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Handbook of Machine Design P53

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Gear trains consist of two or more gears meshed for the purpose of transmitting motion from one axis to another. Ordinary gear trains have axes, relative to the frame, for all gears making up the train. Figure 46.Ia shows a simple ordinary train in which there is only one gear for each axis. | CHAPTER 46 GEAR TRAINS Harold L. Johnson Ph.D. Associate Professor Emeritus School of Mechanical Engineering Georgia Institute of Technology Atlanta Georgia 46.1 ORDINARY GEAR TRAINS I 46.1 46.2 GEAR TYPE SELECTION 46.3 46.3 PLANETARY GEAR TRAINS I 46.5 46.4 DIFFERENTIAL TRAINS 146.14 REFERENCES 46.16 46.7 ORDINARY GEAR TRAINS Gear trains consist of two or more gears meshed for the purpose of transmitting motion from one axis to another. Ordinary gear trains have axes relative to the frame for all gears making up the train. Figure 46.1a shows a simple ordinary train in which there is only one gear for each axis. In Fig. 46.16 a compound ordinary train is seen to be one in which two or more gears may rotate about a single axis. The ratio of the angular velocities of a pair of gears is the inverse of their numbers of teeth. The equations for each mesh in the simple train are n2 n3 n4 n3 n2 n4 - n3 n5 n4 n3 n4 n5 46.1 where n is in revolutions per minute r min and N number of teeth. These equations can be combined to give the velocity ratio of the first gear in the train to the last gear n4 n3 n2 ns n5 n4 n3 ni 46.2 Note that the tooth numbers in the numerator are those of the driving gears and the tooth numbers in the denominator belong to the driven gears. Gears 3 and 4 both drive and are in turn driven. Thus they are called idler gears. Since their tooth numbers cancel idler gears do not affect the magnitude of the input-output ratio but they do change directions of rotation. Note the directional arrows in the figure. Idler gears can also produce a saving of space and money. In Fig. 46.2 the simple train of the previous figure has been repeated. In dotted outline is shown a pair of gears on the same center distance as gears 2 and 5 and having the same inputoutput ratio as the simple train. Finally Eq. 46.2 is simplified to become 46.1 46.2 STANDARD HANDBOOK OF MACHINE DESIGN n2 ns - n2 N5 46.3 where the minus sign is now introduced to indicate contrarotation of the