Fig. 143Fig. 143.
Fig. 143.
This clearance exists at the sides of the teeth, as inFig. 143, ata, and between the tops of the teeth and the bottoms or roots of the spaces as atb. When, however, the simple term clearance is employed it implies the side clearance as ata, the clearance atbbeing usually designated astop 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 berappedin 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 becomeout 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 tooth7⁄10, of the pitch working depth6⁄10; hence1⁄10of the pitch is allowed for top and bottom clearance, and this is the amount shown atbinFig. 143. The amount of side clearance given by Willis as that ordinarily found in practice is as follows:—“Thickness of tooth5⁄11of the pitch; breadth of space6⁄11; hence, the side clearance equals1⁄11of 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,1⁄4inch, we have thickness of tooth 11⁄4, width of space 13⁄4, or1⁄2inch 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 about1⁄32inch. But in the proportion of1⁄32inch to every 2 inches of diameter, the rapping on a 6-foot wheel would amount to 11⁄16inches, whereas, in actual practice, a 6-foot wheel would not enlarge the mould more than at most1⁄8inch from the rapping.
It is obvious, then, that it would be more in accordance with the requirements to proportion the amount of clearance to the diameter of the wheel, so as to keep the clearance as small as possible. This will possess the advantage that the teeth will be stronger, it being obvious that the teeth are weakened both from the loss of thickness and the increase of height due to the clearance.
It is usual in epicycloidal teeth to fill in the corner at the root of the tooth with a fillet, as atc,d, inFig. 143, to strengthen it.This is not requisite when the diameter of the generating circle is so small in proportion to the base circle as to produce teeth that are spread at the roots; but it is especially advantageous when the teeth have radial flanks, in which case the fillets may extend farther up the flanks than when they are spread; because, as shown inFig. 47, the length of operative flank is a minimum in teeth having radial flanks, and as the smallest pinion in the set is that with radial flanks, and further as it has the least number of teeth in contact, it is the weakest, and requires all the strengthening that the fillets in the corners will give, and sometimes the addition of the flanges on the sides of the pinion, such gears being termed “shrouded.”
The proportion of the teeth to the pitch as found in ordinary practice is given by Professor Willis asfollows:—
The depth to pitch line is, of course, the same thing as the height of the addendum, and is measured through the centre of the tooth from the point to the pitch line in the direction of a radial line and not following the curve of tooth face.
Referring to the working depth, it was shown inFigs. 42and44that the height of the addendum remaining constant, it varies with the diameter of the generating circle.
Fig. 144Fig. 144.
Fig. 144.
From these proportions or such others as may be selected, in which the proportions bear a fixed relation to the pitch, a scale may be made and used as a gauge, to set the compasses by, and in marking off the teeth for any pitch within the capacity of the scale. A vertical linea binFig. 144, is drawn and marked off in inches and parts of an inch, to represent the pitches of the teeth; at a right angle toa b, the lineb cis drawn, its length equalling the whole depth of tooth, which since the coarsest pitch in the scale is 4 inches will be7⁄10of 4 inches. From the end of linecwe draw a diagonal line toa, and this gives us the whole depth of tooth for any pitch up to 4 inches: thus the whole depth for a 4-inch pitch is the full length of the horizontal lineb c; the whole depth for a 3-inch pitch will be the length of the horizontal line running from the 3 on linea b, to linea con the right hand of the figure; similarly for the full depth of tooth for a 2-inch pitch is the length of the horizontal line running from 2 toa c. The working depth of tooth being6⁄10of the pitch a diagonal is drawn fromameeting linecat a distance frombof6⁄10of 4 inches and we get the working depth for any other pitch by measuring (along the horizontal line corresponding to that pitch), from the line of pitches to the diagonal line for working depth of tooth. The thickness of tooth is5⁄11of the pitch and its diagonal is distant5⁄11of 4 (fromb) on lineb c, the thickness for other pitches being obtained on the horizontal line corresponding to those pitches as before.
Fig. 145Fig. 145.
Fig. 145.
