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Fig. 8 shows an arrangement often used in woollen-mills, where the guides are calledcarrier pulleys, or, sometimes, gallows pulleys. The guides are ordinarily set at the same height, an arrangement that can never admit of a perfect running belt; although it will answer a purpose, when little power is to be transmitted. Mr. Sellers of Philadelphia has, I think, a hanger for the guides, that is applicable for one position of the driven-pulley in reference to the driver. For all other cases the position must be determined specially, by lines or drawings, as before stated, if it is important to have a perfect running belt.
The next model (Fig. 14) shows two pulleys which are not in line, are not of same size, are not square with each other. One shaft is not horizontal, and differs in height from the other, and the belt is crossed ; thus presenting, I think, all the difficulties usually met with : yet the belt runs perfectly in either direction by means of two guides.
Referring again to the case of shafts at angles, having considerable difference in height. Here is a model (Fig. 19) with a cord stretched over the working-pulleys, and the ends brought together in a point of the cord between the two working-pulleys, so that the portions of cord about each pulley are in the plane of that pulley : a guide-pulley, to run perfectly, must lie in the plane of, and touch, the two end portions of cord thus placed.
It is not uncommon practice to place guides on the slack side, in positions having a resemblance to those here shown (Figs. 1 and 5), but with this important difference, that the belt draws at one edge, having the same fault as the quarter-turn without guides (Fig. 4), except that the defect is transferred wholly to the slack side of belt.
There have been in use two different schemes to guide the belt in this defective way: one leads the belt off to one side from the driving-pulley on to a guide which is at first set on a horizontal shaft, with one of its faces in the plane of the driven-pulley, and then direct on to the driven-pulley; the guide is then canted by trial until it will retain the belt. A guide so placed is in a very different position from that shown in Fig. 1, and requires constant changes in position to keep the belt in place with varying loads, and at once runs off if the motion is reversed. If two guides are used, the second (H, Fig. 16) is placed in the plane of the driven-pulley with a face in a vertical line with the face of the first guide as set before being canted. When the two guides are properly arranged in this scheme, the belt draws properly over both guides, and has a tearing strain only at the point (K, Fig. 16) where it leaves the driving-pulley. The guide in the plane of the driven-pulley can be used as a tightener, by vertical adjustment. This arrangement will run only in one direction, and, at best, gives only partial satisfaction.
In the second scheme (Fig. 17), when a single guide is used, it is set in a plane passing through the portion of belt leading from the driving-pulley, with its shaft in a vertical plane parallel to that portion of the belt. The guide-pulley is set so as to deliver the belt in the plane of the driven-pulley, but the pulley itself is not set in the plane of the two straight portions of belt in contact with it: there is, therefore, a side strain on the belt at the point (L) where it leaves the guide. In short, this scheme to use a single guide, like the last damed, will not work as laid out; and its position is varied by trial until the belt will retain its place for a time. When two guides are used, the second is placed in the plane of the driving-pulley, and near to it, bringing the belt near to its tight side. The canted guide is placed between that guide-pulley and the driven-pulley as before (Fig. 18). With two guides there is less cant in the first guide; and the fault of side draught is lessened, but can never be fully corrected. If a wedge were placed on a vertical surface parallel to the drivenpulley, to give the necessary cant to a stud carrying the guide, the thin edge of the wedge (M, Figs. 17, 18) would be, by this arrangement, horizontal; while, when the guide is correctly placed (as in Fig. 1 or Fig. 19), the thin edge would be parallel to the portion of belt between the guide and driven pulley. The wedge itself would be of a different angle from that used in the imperfect scheme mentioned. The correct construction would bring the thin edge of the wedge horizontal only when the top of the guide is at the same height as the bottom of the driven-pulley, — a position impossible to attain in practice. The better way is, to select a point near each working-pulley, in the plane of that pulley, and at a safe distance from the tight side of the belt, and trace out this path with a cord; then, as before explained, put the guides in the plane of the adjoining portions of the cord. Fig. 5 is an example of this practice.
It may, or may not, be important to run the belt at any time in a reverse direction ; but the fact, that the belt can so run, is proof that the belt is drawing evenly at each edge; and that the whole capacity of the belt can be used in transmitting power, beside reducing the extent and inequality of stretching. The fault of side strain is very different from the stretch due to twisting a belt about its centre: the one is excessive, and at one point of the belt; the other is slight, and distributed, and need never be as great as the stretch of the outside of a belt more than that of its centre, when wrapping round a pulley of ordinary size. This never gives concern, and is hardly recognized as existing. The fault due to twisting never occurs at the same time as that due to wrapping; and as it is, or may be, less in amount, it will be covered by the last-named fault.
