Fig. 13. As the size of the drum shaft was determined by considering the rope wound close up to the brake, thus giving in combination with the load on the gear tooth the maximum reaction at the bearing as 6,748 pounds, the cap and bolts should be designed to carry the same load.
For a bearing but 6 inches long, two bolts are sufficient under ordinary conditions and might perhaps do for this case. The load is pretty heavy, however, and it is deemed wise to provide four bolts, thus securing extra rigidity, and permitting the use of bolts of comparatively small size. If the load were distributed equally over all the bolts each would take one-fourth of the whole load, but it is not usually safe to figure them on this basis, because it is difficult to guarantee that each bolt will receive its exact share of stress. Assuming that the two bolts on one side take 8/3 the whole load instead of ½, which provides for this uncertain extra stress, each bolt must take care of 1/3 of 6,748, or 2,249, pounds. Allowing 8,000 pounds per square inch fibre stress calls for an area at the root of the thread of 2,249/8,000 = .281 square inch. Consulting a table of bolts we find that the next standard size of bolt greater than this is ¾, which gives an area of .302 square inch.
Choosing this size as satisfactory, the bolts should be located as close to the shaft as will permit the hole to be drilled and tapped wituout breaking out. A center distance of 5½ inches accomplishes this result. The distance between centers in the other direction is somewhat arbitrary, although the theoretical distance between the bolt and the end of the bearing to give equal bending moment at the center of the cap and at the line of the bolts is about 5/24 of the length, or 5/24 of 6 = 1¼ inches. This proportion answers well for the present case, although for long caps it brings the bolts too far in to look well.
The thickness of the cap may be determined by assuming it to be a beam supported at the bolts and loaded at the middle. This is not strictly true, for the load is distributed over at least a portion of the shaft diameter; moreover, the bolts to some extent make the beam fixed at the ends. It being impossible to determine the exact nature of the loading, we may take it as stated, supported at the ends and loaded in the middle, and allow a higher fibre stress than usual, say 3,500. The longitudinal section at the middle of the cap is rectangular, of breadth 6 inches, and depth unknown, say A. The equation of moments is W x l / 4 = S x I / c = S x b x h2 / 6.
6,748 X 5.5 / 4 x 3,500 x 6 x h2 / 6 h2 = 64X0,748X5.5 / 4 x 3,500 x 6 = 2.65 h = √ 2.65 will probably answer).
For the other bearing next to the pinion, the load on the tooth acts downward, and the resultant pull of the belt is nearly horizontal, hence the cap and bolts must stand but little load, and calculation would give minute values. In a case like this it is well to make the size the same as for the larger bearing, unless the construction becomes very clumsy thereby. This saves changing drills and taps in making the holes, and preserves the symmetry of the bracket. The ¾-inch bolts are good proportion for the smaller bearing, hence that size will be maintained throughout.
The body of the bracket is conveniently made with the web at the side and horizontal ribs extending to the outside. The load due to the rope is carried directly down the side ribs and web into the bottom flanges and to the bolts. The analysis of the forces on these bolts is shown in Fig. 14. It is evident from the figure that the resultant belt pull tends to hold the bracket down, while the load on the rope tends to pull it up, the point about which it tends to rotate being the corner furthest from the drum. It is also evident that the bolts nearest this corner can have little effect on the holding down, because their leverage is so small about the corner, hence we shall assume that the pair of bolts at the right-hand end of the bracket takes all the load. The belt pull, being horizontal, tends to slide the bracket along the base, but this tendency is small, and at any rate is easily taken care of by the two dowel pins, which are. thus put in shear.
The load on the bolts being 4,954 pounds, a heavy bending moment is thrown on the flange of the bracket, tending to break it off at the root of the fillet. The distance to the root of the fillet is ¾ inch; the section tending to break is rectangular, of breadth 5½ inches, and unknown depth A. The equation of moments is:
W x l = S x I / c = S x b x h2 / 6
4,954X3 / 4 = 2,500 X 5.5 x h2 / 6
6X4,954X3 h2 = 6 x 4,954 x 3 / 4X2,500X5.5 = 1.62 h = √ 1. 62 = 1.3 (sayl¼). The thickness of the web and ribs of this bracket is hardly capable of calculation. The figure | inch has been chosen in proportion to the size of the large drum bearing, giving ample stiffness and rigidity, and permitting uniform flow and cooling of the metal in the mold. The opening in the center is made merely to save material, as in that part little stress would exist, the two sides carrying the load down to the base bolts, and the top serving as a tie between the bearings.
This bracket might be made with the web in the center of the bearings instead of at the side, in which case the expense of the pattern would be slightly greater. It could also be made of closed box form, but would in that case probably weigh more than as shown.
TROLLEY OF IS TONS CAPACITY. The Case Mrg Co.