The construction of a pattern wherefrom to make a foundry mould, in which to cast a spur gear-wheel, is as shown in section, and in plan ofFig. 145. The method of constructing these patterns depends somewhat on their size. Large patterns are constructed with the teeth separate, and the body of the wheel is built of separate pieces, forming the arms, the hub, the rim, and the teeth respectively. Pinion patterns, of six inches and less in diameter, are usually made out of a solid piece, in which case the grain of the wood must lie in the direction of the teeth height. The chuck or face plate of the lathe, for turning the piece, must be of smaller diameter than the pinion, so that it will permit access to a tool applied on both sides, so as to strike the pitch circle on both sides. A second circle is also struck for the roots or depths of the teeth, and also, if required, an extra circle for striking the curves of the teeth with compasses, as was described inFig. 130. All these circles are to be struck on both sides of the pattern, and as the pattern is to be left slightly taper, topermit of its leaving the mould easily, they must be made of smaller diameter on one side than on the other of the pattern; the reduction in diameter all being made on the same side of the pattern. The pinion body must then be divided off on the pitch line into as many equal divisions as there are to be teeth in it; the curves of the teeth are then marked by some one of the methods described in the remarks on curves of gear-teeth. The top of the face curves are then marked along the points of the teeth by means of a square and scribe, and from these lines the curves are marked in on the other side of the pinion, and the spaces cut out, leaving the teeth projecting. For a larger pinion, without arms, the hub or body is built up of courses of quadrants, the joints of the second coursebreaking jointwith those of the first.
The quadrants are glued together, and when the whole is formed and the glue dry, it is turned in the lathe to the diameter of the wheel at the roots of the teeth. Blocks of wood, to form the teeth, are then planed up, one face being a hollow curve to fit the circle of the wheel. The circumference of the wheel is divided, or pitched off, as it is termed, into as many points of equal division as there are to be teeth, and at these points lines are drawn, using a square, having its back held firmly against the radial face of the pinion, while the blade is brought coincidal with the point of division, so as to act as a guide in converting that point into a line running exactly true with the pinion. All the points of division being thus carried into lines, the blocks for the teeth are glued to the body of the pinion, as denoted bya, inFig. 145. Another method is to dovetail the teeth into the pinion, as inFig. 145atb. After the teeth blocks are set, the process is, as already described, for a solid pinion.
Fig. 146Fig. 146.
Fig. 146.
Fig. 147Fig. 147.
Fig. 147.
Fig. 148Fig. 148.
Fig. 148.
Fig. 149Fig. 149.
Fig. 149.
The construction of a wheel, such as shown inFig. 145, is as follows: The rimrmust be built up in segments, but when the courses of segments are high enough to reach the flat sides of the arms they should be turned in the lathe to the diameter on the inside, and the arms should be let in, as shown in the figure ato. The rest of the courses of segments should then be added. The arms are then put in, and the inside of the segments last added may then be turned up, and the outside of the rim turned. The hub should then be added, one-half on each side of the arms, as in the figure. The ribscof the arms are then added, and the body is completed (ready to receive the teeth), by filleting in the corners. An excellent method of getting out the teeth is as follows: Shapeapiece of hard wood, as inFig. 146, making it some five or six inches longer than the teeth, and about three inches deeper, the thickness being not less than the thickness of the required teeth at the pitch line. Parallel to the edgeb c, mark the linea d, distant fromb cto an amount equal to the required depth of tooth. Mark off, about midway of the piece, the linesa bandc d, distant from each other to an amount equal to the breadth of the wheel rim, and make two saw cuts to those lines. Take a piece of board an inch or two longer than the radius of the gear-wheel and insert a piece of wood (which is termed a box) tightly into the board, as shown inFig. 147,erepresenting the box. Let the pointfon the board represent the centre of the wheel, and draw a radial linerfromfthrough the centre of the box. From the centref, with a trammel, mark the addendum lineg g, pitch lineh i, and linej kfor the depth of the teeth (and also a line wherefrom to strike the teeth curves, as shown inFig. 