2015 09 07

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Master of Science in Mechanical Engineering Politecnico di Milano Course of Machine Design 2 (Prof. S. Beretta, Prof.ssa L. Vergani) Written test – 07.09.2015 Name: Surname: Polimi-ID: Do not write here 1 2 TOTAL Exercise 1. Figure 1 shows an agitator composed by a central rotating shaft, three supports and a stirrer with two paddles . The power is supplied by a helical gear (axial force is directed toward the hinge support). At the extremities of each paddle of the stirrer two forces (F, A) are applied, representing the resistance of the fluid to the motion. Requests: 1) Determine the internal forces in the shaft. 2) Perform fatigue assessment in section ZZ (use b2,b3,and SC for local approach). 3) In the most stressed point of the external surface of the shaft in ZZ a 0-45-90 Strain gauge rosette is p laced, calculate the highest strain values during a cycle. 0 axis is parallel to shaft axis (Y direction). 4) Calculate the rotation for each plane at the lower bearing. Data a = 150 mm (shaft size) b= 100 mm (shaft size) h= 300 mm (paddle size) F = A = 500 N (forces on the stirrer) αn=25° (gear pressure angle) Figure 1 β=15° (gear helix angle) Dgear= 200 mm (pitch diameter of the gear mounted on the shaft) b2=0.8 (fatigue assessment coefficient for ZZ section) b3=0.8 (fatigue assessment coefficient for ZZ section) Kt(Mf)=1.5 (SC coefficient for ZZ section) Kt(Mt)=1.3 (SC coefficient for ZZ section) d= 30 mm (Diameter of the shaft) UTS=600 MPa (strength of the shaft) Exercise 2. Let us consider the shaft of a transmission: the shaft is subjected to a combination of a bending moment and a torque (Mb=Mt). The service consists in a sequence of start -stop cycles, during which pulsating torque and alternate bending are in phase. (d=60 mm, Kt,f=2.6, Kt,t=2.2) 1) Considering…