If one of the change gears is given, and it is desired to find the number of teeth in the other change gear, in order to cut a given number of threads to the inch, use either formula 3 or formula 4, according as the number of teeth in gear h or in gearf is required. After the examples given, these formulas will not need explanation. In a simple geared screw cutting lathe, it is often possible to cut a fractional number of threads to the inch, as is the case in the following example. EXAMPLE. If the lead screw g has two threads per inch, and the gear a has 20 teeth, and the gear c has 20 teeth, how many teeth must there be in each of the change gears ƒ and h, in order to cut 54 threads to the inch? Then, choosing a gear whose number of teeth, say 32, is divisible by 2, divide 32 by 2 and the quotient is 16. Then, 514 × 16 2 X 16 84 =; that is, h has 84 teeth and f, 32 teeth. In many 32 cases, however, it is impossible, out of the assortment of gears supplied with a simple geared screw cutting lathe, to find gears to cut a screw of the required number of threads to the inch. In such cases, it becomes necessary, either to make suitable gears or to resort to a compound geared lathe. THE COMPOUND GEARED LATHE. In Fig. 2 is shown the usual arrangement of the change gears of a compound geared screw cutting lathe. The difference between this and the simple geared lathe lies in putting two change gears of different sizes on one spindle, in place of the idler, between the gear on the stud and the gear on the lead screw. These two gears on one spindle are shown at i and j in Fig. 2, the gear j meshing with gear h on the lead screw, and gear i meshing with gear ƒ on the stud. FIG. 2. From the following formulas, the numbers of teeth in each change gear, or the number of threads per inch which can be cut with given change gears, can be found. Let a = the number of teeth in the spindle gear a. f the number of teeth in the change gear ƒ. h the number of teeth in the change gear h. i = the number of teeth in the change gear i which meshes with the change gear f. = j the number of teeth in the change gear j which meshes with the change gear h. the number of threads to the inch in the lead screw. the number of threads to the inch to be cut. Now, remembering that gears af and j are the drivers, and gears c, h and i are the driven gears, and also that the idlers are ignored in all calculations, we can, from formula 5, deduce the following rule for compound geared screw cutting lathes : RULE.-The number of threads to the inch to be cut is equal to the number of threads to the inch in the lead screw, multiplied by the product of the number of the teeth in each of the driven gears, and divided by the product of the number of teeth in each of the driving gears. EXAMPLE. If the lead screw g of a compound geared lathe has 2 threads to the inch, and the gear a has 20 teeth; gear c, 40 teeth; change gearf, 48 teeth; change, gear i, 72 teeth; change gear j, 36 teeth; and change gear h, 96 teeth, how many threads to the inch will be cut? If it is desired to find what combination of change gears will enable us to cut a given number of threads to the inch, the following formula may be used, From this formula the following rule is deduced: RULE. Of the change gears of a lathe, any driven gear divided by any driver gear is equal to the product of the numbers of teeth in each of the other driver gears and the number of threads to the inch to be cut, divided by the product of the numbers of teeth in each of the other driven gears and the number of threads to the inch in the lead screw. EXAMPLE.-In a compound geared lathe, in which the lead screw has 5 threads to the inch, gear a, 20 teeth, gear c, 40 teeth, and the number of threads per inch to be cut is 32, what must be the numbers of teeth in each of the change gears h, i, j, ƒ? SOLUTION.-Using formula 6, we have, From the assortment of gears belonging to the lathe, choose, for the driven gear h, one whose number of teeth, say 28, can be divided by the number of threads per inch to be cut, in this case 32; 28 is a multiple of 3% because it is obtained by multiplying 3% by 8. Substitute this value in place of h; then choose any gear of convenient size, say one having 40 teeth, and substitute 40 in place of f; we shall then have, or, substituting the given values of n, a, g, Choose, for j, a gear whose number of teeth, say 60, is divisible by 2; then dividing the number of teeth in j by 2, we have 60 + 2= 30. Now multiplying both terms of the fraction by 30, ; that is, i = 30 and j = 60. Hence, one solu tion of the problem is, h = 28; i = 30; j = 60; ƒ = 40. THE SLIDE VALVE. Figs. A, B, C and D show sections of an ordinary D slide valve at different points of its travel. Fig. A shows the valve in its central position, with the center of the valve in line with the center line of the exhaust port. The names of the various parts are as follows: p and p are the steam ports; e is the exhaust port; ss is the valve seat; the amount, o, by which the valve overlaps the outer edges of the steam ports is the outside lap: the amount, i, by which the valve overlaps the inside edges of the steam port is the inside lap; the amount, 7, (Fig. C,) which the port is open when the piston is at the end of the stroke is the lead. The valve travel is the total distance in one direction which the valve can be moved by the eccentric; it is the total distance between two extreme positions of the valve. The displacement of the valve is the distance which the valve has moved (in either direction) from its central position. The line joining the center of the eccentric with the center of the crank shaft is called the eccentric radius. When the eccentric radius makes a right angle with the center line of the crank, that is, when the eccentric radius is vertical (see o e, Fig. E), the valve is in its central position, provided the valve seat is horizontal, as is usually the case. When the crank is on a dead center, say a, Fig. E, the valve must be in the position shown in Fig. C; that is, it must have moved from its central position an amount equal to the outside lap plus the lead. In order that this may happen the eccentric must be at c, Fig. E. The angle, e o c, which the eccentric must be moved from its vertical posi. tion when crank is on a dead center is called the angle of advance. |