Rotor System Vibration Analysis Of The Overall Transfer Matrix Method

With the increase of rotational speed of rotary and the improvement of its performance, the vibration characteristic of the rotor system has been becoming a research foqus. Usually several rotors linked with some gears or couplings constitute a complex rotor system with multiple rotors, rotation speeds and rotation directions. Many engineering problem indicate a multi-rotor system should be taken as a whole to study its vibration characteristic, considering the dynamic property of each rotor, studying lateral vibration, torsional vibration and their coupling effect. Based on Prohl transfer matrix methods and Riccati transfer matrix method, a whole transfer matrix method and its Riccati method are developed to solve the vibration problem of a multi-rotor system. With these method applied, a Multi-rotor System Dynamic Analysis Program (MSDAP) is programmed, whose good performance is testified with several numerical examples.In the first part of this paper, the present research state of rotor dynamics and four types of computation method are introduced.In the second part, the transfer matrix method to calculate the critical speed, the mode and the unbalanced response, is presented. And the torsional vibration and lateral-torsional coupling vibration problem is discussed briefly. Many transfer matrices of different elements are appended in the end.In the third part, the concept of coupling element is derived from the vibration analysis of a four-degree spring-oscillator system, and a whole transfer matrix method is developed on the basis of it. With the advantages of the Riccati transfer matrix method, a Riccati method of whole transfer matrix is proposed. Besides the improvement of numeric stability, it increases the computation efficiency by transforming the high-order sparse matrix calculation into low-order matrix calculation. Since the gear engagement is a common coupling form between rotors, the transfer matrix of skew gear engagement in global coordinate system is deduced based on the concept of coupling element.In the fourth part, a self-programmed multi-rotor system dynamic analysis program and lots of numerical examples are introduced.In the last part, some problem encountered in the research is discussed, and the further study is proposed.