Question

Problem : The intermediate shaft of an industrial gearbox is shown schematically in the Figure below. Total gear force acting shaft is given as F 1,5 kN. Shaft is made of St 50 structural steel. All the required dimensions are given in the Figure. Radii of curvature at the shoulders can be taken as 1 mm. Calculate the safety of the most critical cross-section against fatigue failure. Theoretical stress concentration factor =16. Notch sensitivity factor =09 quality factor =0,9, size factor =0,9. surface 18-85 Lza- 258 5 LJA LA 293.5 28 308,5 138-1 323,5 L617

Answer 1

F = 1.5 Kn = 1500 N r = 1 mm = 10^- 3 K_1 = Theoretical areas concoscentration factor = 1.6 q = Notch sensitives factor = 0.9 K_s = surface quality factor = 0.9 K_z = size factor = 0.9 we know q = K_f - 1/K_t - 1 Rightarrow K_f = 1 + Q(K_t - 1) fatigue stress concentration factor K_f = 1 + 0.9 times (1.6 - 1) K_f = 1.54 Now for equilibrium F_A + F_B = 1500 Sigma = 0 Rightarrow F_B times 617 = 1500 times 293.5 F_B = 713.533 N & F_A = 736.4667 N M_max = F_A times l_3A = 786.4667 times 0.293.5 M_max = 230.83 N - m I = pi/64 d_3^4: Z = pi/32 d^3_3 = pi/32 times (0.04)^3 z = 6.284 times 10^-4 m^3 sigma _b = M/Z = 230.83/6.284 times 10^- 4 = 36.733MPa Allowable stess sigma_a = sigma_e times K_s times K_3 /K_f where sigma _e = Endurance limit for st 50 structural steel sigma_e = 275 MPQ