The Economy of Workshop Manipulation A logical method of learning constructive mechanics. Arranged with questions for the use of apprentice engineers and students. — Background and Themes

re were three kinds of strain mentioned--torsional, deflective, and accidental. To meet these several strains the same means have to be provided, which is a sufficient size and strength to resist them; hence it is useless to consider each of these different strains separately. If we know which of the three is greatest, and provide for that, the rest, of course, may be disregarded. This, in practice, is found to be accidental strains to which shafts are in ordinary use subjected, and they are usually made, in point of strength, far in excess of any standard that would be fixed by either torsional or transverse strain due to the regular duty performed.

This brings us back to the old proposition, that for structures which do not involve motion, mathematical data will furnish dimensions; but the same rule will not apply in machinery. To follow the proportions for shafts that would be furnished by pure mathematical data would in nearly all cases lead to error. Experience has demonstrated that for ordinary cases, where power is transmitted and applied with tolerable regularity, a shaft three inches in diameter, making one hundred and fifty revolutions a minute, its bearings three to four diameters in length, and placed ten feet apart, will safely transmit fifty horse-power.

By assuming this or any other well-proved example, and estimating larger or smaller shafts by keeping their diameters as the cube root of the power to be transmitted, the distance between bearings as the diameter, and the speed inverse as the diameter, the reader will find his calculations to agree approximately with the modern practice of our best engineers. This is not mentioned to give proportions for shafts, so much as to call attention to accidental strains, such as winding belts, and to call attention to a marked discrepancy between actual practice and such proportions as would be given by what has been called the measured or determinable strains to which shafts are subjected.

As a means for transmitting power, shafts afford the very important advantage that power can be easily taken off at any point throughout their length, by means of pulleys or gearing, also in forming a positive connection between the motive-power and machines, or between the different parts of machines. The capacity of shafts in resisting torsional strain is as the cube of their diameter, and the amount of torsional deflection in shafts is as their length. The torsional capacity being based upon the diameter, often leads to the construction of what may be termed diminishing shafts, lines in which the diameter of the several sections are diminished as the distance from the driving power increases, and as the duty to be performed becomes less. This plan of arranging line shafting has been and is yet quite common, but certainly was never arrived at by careful observation. Almost every plan of construction has both advantages and disadvantages, and the best means of determining the excess of either, in any case, is to first arrive at all the conditions as near as possible, then form a "trial balance," putting the advantages on one side and the disadvantages on the other, and footing up the sums for comparison. Dealing with this matter of shafts of uniform diameter and shafts of varying diameter in this way, there may be found in favour of the latter plan a little saving of material and a slight reduction of friction as advantages. The saving of material relates only to first cost, because the expense of fitting is greater in constructing shafts when the diameters of the different pieces vary; the friction, considering that the same velocity throughout must be assumed, is scarcely worth estimating.

For disadvantages there is, on the other hand, a want of uniformity in fittings that prevents their interchange from one part of a line shaft to the other--a matter of great importance, as such exchanges are frequently required. A line shaft, when constructed with pieces of varying diameter, is special machinery, adapted to some particular place or duty, and not a standard product that can be regularly manufactured as a staple article by machinists, and thus afforded at a low price. Pulleys, wheels, bearings, and couplings have all to be specially prepared; and in case of a change, or the extension of lines of shafting, cause annoyance, and frequently no little expense, which may all be avoided by having shafts of uniform diameter. The bearings, besides being of varied strength and proportions, are generally in such cases placed at irregular intervals, and the lengths of the different sections of the shaft are sometimes varied to suit their diameter. With line shafts of uniform diameter, everything pertaining to the shaft--such as hangers, couplings, pulleys, and bearings--is interchangeable; the pulleys, wheels, bearings, or hangers can be placed at pleasure, or changed from one part of the shaft to another, or from one part of the works to another, as occasion may require. The first cost of a line of shafting of uniform diameter, strong enough for a particular duty, is generally less than that of a shaft consisting of sections varying in size. This may at first seem strange, but a computation of the number of supports required, with the expense of special fitting, will in nearly all cases show a saving.

