Various types of power transmission systems such as for marine propulsion, aircraft and automotive applications utilize a planetary gear system as illustrated in Fig. 1(a). In this type of gear arrangement power is transferred from a center sun gear to a large stationary ring gear with internal teeth, by means of the three planet gears shown. The source of the power output is then obtained by the rotation of the planet gear carrier. The analysis of the stresses and deflection of this ring gear is the subject of this paper. The reason for making an accurate analysis of the stresses and deflection of the ring gear is that it is essential to provide the most flexible gear which has at the same time adequate strength. Flexibility in the gear is desired in order to make possible a uniform load distribution between the planet gears and thereby provide maximum power capactiy for the unit. The investigation made consists of the stress and deflection analysis of a circular ring gear subjected to forces P, Q and m as shown in Fig. 1(b). Theoretical procedures using the strain energy method are developed for finding the maximum stress and radial deflection in the ring gear. It is believed that the procedure presented is considerably more accurate than other methods that are sometimes used for the determination of stresses and deflections in ring gears.
The analysis given in this paper also provides a general solution to the problem of a ring subjected to radial and tangential forces and couples acting at various points on the circumference of the ring.


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