Elsevier

Finite Elements in Analysis and Design

Volume 87, 15 September 2014, Pages 43-55
Finite Elements in Analysis and Design

Performance of hydrostatic tilted thrust pad bearings of various recess shapes operating with non-Newtonian lubricant

https://doi.org/10.1016/j.finel.2014.04.009Get rights and content

Highlights

  • Finite element formulation of non-Newtonian lubricant by using Galerkin׳s technique in thrust bearing.

  • An iterative non-linear FEM scheme is used to solve the Reynolds equation for thrust bearing.

  • Effect of tilt on the hydrostatic thrust pad bearing.

  • Performance characteristics of hydrostatic thrust bearing.

Abstract

Hydrostatic thrust bearings are an integral part of hydroelectric power stations. These bearings are usually designed to work under parallel operation, but tilt is inevitable due to manufacturing errors, assembly errors, structural vibrations and structural deformations. Owing to the advent of latest advancements in manufacturing techniques, any geometric shape of recess can be easily manufactured and the designer has a greater flexibility. The geometric shape of recess significantly affects the performance of a bearing. Therefore, the present study is aimed to numerically analyze the influence of the tilt and recess shape on the static and dynamic performance characteristics of the hydrostatic thrust pad bearing system having Rabinowitsch fluid model lubricant. The lubricant obeying Rabinowitsch fluid model with tilt makes the Reynolds equation highly non-linear therefore, finite element method is used to analyze. Three different types of recess shapes of equal area A¯b/A¯oc=4 have been analyzed to model hydrostatic thrust pad compensated by orifice compensator. The numerically simulated results indicate that the tilt angle significantly affects the dynamic and static characteristic parameters. The value of pocket pressure and fluid film reaction of a hydrostatic thrust pad bearing has been found to significantly decrease with tilt whereas the value of lubricant flow, fluid film stiffness coefficient and fluid damping coefficient increase with tilt.

Introduction

In hydropower plants, axial thrust coming from heavy machinery, turbines and generators is very large. To support the heavy axial thrust load with minimum friction, hydrostatic thrust bearings are widely used due to their ability to provide high load carrying capacity. Therefore, the design of hydrostatic thrust pad bearing system under realistic condition is quite important. Hydrostatic thrust pad bearings have been extensively investigated by many researchers during the last few decades and their research efforts, focused on various aspects of hydrostatic thrust pad bearing. The following paragraph details some of the important studies reported in literature.

In recent past, many investigations have been carried out and reported in the area of hydrostatic thrust bearing considering various issues. Osterle and Hughes [1] analyzed the effect of lubricant inertia on the performance of load carrying capacity of hydrostatic thrust bearing and it was found that the load carrying capacity of hydrostatic thrust bearing neglecting the effect of lubricant inertia had significant errors at high speeds, if the effect of lubricant inertia is neglected. Influence of flexibility of pad on the bearing performance was studied by Sinhasan et al. [2], [3], [4]. They computed performance characteristics of hydrostatic thrust bearing by considering different types of restrictor by considering the pad deformation.

In general the hydrostatic thrust pad bearing is designed to work under parallel operation, however, tilt in hydrostatic thrust pad bearing systems is inevitable due to manufacturing, assembly errors, structural vibrations, etc. Therefore, many researchers focused their study to analyzed the effect of tilt on the performance of thrust bearing [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]. Safar and Mote [15] analyzed the hydrostatic thrust bearing system operating with Newtonian lubricant under non-axisymmetric operation. In their analysis, they considered the effect of bearing number, the fluid film thickness variation and bearing offset on the bearing pressure, load carrying capacity and lubricant flow rate. Later on a study by Safar [6] reported semi analytical solution for the pressure distribution in tilted hydrostatic thrust pad bearing by using the series solution method. It was found that the tilt of hydrostatic thrust pad gave rise to negative fluid film pressures and this results cavitation. He further observed that the value of bearing characteristic parameters gets changed significantly by including tilt angle in the analysis. Prabhu and Ganesan [8] studied the effect of tilt and rotation on the performance of a multirecess plane hydrostatic thrust bearing. They studied a hydrostatic thrust bearing configuration with four sectorial type recesses. Studies related to hydrostatic thrust bearings by considering tilt have been carried out not only for the case of plane hydrostatic thrust bearing as well as for conical hydrostatic thrust bearing system [9], [16], [17]. Prabhu and Ganeshan [16] theoretically studied non-parallel operation of annular recess conical hydrostatic thrust bearing compensated with capillary under the tilt and rotation.

