Transfer Matrix Method to Vibration Analysis of Rotors with Coupler Offsets

Abstract

In this paper a general transfer matrix method (TMM) for rotors containing global and local coupler offset was derived. Rotor response due to imbalances and offsets are then studied via the developed method. The studies showed both global and local offsets played as an external excitation that is a combined effect of all the elements behind the offset. Differences between global offset and local offset were compared and the results showed both types basically retain the same mode patterns but different jumps at the offset. The global offset, yet, imposed more significant dynamic effects since all the offsets accumulate thereafter. The whirling orbits in front and behind the offset were illustrated as well. The results, as expected, showed global offset appeared much larger radii especially after offset. The rotor's whirling orientation reversed, as rotation fell within a certain range and this feature was not changed by offsets. The TMM proposed by this study can be well applied to multiple global and local offsets.

A transfer matrix method for free vibration analysis of Euler-Bernoulli beams with variable cross section

“…Finally, the TMM with Bessel's functions was applied successfully to determine the natural frequencies of a complex structure of conical and cylindrical beams. Future developments of the present TMM may include adding the gyroscopic effect for rotating machinery (Firoozian and Zhu, 1991;Lee et al, 1993;Tsai and Huang, 2013), adding a specific matrix corresponding to a transverse crack for cracked structures (Untaroiu et al, 2011;Attar, 2012;Abbas and Rui, 2014;Attar et al, 2014) and integrating it in an optimization approach of mechanical structures/systems (Putnam et al, 2014;Untaroiu and Untaroiu, 2010;Untaroiu et al, 2013;Untaroiu et al, 2014). It is believed that both TMM and the properties of conical beams presented in this study could be applied to the vibration design of various structures that include cylindrical and conical beams (e.g.…”

Finite element analysis of an actively controlled heavy rotor using a PVDF piezoelectric layer as a sensor and actuator

“…To apply input torque to analyze vibrations of the coupled turbo‐generator rotor, different researcher calculates the electromagnetic torque in generator using analytical methods 8‐11 . Reference 12 described Increment Transfer Matrix Method (ITM) to calculate the response of the torsional vibrations in generator torque. Reference 13 described a comprehensive process model for simulation of short circuit faults of initially unloaded synchronous generator, using the generalized dq0 mathematical model.…”

Resonance speed measurement of high-speed spindle using an instruction-domain-based approach

“…The advantage of the TMM is that the order of the matrix does not increase with increases in the degree of freefom in the system, programming is simple, computation is fast, and this is especially suitable for computation by numerical calculation software such as MATLAB. However, this method does not consider the influence of the mass and inertia distribution of the rotor on the rotor motion in the simplification of the rotor system, which affects the accuracy of the analysis results to some extent [18]. The FEM is implemented by dividing the continuous rotor system into a finite number of units, which are then connected by nodes.…”