129if necessary). From the radial liner, as a centre, mark off on the pitch circle, points of division for several teeth, so as to be able to test the accuracy of the spacing across the several points, as well as from one point to the next, and mark the curves for the teeth on the end of the box, as shown. Turn the box end for end in the board, and mark out a tooth by the same method on the other end of the box. The box being removed from the board must now have its sides planed to the lines, when it will be ready to shape the teeth in. The teeth are got out for length, breadth, and thickness at the pitch line as follows: The lumber from which they are cut should be very straight grained, and should be first cut into strips of a width and thickness slightly greater than that of the teeth at the pitch line. These strips (which should be about two feet long) should then be planed down on the sides to very nearly the thickness of the tooth at the pitch line, and hollow on one edge to fit the curvature of the wheel rim. From these strips, pieces a trifle longer than the breadth of the wheel rim are cut, these forming the teeth. The pieces are then planed on the ends to the exact width of the wheel rim. To facilitate this planing a number of the pieces or blank teeth may be set in a frame, as inFigs. 148and149, in whichais a piece having the blocksb baffixed to it.cis a clamp secured by the screws ats s, and 1, 2, 3, 4, 5, 6 are the ends of the blank teeth. The clamp need not be as wide as theteeth, as inFig. 148, but it is well to let the piecesaandb bequal the breadth of the wheel rim, so that they will act as a template to plane the blank teeth ends to. The ends ofb bmay be blackleaded, so as to show plainly if the plane blade happens to shave them, and hence to prevent planingb bwith the teeth. The blank teeth may now be separately placed in the box (Fig. 146) and secured by a screw, as shown in that figure, in whichsis the screw, andtthe blank tooth. The sides of the tooth must be carefully planed down equal and level with the surface of the box. The rim of the wheel, having been divided off into as many divisions as there are to be teeth in the wheel, as shown inFig. 150, ata,a,a, &c., the finished teeth are glued so that the same respective side of each tooth exactly meets one of the linesa. Only a few spots of glue should be applied, and these at the middle of the root thickness, so that the glue shall not exude and hide the linea, which would make it difficult to set the teeth true to the line. When the teeth are all dry they must be additionally secured to the rim by nails. Wheels sufficiently large to incur difficulty of transportation are composed of a number of sections, each usually consisting of an arm, with an equal length of the rim arc on each side of it, so that the joint where the rim segments are bolted together will be midway between the two arms.
Fig. 150Fig. 150.
Fig. 150.
This, however, is not absolutely necessary so long as the joints are so arranged as to occur in the middle of tooth spaces, and not in the thickness of the tooth. This sometimes necessitates that the rim sections have an unequal length of arc, in which event the pattern is made for the longest segment, and when these are cast the teeth superfluous for the shorter segments are stopped off by the foundry moulder. This saves cutting or altering the pattern, which, therefore, remains good for other wheels when required.
When the teeth of wheels are to be cut in a gear-cutting machine the accurate spacing of the teeth is determined by the index plate and gearing of the machine itself; but when the teeth are to be cast upon the wheel and a pattern is to be made, wherefrom to cast the wheel the points of division denoting the thickness of the teeth and the width of the spaces are usually marked by hand. This is often rendered necessary from the wheels being of too large a diameter to go into dividing machines of the sizes usually constructed.
To accurately divide off the pitch circle of a gear-wheel by hand, requires both patience and skilful manipulation, but it is time and trouble that well repays its cost, for in the accuracy of spaces lies the first requisite of a good gear-wheel.
It is a very difficult matter to set the compasses so that by commencing at any one point and stepping the compasses around the circle continuously in one direction, the compass point shall fall into the precise point from which it started, for if the compass point be set the1⁄200th inch out, the last space will come an inch out in a circle having 200 points of divisions. It is, therefore, almost impossible and quite impracticable to accurately mark or divide off a circle having many points of division in this manner, not only on account of the fineness of the adjustment of the compass points, but because the frequent trials will leave so many marks upon the circle that the true ones will not be distinguishable from the false. Furthermore, the compass points are apt to spring and fall into the false marks when those marks come close to the true ones.
