Some aspects of rock machining

Int. J. Rock Mech. Min. Sci. Vol. 9, pp. 205-211. Pergamon Press 1972. Printed in Great Britain

SOME

ASPECTS

OF ROCK

MACHINING

H. M. HUGHES Mining Research and Development Establishment, National Coal Board, Stanhope Bretby, Burton upon Trent, Staffs.

(Received 15 May 1971) Abstract--The cutting energies utilized by rock-working machines are reviewed in relation both to the rock compressive strength and the laws of comminution. The conclusion is drawn that the energy required for breaking into rock is much greater than for breaking it off. The quotient of the rock compressive strength divided by the rock cutting specificenergy has proved roughly constant for given designs of rotary machine and forms a comparative parameter for machine efficiency. A mathematical model of the operation of a rock-working machine is derived: it comprises equating this parameter to the relative efficiencyof the method of fracture multiplied by the relative debris size produced. I. INTRODUCTION SPECIFIC energy (which is the work done per unit volume of rock cut) is the simplest factor for specifying the mechanical performance of a machine in a heading. Compressive strength is the simplest factor for specifying the rock under a t t a c k - - o r the quality of the heading from this point of view. Thus, if we have a machine which utilizes a specific energy E~ when driving a heading in rock of compressive strength fc, then the comparative efficiency of the operation can be conveniently expressed by the dimensionless ratio fdEs. For a given design of rotary machine, optimum ratios offc/Es are remarkably constant whatever the strength of the rock [1]. Many hundreds of tests with the small drill utilized for rock testing at the N.C.B. Mining Research and Development Establishment have given ratios when sharp of the order of 0.25. Rotary drills utilized for shot-holes give about I. Tunnelling machines equipped with roller cutters give about 2; equipped with disks making kerfs a few inches apart, about 3. Roadheaders (i.e. heading machines comprising a rotating head on a universal boom) give 8 or more. The Impact Ripper, which is utilized for enlarging underground openings and comprises an impact mechanism mounted on a drill-type boom, gives over 50 based on the output of the mechanism--although only about 20 based on the output of the power-pack motor. The phenomenon is sufficiently reliable for the ratio to form the basis both of rotary machine design and more generally of operational machine assessment. It is interesting to analyse how it can be interpreted. The following consideration is limited to the energy supplied to the tools for cutting; more energy may be required for debris circulation, secondary crushing, loading out, and for overcoming friction in the machine such as in the pick mats of the Dintheader. This machine incorporates a revolving pick mat on a front jib which is utilized for both cutting and loading out. 2. COMPRESSIVE STRENGTH

The unconfined compressive strength is the most commonly used parameter for specifying rock. The test is relatively easy to do and standardize. When a cylindrical specimen is crushed in a compression machine the load rises steadily from zero to a maximum figure at which point the test piece fails catastrophically. The load immediately falls to zero and 205

206

H.M. HUGHES

fragments fly over the laboratory. The compressive strength is calculated as the quotient of the maximum load divided by the cross-sectional area of the cylinder. It can be analysed as follows. If a cylinder of volume v, area of cross section s, and length/, yields a distance x before failure, and gives a compressive strength off~, then fcS Work done in compressing sample = -~- x. Specific energy = es

f ~sx

f csx

2v

2sl

fox 2l"

A statistical relationship has been noted between Young's modulus and compressive strength for rocks [2]. It has been quoted that Young!s modulus is roughly 350 times compressive strength [3]. Accordingly: Young's modulus --

fd x

-- 350fc.

Thus x l

1 350

L es = 70---0" Thus the specific energy when carrying out a compression test on a rock sample has a direct, if approximate, relation to its unconfined compressivestrength as recorded. No doubt it is for this reason that compressive strength is the most satisfactory rock parameter when considering stone work. The relationship can also be written fc/es -- 700 which may be compared with the figures f o r f f f E , given above for machines. 3. LAWS OF COMMINUTION The operation of rock crushing has been studied for more than one hundred years. Two empirical laws of comminution have been widely debated [4, 5]. Rittinger (1867) postulated that the useful work done in crushing and grinding is directly proportional to the new surface area created. The surface of a batch of pieces increases as they are progressively divided in a geometrically similar fashion. So surface area is usually taken to be proportional to V/D where V is the volume of the batch and D the diameter of the pieces. Kick (1885) postulated that "the energy required for producing analogous changes of configuration of geometrically similar bodies of equal technological state varies as the volumes or weights of these bodies" (after Stadler). This is usually taken to be the same as saying that the energy required for a given size reduction of a given rock is proportional to V irrespectively of the absolute value of D. The difference between the two laws may be illustrated simply as follows, t f a cube of rock is broken into eight equal cubes and each of these again into eight equal cubes, then, according to Rittinger, the work required for the second operation is twice that for the first. According to Kick, the work required for each operation is the same.

