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Tribological study of elastomeric bearings for marine propeller shaft system
ARTICLE IN PRESS Tribology International 42 (2009) 378–390
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Tribological study of elastomeric bearings for marine propeller shaft system Harish Hirani , Manish Verma Department of Mechanical Engineering, IIT Bombay, Powai, Mumbai, Maharashtra 400076, India
a r t i c l e in f o
a b s t r a c t
Article history: Received 6 August 2007 Received in revised form 18 July 2008 Accepted 29 July 2008 Available online 16 September 2008
Elastomeric compounds, due to their favourable properties like sufficient hardness, toughness and natural resistance to abrasion and corrosion, are commonly used as bearing material for propeller shaft system of Indian Coast Guard Ships. Recently unequal and non-uniform wear of these bearings has resulted in unscheduled lay off of the Coast Guard Ships. To solve this problem of bearing wear, a mixed lubrication analysis of sea-water lubricated journal bearing has been attempted in the present study. A computer code was written to estimate lubricating film thickness for a given set of load and speed condition, and to predict the lubrication regime for the specified surface roughness parameters. To validate the theoretical analysis performed in the present study, the results obtained from the computer simulation have been compared with the established studies on the water lubricated bearing. To understand the uneven wear of marine bearings, actual geometric clearances of new and worn out bearings recorded by the ship maintenance team, and the operational data (load, speed and operating hours), obtained from the log books of ICGS Sangram (AOPV) of Indian Coast Guard, are listed in the present paper. The dynamic viscosity of sea water, surface roughness of propeller shaft and bearings, and particulate contamination has been measured. Finally, the suggestions have been enlisted for proper operation of shaft-bearing system so as to maintain the wear within the permissible limits during ship’s operational cycle. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Marine shaft bearing Fluid film thickness Coefficient of wear Bearing life
1. Introduction Indian Coast Guard’s Advanced Offshore Patrol Vessels (AOPVs) are fitted with twin propeller shafts, each powered with 6400 HP engine. Each propeller shaft is 24 m long, weighs 10 tons and rotates inside four elastomeric journal bearings which are lubricated with sea water. These bearings are plain in lower half and grooved in upper half as shown in Fig. 1. Fig. 2 shows the propeller shaft supported in four elastomeric bearings. Dimensional details of these bearings are mentioned in Table 1. In addition, Table 1 lists the bearing reactions which are taken from Ref. [1]. Recently excessive wear of these bearings has resulted in unscheduled lay off of the Coast Guard Ships. First ship, ICGS Samar, commissioned in 1995 had successive bearing failure on both the shafts during two operational cycles (period between two successive dockings). ICGS Sangram, commissioned in 1997 had similar failure in both the shafts on two operational cycles and one shaft (port) in one operational cycle. Similar failures were seen in ICGS Sarang which was commissioned in
Corresponding author. Tel.: +91 222 576 7535; fax: +91 222 572 6875.
E-mail address: [email protected] (H. Hirani). 0301-679X/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2008.07.014
1999. The aim of the present study is to analyse this problem of bearing wear, and suggests a remedial action. Wear down of a water lubricated elastomeric bearing is an obvious phenomenon. However, elastomeric bearings used in all three ships (ICGS Samar, Sangram, and Sarang) were specially designed and fabricated (by Thordon bearings Inc.). In one lab (David Taylor Research Centre, Bethesda, MD) test, bearing wear of 0.002 in (0.051 mm) was observed in over 2000 working hours of propeller shaft running at 10 rpm against designed elastomeric bearing. Expected life of such a bearing is more than 20 years and replacement of bearings after wear depth of 4.7 mm is recommended. However, elementary moment analysis [1] reveals that wearing of bearing 4 redistributes the load, as listed in Table 1, among bearings. As per the gearbox manufacturer, the load ratio force on bearing 5=force on bearing 6 should not exceed 1.3. This constraint is imposed to restrict the impact loading on gear pairs. At the design stage this ratio was 1.1145 (F5/F6 ¼ 182906/164109). However, after 0.3 mm wear of bearing 4, load ratio (F5/F6) increases to (206 453/147401) to 1.4. Therefore, there is a need to review and establish a new limit on bearing wear for the replacement of elastomeric bearings compared to believing on the limit of 4.7 mm wear depth suggested by bearing manufacturer.
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Symbols and notations C radial clearance, m D journal diameter, m H; HPmax non-dimensional film thickness, film thickness at maximum pressure location h depth of wear, m h0 minimum thickness of fluid film, m h¯ EHL film thickness, m effective film thickness, m ht K empirical wear factor or Archard’s wear coefficient L bearing length, m N journal rotational speed, rpm P bearing pressure W/(LD), Pa Pmax maximum pressure, Pa pf fluid pressure (percent of total pressure) pa asperity pressure (percent of total pressure) R journal radius, m S sliding distance, m t tilt ratio or non-dimensional tilt, t ¼ m/C,
Bearing wear can be completely avoided by establishing the hydrodynamic lubrication mechanism in water lubricated journal bearings. However, the bearing wear observed in the present study indicates that bearings were operated under mixed and/or boundary lubricated regimes. One possible reason of mixed lubrication condition is that all patrol vessels, fitted with two engines, operate with single engine during patrol. Under such conditions, the idling shaft speed, which (due to propulsion of the motoring shaft) ranges between 50 and 70 rpm, may be insufficient to form hydrodynamic film. To understand this bearing wear problem, a mixed lubrication analysis of sea-water lubricated journal bearing is required. Further, to streamline the analysis, answers to the following questions are essential: (a) Is hydrodynamic fluid film not getting formed due to: (i) Low rpm operations and/or (ii) Increased radial clearance (b) What are the implications of increased radial clearance of bearings? (c) What is the regime of lubrication in which the bearing operates with the increased radial clearance at a given rpm? (d) What is the effect of particulate contamination in sea water? Is it responsible for abrasive and erosive wear of bearing surface? (e) What is the effect of surface roughness of bearing and shaft sleeve? (f) What is the effect of viscosity of sea water? Is it changing with rpm and temperature? (g) Is it possible to control the wear by changing the dimensions of bearing and shaft? In the present study a systematic design methodology has been employed to answer the abovementioned questions and suggest a suitable remedy to avoid bearing wear in the future. 2. Literature survey To understand the theoretical aspects of journal bearing operation two books, ‘Engineering Tribology’ by Stachowiak and Batchelor [2], and ‘Applied Tribology’ by Khonsari and Booser [3] were referred. Hirani et al. [4] have used two pressure correction
379
T U V W We, Wf
operating time, s journal surface velocity, m/s wear volume, m3 dimensional load capacity, N dimensional load capacity along and perpendicular to line of centres, N WZ ratio of dimensional load capacity to viscosity, m2/s WeZ, WfZ ratio of We, Wf to viscosity, m2/s z coordinate in axial direction, m gO, gS pressure correction factors for Ocvirk’s and Sommerfield bearings L slenderness ratio (L/D) e eccentricity ratio f attitude angle, radian Z viscosity coefficient of lubricant, Pa s y coordinate in circumferential direction, radian sA surface roughness of bearing surface, mm sB surface roughness of shaft sleeve surface, mm s combined roughness of two surfaces, mm l film thickness parameter
factors go and gs to give an analytical expression for maximum pressure. The design table [4] listed in their paper can be used to find out film thickness, pressure and load carrying capacity. However, the formulations in their paper [4] pertained to hydrodynamic lubrication regime only. Johnson et al. [5] have stipulated that provided a major part of the load is carried by elastohydrodynamic action, the separation between the two rough surfaces is given by the film thickness which would exist between two smooth surfaces under the same conditions of load, speed and lubricant. Kraker et al. [6] have described a mixed EHL model for finite length elastic journal bearings. These authors have used commercially available finite element code SEPRAN to discretise the Reynolds equation. Bayer [7] has provided algebraic expression for calculation of depth of bearing wear under aligned and misaligned journal conditions. Messimo Del Din et al. [8] have used an experimental set up to investigate the utility of environmentally adapted rape seed–synthetic ester oil over traditional mineral oil. The wear measurements evaluate the coefficient of wear using Archard’s equation of wear. The methodology discussed in the paper pertains to experimental measurement of wear by difference in weight of bearing liner before and after the experiment and compares two different oils. Hsu et al. [9] have given a comprehensive view of wear under lubricated conditions. As per these authors wear under lubricated conditions can be classified into two main classes: welllubricated systems and marginal lubricated systems. However, the methodology to determine wear is again experimental in nature. Rao and Mohanram [10] have presented comprehensive sets of experiments to study mixed lubrication of journal bearings. The surface topography changes have been statistically analysed. Safar [11] has presented an analysis of a journal bearing describing a maximum allowable value of misalignment at a length to diameter ratio of unity. The author has opined that journal misalignment influences load carrying capacity of the bearing. A misaligned bearing consumes more power due to friction than an aligned one. El-Butch and Ashour [12] have dealt with analysing the performance of a misaligned tilting-pad journal bearing under transient loading condition. Jakeman [13] has presented a model specifically intended to represent the dynamically misaligned sterntube bearing, for the purpose of conducting lateral vibration analyses of marine propeller shafting. The methodologies presented in these papers have been duly taken into account while carrying out the present study.
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(d) Asperity and fluid pressure ratio given by Johnson et al. [5] have been used and correlated with regime of lubrication.
3.1. Derivation of pressure expression The closed form solution to Reynolds equation, for infinitely short bearing (Ockvirk’s solution) and infinitely long bearing (Sommerfeld solution) is combined using two correction factors go and gs to approximate the analytical expression for pressure for a finite bearing [3]. The formulations, given in the design table have been arrived at considering hydrodynamic lubrication regime. Misalignment factor has been provided in the film thickness expression. In misaligned shaft, critical minimum film thickness will occur at the edge of the bearing, as shown in Fig. 3a. The basic parameter to describe the tilt of the shaft is the tilt ratio given by t¼
m C
(1)
Where t is the tilt ratio or non-dimensional tilt, m is the distance between the axes of the tilted and non-tilted shaft measured at the edges of the bearing and C is the radial clearance. Accordingly, expression for non-dimensional film thickness H ( ¼ h0/C) was modified as zt cos y (2) H ¼1þ L where Z is the axial coordinate and L the length of bearing and h0 the minimum film thickness between smooth surfaces. The analytical pressure terms given by Ockvirk and Sommerfeld viz PO and PS and modified with two correction factors go and gs [3] is given by 1 gO gS ¼ þ P PO PS
(3)
where go and gs are given by [3] 5
g O ¼ 1 þ L1:2 ½e 1 3
g S ¼ eð1Þ
Fig. 1. Bearing with housing.
