When at the surface, the foot-pounds will be (36 +4 +7 +7) × 112 = 6,048 lbs. x 812 the leverage = 49,109 8. At the end of the first stroke it will be {6,048 +(17 x 8)} x 8'1250,214 1. At the end of the second stroke it will be {6,048 +(34 x 8)} x 812 the leverage = 51,318 4, and so on, the number of footpounds increasing regularly 1,104'3 at each stroke, so that when the empty cage reaches the pit-bottom the foot-pounds will be (6,048 + (510 x 8)} x 8'12 the leverage 82,239. The actual work done by the engine is shown on the diagram, Fig. 77, by line CC' which is obtained by deducting the foot-pounds of the empty cage from those of the full one. The power necessarily exerted at the lift is 118,617-49,109.869,507 2 footpounds and at the end of the winding 85,488 - 82,239 = 3,249 foot-pounds. A case may readily be imagined where the foot-pounds at the end of the Fig. 77.-DIAGRAM SHOWING THE WORK DONE BY WINDING ENGINE, winding will be a negative instead of a positive number, or in which the engine may have to exercise a retarding influence in consequence of the preponderance of the weight of the descending cage and rope over that of the full cage. For instance, take a shaft 1,530 feet deep as before in which the cage, chains, and tubs are of the same weight as there given, but at which flat ropes 4 inches x weighing 15 lbs. per yard are used for winding by means of a drum whose diameter at the start is 20 feet. Then, by the formula given in Chapter XIX. (see Index, under Winding-engine), the number of revolutions will be Here the weight of the full cage at the lift is {10,528 + (510 × 151)} × 10 the leverage 184,330 foot-pounds. When the full cage reaches the surface the foot-pounds will be 10,528 x 1164 the leverage = 122,546. = = {6,048 + Similarly the weight of the empty cage when at the surface is 6,048lbs. × 11.64 the leverage = 70,399 foot-pounds, and when at the pit-bottom (510 x 15 x 10 the leverage 139,530 foot-pounds. = The power necessarily exerted at the lift then is 184,330 - 70,399 =3 113,931 foot-pounds, and at the end of the winding 122,546 139,530 = 16,984 footpounds that is, instead of a positive, a negative power of 16,984 foot-pounds must be exercised by the engine. Referring again to Fig. 77, the dotted line DD' represents the work actually to be done so that the load may be uniform throughout the winding, because the triangle DEC = the triangle D'EC'. In foot-pounds it is 3.249 + 69,507 36,378, and is represented by FE. In order to keep the load on this line without deviation, it would be necessary to use a counterbalance whose action is shown by the line GG' on the diagram, because the triangle GFO = the triangle CED, and the figure O'C'EF + the triangle G'FO' = the figure O'D'EF. The counterbalance at the lift then must exercise a reducing effect to the load of 69,507′2 – 36,378 = 33,129 2 foot-pounds, but become regularly less as the winding proceeds, until at meetings it is nothing. As the winding continues beyond the cage meetings, the engine has in addition to the load to raise the counterbalance, which at the completion of winding must be represented by 33,129 2 foot-pounds. 2 Fig. 78. PENDULUM COUNTERBALANCE. = Different methods of counterbalancing, with a view of assisting the windingengine at the commencement of the wind, have been adopted at different times, some of which are as follow: Rope balance. This consists of a tail-rope attached to the cages in the shaft. It is fastened to the bottom part of the cage at the surface and is conveyed to a point below the loading-stage in the pit, where it passes round a pulley and then up to the other cage, under which it is secured. The object sought by this method is to make the load uniform; when the cage is lifted from the shaft bottom, the weight of the ropes in the shaft balance each other, and will continue to do so throughout the wind. An objection to the tail-rope in the shaft is the extra strain on the capping of the ropes. Another method is by a pendulum counterbalance, which, however, is only applicable to shallow shafts, where the necessity for counterbalancing is not urgent. A weighted pendulum is raised by a chain attached to a drum on the shaft of the winding-engine, see Fig. 78. At the commencement of winding this pendulum is in a horizontal position, and therefore the full weight is acting to aid the engine against the load. As the winding proceeds to half-winding an increasing portion of the weight is supported by the rod, which at half-winding is in a perpendicular position, and then as the load is brought to the surface the rod returns to a horizontal position, the weight thus acting against the engine with increasing force during the last half-winding. A third method consists in a counterbalance chain, see Fig. 79, which is frequently applied with very good results to assist the winding-engine. This requires a separate pit or well about 50 yards deep for the chain to work in. A rope is fixed to the drum-shaft of the engine and to the balance-chain in the small pit. The balance-chain would be 50 yards long, and is so arranged that with one cage at the surface and the other at the shaft bottom the whole length of chain is hanging in the small pit. The rope by which it is wound up allows the whole of the balance-chain to rest upon the small pit bottom when the ascending and descending cages meet in the shaft. The rope passes over the drum-shaft in a contrary direction to the drawing-rope. A fourth method is that of the inclined plane, Fig. 80. Usually this is only applicable to shallow shafts, but where the engine-house is situated on high ground, and a gradual slope from it can be obtained, it admits of a long travel for the tub or truck, and so becomes applicable to greater depths of winding. Instead of the bunch of chain used in the last described method, a weighted tub or truck is attached, and this travels over an inclined plane the gradient of which must vary throughout its course, and be steepest at the commencement of the plane next the engine-house. Any attempt to use this kind of counterbalance where the gradient is uniform for the tub or truck to move on is quite useless. The rails laid should form a curve, and not break abruptly from one uniformly inclined short portion to another. At half winding the tub or truck reaches the end of its run, and is wound upwards towards the engine-house as Fig. 79.