5) Material selection (5 points) A Mechanical design team wants to select the best material for a shaft. They want to do

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5 Material Selection 5 Points A Mechanical Design Team Wants To Select The Best Material For A Shaft They Want To Do 1 (334.9 KiB) Viewed 24 times

5) Material selection (5 points) A Mechanical design team wants to select the best material for a shaft. They want to do this fundamentally, by using a performance index approach to select the most suitable material. The shaft is hollow and can be characterized by an outer radius R and a wall thickness t. Assume the tube is only subjected to torsion and that the wall thickness is small with respect to the outer radius. The figure below shows the loading condition (note: the tube is hollow). M R M C O b F Figure 4. Load condition of drive shaft. a) Derive that for a given maximum shear stress t and moment M the lowest mass is obtained if p/3 is minimal (1,5 points). The relevant equations are given below: MR T=— I P Ip Material Fe Al TRA 2 b) Discuss the applicability of all materials listed in the table below (1,5 points). c) Which material would you recommend? Please explain why (1 Point). d) If the price of the shaft is included in the analysis, does this change the recommended material? Discuss your answer on the basis of the performance index adapted for this case (1 point). Balsa wood Ti -3Al-2.5V Al2O3 (ceramic) 1 A=TR² - n(R-1)² =Rt (for small t) E (GPa) 210 71 2.5 110 370 Tc (MPa) 450 200 6 500 260 P (g/cm³) 7.8 2.7 0.095 4.5 3.7 Cost (€/kg) 0.45 1.5 10 4.5 25