill is a rolling mill used to produce wire and sheet metal. It is composed of two or more close-coupled stands, and uses tension between the stands as well as compressive force from work rolls to reduce the thickness of steel. It was first patented by Richard Ford in 1766 in England.
Each stand of a tandem mill is set up for rolling using the mill-stand's spring curve and the compressive curve of the metal so that both the rolling force and the exit thickness of each stand are determined. For mills rolling thinner strip, bridles may be added either at the entry and/or the exit to increase the strip tension near the adjacent stands, further increasing their reduction capability.
History.
The first mention of a tandem rolling mill is Richard Ford's 1766 English patent for the hot rolling of wire.
In 1798 he received another patent, this time for the hot rolling of plates and sheets using a tandem mill. The tandem mill's main advantage was increased production: only a single pass was required, saving time; and greater tensions were possible between the stands, increasing the reduction in the stands for the same roll force. One disadvantage was its high capital cost compared to that of a single-stand reversing mill.
The development of transfer bar casting, also called thin slab casting meant that slab roughing mills were no-longer required. Thin strip casting with a thickness of 2 mm has bypassed the tandem hot mill; and further reduction in the casting thickness to produce strip steel the same as annealed cold rolled strip will bypass the tandem cold mill and the annealing process.
The need for tandem rolling mills, and rolling mills in general, is being reduced by the use of continuous casters.
Mill stand characteristics.
The mill stand spring curve is obtained by pressing the work rolls together with increasing force. This causes the work rolls to bend, the screw-downs to compress and the mill housings to stretch. To reduce work roll bending, a much larger roll is positioned above the top work roll and another is placed below the bottom work roll. This arrangement is called a 4-high mill, as shown in sketch 1.
Calculating the screw-down position.
The red line in graph 1 is the linear approximation "F" = "F""d" – "M" ⋅ ("S" – "S""d")
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where "M" is called the mill modulus and is the slope of the spring curve in the area of the datum point ( "S""d", "F""d"). For most mills "M" is approximately 4 MN/mm. Larger values would require much thicker mill housings and screw-downs.
A datum is performed by lowering the screws below face until the measured force equals the required datum force "F""d", at which point the screw-down position is set so that it equals the datum screw position "S""d". At BlueScope Steel's No. 2 temper mill the datum point was 5 mm at a force of 7 MN.
Wood and Ivacheff analysed the information obtained when measuring the mill modulus by pressing the work rolls together until a typical rolling force was reached, and then they continued to measure the force and screw-down position as the rolls were lifted. The shape of the plotted figures (overlaid, looped, or a figure eight) was found to give good indication of the mill stand's condition.
The datum point is chosen so that the screw-down position "S" is never negative. This was necessary with the control computers of the 1960s, such as the GE/PAC 4020 installed at the then Australian Iron &amp; Steel (now BlueScope) Port Kembla plate mill, which used an assembler language that did not like negative numbers.
Also, a datum point is used rather than trying to measure the point at which the force just becomes zero.
The exact equation used to calculate the required screw-down setting for a required force is:
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where: "k" is the value to best suit the measured values and "S""a" is an adapter which corrects for the thermal expansion of the mill housing and rolls as they warm up during rolling. It is set to zero after a work roll change, when the datum is performed with the new rolls at room temperature.
Using the measured values of "F" and "S" during the rolling of one piece of metal, allows the adaptor "S""a" to be calculated for use at the start of the next piece.
Roll force measurement.
Load cells are used to measure the force exerted onto the work rolls by the product.
To obtain the true roll force acting on the work rolls the position of the load cells is important; are they with the filler plates under the bottom backup-roll bearings, or on top of the top backup-roll bearings. Both positions are shown in sketch 2.
Another thing that must be considered (if they are present) is the roll balance cylinders.
The roll balance cylinders act to separate the work rolls (no force between them) when the screw-downs are raised; that is, the force of the balance cylinders "F"bal is just greater than the weight of the top roll set, ("Wt"bu + "Wt"wr).
The above roll weights "Wt"bu and "Wt"wr are only nominal values; the actual values will vary a little depending on how many times the rolls have been ground down between campaigns.
Since the roll weights are only nominal values, any residual error is slowly zeroed out whenever the roll balance is on and the screws are raised sufficiently.
Steel characteristics.
A useful formula for the compression curve of steel is:
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where
"k"0 moves the curve vertically, i.e. it sets the initial yield stress;
"k"3 changes the slope, i.e. the metal's work hardening rate.
The initial steep section in graph 2 is elastic compression. The effective height of this is reduced by the entry and exit tensions when present, as in a tandem mill. Notice that the curve becomes steeper as the thickness approaches zero, i.e. it would take infinite force to make the steel infinitely thin.
The slope of the plastic region around the operating point is normally represented by the letter "Q".
Mathematical modelling.
