Question

The shaft shown in the figure is supported on bearings located at A and D. The shaft is made from steel with a yield strength of 680 MPa and an ultimate strength of 790 MPa. The shaft dimensions are in millimeters and each step has the diameter shown. There are fillets with 2 mm radii at each step in the diameter. The notch sensitivity is 0.840. The shaft has a machined surface finish. A reliability of 99% is desired for this application. The shaft rotates while the force applied as shown is stationary. The force is 2.5 kN. Determine the expected life of the shaft. A B D с * -250 -75 100 125 F -10 -10 30 32 35 38 IR R2

Answer 1

question is solved below

Giren i r- amm Shaft steel Sut = 790MPa Sy= = 680MPA filter nodices notch Sensitivity q- 0.840 F= 2.5 KN The failure will occur at B nather than at e or at the point of man moment. Point B has a smaller cross section moment and higher stees concentration focton thon c Estimating endurance limit :- Se = kako ke kd kese a lignes bending Sut 2 1400 MPa so Se's 0.5 Seet = 0.5*790 ) Rotating berm text endurance limit=se se = 395 MPa Ka = a süt for machined surface a = 4.51 b=-0.265 ka = 4,51 (190)-0.265 ka=77 -0.107 Kb = (30/1-62) 0.858 Kc = kd=1 Ke= 0.814 for 99% reliability Se= 0.77X0.858 X L x 0.8148395 Se=212.422 MPa To find the geometric strees concentration factar Kt we are 38/32 and d = 2/32 = 0.0625 and we read D/d = 1.1875 kt = 1.84 Kf = 1+q(K-1) = 1+ 0.84011.84-1) Kf = 1.7056

now find bending stees at point 6 ŽMA=0 Rą X 550 -2.5 x 325 R2 = 1.477 KN Eryo F= 2.5KN R, = 10227 KN 1475-1610064 125 3 now bending moment at B R Mg M more Roxaso MB MC = 255.68 KN-mm B The reversing bending strees Crew RC 32 MB *(32)3 32x255.68 x103 x 1.84 T (32)3 Trev = 146.24 MPa freut se Drewesy This stress is less than se and Sy this means we have infinite life of shaft in fatigue & greater than 100 cycles)