Fig. 151Fig. 151.
Fig. 151.
InFig. 151is shown a construction by means of which the compass points may be set more nearly than by dividing the circumference of the circle by the number of divisions it is required to be marked into and setting the compasses to the quotient, because such a calculation gives the length of the division measured around the arc of the circle, instead of the distance measured straight from point of division to point of division.
The construction ofFig. 151is as follows:p pis a portion of the circle to be divided, anda bis a line at a tangent to the pointcof the circlep p. The pointdis set off distant fromc, to an amount obtained by dividing the circumference ofp pby the number of divisions it is to have. Take one-quarter of this distancec d, and mark it fromc, giving the pointe, set one point of the compass ateand the other atd, and draw the arcd f, and the distance fromftoc, as denoted byg, is the distance to which to set the compasses to divide the circle properly. The compasses being set to this distanceg, we may rest one compass point atc, and mark the arcf h, and the distance between archand arcd, measured on the linea b, is the difference between the pointsc,fwhen measured around the circlep p, and straight across, as atg.
Fig. 152Fig. 152.
Fig. 152.
A pair of compasses set even by this construction will not, however, be entirely accurate, because there will be some degree of error, even though it be in placing the compass points on the lines and on the points marked, hence it is necessary to step the compasses around the circle, and the best method of doing this is as follows: Commencing ata,Fig. 152, we mark off continuously one from the other, and taking care to be very exact to place the compass point exactly coincident with the line of the circle, the pointsb,c,d, &c., continuing until we have marked half as many divisions as the circle is to contain, and arriving ate, starting again ata, we mark off similar divisions (one half of the total number),f,g,h, arriving ati, and the centrek, between the two linese,i, will be the true position of the point diametrally opposite to pointa, whence we started. These points are all marked inside the circle to keep them distinct from those subsequently marked.
Fig. 153Fig. 153.
Fig. 153.
Fig. 154Fig. 154.
Fig. 154.
It will be, perhaps, observed by the reader that it would be more expeditious, and perhaps cause less variation, were we to set the compasses to the radius of the circle and mark off the pointk, as shown inFig. 153, commencing at the pointa, and marking off on the one side the linesb,c, andd, and on the other sidee,f, andg, the junction or centre, betweengandd, at the circle being the true position of the pointk. For circles struck upon flat surfaces, this plan may be advantageous; and in cases where there are not at hand compasses large enough, a pair of trammels may be used for the purpose; but our instructions are intended to apply also to marking off equidistant points on such circumferences as the faces of pulleys or on the outsides of small rings or cylinders, in which cases the use of compasses is impracticable. The experienced hand may, it is true, adjust the compasses as instructed, and mark off three or four of the marksb,c, &c., inFig. 152, and then open out the compasses to the distance between the two extreme marks, and proceed as before to find the centrek, but as a rule, the time saved will scarcely repay the trouble; and all that can be done to save time in such cases is, if the holes come reasonably close together, to mark off, after the compasses are adjusted, three or four spaces, as shown inFig. 154. Commencing at the pointa, and marking off the pointsb,c, andd, we then set another pair of compasses to the distance betweenaandd, and then mark, fromdon one side and fromaon the other, the marks fromftoland frommtot, thus obtaining the pointk. This method, however expeditious and correct for certain work, is not applicable to circumferential work of small diameter and in which the distance between two of the adjacent points is, at the most,1⁄20of the circumference of the circle; because the angle of the surface of the metal to the compass point causes the latter to spring wider open in consequence of the pressure necessary to cause the compass point to mark the metal. This will be readily perceived on reference toFig. 155in whicharepresents the stationary, andbthe scribing or marking point of the compasses.
Fig. 155Fig. 155.
Fig. 155.
The error in the set of the compasses as shown by the distance apart of the two markseandion the circle inFig. 152is too fine to render it practicable to remedy it by moving the compass legs, hence we effect the adjustment by oilstoning the points on the outside, throwing them closer together as the figure shows is necessary.
Fig. 156Fig. 156.
