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for locomotives, slide bars, etc., while in the machine-building trades these machines do much of the work which was formerly planed. The machine, bed, table, standards, and cross slide are very similar in appearance to a planing machine.

Referring to Fig. 313, it will be seen that the cutter spindle is carried by two adjustable bearings, which will open out to receive a cutter up to 24 in. wide, or a gang of cutters to the same width. The cross slide is made with an inclination so that the periphery of the cutters will just allow the surface of the work to comfortably clear the cross rail. This being so, a cutter of much smaller dimension is available than would be the case were the faces of the cross slide vertical.

To obtain a uniformly smooth surface on the work, spiral-cut gearing is employed to drive the table, while all other gears are machine cut. The feed, which is variable, ranges from in. to 10 in. per minute. Provision is also made for pumping a copious supply of oil or soapy water upon the mills, which keeps the cutting edges cool, and also prevents the cuttings from clogging the teeth. The lubricant is drained. into a tank, and used again.

A somewhat recent development is the screw milling machine. This applies the principle of the milling cutter to the formation of screw threads, and will cut screws of any section from in. to 13 in. diameter, and a pitch of from 2 to 10 threads per inch. The headstock carrying the cutter is situated at the right-hand end of the bed. The spindle and bearings are of hardened steel, and the machine is driven through a train of gears. The headstock may be moved vertically and transversely, and the spindle may be swung to any desired angle up to 25 degrees with the screw which is being milled, either right or left hand to suit the different dies and pitches being cut.

An index is provided by which the spindle may be set to the angle required, and a table is sent out with each machine, from which the correct angles may be ascertained.

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CHAPTER XIII.

GEARING AND GEAR CUTTERS.

THE "diameter," when applied to gears, is always understood to mean the pitch diameter.

Diametral pitch of the gear is the number of teeth to each inch of its pitch diameter. If a gear has 40 teeth, and the pitch diameter is 4 in., there are 10 teeth to each inch of the pitch diameter, and the diametral pitch is 10, or, in other words, the gear is 10 diametral pitch.

Circular pitch is the distance from the centre of one tooth to the centre of the next tooth, measured along the pitch circle. If the distance from the centre of one tooth to the centre of the next tooth, measured along the pitch circle, is in., the gear is in. circular pitch.

The diametral pitch given, to obtain the circular pitch, divide 3°1416 by the diametral pitch. If the diametral pitch is 4, divide 3'1416 by 4, and the quotient o'7854 is the circular pitch.

The circular pitch given, to obtain the diametral pitch, divide 3*1416 by the circular pitch. If the circular pitch is 2 in., divide 3'1416 by 2, and the quotient 15708 is the diametral pitch.

The number of teeth and the diametral pitch given to obtain the pitch diameter, divide the number of teeth by the diametral pitch. If the number of teeth is 40 and the diametral pitch is 4, divide 40 by 4, and the quotient 10 is the pitch diameter.

The number of teeth and the diametral pitch given, to obtain the whole diameter or size of blank of gear, add 2 to the number of teeth, and divide by the diametral pitch. If the number of teeth is 40, and the diametral pitch is 4, add 2 to the 40, making 42, and divide by 4; the quotient 10 is the whole diameter of the gear or blank.

The number of teeth and the diameter of the blank given, to obtain the diametral pitch, add 2 to the number of teeth, and divide by the diameter of the blank. If the number of teeth is 40, and the diameter of the blank is 10 in., add 2 to the number of teeth, making 42, and divide by 10; the quotient 4 is the diametral pitch.

The pitch diameter and the diametral pitch given, to obtain the number of teeth, multiply the pitch diameter by the diametral pitch. If the diameter of the pitch circle is 10 in., and the diametral pitch is 4, multiply 10 by 4, and the product, 40, will be the number of teeth in the gear.

The whole diameter of the blank and the diametral pitch given, to obtain the number of teeth in the gear, multiply the diameter by the

diametral pitch and subtract 2. If the whole diameter is 10, and the diametral pitch is 4, multiply 10 by 4, and the product 42, less 2, or 40 is the number of teeth.

The thickness of a tooth at the pitch line is found by dividing the

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circular pitch by 2, or dividing 1'57 by the diametral pitch. If the circular pitch is 1'047 in., or the diametral pitch is 3, divide 1047 by 2, or 157 by 3, and the quotient, 0'523 in., is the thickness of tooth.

The whole depth of a tooth is found by dividing 2'157 by the diametral pitch. If the diametral pitch of a gear is 6, the whole depth is 2.157 divided by 6, or o 3595.

The whole depth of a tooth is about 11, or, more precisely, o'6866 of the circular pitch. If the circular pitch is 2, the whole depth of tooth is about 1 of 2 in., or nearly 13 in.

The distance between the centres of two gears is found by adding the number of teeth together, and divide half the sum by the diametral pitch. If two gears have 50 and 30 teeth respectively, and are 5 pitch, add 50 and 30, making 80; divide by 2, and then divide this quotient, 40, by the diametral pitch, 5; and the result, 8 in. is the centre distance.1

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Fully Automatic Gear-Cutting Machine. The entirely automatic gear-cutting machine illustrated in Fig. 316 is by Messrs. G. Birch & Co., Manchester. In this machine the mandrel which supports the work is carried by a hollow spindle, the mouth of which is bored conical to give additional bearing, also to ensure perfect contact, which is so essential in all fitting parts, to keep them from vibrating when the cutting tools are in operation.

The mandrel is kept in place by a nut at the back. The bed of the machine is cast with an extension at one end, and is mounted on two standards, the one at the right hand is made wider to give support to the cutter head.

The skeleton or webbed leg supports are giving place to much wider

1 Brown and Sharpe's "Gearing."

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