Modern Machine-Shop Practice Part 15

[Ill.u.s.tration: Fig. 154.]

The error in the set of the compa.s.ses as shown by the distance apart of the two marks E and I on the circle in Fig. 152 is too fine to render it practicable to remedy it by moving the compa.s.s legs, hence we effect the adjustment by oilstoning the points on the outside, throwing them closer together as the figure shows is necessary.

[Ill.u.s.tration: Fig. 155.]

Having found the point K, we mark (on the outside of the circle, so as to keep the marks distinct from those first marked) the division B, C, D, Fig. 156, &c., up to G, the number of divisions between B and G being one quarter of those in the whole circle. Then, beginning at K, we mark off also one quarter of the number of divisions arriving at M in 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 compa.s.ses 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 compa.s.s points. From these four points we may proceed in like manner 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 circ.u.mferential surfaces, the marking off may be performed upon a circle of larger diameter, as shown in Fig. 157. If it is required to mark off the circle A, 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 compa.s.ses, we mark a circle B B of 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, in Fig. 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 only 1/3 of whatever it is in the former.

[Ill.u.s.tration: Fig. 156.]

[Ill.u.s.tration: Fig. 157.]

In this example we have supposed the number of divisions to be an even one, hence the point K, Fig. 152, falls diametrically opposite to A, whereas in an odd number of points of division this would not be the case, and we must proceed by either of the two following methods:--

[Ill.u.s.tration: Fig. 158.]

In Fig. 158 is shown a circle requiring to be divided by 17 equidistant points. Starting from point 1 we mark on the outside of the circ.u.mference 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 compa.s.ses to 17 and 9 we shall find they come too close together, hence we take another pair of compa.s.ses (so as not to disturb the set of our first pair) and find the centre between 9 and 17 as shown by the point A. We then correct the set of our first pair of compa.s.ses, as near as the judgment dictates, and from point A, we mark with the second compa.s.ses (set to one half the new s.p.a.ce of the first compa.s.ses) the points B, C. With the first pair of compa.s.ses, starting from B, we mark D, E, &c., to G; and from I, we mark divisions H, I, &c., to K, and if the compa.s.ses were set true, K and G would meet at the circle. We may, however, mark a point midway between K and G, as at 5. Starting again from points C and I, we mark the other side of the circle in a similar manner, producing the lines P and Q, midway between which (the compa.s.ses not being set quite correct as yet) is the true point for another division. After again correcting the compa.s.ses, we start from B and 5 respectively, and mark point 7, again correcting the compa.s.ses. Then from C and the point between P and Q, 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 in Fig.

159 is more correct for an odd number of points of division. Suppose that we have commenced at the point marked I, we mark off half the required number of holes on one side and arrive at the point 2; and then, commencing at the point I again, we mark off the other half of the required number of holes, arriving at the point 3. We then apply our compa.s.ses to the distance between the points 2 and 3; and if that distance is not exactly the same to which the compa.s.ses are set, we make the necessary adjustment, and try again and again until correct adjustment is secured.

[Ill.u.s.tration: Fig. 159.]

It is highly necessary, in this case, to make the lines drawn at each 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 lines A, B, C, D, in Fig. 159 represent those made on the first trial, and E, 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 lines I, 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 s.p.a.ce, 2 and 3, opposite point 1, instead of a point, as in case of a circle having an even number of divisions.

[Ill.u.s.tration: Fig. 160.]

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 in Fig.

21 be used, no other marks will be used, because the sides of a tooth on each side of a s.p.a.ce may be marked at one setting of the template to the lines or marks of division. If, however, a template, such as shown in Fig. 81 be 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, as G in Fig.

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 in Fig. 142.

But if the arcs for the tooth curves are to be marked by compa.s.ses, the location for the centres wherefrom to strike these arcs may be marked from the points of division as was shown in Fig. 130.

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 in Fig. 160, in which A, B, C, D, represent in section the body of a bevel pinion. F G is the point of a tooth on one side, and E the point of a tooth on the other side of the pinion, while H I are pitch lines for the two teeth. Thus, the cone surface, the points, the pitch lines and the bottom of the s.p.a.ces, projected as denoted by the dotted lines, would all meet at X, which represents the point where the axes of the shafts would meet.