SOME ASPECTS OF ROCK MACHINING

207

4. PREPARATORY WORK REQUIRED FOR ROCK FRACTURE

As a general statement, tools applied to rock do work in two basic modes: the preparatory work of breaking into the rock; and the productive work of breaking off the rock. With drag picks, the greater part of the preparatory work goes in friction. Rigid tools are dragged through the material being cut which causes work to be done against friction which leads to heating and wear. The deeper the penetration of the tools and the wider their spacing, the less the energy absorbed in this way: so this energy can be regarded as inversely proportional to debris size which itself is inversely proportional to the area of the new surfaces created. Rotary tools, when they avoid rubbing, utilize far less energy in this manner. At first sight, it might seem that brittle materials such as rock should not deform plastically. But rocks will deform plastically if subjected to high confining pressures [6]. With rotary tools such as disks, the rock-cutting process involves crushing under the fiat of a periphery pushed into the face under high thrust. While the sides of the kerf can fracture and work their way out, the confined rock at the bottom of the kerr cannot escape: it must be pushed back into the rock mass and be plastically deformed. The wider the tools are spaced, the less the energy utilized in this manner: so this energy can also be regarded as inversely proportional to debris size and thus proportional to the area of the new surfaces created. As deformation is not accompanied by an appreciable change in volume, the rock must flow into the area between kerfs which could assist this debris to break off. Drag picks have clearance angles which enable the debris to escape more easily from under them so that they utilize less energy in plastic deformation than do rotary tools. 5. THE PRODUCTIVE WORK OF ROCK CUTTING

Once the tools have broken into the rock, they proceed to elastically strain it. When the strain energy becomes excessive, the rock fractures by propagating pre-existing cracks [7]. Strain energy is thereby released and can be converted into the following: (a) The surface energy of the freshly formed faces [7]. (b) Work of plastic deformation in zones adjacent to the running cracks [8, 9]. (c) The kinetic energy of the fragments [10]. (d) Chemical reactions in thermally unstable materials [11]. Work ceases when a tool stops moving. However, the conversion of strain energy as above can continue unstably thereafter if sufficient has been induced. But the work under (a) is the only ultimately useful quantity. The minimum work to create new surfaces is that converted to their potential energy: it is not possible to manage with less. Nevertheless, in practice, the proportion of the energy of most rock cutting and comminution processes converted into surface energy is only of the order of one tenth of 1 per cent. It is proportional to the area of the new surfaces created. In ductile materials, a large proportion of the strain energy is absorbed in plastic deformation in zones adjacent to the running crack. Pre-existing cracks in strained material develop high stress concentrations at their leading edges. This energy is again proportional to the area of the new faces created. In the case of brittle materials such as rock, fragments can burst from the work place quite explosively. Obviously, they have kinetic energy. Possibly, the less the strain energy absorbed in plastic deformation, the more which goes into the motion of the fragments. It might be considered that such energy is proportional to the mass of the fragments--and thus to the volume of the unfractured piece since the density of rock does not vary greatly.

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Some of the strain energy released by fracture could be used in promoting chemical reactions in thermally unstable materials: these include carbonates. The reactions are limited to a zone around the crack tip as it progresses, so that this quantity of energy would be proportional to the area of the new surfaces created. 6. EFFICIENCY OF ROCK WORKING

With the exception of the potential energy of new surfaces and any energy absorbed in chemical reactions, the energies referred to above under both 'preparatory work' and 'productive work' reduce to heat. A heat balance made for the 18 ft Bretby tunnelling machine at Cloud Hill quarry, Breedon-on-the-Hill [12] showed that about one half of the energy of the machine went into raising the air temperature and evaporating moisture and and about one third into heating the debris. Only about 10 per cent of the energy was unacccounted for. Moreover, as indicated above, the proportion of the energy of comminu, tion ultimately utilized in the creation of new surfaces is only about one tenth of 1 per cenL It has been considered that this is the energy referred to by Rittinger, But it has to be added that the mechanization of rock working has a remarkably low efficiency for a mechanical engineering process. The gross strain energy (referred to above as "the productive work of rock cutting") is, of course, the energy contemplated by Kick. The quantity of strain energy a brittle material can absorb before failure depends on its volume and its technological state (including its history of straining). In the rock compressive test as described above, virtually no energy is utilized for purposes other than straining the specimen. The work of preparing the sample is done on previous occasions and is not taken into account. It may be observed that the dimensionless ratio fc/e~ for the laboratory test is between 14 and 350 times greater than the corresponding ratiofc/E~ for a machine driving a heading. Moreover, in the latter case, roller cutters produce debris of about l'in. size which is much the same as in the laboratory test. Accordingly, for a similar size of debris in the same rock, some 350 times more energy is expended by a machine in a tunnel than by the apparatus in the laboratory. This indicates that the energy utilized under "preparatory work required for rock fracture" is much greater than that utilized under "the productive work of rock cutting". 7. DEBRIS SIZE

