Predictive capability of various linearization approaches for floating-ring bearings in nonlinear dynamics of turbochargers

Abstract

A floating-ring bearing (FRB) is composed of a journal, a floating ring and a housing which are separated by two thin oil films. This system is inherently nonlinear and if it is lightly loaded or operated at high speeds, it is prone to the fluid-induced instability. The threshold speed for the instability of a journal bearing with one oil film can be estimated using linearized forces acting in the film. However, the linear analysis of FRB might be problematic because results of such an analysis are usually difficult to interpret. Nevertheless, the linear analysis can provide some fundamental insights into system behaviour. This work aims to evaluate in detail the use of linear theory in the stability analysis of rotating systems supported on FRBs. Several approaches for the linearization of the forces acting in FRB are proposed and analysed. The results are visualized in the form of a holistic Campbell diagram which together depicts natural frequencies, whirl frequencies, modal damping and precession of mode shapes. Moreover, it is demonstrated that the holistic Campbell diagram can be used to interpret-and to some extent, also to predict-results of nonlinear analysis.

Performance of Relative Clearance Ratio of Floating Ring Bearing for Turbocharger-Rotor System Stability

“…Based on the mathematical model of the above Formulas (1), ( 2), ( 6) and ( 9), the parameters were taken into dimensionless equations, using the standard four-order Runge-Kutta method to perform numerical calculation. The structure parameters of the floating ring bearing-rotor system and floating ring used in this study are shown in Tables 1 and 2, which are derived from references [4,5]. The relative clearance value is the ratio of the oil-film clearance value and the shaft radius in the floating ring bearing.…”

“…This work aims to evaluate dimension parameters of FRB in the stability analysis of rotating systems supported by FRB. For the dynamic problems of floating ring bearings, researchers have proposed several simplified linear methods to analyze the dynamic characteristics of bearings [5]. The multi-scale finite-element method is used to establish the dynamic model of floating ring bearings, in which paper, the calculation results are compared with the test results to verify its correctness.…”

An Algebraic Approach for Identification of Rotordynamic Parameters in Bearings with Linearized Force Coefficients

“…Furthermore, the obtained results for both cases, constant and variable rotor-bearing velocity, show a transient state of the identifiers before the convergence to the estimated values of stiffness and damping bearing parameters. This behavior is due to the sample time used in the numerical simulations of the identifiers for solving the iterated integrals of Equations ( 15) and (24), which utilize the trapezoidal rule. According to Kharab and Guenther [41], this method presents major calculation errors in comparison with other integration methods.…”

“…These linear force coefficients are derived from the assumption of small amplitude motions about an equilibrium position [22] and have been used to study the dynamic responses and analyze the stability of rotor systems supported by oil-lubricated tilting-pad bearings, cylindrical bearings and foil bearings, as pointed out in [23] and references within. Recently, Dyk et al [24] presented diverse linearization methods in the stability analysis of rotating systems supported on floating ring bearing (FRBs), demonstrating the usefulness of the linear force coefficients to predict the dynamic behavior of non-linear systems such as turbochargers supported by FRBs.…”

The Influence of Ring‐Speed Ratio Dynamic Change on Nonlinear Vibration Response of High‐Speed Turbocharger Rotor System

“…Peixoto et al [18] studied the influence of temperature on vibration characteristics of the turbocharger rotor system. Dyk et al [19] proposed and analyzed several linearization methods of forces acting on floating ring bearings and proved the nonlinear vibration of the rotor system in combination with campbell diagram. Yongfeng et al [20] used the polynomial chaos expansion method to describe the uncertainty of hollow shaft cracked rotor system.…”