Fig. 156.
Fig. 157Fig. 157.
Fig. 157.
Having found the pointk, we mark (on the outside of the circle, so as to keep the marks distinct from those first marked) the divisionb,c,d,Fig. 156, &c., up tog, the number of divisions betweenbandgbeing one quarter of those in the whole circle. Then, beginning atk, we mark off also one quarter of the number of divisions arriving atmin the figure and producing the point 3. By a similar operation on the other side of the circle, we get the true position of point No. 4. If, in obtaining points 3 and 4, the compasses are not found to be set dead true, the necessary adjustment must be made; and it will be seen that, so far, we have obtained four true positions, and the process of obtaining each of them has served as a justification of the distance of the compass points. From these four points we may proceed in likemanner to mark off the holes or points between them; and the whole will be as true as it is practicable to mark them off upon that size of circle. In cases, however, where mathematical precision is required upon flat and not circumferential surfaces, the marking off may be performed upon a circle of larger diameter, as shown inFig. 157. If it is required to mark off the circlea,Fig. 157, into any even number of equidistant points, and if, in consequence of the closeness together of the points, it becomes difficult to mark them (as described) with the compasses, we mark a circleb bof larger diameter, and perform our marking upon it, carrying the marks across the smaller circle with a straightedge placed to intersect the centres of the circles and the points marked on each side of the diameter. Thus, inFig. 157, the lines 1 and 2 on the smaller circle would be obtained from a line struck through 1 and 4 on the outer circle; and supposing the larger circle to be three times the size of the smaller, the deviation from truth in the latter will be only1⁄3of whatever it is in the former.
In this example we have supposed the number of divisions to be an even one, hence the pointk,Fig. 152, falls diametrically opposite toa, whereas in an odd number of points of division this would not be the case, and we must proceed by either of the two followingmethods:—
Fig. 158Fig. 158.
Fig. 158.
InFig. 158is shown a circle requiring to be divided by 17 equidistant points. Starting from point 1 we mark on the outside of the circumference points 2, 3, 4, &c., up to point 9. Starting again from point 1 we mark points 10, 11, &c., up to 17. If, then, we try the compasses to 17 and 9 we shall find they come too close together, hence we take another pair of compasses (so as not to disturb the set of our first pair) and find the centre between 9 and 17 as shown by the pointa. We then correct the set of our first pair of compasses, as near as the judgment dictates, and from pointa, we mark with the second compasses (set to one half the new space of the first compasses) the pointsb,c. With the first pair of compasses, starting fromb, we markd,e, &c., tog; and fromi, we mark divisionsh,i, &c., tok, and if the compasses were set true,kandgwould meet at the circle. We may, however, mark a point midway betweenkandg, as at 5. Starting again from pointscandi, we mark the other side of the circle in a similar manner, producing the linespandq, midway between which (the compasses not being set quite correct as yet) is the true point for another division. After again correcting the compasses, we start fromband 5 respectively, and mark point 7, again correcting the compasses. Then fromcand the point betweenpandq, we may mark an intermediate point, and so on until all the points of division are made. This method is correct enough for most practical purposes, but the method shown inFig. 159is more correct for an odd number of points of division. Suppose that we have commenced at the point markedi, we mark off half the required number of holes on one side and arrive at the point 2; and then, commencing at the pointiagain, we mark off the other half of the required number of holes, arriving at the point 3. We then apply our compasses to the distance between the points 2 and 3; and if that distance is not exactly the same to which the compasses are set, we make the necessary adjustment, and try again and again until correct adjustment is secured.
Fig. 159Fig. 159.
Fig. 159.
It is highly necessary, in this case, to make the lines drawn ateach trial all on the same side of the circle and of equal length, but of a different length to those marked on previous trials. For example, left the linesa,b,c,d, inFig. 159represent those made on the first trial, ande,f,g,h, those made on the second trial; and when the adjustment is complete, let the last trial be made upon the outside or other side of the circle, as shown by the linesi,j,k,l. Having obtained the three true points, marked 1, 2, 3, we proceed to mark the intermediate divisions, as described for an even number of divisions, save that there will be a space, 2 and 3, opposite point 1, instead of a point, as in case of a circle having an even number of divisions.
