Wear identification in rotor-bearing systems by measurements of dynamic bearing characteristics

https://doi.org/10.1016/j.compstruc.2010.08.006Get rights and content

Abstract

During operation of rotating machines, journal and bearing mechanisms are progressively worn down. To prevent catastrophic failure of a rotating system, it is necessary both to detect wear precisely, without shutting down and dismantling the machinery and to predict future replacement needs. In this work, Computational Fluid Dynamics (CFD) analysis is used to solve the Navier–Stokes equations. Diagrams of bearing characteristics such as relative eccentricity, attitude angle, lubricant side flow and friction coefficient versus Sommerfeld number are presented for various wear depths and used for online wear identification. A graphical detection method is analytically presented to identify the wear depth associated with the measured dynamic bearing characteristics.

Introduction

In rotor-bearing systems, a topic of high interest is knowledge of bearing condition, which affects the dynamic behavior as well as the stability of the system and the ability of control. The wear on the bearing material during operation of the system causes changes in the bearing clearance and, therefore, a change in other dynamic characteristics of both the bearings and rotor.

Hydrodynamic journal bearings, which support rotating shafts over a long period of time, are the cause of significant wear in bearing surfaces. Therefore, identification of wear under certain bearing and rotor operating conditions is of great importance.

Worn bearing behavior has been examined by many investigators both for a number of reasons and as a result of various concerns. This work presents the state of the art concerning the behavior of worn bearings and selected papers reviewed here discuss use of the linear Archard’s model to predict wear in several mechanical systems.

The onset and development of wear in plain hydrodynamic journal bearings under repeated stop/start cycles have been studied experimentally by Mokhtar [1]. The wear that occurred was easily discernable, but localized changes in diametric clearance, surface finish and roundness of the bearing bore were measured after varying numbers of operating cycles had been completed. A study of the wear location within the bearings showed that it was caused entirely by the sliding motion that occurred during startup and that no significant contribution to the wear process was a result of shutdown. This group also observed that, once an initial rapid phase of wear was completed, the surface finish of the hardened steel shaft was reproduced in regions of the surface of the bearing subjected to continued wear.

Dufrane et al. [2] investigated wear in steam turbines and took measurements during overhaul periods to determine the extent and nature of the wear. They established two models of wear geometry for use in further analysis of the effect of wear on hydrodynamic lubrication. These wear models are not of circular type. The first of the proposed models is based on the concept of imprinting in the bearing and the second one is based on a hypothetical abrasive wear model with the worn arc at a radius larger than the journal.

Hashimoto et al. [3] theoretically and experimentally investigated the effects of geometric change due to wear on the hydrodynamic lubrication of journal bearings in both laminar and turbulent regimes. The steady-state characteristics of the bearings, such as film pressure, attitude angle and Sommerfeld number, were analyzed by a semi-analytical finite element method for various wear depth parameters and the theoretical results were compared with the experimental results. It was found that the geometric change due to wear has significant effects on the steady-state characteristics in both laminar and turbulent regimes. Good agreement between the theoretical and experimental results was observed in their work.

The performance characteristics of worn journal bearings in both laminar and turbulent flow regimes have been related to the dynamic characteristics of the bearing in the work of Hashimoto et al. [4]. Vaidyanathan and Keith [5] numerically analyzed the characteristics of noncircular bearings while considering the effects of turbulence and cavitation. Kumar and Mishra [6] numerically investigated the effects of geometric change due to wear on stability of hydrodynamic turbulent journal bearings, following Constantinescu’s turbulent lubrication theory and they drew stability curves for various values of wear depth parameter with the consideration of turbulence. They concluded that wear causes deterioration of the rotor stability in the case of lightly loaded bearings and in the case of worn bearings, a lower L/D ratio gives better stability.

Ligterink and de Gee [7] discussed the measurement of wear in radial journal bearings, where a distinction is made between stationary and non-stationary contact conditions. They began with Holm/Archard’s wear law and then derived the equations for calculation of the specific wear rate k of the bearing material as a function of the wear depth d0 as measured after an experiment or a period of use in practice. Fillon and Bouyer [8] presented the thermo-hydrodynamic performance of a worn plain journal bearing. Their study deals with a 100 mm diameter bearing submitted to a static load varying from 5000 to 30,000 N, with a rotational speed varying from 1000 to 10,000 rpm. The defects caused by wear are centered on the load line and range from 10% to 50% of the bearing radial clearance. The main focus was on hydrodynamic pressure, temperature distributions at the film/bush interface, oil flow rate, power losses and film thickness. They observed that defects caused by wear of up to 20% had little influence on bearing performance, whereas above this value (30–50%), the wear may display an interesting advantage: a significant fall in temperature due to the tendency of the journal to operate in the footprint created by the wear. They concluded that the worn bearing presents not only some disadvantages but also advantages, such as lower temperature. In certain cases of significant defects due to wear, the geometry approaches that of a lobe bearing.

