Coupling analysis of tribological and dynamical behavior for a thermal turbulent fluid lubricated floating ring bearing-rotor system at ultra-high speeds

Highlights

• A transient calculation method for the thermal fluid-film pressure in FRB is developed.

• A coupling model of dynamics and tribology for the turbocharger rotor-FRB system is proposed.

• A numerical analysis of the lubrication calculation with nonlinear dynamics is presented.

• A speed region of fluid-induced instability strongly depends on the FRB clearances.

• A stable region is available to guarantee the high-speed operation of turbocharger rotor.

Abstract

The floating-ring bearing supported turbocharger rotor system generally reaches the speeds exceeding 100,000 rpm in high-temperature environment, but the risky sub-synchronous whirl, oscillation, bifurcation, and chaos probably appear due to its unsteady hydrodynamic forces with the high shear rate and low viscosity lubricant. From this perspective of coupling tribology and dynamics, the transient acting pressures at the thermal double fluid-film bearing are computed by employing the turbulent lubrication theory, then a numerical model for the whole rotor-bearing system based on the transfer matrix method is developed to investigate its nonlinear vibration behavior. The results show that an “interval region” characterized by the synchronous unbalance vibration is available to avoid fluid-induced instability of this system at different high-speed requirements.

Introduction

Exhaust gas turbocharging has become a critical technique for improving the air intake capacity of engines to enhance the power and torque [1], [2]. The diesel engine, petrol engine or aeroengine equipped with a turbocharger can increase its maximum power by 40% or more compared with traditional engine devices [3]. In general, the turbocharger rotor mainly consists of three parts: the compressor impeller, the turbine impeller, and the common shaft supported by hydrodynamic lubricated bearings (Fig. 1). As the rotor system is required to operate at ultra-high speeds (generally between 100,000 to 300,000 rpm) with high reliability, the full floating-ring bearing (FRB) with two fluid films have been widely adopted in turbochargers [4], [5]. Compared with conventional single oil-film bearings [6], the main advantage of floating-ring bearings is their improved interactive damping action based on the double oil film [7], which can effectively suppress the resonant vibration and reduce friction losses [8], [9]. However, the oil-film instability characterized by the sub-synchronous whirl/whip motion of the journal or ring remains a potential risk factor [10], which will not only induce discordant vibration noise and fatigue failure of rotors [11], [12], but also reduce the running efficiency and effective life of turbochargers [13]. Therefore, designing a reasonable mathematical model and researching the dynamic characteristics for the turbocharger bearing-rotor system have scientific theory significance and engineering application value [14].

According to the oil-film force model for finite journal bearings, M. Tanaka and Y. Hori [15] investigated the dynamic behaviors of floating-ring bearing with double oil film combined with experiments; they proposed that the floating-ring bearing was more stable than the traditional bearing with single oil film. Based on the short bearing theory, LaRue. G [16] examined the vibration characteristics of the the turbocharger rotor system with double oil film, and verified that several different sub-synchronous frequency responses would appear in the operating speed range. Based on the linear oil-film force model, R.G. Kirk [17], [18] adopted a commercial calculating program for rotordynamics to predict the steady and transient kinetic phenomena of turbocharger rotor system, and the resulting spectrum composition of oil whirl was found to be in accordance with the experimental result. B. Schweizer et al. [19], [20] presented that the vibration of turbocharger rotor-FRB system was composed of three different sub-synchronous frequencies, which could be converted to one another at different working conditions. Combining transient run-up simulation and gyroscopic eigenvalue analysis, they also also found the evidence that the vibration amplitude and bearing eccentricity distinctly enlarges when the sub-synchronous responses approached the resonance state of the inner or outer oil film. On the basis of the nonlinear short bearing model, L. Tian et al. [21], [22] investigated the influence of the FRB clearances on the dynamic characteristics of the turbocharger rotor through the transient simulation. They thought that the linear analysis method could only predict the instability speeds of the first two stages, and increasing the bearing outer clearance could effectively avoid resonance. Dyk et al. [23] provided a general analytical solution of hydrodynamic force improved by correction polynomials. However, their results which overlooked the non-Newtonian fluid and viscosity-temperature effects at high speeds, were somewhat different from the actual situations.

Synthesizing the above studies, the dynamic characteristics of turbocharger rotor has been plentifully explored, but the nonlinear models of oil-film force or the nonlinear dynamics analysis methods was not executed effectively. For the floating-ring bearings supported turbocharger rotor in the high-speed and high-temperature environment, complicated dynamics phenomena [7], [24] including self-excited vibration, jumping, oil whirl/whip and chaos might inevitably occur due to the unsteady fluid-film forces. The traditional linear or simplified models for oil-film force proposed previously [2], [18], [21], [25], [26], such as the application of eight linearized stiffness and damping coefficients or the theory for short/wide/finite length bearing, has been difficult to be in consistent with the nonlinear characteristics of high-speed rotor in experiments [27], [28]. By applying the finite difference method (FDM) to calculate the transient pressure distribution of double fluid film based on the turbulent lubrication theory considering the thermal effect, this paper developed a nonlinear oil-film force model for a FRB through Simpson integration. On this foundation, D′Alembert principle and the transfer matrix method were adopted to establish the nonlinear dynamical differential equations for the flexible turbocharger rotor considering the imbalance effect induced by impellers. Consequently, this work describes a coupling model of dynamics and tribology for the turbocharger bearing-rotor system. The numerical methods in nonlinear dynamics such as phase portrait, Poincare mapping, bifurcation diagram and frequency-response spectrum are then adopted to analyze the stability characteristics of this system vibration, providing theoretical support for the design of turbocharger bearing-rotor system.