3. Approach for analysis of journal bearing parameters The following approaches have been adopted: (a) Reynolds equation, simplified for unidirectional velocity approximation [2,3], has been used. Expression for film thickness given in the design table of Hirani et al. [4] modified to take care of the misalignment. (b) Elastohydrodynamic lubrication film thickness and surface roughness parameter have been incorporated to predict the regime of lubrication. With the given load, rpm and radial clearance each bearing’s film thickness, regime of lubrication and asperity to fluid pressure ratio has been calculated using available formulations. The results have been compared with similar study carried out by Kraker et al. [6] to validate the approach. (c) Wear model based on boundary lubrication regime has been used to assess the depth of wear and associated life of bearing [7].
(4) (5)
where L ¼ L=D, is slenderness ratio. To validate the proposed analytical approach, bearing data given by Sun and Changlin [14] have been used to obtain and plot the pressure profile at various angular misalignments. Pressure profiles shown in Figs. 3b–e are comparable to pressure profiles provided in Ref. [14]. Sun and Changlin used finite-difference method to obtained pressure profile. Further, a comparative study between the values of maximum pressure obtained using the present analytical approach and finite-difference method is listed in Table 2. These graphical and tabular results indicate that the proposed analytical approach can be used to analyze misaligned hydrodynamic journal bearing. 3.2. EHL film thickness and surface roughness parameter The elastomeric water lubricated bearing may experience elastic deformation [6]. Kraker et al. [6] described a mixed elastohydrodynamic lubrication (EHL) model for finite length elastic journal bearing. They employed the finite element method to solve the coupled system of fluid and structural equations to compute Stribeck curves at constant load. In the present study, an analytical approach has been used to evaluate pressure profile and minimum film thickness. To incorporate elastohydrodynamic model and compare the results with Kracker et al. [6], the EHL film thickness in transverse direction (relevant to the present
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Propeller Weight
UDL 4KN/m
Mech. Seal
Gearbox
6
5
PROPELLER
4
40 KN
SHAFT
2
3 6m
6m
1 6m
Fig. 2. Propeller shaft with bearings: (a) Coast Guard Ship in Dry dock, (b) shaft withdrawn and showing location of bearings and (c) schematic of propeller shaft with bearings.
surfaces s is given by (s2A+s2B)0.5. The surface roughness parameter l is calculated to ascertain the regime of lubrication.
study) is obtained using [5] " h ¼ h0
# 7 s 2 1þ 6 h0
(6)
where h is the EHL film thickness and ho is the minimum film thickness for smooth surface. The combined roughness of two
l¼
h0
s
(7)
Bearing is considered to be in boundary lubrication regime when lp3.
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Table 1 Bearing dimensions and reactions [1] Bearing number (PORT and starboard shafting)
Bearing type
Length (mm)
Diameter (mm)
1 2 3 4
Water lubricated sliding bearings
735 735 735 735
365 355 350 345
60 089 27 151 33 145 26 123
60 216 26 414 35 359 17 679
5 (gearbox aft) 6 (gearbox fwd)
Oil lubricated rolling bearings
190 190
265 265
182 906 164 109
206 453 147401
a
Bearing reactions on 0.3 mm wear on bearing no. 4
The reactions are considered positive in the downward direction.
The formulations given in Eqs. (2)–(7) and those given in Ref. [4] have been used to calculate the load carrying capacity of the bearing. The calculated load is compared with the given load and till the time it matches within the prescribed limits, iterations are continued by incrementing the eccentricity ratio. The flow chart for MATLAB code is shown in Fig. 4. To check the correctness of programme, bearing data provided in Ref. [6] and listed in Table 3 were tried out. Output results are listed in Tables 4 and 5 and plotted in Figs. 5 and 6. Logarithmic plots have been presented depicting change in surface roughness parameter and coefficient of friction with increasing radial clearance and increasing composite rms surface roughness values of tribo-pair. The results generated by the computer code used in the present study tally, both quantitatively and qualitatively, with the plots published by Kraker et al. [6].
3.3. Wear model Having established the correctness of computer code for journal bearing parameters, the study was extended to estimate the bearing life. Journal bearing’s wear and performance are usually related to the increase in clearance between the journal and the bearing. Archard’s equation defines depth of wear h as a function of bearing load W and sliding distance S. Coefficient of wear K in the Archard’s equation is a proportionality constant, indicating that wear follows linear relationship. Wear model suggested by Bayer [7], although takes linear relationship between volume of wear V, and K and the depth of wear h has non-linear relation with length L, radius R and volume of wear V. The expression for wear volume V and h is given by V ¼ UTKW a
(8)
where U is the sliding speed in m/s, T the time in s, K the wear coefficient in m2/N and Wa the asperity load in N. The empirical equation for localized depth of wear h, proposed by Bayer [7] for aligned shaft is given by 1=3 2=3
h ¼ 0:66R
L
V
2=3
(9)
where R and L are radius and length of bearing, respectively. In this wear model, the underlying assumption is that negligible wear occurs in the journal. With the known values of depth of wear h, surface velocity U, time T and load shared by asperities Wa, the coefficient of wear K for individual bearings using Eqs. (8) and (9) can be calculated by substitution and rearrangement: K¼
Dynamic bearing reactionsa (N)
ð1:5hÞ3=2 R1=2 L 2pRNTW a
or K ¼ 0:2924
ðhÞ3=2 L R
1=2
NTW a
(10)
3.4. Asperity and fluid pressure ratio In many instances of EHL, direct contact between the deformed asperities will still occur in spite of the presence of EHL film. If the lubricating film separating the surfaces is such that it allows some contact between the deformed asperities then this type of lubrication is called mixed or partial lubrication. Johnson et al. [5] have propounded that, provided a major part of the load is carried by elastohydrodynamic action, the separation between the two rough surfaces is given by the film thickness which would exist between two smooth surfaces under the same conditions of load, speed and lubricant. The authors have shown that an increase in total load is carried by an increase in fluid pressure and a small increase in asperity contact pressure. The fluid pressure to total pressure is given by following expression [5]: 6:3 pf h0 ¼ (11) p h The pressure shared by the asperity can be deduced as pa p ¼1 f p p
(12)
These equations have been used to ascertain pressure sharing between fluid and asperity at various rpm/radial clearance conditions. Under mixed lubrication conditions use of Eqs. (11) and (12) is required to find out the fraction of load (Wa) bared by asperities. Calculated Wa can be used in Eqs. (10) to determine the wear constant for mixed lubrication.
4. Experiments Elastomeric bearings, used in Indian Coast Guard’s Advanced Offshore Patrol Vessels (AOPVs), are lubricated with sea water that may contain particulates. Further, for reliable mixed lubrication analysis the measurement of dynamic viscosity of sea water and surface roughness of propeller shaft and bearings is essential. Therefore, it was necessary to perform particle analysis to check the influence of particulate contamination in sea water (for erosive and abrasive wear), to measure the dynamic viscosity of sea water and its thixotropic behaviour and to determine the surface roughness of bearing and shaft surface. Experiments for viscosity and particulate contamination were conducted at IIT Labs with sample of sea water taken from Naval Dockyard Mumbai, India. Pertometer M2, available at Instrumentation Lab
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Fig. 3. Misaligned hydrodynamic journal bearing: (a) misaligned shaft in a journal bearing [1], (b) pressure profile for aligned bearing, (c) pressure profile for 0.0041 misalignment, (d) misalignment equal to 0.0071 and (e) pressure profile for 0.011 misalignment.
of IIT was used to check the surface roughness of bearing sample obtained from M/S Vanson Mumbai. The details of readings and its possible influence on wear analysis are elucidated in forthcoming paragraphs.
4.1. Measurement of surface roughness by perthometer M2 The surface roughness of the bearing samples was measured using perthometer M2 in IIT machine tool lab. The summary of
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various surface roughness parameters for the bearing surfaces is listed in Tables 6 and 7. Roughness value of 15 mm for bearing surface and 3 mm for shaft sleeve surface has been considered in the present study, which is standard roughness limit stipulated prior fitment in ship.
Table 2 Values of the maximum fluid pressure in misaligned hydrodynamic journal bearing Misalignment (deg)
Present study (MPa)
Finite difference method (MPa) [14]
% difference
0.000 0.004 0.007 0.01
34.75 43.91 73.96 412.51
33.06 39.60 63.58 415.35
4.86 9.82 14.03 0.69
4.2. Measurement of viscosity of sea water Viscosity of sea water was measured at ONGC JRC Lab at IITB. The equipment used was Brookfield make Rheometer. The readings taken during the experiment is given in Table 8. The average
Table 3 Design parameters of reference bearing Description
Parameter
Value
Units
Bearing radius Bearing length Radial clearance Composite surface roughness
R L C Sq or s
25 100 0.125 0.424
mm mm mm mm
Start Get film thickness parameter Acquire parameters
λ>3
Initialise eccratio
λ≤3
Increment ecc ratio Preset ‘max h’
Calculate Load by integrating Pressure term twice Y e s
Mixed/BL Regime Calculate depth of wear
HDL regime Get bearing parameters
Compare calculated load with given Load
L E S S
Compare ‘h’ with ‘max h’ Equal
Difference > terminating residual Get the bearing life No
END Get min film thickness
Fig. 4. Flow chart for programme rpm_vs_ecc_regime.