Bouyer et al. [9] investigated the behavior of two lobe journal bearings subjected to numerous startup and shutdown cycles. During transient periods, direct contact between the journal and bearing induces high friction in the lubricated contact and subsequently results in wear of the lining. The aim of their work was first to present experimental data obtained on a lobed journal bearing subjected to numerous start/stop cycles and also the comparisons between the measured bearing performance and numerical results obtained under the assumption of a thermo-hydrodynamic regime. It was observed that hydrodynamic pressure increases while the temperature at the film/bush interface slightly decreases on both the upper and lower lobes.

Awasthi et al. [10] presented an analytical study in which they attempted to replicate the performance of a worn non-recessed (hole entry) capillary-compensated hybrid journal-bearing system. The authors used finite element analysis to solve the Reynolds equation governing the flow of lubricant in the bearing clearance space (along with the restrictor flow equation) using a suitable iterative technique. The results indicate that wear affects the bearing performance considerably; therefore, due consideration of wear defects should be given for an accurate prediction of the bearing performance over a number of cycles. The computed results further indicate that the influence of wear defects on journal bearing performance may be minimized if the designer selects a suitable bearing configuration.

The total load on a crank bearing was calculated by Han et al. [11] via performance of a load analysis of the crank connecting rod mechanism. The Reynolds equation for hydrodynamic lubrication of the crank bearing was established at the Reynolds boundary condition and was then solved using the Holland method. In their experiments, they showed that the wear condition of the crank bearing could be identified correctly through the vibration signature at the natural frequencies of the connecting rod. The degree of wear can be predicted accurately through the energy content of the high frequency bands.

Papadopoulos et al. [12] presented a theoretical identification method for the bearing radial clearances using response measurements of the rotor at a particular point (usually the midpoint of the rotor). These “measurements” should be taken at two different speeds and from different wear effects. The sum of the squares of the differences between the measured and the computed responses at the abovementioned particular point for two different speeds is used as an objective function to be minimized. The stability of the system as a function of the rotational speed and the wear is also examined. They modeled the rotor using the finite element method with four degrees of freedoms per node, including the gyroscopic effect. The dynamic coefficients of the bearing are calculated by solving the Reynolds equation, thus obtaining the pressure distribution of the oil film and by finding the equilibrium position. The 4 × 4 stiffness and damping matrices, including the force–moment and displacement–rotation relations with all non-diagonal coupling terms, are taken into account for the analysis.

Nikolakopoulos et al. [13] presented an analytical model in order to find the relationship among the friction force, the misalignment angles and wear depth. The Reynolds equation is solved numerically and the friction force is calculated in the equilibrium position. The friction coefficient is presented versus the misalignment angles and wear depths for different Sommerfeld numbers, thus creating friction functions dependent on misalignment and wear of the bearing. The variation in power loss of the rotor-bearing system is also investigated and presented as a function of wear depth and misalignment angles.

The solution of the problem of unequal and non-uniform wear of a sea-water lubricated bearing made of elastomeric compounds and used in a propeller shaft system via a mixed lubrication analysis has been attempted by Hirani and Verma [14]. Computer code was written to estimate the lubricating film thickness for a given set of load and speed conditions and to predict the lubrication regime for the specified surface roughness parameters. To understand the uneven wear of marine bearings, actual geometric clearances of new and worn bearings are listed in the paper, as recorded by the ship maintenance team and the operational data (load, speed and operating hours) obtained from the logbooks of ICGS Sangram (AOPV) of the Indian Coast Guard. The dynamic viscosity of sea water, surface roughness of propeller shaft and bearings and particulate contamination has been measured. Finally, suggestions have been enlisted for proper operation of a shaft-bearing system in order to maintain the wear within the permissible limits during the ship’s operational cycle.

In his wear experiments, Archard [15] indicated that the wear rate is proportional to the load and the results can be explained by assuming removal of lumps at contact areas formed by plastic deformation. Põdra and Andersson [16] presented a wear simulation approach using the commercial finite element (FE) software ANSYS. A modeling and simulation procedure is proposed and used with the linear Archard’s wear law and the Euler integration scheme. A spherical un-lubricated pin-on-disc steel contact was analyzed both experimentally and with FEM and the Lim and Ashby wear map was used to identify the wear mechanism. It was shown that the FEM wear simulation results from a given geometry and loading can be treated on the basis of the equivalence of wear coefficient-sliding distance change. The finite element software ANSYS was used for solution of contact problems as well as the wear simulation. The actual scatter of the wear coefficient was within the limits of ±40–60%, which led to considerable deviation of the wear simulation results. These results must therefore be evaluated on a relative scale to compare different design options.