[Ill.u.s.tration: 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 body A 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 body A B C D to be formed of one piece instead of being put together in segments, the operation is as follows: The face D C is turned off on the lathe, and the piece is reversed on the lathe chuck, and the face A B is 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 angle A 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 face D C in the lathe a fine line circle should be struck around the circ.u.mference of the cone and near D C, on which line the s.p.a.cing for the teeth may be stepped off with the compa.s.ses. 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: In Fig. 161 let the outline in full lines denote the body of a pinion ready to receive the teeth, and A B the circle referred to as necessary for the s.p.a.cing or dividing with the compa.s.ses. On A B take any point, as C, as a centre, and with a pair of compa.s.ses mark equidistant on each side of it two lines, as D, D. From D, D as respective centres mark two lines, crossing each other as at F, and draw a line, joining the intersection of the lines at F with C, 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 to X, in Fig. 160.

[Ill.u.s.tration: Fig. 162.]

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 in Fig. 162, the face _f_ _f_ being fitted to the surface C, in Fig. 161, while the edges of its blade coincide with the line referred to; hence the edge of the blade may be placed coincident successively with each point of division, as D D, and the lines for the place of the length of each tooth be drawn. The second plan is to divide off the line A B before 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 in Fig. 163, in which W is the piece of wood, and A, 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 lines E, F, G in Fig. 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 in Fig. 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 in Fig. 160, where at J are three teeth so marked for the large end, and at K three for the small end, P P representing the pitch circle, and R R a circle for the compa.s.s points. The teeth for bevel pinions are sometimes put on by dovetails, as shown in Fig. 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 lines A, 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 in Fig. 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 toward X (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.

[Ill.u.s.tration: Fig. 163.]

[Ill.u.s.tration: Fig. 164.]

[Ill.u.s.tration: Fig. 165.]

In wheels too large to have their cones tested by a bevel gauge, a wooden gauge may be made by nailing two pieces of wood to stand at the required angle as shown in Fig. 165, which is extracted from _The American Machinist_, or the dead centre C and a straightedge may be used as follows. In the figure the other wheel of the pair is shown dotted in at B, and the dead centre is set at the point where the axes of A and B would meet; hence if the largest diameter of the cone of A is turned to correct size, the cone will be correct when a straightedge applied as shown lies flat on the cone and meets the point of the dead centre E.

The pinion B, however, is merely introduced to explain the principle, and obviously could not be so applied practically, the distance to set _e_, however, is the radius _a_.

Skew Bevel.[9]--When the axles of the shaft are inclined to each other instead of being in a straight line, and it is proposed to connect and communicate motion to the shafts by means of a single pair of bevel-gears, the teeth must be inclined to the base of the frustra to allow them to come into contact.

[9] From the "Engineer and Machinists' a.s.sistant."

[Ill.u.s.tration: Fig. 166.]

To find the line of contact upon a given frustrum of the tangent-cone; let the Fig. 166 be the plane of the frustrum; _a_ the centre. Set off _a_ _e_ equal to the shortest distance between the axes (called the _eccentricity_), and divide it in _c_, so that _a_ _c_ is to _e_ _c_ as the mean radius of the frustrum to the mean radius of that with which it is to work; draw _c_ _p_ perpendicular to _a_ _e_, and meeting the circ.u.mference of the conical surface at _m_; perform a similar operation on the base of the frustrum by drawing a line parallel to _c_ _m_ and at the same distance _a_ _c_ from the centre, meeting the circ.u.mference in _p_.

The line _p_ _c_ is then plainly the line of direction of the teeth. We are also at liberty to employ the equally inclined line _c_ _q_ in the opposite direction, observing only that, in laying out the two wheels, the pair of directions be taken, of which the inclinations correspond.

[Ill.u.s.tration: Fig. 167.]

Fig. 167 renders this mode of laying off the outlines of the wheels at once obvious. In this figure the line _a_ _e_ corresponds to the line marked by the same letters in Fig. 166; and the division of it at _c_ is determined in the manner directed. The line _c_ _m_ being thus found in direction, it is drawn indefinitely to _d_. Parallel to this line and from the point _c_ draw _e_ to _e_, and in this line take the centre of the second wheel. The line _c_ _m_ _d_ gives the direction of the teeth; and if from the centre _a_ with radius at _c_ a circle be described, the direction of any tooth of the wheel will be a tangent to it, as at _c_, and similarly if a centre _e_ be taken in the line _e_ _d_, and with radius _e_ _d_, _c_ _e_ a circle be drawn, the direction of the teeth of the second wheel will be tangents to this last, as at _d_.

Having thus found the direction of the teeth, these outlines may be formed as in the case of ordinary bevel-wheels and with equal exactness and facility, all that is necessary being to find the curves for the teeth as described for bevel-wheels, and follow precisely the same construction, except that the square, Fig. 162, marking the lines across the cones, requires to be set to the angle for the tooth instead of at a right angle, and this angle may be found by the construction shown in Fig. 167, it being there represented by line _d_ _c_. It is obvious, however, that the bottoms of the blocks to form the teeth must be curved to bed on the cone along the line _d_ _c_, Fig. 167, and this may best be done by bedding two teeth, testing them by trial of the actual surfaces.