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Table 4 Results of computer code for design parameters at different rpms (s ¼ 0.43 kept constant) RPM
10 20 30 40 50 70 100 200 300 400 500 600 700 800 900 1000 1100
Radial clearance 0.00025 m R/C ¼ 0.01
Radial clearance 0.000125 m R/C ¼ 0.005
Radial clearance 0.0000625 m R/C ¼ 0.0025
Radial clearance 0.00003125 m R/C ¼ 0.00125
h t/ s
m
ht/s
m
ht/s
m
ht/s
m
1.38 1.38 1.38 1.38 1.38 1.38 1.388 1.388 1.388 1.388 1.388 1.4 2.18 3.75 5.28 6.75 8.16
0.114 0.114 0.114 0.114 0.114 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.09 0.04 0.02 0.01 0.005
1.38 1.38 1.38 1.38 1.38 1.38 1.388 1.87 4.73 7.28 9.63 11.85 13.99 16.06 18.09 20.1 22.1
0.114 0.114 0.114 0.114 0.114 0.11 0.11 0.1 0.03 0.01 0.009 0.007 0.005 0.004 0.003 0.0025 0.001
1.38 1.38 1.38 1.38 1.38 2.07 3.61 7.97 11.9 15.8 19.7 23.7 27.8 – – – –
0.114 0.114 0.114 0.114 0.114 0.09 0.05 0.01 0.004 0.004 0.003 0.002 0.002 – – – –
1.38 1.38 2.24 3.04 3.93 5.5 7.8 15.8 23.5 29.2 – – – – – – –
0.11 0.08 0.08 0.06 0.04 0.02 0.01 0.004 0.002 0.001 – – – – – – –
Table 5 Results of computer code for design parameters at different rpms (radial clearance C ¼ 0.000125 m kept constant) rpm
10 30 50 70 100 200 300 400 500 600 700 800 900 1000 1100 1200
sA ¼ 0.1, sB ¼ 0.2, s ¼ 0.22
sA ¼ 0.2, sB ¼ 0.4, s ¼ 0.43
sA ¼ 0.3, sB ¼ 0.8, s ¼ 0.85
ht/s
m
ht/s
m
h t/ s
m
1.38 1.38 1.38 1.38 1.38 3.7 9.53 14.63 19.3 23.8 28.01 – – – – –
0.11 0.11 0.11 0.11 0.11 0.04 0.009 0.004 0.003 0.002 0.002 – – – – –
1.38 1.38 1.38 1.38 1.38 1.87 4.73 7.28 9.63 11.85 13.09 16.06 18.1 20.1 22.1 –
0.11 0.11 0.11 0.11 0.11 0.1 0.03 0.01 0.009 0.007 0.005 0.004 0.003 0.003 0.003 –
1.38 1.38 1.38 1.38 1.38 1.38 2.45 3.78 5.0 6.16 7.28 8.36 9.4 10.4 11.49 12.51
0.11 0.11 0.11 0.11 0.11 0.11 0.08 0.04 0.03 0.02 0.016 0.012 0.01 0.009 0.007 0.006
value of viscosity at 150 rpm was 0.96 mPa s, at 250 rpm it was 1.08 mPa s and at 500 rpm the average value of viscosity was 1.50. In the present study a curve fit equation 0:8331 þ 0:0006 rpm þ
rpm 2 1000
has been used to represent the water viscosity as a function of rotational speed of shaft.
turbulent. The particle size in sea-water sample had mean diameter of 40–120 nm and the average speed (at 250 rpm of shaft speed) of particle is less than 3 m/s, which is not of any appreciable consequence as far as wear of marine shaft bearing is concerned. The particulate contamination was therefore, not considered in the present study.
5. Data collection 4.3. Measurement of particle size in sea water using particle size analyser The variation in particle size diameter indicates inconsistency of particulate contamination in sea water. The particulate contamination varies depending upon depth, distance from shore line and turbulence level of sea. It was observed that particulate contamination is high during rough weather when sea is
Having obtained the values of characteristic parameters, it was time now to obtain operational data from a ship. It was decided to analyze the wear of propeller shaft bearing of Indian Coast Guard Ship Sangram, an AOPV, which had experienced problems of unequal and unsymmetrical wear in its shaft system bearings. Initial and final radial clearances recorded during the construction of ship, CGS Sangram, at Goa Shipyard
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Surface Roughness Parameter
C = 0.01
C = 0.005
C = 0.0025
C = 0.00125
24 20 16 12 8 4 0 1
10
100 RPM
Sigma = 0.22
1000
Sigma = 0.43
10000
Sigma = 0.85
Surface Roughness Parameter (Sigma)
24 20 16 12 8 4 0 1
10
100
10000
1000
RPM Fig. 5. Variation of surface roughness parameter with (a) increasing radial clearance of bearing and (b) increasing composite rms value (s) of tribo-pair (data refers to Table 4).
C = 0.00025
C = 0.000125
C = 0.0000625
C = 0.00003125
Coeff of friction
0.12
0.08
0.04
0 1
10
100
1000
10000
RPM Sigma = 0.22
Sigma = 0.43
Sigma = 0.85
Coeff of friction
0.12
0.08
0.04
0 1
10
100
1000
RPM Fig. 6. Variation of coefficient of friction with (a) increasing radial clearance of bearing and (b) increasing composite rms value (s) of tribo-pair (data refers to Table 5).
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Ltd and during its two successive docking ships are registered in Table 9. The recorded clearances were diametric and for the present study they have been converted into radial clearance. The exploitation pattern and hours of sailing, obtained from ICGS Sangram’s Main Engine Room Log Book, are listed in Table 10.
6. Results and discussions Table 10 shows that water lubricated bearings undergo transient phenomena of starts and stops (i.e. 304 time shaft was
Table 6 Readings of perthometer M2 for shaft sample Parameter
Reading 1
Reading 2
Reading 3
Reading 4
Sampling length (mm) Lc (mm) Ra (mm) Rz (mm) Rmax (mm) Rt (mm)
5.6 0.8 0.88 3.82 4.41 4.41
17.5 2.5 0.968 4.85 5.25 5.81
5.6 0.8 0.279 2.62 3.51 3.88
17.5 2.5 0.401 3.92 6.92 6.92
Table 7 Readings of perthometer M2 for bearing sample Parameter
Reading 1
Reading 2
Reading 3
Reading 4
Sampling length (mm) Lc (mm) Ra (mm) Rz (mm) Rmax (mm) Rt (mm)
5.6 0.8 1.510 9.80 12.7 14.2
17.5 2.5 2.790 18.6 22.2 22.7
5.6 0.8 1.750 10.5 16.4 16.4
17.5 2.5 2.02 13.0 14.3 16.5
387
started/stopped during May 97 to June 2000). Mokhtar et al. [15] studied the starting behaviour of journal bearing and observed a rapid build up of hydrodynamic film in all the cases. They concluded that hydrodynamic film formed in a very short time, after which shaft moved in a spiral shaped whirling locus to the steady state operating position. Similarly they studied stopping motion and reported that during shutting down the shaft followed a typical hydrodynamic locus until rotation ceased and then a squeeze film trajectory to final resting position was observed. These results indicate that start/stop transient phenomena does not cause major wear on the bearing surface. Under proper load conditions, shaft takes lesser than half rotation to lift off from bearing surface. Therefore, in the present study it is assumed that starts/stops do not affect bearing life significantly. However, excessive load, large clearance and low rotational speed may have affected the bearing life and estimating wear constant may indicate the source of bearing wear.
6.1. Coefficient of wear There are two approaches to find the wear coefficient. In the first approach it is assumed that there are only two lubrication domains: hydrodynamic and boundary. In the hydrodynamic regime (l43), bearing wear is zero and the applied load is bared by full-fluid film. In the boundary regime (lp3), applied load is carried by asperities and bearing wear is definite. The value of l can be determined by computer simulation of algorithm given in Fig. 4 and Eq. (7). By employing this approach, MATLAB code was run with input data of load, bearing length and diameter as listed in Table 1, and different radial clearances. Fig. 7 shows that at radial clearance greater than 0.6 mm, all four bearings operate in boundary lubrication regime, meaning thereby that hydrodynamic film does not form even at the highest operating rpm (254). However, when the radial clearance is reduced to 0.4 mm for bearing 2, 3 and 4, the average minimum rpm for hydrodynamic
Table 8 Viscosity measurement readings rpm
150 250 500
First run
Second run
Third run
Fourth run
Fifth run
Dynamic viscosity (mPa s)
Shear stress (Pa)
Dynamic viscosity (mPa s)
Shear stress (Pa)
Dynamic viscosity (mPa s)
Shear stress (Pa)
Dynamic viscosity (mPa s)
Shear stress (Pa)
Dynamic viscosity (mPa s)
Shear stress (Pa)
0.974 1.083 1.510
0.736 1.364 3.805
0.954 1.075 1.504
0.721 1.354 3.790
0.952 1.077 1.5
0.720 1.356 3.779
0.952 1.078 1.502
0.719 1.358 3.783
0.954 1.080 1.504
0.727 1.361 3.789
Table 9 Radial clearances of bearings Radial clearances Bearing no. 1 (mm) recorded from Installed May 1997 After 3 years
Bearing no. 2 (mm)
Bearing no. 3 (mm)
Bearing no. 4 (mm)
Installed May 1997 After 3 years
Installed May 1997 After 3 years
Installed May 1997 After 3 years
Port Stbd
0.725 0.775
0.675 0.625
0.8 0.8
Port Stbd
Port Stbd
0.75 0.7
1.58 1.6
0.9 0.9
1.4 1.15
1.05 0.95
Initial Oct 2000
Final Dec 2002 Initial Oct 2000
Final Dec 2002 Initial Oct 2000
Final Dec 2002 Initial Oct 2000
Final Dec 2002
0.775 0.575
1.65 1.025
0.65 0.45
1.0 0.7
0.75 0.4
1.175 0.625
0.5 0.5
0.755 0.755
Initial May 2003
Final Sep 2004
Initial May 2003
Final Sep 2004
Initial May 2003
Final Sep 2004
Initial May 2003
Final Sep 2004
0.525 1.025
0.775 1.64
0.275 0.7
0.53 0.8
0.75 0.625
0.9 1.28
0.5 0.575
0.67 0.85
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Table 10 Exploitation pattern of ship for 03 operational cycles Description
May 97–Jun 2000 (H)
Oct 2000–Dec 2002 (H)
May 2003–Sep 2004 (H)
Total engine running hours Total engine running hours in clutched condition Number of starts and stops Hours at engine rpm 500 (shaft rpm 130) Hours at engine rpm 550 (shaft rpm 143) Hours at engine rpm 600 (shaft rpm 156) Hours at engine rpm 650 (shaft rpm 170) Hours at engine rpm 700 (shaft rpm 182) Hours at engine rpm 750 (shaft rpm 195) Hours at engine rpm 800 (shaft rpm 209) Hours at engine rpm 850 (shaft rpm 221) Hours at engine rpm 900 (shaft rpm 235) Hours at engine rpm 950 (shaft rpm 247) Hours at engine rpm 975 (shaft rpm 254)
4109 3800 304 549 67 140 472 1709 618 177 64 01 02 01
5129 4714 191 – 368 15 613 2447 28 864 375 04 – –
3264 3198 122 – 366 25 189 1677 – 753 173 14 01 –
Brg 1
Brg 2
Brg 3
Brg 4
600 500 RPM
400 300 200 100 0 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Radial Clearance (mm) Fig. 7. Rpm below which bearing performs under boundary lubrication.