The equal points of division thus obtained may be taken for the centres of the tooth at the pitch circle or for one side of the teeth, as the method to be pursued to mark the tooth curves may render most desirable. If, for example, a template be used to mark off the tooth curves, the marks may be used to best advantage as representing the side of a tooth, and from them the thickness of the tooth may be marked or not as the kind of template used may require. Thus, if the template shown inFig. 21be used, no other marks will be used, because the sides of a tooth on each side of a space may be marked at one setting of the template to the lines or marks of division. If, however, a template, such as shown inFig. 81be used, a second set of lines marked distant from the first to a radius equal to the thickness of a tooth becomes necessary so that the template may be set to each line marked. If the Willis odontograph or the Robinson template odontograph be used the second set of lines will also be necessary. In using the Walker scale a radial line, asginFig. 142, will require to be marked through the points of equal division, and the thickness of the tooth at the points on the pitch circle and at the root must be marked as was shown inFig. 142.
But if the arcs for the tooth curves are to be marked by compasses, the location for the centres wherefrom to strike these arcs may be marked from the points of division as was shown inFig. 130.
Fig. 160Fig. 160.
Fig. 160.
To construct a pattern wherefrom to cast a bevel gear-wheel.—When a pair of bevel-wheels are in gear and upon their respective shafts all the teeth on each wheel incline, as has been shown, to a single point, hence the pattern maker draws upon a piece of board a sketch representing the conditions under which the wheels are to operate. A sketch of this kind is shown inFig. 160, in whicha,b,c,d, represent in section the body of a bevel pinion.f gis the point of a tooth on one side, andethe point of a tooth on the other side of the pinion, whileh iare pitch lines for the two teeth. Thus, the cone surface, the points, the pitch lines and the bottom of the spaces, projected as denoted by the dotted lines, would all meet atx, which represents the point where the axes of the shafts would meet.
Fig. 161Fig. 161.
Fig. 161.
In making wooden patterns wherefrom to cast the wheels, it is usual, therefore, to mark these lines on a drawing-board, so that they may be referred to by the workman in obtaining the degree of cone necessary for the bodya b c d, to which the teeth are to be affixed. Suppose, then, that the diameter of the pinion is sufficiently small to permit the bodya b c dto be formed of one piece instead of being put together in segments, the operation is as follows: The faced cis turned off on the lathe, and the piece is reversed on the lathe chuck, and the facea bis turned, leaving a slight recess at the centre to receive and hold the cone point true with the wheel. A bevel gauge is then set to the anglea b c, and the cone of the body is turned to coincide in angle with the gauge and to the required diameter, its surface being made true and straight so that the teeth may bed well. While turning the faced cin the lathe a fine line circle should be struck around the circumference of the cone and neard c, on which line the spacing for the teeth may be stepped off with the compasses. After this circle or line is divided off into as many equidistant points as there are to be teeth on the wheel, the points of division require to be drawn into lines, running across the cone surface of the wheel, and as the ordinary square is inapplicable for the purpose, a suitable square is improvised as follows: InFig. 161let the outline in full lines denote the body of a pinion ready to receive the teeth, anda bthe circle referred to as necessary for the spacing or dividing with the compasses. Ona btake any point, asc, as a centre, and with a pair of compasses mark equidistant on each side of it two lines, asd,d. Fromd,das respective centres mark two lines, crossing each other as atf, and draw a line, joining the intersection of the lines atfwithc, and the last line, so produced, will be in the place in which the teeth are to lie; hence the wheel will require as many of these lines as it is to contain teeth, and the sides of the teeth, being set to these lines all around the pinion, will be in their proper positions, with the pitch lines pointing tox, inFig. 160.
Fig. 162Fig. 162.
Fig. 162.
Fig. 163Fig. 163.
Fig. 163.
Fig. 164Fig. 164.
Fig. 164.
