Exercise 11: Forms of Screw Threads.—Draw to a scale of three times full size the sections of screw threads as shown in fig. 9. The pitch for the Whitworth, Sellers, and buttress threads to be 3⁄8 inch, and the pitch of the square and knuckle threads to be 1⁄2 inch.
Dimensions of Whitworth Screws.
| Diameter of screw |
Number of threads per inch |
Diameter at bottom of thread |
Diameter of screw |
Number of threads per inch |
Diameter at bottom of thread |
Diameter of screw |
Number of threads per inch |
Diameter at bottom of thread |
|---|---|---|---|---|---|---|---|---|
| 1⁄8 | 40 | ·093 | 1¼ | 7 | 1·067 | 3½ | 3¼ | 3·106 |
| 3⁄16 | 24 | ·134 | 13⁄8 | 6 | 1·162 | 3¾ | 3 | 3·323 |
| 1⁄4 | 20 | ·186 | 1½ | 6 | 1·286 | 4 | 3 | 3·573 |
| 5⁄16 | 18 | ·241 | 15⁄8 | 5 | 1·369 | 4¼ | 27⁄8 | 3·805 |
| 3⁄8 | 16 | ·295 | 1¾ | 5 | 1·494 | 4½ | 27⁄8 | 4·055 |
| 7⁄16 | 14 | ·346 | 17⁄8 | 4½ | 1·590 | 4¾ | 2¾ | 4·284 |
| 1⁄2 | 12 | ·393 | 2 | 4½ | 1·715 | 5 | 2¾ | 4·534 |
| 5⁄8 | 11 | ·508 | 2¼ | 4 | 1·930 | 5¼ | 25⁄8 | 4·762 |
| 3⁄4 | 10 | ·622 | 2½ | 4 | 2·180 | 5½ | 25⁄8 | 5·012 |
| 7⁄8 | 9 | ·733 | 2¾ | 3½ | 2·384 | 5¾ | 2½ | 5·238 |
| 1 | 8 | ·840 | 3 | 3½ | 2·634 | 6 | 2½ | 5·488 |
| 11⁄8 | 7 | ·942 | 3¼ | 3¼ | 2·856 | |||
Gas Threads[1] (Whitworth Standard).
| Diameter of Screw | 1⁄8 | 1⁄4 | 3⁄8 | 1⁄2 | 5⁄8 | 3⁄4 | 1 | 1¼ | 1½ | 1¾ | 2 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Number of threads per inch | 28 | 19 | 19 | 14 | 14 | 14 | 11 | 11 | 11 | 11 | 11 |
[1] Used for wrought-iron and brass tubes.
Representation of Screws.—The correct method of representing screw threads involves considerable trouble, and is seldom adopted by engineers for working drawings. For an explanation of the method see the author's Text-book on Practical Solid Geometry, Part II., problem 134. A method very often adopted on working drawings is shown in fig. 15; here the thin lines represent the points, and the thick lines the roots of the threads. At fig. 16 is shown a more complete method. The simplest method is illustrated by figs. 10, 11, 13, and 14.
Here dotted lines are drawn parallel to the axis of the screw as far as it extends, and at a distance from one another equal to the diameter of the screw at the bottom of the thread.
| Fig. 10. | Fig. 11. |
Forms of Nuts.—The most common form of nut is the hexagonal shown in figs. 10, 13, 14, 15, and 16; next to this comes the square nut shown in fig. 11. The method of drawing these nuts will be understood by reference to the figures; the small circles indicate the centres, and the inclined lines passing through them the radii of the curves which represent the chamfered or bevelled edge of the nut. In all the figures but the first the chamfer is just sufficient to touch the middle points of the sides, and in these cases the drawing of the nut is simpler.