film to form is 160–190. Bearing 1 continues to operate in boundary lubrication regime even at radial clearance of 0.4. Effect of increased radial clearance on regime of lubrication can be seen in graph shown in Fig. 8. Surface roughness parameter (l) below 3 indicates bearing operates in boundary lubrication regime. This analysis suggests that all four bearings operate under boundary lubrication regime and Eq. (10) can be employed to evaluate the wear constant K. The calculated values of K are listed in Tables 11 and 12. The wear depth of bearings of both shaft lines of one ship for three operational cycles has been obtained by subtracting initial clearance from final clearance. However, referring to Tables 11 and 12, it can be seen that value of K is not consistent for different bearings within the same operational cycle and for same bearing within different operational cycles. For bearing 1, the variation in K is largely dependent upon initially set radial clearance; for bearing 2, K is quite consistent irrespective of initial set radial clearance; and for bearings 3 and 4, K is inconsistent irrespective of initially set radial clearance. Hence, the average of 24 values of K listed in Tables 11 and 12 (0.226 1017 m2/N) cannot be used to estimate the life of water lubricated bearing. However, the results obtained using this approach indicates that bearing 1 is severely loaded and more prone to wear damage. The second approach for wear analysis of water lubricated bearing is to first evaluate the load shared by asperities using Eqs.
(11) and (12) and employ the calculated load to determine the wear constant using Eqs. (8) and (9). To understand this approach let us consider that total applied, 60089 N as shown in Table 1, on the bearing 1 is shared by fluid film and asperity contact. Determine the asperities pressure and calculate the load bared by asperities by area integration of asperity pressure. For bearings 1, 2 and 4 under different speed and clearance conditions, asperity loads are listed in Table 13. The results of this table indicate that asperity load will decrease with increasing rotational speed of the shaft. Further, the minimum value of wear constant equal to 0.35 1011 mm2/N, the maximum value equal to 1.7 1011 mm2/N, and average value equal to 1.0 1011 mm2/N have been estimated. These results indicate more than 50% variation in the value of wear constant. One possible reason for such variation is that the individual bearing (i.e. bearing 1, bearing 2) has been analyzed as a component that is subject to a particular load and speed condition. In reality load shared by all four bearings is completely coupled and dynamic. Larger clearance in one bearing increases the load on other bearings and vise-versa. Table 9 clearly indicates that radial clearance for bearing 1 in first load cycle was 200 mm greater than the clearance provided in third load cycle. Similarly radial clearance for bearing 2 was 500 mm greater in first load cycle compared to clearance in third load cycle. Such high variation in radial clearance drastically changes the load capacity of bearings. In hydrodynamic journal bearing often radial clearance (C) in the range of 0.00075 to 0.001 times shaft radius is preferred. The radial clearances shown in Table 9 demonstrate that two to four times higher clearance was provided for water lubricated bearings. The load capacity of such bearings is proportional to 1/C2 therefore load capacity can be increase by decreasing radial clearance, which is shown in Table 14. This table indicates that if radial clearance of bearing is approximately equal to 0.001 times shaft radius, then there is significant decrease in asperity load. Hence, it can be concluded that major problem in elastomeric bearing used in the Indian Coast Guard Ships is radial clearance of the bearing. Radial clearance between 0.00075 and 0.001 times shaft radius should be maintained for longer life of all four bearings.
7. Conclusions Unequal and non-uniform wear of elastomeric bearings, used in Indian Coast Guard Ships, have been analyzed. Following
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389
@ 150 RPM Bearing 1
Bearing 2
Bearing 3
Bearing 4
Surface Roughness Parameter
4 3 2 1 0 0.2
0.3
0.4
0.5 0.6 Radial Clearance (mm)
0.7
0.8
0.9
@ 185 RPM Bearing 1
Bearing 2
Bearing 3
Bearing 4
Surface Roughness Parameter
5 4 3 2 1 0 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Radial Clearance (mm) Fig. 8. Effect of increased radial clearance on surface roughness parameter.
conclusions can be drawn from the experimental and theoretical study presented in the paper:
Table 11 coefficient of wear (port shaft) Bearing number
1 2 3 4
Coefficient of wear K (m2/N) ( 1017)
Sea water shows thixotropic behaviour and its dy-
Operational cycle 1
Operational cycle 2
Operational cycle 3
0.506 0.187 0.159 0.198
0.366 0.231 0.255 0.024
0.092 0.212 0.079 0.101
1 2 3 4
Table 12 Depth of wear and coefficient of wear (Stbd Shaft) Bearing number
Coefficient of wear K (m2/N) ( 1017) Operational cycle 1
Operational cycle 2
Operational cycle 3
0.587 0.090 0.47 0.092
0.15 0.134 0.098 0.024
0.354 0.05 0.717 0.247
namic viscosity increases with increase in rotational speed. Particle size of sea-water contamination is very small (40–120 nm). Such small size of particles does not cause bearing wear. All four elastomeric bearings, used to support propeller shaft, operated in mixed lubrication at operating conditions provided in Table 10. All four bearings have unplanned excessive radial clearance, which reduce their load capacity and result uneven rapid wear. Bearing life can be enhanced by proper selection of radial clearance for all four bearings.
Acknowledgement Our sincere thanks to Indian Coast Guard Ship Sangram, from where valuable and dependable data of shaft clearance and engine running hours were provided.
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Table 13 Asperity load and wear constant for bearings 1, 2 and 4 rpm
130 143 156 170 182 195 209 221 235 247 254
Load shared by asperities of bearing 1, Wa (N)
Load shared by asperities of bearing 2, Wa (N)
Load shared by asperities of bearing 4, Wa (N)
Cycle 1
Cycle 2
Cycle 3
Cycle 1
Cycle 1
Cycle 2
Cycle 3
52 467 51767 51 098 50 349 49 658 48 951 48 257 47 574 46 822 46 125 45 690
– 51 942 51 294 50 582 49 951 49 279 48 500 47 922 47 135 – –
– 49 081 48 199 47 215 46 421 – 44 543 43 674 42 693 41885 –
20 708 20 242 19 811 19 244 18 813 18 342 17 840 17408 16 923 16 470 16 207
– 17 778 17 116 16 412 15 831 15 208 14 507 13 937 13 248 – –
17 778 17 116 16 412 15 831 – 14 507 13 937 13 248 12 671 –
1.7
1.43
0.35
20 887 – – 20 341 19 764 13 307 19 784 19 142 12 320 19 228 18 554 11 259 18 732 17 995 10 342 18 185 17 452 – 17 606 16 809 8556 17 125 16 260 7715 16 502 15 707 6647 16 029 – 5925 15 704 – – 2 11 Wear constant (mm /N) ( 10 ) 0.44 1.0 1.6
0.76
0.73
0.49
Cycle 2
Cycle 3
Table 14 The effect of clearance reduction on asperity load Description
Total engine running condition Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm
May 97–Jun 2000 (h)
hours in clutched
3800
500 550 600 650 700 750 800 850 900 950 975
549 67 140 472 1709 618 177 64 01 02 01
(shaft (shaft (shaft (shaft (shaft (shaft (shaft (shaft (shaft (shaft (shaft
rpm rpm rpm rpm rpm rpm rpm rpm rpm rpm rpm
130) 143) 156) 170) 182) 195) 209) 221) 235) 247) 254)
Load shared by asperities of bearing 1, Wa (N)
Load shared by asperities of bearing 4, Wa (N)
Bearing clearance (0.75 mm)
Bearing clearance (0.175 mm)
Bearing clearance (0.8 mm)
Bearing clearance (0.175 mm)
52 467 51767 51 098 50 349 49 658 48 951 48 257 47 574 46 822 46 125 45 690
36 933 35 032 33 669 31157 29 736 27 905 25 972 23 877 22 109 20 044 18 304
20 708 20 242 19 811 19 244 18 813 18 342 17 840 17408 16 923 16 470 16 207
8807 7477 6176 4811 3667 2452 1172 366 0 0 0
References [1] Allais B. Calculations of bending moments and bearing reaction calculation. A Technical Note from M/S acbLIPS company, 1991. [2] Stachowiak GW, Batchelor AW. Engineering tribology. 2nd ed. USA: Butterworth-Heinemann; 2001. [3] Khonsari MM, Booser RE. Applied tribology. Wiley; 2001. [4] Hirani H, Rao TVVLN, Athre K, Biswas S. Rapid performance evaluation of journal bearings. Tribol Int 1997;30:825–34. [5] Johnson KL, Greenwood JA, Poon SY. A simple theory of asperity contact in elastohydrodynamic lubrication. Wear 1972;19:91–108. [6] Kraker Alex de, van Ostayen Ron AJ, Rixen Daniel J. Calculation of stribeck curves for (water) lubricated journal bearings. Tribol Int 2007;40:459–69. [7] Bayer RG. Engineering design for wear. 2nd ed. New York, USA: Marcel Dekker Inc.; 2004. [8] Massimo Del Din, Kassfeldt Elisabet. Wear characteristics with mixed lubrication conditions in a full scale journal bearing. Wear 1999;232:192–8.
