There seems to be considerable difference in opinion regarding the various ways of applying rope to the sheaves in rope driving, viz., multiple- or separate-rope system, continuous-wrap or single-rope system with the rope from one of the grooves running on a traveling take-up device, continuous-wrap or single-rope system with the take-up working directly on all the wraps.

The multiple- or separate-rope system on a horizontal drive where the distance between centers is great enough so that the weight of the rope will give the required tension, having the tight or pulling part on the lower side and the sheaves of the same diameter, as in Fig. 85, should be very satisfactory, as old or worn ropes may be replaced by new ones of larger diameter, or some of the ropes may be tighter than others and still not alter the efficiency of the drive. It will be noticed in this case that a larger rope does not alter the proportional pitch diameters of the rope on the driving and driven sheaves; but if one of the sheaves is larger than the other, as in Figs. 86 and 87, and a new or larger rope is substituted for a worn or smaller one, or if some of the ropes are a great deal tighter than others, a differential action will be produced on the ropes owing to the fact that the larger or slack rope will not go as deeply into its grooves as the smaller or tight one. Consequently the proportionate pitch diameter on the rope on the driver and driven sheave will be changed. The action will depend upon whether the large or the small sheave is the driver. If the driver is the larger, and of course assuming that the slack or large rope is weaker than the combined tight or smaller ones, then it will have less strain on the pulling side; but if the driver is smaller, then the new or large rope will have greater strain on the pulling side. Whether the driver is larger or smaller, a large or slack rope affects the action oppositely to a small or tight rope. Fig. 87 shows how the action is reversed from Fig. 86.

For clearness we will exaggerate the differences in diameter in the sketches and figure the speeds that the different size ropes would produce. We will take A as normal, B 1 inch farther out of the groove, producing a difference in diameter of 2 inches; C 1 inch deeper in the groove, producing a difference in diameter of 2 inches. In Fig. 85 assume for the normal diameter of driver and driven 40 inches, 42 inches for B and 38 inches for C, with a speed of 200 revolutions per minute for the driver. Either A, B or C will give 200 revolutions per minute for the driven sheave, omitting slippage, of course. In Fig. 86 say the normal diameter of the driver for rope A is 60 inches and of the driven 30 inches, a speed of the driver of 200 revolutions per minute will give the driven sheave a speed of 400 revolutions per minute; B, with the driver 62 inches and the driven sheave 32 inches diameter, will give the latter a velocity of 387½ revolutions per minute. With C the driver is 58 inches, the driven 28 inches, and the speed given the latter 414 2/7 revolutions per minute. In Fig. 87, the normal diameter of the driving sheave being 30 inches and the driven 60 inches, a speed of the driver of 200 revolutions per minute will give a speed of the driven member of 100 revolutions per minute. With B, if the driver is 32 and the driven 62 inches, the driven sheave will have a speed of 103 7/31 revolutions per minute; C, with the driver 28 inches and the driven sheave 58 inches, will give the latter a speed of 96 16/29 revolutions per minute. So it will be readily seen what effect a large or a small rope would have.

There are some who claim that slack ropes will transmit more power owing to more wrap on the sheaves, while others claim that tight ropes are better. If a drive with all the ropes slack gave trouble by the ropes slipping, the first remedy tried would be tightening the ropes. But if the conditions were like Fig. 87, it would not be particularly harmful to have some of the ropes longer than others; in fact, it might be well, as the longer ropes would not make a complete circuit as quickly as the shorter ones; consequently the position of the splices would be continually changing. However, it seems more natural to have about the same pull on all the ropes, that is, not have them as shown in Fig. 88. In conclusion for the system, it should be noted that it has no means of tightening the ropes except by resplicing; it is not as well adapted to various conditions as the other forms; it is the cheapest form to install and in some cases should give excellent satisfaction.

With the continuous-wrap system having the rope from one of the grooves pass over a traveling take-up, the latter has a tendency to produce an unequal strain in the rope. In taking up, or letting out, the rope must either slide around the grooves, or the strands having the greatest pull will wedge themselves deeper into the grooves, producing a smaller pitch diameter than the ones having less pull, making a differential action on the ropes. It is therefore probable that it is the differential action that takes up or lets out the ropes, the take-up merely acting in a sense as an automatic adjustable idler. In tightening, when the rope stretches or dries out, or even in running normal, the greatest pull will be near the take-up, but if the drive is exposed to moisture, and the rope shortens, it will be farthest from the take-up, depending proportionately on the number of grooves the take-up controls; so in large drives it is best to have more than one take-up.

If one should use an unyieldable substance, as, for experiment, a plain wire on two drums wrapped a number of times around and also over a take-up, and the drums were moved together or apart, he would find that the wire would have to slide around the drum; but, of course, with a rope in a groove it is different. The rope will yield some. It will also go deeper into the groove. This system costs more than the preceding form, owing to extra expense for the traveling take-up, but may be applied readily to different conditions and will be quite satisfactory in general, if properly designed and installed.

The continuous-wrap system with a take-up or tightener acting directly on all the wraps has practically none of the objectionable features mentioned in the other two forms, and is quick in action, making it applicable where power is suddenly thrown on or off. If the tightener is made automatic, it may be controlled in numerous ways, as with a weight or weight and lever or tackle blocks and weight, etc. It also may be fitted with a cylinder and piston, with a valve to prevent too quick action if power is suddenly thrown off or on. There is ordinarily practically no unequal strain on the rope. This system may be applied to different conditions as readily as the preceding form. Its cost is more than that of either of the others, as the tightener must have as many grooves as there are wraps. It must also have a winder to return the last wrap to the first groove, and to give its highest efficiency it must be properly designed and installed.

In either of the continuous-wrap systems, if a portion of larger rope is used, it will produce a greater strain directly behind the large rope, owing to its traveling around the sheave quicker. In angle work there is always extra wear on the rope in the side of the groove, as only the center or one rope may be accurately lined; so it is not advisable to crowd the centers in angular drives, as the shorter the centers and wider the sheaves the greater the wearing angle. It must be remembered that the foregoing applies to ordinary simple drives as shown in the sketches; where the drive is complicated, it may be necessary to make other allowances.

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