Suppose it is required to make a gauge for a pitch of 6 per inch, then a piece of iron of any diameter may be put in the lathe and turned up to the required diameter for the top of the thread. The end of this piece should be turned up to the proper diameter for the bottom of the thread, as at g, in Fig. 287. Now, it will be seen that the angle of the thread to the axis a of the iron is that of line c to line a, and if we require to find the angle the thread passes through in once winding around the bolt, we proceed as in Fig. 288, in which d represents the circumference of the thread measured at a right angle to the bolt axis, as denoted by the line b in Fig. 287. f, Fig. 288 (at a right angle to d), is the pitch of the thread, and line c therefore represents the angle of the thread to the bolt axis, and corresponds to line c in Fig. 287. We now take a piece of iron whose length when turned true will equal its finished and threaded circumference, and after truing it up and leaving it a little above its required finished diameter, we put a pointed tool in the slide-rest and mark a line a a in Fig. 289, which will represent its axis. At one end of this line we mark off below a a the pitch of the thread, and then draw the line h j, its end h falling below a to an amount equal to the pitch of the thread to be cut. The piece is then put in a milling machine and a groove is cut along h j, this groove being to receive a tightly-fitting piece of sheet metal of which a thread gauge is to be made. This piece of sheet metal must be firmly secured in the groove by set-screws. The piece of iron is then again put in the lathe and its diameter finished to that of the required diameter of thread. Its two ends are then turned down to the required diameter for the bottom of the thread, leaving in the middle a section on which a full thread can be cut, as in Fig. 290, in which f f represents the sheet metal for the gauge. After the thread is cut, as in Fig. 290, we take out the gauge and it will appear as in Fig. 291, and all that is necessary is to file off the two outside teeth if only one tooth is wanted.

The philosophy of this process is that we have set the gauge at an angle of 90°, or a right angle to the thread, as is shown in Fig. 289, the line c representing the angle of the thread to the axis a a, and therefore corresponding to the line c in Fig. 287. A gauge made in this way will serve as a test of its own correctness for the following reasons: Taking the middle tooth in Fig. 291, it is clear that one of its sides was cut by one angle and the other by the other angle of the tool that cut it, and as a correctly formed thread is of exactly the same shape as the space between two threads, it follows that if the gauge be applied to any part of the thread that was cut in forming it, and if it fits properly when tried, and then turned end for end and tried again, it is proof that the gauge and the thread are both correct. Suppose, for example, that the tool was correct in its shape, but was not set with its two angles equal to the line of lathe centres, and in that case the two sides of the thread will not be alike and the gauge will not reverse end for end and in both cases fit to the thread. Or suppose the flat on the tool point was too narrow, and the flat at the bottom of the thread will not be like that at the top, and the gauge will show it.

Referring to the fifth requirement, that the angles of the sides of the threads shall be as acute as is consistent with the required strength, it is obvious that the more acute the angles of the sides of the thread one to the other the finer the pitch and the weaker the thread, but on the other hand, the more acute the angle the better the sides of the thread will conform one to the other. The importance of this arises from the fact that on account of the alteration of pitch, already explained, as accompanying the hardening of screw-cutting tools, the sides of threads cut even by unworn tools rarely have full contact, and a nut that is a tight fit on its first passage down its bolt may generally be caused to become quite easy by running it up and down the bolt a few times. Nuts that require a severe wrench force to wind them on the bolt, may, even though they be as large as a two-inch bolt, often be made to pass easily by hand, if while upon the bolt they are hammered on their sides with a hand hammer. The action is in both cases to cause the sides of the thread to conform one to the other, which they will the more readily do in proportion as their sides are more acute. Furthermore, the more acute the angles the less the importance of gauging the threads to precise diameter, especially if the tops and bottoms of the male and female thread are clear of one another, as in Fig. 273.

Referring to the sixth requirement, that the nut shall not be unduly liable to become loose of itself in cases where it may require to be fastened and loosened occasionally, it may be observed, that in such cases the threads are apt from the wear to become a loose fit, and the nuts, if under jar or vibration, are apt to turn back of themselves upon the bolt. This is best obviated by insuring a full bearing upon the whole area of the sides of the thread, and by the employment of as fine pitches as is consistent with sufficient strength, since the finer the pitch the nearer the thread stands at right angle to the bolt axis, and the less the tendency to unscrew from the pressure on the nut face.

