Answer to Question #151944 in Mechanical Engineering for Banda

Question #151944
A hollow shaft is 225mm out side diameter and 150mm inside diameter . calculate,
1. the maximum power this shaft can transmit at 150rev/min if the maximum shear stress in not to exceed 70MN/m^2....?
2. The diameter of a solid shaft of the same material which would transmit the same maximum power at the same speed with the same stress
1
Expert's answer
2020-12-22T05:07:29-0500

"J=\\frac{\\pi}{2}(r_2^4-r_1^4)=\\frac{\\pi}{2}(0.1125^4-0.075^4)=0.0002(m^4)"


"T=\\frac{J\\tau}{r_2}=\\frac{0.0002\\cdot70\\cdot10^6}{0.1125}=124.444(kN\\cdot m)"


1) At "110 (rev\/min)" the power generated is


"124444\\cdot 2\\cdot3.14\\cdot \\frac{110}{60}=1.43(MW)" . Answer


2) "J=\\frac{\\pi r^4}{2}=\\frac{3.14 r^4}{2}=1.57r^4"


"\\frac{J\\tau}{r_2}\\cdot2\\pi\\nu= \\frac{1.57r^4\\tau}{r}\\cdot2\\pi\\nu"


"\\frac{J}{r_2}= \\frac{1.57r^4}{r}\\to r=(\\frac{J}{1.57r_2})^{1\/3}=(\\frac{0.0002}{1.57\\cdot 0.1125})^{1\/3}=0.104(m)"


"=(\\frac{1430000}{2\\cdot3.14\\cdot(110\/60)\\cdot1.57\\cdot40\\cdot10^6})^{1\/3}=0.1255(m)"


"d=2\\cdot0.104=0.208(m)" . Answer




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