Mills, furnaces, kilns and drilling rigs

The first five chapters built the discipline layer by layer: choosing the prime mover, controlling centrifugal loads, four-quadrant vertical transport, multi-axis cranes, and synchronised continuous transport. This last chapter introduces no new kind of mechanism. It shows the same principles combined across industry, and it sets up the mini-project in which you combine them yourself. In each case study, look for which earlier chapter is at work: the load classification of Chapter 1, the power electronics of Chapter 2, the four-quadrant and braking analysis of Chapters 3 and 4, the multi-drive coordination of Chapter 5. This lesson is course sections 6.1.1 to 6.1.3.

The reversing rolling mill

A reversing rolling mill is among the most demanding drive applications there is. To reduce a steel slab's thickness it is passed back and forth through the work rolls, and the drive reverses at full torque many times a minute. That calls for enormous torque, very fast and controlled speed reversal, and full four-quadrant operation with energy recovery at every deceleration. Once served by large DC drives or cycloconverter-fed synchronous motors, modern mills use vector-controlled AC drives rated in tens of megawatts. The control couples a speed loop with a tension loop between successive stands, so the strip tension between mills stays regulated even as the strip lengthens.

Because the mill reverses continuously, the energy exchanged at each deceleration is what sizes the regenerative front end:

$$E_\text{rev} = \tfrac{1}{2} J_\text{eq}\left(\omega_1^2 - \omega_2^2\right) \tag{6.1}$$

Inertia J_eq (at the motor)

4,200 kg·m²

Rolling speed ω

60 rad/s

Reversal time (each ramp)

2.5 s

Time at speed per pass

3.0 s

• Speed
• Inertial power

Energy per reversal

7.56 MJ

Mean power while slowing

3.02 MW

Peak regenerated power

6.05 MW

Average over the cycle

0.95 MW

At 7.5 reversals a minute, a resistor would have to dissipate 0.95 MW continuously, on top of the peaks. That is why reversing mills are always specified with a fully regenerative supply.

E_rev = ½ J_eq (ω₁² − ω₂²) ; P_mean = E_rev / t_r ; P_peak = J ω α

Predict first

Keep the mill's inertia and speed, and halve the reversal time from 2.5 s to 1.25 s. What happens to the energy per reversal and to the peak regenerated power?

Both halveThe energy stays the same; the peak power doublesBoth double

The electric arc furnace

The electric arc furnace is a different challenge. The load is the arc itself, whose length, and therefore current, is regulated by raising and lowering the electrodes through fast position drives, while the supply copes with the violent, fluctuating and unbalanced current the arc draws. The drive is small, but the control is fast and the power-quality context severe: lesson 3's harmonics at their worst.

Process industries and the cement kiln

In the process industries, the mechanisms are the pumps, fans, mixers and kilns that sustain a continuous chemical or physical transformation. The large pumps and mixers of a chemical plant are the centrifugal and constant-torque loads of Chapters 1 and 2, run on VFDs for both process control and energy saving.

The cement kiln is especially instructive: a long, inclined, rotating cylinder, driven at very low speed through a large girth gear, that must turn with high and absolutely uninterrupted torque. It must never stop while hot, because an unevenly cooled kiln sags and is destroyed. So the drive includes an independent auxiliary (inching) drive that keeps the kiln turning slowly through a main-drive or power failure: the redundancy and fail-safe principle of Chapter 5 again.

Energy and oil: drilling and heavy pumping

In drilling, the top drive that turns the drill string is a high-torque, variable-speed drive that must also regulate torque precisely to protect the string. The draw-works that raises and lowers the string is a large four-quadrant hoist, a direct counterpart of Chapter 3's mine hoist, with regenerative lowering and fail-safe braking. Pipeline and injection pumps are large centrifugal loads on medium-voltage VFDs, often soft-started or speed-controlled to manage the inrush and to match flow to demand.

One map for all of them

Every case above is a mechanism you have already met, in another industry. The course's Table 6.1 puts them side by side:

Sector / machine	Dominant load character	Quadrants	Chapter
Reversing rolling mill	high inertia, rapid full-torque reversal	I–IV	3, 4
Electric arc furnace	fast electrode position control	I, III	2
Cement kiln	constant torque, uninterruptible	I	1, 5
Drilling draw-works	active, overhauling (a hoist)	I–IV	3
Pipeline pumping	variable torque (centrifugal)	I	2
Paper / film winder	constant power, tension-regulated	I, II	1, 5

FoundationStart here if this is new to you

A playground roundabout spun up by a group of children stores energy. Stop it by grabbing the rail and that energy goes somewhere: into your arms, as heat and effort. A rolling mill is a roundabout weighing tonnes, stopped and restarted the other way every few seconds, and its drive must catch all that energy each time instead of letting it go to waste.

ExplorerGo deeper: derivations and open questions

Mill front end. With the widget's default cycle, what fraction of the time is the drive regenerating? Estimate the rating of the active front end, and explain why it is set by the peak rather than the average.

Draw-works. A draw-works lowers a 150 t string at 1 m/s with 90 % efficiency. Using Chapter 3, what power does it return, and in which quadrant does it work?