For a rolling mill to operate, the work roll gap is set prior to the product entering the mill. Originally this setting was empirical; that is, set by the operators according to their experiences of that product's initial dimensions and the required finished thickness.
With a reversing mill, the profile of intermediate thicknesses was also empirical. To obtain greater consistency, attempts were made to characterize the rolling process. In 1948, Bland and Ford
 were one of the first to publish such a mathematical model.
Essentially such mathematical models represent the mill (its spring curve) and the compressive behavior of the product to calculate the mill's "setup".
Mill setup calculation.
The term "setup" is used for the calculation of the actuator settings required by each mill stand to roll the product. These settings include the initial screw-down position, the main drive speed, and the entry and exit tension references where applicable.
This setup calculation is normally performed either in a lower-level computer or a PLC that controls a rolling mill stand(s).
A graphical representation of a mill model can be obtained by plotting the mill stand spring curve and the compression curve for the strip against the same distance axes; then the intersection point gives the solution of expected rolling force "F", and final Strip Thickness "h", and also the required initial screw-down position "So". See graph 3.
In its simplest form
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This equation is known as the BISRA equation. It is also known as the gaugemeter equation because measurements of "S" and "F" can be used to calculate the exit thickness as measured by an instrument called a thickness gauge.
If the work rolls are initially pressed together by the screw-downs, then there will be a force "F""o" acting between the top and bottom work rolls before the strip is present. In this situation, the Mill is said to be set "below face", as shown in graph 3. This is often the case with thin strip.
However, if there is an actual gap before the metal enters the mill, then "F""o" will be zero, and (from equation 1) "S""o" must be greater than "S""d" + "F""d" / "M"
The calculation is repeated for the following stands with the exit thickness "h" of the one stand becoming the entry thickness "H" of the next stand. Note that the compression curve has a greater or lesser elastic region depending on the entry and exit tension stresses of that next stand.
Interstand tensions.
One could say the steel is compressed by the force of the work rolls, equivalent to forging; however, if there are tensions present, then it could be said that the steel is stretched by the tension pulling it through the rotating work rolls, as in extruding through a die. See sketch 3.
The tensions reduce the effective elasticity of the product by an amount equal to the induced tension strain. This tension effect is represented in graphs 2 and 3 by drawing the steel compression curve with the elastic region reduced accordingly.
The relationship of the rolling force to the entry and exit strip tensions is important in determining the finished strip flatness. Too much force produces strip with edge wave (often called "pressure wave"). Too much tension, that is too little force, can cause center buckle (depending on the crown of the rolls).
The tension stress is 30% to 50% of the yield stress for cold mills and often higher in hot mills (which can result in heavy necking and even strip breaks).
In sketch 4, observe that the force is offset from the work roll centers because the strip is thicker at the entry than at the exit; this is one component of the torque that the main drives must supply. The other component is the difference in the tension forces. If the exit tension force is much greater than the entry tension force, then the tension torque may be larger than the torque due to the rolling-force and the main drives will generate power.
The neutral point, or no-slip point is the point within the roll bite where the work rolls and the strip are doing the same speed.
The position of the neutral point is influenced by the entry and exit tensions.
Shudder occurs when the neutral point is at an edge of the roll bite; that is the work rolls are alternately grabbing the strip and letting it slip.
Forward slip (1+"f") is the ratio of the exit strip speed to the work rolls peripheral speed. Backward slip (1−"b") is the ratio of the entry strip speed to the work rolls peripheral speed.
Roll wear.
As the strip slides through the work rolls it polishes them and the strip. This changes the friction coefficient of the strip-to-roll surface. So, to predict the forces and the power required to drive the work rolls, the mill modelling estimates this roll wear based on the length of strip rolled.
To reduce the friction in the roll bite, a warm oil-water emulsion is sprayed at the entry side of the roll bite in cold rolling mills.
The work rolls of all the stands in a tandem mill are normally changed at the same time. The new work rolls will have been ground to restore their desired crown and roughness. When this is done, the roll wear is reset to zero in the modelling.
The heat generated in the roll bite of a cold mill warms both the strip and the rolls. Since the cold mill rolls have no coolant applied, just a small amount of warm oil-water emulsion, the work rolls in a cold mill become hotter than those in a hot mill, where copious amounts of cold water are sprayed at the exit side of the roll bite.
Back-up roll bearings speed effect.
The back-up roll bearings are usually white-metal bearings which rely on a film of oil between the shaft and the white-metal to reduce the friction; as seen in sketch 5.
As the speed increases more oil is dragged into the active region of the bearing and this increases the thickness of the oil film in this region. This pushes the top work roll down and the bottom work roll up, which reduces the roll gap in the same manner as running the screws down. To compensate for this, most screw-down control loops include a feed-forward parameter derived from either; an equation of rolling speed,