Improved Rotordynamic Unbalance Response Calculations Using the Polynomial Method

Abstract

Abstract For rotordynamic calculations the conventional transfer matrix (CTM) method is known for its ease of application and speed of execution. This is true for eigenvalue analyses as well as forced response calculations. In 1983, Murphy and Vance significantly improved the conventional transfer matrix method for eigenvalues by developing Polynomial Transfer Matrix (PTM) method. For eigenvalue calculations this resulted in one to two orders of magnitude increase in calculation speed, and eigenvalues could be found without missing any modes. This paper extends the polynomial method to forced response calculations. The polynomial method “compiles” a polynomial representation of a rotor bearing system. Responses at many frequency increments can then be computed with amazing rapidity. Similar to the case of eigenvalue calculations, an automatic dynamic condensation feature helps the PTM attain nearly a tenfold increase in speed over the CTM method. This paper details the polynomial method applied to forced response calculations. Two example calculations are presented to compare the PTM to the CTM method and finite element method. All computations were carried out on an IBM-PC compatible computer.