# Miscellaneous Papers on Mechanical Subjects/A Paper on an Uniform System of Screw Threads

A PAPER ON AN UNIFORM SYSTEM OF SCREW THREADS.
[READ AT THE INSTITUTION OF CIVIL ENGINEERS IN 1841.]
The screw threads which form the subject of this paper are those of bolts and screws, used in fitting up steam engines and other machinery. Great inconvenience is found to arise from the variety of threads adopted by different manufacturers. The general provision for repairs is rendered at once expensive and imperfect. The difficulty of ascertaining the exact pitch of a particular thread, especially when it is not a multiple or submultiple of the common inch measure, occasions extreme embarrassment. This evil would be completely obviated by uniformity of system, the thread becoming constant for a given diameter. The same principle would supersede the costly variety of screwing apparatus, required in many establishments, and remove the confusion and delay occasioned thereby. It would also prevent the waste of bolts and nuts which is now unavoidable. The impulse and direction given to machinery during ​late years have tended to increase these evils, and must, ultimately, lead to a change of system. Take, for example, the refitting shop of a railway or steam packet company. Here the variety of apparatus rendered necessary by the want of uniformity will correspond with the number of different manufacturers by whom the engines are supplied, whereas, if the same system of screw threads were common to the different engines, a single set of screwing tackle would suffice. The economy and manifold advantages resulting from uniformity in this instance, would be sufficiently obvious.
Supposing the same principle extended throughout engineering and other establishments until its application became general, the advantage would be proportionally greater, and would assume a character of public importance. Public convenience would be promoted in various ways easy to trace, though leading to results perhaps little to be expected, and the economy of screwing apparatus, however considerable, would become insignificant when compared with the contingent benefit to other interests.
Were an uniform system adopted for marine or locomotive engines there can be no doubt that it would be extended to engines and ​machinery of almost every description. Peculiar threads will, of course, be always required for particular purposes, but in screws for general use in fitting up machinery, the advantage of uniformity would be paramount to every other consideration.
It does not appear that any combined effort has been hitherto made to attain this object. As yet there is no recognized standard. This will not be matter of surprise, when it is considered that any standard must be, to a great extent, arbitrary. It is impossible to deduce a precise rule for the threads of screws from mechanical principles, or from any number of experiments. On the other hand, the nature of the case is such that mere approximation would be unimportant, absolute identity of thread for a given diameter being indispensable.
To how great an extent the choice of thread is arbitrary will appear from a cursory consideration of the principles affecting it. Without attempting to discuss these in detail, which would be foreign to the present purpose, it may be interesting to notice the general outline and bearings of the subject.
The use of the screw bolt is to unite certain parts of machinery in close and firm contact. It is peculiarly adapted for this purpose by the compact form in which it possesses the necessary ​strength and mechanical power. The extreme familiarity of the object tends to prevent the observation of its peculiar fitness. Yet, among all the applications of mechanics, there is, perhaps, no instance of adaptation more remarkable. The ease with which distinct parts of machinery can be united, the firmness with which they are held together, and the facility with which they may be separated, are conditions of the utmost importance, which by no other contrivance could be combined in an equal degree.
While, however, the utility of the screw in this application is abundantly obvious, it is by no means evident what may be the precise formation most advantageous under all circumstances. No exact data of any kind can be obtained for calculation, and the problem will be found to be capable only of approximate solution.
The principal conditions required in the screw bolt are power, strength, and durability—the latter having reference to the wear occasioned by frequent fixing and unfixing. But none of these conditions can be reduced to a definite quantity. We cannot, for example, determine the exact amount of power necessary to draw the parts of a machine into due contact, or the precise degree of strength which may suffice for resisting the strains to which they ​may be afterwards exposed. Hence, we cannot lay down any rule for choosing the diameter of the screw bolt required for a given purpose. Practical men can judge of the proper size with considerable nicety, but they have no means of ascertaining it with absolute precision.
If the diameter be given, and it be required to find the proper thread, the nature of the question is not essentially altered. The amount neither of power, nor of strength (nor any other condition), is thereby determined. A certain limit is assigned, but within that limit the proportions of strength and power, &c., may vary indefinitely, according to the actual formation of the thread.
There are three essential characters belonging to the screw thread, viz., pitch, depth, and form. Each of these may be indefinitely modified independently of the others, and any change will more or less affect the several conditions of power, strength, and durability.—The mechanical power of the screw depends on the pitch, which for a given diameter determines the angle of the inclined plane, and on the form of thread which regulates the direction in which the force applied will act.—The strength of the screw in the thread varies with each of the three characters; in the centre part, being as the area, it is little affected, except by change of depth.—The durability of ​the thread also depends chiefly on its depths and the proper depth is determined principally with reference to this condition. In the selection of the thread considerable latitude of choice will be found to prevail with reference to all the characters, No definite rule can be given for determining any one of them. It may be manifest that particular threads are too coarse or too fine, too deep or too shallow; but there are intermediate degrees within which the choice of thread like that of the diameter is arbitrary, and must be guided rather by discretion than by calculation.
