“Introduction:

Traditional lateral and torsional rotordynamics analyses involve taking the physical dimensions of a rotor system and its associated bearings and supports and building a mathematical analog. Many papers by this author and books and papers by others listed in the references describe in detail these methods, capabilities and limitations. The traditional analysis approach views the dynamics of a rotor-bearing system as a function of frequency. In this paper we will explore rotordynamics in the time domain and, by extension into the non-linear regime.

For train torsional analysis we are primarily interested in resonant frequencies, mode shapes and forced response due to torque pulsations. While standard undamped torsional resonant frequencies and mode shapes are very easy to calculate, one must be very careful to define the alternating applied torques when attempting to calculate torsional twist amplitudes with a forced response calculation. Alternating torques may be created by mechanical means from gear sets or couplings, may be a consequence of the driving torques developed by the prime mover as in a synchronous motor or may be generated by the process side of the machinery like a reciprocating compressor. All of these factors become extremely important when calculating fatigue life of components that are subjected to periodic torsional shear stresses. It will be shown that one often needs to enter the time domain to adequately describe the torsional forcing functions and the resultant stresses if the goal of realistic fatigue life is to be attained.

For lateral rotordynamics we are very interested in critical speeds, mode shapes, forced response and stability. An undamped lateral critical speed analysis is very useful to give the user a feeling for the critical speeds and mode shapes. A critical speed map, especially with the predicted bearing coefficients cross-plotted, is a very useful design tool. However, for predicting actual frequencies of maximum rotor amplitudes, the vibration magnitudes that can be expected and the rotor stability it is necessary to include damping. Some of the elements in the forced response and stability analyses such as seal and bearing stiffness and damping coefficients are not linear (we calculate them as a function of rotor speed). However, in the standard linear synchronous unbalance response analysis the amplitude, phase and frequency calculations are linear at each speed step. To get the response predictions we simply connect the “dots” to produce the normal Bodé type plots.”