THE SCREW.
277. The inclined plane as a mechanical power is often used in the form of a wedge or in the still more disguised form of a screw. A wedge is an inclined plane which is forced under the load; it is usually moved by means of a hammer, so that the efficiency of the wedge is augmented by the dynamical effect of a blow.
278. The screw is one of the most useful mechanical powers which we possess. Its form may be traced by wrapping a wedge-shaped piece of paper around a cylinder, and then cutting a groove in the cylinder along the spiral line indicated by the margin of the paper. Such a groove is a screw. In order that the screw may be used it must revolve in a nut which is made from a hollow cylinder, the internal diameter of which is equal to that of the cylinder from which the screw is cut. The nut contains a spiral ridge, which fits into the corresponding thread in the screw; when the nut is turned round, it moves backwards or forwards according to the direction of the rotation. Large screws of the better class, such as those upon which we shall first make experiments, are always turned in a lathe, and are thus formed with extreme accuracy. Small screws are made in a simpler manner by means of dies and other contrivances.
279. A characteristic feature of a screw is the inclination of the thread to the axis. This is most conveniently described by the number of complete turns which the thread makes in a specified length of the screw, usually an inch. For example: a screw is said to have ten threads to the inch when it requires 10 revolutions of the nut in order to move it one inch. The shape of the thread itself varies with the purposes for which the screw is intended; the section may be square or triangular, or, as is generally the case in small screws, of a rounded form.
280. There is so much friction in the screw that experiments are necessary for the determination of the law connecting the power and the load.
281. We shall commence with an examination of the screw by the apparatus shown in [Fig. 43].
The nut a is secured upon a stout frame; to the end of the screw hooks are attached, in order to receive the load, which in this apparatus does not exceed 224 lbs.; at the top of the screw is an arm e by which the screw is turned; to the end of the arm a rope is attached, which passing over a pulley d, carries a hook for receiving the power c.
Fig. 43.
282. We first apply the principle of work to this screw, and calculate the relation between the power and the load as it would be found if friction were absent. The diameter of the circle described by the end of the arm is 20"·5; its circumference is therefore 64"·4. The screw contains three threads in the inch, hence in order to raise the load 1" the power moves 3 × 64"·4 = 193" very nearly; therefore the velocity ratio is 193, and were the screw capable of working without friction, 193 would represent the mechanical efficiency. In actually performing the experiments the arm E is placed at right angles to the rope leading to the pulley, and the power hook is weighted until, with a slight start, the arm is steadily drawn; but the power will only move the arm a few inches, for when the cord ceases to be perpendicular to the arm the power acts with diminished efficiency; consequently the load is only raised in each experiment through a small fraction of an inch, but quite sufficient for our purpose.
Wrought iron screw, square thread, diameter 1"·25, with 3 threads to the inch, length of arm 10"·25; nut of cast iron, bearing surfaces oiled, velocity ratio 193, useful effect 36 per cent., mechanical efficiency 70; formula P = 0·0143 R.
| Number of Experiment. | R. Load in lbs. | Observed power in lbs. | P. Calculated power in lbs. | Difference of the observed and calculated powers. |
|---|---|---|---|---|
| 1 |  28 | 0·4 | 0·4 | 0·0 |
| 2 |  56 | 0·8 | 0·8 | 0·0 |
| 3 |  84 | 1·2 | 1·2 | 0·0 |
| 4 | 112 | 1·6 | 1·6 | 0·0 |
| 5 | 140 | 2·0 | 2·0 | 0·0 |
| 6 | 168 | 2·4 | 2·4 | 0·0 |
| 7 | 196 | 2·7 | 2·8 | +0·1  |
| 8 | 224 | 3·3 | 3·2 | -0·1  |
283. The results of the experiments are shown in [Table XVI]. If the motion had not been aided by a start the powers would have been greater. Thus in experiment 6, 2·4 lbs. is the power with a start, when without a start 3·2 lbs. was found to be necessary. The experiments have all been aided by a start, and the results recorded have been corrected for the friction of the pulley over which the rope passes: this correction is very small, in no case exceeding 0·2 lb. The fourth column contains the values of the powers computed by the formula P = 0·0143 R. This formula has been deduced from the observations in the manner described in the Appendix. The fifth column proves that the experiments are truly represented by the formula: in each of the experiments 7 and 8, the difference between the calculated and observed values amounts to 0·1 lb., but this is quite inconsiderable in comparison with the weights we are employing.
284. In order to lift 100 lbs. the expression 0·0143 R shows that 1·43 lbs. would be necessary: hence the mechanical efficiency of the screw is 100 ÷ 1·43 = 70. Thus this screw is vastly more powerful than any of the pulley systems which we have discussed. A machine so capable, so compact, and so strong as the screw, is invaluable for innumerable purposes in the Arts, as well as in multitudes of appliances in daily use.
285. It is evident, however, that the distance through which the screw can raise a weight must be limited by the length of the screw itself, and that in the length of lift the screw cannot compete with many of the other contrivances used in raising weights.
286. We have seen that the velocity ratio is 193; therefore, to raise 100 lbs. 1 foot, we find that 1·43 × 193 = 276 units of energy must be expended: of this only 100 units, or 36 per cent., is usefully employed; the rest being consumed in overcoming the friction of the screw. Thus nearly two-thirds of the energy applied to such a screw is wasted. Hence we find that friction does not permit the load to run down, since less than fifty per cent. of the applied energy is usefully employed ([Art. 222]). This is one of the valuable properties which the screw possesses.
287. We may contrast the screw with the pulley-block ([Art. 199]). They are both powerful machines: the latter is bulky and economical of power, the former is compact and wasteful of power; the latter is adapted for raising weights through considerable distances, and the former for exerting pressures through short distances.
Fig. 44.