Attention has been called to this case as one wherein the conditions of operation obviously furnish true data to govern the arrangement of machinery, instead of the determinable strains to which the parts are subjected, and as a good example of the importance of studying mechanical conditions from a practical and experimental point of view. If the general diameter of a shaft is based upon the exact amount of power to be transmitted, or if the diameter of a shaft at various parts is based upon the torsional stress that would be sustained at these points, such a shaft would not only fail to meet the conditions of practical use, but would cost more by attempting such an adaptation. The regular working strain to which shafts are subjected is inversely as the speed at which they run. This becomes a strong reason in favour of arranging shafts to run at a maximum speed, provided there was nothing more than first cost to consider; but there are other and more important conditions to be taken into account, principal among which are the required rate of movement where power is taken off to machines, and the endurance of bearings.

In the case of line shafting for manufactories, if the speed varies so much from that of the first movers on machines as to require one or more intermediate or countershafts, the expense would be very great; on the contrary, if countershafts can be avoided, there is a great saving of belts, bearings, machinery, and obstruction. The practical limit of speed for line shafts is in a great measure dependent upon the nature of the bearings, a subject that will be treated of in another place.

(1.) What kind of strains are shafts subjected to?--(2.) What determines the strength of shafts in resisting transverse strain?--(3.) Why are shafts often more convenient than belts for transmitting power?--(4.) What is the difference between the strains to which shafts and belts are subjected?--(5.) What is gained by constructing a line shaft of sections diminishing in size from the first mover?--(6.) What is gained by constructing line shafts of uniform diameter?

_BELTS FOR TRANSMITTING POWER._

The traction of belts upon pulleys, like that of locomotive wheels upon railways, being incapable of demonstration except by actual experience, for a long time hindered the introduction of belts as a means of transmitting motion and power except in cases when gearing or shafts could not be employed. Motion is named separately, because with many kinds of machinery that are driven at high speed--such as wood machines--the transmission of rapid movement must be considered as well as power, and in ordinary practice it is only by means of belts that such high speeds may be communicated from one shaft to another.

The first principle to be pointed out in regard to belts, to distinguish them from shafts as a means of transmitting power, is that power is communicated by means of tensile instead of torsional strain, the power during transmission being represented in the difference of tension between the driving and the slack side of belts. In the case of shafts, their length, or the distance to which they may be extended in transmitting power, is limited by torsional resistance; and as belts are not liable to this condition, we may conclude that unless there are other difficulties to be contended with, belts are more suitable than shafts for transmitting power throughout long distances. Belts suffer resistance from the air and from friction in the bearings of supporting pulleys, which are necessary in long horizontal belts; with these exceptions they are capable of moving at a very high rate of speed, and transmitting power without appreciable loss.

Following this proposition into modern engineering examples, we find how practice has gradually conformed to what these properties in belts suggest. Wire and other ropes of small diameter, to avoid air friction, and allowed to droop in low curves to avoid too many supporting pulleys, are now in many cases employed for transmitting power through long distances, as at Schaffhausen, in Germany. This system has been very successfully applied in some cases for distributing power in large manufacturing establishments. Belts, among which are included all flexible bands, do not afford the same facilities for taking off power at different points as shafts, but have advantages in transmitting power to portable machinery, when power is to be taken off at movable points, as in the case of portable travelling cranes, machines, and so on.

An interesting example in the use of belts for communicating power to movable machinery is furnished by the travelling cranes of Mr Ramsbottom, in the shops of the L. & N. W. Railway, at Crewe, England, where powerful travelling cranes receive both the lifting and traversing power by means of a cotton rope not more than three-fourths of an inch in diameter, which moves at a high velocity, the motion being reduced by means of tangent wheels and gearing to attain the force required in lifting heavy loads. Observing the operation of this machinery, a person not familiar with the relations between force and motion will be astonished at the effect produced by the small rope which communicates power to the machinery.

