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being keyed on the same socket as the stud-wheel. The wheel on the lathe-spindle is the first driver, the stud-pinion is the second driver, the studwheel is the first driven wheel, and the leading screw-wheel is the second driven wheel.

The Number of Teeth in the change-wheels must have the same proportion as the number of threads per inch of the leading screw has to the number of threads per inch of the screw to be cut. Thus, to cut a screw of 8 threads per inch with a leading screw of 2 threads, wheels are required in the ratio of 4 to 1; say a wheel with 20 teeth on the lathe spindle, and a wheel with 80 teeth on the leading screw, connected with an intermediate wheel. When the number of threads to be cut does not exceed 12 per inch, a single train of wheels can be used. To cut a screw of a finer pitch than the leading screw, the following rules will give the required wheels:

Rule 1. Place the number of threads per inch of the leading screw for a numerator, and the number of threads per inch of the screw to be cut for a denominator, then add a cipher to each, which will give the required change wheels. Thus, to cut a screw of 8 threads per inch, with a leading screw 2 threads in leading screw of 2 threads per inch :; adding a cipher= 8 threads in screw to be cut

20 driver

So driven

The wheel representing the numerator is placed on the lathe-spindle, and the wheel representing the denominator on the leading screw.

say

Rule 2. When the number of threads to be cut is uneven 2 threads per inch, multiply the whole number by the denominator of the fraction; and multiply also the number of threads per inch of the leading 2 threads per inch in leading screw × 4 2 threads per inch in screw to be cut × 4 80 driver 110 driven

screw by the same multiplier:

Add a cipher =

When the numbers of teeth of wheels as found by this rule are too large, they may be reduced by dividing them by any suitable common divisor; and, if too small, they may be increased by multiplying them by any suitable common multiplier.

When a double train, or 4 change-wheels, are used, fix upon any 3 wheels for the lathe-spindle and stud-wheels, and the fourth or leading screw wheel may be found by the following rule.

Rule 3. Multiply the number of teeth in the wheel on the lathespindle by the ratio of the screw to be cut and the leading screw; and by the number of teeth in the second driver or stud-pinion; and divide the product by the number of teeth in the first driven wheel. Thus, to cut a screw of 16 threads per inch with a leading screw of 2 per inch, the ratio is 8 to 1. Lathe-spindle wheel 20 teeth, stud-pinion or second driver 50 teeth, stud-wheel or first driven wheel 80 teeth; required the

number of teeth in the leading-screw wheel. 20 × 8 × 50

The above arrangement will cut a right-hand thread.

80

= 100 teeth.

To cut a left-hand thread, place another wheel between a driver and a driven wheel to reverse the motion of the saddle.

Rule 4. The wheels may also be found by assuming a pair of wheels in conjunction with Rule 1, say 1088, and by dividing one of the drivers and one of the driven wheels by any suitable number. Thus, to take the screws

in the last example, add a cypher, 100 driver

20 driver 160 driven

Assume a pair of wheels,

then by dividing the first driven wheel and the second driver by

100 driven'
two, the required wheels are:

20 50 driver

80 100 driven

Rule 5. To prove the correctness of the change-wheels when the screw to be cut is of finer pitch than the leading screw, multiply the driving. wheels together, and multiply the driven wheels together; and divide the greater product by the less. The quotient multiplied by the number of threads per inch of the leading screw, will give the number of threads per inch 80 x 100 of the screw to be cut. To prove the wheels in the last example, 8 x 2 = 16 threads per inch in the screw to be cut.

20 × 50

To Cut Coarse-Pitch Screws.-To find the change-wheels to cut a screw of coarser pitch than the leading screw, it is necessary to assume as many pairs of wheels as will sufficiently reduce the size of the first driver, the ratio of the wheels being the numerator (instead of the denominator as used for pitches finer than the leading screw in the above rules) in coarse pitches. Rule, multiply the pitch in inches of the screw to be cut, by the number of threads per inch of the leading screw, which will give the number of threads of the leading screw, in a length equal to the pitch to be cut, and therefore the ratio of the wheels required to cut the pitch. Thus, to cut a screw of 20-inch pitch with a leading screw of 2 threads per inch, 20 × 2 the ratio required, the denominator must be increased by multiplying it by some suitable number to obtain a wheel of proper size, and the numerator must be increased in the same proportion, say 20, then, 40 x 20 800 first driver If two pairs of wheels are assumed, it will stand thus: 20 first driven' 800 first driver, 100 second driver, 100 third driver 20 first driven, 100 second driven, 100 third driven the first driver, divide the first driver and second driven by four, which will give wheels 200, 100, 100; and to still further reduce the size of the first driver, divide the first driver and last driven by four, which will give 50 100 100 drivers

=

20

25 25 driven'

the wheels required.

