A planetary train similar to Figure 15.32 has a band brake that holds the ring fixed.The
Chapter 15, Problem 15.48(choose chapter or problem)
A planetary train similar to Figure 15.32 has a band brake that holds the ring fixed. The sun is driven clockwise at 800 rpm with a torque of 16 N \(\cdot\) m. The arm drives a machine. The gears have a module m of 2.0 (mm/tooth) and \(\phi\) = \(20^{\circ}\). The ring has 70 teeth. Only two planets are used, each having 20 teeth.
(a) What is the circular pitch p?
(b) Sketch each member of the train as a free body in equilibrium (neglect gravity loads).
(c) What is the output torque?
(d) What is the arm rpm? Does it rotate clockwise or counterclockwise?
(e) What pitch line velocity should be used in determining the velocity factor for each of the gears? (Hint: The velocity must be determined with respect to the proper member. For example, the appropriate pitch line velocity for the pinion and gear of a simple aircraft engine reduction gear when the plane is doing a "barrel roll" is the velocity with respect to the frame, not with respect to the ground.)
(f) What are the nominal radial loads imposed on the bearings supporting each of the gears?
(g) What torque must the brake provide in order to hold the ring fixed?
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