A countershaft has a helical gear (B), a bevel gear (D), and two supporting bearings(A

Chapter 17, Problem 17.33

(choose chapter or problem)

A countershaft has a helical gear (B), a bevel gear (D), and two supporting bearings (A and C) as shown in Figure P17.33. Loads acting on the bevel gear are known. Forces on the helical gears can be determined. Shaft dimensions are known. All shoulder fillets have a radius of 5 mm. Only bearing A takes thrust. The shaft is made of hardened steel having values of \(S_u\) = 1069 MPa and \(S_y\) = 896 MPa. All important surfaces are finished by grinding.

(a) Draw load, shear force, and bending moment diagrams for the shaft in the xy and xz planes. Also draw diagrams showing the intensity of the axial force and torque along the length of the shaft.

(b) At points B, C, and E of the shaft, calculate the equivalent stresses in preparation for making a fatigue safety factor determination. (Note: Refer to Figure 8.16 and Table 8.2).

(c) For a reliability of 99% (and assuming \(\sigma\) = 0.08 \(S_n\)), estimate the safety factor of the shaft at points B, C, and E.