| Fig. 13. | Fig. 14. |
Forms of Bolts.—At (a), fig. 12, is shown a bolt with a square head and a square neck. If this form of bolt is passed through a square hole the square neck prevents the bolt from turning when the nut is being screwed up. Instead of a square neck a snug may be used for the same purpose, as shown on the cup-headed bolt at (b). The snug fits into a short groove cut in the side of the hole through which the bolt passes. At (a) the diagonal lines are used to distinguish the flat side of the neck from the round part of the bolt above it. At (c) is shown a tee-headed bolt, and at (d) an eye-bolt. Fig. 13 represents a hook bolt. A bolt with a countersunk head is shown in fig. 11. If the countersunk head be lengthened so as to take up the whole of the unscrewed part of the bolt, we get the taper bolt shown in fig. 14, which is often used in the couplings of the screw shafts of steamships. The taper bolt has the advantage of having no projecting head, and it may also be made a tight fit in the hole with less trouble than a parallel bolt. Bolts may also have hexagonal heads.
Studs, or stud bolts, are shown in figs. 15 and 16; that in fig. 15 is a plain stud, while that in fig. 16 has an intermediate collar forged upon it, and is therefore called a collared stud.
Proportions of Nuts and Bolt-heads.—In the hexagonal nut the diameter D across the flats is 1½d + 1⁄8, where d is the diameter of the bolt. The same rule gives the width of a square nut across the flats. A rule very commonly used in making drawings of hexagonal nuts is to make the diameter D, across the angles equal to 2d. H, the height of the nut, is equal to the diameter of the bolt. In square and hexagonal headed bolts the height of the head varies from d to 2⁄3d; the other dimensions are the same as for the corresponding nuts.
Washers are flat, circular, wrought-iron plates, having holes in their centres of the same diameter as the bolts on which they are used. The object of the washer is to give a smooth bearing surface for the nut to turn upon, and it is used when the surfaces of the pieces to be connected are rough, or when the bolt passes through a hole larger than itself, as shown in fig. 10. The diameter of the washer is a little more than the diameter of the nut across the angles, and its thickness about 1⁄8 of the diameter of the bolt.
Exercise 12.—Draw, full size, the views shown in fig. 10 of an hexagonal nut and washer for a bolt 1¼ inches in diameter. The bolt passes through a hole 1¾ × 1¼. All the dimensions are to be calculated from the rules which have just been given.
Exercise 13.—Draw, full size, the plan and elevation of the square nut and bolt with countersunk head shown in fig. 11, to the dimensions given.
Exercise 14.—Draw, full size, the elevation of the hook bolt with hexagonal nut shown in fig. 13 to the dimensions given, and show also a plan.
Exercise 15.—Draw, to a scale of 4 inches to a foot, the conical bolt for a marine shaft coupling shown in fig. 14. All the parts are of wrought iron.
Exercise 16.—Fig. 15 is a section of the mouth of a small steam-engine cylinder, showing how the cover is attached; draw this full size.
Exercise 17.—Fig. 16 shows the central portion of the india-rubber disc valve which is described on page 68. A is the central boss of the grating, into which is screwed the stud B, upon which is forged the collar C. The upper part of the stud is screwed, and carries the guard D and an hexagonal nut E. F is the india-rubber. The grating and guard are of brass. The stud and nut are of wrought iron. Draw full size the view shown.
Lock Nuts.—In order that a nut may turn freely upon a bolt, there is always a very small clearance space between the threads of the nut and those of the bolt. This clearance is shown exaggerated at (a), fig. 17, where A is a portion of a bolt within a nut B. Suppose that the bolt is stretched by a force W. When the nut B is screwed up, the upper surfaces of the projecting threads of the nut will press on the under surfaces of the threads of the bolt with a force P equal and opposite to W, as shown at (b), fig. 17. When in this condition the nut has no tendency to slacken back, because of the friction due to the pressure on the nut. Now suppose that the tension W on the bolt is momentarily diminished, then the friction which opposes the turning of the nut may be so much diminished that a vibration may cause it to slacken back through a small angle. If this is repeated a great many times the nut may slacken back so far as to become useless.
| Fig. 17. | Fig. 18. |
A very common arrangement for locking a nut is shown at (a), fig. 18. C is an ordinary nut, and B one having half the thickness of C. B is first screwed up tight so as to act on the bolt, as shown at (b), fig. 17. C is then screwed on top of B. When C is almost as tight as it can be made, it is held by one spanner, while B is turned back through a small angle with another. The action of the nuts upon the bolt and upon one another is now as shown at (b), fig. 18. It will be seen that the nuts are wedged tight on to the bolt, and that this action is independent of the tension W in the bolt. The nuts will, therefore, remain tight after the tension in the bolt is removed.
