There is a growing tendency toward the substitution of hemp and cotton ropes for belting and line shafting as a means of transmitting power in large factories and shops. The advantages claimed for the rope-driving system are: 1. Economy; for a rope system is cheaper to install than either leather belting or shafting. 2. In the rope system there is less loss of power by slipping. 3. Flexibility; that is, the ease with which the power is transmitted to any distance and in any direction. In this country, a single rope is carried round the pulley as many times as is necessary to produce the required power, and the necessary tension is obtained by passing the rope round a tension pulley weighted to give the desired tension. The ropes used in rope transmission are either of hemp, manila, or cotton. Manila ropes are mostly used in this country. They are of three strands, hawser laid, and may be from in. to 2 in. in diameter. The weight of ordinary manila or cotton rope is about .3 D2 lb. per ft. of length, where D represents the diameter of the rope in inches. Letting w = the weight per foot of length, w = .3 D2. The breaking strength of the rope varies from 7,000 to 12,000 lb. per sq. in. of cross-section. The average value may be taken as 7,000 D2, when D is the diameter of rope. For a continuous transmission, it has been determined by experiment that the best results are obtained when the tension in the driving side of the rope is about of the breaking strength. That is, Ti = tension in tight side 7,000 D2 200 D2. The ropes run in V-shaped grooves, and the coefficient of friction is, of course, greater than on a smooth surface. The coefficient for grooves with sides at an angle of 45° may be taken at from .25 to .33. The horsepower that can be transmitted by a single rope running under favorable conditions is given by the formula in which H D = horsepower transmitted; diameter of rope in inches; V= velocity of rope in feet per second. The maximum power is obtained at a speed of about 84 ft. per sec. For higher velocities, the centrifugal force becomes so great that the power is decreased, and when the speed reaches 145 ft. per sec. the centrifugal force just balances the tension, so that no power at all is transmitted. Consequently, a rope should not run faster than about 5,000 ft. per min., and it is preferable on the score of durability to limit the velocity to 3,500 ft. per min. EXAMPLE.-A rope flywheel is 26 ft. in diameter, and makes 55 rev. per min. The wheel is grooved for 35 turns of 1 rope. What horsepower may be transmitted? SOLUTION.-Velocity in feet per second = De (200 H = 825 EXAMPLE.-How many times should a 1" rope be wrapped around a grooved wheel in order to transmit 200 horsepower, the speed being 3,500 ft. per min.? Rope pulleys differ from belt pulleys only in their rims. The inclination of the sides of the grooves may vary from 30° to 60°. The more acute the angle, the greater the coefficient and, consequently, the wear on the rope. A section of a grooved rim in which the sides of the grooves are formed with circular arcs is shown in the figure. The radii r1 and r2 are to be found by trial; they should be of such lengths as to make the curves drawn by them tangent to the required lines. f = D + "; g= D; h = D+". |