Extension of the Transfer Matrix Method for Rotordynamic Analysis to Include a Direct Representation of Conical Sections and Trunnions

The transfer matrix method for rotordynamic analysis (alternately known as the HMP or LMP method) has enjoyed wide popularity due to its flexibility and ease of application. A number of computer programs are generally available which use this method in various forms to perform undamped critical speed, unbalance response, damped critical speed and stability analyses. For all of these analyses, the assembly of the transfer matrices from the rotor model is essentially the same. In all cases, the rotor model must be composed entirely of cylindrical beam elements. There are two situations when this limitation is not desirable. The first situation is when the rotor being modelled has one or more sections whose cross sections vary continually in the axial direction. The most common of these sections is the conical section. Presently, a conical section must be modelled as a series of “steps” of cylindrical sections. This adversely affects both the simplicity and accuracy of the rotor model. The second situation when current transfer matrix techniques are not accurate is when the rotor being modelled has one or more sections that do not behave as beam elements. The most common example is a trunnion which behaves as a plate. This paper describes the analytical basis and the method of application for direct representation of conical sections and trunnions for a transfer matrix analysis. Analytical results are currently being generated to demonstrate the need for and advantages of these modelling procedures.