Question

Question: Analyse the efficiency of transmitting power using a solid shaft of diameter "d" compared to a hollow shaft of diameters "Do" and "Di". The ratio "r" = Do/Di should be varied from 1.5, 1.6, 1.7, 1.8; 1.9; and 2.0 but the weight of the hollow shaft must be equal to the weight of the solid shaft. Assume the length of the shaft between the two bearings (see figure below) to be the same. must be until you find the critical ration the will give. The analysis should be in two parts, assume: (a) The torque transmitted is the same, compares the stress of the two shafts. Plot a graph of (Shear Stress) vs ("") (b) The shear stress is the same, compare the Torque transmitted by the two shafts. (Torque) vs ("T") Analyse the above results and identify the best shaft ratio. USE Excel to tabulate you computed results. Driven machine Motor Coupling (2) Shaft Bearing (2) 27 167 Solid shaft (3.5c) 22 167D 2TR Hollow shaft (3.5d) +(R* -»*) -(D* -d*) Equations (3.5e) and (3.5d) are called the torsion formulas. Hollow shaft Solid shaft 32 Figure 3.6 Polar moments of inertia of circular areas.

Answer 1

Sols Griven that weight of equal to the weight of the solid shaft. hollow shaft must be Wsolid Whollow je li u og ge= p [ 119,-45]4 --":- 2 D d2 D S ast any a) Griven, terque transmitted is the same Ts TH Ts Js Tu Ju Rx enx (17/ 10"-d",) 32 TSX ( ED") e TS DE en Con-dy) D

T, D - Сп Б3 (1- 2 ЛЧ А) тах в° (3-5 -4 в° (1) (1) (1) Ts Си Я es Си 3 4 Considering Solid Shaft Es Js Rs Ts Тkr = TSX Тук (9) 16 Ts пр. 3 1 0,4 46 Ts Тg = пя[р? (1-5] 1 Tsar a साद

3 * C . es Considering Hollow Shaft: Tn Ru Jn ( T, X () ) AK T D" (1) TT D 3 (1 - 1- 4 5. . 4 X 1- 1 ။ 4 Zsa (---)

Griven 4 same. Then, Shear Stress is Zg=en ThRn Js TS Rs In TSX ( 8 ) Tax ( 2 / 2 I (0) 32 II 04 (11 ry 32 16 TS 16 Tn TDg² 1103 (+ 94 Ts 11 Tu of 2-533 03 (2 1- 94 Is Tu 1 - १५ far r= 2.0 T Maximum Ти Best shaft Ratio, r= 2.0 Completed