Comparison of Experimentally and Numerically Determined Dynamic Coefficients of the Hydrodynamic Slide Bearings Operating in the Nonlinear Rotating System

Abstract

The article presents the calculation results of dynamic coefficients of hydrodynamic slide bearings obtained using three different methods. The numerical analysis based on a linear and nonlinear algorithm was carried out. The software developed at the Institute of Fluid-Flow Machinery PAN was applied for this purpose. In the experimental research, we used the impulse response method for the determination of dynamic coefficients of hydrodynamic bearings. This method is based on a linear algorithm and allows the calculation of stiffness, damping and mass coefficients for the rotor – bearings system. It allows calculating the complete set of coefficients in only one calculation step. During experimental research, vibrations of the rotor supported on two slide bearings are excited using an impact hammer at the middle part of the shaft. Stiffness, damping and mass coefficients are determined after the analysis of displacements of the journals and the registered excitation forces. The shaft mass is known, therefore mass coefficients can be used for quick verification of the obtained results — by comparing their values with the shaft mass. The experimental tests were carried out on the test rig produced by SpectraQuest. The basic dynamic characteristics of the test rig were determined in the framework of this research, including vibration trajectories of the journals for both bearings — at rotational speeds between 2250 and 6000 rpm. In this speed range, a resonant speed of the rotor was noticed. The vibration trajectories of the journals were used to verify calculated coefficients of the hydrodynamic slide bearings. Since the tested system exhibits nonlinear properties, the three different calculation methods produced large differences in results. The numerical calculations conducted with a linear algorithm provide only one set of stiffness and damping coefficients for each rotational speed (two main and two cross-coupling coefficients for each bearing). In the case of calculations utilizing nonlinear algorithm, the values of coefficients vary over time, notwithstanding the fact that the rotational speed is a fixed value. In each time step, we have different values of stiffness and damping coefficients of the hydrodynamic bearings. In the case of calculations based on the results obtained from experimental research, we receive one set of coefficients for each rotational speed, just as it is for the linear algorithm. The mean and standard deviation of stiffness, damping and mass coefficients are obtained by repeating many times experimental tests followed by statistical calculations. To get values of the coefficients for more than one rotational speed, calculations must be made for each one separately. As a matter of fact, most mechanical systems exhibit certain nonlinear properties. In rotating machinery, we sometimes face distortions of their operation caused by, for example, couplings or supporting structures. In the ideal case, if the system had linear properties and operated correctly without any distortion, the results obtained from all three methods would be the same. The reality is that the experimentally and numerically determined coefficients of the hydrodynamic journal bearings differed, and their differences were discussed in this article. These differences arise from the adopted assumptions and abilities of the three different calculation models. In numerical calculations based on a linear algorithm, it is assumed that the bearing journal is in static equilibrium during its operation. For nonlinear calculations, the solution is found by iterations. The stiffness and damping coefficients are determined for sufficiently small time steps such that we can replace their values in every position of the bearing journal. In experimental research, it is essential that the bearing operation should be considered as the operation in the linear range.