About 1856 James Combe, of Belfast, intro duced the practice of transmitting power by means of ropes run ping in grooves turned circumferentially in the rim of the pulley (fig. 3). The ropes may be led off in groups to the different floors of the factory to pulleys keyed to the distributing shafting. A groove was adopted having an angle of about
and this is the angle still used in the practice of Messrs. Combe, Barbour and Combe, of Belfast. A section of the rim of a rope driving wheel showing the shape of the groove for a rope of i a in. diameter is shown in fig. 4, and a rope driving pulley designed for six I a in. ropes is shown in fig. 5. A rope is less flexible than a belt, and therefore care must be taken not to arrange rope drives with pulleys having too small a diameter relatively to the diameter of the rope. The principles of §§ 3, 4, 5 and 6, apply equally to ropes, but with the practical modification that the working stress in the rope is a much smaller fraction of the ultimate strength than in the case of belting and the ratio of the tensions is much greater. The following table, based upon the experience of Messrs. Combe, presents the practical possibilities in a convenient form:— The speed originally adopted for the rope was 55 ft. per second. This speed has been exceeded, but, as indicated above, for any particular case there is one speed at which the maximum horse power is transmitted, and this speed is chosen with due regard to the effect of centrifugal tension and the loss due to the con tinual bending of the rope round the pulley Instead of using one rope for each groove, a single continuous rope may be used, driving from one common pulley several shafts at different speeds. For further information see Abram Combe, Proc. Inst. Mech. Eng. (July 1896). Experiments to compare the efficiencies of rope and belt driving were carried out at Lille in 1894 by the Societe In dustrielle du Nord de la France, for an account of which see D. S. Capper, Proc. Inst. Mech. Eng. (October 1896). Cotton ropes are used extensively for transmitting power in factories, and though more expensive than Ma nila ropes, are more durable when worked under suitable conditions.
When a shaft trans mits power from a prime mover to a machine, every section of it sustains a turning couple or torque T, and if (.,) is the angular velocity of rotation in radians per second, the rate of transmis sion is Tco foot-pounds per sec ond, and the relation between the horse power, torque and angular velocity is The problem involved in the design of a shaft is so to proportion the size that the stress produced by the torque shall not exceed a certain limit, or that the relative angular displacement of two sections at right angles to the axis of the shaft at a given distance apart shall not exceed a certain
the particular features of the problem determining which condition shall operate in fixing the size. At a section of a solid round shaft where the diameter is D inches, the torque T inch-pounds, and the maximum Calculate the horse power which a shaft 4 in. diameter can transmit, revolving 120 times per minute (12-56 radians per second), when the maximum shearing stress f is limited to I I,000 lb. per square inch. From equation (7) the maximum torque which may be applied to the shaft is T = 138,40o inch-pounds.
40o X ' From (6) H.P. = 138, =264. The example may be 12X 12 56 550 continued to find how much the shaft will twist in a length of Io ft. Substituting the value of the torque in inch-pounds in
equation (8), and taking a i,50o,000 for the value of C, 138,400X120X32 0= =o 057 radians,
11,5oo,000 X3-14 X 25o and this is equivalent to 3-3°.
In the case of hollow round shafts where D is the external diameter and d the internal diameter equation (7) becomes T =
16D, (9) The assumption tacitly made hitherto that the torque T re mains constant is rarely true in practice; it usually varies from instant to instant, often in a periodic manner, and an appropriate value of f must be taken to suit any particular case. Again it rarely happens that a shaft sustains a torque only. There is usually a bending moment associated with it. For a discussion of the proper values of f, to suit cases where the stress is variable, and the way a bending moment of known amount may be com bined with a known torque, see STRENGTH OF MATERIALS. It is sufficient to state here that if M is the bending moment in inch pounds, and T the torque in inch-pounds, the magnitude of the greatest direct stress in the shaft due to the effect of the torque and bending moment acting together is the same as would be produced by the application of a torque of It will be readily understood that in designing a shaft for the distribution of power to a factory where power is taken off at different places along the shaft, the diameter of the shaft near the engine must be proportioned to transmit the total power transmitted whilst the more remote parts of the shaft are made smaller, since the power transmitted there is smaller.
Gearing is used to transmit power from one shaft to another. The shafts may be parallel; or inclined to one another, so that if produced they would meet in a point; or inclined to one another so that if produced they would not meet in a point. In the first case the gear wheels are called spur wheels, sometimes cog wheels; in the second case bevel wheels, or, if the angle between the shafts is 90°, mitre wheels; and in the third case they are called skew bevels. In all cases the teeth should be so shaped that the velocity ratio between the shafts remains constant, although in very rare cases gearing is designed to work with a variable velocity ratio as part of some special machines. For the principles governing the shape of the teeth to fulfil the condition that the velocity ratio between the wheels shall be con stant, see MECHANICS, § Applied. The size of the teeth is deter mined by the torque the gearing is required to transmit.
Gearing is noisy at high speeds unless special care is taken in the manufacture to secure exact uniformity in pitch. Great impetus was given to the development of improved methods of manufacture by the need of gearing the high speed marine steam turbine to the low speed propeller. The first turbine geared ship the "Vespasian" was described in a paper by Sir Charles Parsons entitled "On the application of the marine steam turbine and mechanical gearing to merchant ships." Proc. Inst. Naval Archi tects, Vol. LII. 1910. The motor car gear box, back axle and differential gear call for silent gearing and the demand has brought the manufacture of gearing to a high pitch of accuracy. In the best class of work the gears are ground to exact pitch and shape after hardening.