  Velocity Ratio in Belt Gearing.—Let two pulleys A and B be connected by a belt, and let their diameters be D1 and D2; and let their speeds, in revolutions per minute, be N1 and N2 respectively. If there is no slipping, the speeds of the rims of the pulleys will be the same as that of the belt, and will therefore be equal. Now the speed of the rim of A is evidently = D1 × 3·1416 × N1; while the speed of the rim of B is = D2 × 3·1416 × N2. Hence D1 × 3·1416 × N1 = D2 × 3·1416 × N2, and therefore
Pulleys for Flat Bands.—In cross section the rim of a pulley for carrying a flat band is generally curved as shown in figs. 31 and 32, but very often the cross section is straight. The curved cross section of the rim tends to keep the band from coming off as long as the pulley is rotating. Sometimes the rim of the pulley is provided with flanges which keep the band from falling off. Pulleys are generally made entirely of cast iron, but a great many pulleys are now made in which the centre or nave only is of cast iron, the arms being of wrought iron cast into the nave, while the rim is of wrought sheet iron. The arms of pulleys when made of wrought iron are invariably straight, but when made of cast iron they are very often curved. In fig. 31, which shows an arrangement of two cast-iron pulleys, the arms are straight; while in fig. 32, which shows another cast-iron pulley, the arms are curved. Through unequal cooling, and therefore unequal contraction of a cast-iron, pulley in the mould, the arms are generally in a state of tension or compression; and if the arms are straight they are very unyielding, so that the result of this initial stress is often the breaking of an arm, or of the rim where it joins an arm. With the curved arm, however, its shape permits it to yield, and thus cause a diminution of the stress due to unequal contraction. The cross section of the arms of cast-iron pulleys is generally elliptical. Fig. 31. Fig. 31. Exercise 31: Fast and Loose Pulleys.—Fig. 31 shows an arrangement of fast and loose pulleys. A is the fast pulley, secured to the shaft C by a sunk key; B is the loose pulley, which turns freely upon the shaft. The loose pulley is prevented from coming off by a collar D, which is secured to the shaft by a tapered pin as shown. The nave or boss of the loose pulley is here fitted with a brass liner, which may be renewed when it becomes too much worn. Draw the elevations shown, completing the left-hand one. Scale 6 inches to a foot. By the above arrangement of pulleys a machine may be stopped or set in motion at pleasure. When the driving band is on the loose pulley the machine is at rest, and when it is on the fast pulley the machine is in motion. The driving band is shifted from the one pulley to the other by pressing on that side of the band which is advancing towards the pulleys. Fig. 32. Fig. 32. Exercise 32: Cast-iron Pulley with Curved Arms and Cone Keys.—Draw a complete side elevation and a complete cross section of the pulley represented in fig. 32 to a scale of 3 inches to a foot. In drawing the side elevation of the arms first draw the centre lines as shown; next draw three circles for each arm, one at each end and one in the middle; the centres of these circles being on the centre line of the arm, and their diameters equal to the widths of the arm at the ends and at the middle respectively. Arcs of circles are then drawn to touch these three circles. The centres and radii of these arcs may be found by trial. The cone keys for securing the pulley to the shaft were described on p. 23. Pulleys for Ropes.—Ropes made of hemp are now extensively used for transmitting power. These ropes vary in diameter from 1 inch to 2 inches, and are run at a speed of about 4,500 feet per minute. The pulleys for these ropes are made of cast iron, and have their rims grooved as shown in fig. 33, which is a cross section of the rim of a pulley carrying three ropes. The angle of the V is usually 45°, and the rope Fig. 33. Fig. 33. Exercise 33: Section of Rim of Rope Pulley.—Draw, half size, the section of the rim of a rope pulley shown in fig. 33. |
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