Figure P15.23 shows a two-stage gear reducer. Identical pairs of gears are used. (This enables input shaft a and output shaft c to be colinear, which facilitates machining of the housing.) Shaft b, called the countershaft, turns freely in bearings A and B, except for the gear-tooth forces.
(a) Determine the rpm of shafts b and c, the pitch diameters of the pinion and gear, and the circular pitch.
(b) Determine the torque carried by each of the shafts a, b, and c:
(i) assuming 100% gear efficiency, and
(ii) assuming 95% efficiency of each gear pair.
(c) For the 100% gear efficiency case, determine the radial loads applied to bearings A and B, and sketch the countershaft as a free body in equilibrium.
