Waterjetting 25c - more thoughts on jet range

A single waterjet, whether with or without abrasive, will cut a tapering slot as it penetrates into a target material. This is because, as the jet penetrates into the surface, the outer edges of the jet lose their energy in cutting, and the narrower central core remains capable of cutting, on a continually narrowing path, as the cut deepens.

Figure 1 Tapered cut made with a single jet traverse in contrast with the wider cut made with two diverging jets.

While the above statement is generally true, it is not completely so, since if the speed of traverse of the jet is reduced, then the continued addition of further water along the cut plane will be sufficient for the outer layers of the jet to be able to continue to cut and this may reach the point that there is no taper along the edges of the slot, or it may even taper inwards. For an abrasive jet cutting into titanium, that transition occurs at around 0.2 inches/minute, depending on jet parameters. (Note that this is less related to the target thickness, although it is controlled by the cuttability of that material, and that the critical speeds for cutting with water along are at least one and often two orders of magnitude greater).

Figure 2. Plot of taper angle with traverse speed.

Unfortunately the speed at which the edge is cut perpendicular to the top surface of the target is usually too slow to be economic, and, in consequence, the normal process is to slightly tilt the cutting head into the edge with the desired surface, and making the opposing surface carry an exaggerated tilt. This then allows a faster cut, again with the optimal speed being a function of both tilt angle and jet parameters.

When the objective, however, is to achieve a deeper cut, particularly where multiple passes are concerned, and head movement into the cut is allowed, then a different strategy can be followed.

Back when we were developing the longwall mining machine we called Hydrominer, we used a dual-jet system, because, when cutting coal, the material between two adjacent, concurrent cuts is removed as those cuts are made. Thus the jets, in a second pass, do not make contact with the walls of the cut until reaching the back of the previous cut. (The second image in Figure 1).

Figure 3. Slot cut by the Hydrominer, looking down, and with the slot through which the jets cut out from the head visible on the left edge of the machine.

However, in harder materials, including rock with some degree of cohesion, it is possible to run two jets almost side by side, and leave a rib of material between the cuts, so that jet attenuation in dual cutting is still a problem if the jets are parallel.

Again the answer is to tilt the jets, although if small jets are used, multiple jets may lose in overall range, because of the reduced diameter of the individual streams.

In this case it can be more effective to combine the jet flows into a single jet, but to either orbit or rotate this slightly off-axis so that the jet is cutting a slightly wider track along the path, and with a widening slot with depth, so that, again, subsequent passes, where the nozzle moves into the slot, do not encounter the walls of the cut until the back of the previous cut.

Back in the days when we were first testing the coal mining machine, we were mining coal in northern Missouri, and the coal had a large number of pyrite lenses in it. These lenses could be up to four inches thick, and, while the coal was friable and easy to cut, the pyrite lenses were much harder and dense. They could not be easily cut with the jets, which were operating at 10,000 psi, and the machine was not performing very well.

There were two ways in which we overcame the problem. The first was to adjust the two jets that were cutting the slot into which the cutting head was moving. As I mentioned earlier with a slight divergence angle between the jets, the slot was cut wide enough (around 2-inches) for the leading edge of the head to enter the cut, and the depth (around 9-inches) was enough to give leverage for the head to peel the rib of coal from the solid.

Figure 4. Comparison of results in the field with initial lab-designed nozzle.

When we encountered the pyrite, we changed the angle of the jets, so that instead of diverging the converged at varying distances in front of the head. When the two jets come together at this shallow angle (as with shaped charge formation) they form a very high speed jet, as well as a slower moving wider stream.

When this combination replaced the diverging jets on the head, this higher-speed jet was sufficiently powerful that it cut through the pyrite, and gave a free surface for the rest of the lens to break into. (Depths of cut up to 3-ft were achieved, although the slot was less than one-inch wide). This worked well for the side of the slab that was now liberated, since the jet had broken it free, and the head could move it away from the face, and into the conveyor track.

The only problem that we had at the time, was that the convergent jet was formed in the center of the slot being cut and in the center of the leading edge of the mining head. The slot was no longer wide enough for the head to enter (the converging jet gave a slot about half-an-inch wide IIRC). As a result the pyrite on the solid side of the cut now engaged with the leading edge of the head and stopped progress.

The answer to the problem, which we arrived at over time, was to change the angle of the axis of convergence of the jets, so that, instead of being in the center of the slot, the convergent jet was inclined over towards the solid, and cut into the pyrite just ahead of the outer edge of the mining head. In this way, since the material to the free side of the head was being moved out of the way by the advance of the machine, the jets still cut clearance for the head to move forward. At the time we were only able to get the machine up to a speed of 10-feet a minute, but by taking a bite of 36-inches at a time, we were able to match the productivity of existing mining machines of the period. (The coal seam was 5-ft high). The guard design on the head was also changed to give a sharper edge on the solid side of the machine.

Figure 5. Change in head guards to penetrate pyrite.

Very little work has been carried out on convergent jet systems since that time, which is a pity since it allowed us to mine harder material than the main jet pressure available was allowing us to achieve.

Pre-mechanized longwall mining

In the last post on this subject, I wrote about how miners were able to remove almost all the coal from a section, either by leaving small remnant pillars or building packs to hold the roof in place, while that coal was removed. By retreating the face back towards the shafts the overlying roof rock was then allowed to collapse into the void left by the coal removal. However, as this process began to evolve the miners noticed a couple of significant things that helped in the understanding of how the roof was responding, and helped to make longwall a safer and more effective method of mining. The first was that at the roof broke behind them, so the rocks would bulk up (they gain about 60% volume as they break and pile). Within a distance of about 2 seam heights, as the roof was converging, without underlying support, it would then meet the broken pile of rock, and thus get some support from this. As a result any support that the miner installed would not need to carry the full weight of the overlying roof to the surface, but only that of a few feet, which needed much less strength.