Considered as means for transmitting power, the contrast as to advantages and disadvantages lies especially between belts and gearing instead of between belts and shafts. It is true in extreme cases, such as that cited at Crewe, or in conveying water-power from inaccessible places, through long distances, the comparison lies between belts and shafts; but in ordinary practice, especially for first movers, the problem as to mechanism for conveying power lies between belts and gear wheels. If experience in the use of belts was thorough, as it is in the case of gearing, and if the quality of belts did not form so important a part in the estimates, there would be but little difficulty in determining where belts should be employed and where gearing would be preferable. Belts are continually taking the place of gearing even in cases where, until quite recently, their use has been considered impracticable; one of the largest rolling mills in Pittsburg, Pennsylvania, except a single pair of spur wheels as the last movers at each train of rolls, is driven by belts throughout.

Leaving out the matter of a positive relative movement between shafts, which belts as a means of transmitting power cannot insure, there are the following conditions that must be considered in determining whether belts or other means should be employed in transmitting power from one machine to another or between the parts of machines.

1. The distance to which power is to be transmitted.

2. The speed at which the transmitting machinery must move.

3. The course or direction of transmission, whether in straight lines or at angles.

4. The cost of construction and durability.

5. The loss of power during transmission.

6. Danger, noise, vibration, and jar.

In every case where there can be a question as to whether gearing shafts or belts will be the best means of transmitting power, the several conditions named will furnish a solution if they are properly investigated and understood. Speed, noise, or angles may become determinative conditions, and are such in a large number of cases; first cost and loss of power are generally secondary conditions. Applying these tests to cases where belts, shafts, or wheels may be employed, a learner will soon find himself in possession of knowledge to guide him in his own schemes, and enable him to judge of the correctness of examples that come under his notice.

It is never enough to know that any piece of work is commonly constructed in some particular manner, or that a proposition is generally accepted as being correct; a reason should be sought for. Nothing is learned, in the true sense, until the reasons for it are understood, and it is by no means sufficient to know from observation alone that belts are best for high speeds, that gearing is the best means of forming angles in transmitting power, or that gearing consumes more power, and that belts produce less jar and noise; the principles which lie at the bottom must be reached before it can be assumed that the matter is fairly understood.

(1.) Why have belts been found better than shafts for transmitting power through long distances?--(2.) What are the conditions which limit the speed of belts?--(3.) Why cannot belts be employed to communicate positive movement?--(4.) Would a common belt transmit motion positively, if there were no slip on the pulleys?--(5.) Name some of the circumstances to be considered in comparing belts with gearing or shafts as a means of transmitting power.

_GEARING AS A MEANS OF TRANSMITTING POWER._

The term gearing, which was once applied to wheels, shafts, and the general mechanism of mills and factories, has now in common use become restricted to tooth wheels, and is in this sense employed here. Gearing as a means of transmitting motion is employed when the movement of machines, or the parts of machines, must remain relatively the same, as in the case of the traversing screw of an engine lathe--when a heavy force is transmitted between shafts that are near to each other, or when shafts to be connected are arranged at angles with each other. This rule is of course not constant, except as to cases where positive relative motion has to be maintained. Noise, and the liability to sudden obstruction, may be reasons for not employing tooth wheels in many cases when the distance between and the position of shafts would render such a connection the most durable and cheap. Gearing under ordinary strain, within limited speed, and when other conditions admit of its use, is the cheapest and most durable mechanism for transmitting power; but the amount of gearing employed in machinery, especially in Europe, is no doubt far greater than it will be in future, when belts are better understood.

