Question

In the mechanical system represented in Figure 2(a), a motor supplies a torque of 45 kN-m, and powers two machines through gears D and E. The torque delivered to gear E is 8 kN-m The two shafts are made of steel, with E200 GPa, G 80 GPa and yield strength of 300 MPa The shaft AB has an outer diameter of 150 mm and an inner diameter of 80 mm; the shaft DCE has an outer diameter of 80 mm and an inner diameter of 40 mm. The diameters of gears B and C are 450 mm and 150 mm, respectively. a. What would be the magnitude of the torque at point D? b. Determine (i) the rotation angle at gear B with respect to point A, (ii) of gear D with respect to gear C, and (ii) of gear E with respect to gear C What would be the maximum shear stress in each shaft? c. Moreover, at point A, the shaft had been repaired using four bolts having a diameter of 15 mm made of hardened steel with shear strength of 90 MPa, as illustrated in Figure 2(b) Will this connection survive the applied torque? Is the system going to fail at any other point? 1.5 m d. e. 2.5 m Bearings 2 m (a) System (b) Connection at point A

Answer 1

Given that mechanical system represented, a motor supplies a torque 45 k N - m and two machine D & E. here mechanical system a motor supplies Torque = 45 K N - m: E = 200 Gpa G = 80 Gpa: yield strength = 300 mpa therefore having the value in point AB Outer diameter = 150 mm: AB inner diameter = 80 mm DCE = outer diameter = 80 mm DLE = Inner diameter = 40 mm therefore diameter of gears B and C are 450 & 150 mm Respectively (a) magnitude of a torque at point D T_B/TC = phi B/phi C implies T_C = 45 [150/450] T_C = 45 [150/450] T_C = 15 K N - m T_E = 8 k N - m T_b = T_C - T_E = 15 - 8 = 7 K N - m. \r\n determine (i) rotation angle gear B respect to A phi _B/A = T_Bl/Gp