It is evident that if the nuts are screwed up in the manner explained, the outer nut C will carry the whole load on the bolt; hence C should be the thicker of the two nuts. In practice, the thin nut, called the lock nut, is often placed on the outside, for the reason that ordinary spanners are too thick to act on the thin nut when placed under the other.
Another very common arrangement for locking a nut is shown in fig. 19. A is the bolt and B the nut, the lower part of which is turned circular. A groove C is also turned on the nut at this part. The circular part of the nut fits into a circular recess in one of the parts connected by the bolt. Through this part passes a set screw D, the point of which can be made to press on the nut at the bottom of the groove C. D is turned back when the nut B is being moved, and when B is tightened up, the set screw is screwed up so as to press hard on the bottom of the groove C. The nut B is thus prevented from slackening back. The screw thread is turned off the set screw at the point where it enters the groove on the nut.
The use of the groove for receiving the point of the set screw is this: The point of the set screw indents the nut and raises a bur which would interfere with the free turning of the nut in the recess if the bur was not at the bottom of a groove. Additional security is obtained by drilling a hole through the point of the bolt, and fitting it with a split pin E.
Locking arrangements for nuts are exceedingly numerous, and many of them are very ingenious, but want of space prevents us describing them. We may point out, however, that many very good locking arrangements have the defect of only locking the nut at certain points of a revolution, say at every 30°. It will be noticed that the two arrangements which we have described are not open to this objection.
Exercise 18.—Draw, full size, a plan, front elevation, and side elevation of the arrangement of nuts shown in fig. 18, for a bolt 7⁄8 inch diameter.
Exercise 19.—Draw the plan and elevation of the nut and locking arrangement shown in fig. 19. Make also an elevation looking in the direction of the arrow. Scale 6 inches to a foot.
IV. KEYS.
Keys are wedges, generally rectangular in section, but sometimes circular; they are made of wrought iron or steel, and are used for securing wheels, pulleys, cranks, &c., to shafts.
Various sections of keys are shown in fig. 20. At (a) is the hollow or saddle key. With this form of key it is not necessary to cut the shaft in any way, but its holding power is small, and it is therefore only used for light work. At (b) is the key on a flat, sometimes called a flat key. The holding power of this key is much greater than that of the saddle key. At (c) is the sunk key, a very secure and very common form.
The part of the shaft upon which a key rests is called the key bed or key way, and the recess in the boss of the wheel or pulley into which the key fits is called the key way; both are also called key seats. With saddle, flat, and sunk keys the key bed is parallel to the axis of the shaft; but the key way is deeper at one end than the other to accommodate the taper of the key. The sides of the key are parallel.
The round key or taper pin shown at (d) is in general only used for wheels or cranks which have been previously shrunk on to their shafts or forced on by great pressure. After the wheel or crank has been shrunk on, a hole is drilled, half into the shaft and half into the wheel or crank, to receive the pin.
When the point of a key is inaccessible the other end is provided with a gib head as shown at (e), to enable the key to be withdrawn.
A sliding or feather key secures a piece to a shaft so far as to prevent the one from rotating without the other, but allows of relative motion in the direction of the axis of the shaft. This form of key has no taper, and it is secured to the piece carried by the shaft, but is made a sliding fit in the key way of the shaft. In one form of feather key the part within the piece carried by the shaft is dovetailed as shown at (f). In another form the key has a round projecting pin forged upon it, which enters a corresponding hole as shown at (g). The feather key may also be secured to the piece carried by the shaft by means of one or more screws as shown at (h). The key way in the shaft is made long enough to permit of the necessary sliding motion.