A preference is often expressed for the arrangement shown in this model (Fig. 5), on account of the extent to which the belt wraps the working-pulleys ; the value of wrap, in increasing the adhesion of the belt, is, perhaps, not generally understood. I have a chart, or diagram (Fig. 20), calculated from the formula generally accepted, for each ten degrees, with a curve drawn through the points thus laid down.
The dark band represents the width of belt required to transmit the strain of the load, - that is, the width of belt that would be required if the adhesion of belt to pulley were perfect; the lighter portion outside shows, by radial measurement, the proportionate width required to carry the strain needed on the slack side, to maintain sufficient adhesion ; while the dark and light portions together, measured radially, show the proportionate width of belt needed to transmit the power, with a given amount of wrap, and maintain the needed adhesion. When the index at the number 180, of the inner circle, is turned to the radial line marked 1.36, the diagram is adapted for that co-efficient, or factor, for friction between iron and leather, which is generally accepted for the case of pulleys of fair size, with belts in good condition. Opposite the mark of inner circle indicating 260 degrees, we find the number 1.17, which indicates that the proportionate width of belt required at 260 degrees is 13% of that required at 180; or, about as 6 to 7. The points to set the index or 180 degree mark, for other factors for friction, are placed on the dark band; and, if I set it at the number 70 (indicating seventy per cent of friction between the belt and pulley, which may be assumed in the case of a leather-covered pulley, and a belt in good condition), we shall now find that the mark indicating 260 degrees of wrap is beyond the point to which I have carried the curve ; but it will be seen that the radial lines are growing shorter very slowly, and, at the point opposite the mark for 260 degrees, would be about 1.06; while at 180 degrees the width is about 1.12, – that is to say, at 260 degrees of wrap a seventeen-inch belt might be used in place of an eighteen-inch belt at 180 degrees. This slight advantage in increased wrap is more than offset by the increased strain needed, on the slack side, to keep the belt on the guide-pulleys when the guides are incorrectly set, as in Figs. 16, 18.
It is generally assumed, that, for ordinary cases, an inch, in width, of double belt will transmit one horse-power, when the belt is running on iron pulleys at the rate of 400 feet per minute; and I know of no cases of failure to do good work, when that proportion has been adopted. If we calculate the necessary width of belt for any required power on this basis, and assume that, as proper for 180 degrees of wrap, then on setting the index for another factor for friction, we can read off the figures for any degree of wrap, and compare with the figures 1.36; thus determining the proportionate width of belt for
the particular case. If a belt running at 4,000 feet per minute were required to deliver 120 horse-power, a twelve-inch belt would be needed ; now, if we make use of a leather-covered pulley by which we could increase the factor for friction to 70, we should have for, let us assume, 150 degrees of wrap, a required width of belt 1.16+1.36X12, or about 104 inches. It is not proposed to calculate to quarter-inches on belting, while there is such a variance in opinion as to the proper width of belt needed for ordinary cases, nor until belts from different manufacturers become more nearly equal in strength.
The diagram illustrates, however, the proportionate widths required for different degrees of wrap, and different factors for friction ; and, if you can determine what is satisfactory for one case, you may,
from the diagram, determine what would be equally satisfactory for another, with a belt having the same strength for an equal section. The diagram presents all the results of somewhat tedious calculations, with more than sufficient precision.
Notes. – If the circle inside the dark band of diagram (Fig. 20) is cut out with a sharp knife, it may then be turned as stated; and if the two portions are mounted on cardboard, and the circle made to turn on a pin, the diagram will be reproduced as exhibited.
Reference having been made, at the meeting, to "a system analogous to" mine, in use at the Allison Car Works, Philadelphia, I wrote to Mr. Allison; and, after sending him drawings of five arrangements, be selected that representing Fig. 6, as being like his, - which has been running about ten years, with a twenty-inch belt. This was unexpected evidence of the practicability of the arrangement, and is offered for the use of those needing that evidence more than I do.
Examples of the second-named imperfect scheme for quarter-turn belt with guides, having one pulley on horizontal shaft, and one, on canted shaft (Figs. 17, 18), may be seen in models at Lowell Machine Shop, also one, arranged for single guide, in actual operation. The agent will undoubtedly bear testimony to the defects of angle belts, based on his practical experience with them.
Examples of the first-named imperfect scheme for quarter-turn belts with guides, being that with guides on horizontal shafts (Fig. 16), in various degrees of perfection, may be seen in a number of the mills at Lowell; and a drawing of one case, made by an eminent mechanical engineer, was in existence not long since, at the office of one of the mills there, which well illustrates the state of the art.