I X 20

=

; to reduce the size of

Rule, to prove the correctness of the change-wheels for coarse-pitch screws, the screw to be cut being coarser in pitch than the leading screw. Multiply the driving wheels together, then multiply the driven wheels together, and multiply the product of the driven wheels by the number of

threads per inch of the screw, with which product divide the product of the driving wheels. Thus, to prove the wheels in the last example :—

50 x 100=100

20 × 25 × 25 × 2

500000
=
= 20 inches pitch.
25000

To Cut French Millimetre Pitches of Screws.-One millimetre pitch is the part of a metre. One metre is approximately 393 inches, and a leading screw of -inch pitch, or two threads per inch, has 393×2=

78.75,

78.75 threads in one metre of its length; hence the proportion is 1000 which, if reduced by, say, multiplying by 8, gives 78.75 × 8.

1000 × 8

=

63

06, and the numerator 63 is a constant number, by which the number of millimetres, in the pitch of the screw to be cut, is to be multiplied.

Example: To find the change wheels to cut a pitch of 8 millimetres. with the above leading screw: 8 x 63 = 504, then 504 resolved into fractions becomes 638 and by adding a cypher to the number 8 and another to the number 10, the required wheels to cut 8 millimetres pitch, are 63 x 80 drivers

80 x 10

10 X 80 driven

B

Angle of Tool

Circumference of the
Screw

Fig. 146.--Angle of Screw-cutting Tool.

To find the angle to be given to a tool in order to cut a square-thread screw without injury to the sides of the threads. In Fig. 146, draw the line AB, equal to the pitch of the screw; draw the horizontal line BC, equal to the circumference of the screw, then draw the line AC, which gives the angle of the screw-cutting tool.

Price of Machined-Work, &c.-The price charged per hour for the use of machine-tools,-workmen's wages and trade expenses being covered by the charge-is usually as follows, viz. :—

:

Grindstones, Is. 3d. per hour.-Emery Wheels, Is. 6d.—Glaziers, 2s. od. -Lathes, 6 to 8 inch Centre, Is. 6d. : 9 to 12 inch, 2s. od.: 13 to 16 inch, 2s. 6d. 17 to 22 inch, 3s.: 24 to 30 inch, 4s.—Surfacing Lathe, medium sized, 4s. large, 5s.-Planing Machines, 1 to 2 feet wide, 2s.: 3 to 4 feet wide, 3s. 4 to 5 feet wide, 4s.: 6 to 8 feet wide, 5s.-Shaping and Slotting Machines, 4 to 6 inch Stroke, 1s. 6d. 8 to 12 inch Stroke, 2s.: 13 to 15 inch Stroke, 2s. 6d. 16 to 18 inch Stroke, 3s.: 20 to 24 inch Stroke, 45.-Vertical Drilling Machine, small, Is. 6d. : medium sized, 2s.: large, 3s. 6d.—Radial Drilling Machine, small, 2s.: large, 3s. 6d.—Cylinder Boring Machine, small, 2s. 6d. : medium size, 4s.-Slot Drilling Machines, 25.-Screwing Machine, up to 1 inches, 2s.: up to 2 inches, 2s. 6d.— Milling Machine, 2s. 6d.-Wheel-Cutting Machine, 3s.-The price of Fitters' Best Work per day is equal to double the wages for ordinary work; 2 times for special or intricate work; and 3 times the wages for very exact work. Planing work per square foot, for large flat work, 4s.: for small ditto, 6s.: 5s. for angles; and 6s. for undercut work. Turning work per square foot for large plain turning and surfacing work = the same prices as for planing.

LEADING SCREW.

Table 66.-CHANGE WHEELS FOR SCREW-CUTTING.

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TABLE 66 continued.-CHANGE WHEELS FOR SCREW-CUTTING.
SCREW, 2 THREADS PER INCH.

LEADING

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