Exam 2022 07 18 WT1 text

Page 1

Exercise 1 Consider a part of the crank shaft shown in Figure 1 (between AF), which lies in the plane of XOY. At point G, which is in the middle of CD , there is a force F always perpendicular to the plane of whole structure . The diameter 𝑑𝑠 can be regarded as the dimension of the section for the whole structure. The H-H indicated in the Figure are the mid points of DE. Figure 1 Considering the structure is rotat ing at a constant angular speed ω, it is required to: 1. Determine the torque T considering the application of force F. 2. Plot the diagrams of internal forces (bending, torsion, shear) for the structure considering the application of force F . 3. Perform the static assessment at section H-H. If 𝐹 = 𝐹𝑡, and 𝐹𝑡 = 𝐹𝑚 + 𝐹𝑎sin⁡(𝑤𝑡): 4. Perform the fatigue assessment at section H-H with the variable force F t applied . Data Loads Fatigue parameters: 𝐹⁡ = 1500⁡𝑁 𝑏2 = 0.85 𝐹𝑚 = 1500⁡𝑁 𝑏3 = 0.85 𝐹𝑎 = 600⁡𝑁 𝐾𝑡 = 1 Geometry Material: 𝑎⁡ = ⁡150⁡𝑚𝑚 𝜎𝑦 = 500⁡𝑀𝑃𝑎 𝑏⁡ = ⁡100⁡𝑚𝑚 𝜎𝑈𝑇𝑆 = 600⁡𝑀𝑃𝑎 𝑐⁡ = ⁡150⁡𝑚𝑚 𝑑𝑠 = 22⁡𝑚𝑚 Politecnico di Milano - Master of Science in Aeronautical Engineering Academic year 20 21-22 Course of Machine Design (Prof. M. Giglio) Written test 1 – July 18, 2022 NAME : SURNAME : Polimi-ID : Do not write here: 1 2 3 Total Exercise 2 The plate shown in Figure 2 is subjected to a far-field loading P. There are three through-thickness cracks: one of them is a central crack and the other two are side ones . Assuming 𝑃 = 𝑃0, it is required to: 1. Identify the most critical crack: central crack or the side one . 2. Calculate the most critical lengths of the critical crack for both plastic and brittle failure and identify the most critical failure condition . Assuming P is a cyclic loading, and in each cycle 𝑃𝑚𝑎𝑥 = 𝑃0, 𝑃𝑚𝑖𝑛 = 𝑃𝑚, it is required to: 3. Check if the…