For a pair of wheels Mr. Walker strikes the face curve by a point on the pitch rolling circle, and the flanks by a point on the addendum circle, fastening a piece of wood to the pitch circle to carry the tracing point. The flank of each wheel is struck with a tracing point, thus attached to the pitch circle of the other wheel.
The proportions of teeth and of the spaces between them are usually given in turns of the pitch, so that all teeth of a given pitch shall have an equal thickness, height, and breadth, with an equal addendum and flank, and the same amount of clearance.
The term “clearance” as applied to gear-wheel teeth means the amount of space left between the teeth of one wheel, and the spaces in the other, or, in other words, the difference between the width of the teeth and that of the spaces between the teeth.
Fig. 143.
This clearance exists at the sides of the teeth, as in [Fig. 143], at a, and between the tops of the teeth and the bottoms or roots of the spaces as at b. When, however, the simple term clearance is employed it implies the side clearance as at a, the clearance at b being usually designated as top and bottom clearance. Clearance is necessary for two purposes; first, in teeth cut in a machine to accurate form and dimensions, to prevent the teeth of one wheel from binding in the spaces of the other, and second, in cast teeth, to allow for the imperfections in the teeth which are incidental to casting in a founder’s mould. In machine-cut teeth the amount of clearance is a minimum.
In wheels which are cast with their teeth complete and on the pattern, the amount of clearance must be a maximum, because, in the first place, the teeth on the pattern must be made taper to enable the extraction of the pattern from the mould without damage to the teeth in the mould, and the amount of this taper must be greater than in machine-moulded teeth, because the pattern cannot be lifted so truly vertical by hand as to avoid, in all cases, damage to the mould; in which case the moulder repairs the mould either with his moulding tools and by the aid of the eye, or else with a tooth and a space made on a piece of wood for the purpose. But even in this case the concentricity of the teeth is scarcely likely to be preserved.
It is obvious that by reason of this taper each wheel is larger in diameter on one side than on the other, hence to preserve the true curves to the teeth the pitch circle is made correspondingly smaller. But if in keying the wheels to their shafts the two large diameters of a pair of wheels be placed to work together, the teeth of the pair would have contact on that side of the wheel only, and to avoid this and give the teeth contact across their full breadth the wheels are so placed on their shafts that the large diameter of one shall work with the small one of the other, the amount of taper being the same in each wheel irrespective of their relative diameters. This also serves to keep the clearance equal in amount both top, and bottom, and sideways.
A second imperfection is that in order to loosen the pattern in the sand or mould, and enable its extraction by hand from the mould, the pattern requires to be rapped in the mould, the blows forcing back the sand of the mould and thus loosening the pattern. In ordinary practice the amount of this rapping is left entirely to the judgment of the moulder, who has nothing to guide him in securing an equal amount of pattern movement in each direction in the mould; hence, the finished mould may be of increased radius at the circumference in the direction in which the wheel moved most during the rapping. Again, the wood pattern is apt in time to shrink and become out of round, while even iron patterns are not entirely free from warping. Again, the cast metal is liable to contract in cooling more in one direction than in another. The amount of clearance usually allowed for pattern-moulded cast gearing is given by Professor Willis as follows:—Whole depth of tooth 7⁄10, of the pitch working depth 6⁄10; hence 1⁄10 of the pitch is allowed for top and bottom clearance, and this is the amount shown at b in [Fig. 143]. The amount of side clearance given by Willis as that ordinarily found in practice is as follows:—“Thickness of tooth 5⁄11 of the pitch; breadth of space 6⁄11; hence, the side clearance equals 1⁄11 of the pitch, which in a 3-inch pitch equals .27 of an inch in each wheel.” Calling this in round figures, which is near enough for our purpose, 1⁄4 inch, we have thickness of tooth 11⁄4, width of space 13⁄4, or 1⁄2 inch of clearance in a 3-inch pitch, an amount which on wheels of coarse pitch is evidently more than that necessary in view of the accuracy of modern moulding, however suitable it may have been for the less perfect practice of Professor Willis’s time. It is to be observed that the rapping of the pattern in the founder’s mould reduces the thickness of the teeth and increases the width of the spaces somewhat, and to that extent augments the amount of side clearance allowed on the pattern, and the amount of clearance thus obtained would be nearly sufficient for a small wheel, as say of 2 inches diameter. It is further to be observed that the amount of rapping is not proportionate to the diameter of the wheel; thus, in a wheel of 2 inches diameter, the rapping would increase the size of the mould about 1⁄32 inch. But in the proportion of 1⁄32 inch to every 2 inches of diameter, the rapping on a 6-foot wheel would amount to 11⁄16 inches, whereas, in actual practice, a 6-foot wheel would not enlarge the mould more than at most 1⁄8 inch from the rapping.