### Adequacy ranges of linear and nonlinear methods for determining the dynamic properties of the rotating machinery (in Polish:Przedziały adekwatności liniowych i nieliniowych metod określania właściwości dynamicznych łożysk hydrodynamicznych)

Rotating machines are the basic power machines, they also find other wide applications. The main components of a rotating machine are the rotor with blades and bearings along with the support structure. The rotor line concentrates the interactions of all the sub-systems of a rotating machine. Of particular importance here are the interactions of the sliding bearings expressed in terms of stiffness coefficients and oil film damping. It is worth noting that from a mathematical point of view, these coefficients link together the ordinary differential equations describing the motion of the entire system with the partial differential equations describing the spatial distributions of hydrodynamic pressure. In the project, the coefficients of stiffness and damping of sliding bearings were calculated for the system in the linear and nonlinear range, i.e. in the range occurring in practice. In the calculation model adopted, the Finite Element Method (FEM) with beam elements of six degrees of freedom at each node was used for the rotor line. A major computational problem is the calculation of the stiffness and damping coefficients of the sliding bearings at each time step of the iterative procedure. This fact makes the numerical calculations nonlinear. Even the most advanced commercial programs do not offer such solutions. The NLDW program developed and developed at the Institute of Fluid Flow Machinery, Polish Academy of Sciences, Gdansk, Poland, was used in this work.

In this project, special attention has been given to the relationship between a machine and its bearings. These relationships are not always made explicit enough in publications on plain bearings and rotating machinery. Specialists in rotor dynamics often treat bearings as part of a system with constant, linear stiffness and damping coefficients. In reality, this type of approach is valid only in certain cases. The project aims to indicate the ranges in which this kind of approach can generate qualitative errors. The project determined the stiffness, damping and mass coefficients of a system consisting of a rotor and hydrodynamic bearings on a real object using an experimental impulse method. A linear algorithm was used for these calculations, which has been extended to allow for the determination of mass coefficients. The determination of mass coefficients provides a preliminary verification of the experimental calculation results. The impulse method consists of forcing the vibrations of a rotating shaft with a modal hammer. On the basis of the recorded displacement signal in the bearings, it is possible to identify the stiffness, damping and mass coefficients of the rotor-bearing system. The experimental tests were performed on a laboratory bench with a 3/4'' diameter rotor and hydrodynamic bearings. The maximum speed of this bench is 14,000 rpm. As a result of this experiment, a set of 24 coefficients characterizing the two hydrodynamic bearings and their uncertainties will be determined. The juxtaposition of the results of the nonlinear and linear numerical calculations and the experimental results were provided with a complete picture of the computational capabilities of the dynamic coefficients of the plain bearings. Hydrodynamic bearings have a decisive influence on the dynamics of rotating machinery. In large multi bearing power turbine units, the bearings may operate in the nonlinear range for extended periods of time. The coefficients of the hydrodynamic bearings then change during operation even if the machine runs at a constant speed. The dynamic bearing coefficients are influenced by the flow phenomena, the interactions in the bearing and the dynamic interactions of the entire rotating machine. To calculate these coefficients accurately, it is necessary to use nonlinear calculation methods. The results of the work in the project answered the question in which range the use of linear simplifications is acceptable, and when it is necessary to take into account during calculations additional parameters related to the movement of the rotor in the bearing. The proposed experimental research method may in future also find application in calculations of other bearing types, e.g. magnetic or foil bearings.