An approach of simulating journal bearings-gear pump system including components’ cavitation

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Abstract

The present study aims to solve a system-level problem regarding a journal bearings-gear pump based on a novel simulation model. The developed model consists of different modules: a fluid dynamic model for the pump, a lubrication model for the bearings, a model for the evaluation of shaft motion and a geometrical model. Cavitation models, i.e., the Jakobsson-Floberg-Olsson (JFO)-based model for bearing conformal contacts and the real liquid property model for the pump displacement chamber, are also integrated as submodels to obtain accurate cavitation results of the system. To acquire precise results, the bearing transient lubrication model includes the combined effect of the misalignment and surface roughness. These acquired solutions were based on Reynolds’ theory. The proposed model allows an analysis of the characteristics of the pump-bearing system, including the pump internal flow, bearings lubrication and components’ cavitation, which is applied to calculate the journal bearings-gear pump system used in an aero-engine.

Introduction

External gear pumps (EGPs) continue to be widely applied in aero-engines. The factors of success for this hydrostatic unit are reflected by its simplicity, efficiency and low cost. Following the hydrodynamic lubrication principle, the hydrodynamic journal bearing (HJB) is one of the key design units of EGPs. During the pump operation cycle, the gear shaft and bush are separated by a thin film between the shaft and HJB, which allows the shaft to rotate freely without metal-to-metal contact. Thus, the lubrication performance of HJBs is often one of the decisive factors in limiting the pump performance.

In rotodynamic pumps, cavitation is seen as an undesirable situation, which may cause many problems, such as noise, vibration, erosion and efficiency loss. To determine the hydraulic head loss of a pump, a well-known parameter, namely, the net positive suction head required (NPSHR), has been established [1] for several applications. An accurate numerical model of cavitating flows in rotodynamic pumps is essential. Over the years, several kinds of cavitation models have been proposed (Singhal et al. [2], Zwart et al. [3] and Schnerr et al. [4]) with application and validation [1,[5], [6], [7]]. In addition, the serious cavitation phenomenon in conformal contacts is also undesirable, which may cause an oil film oscillation [8]. While several studies regarding cavitation have been presented during the last decade, one of the major contributions came from Jakobsson, Floberg, and Olsson's published work [9,10]. Their theory, called JFO boundary, considers mass conservation on the film boundary and satisfies both accuracy and practicality; this theory has been widely used as a theoretical basis in cavitation numerical models. The most prominent studies of cavitation numerical modeling came from Elrod and Adams [11,12], who proposed the efficient numerical method for HJB cavitation. These models obeyed the physical laws of the JFO boundary and successfully embodied this theoretical improvement into the numerical simulation. The JFO-based mass-conserving cavitation algorithm shows its strong applicability, and examples of it can be found in [13], [14], [15], [16], [17] for journal bearings, in [18,19] for parallel bearings, in [20] for ring-liner conjunctions, in [21,22] for thrust bearings and in [23,24] for piston rings-liner.

Ideally, the shaft is widely considered parallel in bearing lubrication calculations. Nevertheless, this ideal situation rarely exists in rotation machines due to a multiplicity of factors, including manufacturing tolerances, installation errors and many elements during the operating cycle [25]. McKee et al. [26] made one of the first documented experimental observations that pointed out that the hydrodynamic pressure will be influenced by a misalignment; therefore, a misalignment bearing investigation is one of the subjects of experimental studies [27], [28], [29], [30]. In terms of numerical research, Vijayaraghavan and Keith presented the performance investigation of a grooved misaligned journal bearing considering cavitation [31,32]. Lahmar et al. [33] analyzed dynamically loaded engine main crankshaft bearings considering the misalignment effect. These researchers concluded that constant misalignment causes an obvious reduction in the film thickness, which should be considered carefully in bearing design. The static and dynamic characteristics were both investigated by Sharma et al. [34] considering the combined effect of misalignment and surface topography. Monmousseau and Fillon [35] studied the effects of misalignment on the static and dynamic characteristics of a tilting-pad journal bearing. These investigators pointed out that the bearing characteristics are directly related to the misalignment amplitude. Xu et al. [36] carried out a comprehensive analysis of the bearing performance with turbulent and thermo effects. Their study also indicated that misalignment may be detrimental to film generation. Jang and Khonsari [37] investigated the effect of wear on the bearing performance considering misalignment.

As one of the typical father components of journal bearings, the working principle of an external gear pump is uncomplicated: The fluid in the pump moves from the inlet to the outlet port during the gear rotating process, realizing fluid transfer. Due to the similar nature of the gear teeth, the gears stay at the same position at a certain angle. The flow pressure distribution varies periodically at a cycle in correspondence with the teeth number, which leads to periodic forces acting on the shaft. Subsequently, the periodic forces on the shaft cause changed shaft micromotion, film geometry, and lubrication characteristics. Regarding the EGPs in aero-engines, these forces have a high amplitude, which cannot be neglected in lubrication calculations. Thus, the lubrication problem of HJBs in an aero-engine EGP should be treated as a system-level problem. Castilla et al. [38,39] presented a novel method for journal bearing shaft movement in gear pumps with an experimental study. Pellegri et al. [40] established a computational fluid dynamics (CFD)-radial motion coupled model for EGP journal bearings, but their work did not consider the influence of cavitation. Du et al. [41] proposed a numerical analysis of journal bearing lubrication characteristics in a water hydraulic internal gear pump considering the effect of surface elastic deformation. To enhance the load support of the water film in the gap between the gear shaft and bush, Zhou et al. [42] investigated the influence of microshapes on gear pump journal bearings using an elastohydrodynamic model. Based on dynamic mesh techniques, Mo et al. [43,44] proposed a thermohydrodynamic calculation method for gear pump self-circulating bearings.

The simulation of the EGP-HJB system poses a major challenge because it involves a theory of different subjects, including lubrication, multiphase flow and rotodynamics. This paper presents an approach for solving this problem and details a methodology for solving the bearings lubrication problem and its coupling with the pump CFD model. Moreover, the cavitation models are integrated into the simulation framework to provide precise component cavitation analysis. This framework not only can be used to drive the designs of the lubrication and flow components but also allows a limitation in the pump conditions to avoid damage caused by severe wear or cavitation.

Section snippets

EGP-HJB simulation model details

A 3D model of the EGP-HJB system with a plane cross is depicted in Fig. 1, where the research components are highlighted. The input/output sample of the EGP-HJB simulation model can also be seen in Fig. 1. As represented in the figure, the proposed code has several main modules: the EGP CFD model, the film geometry model, the HJB lubrication model, and the model for the calculation of the gear shaft transient position and the geometrical model. To acquire precise results, the lubrication model

Results and discussion

In the current section, the results of the extensive sets of simulations for the HJB-EGP system are proposed. The specifications of the components are detailed in Table 1. Unless specified otherwise, these parameters are implemented in all simulations.

Conclusion

This paper presents a simulation framework to solve an engineering system-level problem for HJB-EGP based on lubrication and CFD simulation methods. As integrated submodels within this framework, different cavitation models are provided to enable an accurate representation of the cavitation in the system. The significant observations include the following:

  • 1.

    The results highlight the importance of the EGP influence on HJB lubrication. The maximum amplitude of the force fluctuation due to the gear

Funding

This work was supported by the National Science and Technology Major Project of China (grant no. 2017-V-0013-0065).

Declaration of Competing Interest

The authors declare that they have no conflict of interest.

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