Cone Keys.—These are sometimes fitted to pulleys, and are shown in fig. 32, page 38. In this case the eye of the pulley is tapered and is larger than the shaft. The space between the shaft and the boss of the pulley is filled with three saddle or cone keys. These keys are made of cast iron and are all cast together, and before being divided the casting is bored to fit the shaft and turned to fit the eye of the pulley. By this arrangement of keys the same pulley may be fixed on shafts of different diameters by using keys of different thicknesses; also the pulley may be bored out large enough to pass over any boss which may be forged on the shaft.
Proportions of Keys.—The following rules are taken from Unwin's 'Machine Design,' pp. 142-43.
| Diameter of eye of wheel, or boss of shaft | = d. |
| Width of key | = 3⁄4d + 1⁄8. |
| Mean thickness of sunk key | = 1⁄8d + 1⁄8. |
| ” key on flat | = 1⁄16d + 1⁄16. |
The following table gives dimensions agreeing with average practice.
Dimensions of Keys.
| D | = | diameter of shaft. |
| B | = | breadth of key. |
| T | = | thickness of sunk key. |
| T1 | = | thickness of flat key, also = thickness of saddle key. Taper of key 1⁄8 inch per foot of length, i.e. 1 in 96. |
| D | ¾ | 1 | 1¼ | 1½ | 1¾ | 2 | 2¼ | 2½ | 2¾ | 3 | 3½ |
|---|---|---|---|---|---|---|---|---|---|---|---|
| B | 5⁄16 | 3⁄8 | 7⁄16 | 1⁄2 | 9⁄16 | 5⁄8 | 11⁄16 | 11⁄16 | 3⁄4 | 7⁄8 | 1 |
| T | 1⁄4 | 1⁄4 | 1⁄4 | 5⁄16 | 5⁄16 | 5⁄16 | 3⁄8 | 3⁄8 | 3⁄8 | 7⁄16 | 1⁄2 |
| T1 | 3⁄16 | 3⁄16 | 3⁄16 | 3⁄16 | 1⁄4 | 1⁄4 | 1⁄4 | 5⁄16 | 5⁄16 | 5⁄16 | 3⁄8 |
| D | 4 | 4½ | 5 | 5½ | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| B | 11⁄8 | 11⁄4 | 13⁄8 | 11⁄2 | 15⁄8 | 17⁄8 | 21⁄8 | 23⁄8 | 25⁄8 | 27⁄8 | 31⁄8 |
| T | 1⁄2 | 9⁄16 | 5⁄8 | 11⁄16 | 3⁄4 | 13⁄16 | 15⁄16 | 1 | 11⁄16 | 13⁄16 | 11⁄4 |
| T1 | 7⁄16 | 1⁄2 | 1⁄2 | 9⁄16 | 5⁄8 | 11⁄16 | 3⁄4 | 7⁄8 | 15⁄16 | 11⁄16 | 11⁄8 |
V. SHAFTING.
Shafting is nearly always cylindrical and made of wrought iron or steel. Cast iron is rarely used for shafting.
Axles are shafts which are subjected to bending without twisting.
The parts of a shaft or axle which rest upon the bearings or supports are called journals, pivots, or collars.
In journals the supporting pressure is at right angles to the axis of the shaft, while in pivots and collars the pressure is parallel to that axis.
Shafts may be solid or hollow. Hollow shafts are stronger than solid shafts for the same weight of material. Thus a hollow shaft having an external diameter of 10¼ inches and an internal diameter of 7 inches would have about the same weight as a solid shaft of the same material 7½ inches in diameter, but the former would have about double the strength of the latter. Hollow shafts are also stiffer and yield less to bending action than solid shafts, which in some cases, as in propeller shafts, is an objection.
