Hunt('/irons. A. E., vol. Nii) gives a calculation of the horse-power of rope drives, from which the following is condensed : f= circumference of rope in inches. 1) = sag of the rope in inches. I'' = centrifugal force ill pounds. 9 = gravity. if = horse power. L = iA.ance between pulleys in feet. .p= pounds per foot of rope. Average value = .032 R = force in pounds doing useful work. S = strain in pounds on the rope at the pulley. T= tension in pounds on driving side of the rope. I = tension in pounds on slack side of the rope. v = velocity of the rope in feet per second. u = working strain in pounds. Average value = '20 W= ult,imate breaking strain in pounds. Average value = .720 This makes the normal working strain equal to one thirty-sixth of the breaking strength. and about one twenty-fifth of the strength at the splice. The actual strains are or dinarily much greater, owing to the vibrations in running, as well as from imperfectly adjusted tension mechanism. Assuming that the strain on the driving side of a rope is equal to 200 lbs. on a rope 1 in. in diameter, and that the rope is in motion at various velocities of from 10 to 140 ft. per second. Under this assumption. we will have in all cases a fiber Strain of 200 lbs. on the driving side of a 1-in. rope. and an equivalent strain for other sizes. The centrifugal force of the rope in tomnimx over the pulley will reduce the amount of force available for the transmission of power. The centrifugal force of the rope is computed by the formula P . . ..... (1).
At a speed of about 80 ft. per second. the centrifugal force increases faster than the power from increased velocity of the rope. and about 140 ft. per second equals the assumed allowable tension of the rope. Computing this force at various speeds and then subtracting it from the assumed maximum tension, we have the force available for the transmission of power. The terrsion, t, required to transmit the normal horse-power for the ordinary speeds and sizes of rope is computed by formula (4). The total tension, T, on the driving side of the rope is as slimed to be the same at all speeds. The centrifugal force, as well as an amount equal to the tension for adhesion on the slack side of the rope, must be taken from the total tension, T. to ascertain the amount of force available for the transmission of power. The tension on the slack side necessary for giving adhesion is taken as equal to one half the force doing useful work on the driving side of the rope; hence the force for useful work is: 2 (T R (2), and the tension on the slack side to give the required adhesion is (T F) , . . ..... (3).
3 4 (T F) Hence, I F . . . . . . (4).
The sum of the tensions, T and is not the same at different speeds, as the equation (4) indi cates. As varies as the square of the velocity, there is, with an increasing speed of the rope, a decreasing useful force, and an increasing total tension, t, on the slack side. With these assumptions of allowable strains, the horse-power will be: 2 (T = 3 X 550 Transmission ropes are usually from 1 to 11 in. in diameter. A emnimtation of the horse power for four sizes at various speeds and under ordinary conditions, based on a maximum strain equivalent to 200 lbs. for a rope 1 in. in diame ter. is given in Fig. S. The horse-power of other sizes is readily obtained from these. The maximum power is transmitted, under the as sumed conditions, at a speed of about 80 ft. per second. The first cost of the rope will be small est when the power transmitted by it is great est, and under the assumed conditions will be a minimum for a given power when the velocity of the rope is about 80 ft. per second. The de flection of t he rope between the pulleys on the slack side varies with each change of the load or change of the speed, as the tension equation (4) indicates, The curves in Fig. 9, giving the deflection of the rope, were computed for the assumed value of T and I by the parabolic for mula: S= /' S hieing the assumed strain. T. on the thriving side, and t, calculated by equation (4), on the slack side. The tension, t, varies with the speed, and the curves, showing the sag of the rope in inches, are calculated for speeds of 40, CO, and 80 ft. per second, and for spans com monly used in rope driving. The following table of the horse-power of transmission robe is calculated by formula (5), which makes the total strain on the driving side of the rope, when transmitting the normal power, the seine at all speeds, and takes into considerat ion the effect of the centrifugal force in reducing the driving power of the rope : The English rule for diameters of pulleys with cotton rope is from 30 to 36 times the diameter of the rope. For comparison with Mr. hunt's table, given above, Mr. Webber gives the following figures, taken from an English table, of the power transmissible by a cotton rope at 50 ft. per second, or 3,000 ft. per minute: Manilla. Cotton.
1-in. rope 10.75 10.50 1+ " . ii ,. 24 30 lt " 42 In England. hemp and manilla ropes have been largely superseded by ropes of cotton, the reason assigned being that dry manilla ropes wear out too fast, while the lubricated ones give too low a coefficient of friction.
Bending Machine: see Presses, Forging.