7 A bevel pinion and shaft are shown in Figure 71 below Bear

7. A bevel pinion and shaft are shown in Figure 7.1 below. Bearing A takes thrust. The left end of the shaft is coupled to an electric motor, and the right end is free. Load components applied by the mating bevel gear is shown.

a) Draw load, shear force, and bending moment diagrams for the shaft in both horizontal and vertical planes, plus torsional-load and axial-load and axial-load diagrams. (The desired diagrams include the seven shown in Figure 7.2 plus a similar diagram for axial loads, with tension plotted as positive.)

b) Determine the radial and thrust loads applied to the two bearings.

Fr = 2.4 kN Bcaring A F 4.0 kN Fa = 1.5 kN Bearing B Shaft Machined steel, ground finish Su = 900 MPa Sy = 700 MPa Kf13 (bending) Kf 1.2 (torsion) Kf = 1.3 (axial) 125 mm 50 mm Note: Gear forces act at a 75 mm radius d33 mm from the shaft axis.

Solution

W = 10 kW, n1 = 600 rpm, n2 = 200 rpm Shaft angle: = 1+ 2=60o , The semi pitch cone angles are shown in Fig.14.1. d1 = 200 mm, = 20o and b = 40mm. 1 2 n 600 i 3 n 200

Solution: d2 = i d1 = 3 x 200 = 600 mm r1 = 0.5 d1 = 0.5x200 = 100 mm r2 = 0.5 d2 = 0.5x600 = 300 mm o 2 o o 2 sin sin60 tan = = =1.0392 1 1 +cos +cos60 i 3 =46.1 1 = - 2 = 60 – 46.1 = 13.9o r2av = r2 – 0.5bsin 2 = 300 - 0.5x40x sin46.1 = 285.59 mm r1av = r1 – 0.5bsin 1 = 100 - 0.5x40x sin13.9 = 95.2 mm