[9] Hsu SM, Munro RG, Shen MC, Gates RS. Boundary lubricated wear. Wear—materials, mechanisms and practice. New York: Wiley; 2005. [10] Rao AR, Mohanram PV. A study of wear characteristics of journal bearings operating under mixed-lubrication conditions. Wear 1994;172: 11–22. [11] Safar ZS. Energy loss due to misalignment of journal bearings. Tribol Int 1984;17:107–9. [12] El-Butch AM, Ashour NM. Transient analysis of misaligned elastic tilting-pad journal bearing. Tribol Int 2005;38:41–8. [13] Jakeman RW. Non-linear oil film response model for the dynamically misaligned sterntube bearing. Tribol Int 1989;22:3–10. [14] Sun J, Changlin G. Hydrodynamic lubrication analysis of journal bearing considering misalignment caused by shaft deformation. Tribol Int 2004; 37:841–8. [15] Mokhtar MOA, Howarth RB, Davis PB. The behaviour of plain hydrodynamic journal bearings during starting and stopping. ASLE 1977;20(3): 183–90.
Contents lists available at ScienceDirect
Tribology International journal homepage: www.elsevier.com/locate/triboint
Tribological study of elastomeric bearings for marine propeller shaft system Harish Hirani , Manish Verma Department of Mechanical Engineering, IIT Bombay, Powai, Mumbai, Maharashtra 400076, India
a r t i c l e in f o
a b s t r a c t
Article history: Received 6 August 2007 Received in revised form 18 July 2008 Accepted 29 July 2008 Available online 16 September 2008
Elastomeric compounds, due to their favourable properties like sufficient hardness, toughness and natural resistance to abrasion and corrosion, are commonly used as bearing material for propeller shaft system of Indian Coast Guard Ships. Recently unequal and non-uniform wear of these bearings has resulted in unscheduled lay off of the Coast Guard Ships. To solve this problem of bearing wear, a mixed lubrication analysis of sea-water lubricated journal bearing has been attempted in the present study. A computer code was written to estimate lubricating film thickness for a given set of load and speed condition, and to predict the lubrication regime for the specified surface roughness parameters. To validate the theoretical analysis performed in the present study, the results obtained from the computer simulation have been compared with the established studies on the water lubricated bearing. To understand the uneven wear of marine bearings, actual geometric clearances of new and worn out bearings recorded by the ship maintenance team, and the operational data (load, speed and operating hours), obtained from the log books of ICGS Sangram (AOPV) of Indian Coast Guard, are listed in the present paper. The dynamic viscosity of sea water, surface roughness of propeller shaft and bearings, and particulate contamination has been measured. Finally, the suggestions have been enlisted for proper operation of shaft-bearing system so as to maintain the wear within the permissible limits during ship’s operational cycle. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Marine shaft bearing Fluid film thickness Coefficient of wear Bearing life
1. Introduction Indian Coast Guard’s Advanced Offshore Patrol Vessels (AOPVs) are fitted with twin propeller shafts, each powered with 6400 HP engine. Each propeller shaft is 24 m long, weighs 10 tons and rotates inside four elastomeric journal bearings which are lubricated with sea water. These bearings are plain in lower half and grooved in upper half as shown in Fig. 1. Fig. 2 shows the propeller shaft supported in four elastomeric bearings. Dimensional details of these bearings are mentioned in Table 1. In addition, Table 1 lists the bearing reactions which are taken from Ref. [1]. Recently excessive wear of these bearings has resulted in unscheduled lay off of the Coast Guard Ships. First ship, ICGS Samar, commissioned in 1995 had successive bearing failure on both the shafts during two operational cycles (period between two successive dockings). ICGS Sangram, commissioned in 1997 had similar failure in both the shafts on two operational cycles and one shaft (port) in one operational cycle. Similar failures were seen in ICGS Sarang which was commissioned in
Corresponding author. Tel.: +91 222 576 7535; fax: +91 222 572 6875.
E-mail address: [email protected] (H. Hirani). 0301-679X/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2008.07.014
1999. The aim of the present study is to analyse this problem of bearing wear, and suggests a remedial action. Wear down of a water lubricated elastomeric bearing is an obvious phenomenon. However, elastomeric bearings used in all three ships (ICGS Samar, Sangram, and Sarang) were specially designed and fabricated (by Thordon bearings Inc.). In one lab (David Taylor Research Centre, Bethesda, MD) test, bearing wear of 0.002 in (0.051 mm) was observed in over 2000 working hours of propeller shaft running at 10 rpm against designed elastomeric bearing. Expected life of such a bearing is more than 20 years and replacement of bearings after wear depth of 4.7 mm is recommended. However, elementary moment analysis [1] reveals that wearing of bearing 4 redistributes the load, as listed in Table 1, among bearings. As per the gearbox manufacturer, the load ratio force on bearing 5=force on bearing 6 should not exceed 1.3. This constraint is imposed to restrict the impact loading on gear pairs. At the design stage this ratio was 1.1145 (F5/F6 ¼ 182906/164109). However, after 0.3 mm wear of bearing 4, load ratio (F5/F6) increases to (206 453/147401) to 1.4. Therefore, there is a need to review and establish a new limit on bearing wear for the replacement of elastomeric bearings compared to believing on the limit of 4.7 mm wear depth suggested by bearing manufacturer.
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Symbols and notations C radial clearance, m D journal diameter, m H; HPmax non-dimensional film thickness, film thickness at maximum pressure location h depth of wear, m h0 minimum thickness of fluid film, m h¯ EHL film thickness, m effective film thickness, m ht K empirical wear factor or Archard’s wear coefficient L bearing length, m N journal rotational speed, rpm P bearing pressure W/(LD), Pa Pmax maximum pressure, Pa pf fluid pressure (percent of total pressure) pa asperity pressure (percent of total pressure) R journal radius, m S sliding distance, m t tilt ratio or non-dimensional tilt, t ¼ m/C,
Bearing wear can be completely avoided by establishing the hydrodynamic lubrication mechanism in water lubricated journal bearings. However, the bearing wear observed in the present study indicates that bearings were operated under mixed and/or boundary lubricated regimes. One possible reason of mixed lubrication condition is that all patrol vessels, fitted with two engines, operate with single engine during patrol. Under such conditions, the idling shaft speed, which (due to propulsion of the motoring shaft) ranges between 50 and 70 rpm, may be insufficient to form hydrodynamic film. To understand this bearing wear problem, a mixed lubrication analysis of sea-water lubricated journal bearing is required. Further, to streamline the analysis, answers to the following questions are essential: (a) Is hydrodynamic fluid film not getting formed due to: (i) Low rpm operations and/or (ii) Increased radial clearance (b) What are the implications of increased radial clearance of bearings? (c) What is the regime of lubrication in which the bearing operates with the increased radial clearance at a given rpm? (d) What is the effect of particulate contamination in sea water? Is it responsible for abrasive and erosive wear of bearing surface? (e) What is the effect of surface roughness of bearing and shaft sleeve? (f) What is the effect of viscosity of sea water? Is it changing with rpm and temperature? (g) Is it possible to control the wear by changing the dimensions of bearing and shaft? In the present study a systematic design methodology has been employed to answer the abovementioned questions and suggest a suitable remedy to avoid bearing wear in the future. 2. Literature survey To understand the theoretical aspects of journal bearing operation two books, ‘Engineering Tribology’ by Stachowiak and Batchelor [2], and ‘Applied Tribology’ by Khonsari and Booser [3] were referred. Hirani et al. [4] have used two pressure correction
379
T U V W We, Wf
operating time, s journal surface velocity, m/s wear volume, m3 dimensional load capacity, N dimensional load capacity along and perpendicular to line of centres, N WZ ratio of dimensional load capacity to viscosity, m2/s WeZ, WfZ ratio of We, Wf to viscosity, m2/s z coordinate in axial direction, m gO, gS pressure correction factors for Ocvirk’s and Sommerfield bearings L slenderness ratio (L/D) e eccentricity ratio f attitude angle, radian Z viscosity coefficient of lubricant, Pa s y coordinate in circumferential direction, radian sA surface roughness of bearing surface, mm sB surface roughness of shaft sleeve surface, mm s combined roughness of two surfaces, mm l film thickness parameter
factors go and gs to give an analytical expression for maximum pressure. The design table [4] listed in their paper can be used to find out film thickness, pressure and load carrying capacity. However, the formulations in their paper [4] pertained to hydrodynamic lubrication regime only. Johnson et al. [5] have stipulated that provided a major part of the load is carried by elastohydrodynamic action, the separation between the two rough surfaces is given by the film thickness which would exist between two smooth surfaces under the same conditions of load, speed and lubricant. Kraker et al. [6] have described a mixed EHL model for finite length elastic journal bearings. These authors have used commercially available finite element code SEPRAN to discretise the Reynolds equation. Bayer [7] has provided algebraic expression for calculation of depth of bearing wear under aligned and misaligned journal conditions. Messimo Del Din et al. [8] have used an experimental set up to investigate the utility of environmentally adapted rape seed–synthetic ester oil over traditional mineral oil. The wear measurements evaluate the coefficient of wear using Archard’s equation of wear. The methodology discussed in the paper pertains to experimental measurement of wear by difference in weight of bearing liner before and after the experiment and compares two different oils. Hsu et al. [9] have given a comprehensive view of wear under lubricated conditions. As per these authors wear under lubricated conditions can be classified into two main classes: welllubricated systems and marginal lubricated systems. However, the methodology to determine wear is again experimental in nature. Rao and Mohanram [10] have presented comprehensive sets of experiments to study mixed lubrication of journal bearings. The surface topography changes have been statistically analysed. Safar [11] has presented an analysis of a journal bearing describing a maximum allowable value of misalignment at a length to diameter ratio of unity. The author has opined that journal misalignment influences load carrying capacity of the bearing. A misaligned bearing consumes more power due to friction than an aligned one. El-Butch and Ashour [12] have dealt with analysing the performance of a misaligned tilting-pad journal bearing under transient loading condition. Jakeman [13] has presented a model specifically intended to represent the dynamically misaligned sterntube bearing, for the purpose of conducting lateral vibration analyses of marine propeller shafting. The methodologies presented in these papers have been duly taken into account while carrying out the present study.
