For future reference, it is desirable at this point to tabulate the torsional moment, or torque, about each of the three shaft axes, assuming reasonable efficiencies for the various parts, as follows:
Efficiency between drum and pinion shaft...........90 per cent.
Efficiency between drum and motor shaft...........80 per cent.
Inch Lbs. Torque at 100 Per Cent Efficiency.
Inch Lbs. Torque, Efficiency as Above.
5,000 x27/2 ...........= 67,500
67,500/.95 = 71,052
5,000 x (27/2) x (13/12)... = 12,187
5,000 x( 27/2) x (13/72) x(10.5/42) =3,047
This means that the motor develops a torque of 3,809 inch-pounds delivering to pinion shaft 13,541 inch-pounds, and to drum 71,052 inch-pounds.
The page of calculation for belt width is reproduced in Fig. 3.
The calculation as given is strictly scientific, based on the working strength of a cemented joint (t=400 lbs. per square inch). This is a favorable situation for the use of a cemented joint, because it is easy to provide means of adjusting the belt tension by placing the motor on a sliding base. Otherwise a laced joint could be used, requiring relacing when the belt slackens through its stretch in service. Under the assumption that a double laced belt is used, the empirical formula below is one often applied:
H.P. = w x v/540 = w x1,300/540 = 30.
This gives w= 540 X 30/1,300 =12.4 inches (say 12 inches).
It should be remembered that this value is purely empirical; it applies to a laced joint, and could not be expected to check the value of 9 inches obtained by the first computation for a cemented joint. It is fairly in proportion. For the quite definite service required of the belt in the present case, the width of 9 inches is doubtless sufficient, considering the cemented joint.
Considerable latitude in choice of length of bearings is permissible, especially in such slow-speed machinery. There is probably little danger from heating, and the question then becomes one of wear. It is better in such cases as the one in question, to choose boldly a length which seems to be reasonable and proceed with the design on that basis, even if the length be later found out of proportion to the shaft diameter, than to waste too much time in the preliminary calculation over the exact determination of this question. Probably in most cases of commercial practice the existence of patterns, or some other practical consideration, will decide the limits of length.
In the present instance it seems reasonable that a length of 6 inches would fill the requirement for the worst case, that of the drum shaft, and it is obvious that the bearings for the pinion shaft would naturally be of the same length on account of being cast on the same bracket, and faced at the same setting of the planer tool.
The large pulley should naturally swing clear of the floor. This will require, say, a total height of 23 inches, out which we may take 4 inches for the base, leaving 19 inches as the height, center of bearing to base of bracket.
The data as found above should now be put on the sketch previously made; it will then have the appearance shown in Fig. 1.
This sketch is now in form to control all the subsequent detail design, and it is expected that the figured dimensions as shown can be maintained. It is impossible to predict this with positiveness, however, as in the working out of the minor details certain changes may be found desirable, when, of course, they should be made.
The shaft sizes do not appear on this sketch, hence before proceeding further the several shaft diameters must be calculated.
The calculations of the shaft diameters are good instances of systematic engineering computations, hence they are reproduced in the exact form in which they were made. The student should learn a valuable lesson in making and recording calculations by following these carefully. Note that each set of figures is independent, both in the statement of given data, as well as in the actual computation. Observe how easy it would be for the author of these figures or anyone else to check them even after a long lapse of time. If the machine should unexpectedly fail in service the figures are always available to prove or disprove theoretical weakness. The right triangles merely indicate that the value of √B2 + T2 was found by the graphical method suggested in Part IT, "Shafts," the figures being put on the triangle as a simple and direct way of recording both process and result.
Attention is especially called to the fact that in the pinion shaft the size is changed for each piece upon the shaft. This is done partly because it is desired to show the student that the shaft at each of these points should bo theoretically of different size. It is also done because as a practical feature of construction it is a good plan to change the size when the fit changes, partly for rea-Bunn of production in the shop, partly for ease in slipping pieces freely endwise on the shaft until they reach their proper fit and location in the assembling of the machine.
This should not be taken as an absolute requirement in any sense. A straight shaft would be satisfactory in the present case; but the shouldered shaft is a little better construction, in a mechanical sense, and does not cost much more. Hence it is used. For the drum the straight shaft seems to answer the requirement well enough.
Small Pulley Bore. Fig 4.
Large Pulley Bore. Fig. 5.
Bearing Next to Large Pulley. Fig. 6.
The diameter, 2 11/16, as calculated, is based on the supposition that the greatest bending moment is caused by the belt pull on the overhanging pulley, that is, by the forces existing at the left-hand aide of the center of the bearing.
Bat the pinion tooth load produces a heavy bending on the shaft in the bearing, the shaft in this case acting as a beam sapported at the two bearings and having the tooth load applied as shown. If this latter effect be greater than the former, that is, if the bending moment produced by the pinion tooth load be greater than the bending moment produced by the belt pull, then the diameter must be increased to satisfy the latter case. As is seen by the second calculation of Fig. 6, this is not the case, and the diameter stands at 211/16 as made.