Rotor-bearing system having discrete discs and bearings and shaft with distributed mass and elasticity is considered in the present study. Dynamic modeling of the rotor-bearing system using finite elements developed by Nelson and McVaugh19 and the extended model by Ozguven and Ozkan20 have been used in the current work. Internal damping is neglected here. The rotor shaft is discretized into finite beam elements as shown in Figure 1. The beam element has two nodes and four degrees of freedom at each node represented by q1 – q8 for bending mode. Two translational degrees of freedom are represented by q1, q2, q5, and q6, and two...

Rotor-bearing system having discrete discs and bearings and shaft with distributed mass and elasticity is considered in the present study. Dynamic modeling of the rotor-bearing system using finite elements developed by Nelson and McVaugh19 and the extended model by Ozguven and Ozkan20 have been used in the current work. Internal damping is neglected here.

The rotor shaft is discretized into finite beam elements as shown in Figure 1. The beam element has two nodes and four degrees of freedom at each node represented by q1 – q8 for bending mode. Two translational degrees of freedom are represented by q1, q2, q5, and q6, and two rotational degrees of freedom are represented by q3, q4, q7 and q8. Even though the element is shown in Figure 1. is a transverse cracked element, the degrees of freedom considered are the same for an uncracked element.

The equation of motion of the complete rotor system in a fixed co-ordinate system can be written as

[M]{q ̈ }+[D]{(q}) ̇+[K]{q}={Q}

The rotary and translational mass matrices of the shaft and the rigid disc mass, and the diametral moment of inertia are included in the mass matrix [M]. The matrix [D] includes the gyroscopic moments and the bearing damping. The stiffness matrix comprises the stiffness of the shaft elements (cracked shaft element in case of the cracked rotor) and the bearing stiffness. The details of mass, damping and stiffness matrices of equation (1), except for the cracked element, are given in references19,20.

The unbalance forces due to a disc having mass m and eccentricity e and the weight of the disc are included in the excitation matrix {Q} in equation (1) at appropriate degrees of freedom. The unbalance force components in x and y directions for angular rotation are given as,

F_x=me {θ ̈ sin〖∅ + 〗 〖 (θ^2 ) ̇ cos〗〖∅ } 〗

F_y=me {- θ ̈ cos〖∅ + 〗 〖 (θ^2 ) ̇ sin〗〖∅ } 〗