ABSTRACT
In previous chapters, we mainly studied transverse vibrations of simple rotor-bearing systems. It was pointed out that transverse vibrations are very common in rotor systems due to residual imbalance, which is the most inherent fault in a rotor. We studied the speed-independent bearing dynamic parameters that affected the behavior of rotors. The effect of gyroscopic couples on natural whirl frequencies and critical speeds have also been investigated in detail. In the present chapter, we extend the analysis of simple rotors to torsional vibrations. We analyze the torsional vibrations of the single-disc, two-disc, and three-disc rotor systems with the conventional Newton's second law of motion as well as energy methods. We also analyze stepped shafts, simple geared rotor systems, and branched geared rotor systems. For the multi-degree-of-freedom (DOF) rotor system, a general procedure of the transfer matrix method (TMM) is discussed for both undamped and damped cases. Advantages and disadvantages of the TMM are outlined. In reciprocating engines, large variations in torque take place periodically. This leads to torsional resonances, and to analyze the free and forced vibrations of these systems, we convert them to an equivalent multi-DOF rotor system. The present chapter paves the road for the TMM to be extended for the analysis of transverse vibrations of multi-DOF rotor systems in subsequent chapters.