The mutual dependence of the several conditions required in the thread may be noticed as having a tendency to perplex the choice. Thus increase of power is necessarily attended with diminution of strength. The square thread which has the advantage in respect of power is proportionally weaker than the angular thread. A fine thread loses in strength, while it gains mechanically as compared with a coarser. Deep threads also, while they are more durable than shallow, materially detract from the strength of the bolt.
The selection of the thread is also affected by the mutual relation subsisting between the three constituent characters of pitch, depth, and form. Each of these, as before observed, may be ​separately modified; but practically no one character can be determined irrespective of the others. The pitch of the square thread is generally twice that of the angular for the same diameter, to retain similar proportions of power and strength. Coarse threads should be deep as compared with fine, to provide against the wear from friction. A coarse angular thread will also require additional depth to preserve the due proportion of power, and to prevent the longitudinal strain from being thrown too much sideways on the nut. Hence, each character acts as a limit to the variation of the others, and in some instances (that is, in the case of certain diameters), it will be found that the leading consideration in fixing one character is the resulting effect on another. Thus, in some of the smaller sizes, the pitch is determined principally by reference to the depth—a coarser thread being objectionable, because the extra depth would too much weaken the centre part of the bolt—while the necessary shallowness of a finer thread would render it too liable to wear with friction.
The proportional strength of the thread and centre part of the screw is regulated mainly by the depth of the nut, which is generally of the same measure as the diameter of the bolt. Assuming that dimension as fixed, the proportion of strength between the two parts will vary with ​the different characters of thread, and more particularly with the depth. The centre part not being liable to wear while the thread is subject to friction and accidental injury, the original proportion of strength ought to be considerably in favour of the thread.
Such being the variety and vagueness of the principles avowed in the subject, a corresponding latitude might naturally be expected in their practical application, and accordingly we find, instead of that uniformity which is so desirable, a diversity so great as almost to discourage any hope of its removal. The only mode in which this could be attempted with any probability of success would be by a sort of compromise, all parties consenting to adopt a medium for the sake of common advantage. The average pitch and depth of the various threads used by the leading engineers would thus become the common standard; which would not only have the advantage of conciliating general concurrence, but would, in all probability, be nearer the true standard for practical purposes than any other.
Messrs. Whitworth and Company were led, some years ago, to alter the threads of their screws on this principle, in consequence of various objections urged against those they had previously adopted, and the result of the experiment has been abundantly satisfactory. ​An extensive collection was made of screw bolts from the principal workshops throughout England, and the average thread was carefully observed for different diameters. The ¼, ½, 1, and 1½ inches were particularly selected and taken as the fixed points of a scale by which the intermediate sizes were regulated. The only deviation made from the average was such as might be necessary to avoid the great inconvenience of small fractional parts in the number of threads to the inch. The scale was afterwards extended to 6 inches.
The pitches thus obtained for angular threads are shown in the following table:—
| Diameter in Inches | .. | $^1$⁄$_4$ | $^5$⁄$_{16}$ | $^3$⁄$_8$ | $^7$⁄$_{16}$ | $^1$⁄$_2$ | $^5$⁄$_8$ | $^3$⁄$_4$ | $^7$⁄$_8$ | 1 | 1+$^1$⁄$_8$ | 1+$^1$⁄$_4$ |
| Threads to the Inch | .. | 20 | 18 | 16 | 14 | 12 | 11 | 10 | 9 | 8 | 7 | 7 |
| Diameter in Inches | .. | 1+$^3$⁄$_8$ | 1+$^1$⁄$_2$ | 1+$^5$⁄$_8$ | 1+$^3$⁄$_4$ | 1+$^7$⁄$_8$ | 2 | 2+$^1$⁄$_4$ | 2+$^1$⁄$_2$ | 2+$^3$⁄$_4$ | 3 | 3+$^1$⁄$_4$ |
| Threads to the Inch | .. | 6 | 6 | 5 | 5 | 4+$^1$⁄$_2$ | 4+$^1$⁄$_2$ | 4 | 4 | 3+$^1$⁄$_2$ | 3+$^1$⁄$_2$ | 3+$^1$⁄$_4$ |
| Diameter in Inches | .. | 3+$^1$⁄$_2$ | 3+$^3$⁄$_4$ | 4 | 4+$^1$⁄$_4$ | 4+$^1$⁄$_2$ | 4+$^3$⁄$_4$ | 5 | 5+$^1$⁄$_4$ | 5+$^1$⁄$_2$ | 5+$^3$⁄$_4$ | 6 |
| Threads to the Inch | .. | 3+$^1$⁄$_4$ | 3 | 3 | 2+$^7$⁄$_8$ | 2+$^7$⁄$_8$ | 2+$^1$⁄$_4$ | 2+$^3$⁄$_4$ | 2+$^5$⁄$_8$ | 2+$^5$⁄$_8$ | 2+$^1$⁄$_2$ | 2+$^1$⁄$_2$ |
It will be observed that above 1-inch diameter the same pitch is used for two sizes. This could not have been avoided without introducing small fractional parts. The economy of screwing apparatus was also promoted by repetition of the thread.