Thus by about 1870, and possibly in the Lancashire coalfield in the UK, they had modified the process further, and were only supporting the roof around the actual mining operation. How could they get away with this?

There was one other fact that helped make it possible. In some of the earliest tech talks I mentioned that the weight of the overlying ground can be simplified to being around 144 lb./sq ft for every foot of depth – based on the simplifying assumption that a cubic foot of rock weighs 144 lb. Thus converting this to a pressure in lbs/sq inch. (of which there 144 sq ins to a sq ft) this means simplistically that for every foot of depth one goes into the ground, the pressure increases by 1 psi.

Now when you make a hole in the ground, that load, or equivalent rock pressure, has to move somewhere. And it moves just a little so that the weight of the ground over the hole is carried by the rock on either side. However, what happens if this additional load is too high for the rock and it fails?


Well if the rock were just a thin column it would collapse, but if it were thicker, then the weight would just move further into the coal. Now if we came along and moved the coal that had failed, then the hole would just continue to get bigger. But if we leave the coal in place, then the broken coal acts to confine the coal further into the solid. And this confinement gets higher, as the failing pressure continues to move into the wall. And what happens is that this confinement builds up the strength of the coal, so that at some distance into the wall (or face) the coal strength reaches a point that it can carry the weight of the ground above the working area.(For a simple analogy think of a deck of cards, which individually cannot bear weight, but when held together by a rubber band, or a carton, can support quite a bit of weight). (And for those who prefer a more scientific description – the lateral confinement moves the failure from two-dimensions into three, with the minimum principal stress building as one moves into the solid material, and raising the overall failure stress behind it).

This works not only for the coal in pillars, or ahead of the working face of the longwall, but also for the rock that has fallen into the waste and is confined by the rock around each piece allows it to regain some strength, and so collectively the broken rock behind the working face (called the goaf or waste) will continue to compress as the full load comes on it, but will carry the weight of the ground from about twice the seam height, all the way to the surface, and with the other end of the "bridge" as it were resting on the confined coal ahead of the working face.(While the width of this bridge varies with depth, coal and rock strength etc, for an initial estimate you can imagine it as being around 500 ft).

Simplified side view of the coal as the miners removed the coal along the face, moving to the left. They put up wooden supports (three wooden props and a top bar) and let the roof behind the working face that these protected, collapse.

Thus the miner, working at the face, needed only to support only the rock that is up about twice the seam height he was working (in those days women did not do the actual mining). And this could be done with relatively small tree limbs, called props. However, because the rock could break into pieces, the prop support would be distributed, by having a plank, or half split timber, as a bar on top of the prop. Putting one prop at each end thus gave a sort of "goal post" support. Thus, along the face, there would be, at about 4-5 ft intervals, these prop supports holding the roof up.(The coal is made slightly blue in the pictures to give a better contrast - sorry!)

View looking down on the working area from the top of the fallen rock pile. I have erased a small section of the coal to show the position of the cutter bar of the coal-cutter as it is either dragged, or self propels itself along a cable stretched down the working face.

In the initial working of the longwall panel, the coal was undercut by a team of holers, who each cut a slot at the bottom of the seam, to a depth of about 3-ft, and collectively undercut the face over the course of a shift. As the faces grew longer there was a search for a machine that would make that undercut without the intensive manpower. One such tried to mechanize the simple swinging action of the pick.

Early coal cutting machine used at Garth Colliery in Wales in 1863. (National Museum Wales )

The development of the machine, the coal-cutter, dates from around 1876 when a compressed air machine was developed by Francis Lechner, in which picks mounted on a chain, did the cutting of the coal. (The more modern versions of this look like a chain saw on its side). It took a number of years for the machine to evolve into something that was widely accepted, and by that time the company had been taken over by Joseph Jeffrey (a banker) and became Jeffrey Manufacturing Company. (By the time my dad worked for them they had become British Jeffrey Diamond, and they later became part of the Dresser Group). They had spread to Europe by 1905.

And electrically driven machines were developed, which have not changed that much in the intervening years.

Early Coal Cutter (Iron Miners )

With these machines pulled along the face, undercutting the coal, to give a cut depth that was more typically 7-ft deep, the next step was to break down the overlying coal. Sprags (small wooden wedges) were slipped into the slot at intervals, as the cutter passed up the face – usually run by three men. At the same time holes were being drilled along the face, about 6 ft apart, with a stick of dynamite placed in each one.

After the face had been undercut the coal was blasted down between shifts (7.5 hours) then the collier shift would come in and each man would have about 10 yards of face to load the coal from, and to re-support. To get the coal from the face, a rubber conveyor belt was run along the back end of the supports that were in place before the blast, and the coal would normally not break that far from the face. As the miner shoveled he would also put in a new set of timbers, overlapping the old, and supporting the new working area. Typically this would take another seven hours, with an ideal seam height being about 4.5 ft. Above that the coal volume to move was much greater, and below that it got a bit awkward. For example, below 2 ft thick you lie on your back, with a prop under your shoulder and shovel over your head - how would I know? Yes, there was a reason to go to college).

View of the face, after the coal has been loaded out. The rubber coal conveyor between the last two rows of props must now be broken into strips, and moved forward a row, ready for the next cycle. Then the back props and bars are removed. (Saving the front two props and chopping out the back one).

In the third shift, the men would come in and break down and move over the conveyor belt, and then remove the last row of wooden supports, bringing the roof down, beyond the new line of supports.(Smart folk would use a come-along and a chain to pull down the props, young idiots (guess who) would go in with an axe to chop them first). For this was the state of the industry when I went to work in it in 1961. There have been many changes since.