LECTURE XIV.

CONTENTS.-Screws-The Spiral, Helix, or Ideal Line of a Screw Thread -The Screw viewed as an Inclined Plane-Characteristics and Conditions to be Fulfilled by Screw Threads--Different Forms of Screw Threads-Whitworth's V-Threads-Whitworth's Tables of Standard V-Threads, Nuts and Bolt Heads-Seller's V-Thread-The Square Thread-The Rounded Thread-The Buttress Thread-Right and Left-hand Screws-The Screw Coupling for Railway CarriagesSingle, Double and Treble Threaded Screws--Backlash in Wheel and Screw Gearings--Questions.

Screws. Every one is more or less familiar with the form and uses of the screw nail for securing pieces of wood together, and of the bolt with its nut for fixing metal plates in position; but every one is not so familiar with the principle upon which screws are generated and act, or with the best shape to be given to a screw under different circumstances. We shall therefore endeavour in this Lecture to explain these points in an elementary manner, instancing a few examples of the practical applications of screws, but reserving for the following Lecture questions on the work done by screws and their efficiency.

The Spiral, Helix, or Ideal Line of a Screw Thread.A very good idea of the form of a screw is obtained from the accompanying figure, which represents one means of elevating or trans

4.AA

SPIRAL OR SCREW FOR MOVING GRAIN.

ferring grain, flour or other powdered substances from one part of a milling works to another. It consists of a steel band twisted around a cylindrical shaft in a continuous and uniformly pitched spiral. This shaft and screw are placed in a trough, tube or pipe. The grain or powdered substance is fed in at one end of the pipe, and by rotating the screw with a wheel or lever fixed

to one end of the shaft, the loose material is gradually pressed forward until it reaches the other end, from which it may be dropped into sacks or put through another process. It is evident from an inspection of the figure that as the screw is turned round by the lever, the particles of matter are forced along the face of the continuous inclined plane formed by the spiral steel band.

The principle upon which the screw acts is, therefore, a combination of the inclined plane and the lever.

To bring this view of the case still more forcibly before the student, take a cylinder and fix along the side thereof parallel to

its axis (by gum or drawing pins) a rectangle, ACDE, of paper or white cloth, having its sides, AC and DE exactly equal to the circumference of the cylinder. Then, when the envelope is wound round the cylinder by the turning of the handle, H (in the direction shown by the arrow at P), it exactly covers its cylindrical surface. On the outside of this rectangle when unfolded, draw any convenient number of parallel inclined black lines, AB, &c., equidistant from each other as shown by the figure, and again wrap it round the cylinder. These lines will be found to form a continuous spiral, helix, or screw-thread line from one end of the cylinder to the other. And the side AC of the right-angled triangle ACB forms the circumference, BC the pitch, AB the length of the thread (for one complete turn of the cylinder), and the angle BAC is the inclination or angle of the screw.

The Screw Viewed as an Inclined Plane.-Take another cylinder having an evenly pitched screw-thread line drawn upon it. Cut a sheet of flexible cardboard into the form of a rightangled triangle with its height BC or h equal to the pitch (or dis

tance between two consecutive threads when measured parallel to the axis of the cylinder); AC or b equal to the circumference of the screw and wrap it round the cylinder, taking care to keep BC parallel to the axis. Then the hypothenuse AB or length 7 of the inclined plane will coincide with the contour of the screwthread for one complete turn, and BAC or, a, is the angle of the thread to the plane at right angles to the axis of the cylinder.

Now conceive this screw-thread instead of being a mere line to be an inclined plane of known breadth, as in the case of the grain elevator.* Let the total weight of material being urged

FIGURE TO PROVE THAT A SCREW THREAD IS AN INCLINED PLANE.

forward or upwards by the turning of the screw be W lbs., and let the resistance due to this load be uniformly distributed along the screw thread or inclined plane. Then, comparing the first and the third figures, it is evident that any small portion of the load having a weight W, lbs. will have a corresponding reaction R, lbs., and will require a part P, lbs. (of the total force, P, applied to turn the screw at the radius at which this portion is situated) to move it along the screw-plane against the frictional resistance F.

1

Imagine the work done to be transferred to the inclined plane, AB, then any portion of the load having a weight W, lbs. will have a corresponding reaction R, lbs., and will require a part P, lbs. (of the total force, P, applied parallel to the base to pull the whole load up the inclined plane) to move it along the plane against the frictional resistance F. Now, these forces act in identically the same way as the second case of the inclined plane, which was discussed in Lecture IX., consequently

* Or, that the screw-thread has a certain depth as measured radially from the axis of cylinder.

Or,

P_CB_height_h

=

W AC base b

pitch of thread circumference of screw.

We therefore see that a screw may be treated as an inclined plane where the force turning the screw-i.e., overcoming the resistance to motion-acts parallel to the base of the incline. The same reasoning may be applied to any screw turning in a nut or to a nut turning on a screw.

Characteristics of and Conditions to be Fulfilled by Screw Threads.-The essential characteristics of a screw-thread are its pitch, depth, and form.

The principal conditions to be fulfilled by a screw-thread are: (1) efficiency; (2) strength; (3) durability.

(1) The efficiency depends on the pitch and the friction, and hence on the pitch and form of thread.

(2) The strength depends upon the form or the shearing thickness and depth, or area of the cross section parallel to the axis. (3) The durability depends chiefly on the depth—that is, upon the extent of bearing surface.

Different Forms of Screw Threads. Sir Joseph Whitworth, the famous tool and gun manufacturer, was so impressed with the great inconvenience and loss of money which arose from the use of different pitches and forms of threads for screws and nuts, that he published the following tables giving the dimensions of what has now become known as the Whitworth standard. Prior to 1841, the year in which Whitworth proposed the adoption of standard sizes for screws, and for several years afterwards, different engineering works in this country not only used different pitches for screws of the same diameter, but it was no uncommon thing to find a want of uniformity in the same shop. Now, every one in Great Britain and her colonies uses the Whitworth standard sizes for V-threaded bolts and nuts of 4-inch and upwards, and the British Association standard for smaller screws in electrical and philosophical instruments.

Whitworth's V Thread.*—The following figures of a Whitworth thread and nut, together with the tables, will serve to give full information regarding the number of threads per inch for different diameters of screw-bolts, nuts and bolt-heads, &c.

The angle between opposite sides of the threads and of the intervening spaces is 55°. One-sixth of the depth of the thread is rounded off at both the top and the bottom for the purpose of preventing a sharp nick at the bottom (which would weaken a

* For a description of Whitworth's screw-taps, plates, stocks, dies and combs, see "Workshop Appliances" by Professor Shelley. And for a table of the B.A. Standard for Small Screws,see Munro and Jamieson's Electrical Rules and Tables, 13th ed., p. 67.