VI. SHAFT COUPLINGS.
For convenience of making and handling, shafts used for transmitting power are generally made in lengths not exceeding 30 feet. These lengths are connected by couplings, of which we give several examples.
Solid, Box, or Muff Couplings.—One form of box coupling is shown in fig. 21. Here the ends of the shafts to be connected butt against one another, meeting at the centre of the box, which is made of cast iron. The shafts are made to rotate as one by being secured to the box by two wrought-iron or steel keys, both driven from the same end of the box. A clearance space is left between the head of the forward key and the point of the hind one, to facilitate the driving of them out, as then only one key needs to be started at a time. Sometimes a single key the whole length of the box is used, in which case it is necessary that the key ways in the shafts be of exactly the same depth.
The half-lap coupling, introduced by Sir William Fairbairn, is shown in fig. 22. In this form of box coupling the ends of the shafts overlap within the box. It is evident that one shaft cannot rotate without the other as long as the box remains over the lap. To keep the box in its place it is fitted with a saddle key.
It will be noticed that the lap joint is sloped in such a way as to prevent the two lengths of shaft from being pulled asunder by forces acting in the direction of their length.
Half-lap couplings are not used for shafts above 5 inches in diameter.
It may here be pointed out that the half-lap coupling is expensive to make, and is now not much used.
As shafts are weakened by cutting key ways in them, very often the ends which carry couplings are enlarged in diameter, as shown in fig. 21, by an amount equal to the thickness of the key. An objection to this enlargement is that wheels and pulleys require either that their bosses be bored out large enough to pass over it, or that they be split into halves, which are bolted together after being placed on the shaft.
Dimensions of Box Couplings.
| D | = | diameter of shaft. |
| T | = | thickness of metal in box. |
| L | = | length of box for butt coupling. |
| L1 | = | length of box for lap coupling. |
| l | = | length of lap. |
| D1 | = | diameter of shaft at lap. |
| D | 1½ | 2 | 2½ | 3 | 3½ | 4 | 4½ | 5 | 5½ | 6 |
|---|---|---|---|---|---|---|---|---|---|---|
| T | 11⁄8 | 15⁄16 | 1½ | 1¾ | 115⁄16 | 21⁄8 | 25⁄16 | 2½ | 2¾ | 215⁄16 |
| L | 5¾ | 7 | 8¼ | 9½ | 10¾ | 12 | 13¼ | 14½ | 15¾ | 17 |
| L1 | 41⁄8 | 5¼ | 63⁄8 | 7½ | 85⁄8 | 9¾ | 107⁄8 | 12 | — | — |
| l | 71⁄16 | 17⁄8 | 25⁄16 | 2¾ | 33⁄16 | 35⁄8 | 41⁄16 | 4½ | — | — |
| D2 | 25⁄16 | 3 | 311⁄16 | 43⁄8 | 51⁄16 | 5¾ | 67⁄16 | 71⁄8 | — | — |
Slope of lap 1 in 12.
Fig. 23.
Exercise 20: Solid Butt Coupling.—From the above table of dimensions make a longitudinal and a transverse section of a solid butt coupling for a shaft 2½ inches in diameter. Scale 6 inches to a foot.
Exercise 21: Fairbairn's Half-Lap Coupling.—Make the same views as in the last exercise of a half-lap coupling for a 3-inch shaft to the dimensions in the above table. Scale 6 inches to a foot.
Flange Couplings.—The form of coupling used for the shafts of marine engines is shown in fig. 23. The ends of the different lengths of shaft have flanges forged on them, which are turned along with the shaft. These flanges butt against one another, and are connected by bolts. These bolts may be parallel or tapered; generally they are tapered. A parallel bolt must have a head, but a tapered bolt will act without one. In fig. 23 the bolts are tapered, and also provided with heads. In fig. 14, page 17, is shown a tapered bolt without a head. The variation of diameter in tapered bolts is 3⁄8 of an inch per foot of length.