[Ill.u.s.tration: Fig. 168.]

Then two teeth may be set in as No. 1 and No. 6 in the box shown in Fig.

148, the intermediate ones being dressed down to them.

Where a bevel-wheel pattern is too large to be constructed in one piece and requires to be built up in pieces, the construction is as in Fig.

168, in which on the left is shown the courses of segments 1, 2, 3, 4, 5, &c., of which the rim is built up (as described for spur wheels), and on the right is shown the finished rim with a tooth, _c_, in position.

The tooth proper is of the length of face of the wheel as denoted by _b b'_; now all the lines bounding the teeth must converge to the point X.

Suppose, then, that the teeth are to be shaped for curve of face and flank in a box as described for spur-wheel teeth in Fig. 146, then in Fig. 168 let _a_, _a_ represent the bottom and _b b'_ the top of the box, and _c_ a tooth in the box, its ends filling the opening in the box at _b b'_ then the curve on the sides of the box at _b'_ must be of the form shown at F, and the curve on the sides of the box (at the point _b_ of its length) must be as shown at G, the teeth shown in profile at G and U representing the forms of the teeth at their ends, on the outside of the wheel rim at _b'_, and on the inside at _b_; having thus made a box of the correct form on its sides, the teeth may be placed in it and planed down to it, thus giving all the teeth the same curve.

The s.p.a.cing for the teeth and their fixing may be done as described for the bevel pinion.

[Ill.u.s.tration: Fig. 169.]

To construct a pattern wherefrom to cast an endless screw, worm, or tangent screw, which is to have the worm or thread cut in a lathe.--Take two pieces, each to form one longitudinal half of the pattern; peg and screw them together at the ends, an excess of stuff being allowed at each end for the accommodation of two screws to hold the two halves together while turning them in the lathe, or dogs, if the latter are more convenient, as they might be in a large pattern. Turn the piece down to the size over the top of the thread, after which the core prints are turned. The body thus formed will be ready to have the worm or thread cut, and for this purpose the tools shown in Figs. 169 and 140 are necessary.

That shown in Fig. 169 should be flat on the face similar to a parting tool for cast iron, but should have a great deal more bottom rake, as strength is not so much an object, and the tool is more easily sharpened. It has also in addition two little projections A B like the point of a penknife, formed by filing away the steel in the centre; these points are to cut the fibres of the wood, the severed portion being sc.r.a.ped away by the flat part of the tool.

[Ill.u.s.tration: Fig. 170.]

The degree of side rake given to the tool must be sufficient to let the tool sides well clear the thread or worm, and will therefore vary with the pitch of the worm.

The width of the tool must be a shade narrower than the narrowest part of the s.p.a.ce in the worm. Having suitably adjusted the change wheels of the lathe to cut the pitch required the parting tool is fed in until the extreme points reach the bottom of the s.p.a.ces, and a square nosed parting tool without any points or spurs will finish the worm to the required depth. This will have left a square thread, and this we have now to cut to the required curves on the thread or worm sides, and as the cutting will be performed on the end grain of the wood, the top face of the tool must be made keen by piercing through the tool a slot A, Fig. 170, and filing up the bevel faces B, C and D, and then carefully oilstoning them. This tool should be made slightly narrower than the width of the worm s.p.a.ce, so that it may not cut on both sides at once, as it would have too great a length of cutting edge.

[Ill.u.s.tration: Fig. 171.]

Furthermore, if the pattern is very large, it will be necessary to have two tools for finishing, one to cut from the pitch line inwards and the other to complete the form from the pitch line outwards. It is advisable to use hard wood for the pattern.

If it is decided to cut the thread by hand instead of with these lathe tools, then, the pattern being turned as before, separate the two halves by taking out the screws at the ends; select the half that has not the pegs, as being a little more convenient for tracing lines across. Set out the sections of the thread, A, B, C, and D, Fig. 171, similar to a rack; through the centres of A, B, C, and D, square lines across the piece; these lines, where they intersect the pitch line, will give the centres of teeth on that side: or if we draw lines, as E, F, through the centres of the s.p.a.ces, they will pa.s.s through the centres of the teeth (so to speak) on the other side; in this position complete the outline on that side. It will be found, in drawing these outlines, that the centres of some of the arcs will lie outside the pattern. To obtain support for the compa.s.ses, we must fit over the pattern a piece of board such as shown by dotted lines at G H.