No subject connected with mechanics has been more thoroughly investigated than that of gearing. Text-books are replete with every kind of information pertaining to wheels, at least so far as the subject can be made a mathematical one; and to judge from the amount of matter, formulæ, and diagrams, relating to the teeth of wheels that an apprentice will meet with, he will no doubt be led to believe that the main object of modern engineering is to generate wheels. It must be admitted that the teeth of wheels and the proportions of wheels is a very important matter to understand, and should be studied with the greatest care; but it is equally important to know how to produce the teeth in metal after their configuration has been defined on paper; to understand the endurance of teeth under abrasive wear when made of wrought or cast iron, brass or steel; how patterns can be constructed from which correct wheels may be cast, and how the teeth of wheels can be cut by machinery, and so on.

A learner should, in fact, consider the application and operative conditions of gearing as one of the main parts of the subject, and the geometry or even the construction of wheels as subsidiary; in this way attention will be directed to that which is most difficult to learn, and a part for which facilities are frequently wanting. Gearing may be classed into five modifications--spur wheels, bevel wheels, tangent wheels, spiral wheels, and chain wheels; the last I include among gearing because the nature of their operation is analogous to tooth wheels, although at first thought chains seem to correspond more to belts than gearing. The motion imparted by chains meshing over the teeth of wheels is positive, and not frictional as with belts; the speed at which such chains may run, with other conditions, correspond to gearing.

Different kinds of gearing can be seen in almost every engineering establishment, and in view of the amount of scientific information available, it will only be necessary to point out some of the conditions that govern the use and operation of the different kinds of wheels. The durability of gearing, aside from breaking, is dependent upon pressure and the amount of rubbing action that takes place between the teeth when in contact. Spur wheels, or bevel wheels, when the pitch is accurate and the teeth of the proper form, if kept clean and lubricated, wear but little, because the contact between the teeth is that of rolling instead of sliding. In many cases, one wheel of a pair is filled with wooden cogs; in this arrangement there are four objects, to avoid noise, to attain a degree of elasticity in the teeth, to retain lubricants by absorption in the wood, and to secure by wear a better configuration of the teeth than is usually attained in casting, or even in cutting teeth.

Tangent wheels and spiral gearing have only what is termed line contact between the bearing surfaces, and as the action between these surfaces is a sliding one, such wheels are subject to rapid wear, and are incapable of sustaining much pressure, or transmitting a great amount of power, except the surfaces be hard and lubrication constant. In machinery the use of tangent wheels is mainly to secure a rapid change of speed, usually to diminish motion and increase force.

By placing the axes of tangent gearing so that the threads or teeth of the pinions are parallel to the face of the driven teeth, as in the planing machines of Messrs Wm. Sellers & Co., the conditions of operation are changed, and an interesting problem arises. The progressive or forward movement of the pinion teeth may be equal to the sliding movement between the surfaces; and an equally novel result is, that the sliding action is distributed over the whole breadth of the driven teeth.

In spiral gearing the line of force is at an angle of forty-five degrees with the bearing faces of the teeth, and the sliding movement equal to the speed of the wheels at their periphery; the bearing on the teeth, as before said, is one of line contact only. Such wheels cannot be employed except in cases where an inconsiderable force is to be transmitted. Spiral wheels are employed to connect shafts that cross each other at right angles but in different planes, and when the wheels can be of the same size.

It may be mentioned in regard to rack gearing for communicating movement to the carriages of planing machines or other purposes of a similar nature: the rack can be drawn to the wheel, and a lifting action avoided, by shortening the pitch of the rack, so that it will vary a little from the driving wheel. The rising or entering teeth in this case do not come in contact with those on the rack until they have attained a position normal to the line of the carriage movement.

(1.) Into what classes can gearing be divided?--(2.) What determines the wearing capacity of gearing?--(3.) What is the advantage gained by employing wooden cogs for gear wheels?--(4.) Why are tangent or worm wheels not durable?

_HYDRAULIC APPARATUS FOR TRANSMITTING POWER._