Belt and Pulley Drives, Lecture notes of Kinematics

Download Belt and Pulley Drives and more Lecture notes Kinematics in PDF only on Docsity! Belt and pulley Drives Belt and pulley Drives The belts or ropes are used to transmit power from one shaft to another by means of pulleys which rotate at the same speed or at different speeds. The amount of power transmitted depends upon the following factors : 1. The velocity of the belt. 2. The tension under which the belt is placed on the pulleys. 3. The arc of contact between the belt and the smaller pulley. 4. The conditions under which the belt is used. It may be noted that (a) The shafts should be properly in line to insure uniform tension across the belt section. (b) The pulleys should not be too close together, in order that the arc of contact on the smaller pulley may be as large as possible. (c) The pulleys should not be so far apart as to cause the belt to weigh heavily on the shafts, thus increasing the friction load on the bearings. Types of Belts Though there are many types of belts used these days, yet the following are important from the subject point of view : 1. Flat belt. The flat belt, as shown in Fig. a, is mostly used in the factories and workshops, where a moderate amount of power is to be transmitted, from one pulley to another when the two pulleys are not more than 8 metres apart. 2. V-belt. The V-belt, as shown in Fig. b, is mostly used in the factories and workshops, where a moderate amount of power is to be transmitted, from one pulley to another, when the two pulleys are very near to each other. 3. Circular belt or rope. The circular belt or rope, as shown in Fig. c, is mostly used in the factories and workshops, where a great amount of power is to be transmitted, from one pulley to another, when the two pulleys are more than 8 meters apart. If a huge amount of power is to be transmitted, then a single belt may not be sufficient. In such a case, wide pulleys (for V-belts or circular belts) with a number of grooves are used. Then a belt in each groove is provided to transmit the required amount of power from one pulley to another. Material used for Belts The material used for belts and ropes must be strong, flexible, and durable. It must have a high coefficient of friction. The belts, according to the material used, are classified as follows : 1. Leather belts. The most important material for the belt is leather. The best leather belts are made from 1.2 metres to 1.5 metres long strips. The hair side of the leather is smoother and harder than the flesh side, but the flesh side is stronger. The fibres on the hair side are perpendicular to the surface, while those on the flesh side are interwoven and parallel to the surface. Therefore for these reasons, the hair side of a belt should be in contact with the pulley surface. This gives a more intimate contact between the belt and the pulley and places the greatest tensile strength of the belt section on the outside, where the tension is maximum as the belt passes over the pulley. The leather may be either oak-tanned or mineral salt tanned e.g. chrome tanned. In order to increase the thickness of belt, the strips are cemented together. The belts are specified according to the number of layers e.g. single, double or triple ply and according to the thickness of hides used e.g. light, medium or heavy. The leather belts must be periodically cleaned and dressed or treated with a compound or dressing containing neats foot or other suitable oils so that the belt will remain soft and flexible. 2. Cotton or fabric belts. Most of the fabric belts are made by folding canvass or cotton duck to three or more layers (depending upon the thickness desired) and stitching together. These belts are woven also into a strip of the desired width and thickness. They are impregnated with some filler like linseed oil in order to make the belts water proof and to prevent injury to the fibres. The cotton belts are cheaper and suitable in warm climates, in damp atmospheres and in exposed positions. Since the cotton belts require little attention, therefore these belts are mostly used in farm machinery, belt conveyor etc. 3. Rubber belt. The rubber belts are made of layers of fabric impregnated with rubber composition and have a thin layer of rubber on the faces. These belts are very flexible but are quickly destroyed if allowed to come into contact with heat, oil or grease. One of the principal advantage of these belts is that they may be easily made endless. These belts are found suitable for saw mills, paper mills where they are exposed to moisture. 4. Balata belts. These belts are similar to rubber belts except that balata gum is used in place of rubber. These belts are acid proof and water proof and it is not effected by animal oils or alkalies. The balata belts should not be used at temperatures above 40° C because at this temperature the balata begins to soften and becomes sticky. The strength of balata belts is 25 per cent higher than rubber belts. Types of Flat Belt Drives The power from one pulley to another may be transmitted by any of the following types of belt drives: 1. Open belt drive. The open belt drive, as shown in Fig., is used with shafts arranged parallel and rotating in the same direction. In this case, the driver A pulls the belt from one side (i.e. lower side RQ) and delivers it to the other side (i.e. upper side LM). Thus the tension in the lower side belt will be more than that in the upper side belt. The lower side belt (because of more tension) is known as tight side whereas the upper side belt (because of less tension) is known as slack side, 4. Belt drive with idler pulleys. A belt drive with an idler pulley, as shown in Fig. (a), is used with shafts arranged parallel and when an open belt drive cannot be used due to small angle of contact on the smaller pulley. This type of drive is provided to obtain high velocity ratio and when the required belt tension cannot be obtained by other means. When it is desired to transmit motion from one shaft to several shafts, all arranged in parallel, a belt drive with many idler pulleys, as shown in Fig. (b), may be employed. 