To avoid, however, the labor involved in producing these lines for each tooth, two other plans may be adopted. The first is to make a square, such as shown inFig. 162, the facef fbeing fitted to the surfacec, inFig. 161, while the edges of its bladecoincide with the line referred to; hence the edge of the blade may be placed coincident successively with each point of division, asd d, and the lines for the place of the length of each tooth be drawn. The second plan is to divide off the linea bbefore removing the body of the pinion from the lathe, and produce, as described, a line for one tooth. A piece of wood may then be placed so that when it lies on the surface of the hand-rest its upper surface will coincide with the line as shown inFig. 163, in whichwis the piece of wood, anda,b,c, &c., the lines referred to. If the teeth are to be glued and bradded to the body, they are first cut out in blocks, left a little larger every way than they are to be when finished, and the surfaces which are to bed on the cone are hollowed to fit it. Then blocks are glued to the body, one and the same relative side of each tooth being set fair to the lines. When the glue is dry, the pinion is again turned on the lathe, the gauge for the cone of the teeth being set in this case to the linese,f,ginFig. 160. The pitch circles must then be struck at the ends of the teeth. The turned wheel is then ready to have the curves of the teeth marked. The wheel must now again be divided off on the pitch circle at the large end of the cone into as many equidistant points as there are to be teeth on the wheel, and from these points, and on the same relative side of them, mark off a second series of points, distant from the points of division to an amount equal to the thickness the teeth are required to be. From these points draw in the outline of the teeth (upon the ends of the blocks to form the teeth) at the large end of the cone. Then, by use of the square, shown inFig. 162, transfer the points of the teeth to the small end of the cone, and trace the outline of the teeth at the small end, taking centres and distances proportionate to the reduced diameter of the pitch circle at the small end, as shown inFig. 160, where atjare three teeth so marked for the large end, and atkthree for the small end,p prepresenting the pitch circle, andr ra circle for the compass points. The teeth for bevel pinions are sometimes put on by dovetails, as shown inFig. 164, a plan which possesses points of advantage and disadvantage. Wood shrinks more across the grain than lengthwise with it, hence when the grain of the teeth crosses that of the body with every expansion or contraction of the wood (which always accompanies changes in the humidity of the atmosphere) there will be a movement between the two, because of the unequal expansion and contraction, causing the teeth to loosen or to move. In the employment of dovetails, however, a freedom of movement lengthways of the tooth is provided to accommodate the movement, while the teeth are detained in their proper positions. Again, if in making the founders’ mould, one of the mould teeth should break or fall down when the pattern is withdrawn, a tooth may be removed from the pattern and used by the moulder to build up the damaged part of the mould again. And if the teeth of a bevel pinion are too much undercut on the flank curves to permit the whole pattern from being extracted from the mould without damaging it, dovetailed teeth may be drawn, leaving the body of the pattern to be extracted from the mould last. On the other hand, the dovetail is a costly construction if applied to large wheels. If the teeth are to be affixed by dovetails, the construction varies as follows: Cut out a wooden template of the dovetail, leaving it a little narrower than the thickness of the tooth at the root, and set the template on the cone at a distance from one of the linesa,b,c,Fig. 163, equal to the margin allowed between the edge of the dovetail and the side of the root of the tooth, and set it true by the employment of the square, shown inFig. 162, and draw along the cone surface of the body lines representing the location of the dovetail grooves. The lines so drawn will give a taper towardx(Fig. 160), providing that, the template sides being parallel, each side is set to the square. While the body is in the lathe, a circle on each end may be struck for the depth of the dovetails, which should be cut out to gauge and to template, so that the teeth will interchange to any dovetail. The bottom of the dovetails need not be circular, but flat, which is easier to make. Dovetail pieces or strips are fitted to the grooves, being left to project slightly above the face of the cone or body. They are drawn in tight enough to enable them to keep their position while being turned in the lathe when the projecting points are turned down level with the cone of the body. The teeth may then be got out as described for glued teeth, and the dovetails added, each being marked to its place, and finally the teeth are cut to shape.