A double disc rotor system, consisting of a rotating shaft, two discs and bearin

Question

A double disc rotor system, consisting of a rotating shaft, two discs and bearings represented as clamped supports at each end of the shaft, is modeled as shown in FIGURE Q1. Assume G_1 = G_2 = G_3 = 80 times 10^9 N/m^2, J_1 = J_2 = J_3 = 1.5 times 10^-8 m^4, L_1 = L_3 = 1.5L and L = 0.4 m. The mass moments of inertia of disc 1 and disc 2 are 1.5 and 0.81 kg.m^2 respectively. Model the system as two degree-of-freedom system and determine the torsinal stiffness k_g k_12 k_3 Derive the differential equations of the system theta _1 and theta _2 as genararalised coordinates. Determine the natural frequencies and mode shapes.

Explanation / Answer

Cannot read the individual parameters, so giving a general analysis, you have to put in the numbers.

1)Torsional stiffness: Kt =GJ/l

2)let phi i be the angle at disci

I1 phi1" +Kt( ph1 1-phi2) =0, Kt is the torsion stiffness of the shaft

I 2 phi 2 " +Kt( phi2 -phi1) =0

for free vibrations assume a soln phi" = - w2 phi

substitute in the eqns,

coupled differential eqns are reduced to eigenvalue problem:

K t - I1 w2 -Kt

=0

-Kt Kt-I2w2

3) solve for w2

from [D- w2I]U`= w2 U , where U is the mode shape solve knowing w2

Best!

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