Thus, by far the greater part of the effort in rock machining in a heading below ground goes in the preparatory work of breaking into the face. The further apart the tools can be placed while adequately breaking off the rock between kerfs, the less the work done; and also the larger the debris size. Moreover, as may be seen above, some at least of the productive work of breaking off the rock also depends on the new surface area and thus the debris size. For these reasons, Rittinger's law does accord with mechanized stone working. Suppose, therefore, that a machine in a mechanized heading removes a Volume V of rock and creates debris of diameter D. Let the specific energy of the process Work out at Es. Then the work done is Es V. So

GV E~V-----~ D

SOME ASPECTS OF ROCK MACHINING

209

or

E~--

G D

where G is a constant for the regime in the heading and is proportional to the energy required per unit new surface area. Suppose, also, that the rock in the heading gave a compressive strengthf¢ in the laboratory. If the debris size in the laboratory was d, and the specific energy of the test there es, we can also say g es - - ~[

where g is a similar factor for the regime in the laboratory. From the equation in Section 2 above fc = 700 es so that

fc--

700 g

d

8. C O M P A R A T I V E E F F I C I E N C I E S

Thus, the dimensionless comparative parameter for the mechanical efficiency of mechanized stone working becomes

gD Gd"

fc _ 7 0 0 -

E~

As the debris size of the cylindrical specimens tested in the laboratory does not vary greatly, D/d is a relative indication of the debris size produced by the machine. We can denote it by a rock number NR. The ratio giG is a comparison of the specific energy required for a given debris size in the laboratory with that required for the same debris size under the operating conditions in the heading. 700 giG can thus be replaced by -q where ~/is an efficiency factor for the method of fracturing. Accordingly, the dimensionless comparative parameter for the mechanical efficiency of a stone machine becomes the following mathematical model :

L -- "qNR. E~ 9. P R A C T I C A L I N T E R P R E T A T I O N S

The above mathematical model is useful in giving a practical lead both to the development and to the utilization of stone-working machines. For example, in a given isotropic and homogeneous rock, the larger the debris which can be produced, the larger is NR: consequently, the less the work required and the less need be the power of the machine. This effect is in accordance with experience. The sizes of debris produced by the equipments mentioned in the introduction above are as follows: the small test drill--minute; shot-hole drills--~1 in. ; roller cutters--l-in. ; disks at a few inches spacing--a few inches; Roadheaders-about 5 in. Impact Rippers produce debris of some 12 in. typical size. Thusfr/E, increases ROCK9/2--t~