-CHAIN COUNTERBALANCE. Fig. 80.-INCLINED. PLANE COUNTERBALANCE. the winding proceeds; on completion of the winding it returns to its starting point. Other methods of counterbalancing are by using the cone and scroll drums in preference to plain or cylindrical drums, and these have already been alluded to. A plain conical drum, to be effective as a counterbalance, requires an angle so great as to be dangerous on account of the liability of the rope to slip. Any advantage to be derived from having a safe angle being trifling, it is really not worth the risk. Rule 29 of the Mines Act, 1887, renders the use of flanges or horns to the drum compulsory, and if the drum is conical, there must be appliances sufficient to prevent the rope from slipping. Supposing, in the instance we have been considering, a rope-balance be applied, and that it is of precisely the same weight per yard as the round winding rope, then it is obvious that no calculations are required, for the ropes, cages and tubs must balance each other throughout the wind; the line EF, the actual weight of the coal will be the load on the engine which will be uniform during the ascent of the cage from the shaft bottom to the surface. The pendulum counterbalance is not applicable to a pit of this depth, we therefore proceed to consider the chain counterbalance in the instance given. Assuming the bunch of chain has to be hung in a 51-yard pit, then as the engine makes 30 revolutions, the rope roll for the counterbalance must have a circumference of 51 X 3 X 2 = 10'2 feet, or a diameter of 3 24675 feet. The leverage 30 then is 162338 foot, so that the weight of the bunch must be 33,129 2 lbs., or 9 tons, 2 cwt., 23 lbs. 162338 = 20,407'5 When the cages are at meetings, and the whole of the bunch is lying coiled at the bottom of the counterbalance pit, there would not be such relief as would arise from a perfect counterbalancing effect, because there would be the rope in the counterbalance pit, 51 yards and possibly 19 above the pit = 70 yards at, say, 10 lbs. per yard 700 lbs. x 1.62338 1,136 foot-pounds. The effect of this would cause the line DD' to deviate from a straight one slightly at E, but a very good attempt would be made to produce a counterbalance. = = Next to design an inclined plane counterbalance in the example we are considering, which is, say, 51 yards long and the diameter of counterbalance rope roll 162338 foot as before:-Let a weighted truck of, say, 30 tons be used. Then for its effective weight to be similar to that of the chain bunch or 9 tons, 2 cwt. 23 lbs., the inclination for the first stroke or 102 feet = 30 tons 9 tons, 2 cwt., 23 lbs., 3 293. The foot-pounds at the next stroke must be reduced th or 2,208.6. 33,1292 - 2,208.6 = 30,920'6. 15 = I in 33,129 2 = = 19,047 lbs. The incli The foot 30,920'6 nation for the next stroke then must be 30 x 2,240 pounds must be reduced at the next or 3rd stroke = 1 in 3'799. 17,686.5 30 X 2,240 16,326 30 X 2,240 30 X 2,240 13,605 30 X 2,240 12,244'5 30 X 2,240 10,884 30 X 2,240 9,523'5 30 X 2,240 30 X 2,240 30 x 2,240 = 1 in 4'116. = 1 in 4'49. = 1 in 4'939. = 1 in 5'488. = 1 in 6'174. = 1 in 7056. = 1 in 8.232. = 1 in 9.878. = 1 in 12 349. At the commencement of the 13th stroke 30 × 2,240 = 1 in 16'464. 4,081'5 30 X 2,240 = 1 in 24-697. 15th 15th 2,721 = 1 in 49'393. As the winding proceeds toward completion, the loaded tub changes its direction after the 15th stroke and returns over the inclined plane whose gradients have just been estimated. Now, to consider the last system of counterbalancing, viz., the spiral drum. If the initial diameter be 16 feet, the weight of the full cage is represented by (10,528 +4,080) x 8 the leverage 116,864 foot-pounds. The weight of the coal must always remain to be overcome by the engine even in a perfect counterbalance. This would be 20 + 20 = 40 cwt. of coal × 112 × 8: = 35,840 footpounds, and as the empty cage and tubs at the surface weigh 6,048 lbs., the final radius would be 116,864-35,840 6,048 13'39 or a diameter of 26.78, changing regularly for each revolution. The number of revolutions such drum would Where a flat rope is used for winding, lapped one coil over the other, it has to a very slight extent, a counterbalancing effect. The difference between the extreme diameters is, however, a negligible quantity. MISCELLANEOUS.-In laying out the surface arrangements, a considerable amount of thought is necessary to ensure a thoroughly satisfactory and economical working after completion. The particular circumstances and requirements of each colliery must be thoroughly mastered in order to design an effective scheme. The engines and buildings must be adapted to their work, and after the coal is brought to the surface every operation connected with its weighing, screening, cleaning, and after-disposal, should be calculated to give as little manual labour as possible in working, and at the same time yield the various sizes of coal in a good, clean, and marketable condition. A carelessly laid out bank top renders it necessary to keep employed a large number of workmen to deal with the daily out-put, and thus add to the cost of production. In times of keen competition even a penny extra cost on the tonnage price in raising the coal may place a colliery at a disadvantage as compared with a neighbouring one, and result in loss of contracts; with greatly increased cost prices, it may be impossible to work the colliery at all. Mr. C. M. Percy, in his excellent work on The Mechanical Engineering of Collieries, gives the following rules for winding-engines. (1) To find the load which a given pair of engines will start. Multiply the area of one cylinder by the pressure of steam and twice the length of stroke. Divide this by circumference of drum and deduct for friction, &c. The result is the load the engines can start. For instance, 2 - 20-inch diameter cylinders by 40-inch stroke, with a 12-foot diameter drum and the steam pressure at boilers 50 lbs. 314 X 50 X 80 = 2,766 or 922 1,844 lbs. the load. N.B.-The load 454 in. |