2。1 effect of rim thickness on internal gear stress and deflection

In Fig。5, the maximum principal stress (Mises stress) of the ring at each discrete position is plotted against the carrier rotation angle for four different ring rim thickness ( =1。0,1。5,2。0,2。5)。 here, the spring stiffness is 33N/mm。

From Fig。5, we can see that with the decrease of , the maximum stress in the ring increases 。 hence, the rim thickness of the ring cannot be too small for the sake of gear durability。 And further investigations reveal that the critical point at which the maximum  stress occurs moves from the fillet region to the root of tooth when  decrease。

Fig。6 shows the deflection shapes of rings with different rim thickness。 The ring deflections for   =1。0 and   =2。0 are demonstrated in Fig。7 with the same deflection magnification  factor of 50。

Obviously, when increases , the deflection of ring decreases。 The amount of radial deflection of the ring in both outward and inward direction is plotted as a function of in Fig。7。 here, the positive amounts denote the outward deflections while the negative ones denote the inward deflection。 When =1。0, the maximum out-ward and inward radial deflections are predicted to be  0。139  and  0。122  mm,  respectively。 If the ring  si permitted  to deflect so much,

those manufacturing errors associated with the internal gear such as the roundness error and run-out error can be tolerated as long as their magnitudes are less the amount of deflection 。

2。2 effect of spring stiffness on internal gear stress and deflection

The maximum principal stress of the ring with varied spring stiffness k is shown in Fig。8。 here, the unit of stiffness is N/mm。 obviously, the maximum principal stress of the ring with =1。0 is much more sensitive to the support stiffness than that of the ring with =2。5。 and for a ring with a given  , the maximum principal stress increases with the decrease of spring stiffness。

Fig。9 demonstrates the influence of spring stiffness on the maximum radial deflection of the ring。 Similarly the maximum radial deflections of the ring with =1。0 is much more sensitive to

the support stiffness than that of the ring with =2。5。 and for a ring with a given , the maximum deflection increase with the decrease of spring stiffness。

3 conclusions

In this paper, a finite element analysis model is employed to investigate the effect of flexibility of internal ring gear on stresses and deflections。 Based on the results presented above, some conclusions are as follows。

The rim thickness of ring is influential to its stresses。 With the decrease of rim thickness, the maximum principal stress of internal ring gear increases and the critical point at which the maximum stress occurs moves from fillet region to the root of tooth。

The rim thickness also influences internal ring gear deflections。 A ring with a thin rim produces larger deflections than a ring with thick rim。 When the deflection is large enough, some manufacturing errors associated with internal ring gear such as roundness error and  run-out error can be tolerated。

The spring stiffness both affects the stress and deflection of internal ring gear。 An internal gear ring with larger spring stiffness tends to produce smaller stress and deflection。

An alternative way of using gears to transmit torque is to make one or more gears, i。e。, planetary gears, rotate outside of one gear, i。e。 sun gear。 Most planetary reduction gears, at conventional size, are used as well-known compact mechanical power   transmission  systems  [1]。   The   schematic   of  the  planetary   gear   system