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Ch-13 - CONTENTS CONTENTS 428 l Theory of Machines 13 eatur...

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Gear Gear Gear Gear Gear T T Trains rains rains rains 13 F ea ea tur es 1. Introduction. 2. Types of Gear Trains. 3. Simple Gear Train. 4. Compound Gear Train. 5. Design of Spur Gears. 6. Reverted Gear Train. 7. Epicyclic Gear Train. 8. Velocity Ratio of Epicyclic Gear Train. 9. Compound Epicyclic Gear Train (Sun and Planet Wheel). 10. Epicyclic Gear Train With Bevel Gears. 11. Torques in Epicyclic Gear Trains. 13.1. 13.1. Intr Intr Introduction oduction Sometimes, two or more gears are made to mesh with each other to transmit power from one shaft to another. Such a combination is called gear train or train of toothed wheels . The nature of the train used depends upon the velocity ratio required and the relative position of the axes of shafts. A gear train may consist of spur, bevel or spiral gears. 13.2. 13.2. Types of Gear ypes of Gear ypes of Gear ypes of Gear Trains rains rains rains Following are the different types of gear trains, de- pending upon the arrangement of wheels : 1. Simple gear train, 2. Compound gear train, 3. Re- verted gear train, and 4. Epicyclic gear train. In the first three types of gear trains, the axes of the shafts over which the gears are mounted are fixed relative to each other. But in case of epicyclic gear trains, the axes of the shafts on which the gears are mounted may move relative to a fixed axis. 13.3. Simple Gear Simple Gear Train rain When there is only one gear on each shaft, as shown in Fig. 13.1, it is known as simple gear train . The gears are represented by their pitch circles. When the distance between the two shafts is small, the two gears 1 and 2 are made to mesh with each other to 428
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Chapter 13 : Gear Trains l 429 transmit motion from one shaft to the other, as shown in Fig. 13.1 ( a ). Since the gear 1 drives the gear 2, therefore gear 1 is called the driver and the gear 2 is called the driven or follower . It may be noted that the motion of the driven gear is opposite to the motion of driving gear. ( a ) ( b ) ( c ) Fig. 13.1. Simple gear train. Let N 1 = Speed of gear 1(or driver) in r.p.m., N 2 = Speed of gear 2 (or driven or follower) in r.p.m., T 1 = Number of teeth on gear 1, and T 2 = Number of teeth on gear 2. Since the speed ratio (or velocity ratio) of gear train is the ratio of the speed of the driver to the speed of the driven or follower and ratio of speeds of any pair of gears in mesh is the inverse of their number of teeth, therefore Speed ratio 1 2 2 1 N T N T = = It may be noted that ratio of the speed of the driven or follower to the speed of the driver is known as train value of the gear train. Mathematically, Train value 2 1 1 2 N T N T = = From above, we see that the train value is the reciprocal of speed ratio. Sometimes, the distance between the two gears is large. The motion from one gear to another, in such a case, may be transmitted by either of the following two methods : 1. By providing the large sized gear, or 2. By providing one or more intermediate gears.
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