Kim et al. [17] presented a numerical approach that simulates the progressive accumulation of wear in oscillating metal-on-metal contacts. The approach uses a reciprocating pin-on-disc tribometer to measure wear rate for the material pair of interest. This wear rate is used as an input to a finite element analysis that simulates a block-on-ring experiment. After the simulation, two block-on-ring experiments were performed with the same materials studied in the reciprocating pin-on-disc experiments. The results from the finite element analysis were in close agreement with the block-on-ring experimental results. Hegadekatte et al. [18] presented a very efficient incremental implementation of Archard’s wear model on the global scale for pin wear and disc wear in a pin-on-disc tribometer. Their results from the model are in good agreement with experimental results. The identified wear model is implemented in a finite element based tool (Wear-Processor) for 3D wear simulations and the results compare favorably with that from the global wear modeling scheme. The study of wear in complex micro-mechanical components is often accomplished experimentally using a pin-on-disc and twin-disc tribometer. The paper by Hegadekatte et al. [19] propose an approach that involves a computationally efficient incremental implementation of Archard’s wear model on the global scale for modeling of sliding and slipping wear in pin-on-disc and twin-disc tribometer experiments. It was shown that the proposed approach has potential for use in predicting wear and the effective life span of any general tribosystem using the identified wear coefficient from relevant tribometry data. Wu et al. [20] experimentally monitored the wear condition of a journal bearing with an On-Line Visual Ferrograph system. The round bearing was made of 45# steel with a Babbitt alloy bushing and the bearing journal was made of 45# steel. High levels of stress from water content of 0%, 1% and 3% in lubricant, ten times the normal load of 2200 N and rotating speeds at 500, 1000 and 2000 rpm were adopted in an accelerated experiment. They concluded that the corresponding dominant wear mechanisms were that of micro-plowing and micro-cutting induced by rough initial surfaces in the run-in stage, local rubbing due to vibration in the normal stage and fatigue and abrasive wear in the failure initiation stage.

There are several methods presented in the literature for torque measurement of the journal. Friction loss has been typically determined based on measurements of torque caused by the friction. Del Din and Kassfeldt [21] used a lever arm equipped with strain gauges to measure friction torque in test rig experiments performed to study wear characteristics under mixed lubrication conditions in a journal. Brito et al. [22] used a static torque sensor to measure the torque applied to a bushing surrounding the bearing. They calculated the friction loss as a function of the bush torque, applied load, shaft eccentricity, attitude angle and angular velocity.

This work is a theoretical approach. The proposed method is applied for the wear depth detection, supposing that the resultant friction torque has been measured by one of the methods presented.

The current paper is an updated and revised version of a conference paper [23] and presents a general methodology for online prediction of the wear depth using bearing performance characteristic measurements. The basic bearing characteristics, such as eccentricity, attitude angle, hydrodynamic friction and side oil flow, are calculated as a function of several wear depths using the FLUENT CFD package. Archard’s model is also used to predict the wear depth progress when the journal is in full contact with the bearing pad. The developed model can be used for online identification of the wear depth based on a graphical method that can be applied during operation of rotating machines. This model presupposes measurements and accurate numerical calculations of the eccentricity, attitude angle and side oil flow and friction coefficient in order to predict the wear depth of the bearing. All of the aforementioned bearing parameters can be accurately calculated with the developed methodology in the present paper.

Despite the wide use of wear-resistant material and the fact that wear becomes smaller with time, the use of instruments with high sensitivity in real machines gives the ability to obtain accurate online measurements, making the present methodology very attractive for online wear identification.

Section snippets

Bearing model formulation

In this paper, the bearing is considered as rigid rather than as elastic because the wear is the main issue. The journal bearing is assumed to operate in the steady-state condition, the flow is chosen as laminar and an isothermal regime is also assumed.

The geometry of the worn bearing follows the model introduced by Dufrane et al. [2] and is shown in Fig. 1, where, Ob and Oj are the bearing and journal centers, Rb and Rj are the bearing and the journal radius, e is the bearing eccentricity, L

Wear mechanisms and Archard’s Model

Due to the complexity of the wear process, no general equations exist for characterizing all types of wear. However, for adhesive and abrasive wear, Archard’s [15] equation has been proven to characterize these two main wear mechanisms quite well. Adhesive wear occurs when two solid surfaces slide over one another under pressure, whether lubricated or not and is formed due to localized bonding between contacting solid surfaces leading to material transfer between the two surfaces or the loss

Wear detection

Wear can take place at every phase in the lifetime of parts or machine elements, including manufacturing, operational or maintenance processes and plays an important role in determining the life span of machine elements. Therefore, timely detection of wear is highly sought after in many applications in order to predict remaining life of elements, avoid further and more extensive damage to the whole system, safeguard product reliability and reduce potential cost.

The detection method presented in

Variation of bearing performance with Sommerfeld number and wear depth

In order to obtain results, we used the geometrical and operational data of the experimental apparatus presented in Ref. [3] to validate our CFD code. The bearing diameter Rb and the bearing length L are 70 mm, so the L/D ration is 1.0, where D is the shaft diameter. The radial clearance c is 287 μm and the maximum wear depth δ0 takes the maximum value 0.5. The shaft rotates with rotational speed N at 16.67 rps or 1000 rpm. The oil viscosity μ, is 14 mPa s at 25 °C and the density ρ is 900 kg/m3. The

Conclusions

Rotor-bearing systems are very complex structures and the wear of the bearing may drive the structure to catastrophic failure. In this paper, a general methodology was developed in order to identify the wear depth of the journal bearings. The method is based on basic bearing performance characteristic measurements for certain bearing operational conditions. FLUENT software was used to solve the continuity and momentum conservation equations.

The eccentricity ratio, attitude angle, friction

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