5. Compound belt drive. A compound belt drive, as shown in Fig., is used when power is transmitted from one shaft to another through a number of pulleys. 6. Stepped or cone pulley drive. A stepped or cone pulley drive, as shown in Fig. is used for changing the speed of the driven shaft while the main or driving shaft runs at constant speed. This is accomplished by shifting the belt from one part of the steps to the other. Velocity Ratio of a Compound Belt Drive Sometimes the power is transmitted from one shaft to another, through a number of pulleys as shown in Fig. 11.7. Consider a pulley 1 driving the pulley 2. Since the pulleys 2 and 3 are keyed to the same shaft, therefore the pulley 1 also drives the pulley 3 which, in turn, drives the pulley 4. Let d1 = Diameter of the pulley 1, N1 = Speed of the pulley 1 in r.p.m., d2, d3, d4, and N2, N3, N4= Corresponding values for pulleys 2, 3 and 4. Slip of Belt Sometimes, the frictional grip between the belts and the shafts becomes insufficient. This may cause some forward motion of the driver without carrying the belt with it. This may also cause some forward motion of the belt without carrying the driven pulley with it. This is called slip of the belt and is generally expressed as a percentage. The result of the belt slipping is to reduce the velocity ratio of the system. As the slipping of the belt is a common phenomenon, thus the belt should never be used where a definite velocity ratio is of importance (as in the case of hour, minute and second arms in a watch). Creep of Belt When the belt passes from the slack side to the tight side, a certain portion of the belt extends and it contracts again when the belt passes from the tight side to slack side. Due to these changes of length, there is a relative motion between the belt and the pulley surfaces. This relative motion is termed as creep. The total effect of creep is to reduce slightly the speed of the driven pulley or follower. Considering creep, the velocity ratio is given by Le We have already discussed in Art. 11.6 that in a cross belt drive. both the pulleys rotate in opposite directions as shown in Fig. 11.12. and Tet ry and 7, 2 z Let the belt leaves the larger pulley at H and G and the smaller pulley at Fand AY. as shown in Fig. 11.12. Through O,. draw O,Ad parallel to FE. Trom the geometry of the tigure. we tind that O,Af will be perpendicular to OF. et the angle 40, O, — m radians. Wwe know that the Iensth of the belt. Frou the geometry of dhe Gaure, we Gud hat sina — Since uo is very small. therefore putting sin & = & (in radians) — Similarly Are FE = 95 (> + =) Fig. 1112) Length of a cross belt drive. Radii of the larger and smaller pulleys. Distance between the centres of two pulleys (ze. O, O,). and Total length of the belt. Are GJE+ EF + arc FRA + HG = 2 (Ar ue + BRE + Arve FED O, Ar OL,e | eat RI re Ao, QA2, x Wt ee a(S) — ato, — fta,0.)7 — co, ary — x — YP ey  Expanding this equation by binomial theorem, lf(mtn Vy Gtny or = xf 3(*28) +... ax - SQ wal?) Substituting the values of arc JE from equation (iii), are FK from equation (iv) and EF from equation (v) in equation (7), we get 2 L=2)7/t+a +x—-Gitny +n4(2+0 2 2x 2 -2|i* > + =2|Zaj +n) + ac; ty) +x- G22 2 2x Gtny +R. tX 2x r +H xT. hla 2 + = mG; +15) + 200% +7) + 2x — TD ar Rtn . . Substituting the value of @ = +—=+ from equation (i), x 20,4 +n LanQtn)+2Gte 5) * G+) + 2x - Gtny x 2G+n) Gtny HTR+H)+ + 2x — x 2 +n = TG +H) + 2x + Giany _(In terms of pulley radii) x n dy t+ doy = Eeay+d,) + 2x +B 4 7 2 _(In terms of pulley diameters) a It may be noted that the above expression is a function of (1, +15). It is thus obvious that if sum of the radii of the two pulleys be constant, then length of the belt required will also remain con- stant. provided the distance between centres of the pulleys remain unchanged. Power Transmitted by a Belt Fig. 11.14 shows the driving pulley (or driver) A and the driven pulley (or follower) B. We have already discussed that the driving pulley pulls the belt from one side and delivers the same to the other side. It is thus obvious that the tension on the former side (i.e. tight side) will be greater than the latter side (i.e. slack side) as shown in Fig. 11.14. Let T1 and T2 = Tensions in the tight and slack side of the belt respectively in newtons, Centrifugal Tension Since the belt continuously runs over the pulleys, therefore, some centrifugal force is caused, whose effect is to increase the tension on both, tight as well as the slack sides. The tension caused by centrifugal force is called centrifugal tension. At lower belt speeds (less than 10 m/s), the centrifugal tension is very small, but at higher belt speeds (more than 10 m/s), its effect is considerable and thus should be taken into account. Consider a small portion PQ of the belt subtending an angle d the centre of the pulley as shown in Fig. Let m = Mass of the belt per unit length m Kg. = oa v = Linear velocity of the belt in m/s. r = Radius of the pulley over which the belt