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(d) Asperity and fluid pressure ratio given by Johnson et al. [5] have been used and correlated with regime of lubrication.
3.1. Derivation of pressure expression The closed form solution to Reynolds equation, for infinitely short bearing (Ockvirk’s solution) and infinitely long bearing (Sommerfeld solution) is combined using two correction factors go and gs to approximate the analytical expression for pressure for a finite bearing [3]. The formulations, given in the design table have been arrived at considering hydrodynamic lubrication regime. Misalignment factor has been provided in the film thickness expression. In misaligned shaft, critical minimum film thickness will occur at the edge of the bearing, as shown in Fig. 3a. The basic parameter to describe the tilt of the shaft is the tilt ratio given by t¼
m C
(1)
Where t is the tilt ratio or non-dimensional tilt, m is the distance between the axes of the tilted and non-tilted shaft measured at the edges of the bearing and C is the radial clearance. Accordingly, expression for non-dimensional film thickness H ( ¼ h0/C) was modified as zt cos y (2) H ¼1þ L where Z is the axial coordinate and L the length of bearing and h0 the minimum film thickness between smooth surfaces. The analytical pressure terms given by Ockvirk and Sommerfeld viz PO and PS and modified with two correction factors go and gs [3] is given by 1 gO gS ¼ þ P PO PS
(3)
where go and gs are given by [3] 5
g O ¼ 1 þ L1:2 ½e 1 3
g S ¼ eð1Þ
Fig. 1. Bearing with housing.
3. Approach for analysis of journal bearing parameters The following approaches have been adopted: (a) Reynolds equation, simplified for unidirectional velocity approximation [2,3], has been used. Expression for film thickness given in the design table of Hirani et al. [4] modified to take care of the misalignment. (b) Elastohydrodynamic lubrication film thickness and surface roughness parameter have been incorporated to predict the regime of lubrication. With the given load, rpm and radial clearance each bearing’s film thickness, regime of lubrication and asperity to fluid pressure ratio has been calculated using available formulations. The results have been compared with similar study carried out by Kraker et al. [6] to validate the approach. (c) Wear model based on boundary lubrication regime has been used to assess the depth of wear and associated life of bearing [7].
(4) (5)
where L ¼ L=D, is slenderness ratio. To validate the proposed analytical approach, bearing data given by Sun and Changlin [14] have been used to obtain and plot the pressure profile at various angular misalignments. Pressure profiles shown in Figs. 3b–e are comparable to pressure profiles provided in Ref. [14]. Sun and Changlin used finite-difference method to obtained pressure profile. Further, a comparative study between the values of maximum pressure obtained using the present analytical approach and finite-difference method is listed in Table 2. These graphical and tabular results indicate that the proposed analytical approach can be used to analyze misaligned hydrodynamic journal bearing. 3.2. EHL film thickness and surface roughness parameter The elastomeric water lubricated bearing may experience elastic deformation [6]. Kraker et al. [6] described a mixed elastohydrodynamic lubrication (EHL) model for finite length elastic journal bearing. They employed the finite element method to solve the coupled system of fluid and structural equations to compute Stribeck curves at constant load. In the present study, an analytical approach has been used to evaluate pressure profile and minimum film thickness. To incorporate elastohydrodynamic model and compare the results with Kracker et al. [6], the EHL film thickness in transverse direction (relevant to the present
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381
Propeller Weight
UDL 4KN/m
Mech. Seal
Gearbox
6
5
PROPELLER
4
40 KN
SHAFT
2
3 6m
6m
1 6m
Fig. 2. Propeller shaft with bearings: (a) Coast Guard Ship in Dry dock, (b) shaft withdrawn and showing location of bearings and (c) schematic of propeller shaft with bearings.
surfaces s is given by (s2A+s2B)0.5. The surface roughness parameter l is calculated to ascertain the regime of lubrication.
study) is obtained using [5] " h ¼ h0
# 7 s 2 1þ 6 h0
(6)
where h is the EHL film thickness and ho is the minimum film thickness for smooth surface. The combined roughness of two
l¼
h0
s
(7)
Bearing is considered to be in boundary lubrication regime when lp3.
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Table 1 Bearing dimensions and reactions [1] Bearing number (PORT and starboard shafting)
Bearing type
Length (mm)
Diameter (mm)
1 2 3 4
Water lubricated sliding bearings
735 735 735 735
365 355 350 345
60 089 27 151 33 145 26 123
60 216 26 414 35 359 17 679
5 (gearbox aft) 6 (gearbox fwd)
Oil lubricated rolling bearings
190 190
265 265
182 906 164 109
206 453 147401
a
Bearing reactions on 0.3 mm wear on bearing no. 4
The reactions are considered positive in the downward direction.
The formulations given in Eqs. (2)–(7) and those given in Ref. [4] have been used to calculate the load carrying capacity of the bearing. The calculated load is compared with the given load and till the time it matches within the prescribed limits, iterations are continued by incrementing the eccentricity ratio. The flow chart for MATLAB code is shown in Fig. 4. To check the correctness of programme, bearing data provided in Ref. [6] and listed in Table 3 were tried out. Output results are listed in Tables 4 and 5 and plotted in Figs. 5 and 6. Logarithmic plots have been presented depicting change in surface roughness parameter and coefficient of friction with increasing radial clearance and increasing composite rms surface roughness values of tribo-pair. The results generated by the computer code used in the present study tally, both quantitatively and qualitatively, with the plots published by Kraker et al. [6].
3.3. Wear model Having established the correctness of computer code for journal bearing parameters, the study was extended to estimate the bearing life. Journal bearing’s wear and performance are usually related to the increase in clearance between the journal and the bearing. Archard’s equation defines depth of wear h as a function of bearing load W and sliding distance S. Coefficient of wear K in the Archard’s equation is a proportionality constant, indicating that wear follows linear relationship. Wear model suggested by Bayer [7], although takes linear relationship between volume of wear V, and K and the depth of wear h has non-linear relation with length L, radius R and volume of wear V. The expression for wear volume V and h is given by V ¼ UTKW a
(8)
where U is the sliding speed in m/s, T the time in s, K the wear coefficient in m2/N and Wa the asperity load in N. The empirical equation for localized depth of wear h, proposed by Bayer [7] for aligned shaft is given by 1=3 2=3
h ¼ 0:66R
L
V
2=3
(9)
where R and L are radius and length of bearing, respectively. In this wear model, the underlying assumption is that negligible wear occurs in the journal. With the known values of depth of wear h, surface velocity U, time T and load shared by asperities Wa, the coefficient of wear K for individual bearings using Eqs. (8) and (9) can be calculated by substitution and rearrangement: K¼
Dynamic bearing reactionsa (N)
ð1:5hÞ3=2 R1=2 L 2pRNTW a
or K ¼ 0:2924
ðhÞ3=2 L R
1=2
NTW a
(10)
3.4. Asperity and fluid pressure ratio In many instances of EHL, direct contact between the deformed asperities will still occur in spite of the presence of EHL film. If the lubricating film separating the surfaces is such that it allows some contact between the deformed asperities then this type of lubrication is called mixed or partial lubrication. Johnson et al. [5] have propounded that, provided a major part of the load is carried by elastohydrodynamic action, the separation between the two rough surfaces is given by the film thickness which would exist between two smooth surfaces under the same conditions of load, speed and lubricant. The authors have shown that an increase in total load is carried by an increase in fluid pressure and a small increase in asperity contact pressure. The fluid pressure to total pressure is given by following expression [5]: 6:3 pf h0 ¼ (11) p h The pressure shared by the asperity can be deduced as pa p ¼1 f p p
(12)
These equations have been used to ascertain pressure sharing between fluid and asperity at various rpm/radial clearance conditions. Under mixed lubrication conditions use of Eqs. (11) and (12) is required to find out the fraction of load (Wa) bared by asperities. Calculated Wa can be used in Eqs. (10) to determine the wear constant for mixed lubrication.
4. Experiments Elastomeric bearings, used in Indian Coast Guard’s Advanced Offshore Patrol Vessels (AOPVs), are lubricated with sea water that may contain particulates. Further, for reliable mixed lubrication analysis the measurement of dynamic viscosity of sea water and surface roughness of propeller shaft and bearings is essential. Therefore, it was necessary to perform particle analysis to check the influence of particulate contamination in sea water (for erosive and abrasive wear), to measure the dynamic viscosity of sea water and its thixotropic behaviour and to determine the surface roughness of bearing and shaft surface. Experiments for viscosity and particulate contamination were conducted at IIT Labs with sample of sea water taken from Naval Dockyard Mumbai, India. Pertometer M2, available at Instrumentation Lab
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Fig. 3. Misaligned hydrodynamic journal bearing: (a) misaligned shaft in a journal bearing [1], (b) pressure profile for aligned bearing, (c) pressure profile for 0.0041 misalignment, (d) misalignment equal to 0.0071 and (e) pressure profile for 0.011 misalignment.
of IIT was used to check the surface roughness of bearing sample obtained from M/S Vanson Mumbai. The details of readings and its possible influence on wear analysis are elucidated in forthcoming paragraphs.
4.1. Measurement of surface roughness by perthometer M2 The surface roughness of the bearing samples was measured using perthometer M2 in IIT machine tool lab. The summary of
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various surface roughness parameters for the bearing surfaces is listed in Tables 6 and 7. Roughness value of 15 mm for bearing surface and 3 mm for shaft sleeve surface has been considered in the present study, which is standard roughness limit stipulated prior fitment in ship.
