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Exercise 2. Describe the Sines criterion and its base hypotheses. Master of Science in Mechanical Engineering Politecnico di Milano Course of Machine Design 2 (Prof. S. Beretta, Prof. M. Giglio, Prof.ssa L. Vergani) Written test – 04.07.2017 Name: Surname: Polimi-ID: Do not write here 1 2 3 4 TOTAL Exercise 1. Figure 1 shows a shaft with three supports placed in A, B, and C. The shaft is aligned to axis x, according to the provided reference system. Two gears are joined to the shaft. Requests: a. Plot the diagrams of bending moments and torque b. Perform the fatigue assessment c. Calculate the maximum deflection in correspondence of Gear 1 Figure 1 – Schematic of the structure. Data: a = 200 mm; d1 = 350 mm; d2 = 450 mm Ft2 = 600 N Fr1 = 281 N; Fr2 = 218 N ds = 25 mm UTS = 600 MPa Geometrical quantities Nominal diameters of gear 1 and gear 2 Tangential force on gear 1 Radial force on gear 1 and gear 2 Shaft diameter Ultimate tensile strength Master of Science in Mechanical Engineering Politecnico di Milano Course of Machine Design 2 (Prof. S. Beretta, Prof. M. Giglio, Prof.ssa L. Vergani) Written test – 04.07.2017 Name: Surname: Polimi-ID: Exercise 3. In a structural component subjected to a pulsating tension, internal penny shaped (circular) crack s are detected with a diameter 2a 0, that is much smaller than the wall thickness of the component. The material is an aluminum alloy for which the crack growth is governed by the following law: 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑= 𝐶𝐶(Δ𝐾𝐾𝐼𝐼)𝑛𝑛 , da/dN [m/cycle]; ΔKI [MPa√m]; a) Determine the maximum stress range that can be allowed without any crack growth. b) Determine the stress range that can be allowed so that no unstable crack growth occurs for 104 load cycles. Choose a safety factor s = 1.5 with respect to the load. Geometrical data β = 0.64 a0…