210

H.M. HUGHES

with debris size so that in a given rock, the specific energy reduces as the debris size increases. As rotational head speeds are restricted, the less the power the less need be the strength and hence weight of a rotary machine. Analytical considerations also show that the forces required for fracturing an isotropic and homogeneous rock of given strength increase rapidly with the feed size [t 3]. The stronger the rock, the smaller the pieces which can readily be mechanically broken off: Thus, in a strong rock, not only isfc large but NR has to be small: and the more the power required the bigger and heavier becomes the machine. This again accords with experience. As rocks get stronger, so we progress on rotary machines from picks to disks; and finally to roller cutters which produce very small debris but require very large and heavy machines. The forces, of course, limit drag picks in any case not only in coal mines from considerations of physical strength and wear but on account of frictional heating and the dangers of the ignition of methane. Rocks in a heading, in practice, are seldom isotropic or homogeneous: they contain weaknesses which can be exploited such as laminations, planes of weakness, joints, cleavages and layers of lower strength. The tensile strength of rock is but about one fifth of its unconfined compressive strength. Moreover, weakness can be artifically induced by creating additional free faces and by relieving the rock: a notable example in coal mines is the ripping lip. The more the advantage which can be taken of these weaknesses, the greater becomes V and the less the power and weight of the machine required. Full-face machines are presented rigidly to the face of a tunnel and can take little advantage of such weaknesses although ~ can be improved by attention to the arrangement of the tools [14]. The more flexible the machine the greater the intelligence an operator can exploit in his mode of attack [15]. This fact is notable with the Roadheader but is particularly so with the Impact Ripper. Here the tool can be accurately oriented to a cleavage in an under-cut rock and so bring down large pieces with a minimum of effort. As noted in the Introduction, the Impact Ripper can give particularly high ratios offc/E~--higher than can be accounted for by the increase in size of the debris alone. 10. CONCLUSIONS The cutting energy required for mechanized stone work can be divided into two parts: the preparatory work of breaking into the rock; and the productive work of breaking off the rock. The former takes incomparably the greater effort with drag picks or rotary tools although the latter provides the bulk of the rock won. When calculating the power requirements of a machine, only the former need normally be taken into account. With drag picks, the greater part of the preparatory effort goes in friction. With rotary tools, it is absorbed in pushing trapped rock back into the rock mass and in plastically deforming it. One consequence of this is that rotary tools can be far less prone to causing frictional ignitions of methane than drag picks. There are two methods for reducing the preparatory work. The first comprises increasing the distance between indentations as far as is efficiently workable; this correspondingly increases the size of the debris. The second involves utilizing the least preparatory effort. The more flexible the machine, the gieater the possibilities it confers of utilizing the least preparatory effort by exploiting weaknesses in the strata. The stronger the rock (and the more nearly isotropic and homogeneous) the smaller the pieces which can readily be mechanically broken off and the greater the preparatory work required.

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211

Acknowledgements--The author wishes to thank the Director of the N.C.B. Mining Research and Development Establishment for permission to publish this paper, and colleagues for the provision of information. The views expressed are, however, those of the author and not necessarily those of the National Coal Board. REFERENCES 1. HUOHESH. M. Mechanised stone work. Min. Engr 128, 689-697 (1969). 2. JuoD W. R. and HUBER C. Correlation of Rock Properties by Statistical Methods, Proceedings of the International Symposium on Mining Research, Missouri, Vol. 2, p. 621, Pergamon Press (1962). 3. FARMERI. W. Engineering Properties of Rocks, p. 39, Spon (1968). 4. GATES A. O. Kick vs. Rittinger: an experimental investigation in rock crushing performed at Purdue University. Trans. Am. Inst. Min. metall. Engrs 52, 875-909 (1915). 5. WALKERD. R. and SHAW M. C. A physical explanation of the empirical laws ofcomminution. Trans. Am. Inst. Min. metall. Engrs 199, 313-320 (1954). 6. WAWERSmW. R. and FAIRHURSTC. A study of brittle rock fracture in laboratory compression experiments. Int. J. Rock Mech. Min. Sci. 7, 561-575 (1970). 7. GRIFFITI-IA. A. The phenomena of rupture and flow in solids. Trans. R. Soe. A221, 163-198 (1920). 8. OROWANE. Fracture and strength of solids. Rep. Progr. Phys. 12, 185-232 (1949). 9. IRWIN G. R. Fracturing of metals. (A.S.M. Symposium, Chicago 1947). Trans. Am. Soc. Metals 40A, 147-166 (1948). 10. Moa-'r N. F. Fracture of metals: some theoretical considerations. Engineering 165, 16-18 (1948). 11. Fox P. G. and SORTA-Rt~z J. Fracture-induced thermal decomposition in brittle crystalline solids. Proe. R. Soc. A317, 79-90 (1970). 12. LAWRENCEB. F. and KING B. J. Climatic Conditions during Trials of the C.E.E. Tunnelling Machine at Cloud Hill Quarry, M.R.E. Laboratory Note 168 (Internal N.C.B. Report) (1963). 13. BERGSTROMB. H., CRABTREED. D. and SOLLENBERGERC. L. Feed size effects in single particle crushing Trans. Am. Inst. Min. metall. Engrs 226, 433-441 (1963). 14. POMEROYC. D. and ROBINSOND. J. Laboratory Investigations of some Rock and Coal Cutting Problems including Corner Cutting, M.R.D.E. Report 4 (Internal N.C.B. Report) (1970). 15. BAILEYJ. J. and DEAN R. C. JR Rock Mechanics and the Evolution of Improved Rock Cutting Methods, Proceedings of the Eighth Symposium on Rock Mechanics, University of Minnesota, September 1966, pp. 396~J,09, A.I.M.E., New York (1967).