Table 2 Values of the maximum fluid pressure in misaligned hydrodynamic journal bearing Misalignment (deg)
Present study (MPa)
Finite difference method (MPa) [14]
% difference
0.000 0.004 0.007 0.01
34.75 43.91 73.96 412.51
33.06 39.60 63.58 415.35
4.86 9.82 14.03 0.69
4.2. Measurement of viscosity of sea water Viscosity of sea water was measured at ONGC JRC Lab at IITB. The equipment used was Brookfield make Rheometer. The readings taken during the experiment is given in Table 8. The average
Table 3 Design parameters of reference bearing Description
Parameter
Value
Units
Bearing radius Bearing length Radial clearance Composite surface roughness
R L C Sq or s
25 100 0.125 0.424
mm mm mm mm
Start Get film thickness parameter Acquire parameters
λ>3
Initialise eccratio
λ≤3
Increment ecc ratio Preset ‘max h’
Calculate Load by integrating Pressure term twice Y e s
Mixed/BL Regime Calculate depth of wear
HDL regime Get bearing parameters
Compare calculated load with given Load
L E S S
Compare ‘h’ with ‘max h’ Equal
Difference > terminating residual Get the bearing life No
END Get min film thickness
Fig. 4. Flow chart for programme rpm_vs_ecc_regime.
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Table 4 Results of computer code for design parameters at different rpms (s ¼ 0.43 kept constant) RPM
10 20 30 40 50 70 100 200 300 400 500 600 700 800 900 1000 1100
Radial clearance 0.00025 m R/C ¼ 0.01
Radial clearance 0.000125 m R/C ¼ 0.005
Radial clearance 0.0000625 m R/C ¼ 0.0025
Radial clearance 0.00003125 m R/C ¼ 0.00125
h t/ s
m
ht/s
m
ht/s
m
ht/s
m
1.38 1.38 1.38 1.38 1.38 1.38 1.388 1.388 1.388 1.388 1.388 1.4 2.18 3.75 5.28 6.75 8.16
0.114 0.114 0.114 0.114 0.114 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.09 0.04 0.02 0.01 0.005
1.38 1.38 1.38 1.38 1.38 1.38 1.388 1.87 4.73 7.28 9.63 11.85 13.99 16.06 18.09 20.1 22.1
0.114 0.114 0.114 0.114 0.114 0.11 0.11 0.1 0.03 0.01 0.009 0.007 0.005 0.004 0.003 0.0025 0.001
1.38 1.38 1.38 1.38 1.38 2.07 3.61 7.97 11.9 15.8 19.7 23.7 27.8 – – – –
0.114 0.114 0.114 0.114 0.114 0.09 0.05 0.01 0.004 0.004 0.003 0.002 0.002 – – – –
1.38 1.38 2.24 3.04 3.93 5.5 7.8 15.8 23.5 29.2 – – – – – – –
0.11 0.08 0.08 0.06 0.04 0.02 0.01 0.004 0.002 0.001 – – – – – – –
Table 5 Results of computer code for design parameters at different rpms (radial clearance C ¼ 0.000125 m kept constant) rpm
10 30 50 70 100 200 300 400 500 600 700 800 900 1000 1100 1200
sA ¼ 0.1, sB ¼ 0.2, s ¼ 0.22
sA ¼ 0.2, sB ¼ 0.4, s ¼ 0.43
sA ¼ 0.3, sB ¼ 0.8, s ¼ 0.85
ht/s
m
ht/s
m
h t/ s
m
1.38 1.38 1.38 1.38 1.38 3.7 9.53 14.63 19.3 23.8 28.01 – – – – –
0.11 0.11 0.11 0.11 0.11 0.04 0.009 0.004 0.003 0.002 0.002 – – – – –
1.38 1.38 1.38 1.38 1.38 1.87 4.73 7.28 9.63 11.85 13.09 16.06 18.1 20.1 22.1 –
0.11 0.11 0.11 0.11 0.11 0.1 0.03 0.01 0.009 0.007 0.005 0.004 0.003 0.003 0.003 –
1.38 1.38 1.38 1.38 1.38 1.38 2.45 3.78 5.0 6.16 7.28 8.36 9.4 10.4 11.49 12.51
0.11 0.11 0.11 0.11 0.11 0.11 0.08 0.04 0.03 0.02 0.016 0.012 0.01 0.009 0.007 0.006
value of viscosity at 150 rpm was 0.96 mPa s, at 250 rpm it was 1.08 mPa s and at 500 rpm the average value of viscosity was 1.50. In the present study a curve fit equation 0:8331 þ 0:0006 rpm þ
rpm 2 1000
has been used to represent the water viscosity as a function of rotational speed of shaft.
turbulent. The particle size in sea-water sample had mean diameter of 40–120 nm and the average speed (at 250 rpm of shaft speed) of particle is less than 3 m/s, which is not of any appreciable consequence as far as wear of marine shaft bearing is concerned. The particulate contamination was therefore, not considered in the present study.
5. Data collection 4.3. Measurement of particle size in sea water using particle size analyser The variation in particle size diameter indicates inconsistency of particulate contamination in sea water. The particulate contamination varies depending upon depth, distance from shore line and turbulence level of sea. It was observed that particulate contamination is high during rough weather when sea is
Having obtained the values of characteristic parameters, it was time now to obtain operational data from a ship. It was decided to analyze the wear of propeller shaft bearing of Indian Coast Guard Ship Sangram, an AOPV, which had experienced problems of unequal and unsymmetrical wear in its shaft system bearings. Initial and final radial clearances recorded during the construction of ship, CGS Sangram, at Goa Shipyard
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Surface Roughness Parameter
C = 0.01
C = 0.005
C = 0.0025
C = 0.00125
24 20 16 12 8 4 0 1
10
100 RPM
Sigma = 0.22
1000
Sigma = 0.43
10000
Sigma = 0.85
Surface Roughness Parameter (Sigma)
24 20 16 12 8 4 0 1
10
100
10000
1000
RPM Fig. 5. Variation of surface roughness parameter with (a) increasing radial clearance of bearing and (b) increasing composite rms value (s) of tribo-pair (data refers to Table 4).
C = 0.00025
C = 0.000125
C = 0.0000625
C = 0.00003125
Coeff of friction
0.12
0.08
0.04
0 1
10
100
1000
10000
RPM Sigma = 0.22
Sigma = 0.43
Sigma = 0.85
Coeff of friction
0.12
0.08
0.04
0 1
10
100
1000
RPM Fig. 6. Variation of coefficient of friction with (a) increasing radial clearance of bearing and (b) increasing composite rms value (s) of tribo-pair (data refers to Table 5).
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Ltd and during its two successive docking ships are registered in Table 9. The recorded clearances were diametric and for the present study they have been converted into radial clearance. The exploitation pattern and hours of sailing, obtained from ICGS Sangram’s Main Engine Room Log Book, are listed in Table 10.
6. Results and discussions Table 10 shows that water lubricated bearings undergo transient phenomena of starts and stops (i.e. 304 time shaft was
Table 6 Readings of perthometer M2 for shaft sample Parameter
Reading 1
Reading 2
Reading 3
Reading 4
Sampling length (mm) Lc (mm) Ra (mm) Rz (mm) Rmax (mm) Rt (mm)
5.6 0.8 0.88 3.82 4.41 4.41
17.5 2.5 0.968 4.85 5.25 5.81
5.6 0.8 0.279 2.62 3.51 3.88
17.5 2.5 0.401 3.92 6.92 6.92
Table 7 Readings of perthometer M2 for bearing sample Parameter
Reading 1
Reading 2
Reading 3
Reading 4
Sampling length (mm) Lc (mm) Ra (mm) Rz (mm) Rmax (mm) Rt (mm)
5.6 0.8 1.510 9.80 12.7 14.2
17.5 2.5 2.790 18.6 22.2 22.7
5.6 0.8 1.750 10.5 16.4 16.4
17.5 2.5 2.02 13.0 14.3 16.5
387
started/stopped during May 97 to June 2000). Mokhtar et al. [15] studied the starting behaviour of journal bearing and observed a rapid build up of hydrodynamic film in all the cases. They concluded that hydrodynamic film formed in a very short time, after which shaft moved in a spiral shaped whirling locus to the steady state operating position. Similarly they studied stopping motion and reported that during shutting down the shaft followed a typical hydrodynamic locus until rotation ceased and then a squeeze film trajectory to final resting position was observed. These results indicate that start/stop transient phenomena does not cause major wear on the bearing surface. Under proper load conditions, shaft takes lesser than half rotation to lift off from bearing surface. Therefore, in the present study it is assumed that starts/stops do not affect bearing life significantly. However, excessive load, large clearance and low rotational speed may have affected the bearing life and estimating wear constant may indicate the source of bearing wear.