The pitches, diameters, and widths of flat of the United States standard thread are as per the following table:—

UNITED STATES STANDARD SCREW THREADS.

The standard pitches for the sharp V-thread are as follows:—

SIZE OF BOLT.

The following table gives the threads per inch, pitches and diameters at root of thread of the Whitworth thread. The table being arranged from the diameter of the screw as a basis.

The standard degree of taper, both for the taps and the dies, is ¹⁄₁₆ inch per inch, or ³⁄₄ inch per foot, for all sizes up to 10-inch bore.

The sockets or couplings, however, are ordinarily tapped parallel and stretched to fit the pipe taper when forced on the pipe. For bores of pipe over 10 inches diameter the taper is reduced to ³⁄₈ inch per foot. The pipes or casings for oil wells are given a taper of ³⁄₈ inch per foot, and their couplings are tapped taper from both ends. There is, however, just enough difference made between the taper of the socket and that of the pipe to give the pipe threads a bearing at the pipe end first when tried with red marking, the threads increasing their bearing as the pieces are screwed together.

The United States standard thread for steam, gas and water pipe is given below, which is taken from the Report of the Committee on Standard Pipe and Pipe Threads of The American Society of Mechanical Engineers, submitted at the 8th Annual Meeting held in New York, November-December, 1886.

“A longitudinal section of the tapering tube end, with the screw-thread as actually formed, is shown full size in Fig. 291a for a nominal 2¹⁄₂ inch tube, that is, a tube of about 2¹⁄₂ inches internal diameter, and 2⁷⁄₈ inches actual external diameter.

“The thread employed has an angle of 60°; it is slightly rounded off both at the top and at the bottom, so that the height or depth of the thread, instead of being exactly equal to the pitch, is only four fifths of the pitch, or equal to 0.8 × 1/n if n be the number of threads per inch. For the length of tube end throughout which the screw thread continues perfect, the empirical formula used is (0.8D + 4.8) × 1/n, where D is the actual external diameter of the tube throughout its parallel length, and is expressed in inches. Further back, beyond the perfect threads, come two having the same taper at the bottom, but imperfect at the top. The remaining imperfect portion of the screw thread, furthest back from the extremity of the tube, is not essential in any way to this system of joint; and its imperfection is simply incidental to the process of cutting the thread at a single operation.”

The standard thicknesses of the pipes and pitches of thread are as follows:—

STANDARD DIMENSIONS OF WROUGHT IRON
WELDED TUBES.

The taper of the threads is ¹⁄₁₆ inch in diameter for each inch of length or ³⁄₄ inch per foot.

WHITWORTH’S SCREW THREADS FOR GAS, WATER, AND HYDRAULIC IRON PIPING.

Note.—The Internal and External diameters of Pipes, as given below, are those adopted by the firm of Messrs. James Russell & Sons, in Pipes of their manufacture.

The English pipe thread is a sharp V-thread having its sides at an angle of 60°, and therefore corresponds to the American pipe thread except that the pitches are different.

The standard screw thread of The Royal Microscopical Society of London, England, is employed for microscope objectives, and the nose pieces of the microscope into which these objectives screw.

The thread is a Whitworth one, the original standard threading tools now in the cabinet of the society having been made especially for the society by Sir Joseph Whitworth. The pitch of the thread is 36 per inch. The cylinder, or male gauge, is .7626 inch in diameter.

The following table gives the Whitworth standard of thread pitches and diameters for watch and mathematical instrument makers.

WHITWORTH’S STANDARD GAUGES FOR WATCH AND
INSTRUMENT MAKERS, WITH SCREW THREADS FOR
THE VARIOUS SIZES, 1881.

For the pitches of the threads of lag screws there is no standard, but the following pitches are largely used.

Screw-Cutting Hand Tools.

For cutting external or male threads by hand three classes of tools are employed.