Sometimes a projection is formed on the centre of one flange which fits into a corresponding recess in the centre of the other, for the purpose of ensuring the shafts being in line.
Occasionally a cross-key is fitted in between the flanges, being sunk half into each, for the purpose of diminishing the shearing action on the bolts.
Exercise 22: Marine Coupling.—Draw the elevation and section of the coupling shown in fig. 23; also an elevation looking in the direction of the arrow. Scale 3 inches to a foot.
The following table gives the dimensions of a few marine couplings taken from actual practice.
Examples of Marine Couplings.
| Diameter of shaft | 23⁄8 | 9¾ | 127⁄8 | 16½ | 22½ | 23 |
|---|---|---|---|---|---|---|
| Diameter of flange | 6 | 19 | 24 | 32 | 35 | 38 |
| Thickness of flange | 1 | 2¾ | 31⁄8 | 4¼ | 6 | 5 |
| Diameter of bolts | ¾ | 2¾ | 211⁄16 | 3½ | 4¼ | 4¼ |
| Number of bolts | 3 | 6 | 6 | 8 | 9 | 8 |
| Diameter of bolt circle | 41⁄8 | 141⁄8 | 1813⁄16 | 25 | 28¾ | 303⁄8 |
All the above dimensions are in inches.
Exercise 23.—Select one of the couplings from the above table, and make the necessary working drawings for it to a suitable scale.
The cast-iron flange coupling is shown in fig. 24. In this kind of coupling a cast-iron centre or boss provided with a flange is secured to the end of each shaft by a sunk key driven from the face of the flange. These flanges are then connected by bolts and nuts as in the marine coupling.
To ensure the shafts being in line the end of one projects into the flange of the other.
In order that the face of each flange may be exactly perpendicular to the axis of the shaft they should be 'faced' in the lathe, after being keyed on to the shaft.
If the coupling is in an exposed position, where the nuts and bolt-heads would be liable to catch the clothes of workmen or an idle driving band which might come in the way, the flanges should be made thicker, and be provided with recesses for the nuts and bolt-heads.
Dimensions of Cast-iron Flange Couplings.
| Diameter of shaft D |
Diameter of flange F |
Thickness of flange T |
Diameter of boss B |
Depth at boss L |
Number of bolts |
Diameter of bolts d |
Diameter of bolt circle C |
|---|---|---|---|---|---|---|---|
| 1½ | 7¼ | 7⁄8 | 3½ | 25⁄8 | 3 | 5⁄8 | 5½ |
| 2 | 87⁄8 | 11⁄16 | 43⁄8 | 33⁄16 | 4 | 3⁄4 | 6¾ |
| 2½ | 105⁄8 | 1¼ | 55⁄16 | 3¾ | 4 | 7⁄8 | 81⁄8 |
| 3 | 123⁄8 | 17⁄16 | 6¼ | 45⁄16 | 4 | 1 | 9½ |
| 3½ | 131⁄8 | 15⁄8 | 71⁄8 | 47⁄8 | 4 | 1 | 105⁄16 |
| 4 | 14 | 1¾ | 8 | 57⁄16 | 6 | 1 | 11¼ |
| 4½ | 155⁄8 | 2 | 87⁄8 | 6 | 6 | 11⁄8 | 12½ |
| 5 | 173⁄8 | 21⁄8 | 913⁄16 | 65⁄8 | 6 | 1¼ | 1313⁄16 |
| 5½ | 18¼ | 25⁄16 | 10¾ | 7¼ | 6 | 1¼ | 14¾ |
| 6 | 197⁄8 | 2½ | 115⁄8 | 7¾ | 6 | 13⁄8 | 16 |
The projection of the shaft p varies from 1⁄4 inch in the small shafts to 1⁄2 inch in the large ones.
Exercise 24: Cast-iron Flange Coupling.—Draw the views shown in fig. 24 of a cast-iron flange coupling, for a shaft 4½ inches in diameter, to the dimensions given in the above table. Scale 4 inches to a foot.