A non-linear transfer matrix technique for statically indeterminate rotor bearing systems

Abstract Transfer matrix (TM) methods have long been used to obtain the vibration behaviour of linearized rotor bearing systems. Recently the technique has been enhanced to find the unbalance response of statically determinate systems with hydrodynamic bearing type non-linearities. This paper further extends the non-linear approach to statically indeterminate systems, enabling application to practical rotating machinery. The technique is illustrated on simple unbalanced rotor bearing systems with two and four bearings. It is shown that, in statically indeterminate systems, unbalance may affect not only the orbit size and shape but also the load distribution between the bearings.