It is important to remark that the proportion ​between the pitch and the diameter varies throughout the entire scale. Thus the pitch of the ¼ inch is one-fifth of the diameter—that of the ½-inch, one-sixth—of the 1-inch, one-eighth—of the 4-inch, one-twelfth—of the 6-inch, one-fifteenth. It is obvious that more power is required as the diameter increases. But this consideration alone will not account for the actual deviation, which is much less than it would be if the scale were calculated with reference to the power required. The amount of power necessary must be determined in relation to the muscular force of the human arm, aided by the leverage of the screw key. Now, in the case of smaller screws, there is a considerable excess of force. Again, in the larger, there will be found a deficiency of power, for with all the leverage which can generally be applied, it requires the force of several men to fix a bolt of six inches diameter. Hence it is evident that at the two extremes of the scale the amount of power required is not the leading consideration in fixing the pitch of the thread. In the smaller sizes the necessary depth of a coarser thread—as before observed—would too much weaken the centre part of the screw. It may also be mentioned that coarse threads would render small screws apt to work loose for want of sufficient hold to prevent the effect of jarring. ​On the other hand, finer threads on large bolts besides being weaker and less durable, would render it difficult to unfix them when occasion required.
It will be remembered that the threads, of which the preceding table shows the average, are used in cast iron as well as wrought; and this circumstance has had its effect in rendering them coarser than they would have been, if restricted to wrought iron.
The variation in depth among the different specimens was found to be greater proportionally than in pitch. The angle made by the sides of the thread will afford a convenient expression for the depth. The mean of the variations of this angle in 1-inch screws was found to be about 55°, and this was also pretty nearly the mean of the angle in screws of different diameters. As it is for various reasons desirable that the angle should be constant, more especially with reference to general uniformity of system, the angle of 55° has been adopted throughout the entire scale. A constant proportion is thus established between the depth and the pitch of the thread. In calculating the former, a deduction is to be made for the quantity rounded off, amounting to one-third of the whole depth—that is, one-sixth from the top, and one-sixth from the bottom of the thread. Making this ​deduction it will be found that the angle of 55° gives for the actual depth rather more than three-fifths and less than two-thirds of the pitch. The precaution of rounding off is adopted to prevent the injury which the thread of the screw, and that of the taps and dies, might sustain from accident.
The system of threads selected in the manner above described has already obtained greater extension than any other. It has been adopted exclusively on many of the railways, and in some of the most extensive engineering establishments in England and Scotland. During the present year it has been introduced into the Royal Dockyard at Woolwich, and it is now being applied to the engines constructing for the Royal Mail Steam Packet Company. There is therefore reason to hope this system may be instrumental in promoting the proposed object of uniformity, of which it already exemplifies the practicability and advantage.
But the difficulty of obtaining a concurrence of opinion in favour of a particular system is not the only one to be encountered. The inconvenience to existing establishments which any change would involve is calculated to retard the prevalence of an approved system, nor could general co-operation be reasonably expected unless there were a certain prospect of success. ​This, however, is an obvious reason why the attention of engineers should, without loss of time, be directed to the subject.
It will probably occur to practical men that there are other obstacles to be surmounted before the principle of uniformity can be carried into full operation. The great want of accuracy in screwing and tapping by the ordinary process may be particularly mentioned. To whatever extent this may prove an obstruction, it may be also regarded as an additional motive for urging the subject on general attention. The necessity for greater correctness will thus be placed in a new and stronger light, and the effect no doubt will be a material improvement in this essential respect. It is mainly for want of accuracy that screw bolts so frequently fail. Unless the threads of the screw and nut exactly correspond in every part, and coalesce throughout their whole length and depth, their mutual action is completely deranged, power and strength are both sacrificed, and friction is proportionally increased. The immense consumption of bolts and nuts in fitting up and working machinery may give some idea of the extent to which greater accuracy might be productive of economy.
To maintain uniformity, provision must be made for multiplying standards of the diameters and threads. This may be easily done, and will ​prevent the screwing tackle from degenerating by use and propagation.
This part of the case is connected with a subject of great extent which, under every aspect, lays claim to the attention of practical engineers. We allude to the general use of standard gauges, graduated to a fixed scale, as constant measures of size. It is quite practicable by such means to work to a common measure with a degree of accuracy sufficient for all ordinary purposes. Corresponding parts, instead of being got up one to another, might be prepared separately. The indefinite multiplication of sizes would thus be prevented, and the economy of the workshop simplified to an extent beyond calculation.
This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.
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