Due to the stringent requirements of modern machinery system, it is imperative to look for the enhancement in lubricating performance. A number of additive packages are generally mixed to achieve the desired lubricating performance. Addition of additives in the lubricant makes lubricant behavior non-Newtonian. To study the additized lubricant behavior, various non-Newtonian lubricant models such as Bingham plastic fluid [18], Cason models [19], micropolar [20], [21], [22] and power law [23] have been proposed. Among these models a non-Newtonian model named as Rabinowitsch fluid model was experimentally established by Wada and Hayashi [24], [25]. In their experimental study, they showed that the blending of additives improved the viscosity index of lubricant. After Wada and Hayashi, many researchers used this model in their studies [26], [27], [28]. Sinhasan and Sah [27] analyzed orifice compensated journal bearing system by using this model. They used finite element method and Newton Raphson iterative scheme to analyze the performance of journal bearing system. Very recently, Singh et al. [29] made use of this model in their study to analyze the effects of centrifugal inertia on the performance of annular ring hydrostatic thrust bearing. Lin [26] analyzed squeeze film characteristics of annular ring thrust bearing system with Rabinowitsch model lubricant. Closed form expressions for squeeze film load carrying capacity were derived after making approximations in Reynolds׳s equation.

The available studies in literature clearly reveals that consideration of both lubricant behavior as well as tilt is very important to generate the realistic design data [7], [26], [30], [31]. No study in the literature has yet been reported that demonstrates the behavior of thrust bearing operation with Rabinowitsch lubricant with tilt consideration. Recently, some studies have been carried out in the case of parallel operation thrust bearing by using Rabinowitsch fluid model. However, these studies are not practical as they ignored the effect of tilt. Thus, the present work has been planned to bridge this gap in the literature. The present work deals with a tilted pad hydrostatic thrust pad bearing operating with non-Newtonian lubricant. To analyze the effect of tilt, three different types of recess geometries have been chosen from the literature [32], [33]. Further, it has been found that the tilt of hydrostatic thrust pad significantly affects the static and dynamic performance characteristics parameters. The numerically simulated results presented in the paper are expected to be quite useful to the academic community and bearing designers.

Section snippets

Governing Reynolds equation

A schematic diagram of a hydrostatic thrust pad bearing system with tilt and compensated with orifice restrictor is shown in Fig. 1. The modified Reynolds equation governing the flow of non-Newtonian lubricant in bearing clearance space of a hydrostatic tilted pad thrust bearing shown in Fig. 1 is expressed in dimensionless as follows [27], [32].

Finite element formulation

The bearing performance characteristic parameters of a tilted pad thrust bearing operating with Rabinowitsch fluid model lubricant have been computed by obtaining the numerical solution of governing modified Reynolds equation. Therefore, a FEM program in MATLAB is developed to calculate performance characteristic parameters of a thrust bearing. Discretization of flow field for FEM calculation is done by using four-noded bilinear isoparametric quadrilateral elements. The fluid film pressure

Solution procedure

For the present case, Reynolds equation is non-linear in nature. Thus, a numerical simulation of Reynolds equation can be obtained by only numerical iterative methods. Therefore, an iterative solution procedure shown in Fig. 2 is applied with above formulation. The numerical procedure applied for the computation of static and dynamic performance characteristic parameters contain the following steps.

  • 1.

    Hydrostatic thrust pad bearing domain is discretized into the 4-noded quadrilateral isoparametric

Result and discussion

The solution algorithm as described in the flowchart is used to compute the performance characteristics of the thrust bearing system. The values of bearing geometric and operating parameters are judiciously chosen on the basis of the available published literature [6], [27], [32], [38]. To check the validity of the developed algorithm the simulated results are compared with the previously obtained result of hydrostatic thrust bearing. As stated earlier finite element formulation of thrust

Conclusions

In the present work, hydrostatic thrust pad bearing lubricated with Rabinowitsch fluid model, the influence of the tilt parameter having different geometric shapes of recesses on the static and dynamic performance characteristic is carried out. The modified Reynolds equation with tilt is solved by using an iterative FEM Formulation. On the basis of numerically simulated results following general conclusions have been drawn.

  • 1.

    The static and dynamic performance of a circular hydrostatic tilted

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