Question

Please, show all work in a detailed manner. Thanks.

Problem #1 The motor shown operates at a steady 500 rpm with a power output of 4 horsepower. The solid shaft has an outer radius of 0.375 in. (1) What is the current magnitude of the maximum shear stress in the shaft? (2) If the shaft is replaced with a hollow shaft of outer radius 0.50 in, what is the smallest wall thickness (t) that will keep the maximum shear stress under 6 ksi?

Answer 1

60. (Oo) 33 00 O 4- 52.52ソ 500 J p 尸 incb 12x 12.016 lb.ft 0,395) ーターと)ßheccl 1014.45 x12- -12143.41 psi (on) 12.1 3시iksi 42.016 xIO3 xI2 6 XIo Dİ : O,2696c" 2

Answer 2

"P = 4 Hp = 4 times 746 = 2984 watts = 2. 984 kw N = 500 r. p. m p = ()2 pi times N times T/60) (or) = (torque) times (2 pi) times rotational speed/33000 4 = (T times RPM/5252) T = 4 times 5252/500 = 42. 016 ft. lb T/j_p = /R 12 times 42. 016 lb.ft/ pi /32 (0. 75)^4 = q_ /(0. 375) rightarrow q_shear = 1014. 45 times 12 = 12173. 41 psi (or) = 12. 17341 ksi tau_max = 6 ksi T/j_p = q_max/R 42. 016 times 10^-3 times 12/ pi /32 (D^4_0 - D^4_i) = (6/0. 5) (D^4_0 - D^4_i) = 427 97 times 10^-3 (1)^4 - (D_i)^4 = 0. 42797 (D_i)^4 = 0. 572 D_i = 0. 86966"" t = D_0 - D_i/2 = 1 - 0. 86966/2 t = 0. 065 inches"