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9 Gears wheel systems and their functions
- 1. Epicyclic Gear Train Wehave already discussed that in an epicyclic gear train, the axes of the shafts, over which the gears are mounted, may move relative to a fixed axis. A simple epicyclic gear train is shown in Fig. 13.6, where a gear A and the arm C have a common axis at O1 about which they can rotate. The gear B meshes with gear A and has its axis on the arm at O2, about which the gear B can rotate. If the arm is fixed, the gear train is simple and gear A can drive gear B or vice- versa, but if gear A is fixed and the arm is rotated about the axis of gear A (i.e. O1), then the gear B is forced to rotate upon and around gear A. Such a motion is called epicyclic and the gear trains arranged in such a manner that one or more of their members move upon and around another member are known as epicyclic gear trains (epi. means upon and cyclic means around). The epicyclic gear trains may be simple or compound. The epicyclic gear trains are useful for transmitting high velocity ratios with gears of moderate size in a comparatively lesser space. The epicyclic gear trains are used in the back gear of lathe, differential gears of the automobiles, hoists, pulley blocks, wrist watches etc.
- 2. Velocity Ratios ofEpicyclic Gear Train First of all, let us suppose that the arm is fixed. Therefore the axes of both the gears are also fixed relative to each other. When the gear A makes one revolution anticlockwise, the gear B will make TA / TB revolutions, clockwise. Assuming the anticlockwise rotation as positive and clockwise as negative, we may say that when gear A makes + 1 revolution, then the gear B will make (– TA / TB) revolutions. This statement of relative motion is entered in the first row of the table (see Table 13.1)
- 3. Secondly, if thegear A makes + x revolutions, then the gear B will make – x × TA / TB revolutions. This statement is entered in the second row of the table. In other words, multiply the each motion (entered in the first row) by x. Thirdly, each element of an epicyclic train is given + y revolutions and entered in the third row. Finally, the motion of each element of the gear train is added up and entered in the fourth row. A little consideration will show that when two conditions about the motion of rotation of any two elements are known, then the unknown speed of the third element may be obtained by substituting the given data in the third column of the fourth row
- 9. The reverted epicyclicgear train is shown in Fig. 13.8. First of all, let us find the number of teeth on gear E (TE). Let dB , dC , dD and dE be the pitch circle diameters of gears B,C, D and E respectively. From the geometry of the figure, Since the number of teeth on each gear, for the same module, are proportional to their pitch circle diameters, therefore
- 12. Compound Epicyclic GearTrain—Sun and Planet Gear A compound epicyclic gear train is shown in Fig. 13.9. It consists of two co-axial shafts S1and S2, an annulus gear A which is fixed, the compound gear (or planet gear) B-C, the sun gear D and the arm H. The annulus gear has internal teeth and the compound gear is carried by the arm and revolves freely on a pin of the arm H. The sun gear is co- axial with the annulus gear and the arm but independent of them. The annulus gear A meshes with the gear B and the sun gear D meshes with the gear C. It may be noted that when the annulus gear is fixed, the sun gear provides the drive and when the sun gear is fixed, the annulus gear provides the drive. In both cases, the arm acts as a follower. Note : The gear at the centre is called the sun gear and the gears whose axes move are called planet gears.