Problem 3

A shaft carrying two spur gears of different radii is shown in the figure. Gear D receives power from another gear, not pictured. The power is then transmitted through the shaft and delivered to gear C. Gear C transfers power out of the system. As a result of these gear interactions, two forces in the z and y directions are exerted on gears C and D, respectively, as shown in the figure.

The shaft is supported by two smooth journal bearings at A and B, that can exert only radial components of force (i.e., y and z directions) on the shaft (you may treat them as simple pin supports). The shaft is made from 1050 CD steel and has a diameter of 40 mm.

(a) Determine the bearing loads (support reactions at A and B). The bearing loads are crucial for for bearing selection from different catalogs.

(b) Find the torque on the shaft (transmitted torque, T,,between points C and D)

(c) Determine the maximum bending moment, M, is in the shaft (Hint. Use two 2D M diagrams, one for M; and the other for My, then combine them).

(d) At the point of maximum bending moment, determine the principal and maximum shear stresses.

(e) Determine the safety factor for the same critical point using the maximum-shear-stress (Tresca) theory.