6.1. Coefficient of wear There are two approaches to find the wear coefficient. In the first approach it is assumed that there are only two lubrication domains: hydrodynamic and boundary. In the hydrodynamic regime (l43), bearing wear is zero and the applied load is bared by full-fluid film. In the boundary regime (lp3), applied load is carried by asperities and bearing wear is definite. The value of l can be determined by computer simulation of algorithm given in Fig. 4 and Eq. (7). By employing this approach, MATLAB code was run with input data of load, bearing length and diameter as listed in Table 1, and different radial clearances. Fig. 7 shows that at radial clearance greater than 0.6 mm, all four bearings operate in boundary lubrication regime, meaning thereby that hydrodynamic film does not form even at the highest operating rpm (254). However, when the radial clearance is reduced to 0.4 mm for bearing 2, 3 and 4, the average minimum rpm for hydrodynamic
Table 8 Viscosity measurement readings rpm
150 250 500
First run
Second run
Third run
Fourth run
Fifth run
Dynamic viscosity (mPa s)
Shear stress (Pa)
Dynamic viscosity (mPa s)
Shear stress (Pa)
Dynamic viscosity (mPa s)
Shear stress (Pa)
Dynamic viscosity (mPa s)
Shear stress (Pa)
Dynamic viscosity (mPa s)
Shear stress (Pa)
0.974 1.083 1.510
0.736 1.364 3.805
0.954 1.075 1.504
0.721 1.354 3.790
0.952 1.077 1.5
0.720 1.356 3.779
0.952 1.078 1.502
0.719 1.358 3.783
0.954 1.080 1.504
0.727 1.361 3.789
Table 9 Radial clearances of bearings Radial clearances Bearing no. 1 (mm) recorded from Installed May 1997 After 3 years
Bearing no. 2 (mm)
Bearing no. 3 (mm)
Bearing no. 4 (mm)
Installed May 1997 After 3 years
Installed May 1997 After 3 years
Installed May 1997 After 3 years
Port Stbd
0.725 0.775
0.675 0.625
0.8 0.8
Port Stbd
Port Stbd
0.75 0.7
1.58 1.6
0.9 0.9
1.4 1.15
1.05 0.95
Initial Oct 2000
Final Dec 2002 Initial Oct 2000
Final Dec 2002 Initial Oct 2000
Final Dec 2002 Initial Oct 2000
Final Dec 2002
0.775 0.575
1.65 1.025
0.65 0.45
1.0 0.7
0.75 0.4
1.175 0.625
0.5 0.5
0.755 0.755
Initial May 2003
Final Sep 2004
Initial May 2003
Final Sep 2004
Initial May 2003
Final Sep 2004
Initial May 2003
Final Sep 2004
0.525 1.025
0.775 1.64
0.275 0.7
0.53 0.8
0.75 0.625
0.9 1.28
0.5 0.575
0.67 0.85
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Table 10 Exploitation pattern of ship for 03 operational cycles Description
May 97–Jun 2000 (H)
Oct 2000–Dec 2002 (H)
May 2003–Sep 2004 (H)
Total engine running hours Total engine running hours in clutched condition Number of starts and stops Hours at engine rpm 500 (shaft rpm 130) Hours at engine rpm 550 (shaft rpm 143) Hours at engine rpm 600 (shaft rpm 156) Hours at engine rpm 650 (shaft rpm 170) Hours at engine rpm 700 (shaft rpm 182) Hours at engine rpm 750 (shaft rpm 195) Hours at engine rpm 800 (shaft rpm 209) Hours at engine rpm 850 (shaft rpm 221) Hours at engine rpm 900 (shaft rpm 235) Hours at engine rpm 950 (shaft rpm 247) Hours at engine rpm 975 (shaft rpm 254)
4109 3800 304 549 67 140 472 1709 618 177 64 01 02 01
5129 4714 191 – 368 15 613 2447 28 864 375 04 – –
3264 3198 122 – 366 25 189 1677 – 753 173 14 01 –
Brg 1
Brg 2
Brg 3
Brg 4
600 500 RPM
400 300 200 100 0 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Radial Clearance (mm) Fig. 7. Rpm below which bearing performs under boundary lubrication.
film to form is 160–190. Bearing 1 continues to operate in boundary lubrication regime even at radial clearance of 0.4. Effect of increased radial clearance on regime of lubrication can be seen in graph shown in Fig. 8. Surface roughness parameter (l) below 3 indicates bearing operates in boundary lubrication regime. This analysis suggests that all four bearings operate under boundary lubrication regime and Eq. (10) can be employed to evaluate the wear constant K. The calculated values of K are listed in Tables 11 and 12. The wear depth of bearings of both shaft lines of one ship for three operational cycles has been obtained by subtracting initial clearance from final clearance. However, referring to Tables 11 and 12, it can be seen that value of K is not consistent for different bearings within the same operational cycle and for same bearing within different operational cycles. For bearing 1, the variation in K is largely dependent upon initially set radial clearance; for bearing 2, K is quite consistent irrespective of initial set radial clearance; and for bearings 3 and 4, K is inconsistent irrespective of initially set radial clearance. Hence, the average of 24 values of K listed in Tables 11 and 12 (0.226 1017 m2/N) cannot be used to estimate the life of water lubricated bearing. However, the results obtained using this approach indicates that bearing 1 is severely loaded and more prone to wear damage. The second approach for wear analysis of water lubricated bearing is to first evaluate the load shared by asperities using Eqs.
(11) and (12) and employ the calculated load to determine the wear constant using Eqs. (8) and (9). To understand this approach let us consider that total applied, 60089 N as shown in Table 1, on the bearing 1 is shared by fluid film and asperity contact. Determine the asperities pressure and calculate the load bared by asperities by area integration of asperity pressure. For bearings 1, 2 and 4 under different speed and clearance conditions, asperity loads are listed in Table 13. The results of this table indicate that asperity load will decrease with increasing rotational speed of the shaft. Further, the minimum value of wear constant equal to 0.35 1011 mm2/N, the maximum value equal to 1.7 1011 mm2/N, and average value equal to 1.0 1011 mm2/N have been estimated. These results indicate more than 50% variation in the value of wear constant. One possible reason for such variation is that the individual bearing (i.e. bearing 1, bearing 2) has been analyzed as a component that is subject to a particular load and speed condition. In reality load shared by all four bearings is completely coupled and dynamic. Larger clearance in one bearing increases the load on other bearings and vise-versa. Table 9 clearly indicates that radial clearance for bearing 1 in first load cycle was 200 mm greater than the clearance provided in third load cycle. Similarly radial clearance for bearing 2 was 500 mm greater in first load cycle compared to clearance in third load cycle. Such high variation in radial clearance drastically changes the load capacity of bearings. In hydrodynamic journal bearing often radial clearance (C) in the range of 0.00075 to 0.001 times shaft radius is preferred. The radial clearances shown in Table 9 demonstrate that two to four times higher clearance was provided for water lubricated bearings. The load capacity of such bearings is proportional to 1/C2 therefore load capacity can be increase by decreasing radial clearance, which is shown in Table 14. This table indicates that if radial clearance of bearing is approximately equal to 0.001 times shaft radius, then there is significant decrease in asperity load. Hence, it can be concluded that major problem in elastomeric bearing used in the Indian Coast Guard Ships is radial clearance of the bearing. Radial clearance between 0.00075 and 0.001 times shaft radius should be maintained for longer life of all four bearings.
7. Conclusions Unequal and non-uniform wear of elastomeric bearings, used in Indian Coast Guard Ships, have been analyzed. Following
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@ 150 RPM Bearing 1
Bearing 2
Bearing 3
Bearing 4
Surface Roughness Parameter
4 3 2 1 0 0.2
0.3
0.4
0.5 0.6 Radial Clearance (mm)
0.7
0.8
0.9
@ 185 RPM Bearing 1
Bearing 2
Bearing 3
Bearing 4
Surface Roughness Parameter
5 4 3 2 1 0 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Radial Clearance (mm) Fig. 8. Effect of increased radial clearance on surface roughness parameter.
conclusions can be drawn from the experimental and theoretical study presented in the paper:
Table 11 coefficient of wear (port shaft) Bearing number
1 2 3 4
Coefficient of wear K (m2/N) ( 1017)
Sea water shows thixotropic behaviour and its dy-
Operational cycle 1
Operational cycle 2
Operational cycle 3
0.506 0.187 0.159 0.198
0.366 0.231 0.255 0.024
0.092 0.212 0.079 0.101
1 2 3 4
Table 12 Depth of wear and coefficient of wear (Stbd Shaft) Bearing number
Coefficient of wear K (m2/N) ( 1017) Operational cycle 1
Operational cycle 2
Operational cycle 3
0.587 0.090 0.47 0.092
0.15 0.134 0.098 0.024
0.354 0.05 0.717 0.247
namic viscosity increases with increase in rotational speed. Particle size of sea-water contamination is very small (40–120 nm). Such small size of particles does not cause bearing wear. All four elastomeric bearings, used to support propeller shaft, operated in mixed lubrication at operating conditions provided in Table 10. All four bearings have unplanned excessive radial clearance, which reduce their load capacity and result uneven rapid wear. Bearing life can be enhanced by proper selection of radial clearance for all four bearings.
Acknowledgement Our sincere thanks to Indian Coast Guard Ship Sangram, from where valuable and dependable data of shaft clearance and engine running hours were provided.
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Table 13 Asperity load and wear constant for bearings 1, 2 and 4 rpm
130 143 156 170 182 195 209 221 235 247 254
Load shared by asperities of bearing 1, Wa (N)
Load shared by asperities of bearing 2, Wa (N)
Load shared by asperities of bearing 4, Wa (N)
Cycle 1
Cycle 2
Cycle 3
Cycle 1
Cycle 1
Cycle 2
Cycle 3
52 467 51767 51 098 50 349 49 658 48 951 48 257 47 574 46 822 46 125 45 690
– 51 942 51 294 50 582 49 951 49 279 48 500 47 922 47 135 – –
– 49 081 48 199 47 215 46 421 – 44 543 43 674 42 693 41885 –
20 708 20 242 19 811 19 244 18 813 18 342 17 840 17408 16 923 16 470 16 207
– 17 778 17 116 16 412 15 831 15 208 14 507 13 937 13 248 – –
17 778 17 116 16 412 15 831 – 14 507 13 937 13 248 12 671 –
1.7
1.43
0.35
20 887 – – 20 341 19 764 13 307 19 784 19 142 12 320 19 228 18 554 11 259 18 732 17 995 10 342 18 185 17 452 – 17 606 16 809 8556 17 125 16 260 7715 16 502 15 707 6647 16 029 – 5925 15 704 – – 2 11 Wear constant (mm /N) ( 10 ) 0.44 1.0 1.6
0.76
0.73
0.49
Cycle 2
Cycle 3
Table 14 The effect of clearance reduction on asperity load Description
Total engine running condition Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm Hours at engine rpm
May 97–Jun 2000 (h)
hours in clutched
3800
500 550 600 650 700 750 800 850 900 950 975
549 67 140 472 1709 618 177 64 01 02 01
(shaft (shaft (shaft (shaft (shaft (shaft (shaft (shaft (shaft (shaft (shaft
rpm rpm rpm rpm rpm rpm rpm rpm rpm rpm rpm
130) 143) 156) 170) 182) 195) 209) 221) 235) 247) 254)
Load shared by asperities of bearing 1, Wa (N)
Load shared by asperities of bearing 4, Wa (N)
Bearing clearance (0.75 mm)
Bearing clearance (0.175 mm)
Bearing clearance (0.8 mm)
Bearing clearance (0.175 mm)
52 467 51767 51 098 50 349 49 658 48 951 48 257 47 574 46 822 46 125 45 690
36 933 35 032 33 669 31157 29 736 27 905 25 972 23 877 22 109 20 044 18 304
20 708 20 242 19 811 19 244 18 813 18 342 17 840 17408 16 923 16 470 16 207
8807 7477 6176 4811 3667 2452 1172 366 0 0 0
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