The Morse Twist-drill and Machine Co. recommends the rates

of speed of twist-drills given in the following table:

They also give the rate of feed for twist-drills as follows:

tions per inch depth

of hole.

4 1 1%

125 125 120 to 140 1 inch feed per minute.

Speed of Emery Wheels.

The speed most strongly recommended by their manufacturers is a peripheral velocity of 5,500 feet per minute for all

sizes. All things being considered, it is stated that there is no advantage to be gained in exceeding this speed. If run much slower than this, the wear on the wheels is much greater in proportion to the work accomplished, and if run much faster, the wheel is likely to burst.

Speed of Grindstones.

Grindstones used for grinding machinists' tools are usually run so as to have a peripheral speed of about 900 feet per minute, and those used for grinding carpenters' tools at about 600 feet per minute. In regard to safety, it may be stated in general that with any size of grindstone having a compact and strong grain, a peripheral velocity of 2,800 feet per minute should not be exceeded.

Speed of Polishing Wheels.

Polishing wheels are run at about the following peripheral speeds:

Leather-covered wooden wheels..

Walrus-hide wheels...

Rag-wheels....

.7,000 feet per minute.

Change Gears Required for Cutting Screw Threads.

The pitch of a single threaded screw is the distance between two adjacent threads, measured on a line parallel to the axis of the screw; or, in any screw, whether single or multiple threaded, it is the distance the nut is moved by one revolution of the screw. Usually, a screw is spoken of as having a certain number of threads to the inch, and this is equal to the number of revolutions the screw must make in order to move the nut a distance of one inch; so, whether the screw be single or multiple threaded, the pitch is always equal to 1 divided by the number of revolutions that the screw must make in order to move the nut one inch.

THE SIMPLE GEARED LATHE.

In Fig. 1 is shown the usual arrangement of the change gears of a simple geared screw cutting lathe. By a simple geared lathe is meant a lathe in which the change gears are so arranged that the circumferential velocity of the change gear on

the stud is the same as that of the change gear on the lead screw, which means that, when the change gear on the stud has rotated, say, five teeth, the change gear on the lead screw has also rotated five teeth, whatever the diameter of these gears, or of any intermediate gears between them, may be.

By the following formulas and rules, the numbers of teeth required in the change gears in order to cut a given number of threads to the inch, or the number of threads to the inch that given change gears will produce may be found.

Let a =

the number of teeth in the spindle gear a.

c = the number of teeth in the gear c.

f

the number of teeth in the change gear on stud.

h the number of teeth in the change gear on lead screw.

g

the number of threads to the inch in the lead screw. n the number of threads to the inch to be cut.

Now, of the gears h, f, c, a, a and ƒ are the drivers, and c and h, being driven by a and ƒ, are called the driven gears; remembering this, we deduce, from formula 1, the following rule for simple 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 numbers of teeth in the driven gears, and divided by the product of the numbers of teeth in the driving gears.

EXAMPLE.-If the lead screw, g, of a simple geared lathe has 5 threads to the inch, and the gear a has 21 teeth, the gear c, 42 teeth; the change gear ƒ, 60 teeth; and the change gear h, 72 teeth; how many threads to the inch will be cut?

SOLUTION.-Using formula 1, we have,

From formula 2, we deduce the following rule for simple geared screw cutting lathes.

RULE.-The number of teeth in the change gear on the lead screw, divided by the number of teeth in the change gear on the stud, is equal to the product of the number of threads to the inch to be cut

and the number of teeth in the driving spindle gear, divided by the product of the number of threads to the inch in lead screw and the number of teeth in the fixed gear on the stud.

EXAMPLE.-If the lead screw g, of a simple geared lathe has 8 threads to the inch, and the gear a has 16 teeth, and the gear c, 32 teeth, how many teeth must there be in each of the gears, f and h, in order that the lathe may cut 10 threads to the inch? SOLUTION.-Using formula 2,

f g c

and, if it were possible to have gears with 5 and 8 teeth respectively, then a solution of the problem would be, h = 5; f = 8. It is evident that such gears are impracticable; but, as it does not change the value of a fraction to multiply both numerator and denominator by the same number, we may multiply 5 and 8, each by such a number that the resulting numbers of teeth in the gears are satisfactory. There is evidently, therefore, more than one solution to the problem-for if we multiply by 10 we shall have, h = 50; f 80, which would give 12 threads to the inch; and if we multiply by 13, we shall have, as another solution, h = 65: f = 104, which would also give 12 threads to the inch, because 15%.

Having found that

=

h

f

5%, it is customary in practice to

choose the change gears in the following manner. From the assortment of gears belonging to the lathe, choose one of convenient diameter, the number of whose teeth is divisible by either the numerator 5 or the denominator 8, and after dividing by one of these numbers, multiply both numerator and denominator by the quotient.

EXAMPLE.-Given

h

f

5%; to find the numbers of teeth in

the change gears h and f, respectively.

SOLUTION.-Choose a gear of convenient diameter, the number of whose teeth, say 60, is divisible by either 5 or 8, in this case

by 5; divide 60 by 5 and the answer is 12.

that is h has 60 teeth and f, 96 teeth.

Then,

5 x 12 60

= ;

8 × 12 96