A bladed disc of a radial compressor (shown in Fig.1a) rotates in normal operating conditions with rotation speed 7000 rpm and a static pressure of 4 kPa applied to each blade at its concave surface. The bladed disc is fixed rigidly to a shaft in such a way that all displacements at the inner radius of the disc are zero. The bladed disc is manufactured from titanium with material properties: elasticity modulus: 1.16E= GPa; Poisson ratio:0.34ν=, density: 4500kg/m3 and the yield strength 135MPa.
Since the bladed disc is cyclically symmetric, a sector model (see Fig.1b) has been created and the geometry of the sector model is provided in a file: “[login to view URL]” where all dimensions are given in millimetres.
In this coursework you should use this sector model in order to:
1) Analyse static deformation and stresses of the bladed disc under simultaneous action of the centrifugal forces and the pressure. Comment on the stress levels obtained, and, if the stresses appear to be excessive, make suggestions by which the stresses might be reduced and then carry out an analysis of a modified design to show that such modifications will reduce the stresses.
2) Calculate natural frequencies and mode shapes of the bladed disc in the rotating reference frame for harmonic index values from 2 to 8 at the normal operating conditions. For each harmonic index you should determine and provide first 5 different frequencies and corresponding mode shapes. Do not forget to take into account the effects of the pre-stressed static state on the modal properties of the bladed disc. Compare results with the natural frequencies calculated without allowing for the pre-stressed state. Assuming that there is engine-order excitation coming from the gas flow for all harmonic indices analysed: from 2 to 8, comment on the possibility of resonance vibrations at the normal rotation speed.
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