:) Consider the geared rotor as shown in Fig. 1, where M0 is a driving torque, J

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Consider the geared rotor as shown in Fig. 1, where M0 is a driving torque, J and J, are the mass moments of inertia of the gear shaft and rotor respectively, bg and br are the damping coefficients of the bearings, is the gear ratio, and k is a torsional spring coefficient representing the elastic property of the shafts. Write down all the governing equations of the rotor system. Derive the transfer function Ohm r(s)/Ma(s) , where Ma(s) and Ohm r(s) are the Laplace transform of the torque Ma(t) and the rotation speed omega r(t)= theta (t),respectively. Obtain a state representation for the rotor, with Ma(t) as the input ,and omega r(t) as the output. Task 2. Simulation of the Geared Rotor Assume that all the parameters are of non-dimensional values. Let the parameters of the geared rotor system in Task 1 be Jg =10, bg =0.1; Jr =30, br =0.15; n1/n2 =1/5. Build a SIMULINK model of the geared rotor system. For the stiffness k = 50, 100, 1,000, 5,000 and 10,000, plot the rotation speed omega r(t) subject to an impulse input M0(t) = 50- delta (t), where delta (t) is a delta function. Discuss the effect of the stiffness on the system response. For the stiffness k = 10, 50, 100, 1,000 and 10,000, plot the rotation speed omega r (t) subject to a step input Ma(t) = 50, t gt 0. Discuss the effect of the stiffness on the system response.

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