runs in metres, and T, = Centrifugal tension acting tangentially at Pand O in newtons. We know that length of the belt PO =r.d@ and mass of the belt PO =m.r.de /. Centrifugal force acting on the belt PO, — (n-r.d0) =m.d@.v" r The centrifugal tension T,, acting tangentially at Pand O keeps the belt in equilibrium. Now resolving the forces (i.e. centrifugal force and centrifugal tension) horizontally and equating the same. we have T. sin (2)- T. sin (2)-« =m.d0.v do do Since the angle d@ is very small, therefore, putting sin( 22 &* in the above expression, de > 27. (S)- m.d@.v" or T,=m.v Notes : 1. When the centrifugal tension is taken into account, then total tension in the tight side, Ty = T+To and total tension in the slack side, Ty = T2+Te 2. Power transmitted, P = (Iy-Tp)v _-Gan watts) = (T,+T—y+ Tov =(,-T,)v __(game as before) Thus we see that centrifugal tension has no effect on the power transmitted. 3. The ratio of driving tensions may also be written as h-k 2.3log] —1—— T2-Te where Ty ne = Maximum or total tension in the belt. Maximum Tension in the Belt A little consideration will show that the maximum tension in the belt (T) is equal to the total tension in the tight side of the belt (T,,). Let © = Maximum safe stress in N/mm?, 6 = Width of the belt in mm, and ¢ = Thickness of the belt in mm. We know that maximum tension in the belt, T = Maximum stress » cross-sectional area of belt =o. BD. t When centriftigal tension is neglected, then T(orT,,) = T,, ie. Tension in the tight side of the belt and when centrifugal tension is considered, then T(orT,,) = T,+T,. V-belt drive V-belt is mostly used in factories and workshops where a great amount of power is to be transmitted from one pulley to another when the two pulleys are very near to each other. The V-belts are made of fabric and cords moulded in rubber and covered with fabric and rubber, as shown in Fig. (a). These belts are moulded to a trapezoidal shape and are made endless. These are particularly suitable for short drives i.e. when the shafts are at a short distance apart. The included angle for the V-belt is usually from 30° – 40°. In case of flat belt drive, the belt runs over the pulleys whereas in case of V-belt drive, the rim of the pulley is grooved in which the V-belt runs. The effect of the groove is to increase the frictional grip of the V-belt on the pulley and thus to reduce the tendency of slipping. In order to have a good grip on the pulley, the V-belt is in contact with the side faces of the groove and not at the bottom. The power is transmitted by the wedging action between the belt and the V-groove in the pulley. The wedging action of the V-belt in the groove of the pulley results in higher forces of friction. A little consideration will show that the wedging action and the transmitted torque will be more if the groove angle of the pulley is small. But a smaller groove angle will require more force to pull the belt out of the groove which will result in loss of power and excessive belt wear due to friction and heat. Hence a selective groove angle is a compromise between the two. Usually the groove angles of 32° to 38° are used. A clearance must be provided at the bottom of the groove, as shown in Fig. (b), in order to prevent touching to the bottom as it becomes narrower from wear. The V-belt drive, may be inclined at any angle with tight side either at top or bottom. In order to increase the power output, several V- belts may be operated side by side. It may be noted that in multiple V-belt drive, all the belts should stretch at the same rate so that the load is equally divided between them. When one of the set of belts break, the entire set should be replaced at the same time. If only one belt is replaced, the new unworn and unstressed belt will be more tightly stretched and will move with different velocity. Advantages and Disadvantages of V- belt Drive Over Flat Belt Drive Following are the advantages and disadvantages of the V-belt drive over flat belt drive. Advantages 1. The V-belt drive gives compactness due to the small distance between the centres of pulleys. 2. The drive is positive, because the slip between the belt and the pulley groove is negligible. 3. Since the V-belts are made endless and there is no joint trouble, therefore the drive is smooth. 4. It provides longer life, 3 to 5 years. 5. It can be easily installed and removed. 6. The operation of the belt and pulley is quiet. 7. The belts have the ability to cushion the shock when machines are started. 8. The high velocity ratio (maximum 10) may be obtained. 9. The wedging action of the belt in the groove gives high value of limiting ratio of tensions. Therefore the power transmitted by V-belts is more than flat belts for the same coefficient of friction, arc of contact and allowable tension in the belts. 10. The V-belt may be operated in either direction with tight side of the belt at the top or bottom. The centre line may be horizontal, vertical or inclined. Disadvantages 1. The V-belt drive cannot be used with large centre distances. 2. The V-belts are not so durable as flat belts. 3. The construction of pulleys for V-belts is more complicated than pulleys for flat belts. 4. Since the V-belts are subjected to certain amount of creep, therefore these are not suitable for constant speed application such as synchronous machines, and timing devices. 5. The belt life is greatly influenced with temperature changes, improper belt tension and mismatching of belt lengths. 6. The centrifugal tension prevents the use of V-belts at speeds below 5 m/s and above 50m/s.